SSS ae SS SSS Se Clercest,, FPG eS NISTITUTION ARCHIVES W.H.O.1. DATA LIBRARY WOODS HOLE. MA. 02343 E T@SELOO TOEO Oo MAA 0 A 1OHM/18 Geophysical Monograph Number 5 PHYSICS OF PRECIPITATION PROCEEDINGS OF THE CLOUD PHYSICS CONFERENCE WOODS HOLE, MASSACHUSETTS June S—9; 1959 INSTITUTION ARCHIVES W.H.O.1. DATA LIBRARY WOODS HOLE. MA. 02543 Edited by HELMuT WEICKMANN Sponsors: CLoup PuHysics COMMITTEE OF THE AMERICAN GEOPHYSICAL UNION and the NATIONAL SCIENCE FOUNDATION GEOPHYSICAL MONOGRAPH SERIES Watpo E. SmirH, MANAGING EDITOR PUBLISIFFED by AMERICAN GEOPHYSICAL UNION OF THE NATIONAL ACADEMY OF SCIENCES— NATIONAL RESEARCH COUNCIL Publication No. 746 1960 Geophysical Monograph No. 5 PHYSICS OF PRECIPITATION Helmut Weickmann, Editor Copyricut 1960 By THE AMERICAN GEOPHYSICAL UNION 1515 MassacuuseTrs AVENUE, N. W. WASHINGTON 5, D. C. Library of Congress Catalogue Card No. 60-60010 List Price, $12.50 PRINTED BY THE WAVERLY PRESS, INC. BALTIMORE, MD. Table of Contents IT OMELS PLE CE hae eusie ty wear rete ah er asta inman Madea Aetna aol mito cie ce cian lesiys wage cla Ce eee nner Reta he, Net sisitet csare saoc a Si ors deel aah ea Saas Worps 0F WELCOME Welcoming Address on behalf of the American Geophysical Union Helmut Weickmann Welcoming Address on behalf of the National Science Foundation Earl G. Droessler Welcoming Address on behalf of Woods Hole Oceanographic Institution Paul M. Fye Address of the Honorary Chairman of the Conference, Problems and Methods Onkamtallinvestigationa: ... sae ctee se gaee aes sees Tor Bergeron MorpPHOLOGY OF PRECIPITATION CLOUDS AND CLOUD SYSTEMS WINGO CU GON Aeeue tererese Aer Oe aeons Gia celst nceenchebelaye nan ads secredaee btee tans Joanne Malkus Synoptic and Planetary Scale Phenomena Leading to the Formation and Re- CULLEN Ce(OL EKecipitatiomy ss seer ei eseis ei eest neva es Jerome Namias Cloud Distributions over the Tropical Oceans in Relation to Large-Scale Flow IBarblenm Se nse yaces tian eds ots sicevoias Joanne S. Malkus and Claude Ronne Senucture of Convective storms, «ay. n sere ass sees eels are Tetsuya Fujita Energetics and the Creation of a Self-Sustaining Local Storm. .C, E. Anderson On the Dynamical Prediction of Large-Scale Condensation by Numerical Method sige = cen stent nena heheh enor ae ees Joseph Smagorinsky MorPHOLOGY OF PRECIPITATION AND PRECIPITATION PARTICLES Orographic-Convective Precipitation as Revealed by Radar Bernice Ackerman Microstructure of Storms as Described by Quantitative Radar Data Pauline M. Austin Plume Formation in Thunderstorms..................... Walter Hitschfeld The Structure of Minute Precipitation...............4... Johannes Grunow The Productiveness of Fog Precipitation in Relation to the Cloud Droplet SPCC HUM avatar one. ies REE Se Oe tae Johannes Grunow Horizontal Distribution of Snow Crystals during the Snowfall Ukichiro Nakaya and Keiji Higuchi Snow Crystal Analysis as a Method of Indirect Aerology. . . Johannes Grunow Structure of Snowfall Revealed by Geographic Distribution of Snow Crystals Choji Magono lil 31 32 71 iv TABLE OF CONTENTS Operation and Resultsiot Broject Pluviusyeses eee ee Tor Bergeron FUNDAMENTAL PRECIPITATION PROCESSES Hthqencysor Naturaleaine serie eer eee ee Raymond Wexler The Aerosol Spectrometer and Its Application to Nuclear Condensation Studies A. Goetz and O. Preining Differences in Coalescence Tendencies in Computed Condensation Cloud Droplet SPectralecs caer: = erie cea tee reece een ee W. A. Mordy Computations of the Growth of Cloud Drops by Condensation Using an Elec- tronic Disitali Computer. sy eee M. Neiburger and C. W. Chien The Relation between Cloud Droplet Spectra and the Spectrum of Cloud INUUGLELSG siesta neew et heen owe Per peek ere P. Squires and S. Twomey A Statistical Study of Cloud Droplet Growth by Condensation... .Claes Rooth The Nucleation and Growth of Ice Crystals................... B. J. Mason The Influence of Climate and Weather Elements on the Activity of Natural reezinpsNucleiyay ss tages ee cind sar aeeee Hans-Walter Georgii Recent Observations of Freezing Nuclei Variations at Ground Level Dwight B. Kline Studies on the Effect of Chemisorbed Impurities on Heterogeneous Nuclea- TKO LO eM et ae neti ce neers nem eee Cac ee ea eM ano ge eas eye Seymour J. Birstein Some Observations of Chloride-Sulfate Relationships in the Atmosphere and INsPrecipltatione yy wet er ee mere tye ee ee James P. Lodge Preliminary Results on the Aggregation of Ice Crystals R. E. Hallgren and C. L. Hosler Growth by, Accretion inithedice bhasemer ce. tse eee R. H. Douglas Frequency Distributions of Precipitation................ Oskar Essenwanger Some Aspects of the Optics of the Rainbow and the Physics of Rain Friedrich E. Volz A Possible Effect of Lightning Discharge on Precipitation Formation Process Bernard Vonnegut and Charles B. Moore Estimates of Raindrop Collection Efficiencies in Electrified Clouds C. B. Moore and B. Vonnegut Hart FORMATION Dhe Mechanismyot Hal) Formatione.-. cee heer rae Raymund Singer Design and Operation of the Swiss Hail Tunnel.................Roland List Growth and Structure of Graupel and Hailstones............... Roland List 164 184 191 211 220 226 233 240 247 252 TABLE OF CONTENTS Hailstorm Structure Viewed from 32,000 Feet....... Robert M. Cunningham Severe Hailstorms Are Associated with Very Strong Winds between 6,000 arrclel2 “OOO Mle tensire.stucancrcpntccuysarsac sin actin cccteanitks Gantacsvars H. Dessens Morphology of Thunderstorms and Hailstorms as Affected by Vertical Wind STEVEN PH cm ips A eRe Aree OSES re de OB eaerer my eT ae i Chester W. Newton Analysis of Hailstorms in the Denver Network, 1949-1958 W. Boynton Beckwith Some Behavior Patterns of New England Hailstorms. . Ralph J. Donaldson, Jr., Albert C. Chmela, and Charles Reeve Shackford Hail Studies in Illinois Relating to Cloud Physics G. E. Stout, R. H. Blackmer, and K. E. Wilk ARTIFICIAL PRECIPITATION CONTROL Future Research in Weather Modification................Howard T. Orville The Swiss Randomized Hail Suppression Project in the Tessin Raymund Sanger A Project for a Formation of Cumulonimbus by Artificial Convection Henri Dessens Special Comment on African Meteorology................ Tor Bergeron Physics of Precipitation in Winter Storms at Santa Barbara, California Clement J. Todd Artificial Nucleation of Orographic Cumulus Clouds Louis J. Battan and A. Richard Kassander, Jr. Cloud Seeding in the American Tropics............. ....Wallace E. Howell Artificial Precipitation Potential during Dry Periods in Illinois Richard G. Semonin APPENDIX MIStrOlsParticrpamtsy «crise geste tale acccten csr ecsng oa opaanun ere eer eee ate ae cre 384 388 sarmnbg ‘yyooy ‘atapsseorcy ‘pareyourlg ‘yooopoo,y, ‘edune ‘apsurmg ‘uosiapuy ‘(Surjesuy) UWs.10ar) ‘U184SILg, ‘Laypacy ‘puepyyoyog ‘ATJoy ‘(Futjoouy) [JeMOP ‘lo[sop ‘Suessacy ‘o[ [AIG ‘(Suljaeuy) vayeyH ssypy ‘uUopysnoY ‘lapssoyy ‘(sulpaeuy) preys ‘espoy ‘ekeyen ‘(Surpoouy) YOM ‘weyeig ‘ppoy ‘weysuruuny ‘ouoseyy ‘[lanoyy ‘YIIUIG 2449 OF Yjol ‘MOL YUOLY souuo, ‘tozury “ysvy ‘A UTMOUWIag Indg ‘Ulsny ‘YIIMyoog ‘(puryeq) Yyoq) lowyov[g_ ‘uoles1og TaN ‘(puryeq) BUIYDIO AA UOJMON ‘MOSBY ‘24904 ‘oUITY ‘A[loy 1 0} JJo] ‘MOL YOR ‘yueld ‘desu qooes ‘zepyy ‘ueyeiyg uBA ‘(puryoq SBIWIBNY ‘oO ) LIT [By * uuoy ‘iruesty ‘Ap. ‘XYSULLOSBULG “4 OL [OT u Moun ‘6. ueyyeg : ‘ Preface The Second Woods Hole Conference on Cloud Physics, June 3-5, 1959, was de- voted to the subject Physics of Precipitation. This volume contains the papers which were presented during the sessions as well as the edited discussion remarks. Two antagonistic requirements exist which make a planning of a conference very difficult: (1) one has to be able to discuss the details of the subject matter and (2) one would like to understand the matter in a larger frame and in its general signifi- cance. In modern science and perhaps especially in cloud physics the details of the subject branch out widely into other fields in which the seale and movements of atoms and molecules form the principal size parameters, whereas the larger frame of cloud physics, which is mainly connected to meteorology, of necessity ends in pat- terns determined by the scale and movements of the world-wide atmospheric circu- lation. In the past the large-scale and macrophysical aspects of cloud physics had often been neglected on account of the emphasis which was put on microphysical processes of clouds, and in clouds and cloud particles. In the planning of this Con- ference, an effort was therefore made to do justice to macrophysies and to reconcile this range of 10'° orders of magnitude by illuminating the subject matter from three different vantage points: (1) from the scale of synoptic meteorology, (2) from the scale of clouds and cloud systems, and (3) from the scale of microphysics. In agree- ment with this planning three main sessions evolved: A/orphology of Precipitation Clouds and Cloud Systems, Morphology of Precipitation and Precipitation Particles, and Fundamental Precipitation Processes. It was then considered that, with the ground thus prepared, a fruitful discussion of the problems connected with Artificial Precipitation Control will evolve which would give a fourth session. The letter of invitation sent to the participants outlined this plan. After the pro- posed papers had been received, it turned out that a special session on Hail Forma- tion could easily be formed. The location chosen for the meeting was again the Woods Hole Oceanographic Institution. This was done in order to emphasize the significance of cloud processes at the water-air interface for the supply of water vapor in the planetary circulation. These processes are one of the objectives of the research work of that Institution which has brought about a series of significant studies on microphysical as well as macrophysical processes connected with the formation of clouds or precipitation. The fine hospitality received from this Institution is gratefully acknowledged. With the stage thus set for an interesting conference, it was exceedingly fortunate to have not only many of the cloud-physics experts of the United States but also a number of the foremost scientists from abroad participating. There is, of course, one scientist who is most intimately connected to the subject matter since he is not only one of its founding fathers but also one who is able to speak with authority on all three scales involved: Professor Dr. Tor Bergeron. It was therefore a privilege that he agreed to serve as Honorary Chairman of the Conference. We are glad to express our sincere gratitude for his most inspiring and stimulating participation. We also want especially to mention and express thanks to Dr. G. Wolff and Prof. Dr. A. Goetz for their participation. These scientists are not immediately connected with the subject matter, but serve as consulting experts, the former in crystal phys- ics and the latter in physical chemistry. Prof. Goetz was also representative of the American Physical Society. . vii vill PREFACE Our gratitude is also due to Dr. H. Landsberg, then President of the Section of Meteorology, American Geophysical Union, Dr. Alan Waterman, Director, National Science Foundation, and Dr. Earl Droessler, Director, Atmospheric Sciences Pro- gram, National Science Foundation, for their support in making this Conference possible. Finally, we like to express our thanks to Mr. Waldo E. Smith, Executive Secretary, American Geophysical Union, for his untiring suport and efficient help in all phases of the Conference from the initial planning to the final editing phase. A word should be said with regard to the form of this publication. The practice of publishing the complete proceedings of a conference in book form is becoming in- creasingly popular in recent years, but 1s nevertheless also subject to criticism. It is pointed out that the papers could be published in current journals and that the dis- cussions quite often and of necessity contain thoughts or ideas that are not always well ripened. In spite of this we considered this publication a worth-while under- taking mainly for two reasons: (1) The publication of the papers in one volume will convey to the reader not only much of the present state of the art of precipitation physics, but also of the special scope of this Conference, namely, the significance of this field within the larger scales of atmospheric flow patterns. (2) Many of the dis- cussion remarks greatly contributed to this aim and form therefore important links between the sessions, therefore, much of the stimulus for further research would be lost through their omission. This is particularly true of the very interesting discus- sions related to the last session on Artificial Precipitation Control. It is therefore hoped that this volume conveys to the reader something of the stimulating atmosphere of this Conference which in the consensus of the participants was a full suecess. Professor Bergeron, the Honorary Chairman, called it in his clos- ing remarks one of the best meteorological conferences which he had ever attended throughout his 40 years of professional work. The merits for this success are his own in view of his stimulating papers and his inspiring discussion remarks, and those of the authors for their interesting papers, of the chairmen for their able direction of the sessions (always being under pressure of time), of the participants for their stimulat- ing discussions and endurance (one discussion period lasted until midnight), and last, but not least, of all who took part in arranging and setting up facilities and schedules. On the background of this cooperative effort, the goal of the Conference was achieved in a way which surpassed our expectations. Justice was not only done, in the lectures, to the various scales of precipitation physics, as outlined above, but justice was also done to the next higher level of information, namely, to show how tightly interwoven these scales can be with one another. What we mean is illumi- nated in the contributions which showed the close relationship between the size dis- tribution and concentration of nuclei and the size distribution and concentration of the cloud droplets (W. A. Mordy, M. Neiburger and C. W. Chien, P. Squires and S. Twomey); and between the latter and the size distribution and concentration of ‘aindrops precipitated from these clouds (P. Squires and 8. Twomey). Thus for cer- tain types of rain, no link is missing in the chain which connects the microscale with the mesoscale. Another example from the papers which lead from the study of snow crystals to the fine structure of precipitation processes (U. Nakaya and Ix. Higuchi, J. Grunow, Ch. Magono), or from a microscopic study of the hailstone structure to an under- standing of its life history within the hailstorm, and thus, ultimately, to an under- standing of the hail mechanism (R. List, R. Sanger). These research projects open PREFACE 1x new avenues in precipitation research where snow crystals and hail particles are be- ing used as inexpensive aerological sondes of great resolving power. This may lead to a degree of understanding of the accompanying storms which otherwise cannot be achieved. In other papers different scales were connected: the areal microstructure of the rate of precipitation (mesoscale) reveals the structure of hurricanes or other rain storms (T. Bergeron), and the arrangement of radar echoes points to the structure of orographic convection (B. Ackerman) and to the morphology of squall lines or fronts (P. Austin). Finally, there are the papers and comments which brought the important connec- tion to the synoptic scale, as in the study of cloud distributions over the tropical oceans (C. Ronne and J. Malkus), in the synoptic analysis of the fine structure of convective storms (T. Fujita), or in the analysis of large scale flow patterns which lead to rain or drought (J. Namias), or in the very interesting problems which pre- cipitation processes present to numerical forecasting (J. Smagorinsky). The reader will have noticed that here the significance of cloud physics is illumi- nated not just in the light of two seales—microphysics and macrophysics—but in three according to Bergeron’s definition (see page 61): (1) microphysics dealing with processes related to cloud elements, (2) mesophysics dealing with processes ranging from individual clouds to a cloud system, and (3) macrophysics dealing with processes of synoptic scale. Such a definition would be, as Bergeron pointed out dur- ing the Conference, in better agreement with current use in meteorology of the terms micro, meso and macro. Since it is virtually impossible to discuss the amount of valuable information and inspiration which has come from this Conference, the post-Conference status of some key problems which we had mentioned in our letter of invitation shall shortly be appraised. These were: (1) Can we prove that true sublimation nuclei do not exist and that AgI acts only as freezing nucleus? B. J. Mason’s paper gave an almost complete answer: he showed that AgI not only acts as a freezing nucleus initiating nucleation at water saturation, but also as a sublimation nucleus at temperatures below — 12°C. It is not an ideal sublimation nucleus but still requires 10-15 % supersaturation with respect to ice. (This result was qualitatively anticipated in Anderson’s paper, Re-evaporation Ice Nuclei, which he gave at the First Woods Hole Conference.) Mason’s investigations also explain why hygroscopic substances cannot act as freezing nuclei but may act as sublima- tion nuclei. It appears now that one of the last unsolved questions is how Nature performs in bulk water, the act of crystallization at the freezing point proper. In addition to this work, investigations on concentration and efficiency of freezing nuclei have been reported by H. W. Georgi, D. B. Kline, and 8. J. Birstein. The diligent work of these scientists who are hampered by bulky, unconventional, and heavy equipment which demands great observing skill leads us into an ever-deepen- ing understanding of the microcosmos around us which occupies a key position in the life history of raindrops or snowflakes. Their work furthers not only our under- standing of the fundamental significance of nuclei for the precipitation process but also for an appraisal of the influence of man-made air pollution on precipitation processes (see also the paper of J. P. Lodge). (2) How much does the aerosol spectrum influence cloud structure and therefore also precipitation processes? x PREFACE This question was answered through the contributions of W. A. Mordy, M. Nei- burger and C. W. Chien, Cl. Rooth, and P. Squires and 8. Twomey. While the au- thors of the first three papers showed theoretically and through the application of electronic-computer techniques the close relationship between the aerosol spectrum and the cloud droplet spectrum, the last-named authors confirmed this through i- vestigations of the cloud-droplet spectrum in Cumulus clouds over continents and over the ocean. They were furthermore able to show that not so much the presence of giant nuclei as this difference in the microstructure of the clouds is the determin- ing factor in the formation of warm rain. These papers must be regarded as mile stones for our understanding of cloud formation and of the warm-rain mechanism. As these papers will no doubt lead to an increased research effort into the nature and spectrum of condensation nuclei it was very timely that in the same session Dr. Goetz discussed his aerosol spectrograph. It is an ingenuously designed centrifuge that yields just that size range of aerosols which is crucial for the condensation process. (3) Is the evolution of a soft-hail, hail, or warm-rain particle a process which is traceable back to a distinct initial particle or to just one process, or is it a process whose trail we lose in a great number of eligible particles which have accidentally met after having experienced various life histories? This question has been answered for the warm-rain particle in the aforementioned paper by P. Squires and 8. Twomey. According to these authors the warm-rain drops do not go back to a distinct particle (giant nucleus), but to a population of cloud drops which is favorable for the evolution of a warm-rain particle through coales- cence, or, in other words, for the release of colloidal instability in form of rain. In the case of the soft-hail and hail particles R. Singer and R. List showed convincingly in beautiful cross sections through hailstones and graupel that both, large droplets as well as snow crystals may constitute the initial particle around which coalescence proceeds. (4) What do we know of Nature’s efficiency of the precipitation processes? This problem was illuminated in R. Wexler’s stimulating lecture on this subject and in the ensuing discussion. The problem of the efficiency of the natural rain proc- ess is of prime importance not only for our understanding of the rain mechanism, but more so for our appraisal of artificial precipitation control. It is one of the cen- tral problems of cloud physics and of meteorology in general, and it was in order to underline its significance that Wexler’s lecture appeared in a central position in the program. Bergeron’s Operation Pluvius, Grunow’s, Magono’s and Nakaya’s raindrop and snow-crystal analyses, Hallgren and Hosler’s, and List’s laboratory investiga- tions will ultimately contribute to its solution as well as the excellent work on the physical evaluation of seeding activities in Santa Barbara, California, on which Todd reported. Elliott’s discussion of the Wexler paper indicated again the great impor- tance of a simultaneous consideration of various scales as the efficiency of the natural rain mechanism may come out quite different if the budget of the water vapor is considered for a whole cloud system or for a micro-element within the system. (5) What do we know of the collection efficiency of snow crystals and flakes which seems to play a very important role for the efficiency of both, continuous and con- vective, precipitation? The collection efficiency of ice spheres for crystals has been discussed in the pa- per presented by Hallgren and Hosler. In their observations the importance of the temperature interval near the freezing level was emphasized owing to the formation PREFACE xl of a water film on the crystal surface which facilitates sticking of two crystals to one another after they have collided. We may conclude, then, that aggregation of snow crystals is also enhanced inside a water cloud at low temperatures, which is in agree- ment with the observation that the structure of the largest snow flakes is always a mixture of crystals and frozen or unforzen cloud or drizzle droplets. In a water cloud, of course, the attraction between ice and water particles caused by the vapor-pres- sure difference according to Vierhout’s theory improves aggregation between the snow crystal and the cloud droplets. After the capture of a cloud droplet, Nakaya explained (p. 270) that this may either freeze to the ice surface or evaporate on to it in a strange process that resembles the floating of little water drops over a clean water surface which was first described by O. Reynolds (Papers on Mechanical and Physical Subjects, 1869-1882). The growth by accretion in the ice phase was also the subject of a theoretical paper given by Douglas. He investigated the growth of spherical particles by sublimation and accretion. It would be most interesting if similar investigations could be carried out for simple geometric forms as they actually occur, for instance, stars, prisms, several ‘stars’ interlocked with each other, etc. As in falling, air will pass through the stars, they may collect many more cloud droplets than a spherical particle and there- fore attain a considerable greater growth rate than was found by these authors. (6) What do we know of hail formation; is it due to a very intensive or very per- sistent updraft? Very little definite evidence is available on this subject. When one compares the characteristics of hail clouds with simple thunderstorms using radar data as was done by Donaldson, Chmela, and Shackford, evidence points to the significance of very powerful updrafts. This is also expressed in Beckwith’s report on severe hail damage to aireraft in altitudes at or near 40,000 ft. The extent and pattern of hail damage, derived from crop insurance records, has been successfully used by Stout, Blackmer, and Wilk for a study of path and duration of hail storms, but the data are not detailed enough to yield the life history of a single cell. (7) What is the significance of the zones of high winds (jet streams) which appear to be a typical feature of hailstorms? This subject was discussed in a paper by Dessens which was followed by a stimu- lating discussion. No doubt the problem is still with us to search for a physical ex- planation if the relationship between hailstroms and jet streams can be verified. Data given by Beckwith indicate that only 18% of hailstroms occurred simultane- ously with the jet stream. No criterion exists so far how to judge the significance of this figure. In this search, investigations as reported by Hitschfeld will be of im- mense value as they will help us to analyze the true trajectories of particles which are potential hailstones. Of particular interest was here the discovery that the storm column remains upright in even a strong wind shear in contrary to the typical bend- ing over of trade wind Cumulus clouds. The influence of vertical wind shear on thunderstorm systems has been discussed in an interesting theoretical paper by Newton who found that small clouds may be destroyed whereas large convective systems may be maintained by vertical shear. Also, Anderson discusses theoretically the formation of self-sustaining storms, while Cunningham showed beautiful pic- tures of a hailstorm which had been taken from high-flying aireraft. This completes the discussion of the specific problems which we had raised in the letter of invitation, but we call the readers’ attention also to the stimulating papers given by Essenwanger, Volz, Vonnegut, and Moore. These papers give valuable xil PREFACE background information to the scope of the Conference: Essenwanger discusses the possibilities of a physical interpretation of frequency distributions of precipitation, Volz shows what the rainbow can tell about oscillations in freely falling raindrops, and the papers by Vonnegut and Moore discuss the always stimulating problems of precipitation and atmospheric electricity. The reader is also referred to the extremely interesting session on Artificzal Pre- cipitation Control (papers by Orville, Singer, Dessens, Todd, Battan and Kassander, Howell, and Semonin) which was one of the highlights of the Conference not only on account of the stimulating scheduled papers but also on account of the inspiring discussions. While it is impossible to do justice to the various new ideas and concepts that evolved in this session, this appears to be the place to recall the suggestion, made repeatedly by the Honorary Chairman throughout the Conference, to include in the evaluation of cloud physics or weather-radar projects a good synoptic analysis of the corresponding weather situations. We feel that this suggestion is of special significance in the evaluation of rainmaking or weather-control experiments into which statistical methods have entered deeply. It was therefore refreshing to find that such work is already well underway in the physical evaluation of seeding activi- ties in Santa Barbara, California. Indeed, these investigations will lay the ground work for a new phase in the design and evaluation of seeding experiments which will be greatly superior to and finally end the era where design and evaluation of such experiments were governed by statistical methods only. It is of necessity that all problems discussed in this Conference are still more or less in the basic-research state; and that they cannot as yet be applied to the chief objective of meteorology, namely towards improving weather forecasts in general and precipitation forecast in particular. The fact, however, that the discussions were not only inspired by the participating cloud physicists, but also, and sometimes even more so, by the scientists working in synoptic meteorology and numerical forecasting methods indicates that a most valuable cross fertilization between cloud physics and synoptic meteorology is underway and was achieved to a high degree during this Conference. The Editor, as Chairman of the Cloud Physics Committee, acknowledges the splendid support and assistance given to him by the Committee on Cloud Physics, namely, Charles E. Anderson, Roscoe R. Braham, Jr., Dwight B. Kline, J. KE. MeDonald, Joanne 8. Malkus, and Vincent J. Schaefer. Dr. Helmut Weickmann, Editor Chairman, Cloud Physics Committee American Geophysical Union Asbury Park, N. J. December 1959 Welcoming Address on Behalf of the American Geophysical Union Het~mut WEICKMANN Chairman, Cloud Physics Committee Ladies and Gentlemen: I am very happy to welcome all of you on be- half of the American Geophysical Union to our meeting on cloud physics. As I look around in our big family here, I am especially happy to see Dr. Tor Bergeron, our Honorary Chairman. He has inspired modern me- teorology for over 40 years, and we appreciate his coming over from Swe- den on this long trip. We also have representatives of Australia, Canada, England, France, Germany, Japan, and Switzerland, and others from Swe- den. I would like to ask all of you to get acquainted quickly. Let us be together as one big family of scientists, of researchers, and let us not for- get the ones who are unable to participate because of a very involved pro- cedure of invitation: our friends and fellow scientists from behind the so- called Iron Curtain. I am very happy to see some experts in fields related to the subject of the Conference, such as crystal physicist Dr. G. Wolff of the U.S. Army Signal Laboratories, and chemical physicist Dr. A. Goetz of the Physics Dept., California Institute of Technology, who is also representing the American Physical Society. I might also call Dr. J. Namias and Dr. J. Smagorinsky related experts. Both are well known to us. By inviting them we hope to extend a little bit our view of the precipitation processes of clouds, and to consider the problem of precipitation within the synoptic scale. T am especially happy that the Woods Hole Oceanographic Institution has played the host again. I wish to thank its Director, Dr. Paul Fye, for his fine hospitality and for his and his associates’ assistance in the organ- ization of this large meeting in a relatively small community. There certainly is an idea behind having the meeting here in Woods Hole. The Woods Hole Oceanographic Institution is one of the few insti- tutions which is actively engaged in research of both micro- and macro- physical processes of cloud and precipitation mechanisms. Moreover, it is the water-air interface around which the studies center. This interface is not only very much larger than the ground-air interface, but it is also an extremely important one as the rain which we study ultimately stems from it. The important role which clouds on this interface in the trade- wind region have for the water vapor supply in the large-scale circulation is one of the outstanding results of this Institution’s studies of trade-wind cumulus clouds. The Woods Hole Oceanographic Instutition is therefore a most fitting meeting place for our Conference as it will provide a scientific atmosphere which shall greatly stimulate the discussions and aid in achieving the purpose of this Conference. This purpose is, I should say, to look for a true science adventure and not just for a science fiction story. Tn order to achieve this goal we have tried to arrange the program in a 1 special order: we proceed in three circles to the fundamental problems. In the outer ring we get acquainted with processes in the large synoptic scale which are conducive to precipitation; in the next ring we will discuss the morphology of the precipitation on a medium scale and, thus prepared, we proceed to the inner ring with discussions of the fundamental precipitation processes. Iinbedded here is a separate discussion of the processes of hail forma- tion. As the knowledge of fundamental principles always has to preceed the practical application of these principles it is only logical that the dis- cussion of artificial precipitation control is the concluding session of our Conference. This Conference was made possible through a grant from the National Science Foundation to the American Geophysical Union. We are therefore very much indebted to the Program Director for Atmospheric Sciences, Dr. Earl G. Droessler, for his share in the realization of this endeavor. Welcoming Address on Behalf of the National Science Foundation Eart G. DROESSLER Program Director for Atmospheric Sciences, National Science Foundation Ladies and Gentlemen: It is my special privilege to Join in these words of weleome to you and to bring you the greetings of Dr. Alan T. Water- man, the Director of the National Science Foundation. All of us who in any way helped with the arrangements for this Conference are highly gratified by the enthusiastic response you have shown by your attendance. I believe we can certainly predict a most successful meeting. Early suggestions for this meeting grew naturally out of the very fruit- ful First Conference on the Physics of Cloud Precipitation Particles held about three years ago at Woods Hole. Considerable has happened in the interim. In Washington we have seen the work of the President’s Advisory Com- mittee on Weather Control brought to an orderly close with a final report which stressed the importance of basie research and recommended that the Government give full encouragement and support to the widest pos- sible competent research as the surest, most direct way to success in any attempt at modifying the weather. In July of 1958, central responsibility for Federal support of research and evaluation of weather modification was given by the Congress to the National Science Foundation. A new program was established with the objective of studying more intensively and systematically the scientific basis of weather modification, through support of competent scientists working in cloud physies and allied fields. Accordingly, we were pleased when one of the first grants approved by NSF under the new program was awarded to the American Geophysical Union for the support of this Woods Hole Conference; for we believe the bringing together of the world’s foremost researchers in the field at a meeting such as this represents an important step forward toward the pro- gram objective. Welcoming Address on Behalf of Woods Hole Oceanographic Institution Pauu Fyre Director, Woods Hole Oceanographic Institution Dr. Bergeron, Ladies and Gentlemen: May I weleome you most heartily to the Woods Hole Oceanographic Institution. We are delighted to have you in Woods Hole and hope you will all come back again often. Permit me to tell you a story about some of our proceedings yesterday when we entertained the Congressional Committee which is studying oce- anography. We had, in addition, a number of reporters who were most im- pressed by the presentations of our staff and, in particular, the one made by Dr. Joanne Malkus. In addition to attending the meeting of the Con- gressional Committee they learned that there was a distinguished group of world scientists meeting here today. They were anxious to talk to me, and find out something about your meeting. When they realized this was a group of experts in cloud physics they wanted to know if they could say in the papers that you chose Woods Hole because of its well-known beau- tiful weather and because of the beauties of Cape Cod. About that time the rain clouds began to gather and they appeared to get a little worried. It was then pointed out to them that this group had met in Woods Hole several years ago and that the weather you had for your meeting was the exact opposite of what had been experienced during the rest of that sum- mer. So I understand that during the night the Chamber of Commerce has been breathing easier, that they hope the cloudburst we have had for you so far is only an indication of better things to come for the rest of the summer. What will be said in the papers, I have no idea. Over this, we exercise no control, artificial or otherwise. If I were to try to tell you why the Woods Hole Oceanographic Institu- tion is interested in meteorology or why we have groups like those working with Dr. Malkus and Mr. Woodcock, it would be like an amateur shoe- maker trying to tell professional cobblers how to make shoes. I have no in- tention of doing that. We hope you will return and that your conference is a very profitable one. Problems and Methods of Rainfall Investigation Address of the Honorary Chairman of the Conference Tor BERGERON Meteorological Institute, Uppsala, Sweden Mr. Chairman, Ladies, and Gentlemen: It is a great honor and pleasure for me to have the opportunity of taking part in this Confer- ence on Precipitation, a field that has always been of primary interest to me. I want to thank the American Geophysical Union most fervently for the confidence they have shown by making me Honorary Chairman, thereby enabling me to come to this interesting Conference. I state the Conference is to be very important, since its theme, as we know, is of utmost impor- tance to mankind, and because the papers and abstracts already available show that a mighty attack on the named problem is imminent. The names of the authors and the fact that the pro- gram allows time for proper discussion of each paper seems to ensure, if this plan is followed, a very good result of our joint attack. In 1875 the great physicist and physiologist H. von HeLtMHo.tTz gave a lecture on “Cyclones and Thunderstorms.” He felt that the impos- sibility of predicting the beginning and end of rain touched a sore spot in the minds of physi- cists. He continues thus: “Under the same sky in which the stars pursue their orbits, as symbols of the unchangeable law- fulness of Nature, we see the clouds towering, the rain pouring, and the winds changing, as symbols—as it were—of just the opposite ex- treme, the most capricious of all processes in Nature, impossible to bring inside the fence of its Laws.” However, at Helmholtz’s time, nearly a hun- dred years ago, one only vaguely realized the vital role of these phenomena to mankind. Now, we know how the clouds and their precipitation determine unambiguously the life conditions of the better part of the so-called biosphere, the sphere of living beings. We know, for instance, that the photosynthesis, which is controlled by actinic radiation, and on land by the fresh-water supply from precipitating clouds, is by far the biggest industry on our planet. It outrivals by several orders of magnitude any kind of arti- ficial production of energy on our Earth. We dread the catastrophe of soil erosion, caused both by the excess and lack of rain, as you know very well in the United States. We badly need the hydroelectric power, and we now fear the sink- ing ground-water level; not to speak of other nearby effects of rain or drought. But today, our colleagues the physicists have, on the whole, very successfully repressed that sore point from their conscience, leaving us meteorologists almost alone with these vast, in- tricate and vital problems, which we evidently still have not mastered. (I need only to refer to the last 24-hour rain that we have all experienced here, or perhaps in Boston. It may have been forecast to some extent, probably as some show- ers; but it was certainly not forecast in this amount and of this kind, that is, as a 24-hour abundant rain.) Intense or steady precipitation will generally be the real vital and fatal type, of course. Therefore, it seems reasonable that we now devote our attention to mechanisms produc- ing such precipitation, even if the weak or inter- mittent type also may be of considerable interest. We may hope to find the most clean-cut and typical mechanisms, the most conspicuous fac- tors, behind the intense weather phenomena. This will help the scientific treatment and solu- tion of these meteorological problems, which otherwise often are too complex. These typical cases will also, if treated artificially, point to the best methods of getting artificial precipitation, or to prevent certain kinds of precipitation, as for instance hail. Abundant precipitation will only be produced by what one might call sustained mechanisms; that is, mechanisms producing more or less orderly lifting of air, bringing new moisture and new releasing particles (appropriate nuclei, etc.) continually through a certain limited space of the lower troposphere. These limited spaces will either be fixed geographically, or they will re- main stationary with respect to the leading air- flow, as is the case with frontal rain and rain of convective character. In any case the main 6 TOR BERGERON thing is going on in the lower troposphere as far as the precipitation amount is concerned. Also other forms of precipitation are important to study: especially those that give unexpectedly small amounts, for example, smaller amounts than one would expect under conditions that generally would guarantee a substantial rain. One has hitherto distinguished between micro- physics, macrophysics, and synoptics of clouds. However, I think it would be better to use the terms micro-, meso-, and macrophysies (corres- ponding roughly to cloud particles, individual clouds, and cloud systems) since the name ‘syn- optics of clouds’ introduces an asymmetry, and since one is apt to think that ‘micro’ and ‘macro’ are for us, but ‘synoptics of clouds,’ that is for the weathermen, so we will not bother with = x NS that. In fact, these things hang so intimately together that they cannot be solved separately. We must all collaborate with these problems. Then, another point that I believe is impor- tant. Every cloud or cloud system giving abun- dant rain or snow can be divided into a releasing part and a spending part. I call it the releaser and spender part of the cloud or cloud system, or the ‘seeder’ and the ‘feeder.’ They may not even form parts of one and the same cloud; they may be two different clouds, one above the other, co- operating in some way or other; and they must really cooperate in order to insure efficient pre- cipitation. A cloud without a spender will give very little or no precipitation. A cloud without a releaser will generally give no precipitation at all, or only drizzle, even if the condensation is Cunb cap ASTON x rie me Ch, = ee ES AB 4s Cloud and precipitation ==> Air-current at heat source «eee lce-nucleus level al Isobar ==> Air-current at heat sink Fra. 1—Main precipitation mechanisms; schematic vertical cross sections Sy PROBLEMS AND METHODS OF RAINFALL INVESTIGATION aa iN BN) 10 APRIL IQd7 18530 C.S.T. Vip Slight —moderate rain Rising pressure Imb/3" YU; Heavy rain Falling pressure 5mb/3° rr Pseudo-coldfront Isohypse of 300m ab. s.-l. --~-0 Isallobar Omb/3" Fic. 2—Weather map with convective system over eastern U. 8., April 10, 1947, 18h 30m CST TOR BERGERON ea) oO c o = = cc 3 ° ae ~ T oO) = fo) —-----= 0}0.23iine + Record. gauge ees Alt. > 450m —=—>—=——s w ie sii w = ° cL 9) Sh 30m CST 3—Precipitation intensity, April 10, 1947, Fic. PROBLEMS AND METHODS OF RAINFALL INVESTIGATION 9 rather intense. And that is again a reason why our problems cannot be solved by micro-, meso-, and macrophysics of clouds working separately. I am now going to discuss some important types of precipitation and their mechanisms. Figure 1 tries to show schematic vertical cross sections of the main mechanisms of cloud and precipitation (excluding the drizzle from fog and Stratus) ; and by chance the size of the dif- ferent small pictures roughly corresponds to their relative importance on the globe—The second row shows the convective system, which, together with the ordinary convective clouds of the first row, gives the better part of the pre- cipitation in tropical regions, and even in middle latitudes on land in summer. Correspondingly, over the middle-latitude oceans, the convective clouds give the bulk of the winter precipitation. (In the Middle West, where the convective sys- tems or ‘squall-lines’ bring most of the spring and autumn rains, the warm-fronts then seem to bring relatively small amounts of precipitation.) —The third row contains the opposite kind of mechanism, the tropical hurricane, which brings great amounts of precipitation on the oceans and adjacent coasts in late summer and fall. In this figure there is an outward similarity between the convective system and the tropical hurricane, but at the same time they are opposite. Here I only want to point out that they contain two ‘circulation wheels’ each, a big one C,, and a smaller one C, that is caused by the rainfall cooling. If they cooperate, as within the tropical hurricane, a very efficient mechanism is set up producing a cyclonic vortex, often with ex- tremely low pressure at the center. In the con- vective system, on the other hand, these two circulations counteract each other; Cy, causes a WM VOns.21 csAV gs SS PASO A 20 Mo. Texas ! | 09z : > 03z Isochrone of pressure jump, 35°N ' 2 after M. Tepper +05mb Okla +10 ——- Equiscalar of pressure jump 100° W 2 95° amplitude in mb 1 n Ll ! 1 =a L ! ai Pressure Jump 1-2 June 1951 Fria. 4—Isochrones of the pressure jump of June 1-2, 1951, according to M. Tepper 10 small high in the interior of the convective sys- tem, thereby preventing the formation of any cyclone. Instead, a low-pressure trough formed just outside this small circulation wheel, as shown lately im detailed studies by Dr. Fusira—The lowest row of Figure 1 displays two kinds of orographic cloud and precipitation systems, the high-reaching and the low one, and also the frontal precipitation mechanism. How- ever, integrated over the whole globe these three mechanisms give much less precipitation than the mechanisms of the three upper rows——The next figures give examples of the mechanisms in Figure 1. The synoptic map of the eastern United States 1s 105° W -2 SS N 2 X S 06 LOOT ca wo/ 1010 TOR BERGERON (Fig. 2) shows a convective system that is bor- dered at the eastern edge by what you eall a ‘squall line’. This is, in fact, a pseudo-cold front since the cold air is produced by the intense rain-cooling caused by the convective system that has formed within the tropical-air warm- sector of a cyclone. The main precipitation of this cyclone came from that exceedingly impor- tant mechanism. When, in 1947, I first had made the analysis shown in the cross section of Figure 1, second row, I ‘forecast’ that the maximum precipitation intensity would occur along the leading edge of this convective system, followed by a minimum in the interior because of cloud decay caused by the rain-cooling there; then 2 June 1951, 00h30™z Pu JN=0 Cloudless +2--—— _ Ground ereee © >24km alt. Pseudo-coldfront (and isobar) Pressure -jump line 3-hourly isallobar Fictitious isobar Precip. area at synoptic hour Isohyetal ee within A. 9 12, Shen \ central 7 ° i 12) 95 region S//2 3. 5a—Convective system, June 2, 1951, 00h 30m PROBLEMS AND METHODS OF RAINFALL INVESTIGATION the precipitation intensity would pick up again at the rear edge of it. Some years later I was able to confirm this assumption or ‘forecast’ as seen in Figure 3, which shows the distribution of rainfall during one hour from this very convective system. At the leading edge there is a rainfall intensity of up to two inches per hour. In the interior of the convective system the rain intensity goes down to zero over considerable areas, and further west it reaches values of at least one tenth inch per hour, proving the expected increase at the rear RWERRS NS 11 edge of the system. This whole mechanism moved across the eastern part of the United States, giving from one to eight inches of rain within a few hours. Seemingly, this kind of mechanism is the main rain-spender during the summer-half of the year in the Middle West. Thus, the convective system is a most important mechanism, worthy of all those very minute and ingenious investigations that Dr. Fusrra has made; and also, of course, of being tackled by many more investigators. From Dr. M. Tepper I got data on the ‘pres- IK=O Cloudless Pressure-jump line 3-hourly isallobar Ground Fictitious isobar >24kmalt Pseudo-coldfront (and isobar) Precip. area at synoptic hour > Isohyetal 00 s within eo 2:5 ae central region Fig. 5b—Convective system, June 2, 1951, 09h 30m 12 TOR BERGERON sure jump’ of another case with similar charac- teristics: June 1-2, 1951. Figure 4 shows his isochrones of this pressure jump over Nebraska, Towa, Kansas, Missouri, and Oklahoma; thus it covered quite a vast region. After having studied the numerous barograms from this case, I do not doubt the reality of this pressure Jump; although, naturally one needs not accept the various explanations given. In the United States there exists a wonderful network of pluvio- graphs, and their registrations have been worked up and published in the shape of hourly precipi- tation data, this being the only country in the world that has done anything similar. With the aid of these data, I was able to analyse, in 1953, a series of maps, of which Figure 5 shows a sample. As you see, the results are similar to those reached by Dr. Fusrra in 1955, so our works corroborate each other quite nicely. In this ease there was a long quasistationary Polar front, with a cold-front section extending to- wards SW over Kansas. The warm-front section, over Nebraska and Iowa, gave only weak rain. At the top of the warm sector within the Tropical air, in SE Nebraska, there was, however, a circular convective system with intense rain along its outer edge, but with very little or no pre- cipitation in the interior, and a small High at the Meon temperature for September Meon temperoture for February Temp. of adiabatic lifting with 28°C and 85% RH. of seo-level Temp. of adiabatic lifting with 25°C ond 85% R.H. af sea-level % Lability energy in September Lobility energy in February Fra. 6—E. Palmén’s general hurricane tephigram for the Caribbean Sea very center. All this could be traced by means of the above-mentioned hourly precipitation data. The maps also show the position of the pressure jump taken from Dr. Tepper’s map (Fig. 4). We do not know for certain the origin of convective systems; but they generally form in the warm sector, and often at its top. Some- times the ‘squall line’ is parallel to the cold front; but in such a case as this, with a circular pseudo-front, I am not able to accept the old explanation that a ‘squall line, or convective system, should be caused by the overflowing of cold air at a higher level. Then, why does it not extend down through Texas in this case? In fact, the explanation of the convective system may be quite another one in this case, and we are on the safe side if we start by observing it, then digest and carefully analyse it, and save our explana- tion for a later stage. What I wanted to under- line here is that the pressure jump at the stage of the 00h 30m z map (Fig. 5a) les far behind the ‘squall line’ and also behind the cold front. Whereas, nine hours later (Fig. 5b), the pressure jump has mostly overtaken both the ordinary cold front and the pseudo front. The convective system now forms an almost circular rain area, with hardly any rain at the center. On later maps, the pressure jump even went further into the Tropical air and left both the ordinary cold front and the pseudo front behind it. Thus, one may conclude that in this case the pressure jump was produced, neither by the ‘squall line,’ nor by the cold front; they were in this case three more or less independent agents. Certainly, these phe- nomena are worthy of many more investigations in the future. PatMéN has shown that the tropical hurri- canes form and are maintained according to the convective theory. In Figure 6 the curve of con- vective lifting, in February, when there are no hurricanes, lies mainly to the left of the curve of stratification. The corresponding curves for Sep- tember, in the middle of the hurricane season, show that there is then a great positive area be- tween the curve of lifting and the curve showing the stratification of the air. What I especially wanted to emphasize is that the curves of lifting diverge with height. Thus, a certain difference of temperature at the Earth’s surface corresponds to a two or three times greater difference of temperature at the tropopause, or say at the 300-mb level. This implies that a surplus of 2°C in the rising air at the cloud base will give Temp. Sept. 18-2! Mean. Lemp. In left part of vertical cross-section sale: Air 1°C cooler than the average for this level | PH || Precipitation \ Cloud = => Air-current at heat source ===> Air-current at heat sink September | -72° Km 7 rl8 —77 -735 ae +16 -6f0 etl ai oe 60 638 a 1 =... pee =- NX ". -5I°s oan sha Oe +a? -530 +520 -5/0 -5/7 -515 -528 547 aah ; EN TEs ZB =50—_ -3 7 +2 nage 48 | ae a 10 —3)°o -45 : 28.5 -28B--30,3_-31.0 -3/6 2322 -32.6 -32.6 -347 — 34% [ : . om ° 0" Ny a0 a oY a bile = - ee -253 3 | \ 7 -20° 8 -16°2 -24 amet at! 7 13,5 ~ PGS -/6.5 -18,0 18,4 -180 -177 -186 IGS pone = Cais a 320 -/37 Dpe ree si Ss AP GUA 130 - 5% -06 '- -a Toe “tle ~ 0 ° 8 9 6 ‘05 4 -U8 *-liz -06 eas -4. $3 -65 -70-67-63 -~64% -65 -9H 0. OS = 1. — 36 ee ee +03 ba +40 ° + 8.8 +07 +07 +06 +07 +02 +02 +73 49.0 +93 +90 +80 +95 +94 a +75 ----— ——— (PSS W +107 ° +187 +173 *07T™*Q0 08 +07 +07 +02 t/75 +176 +/75 +180 +180 +181 +/73 +/8.0 +/6% +20 — +/93 SS ee 300°— — — — —— +20%5 it eee ET aj +257 fa) [eh BB 35 4a gon Geeeye ee88 9) {I0x102)Km T.B. 1949 E.P 1948 In central and right part of vertical cross-section and in ground plan Heavy rain yy Main updraught region tthe fe V///, Light to moderate rain Isotherm °C Isentropic line °C Fra. 7—Mean vertical cross section of the major tropical hurricane passing SE U.8., Sept. 17-20, 1947, according to E. Palmén and T. Bergeron 13 14 TOR BERGERON a surplus of 4 to 6°C at the top of the hurricane cloud, thereby increasing greatly the lability energy. If, on the other hand, the temperature is depressed a little at O-level, there will be a great loss of energy. Now, we come to the fact that there is gen- erally a very low pressure at the center of a mature tropical hurricane. This is an important point, to which enough attention has not been paid hitherto. Thus, if the central pressure is lowered, the curve of lifting will move to the right in the diagram, and the lability energy will be increased, provided the condensation level does not rise or the temperature fall. In fact, the air flowing into the Low within the frictional layer over the warm sea will conserve its high temperature in spite of the expansion. Its tem- perature will keep near that of the sea-surface, thanks to the very rapid transfer of heat from this surface up into the air, and the sea-surface cannot by any means be cooled appreciably in a short time. Thereby the wet-bulb potential temperature of the air is raised. By making, so to say, the pressure very low at the center, the hurricane will dispose over a greater store of ability energy. Figure 7 shows a vertical cross-section of the major hurricane that passed Miami and New Orleans in September 1947, which Patmién and I have both been treating. A decisive thing with the hurricane mechanism, as I see it, is that the updraft of the inflowing air takes place inside the region of the most intense precipitation, as indicated in the small map-sketch at the bottom of Figure 7 and in the third row of Figure 1. The central hurricane cloud-mass is often funnel shaped; thereby it will not attain enough height to produce an efficient precipitation release (through ice-nuclei or otherwise) until at some distance from the ‘eye,’ presumably outside the ring of maximum updraft, a good example of cooperation between micro-, meso- and macro- physical cloud factors. In the opposite case the rain cooling, driving C,, would counteract the mechanism C,, and the hurricane would trans- form into one or more convective systems in- stead; this was probably what happened to the hurricane of Figure 8. Unfortunately, I was not able to treat just the major hurricane of September 1947 from this viewpoint. Figure 8 shows another hurricane from the same year. When lying Just outside the coast [cHicaco@ 85 90° +734" '+2/" 40" ro eS) CHICAGO @ 1015 nb 85>" wry ae oH Ea SA 5 os “~-—~ 16 OCT. 1947 14 OCT. 1947 DS ec, ie aon 18" 30™ c.sT. ee ea 00h 30™ cst. 42/° --------- |sotherm of air Q——— Isallobar ° % +233 ——— Isotherm of sea surface YW Rain area Fic. 8—Deeay of a tropical hurricane over Georgia and Alabama, Oct. 14-16, 1947; S indicates areas of rising pressure I7.1X.1947 | | !_—— /sohyetal 20 in/h ; as ODeni ts OS « \ | *Rain, out omount GnRnOGA : a 10 » = = (2 i SS fy) 2 = ee Ae NS ce | ~ a | oshesr! | 12* sow o7EST Sace* : OS"EST 82" woe 2 Fre. 9—Maps of hourly rainfall from the major hurricane of Sept. 1947 when crossing Florida 15 16 TOR BERGERON of Georgia, it was still quite vigorous. At its cen- ter the sea-temperature was about +26°C, and the temperature of the air that was rising from the sea-surface was probably very near this yalue, corresponding to a great amount of la- bility energy. Twenty-four hours later the hur- ricane center had entered land and began to fill rapidly. This effect is generally ascribed to friction. According to my view, however, the main reason for the filling is the precipitative cooling of the air over land within the friction layer, that is, of the only air that can flow into the hurricane and form an updraft. That air was in this case cooled by the rain itself down to +19°C near the center, which implies that the lability energy had become negative. That is like putting a very powerful brake on the whole mechanism, similar to braking a motor car by the engine. if | =. , 19. 1X. 1947 ie | ooMesT | This is a precipitation conference, and the hurricanes were mentioned mainly because they also represent a very important precipitation problem. In fact, a lot of the hurricane damage is done by precipitation. Figure 9 displays the distribution of the precipitation intensity within the major hurricane of September 1947 when passing Florida. It is, of course, analyzed keep- ing the idea in mind that it should have an ‘eye’ without precipitation, and that the region of intense precipitation should form a ring; evi- dently it does. The several small maps show how the precipitation area moves across Florida, and also how it widens during this passage. Gradually it gets two eyes, or even multiple eyes, and parts where the precipitation in the ring is much more intense. Instead of a complete rmg of maximum rainfall all sorts or irregularities occur, presuma- bly because the precipitation area lies over land DEGENID = =s \aj}-— | 0 Isohyetol SOuoY, *Noran 2 os ‘ - = Rain, but amount unknown 4 mall 10 = | ee A = 23N h | P T o 5 23N— HOeGE Sin 8S" es O3s"EST | astw TB. 1950 aecil swe | Mii, Y GH, Fic. 10—Maps of hourly rainfall from the same hurricane as in Fig. 9, developing spiral arms of pre- cipitation PROBLEMS AND METHODS OF RAINFALL INVESTIGATION and is then unevenly affected by the rain-cool- ing. This might also partly explain why many writers have found irregular hurricane paths. In fact, a path need not be so irregular, it may only seem so because of the multiple eyes. Radar has revealed to us the spiral structure of the hurricane precipitation. The hurricane- cloud spirals might at first be composed by sepa- rate convective cells, arranged in rows that are gradually dragged spirally into the Low, at last joining up into real bands. Figure 10 contains a continuation of the series of precipitation maps 17 of Figure 9, showing that the precipitation pat- tern based on rain-gage data also may have a spiral structure. Certainly, it is founded on a rather loose network, so that in some cases one might be able to combine the places that have got precipitation in a different way and thereby fail to attain a clear spiral rain pattern. How- ever, in the map of September 19, 02h EST, which also has isobars and winds, the direction of the spiral arms lies somewhere in between the direction of the wind at the Earth’s surface and the gradient wind. It seems quite reasonable, °F Gr /| 4 HO/ aed a 4 1000 5°) ia = aE tl Ls itd SRA i | Vy a a | 57°N —_| : 6° T5erveron /H8 Coast line 1000 ° —_—mM Jsobar of 995 mb 20, | POT TE IIT | Wind ENE 14 "%s 500 m above MSL (oe oxen Jsotherm 0c at sea-level Fic. 11—Distribution of precipitation, wind, pressure, and temperature in SW Scandinavia during the period March 24-27, 1927 (72 hr), showing marked coastal maxima of precipitation mainly due to orographically conditioned convergence 18 TOR BERGERON then, that they originated from showers that became arranged parallel to the direction of the general flow, merging into solid rain bands of spiral shape and eventually mto one ring-shaped rain-area as they came under the influence of the general updraft. I think that detailed precipita- tion studies of tropical hurricanes might form a useful complement to the radar scanning of them, since, after all, the radar does not render the rain intensity as truly as the gages do. Moreover, the radar patterns do not show the total extent of clouds, but only the patches with efficient release of precipitation. Thus, they per- mit no estimate of the amount of latent heat released. In other words, the release of latent heat need not be so discontinuous as 1t may seem from the radar pictures. The problem of orographic precipitation is old General formula: w I Iw Mee, Aalh_ jotm,imy, | Uy Fulks’ solution: Qos Os Qor 07 0.6 05 and much treated. Therefore, I shall here only enter on a most remarkable case of exceedingly abundant orographie precipitation that occurred over southern Scandinavia in the last week of March 1927, when a front lay quasistationary from the Black Sea over Poland and Denmark to Iceland, and there was frontal precipitation all over southern Scandinavia together with southeasterly winds. Figure 11 gives a close-up of the weather situation over southern Norway and the immense amount of precipitation, 200 mm (8 in.) that fell in exactly three days on the coast. That could not be ordinary orographic precipitation. In this case the static stability of the general southeasterly current made part of it bend outside the mountains and meet the direct southeasterly branch as a northeasterly current. Thereby an orographically conditioned Z 5) 2 w'A*g@ = 6z al = 780 ae - 2166 ‘, T 6T oS ie horizontal area max. spec. humidity air density partial pressure of water vapour = rate of ascent Teton aes (0) Warm cloud Supercooled cloud, not released released THI Supercooled cloud, O° ST 36°C 6 7km Fic. 12—Vertical distribution of maximum condensation intensity Zw in an upslide cloud system PROBLEMS AND METHODS OF RAINFALL INVESTIGATION 19 convergence was set up at the SE coast of Nor- way, with a mighty updraft just at the coast, and consequently a very intense condensation in- side the orographic cloud system. Figure 12 shows the amount of precipitation to expect from an upslide cloud system according to Funks’ formula, assuming +10°C at a cloud base lying very near the zero level. Such dia- grams give a measure of the maximum condensa- tion intensity 7 under the assumption made as to the vertical motion shown by the curves w in the figures. The maximum condensation in the cloud mechanisms in question in each unit layer (100 m thick) is obtained by the Jw curve. Integrating the area enclosed by this curve and the zero line gives the maximum amount of pre- cipitation available under the asumption that there was no entrainment, and that the precipi- tation release was 100%, that is, total and im- mediate. Naturally, in reality one gets much less, generally only about 50 or 60% of the theoretic maximum, which in this case is 0.9 mm/h. Since the temperature at the cloud base in this case was about O°C (instead of +10°C) and the distance to the front line at the Earth’s surface 100-200 km, one can expect at most 30% of the maximum value or not more than about 20 mm precipitation on the Norwegian coast from the upshde surface during those three days. So we have to explain the remaining 180 mm by the above-mentioned orographically conditioned mechanism. A cross section SE-NW over Skage- rak and the southern Norwegian mountains (Fig. 13) shows the frontal upslide surface with the upslide cloud system and snow falling from it. Within the cold air lies the orographically conditioned, local mechanism that causes a much stronger updraft and a much more intense condensation: the feeder cloud. The water con- densed is brought down promptly by snow fall- ing through this cloud from the overlying re- leaser cloud. Ayn 57 = > —— zal SOT So 5 * Inversion ~, 1+-SssTIDSTRI/S RAINS Orographic Precipitation in Detail tes. LEGEND Floating ice-needles Falling precipitation Floating cloud droplets mre Ice mucleus level i le Falling snow 919! DE <——<——— Flow of warm air wr uJ BES Hopes, Front surface > Fic. 13—Schematic vertical cross section of frontal and orographic precipitation mechanisms in Southern Norway, March 24-27, 1927 20 TOR BERGERON Distribution of maximum precipitation intensity at orographically conditioned convergence with w =l [w I Iw m/, —movh mm/h /s 10?m,Im/ 107m m/s at 0.7 km height lo i) Oa = 00 Q) Oz C3 Os Os Oe 07 Os Oo | z la lz ls lakm 10° 75 TAY Pi | 0° -6 Fre. 14—/w diagram of orographically condi- tioned precipitation Figure 14 is an Jw diagram for this case with two alternative temperatures at the cloud base, +10°C and 0°C, the latter applying to our case. The curve J represents the specific intensity of condensation and w the assumption made as 2— Isohyetal 2 in. --—— \Isohypse 150m ab. s-l. is 300" "8 ‘Divide 9 Region of max. rain i g! Be a to the vertical motion, being zero at the ground and at a front surface, 1.4 km above sea level, and 1 m/see halfway in between. We then get an Zw curve that corresponds to a precipitation of 5 mm/hr or double the amount needed, since there are 180 mm in three days to be explained if the other assumptions are correct. Thus, the updraft would have been of the order 0.5 m/sec instead of 1 m/see (as assumed in Fig. 14), a value that goes well with the surface convergence observed. Figure 15 illustrates about 50% of the rain in January, 1937, that produced the famous Ohio- Mississippi flood, which began in the Ohio River drainage basin. This isohyetal map only renders the rainfall during the period January 20-25, reaching 10-14 inches along the river; the maxi- mum total sum for the month was about 24 inches. This is a terrific amount, and the flood was, as you know, one of the biggest on record, rising more than 25 m, or 85 ft, above normal "__[U.S. DEPT. OF AGRICULTURE WEATHER BUREAU OHIO RIVER DRAINAGE BASIN PRECIPITATION JAN. 20- 25,1937 Fic. 15—Rainfall in the Ohio-Mississippi Basin, Jan. 20-25, 1937 LEGEND COLD FRONT { WARM FRONT “\—— +++ = STATIONARY FRONT + UPPER AIR WARM FRONT — — — UPPER AIR COLD FRONT — + — + OCCLUDED FRONT | |SHADED AREA,— PRECIPITATION OCCURRING AT TIME OF OBSERVATION. -{SMALL FIGURES REPRESENT TEMPERATURE AND 24 HOUR PRECIPITATION, RESPECTIVELY. 47:30 a.m.—Jan. 21,1937 air-mass and front symbols) 21 22 TOR BERGERON water-level in some sections. Supplement 37 of the Monthly Weather Review is a report which contains many rainfall maps and tables, pictures and accounts of damage, descriptions of the weather and its changes, and also weather maps, relating to this catastrophe. But, as far as I ean 26. VII. 1950 lis 18" GMT i} SSS AOSSS3 see, there is no real explanation, in all that big report, of the very striking fact that this precipi- tation maximum hes along the Ohio River Val- ley, whereas there is only little precipitation (down to 1 inch) up in the Appalachian moun- tains on the SE side of the valley. The Report Limit of cloud system Us Wherate (S heavy rain trot Cloudless =a OIG) Fictitious isobars —-—- Isallobars (3 hourly) Fo 3hr pressure fall <0.3 mb ;| => "Surface” stream-lines .. Ground >1000m ab. s.-l. Fia. 17—Synoptic map over Scandinavia, July 26, 1950, 18z PROBLEMS AND METHODS OF RAINFALL INVESTIGATION Re, B ENS S=No rain, owing to subsidence Cb= Rain from detached Cunb (true showers) Fr=Rain from frontal cloud system Or=Rain from orographic cloud system Vc=Rain from cloud system connected with rapid vorticity change in homogeneous current <7 1000m isohypse Fig. 18—Rainfall in Sweden, July 26-27, 1950, 07z-07z 24 TOR BERGERON assume that this rain maximum was caused by a stationary front along the Ohio Valley, but as far as I can see from the weather- maps the front was not stationary. Instead, I venture to say that what we have here may be a special orographie effect that is very compli- cated. Time will not allow me to enter in detail upon this problem, but I want to direct your attention to the possible existence of even such queer things as this one in our atmosphere. I think that when the bulk of the rain fell, the gradient wind was southwesterly and very moist; and then there was an overflow of air from the south or southeast across the Appalachians be- cause of friction, causing a convergence on the lee side of the mountain range. In other words: a convergence might occur between a direct SW flow (corresponding to a SE-NW pressure gra- dient) over the Ohio Valley and a SSE flow through the Appalachian region (following the gradient). Naturally it would be important that also the moisture and lability conditions prevail- seems to ing at the occasion were favorable for some precipitation mechanism. There may, of course, also be other explanations. Figure 16 shows two weather maps from the period in question, taken from the Report cited. Those two days the general flow was an easterly to southwesterly, and there was no stationary front over the Ohio Valley, since in this case the Polar front had come down to the Appalachians and even further south. I sincerely hope that some American colleague will collaborate with me on this very interesting case, which I have had in my mind ever since I found it. Here is another case, from Sweden, with a stationary cold front extending N-S over cen- tral Sweden and a postfrontal precipitation area (Fig. 17). That is not unexpected in itself, but the rain also extends far west, to the lee of the Scandinavian mountain range, and it stayed there for three days, giving flooding rains on the lee side of that mountain range. How would you explain that? In fact, the stream lines of Figure aoe Scandes raa777 Coast station ——» 3 Cold air flow — L = _ warm air flow Fic. 19—Tentative schematic map and vertical cross section of rain mechanisms over Scandinavia, July 26-28, 1950 DISCUSSION 25 17 show a convergence along the southern edge of the extended rain area, between the N flow descending from the divide near 63°N and the WSW flow to the south of the convergence line. The air ascending at this line is carried towards NW by the predominant SE flow aloft (see Fig. 19). This may explain why the main part of the rain area lies to the north of the convergence of the flow in the lowest layers. The dynamic trough normally forming to the lee of a moun- tain range will favor a frictional inflow at the Earth’s surface in this region. Usually, however, this inflow will not be powerful enough to cause and sustain any large-scale lifting of this very dry ‘fohn’ air, since this air will never reach the condensation level, the lifting cooling thus being dry-adiabatic. In the case studied here, however, the air in the frictional layer had been moistened by the weak but steady rain from the overhang- ing Altostratus-Nimbostratus sheet behind the stationary front. When the condensation level within this postfrontal mP became low enough, the tendency to a general convergence at low levels would favor an orderly overturning within this conditionally unstable cold mass, leading to the formation of the marked convergence line and rain area in the trough. A scrutiny of the individual vorticity changes in this stationary trough confirms the assumed existence of a marked convergence within it. Figure 18 displays the ensuing precipitation distribution with up to SO millimeters in the region of the downward current at the Earth’s surface. The area of great precipitation extends even over eastern Norway. This case is only partly analogous to the Ohio case, but it shows that there are precipitation systems that have not yet been explained, and occurring where one would not expect them according to conventional theories. They may have been of orographic or frontal origin, but they are now simply condi- tioned by an orderly convergence and lifting, which is of extreme importance because it may give so much precipitation. A cross section from northern to southern Sweden (Fig. 19) shows the down-flow of the northerly wind, the converg- ence, and the resulting lifting, producing this very astonishing precipitation where there is no front and where one would expect a warm and dry fohn instead. Last, I want to show that I think that there are two main precipitative effects superimposed on all different kinds of precipitation: those of the wavy kind and those of the convective kind, or stationary lee-wave precipitation and con- vective streaks of precipitation. Figure 20 shows the precipitation distribution in Holland meas- ured in the morning of October 26, 1945, after 24 hr with a west southwest gradient wind. It shows a succession of rainfall maxima and min- ima from W to E over Holland. Excepting the dunes, northwestern Holland is absolutely flat, lying between one and five meters below sea level. Thus, it must be the difference of friction between sea and land that causes the first maxi- mum, Just above the dunes, and I presume that then a series of stationary lee waves is set up at the level of low clouds, as shown by Figure 21. One day later, on October 27 (Fig. 22), when the gradient wind had hardly changed at all, but the static stability had changed into instabil- ity, the stationary lee-wave system broke down. Instead, there were convective streaks of pre- cipitation more or less parallel with the wind, again reaching great amounts. In the first case a warm front passed Holland; the next day a back-bent occlusion passed over the country. Figure 23 shows the change that took place in the upper air during these two days. Figure 23a is the 500-mb map at the middle of the first pre- cipitation day, with WSW wind aloft and —18 to —20°C at this level over Holland. The next morning (Fig. 23b), still with the same wind, the temperature at 500-mb had sunk to —28°C, this being the reason why the stability pattern had broken down. I presume that these two pat- terns will be more or less superimposed on all other precipitation mechanisms. Discussion Dr. Helmut Weickmann—Thank you, Doctor. It has been a very interesting lecture, which felt like a cool breeze after the heat of many years in which it was tried to increase rain by increas- ing the number of nuclei. It showed very con- clusively that the updraft is of prime importance in the generation of rain. Dr. Horace R. Byers—In your discussion of the ascent of air in tropical hurricanes, you said something about the augmentation of the tem- Jo’ 4“ z ; ARAN el 26 X.1945 saat)", Isohyetal 10 mm ERY Ww = ” 15 ” ‘ . x ~\ “ 20 dy \’ \\ 5 A ‘N \\\ i os A ANS x Bi 40 ; LW NEES x 3 50 - ih x Ca \\ jah OA \ NRA) Be \ Ak : € x Axis of 3rd “rain-wave" 4°L£6r 30" o* Fre. 20—Rainfall over Holland, Oct. 25-26, 1945, 07z-07z ™ m He x : 5 1000 | Profile of the Netherlands | Legenda | along the line a b 1 Zee Oscillatingjeurcent Intensercondensctioniig r and vertical air motion , Frictional updraft, =| = weeenees Sea-level in a quasi-stable SW. current | —_, Quasi-laminar current === Weter Ee 2 2 Turbulence HSER Land 500 = = = 500 100 100 Q ———————————————— 40 ma Profile of Precipitation | : mm [ | 25.—26.X.1945 (07'—079) | : =u (PSS Sse —--4y -------S2¢—---V---- >—- --4 i ' 10 0 g. 21—Tentative vertical cross section of precipitative lee-wave mechanisms over Holland during the rainfall of Fig. 20 26 DISCUSSION 27 27 X. 1945 : het vile, ee Z fg WK /, " = tal 10 mm : oe yt) Uf y)] Oa Isohye a ‘ 15 YP dy, ly Yl, esse 4 ee af [i ws RECESS, : saan 4 (K neers Wy, Uy " 30 " y (eh 7 Uy Wf “ 40: -" UD // / / j //// Yy 7 mC erelgeta yr] / is He hd ee 44 Jo’ Wien, — 30 Fig. 22—Rainfall over Holland, Oct. 26-27, 1945, 07z-07z perature difference that occurs at the surface in contrast with that aloft. I think I misunderstood you. Could you elaborate on that principle a bit? Dr. Tor Bergeron—Well, of course, as you noticed, I had to pass superficially over each item. The fact is that not only the temperature is increased, but also the contents of humidity, assuming with Palmén that the relative humidity remains, for instance, 85% at the ocean surface in both cases. Then, the warmer parcel may reach the cloud base with a temperature that is, say, 1°C higher and follow another moist adiabatic line that is diverging from the former one to- wards higher temperatures. Mr. Jerome Namias—In other words, you as- sume the same relative humidity but an increased specific humidity ? Dr. Bergeron—Yes. The equivalent tempera- ture increases more than 1°C, of course. Mr. Namias—I am puzzled about your state- ment regarding the inability of radar to depict the release or the areas of release of latent energy as well as do precipitation maps. Did you mean the amount of it, or the area of it? Dr. Bergeron—I know that I was a little un- clear on that point; I beg you to excuse me. I do not claim that precipitation maps give a better picture of the areas of release of latent heat than 28 DISCUSSION 504 | 24, isohypse (Dm) of 500 mb surface -24° — — — isotherm (°c) at " " " Fre. 23—500 mb map over NW Europe (a) Oct. 25, 1945, 182; (b) Oct. 26, 1945, 07z the radar. But precipitation maps will probably give a better idea of the rain amount than the radar maps; and then direct cloud observations from aloft and from the ground together with radar patterns will perhaps give the very best pictures of the regions where there is release of latent heat. That is what I meant. Dr. Weickmann—I wonder if the Ohio rains can be completely explained as simple oro- graphic rains without having to consider the release of instability showers? Mr. Namias—I will say something about that in my paper. Of course, it is rather unlikely that the mechanism for long continuous or repetitive rains can be ascribed to any simple orographic factors without considering the whole general circulation. The 1937 case is associated with still larger seale phenomena which Dr. Bergeron did not mention specifically, although he indicated them and lumped them together as ‘synoptic phenomena.’ In other words, first the stage must be set for the cyclone, which in turn provides for the release of small-scale phenomena which, as he pointed out, are amplified by orographic factors, instability, and the like. Dr. Weickmann—lI think we should emphasize still more that they may frequently be associated with thunderstorms and with quite intense in- stability lines. Dr. Bergeron—May I answer this last ques- tion? I had the intention of also showing you the normal January rainfall for North America. Referring to that map, the maximum January rainfall in the eastern states lies roughly where that Ohio flood occurred and peculiarly enough to the west of the Appalachians and not on the coast, or in the mountains, or down in Florida. Now, in this special case, the maximum, not only DISCUSSION 29 for that five-day period, but also for the rest of the month, was so closely patterned within the Ohio Valley that it would be very difficult to assume that there could be a large-scale phe- nomenon that should, just by chance, direct the whole thing, so that you got the maximum Just in that valley. I cannot get away from feeling that there must be some rather local orographic effect. Moreover, the Appalachians have an aver- age height of, say, 1000 meters. Clouds in that region will miss the lowest thousand meters of air, which contain the bulk of humidity, and thereby the best opportunity of getting abun- dant convective rain is lost. It might start better above the mountains, but once it has got started it grows better on the plains, as far as I can see. There may be other orographie effects also; but I want especially to direct your attention to the fact that the average maximum precipitation in January also falls near the Ohio Valley. Dr. C. W. Newton—I studied an example (J. Met. Soc. Japan, 75th Anniversary Vol., pp. 243-245, 1957) that looked very much like the one in January 1937, and I just want to describe what the precipitation looked like on an hourly basis. In that case there was a cyclone that looked very much like this one, moving regularly eastward as in this ease. The long streak of heavy total precipitation in that case was due to repeated movements of four or five heavy con- vective rainstorms over the same region, which I imagine is true also in your example. These storms formed every four hours, and the peculiar thing was that they moved successively over nearly the same track. It was not so surprising that their paths were almost in the same diree- tion since the upper wind direction did not change much, but the odd thing is the rain- storms all started in nearly the same place. This was down in the southwestern corner of Louisi- ana, and at the time I saw this, I thought of your suggestion on convergence near the coast caused by differences in frictional effects, be- cause I cannot see anything else that can pos- sibly account for it. There is no great mountain chain in southwestern Louisiana so I think it was an orographic effect of the kind that you dis- cussed, not due to mountains, but to differences in friction. Dr. Donald M. Swingle—I had oceasion to ob- serve the release of rainfall in the vertical for a year and a half, and the contrast between the fairly orderly release of rainfall in either con- tinuous rain or light showers, and the explosive periodic mechanism in the thunder showers is very clear in the data we have. This also stands out in the size distribution of raindrops, which is almost the same for shower rain and continuous rain. Therefore, relationships between rainfall and radar echo intensities are also almost the same. I think there is quite a contrast between the somewhat constrained semicontinuous or- derly released precipitation as you had in these orographic cases, and the rather sporadic re- lease one has in the strongly convective precipi- tation process. Dr. Bergeron—So you mean if one knows the character of the precipitation, one would be able to evaluate radar pictures into rainfall amounts? Dr. Swingle—Yes. Dr. R. Wexler—I had oceasion to do it by radar. It is very difficult to ascertain in advance where new storms are going to appear. Quite frequently, with a cyclonic system moving into New England, conditions appear to be the same with regard to instability all over the area. Nevertheless, the thunderstorms are bred in a few favored areas which do not seem to be too dependent on orography, but vary from day to day depending on the other conditions. One frequently finds that the outbreak of these thun- derstorms is associated with mesoscale pressure features which are not detected on large-scale maps; but I find it difficult to ascribe these small- scale features entirely to orography. It appears as if the convergence in the area was channeled into a few favored Cumulus which then devel- oped into thunderstorms. Dr. Bergeron—l have now ordered my thoughts a little more concerning that Ohio flood problem, taking into consideration all that has been said here, by Dr. Wexler and others. I agree with Mr. Namias that the stage was set on the whole by a large-scale arrangement. In fact, there is a map showing the average pressure distribution for January 1937, and also the wind and temperature distribution. All those maps show that the trough and convergence between the Bermuda high and another high in the west- ern United States did not le over the Ohio re- gion, but on an average further to the west. The stage for the activity was set in another way in the east. First of all, during those five days frontal cloud areas moved constantly across the Ohio region; thus, the upper air was loaded with any amount of releaser cloud, so that any spender cloud would have been released. Sec- ondly, there was so much moisture coming in 30 DISCUSSION from the southwest that spender clouds could easily form. Then, many of them, perhaps, were simply convective formations at favored spots. We know little about them; but there are cer- tainly such favored spots, and the convective systems probably moved as Dr. Newton said, up the Ohio Valley, maybe because their formation was favored by the lee-side convergence I men- tioned before. That would be my way of sum- ming up what has been said. Perhaps you do not agree, though. Mr. Namias—I am inclined to think that the orography must play a role. There undoubtedly is some mountain effect, but how much remains to be shown. Dy. Bergeron—l agree with Mr. Namias. I am quite aware of these facts. What I wanted to point out is that the bulk of the precipitation is formed within the Gulf air; I am opposed to the view that it was formed at a stationary front. No, it originated within the Gulf air, convective systems forming there; and a preferred locality is the Ohio Valley because of the reasons we both mentioned. As to the convective systems, I am sorry to say, Dr. Fujita, that you do not need a mesoscale network to find them. They may be very well located with the network that we have had in Europe for 50 years and even in the net- work of the United States, although that is much looser; but in order to find the finest details of the convective systems, one needs the time sec- tions that Dr. Fujita has utilized so ingeniously, and one also needs the densest network possible. Morphology of Precipitation Clouds and Cloud Systems Chairman: JOANNE MaALkus Woods Hole Oceanographic Institution, Woods Hole, Massachusetts IntrRopucToRY REMARKS The first session of this Conference on Physics of Precipitation is intended to set the stage or develop the context for the subject matter and papers which are to come. In the atmosphere, there are many different scales of phenomena as- sociated with precipitation, from the macroscale over the mesoscale down to single bubbles or ed- dies within an individual cloud. This is certainly one reason why in all meteorological studie I think most of us will agree that cloud physics is a meteorological study—we must consider the context of the other scales of motion in which this one is operating, and in particular we generally s—and bl find that we must look up the scale to larger scale phenomena. Therefore, it is extremely appropri- ate that the context of the first session include a discussion on the synoptic and larger scale flow patterns and their relation to the precipitation process. Our first speaker on this session is par- ticularly well suited to begin this discussion start- ing with a very large scale motion before we grad- dually work down. I think it is a landmark in cloud physics certainly, and perhaps also even in synoptic meteorology that one of the world’s leading synoptic meteorologists present a paper at a session such as this. | take pleasure in intro- dueing Mr. Namias. Synoptic and Planetary Scale Phenomena Leading to the Formation and Recurrence of Precipitation JEROME NAMIAS U. S. Weather Bureau, Washington, D. C. Abstract—This paper describes certain macroscale features (in both space and time) that play a dominant role in setting the stage for vertical motions, without which it is impossible to consider precipitation problems. First, an empirical relationship of broad- scale total precipitation fields to the geometry of time-averaged flow patterns in mid- troposphere is discussed and to some extent interpreted in terms of the interaction of synoptic and planetary scale systems. Contrasting ‘regimes’ of the order of a month, in which weather processes persistently recur, are illustrated. The amazingly stable regime of October 1952, the driest month in the meteorological history of the United States, is one of these. Another is the period December 1958 through January 1959, when a pre- vailingly dry regime changed abruptly into a wet one. The large-scale physical and synoptic characteristics of these phenomena are discussed in the light of the fine balance of the planetary circulation and against the background of seasonal change. Finally, the various precipitation forms of one of the major storms associated with the January rain-producing pattern which led to flood rains over the Ohio Valley are interpreted with the help of electronically computed charts of vertical motion. INTRODUCTION Of all the problems of prediction with which the synoptic meteorologist or forecaster has to deal, those associated with the formation of pre- cipitation are probably the most formidable and frustrating. For many years, precipitation was (and frequently still is) predicted mainly by re- lating it to the geometry of isobaric patterns at one or more levels as well as to the anticipated evolution of these patterns. Alternatively, polar front and air mass concepts provided a more explicitly physical basis for rainfall prognosis. These concepts forced the forecaster to think in terms of vertical motion, the main causative fac- tor, although this thinking was still indirect and qualitative. During the past decade, as a result of a great world-wide scientific endeavor to ob- jectivize weather prediction, vertical motion has begun to receive attention as a direct forecasting parameter. The development of high-speed com- puting methods is greatly expediting progress in this effort. At the conclusion of this report some mention will be made of the current use of computed ver- tical motions in explaining areas of precipitation ; a detailed account of this basic problem will be found in the following paper by Smagorinsky. The present paper will be concerned mainly with the large-scale or macro-scale features of the general circulation, the centers of action, which are perhaps best brought into focus by averaging over periods of time long compared to the life of an individual cyclone. When such a class of slow- evolving atmospheric motions are examined against the background of climatology they throw a great deal of light upon fundamental problems underlying the recurrence of dry or wet regimes and the often sharp breaks that occur as one re- gime changes to another of entirely different character. Furthermore, these large-scale time- averaged states appear to set the stage for the birth and growth of cyclones in certain areas, but not in others. For complete under§tanding of the physies of precipitation, certainly of its duration and its longer period characteristics, it is difficult to see how the large-scale background and its his- torical development can be ignored. PRECIPITATION Fretps RELATED TO Mip- TrRoposPHERIC TIME-AVERAGED Firow ParrerNs A general model—When time averages of mid- tropospheric contour charts for periods ranging from a few days to a month or a season are pre- pared and related to abnormalities of precipita- tion, it soon is apparent that over most areas in mid-latitudes heavy amounts are usually found on the forward side of troughs and lght on the back side. A schematic model resulting from sta- tistical studies by Klein [1948] employing five- LARGE-SCALE SYNOPTIC PROCESSES UNDERLYING PRECIPITATION eX) ew) — 700 mb. CONTOU ( pees REV AING STORM EACH ine i y | l fo} a ¢ kb & 200 wW ze 100 UNDED ote Ye 1827C 1828 1829 1830C JUN 20'57 Fic. 3—Vertical and time change in centrifugal force acting upon the par- cel circling around the funnel; wind is assumed to be cyclostrophie Now, the illustration shows that the parcels cated at the surface of the same condensation expanding along stream lines A,-A,-C, and A.- _ pressure. On the other hand, the parcels following A.-C, are friction free; therefore, the moisture in- the paths A,-A,-C, and A,-A,-C, would increase side the pareel would condense at C, and C, lo- their entropy through their irreversible expan- 64 TETSUYA FUJITA 40 50 60 70 80 90 100 = (eee | AR 90 110 130 160 180 200 220 MPH SS SS (e) ) / y oe s (Ke > A [o} ie) 200 HEIGHT ABOVE THE GROUND a fo} ie) ~— a 100 ee | —— 1827 1828 1829 1830C JUN 20'57 Fie. 4—Cyclostrophic wind speed computed from the gradient of the edge of the funnel; the maximum speed, 230 mi/hr, appeared shortly before 18h29m CST at the 100-meter level; no computation was made for the por- tion of the rounded bottom where the wind was far from being cyclostrophic 18 289 18.296 CST a fe) aD fe) TANGENTIAL WIND SPEED 8 & fe} 100 150 200m RADIUS ———> Fie. 5—Radial distribution of tangential wind speed in meters per second; arrows in upper figures give the location of the maximum wind speed com- puted along the dotted lines sion, reaching their condensation pressures at C, and C,, respectively. Assuming that the expan- sion along the surface is given by a straight line A,-A,—A/ on the adiabatic diagram, and that the expansion along A,-C; and A,-C, is dry adiabatic and reversible, the temperature and pressure change of parcels flowing into the bottom of the rounded bottom funnel were qualitatively de- scribed. Conclusions—It was found that the cyclo- strophic wind speed computed from the shape of the funnel with the combined use of hydrostatic STRUCTURE OF CONVECTIVE STORMS 65 R METER 200 40 (3) S 150 ~N a a ita LAMINAR FLOW 100 TURBULENT 44 en a 30 20 10 M/S 1827¢ 1828 1829 1830C JUN 2057 Fie. 6—Tangential wind speed shown as a function of time and radius of the funnel; the dashed line indicates the radius of the rounded bottom funnel Fie. 7—The nonadiabatic process taking place beneath a tornado funnel after it is rounded; note that the edge of the rounded funnel no longer represents a surface of condensation pressure and condensation pressure in the parcel method shows reasonable values. However, as soon as the funnel reaches a certain diameter, large enough to provide a long spiral inflow path of the parcels near the ground, the lower portion of the funnel is rounded. At this stage the bottom of the funnel no longer maintains the same condensation pres- sure. A dry adiabatic irreversible process asso- ciated with the near ground inflow was found to be one of the explanations for this. Acknowledgment—The research reported in this paper has been sponsored by the U. S. Weather Bureau under Contract Cwb 9530. 66 DISCUSSION Editor’s Note—After having presented his lece- with isobars and moving precipitation systems, ture Dr. Fujita showed an animated cinema of the (2) the meso-scale analysis of the Tornado Fargo Tornado on June 20, 1957. The film is di- proper, and (3) micro-scale features of the funnel vided into three parts: (1) the synoptic pattern and the movement of clouds near and around it. Discussion Dr. Malkus—I am sure we would all like to film which illustrates it. Only those of us who congratulate Dr. Fujita for a fascinating physical _ tried to make films ourselves realize the enormous study of tornadoes in this marvelous animated amount of effort that goes into ats C. I. ANDERSON Geophysics Research Directorate, Air Force Cambridge Research Center, Bedford, Massachusetts Abstract—The dynamics of the evolution of Cumulus congestus and Cumulonimbus clouds may be described in terms of V. Bjerknes’ second circulation theorem wherein a frequency factor, »*, pertaining to the bouyancy restoring force per unit length, is defined as a function of the temperature lapse rate and the scale of the disturbance. It is shown that either exponential or sinusoidal development of large local storms in the Southwest is described, together with the associated vertical velocity field and precipita- tion release. Although no direct evidence is available that supports an exponential or runaway growth for local thunderstorms, it is suggested that such may be the case for intense local storms of the cloudburst variety. Several examples of this are shown where an ex- ponential solution is possible. The paper concludes with speculations on the creation of self-sustaining local storms by altering the scale of the disturbance through the use Energetics and the Creation of a Self-Sustaining Local Storm of solar energy converting chemicals. On observing the development of Cumulus clouds, one often wonders if it is possible for a small Cumulus to grow to thunderstorm size by continuously enlarging itself. Experience shows how ordinary fair weather Cumuli disappear after fifteen minutes or so, and the maximum size at- tained during their lifetimes is quite small com- pared with a Cumulonimbus cloud. Except in regions of strong orography, one has little oppor- tunity to watch the birth and death of a thunder- storm. The observer usually notes that the thunderstorm drifts into his field of view rather than develops before his eyes. However, in the Southwest of the United States, light prevailing winds and pronounced orography combine to af- ford the study of the life cycles of all ranges of Cumulus types, from the very small to the gi- which may have resulted when the flow fields of several isolated Cumuli merged to form a large and active convective area. Viewing Cumulus growth as a cellular circula- tion, one can introduce the idea of the horizontal scale of the convection cell as having a bearing on its lifetime and vigor. This is accomplished by using a modification of V. Bjerknes’ Second Cir- culation Theorem developed by Hdéiland [1939] and Eliassen and Kleinschmidt [1957]. For a cell- ular circulating system, the circulation of the ac- celeration is equal to the circulation of the verti- cal restoring force au at Ow hes dz PNoi at gantic Cumulonimbus. It was in this region that were data on the growth of Cumulus clouds were ob- gence Beles (2) tained for this study. Tages The data consist of stereo pairs of cloud photo- ' graphs, 9 X 9 inches, which were analyzed stereo- Y = environment lapse rate scopically for the rate of vertical growth of vari- va = dry adiabatic lapse rate ous clouds. These photographs were made at Tucson, Arizona, by the Institute of Atmospheric Physics, University of Arizona, in 1956; and at Flagstaff, Arizona, by personnel of the Cloud Physies Branch, Geophysics Research Directo- rate, in 1958. From the limited number of clouds thus far studied, it appears that thunderstorm-size clouds do not develop by the continuous growth of small Cumuli. The earliest precursor of a thunderstorm is itself a vigorously growing Cumulus congestus 6 = The other symbols have the usual meteorologi- cal meanings. As used in (1), v is the static stability or vertical restoring force per unit length. For a closed streamline, the motion will be either a stable standing oscillation or an un- stable cellular circulation. At a point where the closed streamline of the cell is tangent to the vertical axis of the cloud, we may determine the nature of the vertical velocity variation with time because the frequency of the circulation accelera- 68 C. E. ANDERSON tion applies to all portions of the fluid along the streamline. From (1) we may write for this point Ow — = —p%z (3) ot or Pw = —rw (4) ot When —v? <0, w = A sinh vt, and when —vr? > 0,w = A sinh vtifw = Oatt = 0. When —v > 0, we have an exponential in- crease in circulation with time and when —v? < 0, harmonic oscillations about an equilibrium value of period 22/v are expected. In this latter case, vy may be regarded as a frequency factor. An expanded form of (2) may be employed to demonstrate the influence of horizontal scale on the stability of the circulation. Petterssen [1956] and Beers [1945] have shown that the frequency factor can be expressed —v = (g/To)[ (ys — y) + (ya — y)A+/A-] (5) Here y, = saturated adiabatic lapse rate T,) = temperature of the environment A,/A_ = ratio of updraft area to downdraft area ll ll The horizontal scale of the convection cell may make its influence felt through the parameter A,/A_. Ordinarily, ya > y > Ys, so that oer aA ll = ae || and stable solutions are to be expected in (4) if A,/A_ ~ 1. Unstable solutions are possible if | (va — ys)A3/A_| < | se — v) | and this may be realized whenever the ratio A,./A_ is small enough to make this possible. It is apparent that this parameter has a criti- cal bearing on the stability of convection and varies with different meteorological conditions. One object of the cloud studies made in Arizona was to get an estimate of this ratio. For the clouds studied, a low frequency oscillation was noted in the vertical growth rate. This oscillation was manifested by periods of rapid upward growth followed by periods of slow upward growth. By using the observed frequency to- gether with Raob data, (5) was solved for A,/A_. The results are given in Table 1. The ratio A,/A_, thus computed, suggests for these some- what isolated Cumulus clouds a convective cell whose updraft area is about equal to its down- draft area. The clouds are individual ones whose fields of motion do not extend much beyond their visual borders. This concept should be reasonable for ordinary fair-weather Cumulus development and air-mass showers. It is conceivable that in a meteorological situa- tion of synoptic-map scale low-level convergence and high-level divergence, A,/A_ may be very small if the updrafts are confined to a few very intense storms. This provides for rather narrow regions of strongly ascending air surrounded by broad regions of gently descending air. Under these conditions one might expect to find un- stable solutions to (4). If the circulation increased exponentially with time, one would expect to find rather spectacular results in the local weather. Although there are no data which will allow a direct verification of (5), as in the case of stable oscillations, one might turn to instances of record-breaking rainfalls to determine if the meteorological conditions were right to expect A,/A_ to be small and thus lead to runaway con- vection. In Table 2 is a list of outstanding cloud- burst rainfalls. The two greatest recorded rainfalls in the United States occurred at Thrall, Texas, in 1921 and at Hallett, Oklahoma, in 1940. Lott [1953ab] describes these storms and the attending meteo- rological situations. The Thrall storm was most remarkable in that the bulk of the rain fell in two bursts only lasting about four hours each. Lott attributes the bursts to the passage of an isallo- baric low-pressure center which was the remnant of a small hurricane which entered the Mexican coast. The conditionally unstable lapse rate, high moisture content, and convergence-divergence pattern agree very well with the conditions one should expect for runaway convection. TaBLE 1—Computed values of A,/A~ es Peo Ply Be | A,/A Cloud location Date os | (com- ane puted zs a minute Tueson, Arizona July 23, 1956 | 11 1.0 Tucson, Arizona July 24, 1956 | 11 0.7 Flagstaff, Arizona Aug. 22, 1958} 10 1.0 Mt. Withington, | Aug. 16, 1957) 10.3 | 1.34 N. M.2 Mt. Withington, | Aug. 20, 1957} 8.5 | 1.33 N. M.s ® Vonnegut and others [1959]. DISCUSSION 69 TaBLE 2—Cloudburst rainfall in the United States | Vertical moisture Remarks Location Date Lapse rate Franconia, Va. | Sep. 1, 1952 Unstable Thrall, Texas Sep. 9-10, 1921 | Unstable Hallett, Okla. | Sep. 4, 1940 | Unstable | | Chicago, Il. Oct. 9-19, 1954 | Unstable Surface to 550 mb Surface to 500 mb | = : Tornadoes associated with hurri- cane Able Surface to 700 mb | Record 19.65 inches in 12 hr in two bursts (remnants of Gulf hurri- cane) Surface to 300 mb | 15.5 inches in 9 hr., non-frontal air | mass 6.72 inches in 9 hr., record, all thun- derstorm rain, south of warm front The Hallett storm occurred as an air-mass type in very moist, conditionally unstable air. It is noteworthy that the rain fell between 02h00m and 11h00m CST which signifies that this was < nocturnal storm which had been growing, per- haps, from the previous afternoon and thus must have built into an enormous-sized single thunder- storm. It, too, qualifies as an example satisfying the conditions for runaway convection. The Franconia storm was similar to the Thrall storm in that it was associated with the remnants of a dying hurricane low center. Although no record rains accompanied this storm, it was notable for the tornadoes it spawned. The Chicago storms are additional examples of the conditions resulting in runaway convection. Here one had low-level convergence, high mois- ture, and conditionally unstable air south of a warm front so that it was possible to have small but intense updraft areas and widely distributed downdraft areas [JZeans, 1956]. Following this line of argument, one may in- quire into the possibilities for the creation of intense, self-sustaining, local storms through ar- tificial means. One feature which must be present is the large areal inflow to and outflow from the storm. In addition, high moisture, at least in the inflowing air, should be present. Nature provides ready-made situations of this type in the vicinity of low-pressure areas and one would need only to intensify certain updraft regions to set off run- away convection since the other elements for a self-sustaining storm are present already. One would expect to find the most favorable oppor- tunity in a warm sector where moist tropical air is present with appreciable sunshine. Under these conditions, it seems favorable to encourage the growth of large Cumulus congestus clouds by dust- ing smaller Cumuli with solar energy converting materials such as carbon black. The dusting should be done so as to create a larger flow field by merging several adjacent Cumuli. This seems to be the way nature accomplishes the formation of thunderstorms and we might well begin by trying to imitate her. REFERENCES Beers, N., Atmospheric stability and instability, Handbook of Meteorology (F. A. Berry and others, ed.), pp. 693-725, McGraw-Hill, 1945. Evrassen, A., ann E. Kiernscumipt, Dynamic meteorology, Encyclopedia of Physics (S. Flugge, ed.), 48, Geophysics II, Springer-Verlag, Berlin, pp. 1-154, 1957. H6ruanp, E., On the interpretation and applica- tion of the circulation theorems of V. Bjerknes, Arch. Math. Og Naturv. vol. 42, 68 pp., 1939. Lor, G. A., The unparalleled Thrall, Texas, rain- storm. Mon. Wea. Rev., 81, 195-203, 1953a. Lorr, G. A., An extraordinary rainfall centered at Hallett, Oklahoma, Mon. Wea. Rev., 81, 1-10, 1953b. Means, L. L., Some basic parameters associated with the flood rains at Chicago, Oct. 9-12, 1954, Mon. Wea. Rev., 84, 253-260, 1956. PETTERSSEN, 8., Weather analysis and forecasting, 2nd ed., vol. 2, McGraw-Hill, 266 pp., 1956. VONNEGUT, BERNARD, CHARLES B. Moore, AND ALEXANDER T. Borka, Preliminary results of an experiment to determine initial precedence of organized electrification and precipitation in thunderstorms, J. Geophys. Res., 64, 347-357, 1959. Discussion Mr. Douglas K. Lilly—lVd like to propose an- other possible interpretation of the evidently pe- riodic characteristics of those observations. It seems that there must be some instability in order 70 C. E. ANDERSON for the cloud to rise in the first place. I think possibly that the individual elements, both the small rapidly changing ones and the larger ones are all unstable but have a life cycle because of precipitation processes. It is this life cycle which gives them a semiperiodic appearance, somewhat similar to the occlusion processes that give pe- riodic appearance to cyclones. Mr. C. B. Anderson—In regard to the problem of bubble versus periodic motions, I thought the data I showed from Vonnegut’s work would indi- cate that if these were discrete elements, they could not act over a large segment of the atmos- phere simultaneously. Since we find the motions near the cloud base, within the interior of the cloud, and at the top to be in phase, it is very hard to account for this by assuming some type of discrete element moving upwards. On the Dynamical Prediction of Large-Scale Condensation by Numerical Methods JosEPH SMAGORINSKY U.S. Weather Bureau, Washington 25, D.C. Abstract—The paper discusses properties of the hydrothermodynamic frameworks thus far employed, the approximations regarding the microphysics of precipitation, the quality of results of numerical integrations for different models, further work in the construction of more sophisticated dynamical models, and investigations of the relation of large-scale liquid water content and of water vapor, and the implications for the dynamical prediction of cloud formation and dissipation. A brief survey of the state of the art—Attempts to make dynamical precipitation forecasts by numerical means began over 5 years ago. The first efforts were merely to employ the vertical motions calculated during the course of baroclinic numerical forecasts [Smagorinsky and Collins, 1955; Miyakoda, 1956; and Smebye, 1958]. The hydrodynamics were quasi-geostrophic, the baro- clinic structure was described by information at three levels, and the potential vorticity was lin- earized when it appeared undifferentiated. Fur- thermore, the released latent heat was not per- mitted to add energy to the system. It was assumed that precipitation occurred upon attaining saturation, but it was already realized that the space-averaged relative humid- ity need not be 100% for condensation or precipi- tation to oecur. The possibility of supersatura- tion, supercooling, evaporation from falling drops, or inadequate nucleation was ignored. The results were reasonably encouraging, but further work suggested that departures from observation were to a large extent a result of errors in the large- scale hydrothermodynamics. The most obvious defect was the neglect of released latent heat, which is a destabilizing effect [Smagorinsky, 1956; Aubert, 1957]. This alone can amplify the large- scale upward vertical motions by as much as an order of magnitude giving maxima as large as 50 cm/sec. The degree of destabilization increases with decreasing scale and decreasing static stabil- ity. It was also possible to remove the mathemati- cal limitations of quasi-linearization and to add the barotropic effects of large-scale mountains. Since these models now possessed energy sources and moisture sinks it was desirable to provide a pseudo-boundary layer which would allow for 71 surface friction and evaporation depending on land or sea. The quasi-geostrophic model equa- tions have been recast to be governed instead by the balance (or quasi-non-divergent) condition [Smagorinsky and collaborators, 1959]. The results are often better, especially in the movement of the systems, but also suffer because of new limita- tions introduced. The relatively smaller charac- teristic scale of moisture distributions present special difficulties and somewhat special numeri- cal techniques have been devised to reduce trun- cation error. Although very distinct progress has been made, the remaining hydrodynamic degeneracies leave 24-hour precipitation forecasts with much to be desired. It is quite obvious that the geostrophic approximation as well as the balance condition are really valid for the very large-scale quasi- barotropic components of the motion. Much of the validity is lost when trying to describe the dynamies of the smaller-scale baroclinic develop- ments which occur sporadically as extratropical cyclogenesis. This is probably the major reason why geostrophic and balanced baroclinic models on the average give no better wind forecasts at 500 mb than do barotropic models. The effects of released latent heat are on still a smaller scale, and the inertial-gravitational modes of atmos- pheric motion become even more important, if not essential. The divergent components appear to be of consequence not only in dynamical inter- actions but also for a proper accounting of the moisture budget. There therefore seems to be no question that further progress will depend on our ability to construct an adequate dynamical framework. Until quite recently, attempts to integrate nu- merically the primitive equations had not suc- 72 JOSEPH SMAGORINSKY ceeded. However some progress has now been achieved in devising a stable system for numeri- cally integrating the primitive equations for baroclinic flow [Smagorinsky, 1958; Hinkelmann, 1959] as well as for barotropic flow [Phillips, 1959]. This experience is now being applied to the construction of a near-hemispheric, four-level model allowing moist adiabatic processes. This model will include the baroclinic as well as baro- tropic orographic effects and also a simple ac- counting of boundary layer processes. It is apparent that the much smaller scale con- vective motions pose a special problem. It would, of course, be impractical to consider describing them by explicit dynamics. Ideally desirable is an adequate statistical-dynamical theory of moist convection which can define the classes of un- stable ambient states and account for the system- atic nonlinear interaction between the convective motions and the larger scale motions resolvable by explicit dynamics. Some work in this direction has been done by Malkus and Witt [1958] for dry convection. Moist convection, on the other hand, seems to be inherently different mechanistically and considerably more difficult to cope with. However, there is promise that numerical model experiments will yield further insight into the moist convective process, and work is now being undertaken in this direction. Some gross properties of the macrophysics of condensation and precipitation—Until now the limitations of the hydrodynamic contexts did not warrant refinements in the assumptions regarding the physics of condensation. However, contiguous studies have indicated the way toward a some- what more adequate linkage of the large-scale hydrodynamics and the condensation process. In CLOUD AMOUNT, C 1 2 3 4 5 6 aT 8 2 Lo RELATIVE HUMIDITY, h Fic. 1—Empirically determined relation of mean relative humidity h in the layers 1000-800 mb, 800-550 mb, and 550-300 mb with cloud amount c classed as low, middle, and high, respec- tively particular, it would be desirable to allow for the non-precipitating cloud stage, since until now only a distinction between clear sky and precipita- tion has been attempted. It is generally known that cloudiness and even precipitation are found to occur at space-averaged relative humidities considerably less than 100%. This cannot be dismissed as a purely instrumen- tal aberration. Humidity as measured by the instrument and averaged from the sounding, rep- resents the mean of a frequency distribution of smaller-scale humidity variations with consider- able standard deviation. This must mean that for values of the average humidity considerably less than 100%, some condensation may be occur- ring due to saturation at the high end of the distribution. One would then expect that the amount or density of condensation (that is cloudi- ness) will increase with increasing mean humid- ity. Furthermore, one may view precipitation as resulting from sustained and very dense conden- sation, sufficient to create large enough particles, say for example by coalescence or the ice crystal process, to overcome the upward vertical cur- rents. Indeed one does find empirically that non-con- vective cloud amount, classed as low, middle, and high, is highly correlated with the average relative humidity in the respective layers. Precipitation, if interpreted as corresponding to a cloud amount somewhat greater than 1.0, also fits such a corre- lation. In fact, the simple linear relation c=Bh-—a>0 (1) for each layer yields an excellent fit. Here c is the cloud amount, h is the relative humidity in per cent, and @ and @ are empirical coefficients. The fact that the instantaneous value of ¢ does not appear to depend on the instantaneous vertical velocity is not surprising. One would expect non- precipitating condensation to depend only on the accumulated history of the vertical motion, which after all is reflected in the humidity. For the purpose of establishing the coefficients a and @, it was assumed that the mean relative humidity in the 1000-800 mb layer corresponded to the span of low cloudiness, 800-550 mb to middle cloudiness, and 550-3800 mb to high cloudiness. A graph of the linear relations is shown in Figure 1. (The writer is grateful to 8. Heller- man for his assistance in determining this relation from careful analysis of a substantial volume of synoptic data.) It is of interest that all three levels tend to converge to c = 1.3 forh = 1.0. DYNAMICAL PREDICTION OF LARGE-SCALE CONDENSATION 73 It is well known that in the lowest 100 mb next to the Earth’s surface humidities close to 100% are necessary before condensation is ob- served. This of course is due to the relatively in- tense mixing in the boundary layer. When surface winds are light, condensation in the form of fog may occur with lower humidities, but still con- siderably higher than in the ‘free’ atmosphere. It is of interest that non-industrial haze, which may be regarded as low-density fog, also occurs at high humidity. Under normal surface wind conditions, the intensely mixed layer is capped by an inver- sion through which the turbulence subsides al- most discontinuously, and it is above the inver- sion that some condensation may occur at humidities as low as 60%. The empirical relations found in no way are intended to reflect this discontinuous turbulence structure in the 1000-S00 mb layer, but rather to give a measure of the integrated effect of tur- bulence in the entire layer. To account ade- quately for the finer grain structure of turbulence would require far greater vertical resolution and more refined techniques than have been em- ployed here. One could guess as to what Figure 1 would look like if ‘low clouds’ were stratified according to the mean relative humidity (a) be- tween 800 mb and cloud base, and (b) between cloud base and 1000 mb. For (a) the standard deviation of relative humidity would be larger than the mean in the 1000-800 mb layer due to weaker mixing so that condensation could occur at lower mean relative humidities. Curve (a) would then intercept the ¢ = 0 axis at h ~ 0.45. Since the most intense mixing would be confined to the layer next to the ground, the frequency distribution of relative humidity would be very peaked. The curve (b) would intercept c = 0 at h = 0.85 or 0.90. Of course in this boundary layer c no longer corresponds to cloud amount but rather to the visibility which in the absence of industrial pollutants is fairly good measure of liquid water content in clouds as well as in fog [Houghton and Radford, 1938]. The fact that the visibility decreases with increasing relative hu- midity for humidities over 70% [see, for example, Neiburger and Wurtele, 1949] tends to support the above supposition. An effective means for demonstrating the ‘goodness of fit’ of Figure 1 is to deduce cloud amount from synoptic radiosonde data only and to compare with ‘actual’ cloud observations, rec- ognizing that the upper-level clouds when ob- scured from below must be estimated. All possible data including airways reports were employed. The comparisons are shown in Figures 2 and 3, for two cases, late spring and late fall. Included also are the geopotential fields at the 1000-, 700-, and 500-mb levels. The comparisons in the vicin- ity of the mountains must be ignored since the low-level humidities are fictitious and the ob- served cloud layers correspond to lower pressures than do sea-level observations. The two cases shown in Figures 2 and 3 are from wholly independent data. However, the empirical linear relations of Figure 1 have been found extremely useful as an analysis aid in re- gions of sparse radiosonde data such as over the oceans. Moreover, even over continental U. 3. the radiosonde network is often inadequate to fix the phase of smaller-scale distributions of humid- ity such as are associated with frontal zones. The surprisingly good relation between liquid water content and water vapor suggests a means for incorporating the cloud stage in the water budget, and in fact will lead to a measure of the efficiency of moist adiabatic processes in large- scale condensation. Since cloud cover is a relative two-dimensional measure of liquid water, if we assume the vertical extent of large-scale (non- convective) clouds to be proportional to a lnear measure of the horizontal dimension, then the volumetric measure of liquid water W is propor- tional to c3/*. Defining Wy as the minimum liquid water content necessary for precipitation, which according to Fig. 1 corresponds to ¢ = a = 1, then W = W,c?/2 (2) We denote by the subscript 2 the condition when h = 1, so that co = 1.38. We may now write the continuity equations for mixing ratio 7, mass of liquid (cloud) water per unit mass of air W, and mass of precipitating water per unit mass of air Wp, assuming that water vapor may change by expansional condensation or compressional evaporation, but that precipitating water does not evaporate dr Ym {5 = 0 force = 0 = SOS > (3) dt Pp lore <1 for 0 0 lo < 6* <1 fora 0, 6 does not depend on w since downward motion of a cloud parcel must result in dynamic evaporation so that dW /dt < 0 and dr/dt > 0. We are not free to specify arbitrarily 6 since (1) and (2) must be satisfied simultaneously by (3) and (4). Ignoring variations in a, B, and W,, then (1) and (2) require that (12) dw a3 _ dh a BW. = “dé = 9P : Vier Since by definition (18) then dh 1 fdr. drs dt 7, (é y dt ) ao The first term, the change of h caused by a change in water vapor, is given by (3); the second term also depends on the fraction of mass under- going moist adiabatic changes 6, but of course does not vanish for purely dry adiabatic proc- esses, since it changes with temperature and may be written as drs = rwld-¥m a (15) ar dl = 5) yal ) where 1lnr vat) = »(§ =) =xy—1>0, (6) dp Joxconst and it may easily be verified that Vm = Xd Yn = Va = = Y 1+ ya (17) Hence dh dt 2 E h)é . = (i —=5)R =| » (18) Inserting (4) and (18) into (12) yields = a* + xh Vc va/ym 1+x Weld — h) + hya/yml (19) where = 1.58W,/r; (20) For ¢ < «, we have that 6* = 0 so (19) and (1) uniquely define 6 as a function of ¢ or h. Also, for c. < ¢ < c,andw > 0, we have that 6* = 0, again uniquely defining 6. On the other hand, when w < 0, we have 6,;* = 0 as before, and since all condensing water vapor must be precipitating when ¢ = ¢2 then by (4) 62 = 6.* = 1. Assuming 6* to vary linearly in this range then c—t c—1 6* = ———__ = C2 — C1 0.3 (21) > Ofora 0 and the dashed line for w < 0 sary to explain the amounts of large-scale precipi- tation observed. REFERENCES AUBERT, E. J., On the release of latent heat as a factor in large scale atmospheric motions, J. Met., 14, 527-542, 1957. Aurm Kamer, H. J., anp H. K. WrIcKMANN, Physics of clouds, Met. Res. Rev., 1951-55, Met. Monographs, Amer. Met. Soc., 3, 182-225, 1957. HINKELMANN, K., Ein numerisches Experiment mit den primitiven Gleichungen, C.-G. Rossby Memorial Volume, Esselte A. B., Stockholm, 1959. Hovuenton, H. G., anp W. H. Raprorp, On the measurement of drop size and liquid water con- tent in fogs and clouds, Papers Phys. Oceanogr. Met., Mass. Inst. Tech. and Woods Hole Oceanog. Inst., 4, 31 pp., 1938. Komapayast, M., Some aspects of rain formation in warm cloud (II), Liquid water content as a function of upward velocity, J. Met. Soc. Japan, 35, 266-277, 1957. 78 DISCUSSION Matkus, J. 8., anp G. Wirt, The evolution of a convective element: a numerical calculation, Woods Hole Oceanog. Inst. Cont. 967, 1958. Mason, B. J., The Physics of Clouds, Oxford Press, 1957. Mryakopa, K., Forecasting formula of precipita- tion and the problem of conveyance of water vapour, J. Met. Soc. Japan, 34, 212-225, 1956. NerpurGcer, M., ann M. G. WurtreLe, On the nature and size of particles in haze, fog, and stratus of the Los Angeles region, Chemical Rev., 44, 321-335, 1949. Puruures, N. A., Numerical integration of the primitive equations on the hemisphere, Mon. Wea. Rev., 87, no. 9, 1959. SMAGORINSKY, J., AND G. QO. Coxuins, On the numerical prediction of precipitation, Mon. Wea. Rev., 83, 53-68, 1955. SMAGORINSKY, J., On the inclusion of moist adia- batie processes in numerical prediction models, Berichte des Deutschen Wetterdienstes 38, pp. 82- 90, Symposium iiber Numerische Wettervorher- sage in Frankfurt a.M., 1956. SMAGORINSKY, J., On the numerical integration of the primitive equations of motion for baroclinic flow in a closed region, Mon. Wea. Rev., 86, 457- 466, 1958. SMAGORINSKY, J., AND COLLABORATORS, manu- script in preparation, 1959. Smesye, 8. J., Computation of precipitation from large-scale vertical motion, J. Met., 15, 547-560, 1958. Discussion Mr. Jerome Namias—If the ultimate aim in all this is to predict in detail, at what point there may have to be a cut-off in this prediction scheme. It would have to make inferences about condi- tions responsible for run-away processes and various things down to some scale. That is, must we settle for a certain scale? I'd like to ask Dr. Smagorinsky if he believes there is no cut-off point and if he expects to go to the bitter end and attempt to predict weather on all scales by numerical process. Dr. Joseph Smagorinsky—I would say that one can reasonably place a cut-off at the point where the statistical dynamics of the smaller scale mo- tions are sufficiently stable and well understood. The ability to establish a threshold of turbulence permits the study of the explicit dynamics of the synoptic scale motion with adequate provision for the interaction with the scales of motion ulti- mately responsible for the dissipation of kinetic energy. Such a threshold of the horizontal scale appears to be of the order of 100 km. However, as I pomted out in my paper, the interaction of small scale convection with large scale motions is hardly understood. Orographic-Convective Precipitation as Revealed by Radar BERNICE ACKERMAN Department of Meteorology, University of Chicago, Chicago, Illinois Abstract—Summer cloud systems in the arid and mountainous region around Tucson, Arizona, are predominantly convective in nature. Extensive radar observations of these systems have been made by the Institute of Atmospheric Physics, University of Ari- zona, using height-finding radar. A study of the level of formation of radar echoes, based on data collected during the summer of 1956, indicates that an all-water process, as well as one involving the ice phase, was effective in initiating precipitation. Moreover there appeared important day-to-day differences in the efficiency of the water mechanism. Introduction—For the past four or five years the Institute of Atmospheric Physics, Univer- sity of Arizona, has been investigating the cloud and precipitation characteristics of arid regions. During the course of this investigation extensive radar observations have been made using the AN/TPS-10, a height-finding radar. Radar data obtained during the summer rainy season in 1956 have been used to study precipitation fea- tures around Tucson. In particular, this report is concerned with the heights at which echo clouds first formed; the significance of such in- formation, of course, lies in what may be learned about the mechanisms initiating precipitation. The AN/TPS-10 radar has a 3-em wavelength and an elliptical beam with widths of 0.7° in the vertical and 2° in the horizontal. The radar sys- tem was monitored and power levels maintained at 47 dbm and —79 dbm for transmitted and minimum detectable returned power, respec- tively. Automatic photography of the radar scope gave a permanent record. There was ap- proximately a three-minute interval between successive observations at a given azimuth. The radar, which is located on the campus of the University of Arizona, scanned the area within sixty miles of Tucson. As can be seen in Figure 1, this area is of interest because of its topography as well as its aridity. The terrain varies in elevation from 2000 to almost 10,000 ft msl. Several small but distinctive mountain ranges are in the area; most of these are fairly well defined by the 5000 ft contour. The summer rainy season starts rather sud- denly in late June or the early part of July and continues through August. During these months there are alternating dry and wet periods, the =I We) latter characterized by fairly general Cumulus activity and convective rain. Although association between clouds and mountains is usually observed, the location of the major convective activity varies consider- ably from day to day. On few days are clouds associated with all of the mountain ranges, and as a corollary, a given range does not give rise to cloud systems every day. This variability is illustrated in Figures 2 and 3 in which are shown the locations of precipitation echoes on two of the days studied. (In Fig. 2 and 3 the division of the precipitation areas into groups was made for purposes of a detailed description of the echo patterns given in a more complete report of this work [Ackerman, 1959]). On only two of the seven days studied were the echo patterns simi- lar. It is evident that processes considerably larger in seale than the cloud are factors in de- termining the location of cloud development, even in a region as small as the one being con- sidered. Analysis and discussion—Because of the time- consuming nature of the data reduction, the analysis covered only seven days of the season. The criteria used in the choice of days were sufficiently objective to insure a random sample. They were (1) that convective precipitation, as indicated by radar, has occurred; (2) that radar data be available; and (3) that the days be scat- tered through the summer. The resulting sam- ple was composed of nearly 300 first echoes, that is, first appearances of echo clouds. For all of these cases the area was known to be free of an echo three minutes earlier. In Figure 4 are shown the frequency distribu- tions of the temperatures at the bases and tops ° 10 20 30 40 30 Stotute Miles Contour Interval 200011 7 TUCSON ao \ a % “us ¢ < a) os Se we ice 8, fon UMACACOR 9 s %, 7-20-56 EcHo Groups Fic. 2—Plan view of echo areas on July 20, 1956; areas represent echoes detected on a single 360° azimuth sean at approximately one-hour intervals, time identification to nearest whole or half hour, mst; to simplify the presentation a single outline encloses groups of closely spaced echoes, and, occa- sionally, groups of echoes on consecutive hours when they occupied essentially the same region; on the base chart are shown the 3000 ft contour and elevations greater than 5000 ft msl (shaded areas); dis- tance scale, in miles, is shown to left of center 80 PRECIPITATION AS REVEALED BY RADAR 8-24-56 “ EcHo Groups 81 ZN 5 \4 A \ oe ; (OX 14:3-16 ys a) 3a) aN Fig. 3—Precipitation areas on August 24, 1956; presentation as described in Fig. 2 of the first echoes. The conversion from height to temperature was made using the regular Tuc- son radiosonde. Since the temperature-height relation differed little on the seven days, the histograms for the height (msl) are very similar to those shown in Figure 4. The height at which echo clouds first formed was highly variable, with ranges of over 40°C of temperature (roughly 20,000 ft) m both bases and tops. The latter were smoothly distributed with two-thirds of the cases falling in the inter- val between —4 and —16°C. The modal value of —10°C is similar to that reported for the tops of initial echoes in clouds in New Mexico [Work- man and Reynolds, 1949]. Almost all of the echo clouds had tops above the freezing level when they were first detected, but, as can be seen from the lower section of Figure 4, a large fraction of them (nearly 60%) extended below the freezing level. The height distribution of the bases of first echoes (Fig. 4) is quite different from that of the tops. The bases occurred with high frequency at two levels, one above the freezing level at tem- peratures between —4 and —8°C, the other well below the freezing level with temperatures be- tween +12 and +16°C. Cases for which bases were colder than —4°C were no doubt echoes from particles produced by the Bergeron ice mechanism, but at least portions of the echoes haying bases at temperatures above +10°C must have been composed of particles grown without the involvement of the ice phase. The high incidence of first echoes with bases at these very warm temperatures indicates that an all-water process must be effective in ini- tiating precipitation in some of these Arizona clouds, if not in the entire depth indicated by the first echo, then at least in the lower portion. This conclusion is reached by reasoning similar to that used by Battan [1953] in describing the effectiveness of the all-water mechanism in Ohio; namely, that the large drops at the base of the echo cannot be explained by downward move- ment of large drops from the freezing level be- cause the drop sizes or downward flow of air re- 82 BERNICE ACKERMAN orc 80 + 60k TOP OF W a ECHO P40 O Ww ne 40) Ww = be Lo | uw | S) | a 8° T lJ mk = col BASE 2 OF 2 ECHO 4ob 20 oO n L aise an aes o +8 +16 +24 TEMPERATURE - DEG C Fia. 4—Frequency distributions of the temper- atures at the tops and bases of initial echoes; total sample: 294 first echoes quired (or both) are larger than can reasonably be expected. Since the clouds being discussed extended 5000 or 6000 ft below the freezing level, and that much or more above the freezing level, both coalescence and ice-crystal processes could have been, and probably were, important in the for- mation of the first echoes. It is suggested here that the chief difference between the echoes en- tirely from particles produced through the Ber- geron process and those resulting at least par- tially from a condensation-coalescence process was in the time-wise efficiency of the two mecha- nisms. Where first echoes had low bases the time required by the all-water process to produce large drops in the lower portions of the cloud must have been less than or equal to that re- quired by the ice-crystal mechanism to produce large drops in the cold reaches of the cloud. The data, in fact, contain evidence of inde- pendent and practically simultaneous develop- ment of echoes in lower and upper portions of the cloud. On three occasions the initial appear- ances of echo clouds were in two vertical seg- ments, the lower one completely below the freez- ing level, the upper one completely above it. In Figure 5 are shown the frequency distribu- tions of the levels of echo formation on the in- dividual days. Although there are day-to-day differences in the heights at which the tops of the initial echoes occurred they are not nearly as pronounced as the differences observed for the base heights. The total range of temperatures at which the echo bases occurred was about the same for all days but the ‘characteristic’ base height varied from one of the ‘preferred’ levels to the other. On July 24 and August 17 there was high incidence of first-echo bases at tem- peratures between —4 and —8°C; on August 1 and August 24, there was marked preference for first-echo bases to occur at temperatures around 14°C. The tendency for a ‘preferred’ level is less marked on July 27 and August 13, but on both days the distributions were skewed, toward the colder levels on the former day, toward the warmer ones on the latter. Only on July 20 did the bases oecur with high frequency at both levels. The echoes on this day, in particular, tend to support the thesis that precipitation may be initiated by different proc- esses in different parts of the cloud, and that, the source of variability is in the time require- ments for the two processes. The formation of the echo in the lower parts of the cloud evidently lagged only slightly that in the upper portion. Over 60% of the echoes with high bases when initially detected had bases at the lower ‘pre- ferred’ level (+12 to +16°C) three minutes later. This represented between 6000 and 10,000 ft of descent in three minutes, in many cases coincident with ascent of the echo tops. To date, attempts to find an explanation of the variation in the effectiveness of an all-water process from cloud to cloud and from day to day have been unsuccessful. It is possible to find one that fits the observations for two or three of the days, but what is required, of course, is an ex- planation fitting the observations on all seven days. A consistent relationship could not be found between height of echo base and time of day or time from beginning of convection. Similarly there appeared to be no association between ‘cold’ and ‘warm’ base first echoes and topography. Nor was there any indication that proximity to older rain clouds at the time of formation made a dif- ference. Locale and time of occurrence do not ap- pear to be important factors. The day-to-day differences in the character- istic height of first echo bases must reflect varia- tion in the interval of time required for the ini- PRECIPITATION AS REVEALED BY RADAR 83 MOIS FIRST aoe ECHOES N=77 20- T=-9.1 r ‘cal JUL 20 o 32 24 -16 -8 fo} +8 -16 40 40 N=31 firma N= 31 elk T=-15.4 Viola 420 beats filorscl = = =a = 15 =32i a 2d mcsiGry Tee Oo. 6+8 =\6anmes Ons +85 416 = N=26 N= 26 5 cs = ee toned T=-15.1 T=42°5) 420 7) 12) « t JUL 27 5 a esl [ II i r= al a gha: -32 -24 -16 -8 fo) +8 “16 -8 oO +8 +16 ; 2a 60 | ot | > mao N= 30 N=30 ile 2 e wie ft 7-913 T=+8.0 lees @ 20r a 420 9 WwW [ (ce a ey es ss ae ll eee a i io. fo J! L 3} 4 fo) - EFA 24 16 -8 {e) +8 16 =6 fo +8 +16 w WwW > N= 26 — es = 20 T==9'5 | a {commer aoe Z ol lal Wj, e Ww a 0° an ZaREEEIG -8 lo} +8 ers 40 — 40 N=67 =a al ae TW =2.1 ile 4 eee ine 32 -24 -16 -8 ie) +8 40 40 L N= 32 4 20h M1316) 420 L el eel 4 Al aoe : 40 = -32 -24 -16 -8 {e} +8 TEMPERATURE-DEG C -16 +8 +16 -8 fe} +24 TEMPERATURE-DEG C Fra. 5—Frequency distributions of the temperatures at the tops and bases of first echoes for each of the seven days studied; a few cases for which top height measurements were questionable were not included, causing the small discrepancies noted in sample sizes (N) tiation of precipitation by the ice and water mechanisms. The differences in the thermal and humidity structure of the atmosphere from day to day were relatively small, and no correlation could be found between the heights of echo for- mation and the small fluctuations in the heights of the condensation and freezing levels. Since the sizes and kinds of condensation nu- clei certainly must be a factor in determining the time required for the condensation-coales- cence mechanism to produce precipitation-size drops, it is suggested that a possible explanation of the day-to-day differences mentioned above may lie in the variations in the sizes and kinds of nucleating agents in the atmosphere. A pro- gram for the sampling of condensation nuclei may well prove enlightening. The data reveal that a condensation-coales- cence process is effective in initiating precipita- tion, even in an arid mountainous region. More- over they indicate that precipitation may be initiated either by an all-water process in the lower reaches of a cloud or by the ice-crystal mechanism in the upper reaches or both, either simultaneously or one lagging the other. A criti- cal parameter is the time required for these mechanisms to develop large drops. The factors deciding the time constants remain to be deter- mined. Unexplored also is the problem of the relative efficiency as far as surface rainfall is 84 DISCUSSION concerned; that is, is more or less cloud water realized at the ground when precipitation is ini- tiated low in the cloud before or simultaneously with that in the upper regions. Acknowledgment—This research was spon- sored primarily by the Institute of Atmospheric Physics, University of Arizona, and by the Geo- physics Research Directorate under Contract No. AF19(604)-1134. REFERENCES ACKERMAN, Bernice, Characteristics of summer ra- dar echoes in Arizona, 1956, Sci. Rep. 11, Inst. Atmos. Phys., Univ. of Ariz., Tucson, 1959. Bartan, L. J., Observations on the formation and spread of precipitation in convective clouds, J. Met., 10, 311-324, 1953. Workman, E. J., anp 8. E. Reynoups, Electrical activity as related to thunderstorm cell growth, Bul. Amer. Met. Soc., 30, 142-144, 1949. Discussion Dr. B. J. Mason—I think Miss Ackerman would agree with me that it is difficult to disen- tangle the two processes which may be occurring in the case where the first echo is both above and below the freezing level. I have made ob- servations of it, and this brings me to the ques- tion, What do we mean by a first echo? A first echo is when you first see something on the radar screen, but what it means in terms of size and so forth of the particles in the cloud depends upon the sensitivity and range of the radar. So, I would like to ask Miss Ackerman if she could give some kind of figure in terms of the sensi- tivity of the radar or whatever it might be that she takes for a first echo. Experience in England is that the first radar echo may just straddle the freezing level; but the echoes grow explosively in a minute or two both above and below. If you catch it a minute too late, you might come to a different conclusion, because they change so quickly. To come to the last point, the day-to-day vari- ation, nuclei are the first things microphysicists think about but I am inclined to think that fac- tors controlling the cloud dynamics may be more important. I wonder whether you had at the same time made any measurements of the actual humidity distributions in the air? Miss Bernice Ackerman—The sensitivity of the radar was monitored and kept constant so we could compare the data. I made rough ealcu- lations of the minimum particle size detectable by the radar. The calculations give a diameter of around 400 microns for a range of 20 mi and an assumed water content of 1 g/m*. Of course, the size varies with range and droplet concentra- tion. There was a three-minute time interval be- tween two pictures. This could be part of the reason for the wide range of temperature (40°C) over which these first echoes appeared. I agree some of these echoes with low bases could have started Just below the freezing level, but this still does not mean that they did not develop by a water mechanism, and I am not trying to separate the two types. In the lower portions of these echoes, at least, and possibly in some of the upper portions, the growth of droplets is through a water mechanism. Regarding Dr. Mason’s question on the humid- ity distributions, the only type of data I have for these days is that available from the regular radiosonde. This is, of course, one of the things one looks at immediately. There was essentially no difference in the vertical lapse of temperature and humidity between the days. Mr. C. J. Todd—Did you have available any visual observation of the cloud growth rate? Miss Ackerman—No. Dr. W. Hitschfeld—Did you have any infor- mation about cloud densities at the time the first echo broke out; that is, the amount of wa- ter, the quantity of water per cubic meter? Miss Ackerman—No, the only data available were the radar data. Dr. Hitschfeld—I think that cloud-density studies, even if calculated only roughly from the tephigrams, might allow one to eliminate the un- certainty with respect to the precipitation proc- ess. If the cloud densities are high enough, it might suggest that the East process has a better chance of being active (T.W.R. East, Precipita- tion of convective water clouds, in Artificial Stimulation of Rain, Proceedings of First Woods Hole Conference, Pergamon Press, 1957, p. 192— 201). Dr. Donald M. Swingle—Did you make any correction for the radar beam width uncertainty ? Miss Ackerman—Not as far as the actual cited levels are concerned. I am not trying to say DISCUSSION 85 these are well-defined levels in any sense of the word. They may vary by two degrees or per- haps even four degrees in temperature, because of beam-width effects. Dr. Swingle—Do I understand that, in fact, you have no observation of what the tempera- tures actually were in the cloud? Miss Ackerman—No, but the ‘preferred’ echo heights are very well separated. Dr. R. Wexler—Did you look for any relation- ship between the heights at which these first echoes appeared and the maximum height which was subsequently reached or in other words, for any relation at all between the region where the echo first appeared and the subsequent maximum development? Miss Ackerman—Yes, I tried to do so, using data for one day when there was a high fre- quency of echoes. I did not find any correlation. Dr. W. E. Howell—In a situation where you obviously hope in connection with some of these experiments to have a fairly repeatable cloud condition day after day, I wonder if it is not a little disturbing to find the pattern of echo varies so much from one day to another over these dif- ferent mountain ranges; and I wanted to ask if these had been related in your observations to the previous state of the ground, whether the previous occurrence of precipitation and con- sequent moistness of the ground affected the sub- sequent development on a later day. Miss Ackerman—No, they were not, and out- side of going into the radar data of each day, I do not know how we ean really do it. In the type of region we are talking about, there is not much rain and the rain comes in the form of scattered showers. We tried to see whether there was some correlation between the amount of rainfall reported by the existing stations with any of these data, but there was none. I really did not expect there to be, in view of the seat- tered nature of the echo areas and the sparseness of reporting stations. Dr. C. L. Hosler—Did you note any tendency of echoes when there were few echoes to reach greater heights than on the days when there were many? Miss Ackerman—No, I also thought this might be a possibility. Mr. Jerome Namias—A number of people seem to have suggested quite an ambitious re- search program for Miss Ackerman. In the geo- graphical area concerned, as you undoubtedly know, there is great precipitation sensitivity in the summertime depending on the location of the moist tongue. The gradient of moisture on both sides of this tongue is rather intense. Small shifts of the tongue will influence the whole syn- optic situation. Instead of working just with the Tucson radiosonde, I suggest plotting some isen- tropic charts to highlight this tongue and in this manner get an idea of the lateral mixing which could provide all sorts of variations even within six-hour periods. Miss Ackerman—As I said before, a real syn- optic analysis was not made, but it might be a good idea to do so. Dr. Mason—I think, Miss Ackerman should not be distressed that she can not get these things to tie up. This points to the difficulty of these problems even when one is dealing with everyday Cumulus. It also points out that if one uses one tool such as radar, this is very restric- tive. It only gives a very small part of the picture. We have to regard radar as one tool to be used in conjunction with a lot of others and these problems are very much more complicated than we thought at first. We have to go back and realize that Cumulus evolution is determined by the large-scale distribution of moisture, tem- perature, vertical motion, ete., right up the syn- optic scale, and the more of these data that point this out, the better it will be for long-term research in cloud physics. Miss Ackerman—Yes, I agree with you, and I am not particularly disturbed at not finding a simple explanation. We unquestionably have a complex situation. I would just like to repeat one comment made earlier by Dr. Byers; namely, the danger of taking one situation and develop- ing a general theory from it. In evaluating the data of seven days, we find seven different situ- ations. Microstructure of Storms as Described by Quantitative Radar Data PauLINE M. Austin Weather Radar Research, Massachusetts Institute of Technology, Cambridge, Massachusetts Abstract—Instrumentation which has been developed recently presents radar echoes from precipitation in the form of range-corrected signal-intensity contours, thus making it possible to observe in a quantitative manner the smaller-scale features within the pre- cipitation areas which appear on the normal radar-scope presentation. This paper pre- sents some preliminary results of the analysis of such data for two types of storms: warm-front type rain in an unstable atmosphere, and showers associated with instability lines. Dimensions, durations and motions of areas of heavy rain and of individual shower cells are considered in an attempt to determine the scales of atmospheric cir- culations which are particularly significant in the production of precipitation. INTRODUCTION Studies of basie physical principles and _ per- formance of laboratory experiments have con- tributed greatly to our understanding of the physical processes involved in the development of precipitation particles, such as nucleation, con- densation, and coalescence, and have also shown the influence upon these processes of the imme- diate environment of the particle. However, the manner in which such processes occur in the at- mosphere and the influence of the larger scale environment in encouraging or inhibiting the growth of hydrometeors can be learned only through detailed observations of actual storms. Radar observations provide a description of the distribution of precipitation either aloft or as it reaches the ground, although until recently such information was largely qualitative. Instrumenta- tion described by Kodaira [1957] is now available which presents radar data in the form of range- corrected signal-intensity contours, thus making it possible to observe in a quantitative manner the smaller scale features within the precipitation areas which appear on the normal radar-scope presentation. It is the purpose of this paper to describe some of these small-scale features and their behavior for two types of storms: warm- front type rain in an unstable atmosphere, and squall lines. Dimensions, durations, and motions of rain areas are considered in an attempt to de- termine the scales of the atmospheric circulations which are particularly significant in the produc- tion of precipitation. The signal intensity contours are obtained with an SCR-615-B radar which employs 10-em radia- 86 tion. Therefore the measurements are not dis- torted by attenuation. However, the SCR-615-B radar is not sufficiently sensitive to detect light rain except at very close ranges. Therefore the data are supplemented by photographs of the PPI of the AN/CPS-9 radar maintained by the Air Force at Great Blue Hill and by hourly rain- fall records from the U. 8. Weather Bureau Co- operative Observer Network. Warm Frontat Rain General description of storms—Data are avail- able for four storms where the rain was of the warm-front type but was not associated with a coastal storm. Only two of these storms have been analyzed in detail: October 17-18, 1957, and November 8-9, 1957. In both cases a cold front oriented approximately north-south was ap- proaching from the west, a warm front lay to the south of the station, and the winds aloft were from the southwest. The lapse rate in the warm air ahead of the front was approximately moist adiabatic below 20,000 feet and slightly stable above that level. The rain patterns associated with these storms are very similar. The most striking feature is a broad loose band oriented in the north-south di- rection which was about 250 mi in length and 40-50 mi across. The heaviest part of the pre- cipitation was in this band and it appeared to be about one hundred miles ahead of the surface cold front. On the PPI photographs the band had a pebbly structure, especially at long ranges, in- dicative of many small showers within the gen- eral rain area. RHI photographs also showed the MICROSTRUCTURE OF STORMS BY RADAR 87 J —— Edges of echo on ANICPS-9 em ——-—Level 4 ree eee | Range-corrected © 10 20 mies GSS Level 5 iso-echo contours @ level 6 Fic. 1—Main band of precipitation with smaller areas of heavier rain [A-E] spaced along it at 00h 30m EST, October 19, 1957 small showers which were 15,000 to 20,000 ft in height and were about two or three miles in hori- zontal dimension. The echoes had a well-defined bright band near the 10,000-ft level, but the showers were so small it was difficult to tell whether the bright band actually extended through them or not. The signal intensity contours (Fig. 1) show areas of more intense rain spaced about 30-50 mi apart along the line. These are labelled by the letters A to E in the figure. The areas A and E do not actually show because at the time they were out of range of the SCR-615-B radar. However, they were observed on previous or subsequent contour maps and indicated by the rainfall data. The approximate rainfall rates for each intensity level in Figures 1 and 2 are as follows: Level 3 A be 26 Rainfall rate (mm/hr) Qn 25) OY E25 Preceding the main band in each storm was an area of lighter rain whose internal structure could not be observed in detail by the SCR-615-B radar. In the latter part of the storm the broad band broke up into an irregular rainfall area which showed a tendency to form a series of nar- row bands oriented more nearly northeast-south- west, as shown in Figure 2. Spatial dimensions of storm areas—An attempt has been made to reconstruct the details of the storm structure by combining the information from two radars and the hourly precipitation records. The spatial scales or dimensions have 88 PAULINE M. AUSTIN boil _j ° 10 20 MILES Fic. 2—Irregular rain pattern and narrow bands in later period of storm at 03h00m EST, October 19, 1957 already been described and may be summarized as follows: (1) Synoptic scale storm with low pressure center in one case in the Great Lakes region, and in the other over Hudson Bay, but in both cases with a north-south cold front well to the west of the station and a warm front to the south. (2) Mesoscale areas of precipitation consisting of a poorly defined area of light rain containing only a few heavy showers, then a well-defined broad band containing the heaviest rain, and finally several smaller narrower bands. (3) Areas of heavy rain within the bands whose spacing and dimensions are on the order of 30-50 mi. (4) Individual convective showers which are about two to five miles in horizontal dimension and 15,000 to 20,000 ft in height. Motions of storm areas—The areas of heavier rain, labelled B, C, D in Figure 1, and the indi- vidual showers as indicated by small closed con- tours moved in a very orderly fashion from south- west to northeast. In the two storms studied in detail most of the rain areas seemed to develop or move into radar range at one of two preferred azimuths, roughly due west or southwest. Those appearing in the west often had a slightly more westerly component to their motions than those in the southwest, so that they combined to form a north-south band (Fig. 3). The velocities of the rain areas were in general agreement with the middle-level winds which were nearly uniform between 5000 and 18,000 ft. The large intervals in time and space between radiosonde soundings and the uncertainties in the wind measurements make it impossible to de- MICROSTRUCTURE OF STORMS BY RADAR 89 POSITION OF BAND AT 2100 EST, Fre. 3—Regions and times of development of rain areas, November 8-9, 1957 termine the details of the upper air wind field at a particular time and place and to make a closer comparison with the motions of the rain areas. The large band itself seemed to drift in an easterly direction at a speed slightly less than half that of the individual rain areas. Durations of rain areas—In each of the storms the main band retained its identity as a band for a period of about three hours. Then the pattern broke up and became rather disorganized but showed a tendency to form smaller bands as il- lustrated in Figure 2. The areas of heavy rain within the band and the general area into which it evolved were estimated to have a lifetime of about three hours. Most of them were observed on the contour maps for only 11% to 21% hours. Extrapolations beyond the range of the SCR- 615-B radar were based on photographs of the AN/CPS-9 scope and the hourly rainfall records. A number of ‘individual showers’ as defined by small closed contour lines were tracked and their durations observed. Most of those which could be tracked easily lasted between 20 and 50 min with a few enduring for over an hour, usually the more intense ones. There were also many small areas, especially of light rain, which lasted 15 min or less and were not included in the survey. Development of rain areas—Because of the limitations imposed by the range of detectability of the radars many of the regions of development cannot be determined with certainty. However, whether the rain areas actually developed at or near their estimated positions of origin or whether they moved into radar range at those locations, some very interesting recurrences are observed. Figure 3 shows the estimated times and appear- ances of ten of the heavy rainfall areas in the storm of November 8-9, 1957. They seem to ap- 90 PAULINE M. AUSTIN pear in certain preferred regions at approxi- mately hourly intervals. A similar recurrence was observed in the storm of October 18-19, 1957. Five rain areas appeared in northern Massachu- setts along the Connecticut River valley, between the hours of 23h30m and 02h15m EST, with in- tervals between the appearances of 45 min to one hour. Two heavy-rain areas appeared in the vi- cinity of Hartford, Connecticut, at 22h45m and 23h30m EST respectively and moved along the same path about 80 mi apart. Sufficient data have not been analyzed to per- mit one to assess the respective roles of local topography and larger seale storm dynamics in determining the preferred regions and recurrence intervals for the development of such rain areas. However, the fact that areas of heavy rain move along at 45-65 mi/hr and persist for periods of two to three hours suggests that local topography is not the sole factor in producing the observed patterns. SeuaLL Lines AND Coup-FrRontT Banps General description of storms—During the summer of 1958 intensity contour data were taken on six squall lmes or sharp cold-front bands. A study was initiated to investigate the development of these bands and, in particular, to determine the extent of the similarity in pat- tern details for the different storms. All except one had the characteristic that for a period of several hours they consisted of a long narrow line of intense convective cells. The one exception showed two lines, neither of which was as long or narrow as those associated with the other storms. All of the lines were either ahead or in the vi- cinity of a cold front and exhibited strong con- vective activity, although none would have been classified as a severe squall line. As in the case of warm-front storms, the data from two radars and the hourly rainfall records are being combined to reconstruct the details of the storm as well as possible. The analysis of these storms has not been completed and only a few preliminary re- sults can be presented here. Spatial dimensions—The observed length of the lines at the time of their greatest mtensity and sharpness appeared to be limited by the radar range. Hence it may be concluded that they ex- tended for at least 200 mi. The width of each line was about 20 mi, at least an order of magnitude smaller than the length. Individual convective showers whose dimensions were on the order of five to ten miles were spaced irregularly along the line about 20 to 50 mi apart. A typical pat- tern is shown in Figure 4. The approximate rain- fall rates for each intensity level in Figure 4 are as follows: Level tL 23 4s Rainfall rate (mm/hr) 5 10 25 45 75 Time scales—The development of the line from the time it first appeared as a line (that is, a few scattered showers but definitely lined up) to the time of its maximum intensity and sharpness re- quired two to three hours. For another two or three hours the line persisted and then it began to dissipate. Lifetimes of individual showers, as defined by small closed contours, varied from about 15 min to nearly three hours, but the rela- tively intense ones usually lasted about an hour. Since the order of magnitude of the time scales involved is the point of interest in this discussion and since the definition of ‘showers’ is dependent ina rather arbitrary manner upon the resolution, both in space and intensity, of the instrument, the observations on shower duration are pre- sented as a qualitative estimate rather than a statistical survey. Development of rain areas—The development or intensification of the line itself usually took place between 12h00m and 15h00m EST, ap- parently reflecting the effect of diurnal heating, although in one case maximum intensity was reached as late as 1ShOOm EST. Individual storms sometimes developed within the lne and ocea- sionally ahead or behind it but, in general, there appeared to be several ‘preferred’ regions for shower development. One of these areas was along the Hudson River; on at least two days storms developed there throughout the early afternoon. They appeared on the southern end of the line so that the area of development moved southward along the river valley as the line progressed. In all of the storms the orientation of the line was approximately northeast-southwest and the in- dividual showers moved toward the east-north- east. For some of the storms we have not yet analyzed the AN/CPS-9 data and therefore do not know whether development occurred along the Hudson Valley. A second region where many showers developed was in the mountains of New Hampshire just east of the Connecticut River valley. On three days showers were occurring more or less randomly in that area for several hours before the line formed, and on occasion the line itself seemed to intensify as it passed over the region. A third area of development is in cen- MICROSTRUCTURE OF STORMS BY RADAR 91 (l JULY 1958 (615 EST boot _j Oo 10 20 MILES Fig. 4—Squall line tral Connecticut. There is a tendency for the lower end of the line to broaden and intensify im this region and to move relatively slowly so that the form and orientation of the line becomes al- tered as the northern end progresses more rapidly than the southern end. It is believed that the topography of each of these regions is conducive to the development of storms especially when the surface winds are more southerly than south- westerly, but the major characteristic of the pat- tern, the formation of a very narrow and intense line, must be dependent upon the larger scale circulation. SUMMARY Radar observations have shown that the rain associated with warm fronts is generally wide- spread but exceedingly variable in intensity. Moreover, the variations in intensity do not, at first glance, appear to form any easily recogniz- able patterns. However, the detailed study of storms in which the synoptic situation was very similar has shown that the small-scale rain pat- terns also exhibited a great deal of similarity. In particular, heavy rain appeared in areas 20-30 mi in dimension, each of which contained a num- ber of smaller convective showers. These heavy rain areas appeared to develop in certain ‘pre- ferred’ regions at intervals of 45 min to one hour. They lasted for two or three hours and moved with the wind which was nearly constant between 5000 and 18,000 ft. The individual showers, as defined by small closed contours, rarely lasted more than an hour. In the case of squall lines and cold-front bands the storms were grouped together because of the similarity of the rainfall pattern as depicted by the radar. The synoptic situations were also very similar except that some of the lines formed well ahead of the front and were called squall lines while two of them were in the immediate vicinity of the front. The latter two moved into the radar range as bands; in the case of squall lines, seat- tered showers occurred in the warm air ahead of the front and then became organized into a sharp line. The dimensions of the lines were over 200 mi in length and usually less than 20 mi in width at the time of their greatest intensity and sharpness. They required a period of two to three hours for development and intensifica- 92 DISCUSSION tion, persisted for another two to three hours, and then began to dissipate. Individual showers within the band were on the order of ten miles in dimension and lasted about an hour. There appear to be certain local regions in which showers tend to develop or intensify. Dimensions, durations and development of areas of heavy rain have been considered in order to determine the scale of atmospheric circulation which is especially important in the development of precipitation. It is hoped that the analysis of more cases and different types of storms may provide information regarding the dynamics of this scale of atmospheric motion, especially con- cerning its relation to the larger scale environ- ment and to local topography. Acknowledgment—The author wishes to ex- press appreciation to Searle G. Swisher, Captain, U.S. Air Force, who is carrying out much of the analysis of the squall lines. The research reported on has been carried out under the sponsorship of U.S. Army Signal Research and Development Laboratory, Contract DA 36-039 SC-75030. REFERENCE Kopatra, N., An iso-echo contouring device, Proc. Sixth Weather Radar Conference, Amer. Met. Soc., pp. 307-314, 1957. Discussion Dr. Helmut Weickmann—What is your opin- ion as to the mechanisms for the development and propagation of these rain areas? Dr. Pauline M. Austin—The fact that we find areas of recurrent development suggests topo- graphical reasons. If we compare the wind field with the areas of development, we can draw conclusions regarding the influence of conver- gence. On the other hand, although a heavy rain area usually develops in a particularly preferred region, it then moves along with the wind and keeps on pouring out heavy rain for about three hours, moving right across the area represented on the scope. Clearly there is some dynamic effect continuing to produce rain, so I feel sure both factors are involved; but we have not analyzed enough different cases to provide the answer to your question. Mr. Jerome Namias—I was very fascinated by this. Of course, there are very good reasons, I think, for getting recurrence of synoptic scale events against a planetary scale background; but the amazing part of it is that there are small places in a given situation that keep getting battered by the same type of thing, and it is dif- ficult to attempt to explain it. I do not think it comes out of the synoptic pattern itself, and as you indicate there is a possibility that the synop- tic pattern sets the stage for different orographic influences. Some work done by Charles F. Brooks in Texas about 1926 consisted in studying the distribution of thunderstorms. He indicated that those areas which had thunderstorms one day would be unlikely targets the succeeding day. He explained that it was due to the fact that the ground was wet and the heating would not be so pronounced. Here is something which is highly speculative, but I think it should be considered. The second thing is something that I think Dr. Squires is going to talk about. There is a possi- bility, of course, that variations of the soil and ground-cover complex affected by rain or dry- ness could induce variations in nuclei kind and content and thus in the concentration of droplets, which might have some effect. But the complexity of these recurrence problems sug- gests that we have not only to go deeper into the synoptic physies, but that we may also have to take into account other factors as well. Dr. R. Wexler—The motion of a line depends on: (1) the motion of the individual cells, and (2) the rate of development of new cells which later become part of a new line. In squall line situations it is frequently observed that new cells develop some 10 miles ahead of the existing line. About half an hour later, these new cells become the dominant line while the cells of the former line are dissipated. On other occasions, the new cells develop at the forward edge of the existing line evidently by a mushrooming effect. In such cases, the question arises as to how it can be determined whether a high intensity echo occurs in a previously existing cell or in a newly de- veloping cell. Dr. Austin—The six lines that we have were all observed in the summer of 1958. Some cells formed ahead of the squall lines and some within them. None of the storms was intensely severe. What we did in tracking individual cells was first to overlay successive maps and select a dark DISCUSSION 93 area, corresponding to a high intensity level, which moved along. Then we took the times at which we measured its different positions, which formed a line, and plotted distance against time. As long as the plot was a straight lne, we pre- sumed we were definitely tracking the same cell. If a break in the graph occurred, mdicating an abrupt change in velocity, or if the cell disap- peared, then we ceased tracking it. Dr. C. L. Hosler—We are instituting a similar study in central Pennsylvania, and going along with the idea that much of the influence of the topography on the development of these showers is thermal, we hope to determine the thermal structure of the ground surface by infra-red radiation. Dr. Horace R. Byers—I think the thing that strikes some of us old timers who have worked with the classical synoptic pictures is that we have thought of the cloud system in connection with the warm front as one that is oriented es- sentially parallel to the warm front; yet these pictures show in all cases the line is more nearly perpendicular to this. Dr. Austin—These were peculiar warm fronts in that respect. These did have a cold front ap- proaching so that this cold front may be what de- cided the north-south orientation of that band. Dr. Tor Bergeron—I understand this was mainly a warm-front rain, and of course, I would have liked to have seen a thorough and reliable ordinary synoptic analysis of the case, first of all. Then also I wonder if you have made an analysis of the precipitation during the 24 hours in the region from all the available rainfall sta- tions, because as a result of all my work during almost 40 years, I have found that you can do quite a lot with that network if you really treat it in the best possible way. And you will, for instance, find preferred regions where these con- vective cells are released. It would have been very satisfying for me personally at any rate to see such a thorough analysis of the whole situa- tion and I wonder if there was such a one? Dr. Austin—The cold front approached a certain region, then it slowed down and hovered in the vicinity of Albany. You can follow its progress on 6-hourly or 12-hourly basis maps, but within the few hours we were watching the precipitation on radar, it was difficult to find the exact location of the front. We are carrying the surface analysis a little farther, as far as the total rainfall was concerned. When we consider the total for the whole day, we do find regions with heavier precipitations where these preferred tracks had been, although such regions are not sharply defined. We also found a region of heavier rain down in Connecticut. The complete analysis is still in progress. The point I want to bring out primarily was the space and time scales in- volved—the sizes of the rain areas, the sizes of the showers, how often they recur—so we can de- cide whether, on whatever scale we happen to be working, we are considering a turbulent effect or organized circulation on this scale. The complete analysis is still being carried out. Plume Formation in Thunderstorms Water HitscHFELD McGill University, Montreal, Canada Abstract—Radar data displayed in the form of precipitation maps at constant alti- tude above ground (CAPPI) portray the structure of storms and their anvils in telling manner. Well-developed storms, even in the presence of severe wind shear, were ob- served to remain essentially vertical through their active phase. Instead of being strongly bent by the shear, parts of the storm appeared to be carried off by the wind, forming extensive plume patterns or anvils which trailed down to levels as low as 10,000 ft while evaporating. Size and shape of the plume suggested that its particles had fall speeds ranging from 0.75 to about 5 m sec”, and thus were of precipitation size. Introduction—This paper is concerned with the motion of thunderstorms and their erosion in strong wind shears, as portrayed primarily by CAPPI-processed radar data. As will become apparent, the interpretation of the patterns, without the CAPPI (constant-altitude plan-po- sition indication) accessory to a powerful AN/ CPS-9 radar would have been more difficult or impossible. (Radar wavelength was 3.2 em, peak power 250 kw, pulse duration 5 microseconds, PRF (pulse repetition frequency) 200 sec. The radar is located at Montreal Airport.) A few words will suffice to explain how these constant- level records were obtained. In our procedure, the radar was used as a plan-position indicator, but with its angle of elevation being raised after every revolution in 1-degree steps up to 12°, and in 2- degree steps thereafter to 20°. The complete cycle took 3.6 min, and resulted in 17 photographic frames from which CAPPI displays were synthe- sized by an optical-mechanical technique [ Langle- ben and Gaherty, 1957]. Sets of such records for heights 5, 10, 15,...up to 40 kft (kft = 1000 ft) above ground were built up every 3.6 min, thus providing horizontal slices at these nine heights through all the showers within range. (Improved CAPPI records are now built up directly on the radar screen; in the future it will be possible to generate these displays on an electrical or mag- netic store.) Figure 1 shows in vertical section how the 5, 15, 25, and 35-kft constant-altitude displays are pieced together from successive PPI beams. It may be noted that a CAPPI picture, centered at say 15 kft, really represents a layer which extends in the mean through 15 + 0.75 kft at range 18 mi, and through 15 + 3 kft at range 75 mi. The ranges 18 and 75 mi were mini- mum and maximum for the records to be dis- cussed. 94 On July 1, 1956, a series of isolated well-de- veloped air-mass thunderstorms swept over the area. Figure 2 shows a small selection of the CAPPI record. In the evening these storms gave way to wide-spread heavy rain, ahead of a cold front which passed Montreal at about midnight HEIGHT (KFT) RANGE (miles) Fic. 1—Lines of constant altitude (dashed), corrected for Earth curvature and normal refrac- tion, are plotted against range; while the antenna scans in azimuth continuously, its elevation angle increases progressively; annular segments are selected from photographs of the PPI display at elevations one or two degrees apart to make up the constant-altitude pictures; the sketch shows the segments of which CAPPI pictures at 5, 15, 25, and 35 kft are composed, in vertical section (five-fold vertical exaggeration) EST. The first of the showers, already well de- veloped, was detected to the NW at 14h45m and decayed while still in view at 16h30m. Five sub- sequent showers were picked up at earlier stages of their development, and each could be followed for more than two hours before decay. Their life histories all followed the same pattern: within about 40 min of detection the echoes reached their greatest vertical extent (in excess of 40 kft), then gradually subsided, and during siaquinu yor|q Aq pepoo ark saunyd sitey} puB stwI04s [RIaAeS STU ey ‘aingord Atos jo osut doy UO SLIQUINU . Joos JO SpUBSNOY} UL S}Ystoy aPBOTPUL UUINTOD Jyoy UT STOQGUINU IPIYM - QOCHT al Ayne 10f SplO901 Tq Vi) JO UOlpo9]as V TORM NDERS =) i ae = Z HH ATION FORM E ut PLUM fo) for) Heights © 40kft O35 o e 2 e o,@ 25 @ s x15 1535 1610 1642 05 ——— 25 MILES Fic. 3—Positions of the ‘centers of gravity’ of horizontal sections through Storm 2 at five heights and four instants the last 30 min only weak and diffuse echo resi- dues were detected at heights up to 20 kft. These diffuse echoes, in all cases, could be traced back to high-level echo extensions for which we used the name ‘plumes, for their orientation and development were apparently governed (like that of a smoke plume from the stack of a ship) by the motion of the source and the ambient winds. The intense cores of the echoes, the regions in which the convection occurred and where the precipitation presumably formed, had irregular cross sections of maximum horizontal extents 18 mi at 10 kft, 15 mi at 30 kft and narrowing to less than 6 mi at 40 kft. A striking feature was the uprightness of all the storms in the face of a very strong wind shear. Except for the plumes, the radar echoes did not seem to bend with the wind, and their sections at all heights moved with the same velocity, about 45 mph, due east (from bearings ranging from 265 to 275°). Fig- ure 3 shows sketches made for one of the thun- derstorms over a period of 90 minutes. The relative movement of the centers of the storm sections at various heights is seen to be small and random, and is probably not much greater than the margin of error of the measurements. The wind hodograph is shown in Figure 4. Also shown in this figure is the echo velocity, which agrees in direction with the winds blowing at close to 4 kft and again between 8 and 9 kft; the measured winds are, however, several miles per hour slower than the echo speed. The upper of the two mentioned levels is close to 700 mb, and is representative of a height which has been called the ‘steering level’ of thunderstorms echoes [Ligda, 1953]. The ability of the thunderstorm to maintain itself upright in the face of the severe wind shear WALTER HITSCHFELD is remarkable. The relative wind from 22 to 28 kft was about 30 mph, and between 29 and 40 kft ranged from 40 mph to a maximum of 110 mph at 35 kft! The only apparent effect of the wind-shear was the development of the plume. In our records, plumes started at about 35 kft, and gradually worked their way downwards, eventually dissipating somewhere below 10 kft. (Only in one ease did the plume reach the 5 kft level.) The motion and growth of the plumes ob- served were consistent with the following mecha- nism: at heights at which the velocity of the wind relative to the shower is great, cloud and precipitation laden air was swept out of the storm, probably from its periphery, and carried off horizontally. Gradually, the particles in this air fell into lower layers, always adapting them- selves to the prevailing wind pattern. They thus trailed down through the atmosphere, in a man- ner which was characteristic of their fall speeds and of the wind pattern; the general motion of the plume was equal to the motion of the region where the particles were released into the wind. Comparison of the observed plume pattern with that anticipated on the basis of the wind pattern, allowed estimates of the particle fall speed (and so to some extent of their nature), and helped in pin-pointing the height at which the plume 270° n 1 "Sy 10O0mph 90° Wind ot 30kft relative to echo JULY |, 1956 MANIWAK| WINDS ALOFT O° | 100mph N Fra. 4—Hodograph of the winds on July 1, 1956, up to 40 kft; the average echo velocity (45 mph, from 270°) is also shown; the wind information is based chiefly on the 1000 EST Maniwaki sound- ings, but is supplemented in the light of soundings elsewhere PLUME FORMATION IN THUNDERSTORMS 97 formed. Such a comparison is attempted in the subsequent sections. Derivation of plume patterns from the winds —The trail followed by particles of given fall speed continuously released into the atmosphere can conveniently be constructed by the simple graphical method developed by Douglas, Gunn, and Marshall [1957] for the derivation of the pattern formed by snow trails from generating cells. Figure 5a shows such a trail, derived from the wind hodograph of Figure 4. Each straight- line segment represents the pattern swept out by particles falling through successive 1000-ft layers. The lengths and directions of these segments of the trail are calculated according to AS = (W — W,.)AZ/v Here W is the wind representative of the layer, and W, is the wind of the point of origin of the particles (the wind at 35 kft in this example) ; AZ, the thickness of the layer, was taken to be 1000 ft, and v represents the fall speeds of the echo velocity: 45mph particles in that layer. A proportional variation in the fall speed at all heights leaves the shape of the trail unchanged, but affects the scale. For v = 1 ft sec‘, the over-all length of the trail as pictured here (from its origin at 35 kft to the point where it reaches 10 kft) is in excess of 200 mi. For v = 2, or 4 ft sec”, this length would be just over 100 or 50 mi respectively. The time corresponding to each segment is 1000 see (16.7 min) for 1-ft sec” particles, and 500, and 250 sec respectively for particles falling twice and four times as fast. The trail pattern as a whole must be imagined to move eastwards at 45 mph (the velocity of its origin) so that as long as the parent storm is robbed of material at 35 kft, the trail will appear to remain in contact with the storm echo. The pattern of a trail originating at any level below 35 kft, say at 30 kft, is given by the part of the trail below the point marked 30 kft. The length and direction of plumes at given heights (as they might appear on ideal CAPPI AY Np ve2ft sec-! ee AS \ N Plume ot 3Okft \ \ x \ \ #t (from 35kft) NN NG NOS, vel, 25000 XN Plume ot 25kft \ (from 35kft) Zak \ \ ina echo velocity=45mph 30 XS « Nees 4 ! Plume at 25kft | (from cated / Ms Fie. 5—Derivation of plume patterns from the wind hodograph; (a) the trajectory of a particle de- scending at v = 1 ft sec”! from 35 kft through the wind field of Figure 4; trajectories of faster particles are identical, but scaled down in size proportional to 1/v; (b) heavy dashed line joining 35 and 30 kft rep- resents locus of positions of particles originating in storm at 35 kft, reached after descent to 30 kft; this line suggests the plume pattern at 30 kft formed by particles of fall speed 1 ft sec! and up (part of the plume pattern formed by the same particles at 25 kft is also shown); (c) dashed line here suggests plume at 25 kft formed by particles released at 30 kft 98 WALTER HITSCHFELD pictures) are illustrated by dashed lines. Con- sider the line joining the 35 and 30 kft points in Figure 5b. Its southern extremity would be formed by particles of fall speed v = 1 ft sec”, which would have traveled some 128 mi from their origin at 35 kft, requiring 5000 see (about 84 min) to do so. Particles of twice that fall speed would reach the 30 kft level at the point marked v = 2, about 64 mi from their origin at 35 kft. The northern end of this plume would be formed by particles of increasingly higher fall speeds. The times required by these particles to reach their positions in the plumes also depend on their fall speeds, and three values are indi- cated in the diagram. The plume appearing at a height of 25 kft, and also made up of particles originating in the storm at 35 kft is similarly represented by the dashed line joining the 35 and 25 kft points. If particles from the storm enter the wind field at 30 kft their trail would be as shown in Figure 5c (solid lines). At a height of 25 kft, such particles would give rise to a plume, oriented almost exactly north-south, as shown by the dashed line. Comparison with observations: particle fall speeds—Some of the plume observations are il- lustrated in the CAPPI photographs of Figure 2, and again in the schematic sketches of Figures 40 = \ Sa = Ne 1 l= Sos = £3: a as oe EST Co) —— er 40 a oo T fe) == 1 — 4ob eS me > ~, a OS. 1550 tf ve = = r \ ie) fo) 20 MILES 40 60 Fia. 6—Vertical sections along bearing 340° through Storm 1, showing the gradual decay of the core and development of the plume during one hour; plumes shown in dashed outline (two-fold vertical exaggeration) 6, 7, and 8. Figures 6 and 7 show vertical sec- tions through Storms 1 and 2 and their plumes. The directions of these sections were chosen along the 340°-160° plane to coincide approxi- mately with the longest extent of the plumes. In Figure 7 the progression of the pluming storm through the field of view of the radar is also indi- cated by horizontal sections through the radar patterns at a height of 5 kft. (Where these hori- zontal sections are dashed, they were taken through the plume at 10 kft.) Figure 8 shows the development of Plume 3 as it appeared at 25 kit. These observations are readily interpreted in terms of the preceding analysis. The predomi- nant direction of the plumes in Figure 8 is 835°— 155°, and so agrees exactly with that of the derived pattern shown in Figure 4, for particles originating at 35 kft. That this level is the prin- cipal source of particles is also borne out by an analysis of the rate of southward elongation of the plumes prior to 17hO8m. This rate can be shown to be a function only of the height inter- val through which the particles are falling and the wind pattern they encounter en route, and is independent of particle speed. The rate ob- served here, which is about one mile min”, fits 35 kft as an origin. (For an origin at 30 kft the rate would have been only 0.44 mile min™.) The apparent lengths of the plumes cannot be deter- mined with great accuracy, since the line of de- marcation of storm core and plume cannot easily be drawn. But at 16h57m, the plume at 25 kft is about 32 mi long, which by direct comparison with the plume derived in Figure 5b (length 160 mi for v = 1 ft sec’) would mean that the particles in the southern tip are falling at about 5 ft see*. At 17hOSm, the plume is about 37 mi long and this indicates that particles falling as slowly as 4.3 ft sec* have now reached the 25 kft level. By 17h20m the plume lengthened to its maximum dimension of 45 mi; minimum fall speeds are therefore 3.6 ft see*. One can check the times of departure of these particles from the 35-kft level, and find that they all agree reasonably well, being between 16h15m and 16h30m. The first sign of a plume at that level appeared on the radar records at about 16h27m. The radar record of 17h47m is the last one showing an intense core at 35 kft. This probably was therefore the last instant at which particles entered the free atmosphere at that level. From this time on, the particles already in the trail continued to fall, but the northern end of the PLUME FORMATION IN THUNDERSTORMS 99 Fic. 7—Horizontal sections at 5 kft through Storm 2 indicate motion and development of core; below each sketch, shaded areas are vertical sec- tions, again along bearing 340°; outlines of plumes are shown dashed (2- fold vertical exaggeration); at about 17h00m, the storm core decayed, and the horizontal sections thereafter (shown dashed) were taken through the plume at height 10 kft plumes, which at any level was formed by the fastest particles, fell faster than the rest. For lack of replenishment, the northern end of the plume at any level should therefore have dis- appeared faster than the rest—in agreement with observation. It is tempting to estimate the fastest particle fall speeds associated with the northern tip of the contracting plume. For the times 18h00m, 18h14m, and 18h24m such esti- mates are 23, 13, and 11 ft sec” respectively, based on the plume contraction at these times. These estimates, though plausible, are not unique. Slower particles originating at levels lower than 35 kft could have accounted for the same observed pattern. Thus if the northern end of the plume consisted of particles falling at up to 10 ft sec* which had been released at about 30 kft, the retraction of the plume at 25 kft would also proceed at the observed rate of about 0.5 mile min™. The supposition that these lower levels also contributed is supported to some ex- tent by the change in direction of the plume, for a gradual clockwise rotation of the plumes was observed. All the plumes, those of Storms 2 and 4 even more notably than Plume 3, had their longest dimension in a N-S direction in their later phases. A glance at Figure 5c shows that such rotation is best accounted for by supposing that while plumes formed initially at 35 kft, in their later stages, more and more of the material in them derived from lower levels of the shower. There is no evidence in our records, however, of particles stemming from levels lower than 30 kft. Comparisons of the kind outlined were made for three of the plumes at several levels; the conclu- sions were essentially the same, and will now be summarized. The storms were tall precipitation clouds, which in the face of very strong relative winds 5 ° 25 MILES 50 a L \ N \ 7 \ RADAR ti ' CA TOAOY |. 1630 ® 1642 % NY oxy WAN vis 25kft Sections wy H (Storm 3) 1657 cS NY Ni ~ 1708 Me lees 1720 1734 100 ‘'8I4 1747 Fie. 8—Horizontal sections through Storm 3 at 25 kft, showing development of plume; storm core disappeared at about 18h 00m EST 100 WALTER HITSCHFELD above 29 kft showed little tendency to bend. Instead the winds succeeded in eroding these storms by sweeping material away from them. This erosion was most pronounced at 35 kft, the level of the strongest relative wind, but occurred also to a slight extent above that level, and grad- ually spread down towards 30 kft. The evidence is clear that the plumes detected by the radar consisted of particles whose fall speeds were in excess of 3.6 ft sec’, and are thus probably pre- cipitation, rather than cloud, particles. The 35- kft temperature was —50°C. At 30 kft, it was —37°C, and it therefore is unlikely that any liquid material was involved. Fall speeds of pre- cipitation particles vary with height of course. Douglas, Gunn, and Marshall [1957] used the re- lation Vv x 702% 0-4 where 7 is the viscosity and p the density of the surrounding air. On this basis the factors of Ta- ble 1 were derived. Using an average factor of 1.55 for the trajectory of the particles explicitly considered above would indicate fall speeds (cor- rected to 1000 mb and 0°C) ranging from 3.6/ 1.55 = 2.3 to 23/1.55 = 14.9 ft sec”, or in metric units from 0.75 to 4.9 m see”. Using Langleben’s [1954] measurements of the fall speeds of snow crystals, the lower speeds could be associated with dendrites of melted di- ameter about 0.8 mm; the fast speeds (around 4 m see") were too high for aggregates, and probably indicate frozen rain or small hail. Us- ing Weickmann’s [1955] compilation for hail par- ticles of specific gravity 0.8, the melted diameter TaBLe 1—Increase of terminal fall speeds of particles with height in the atmosphere Height Pressure Temp f = v/vo*® kft mp | Se 40 190 —58 1.9 35 240 —50 iS 30 300 =3i 1.5 25 | 375 —22 1.4 20 470 —138 1.3 15 | 570 —3 1.3 10 | 700 +6 1.2 5 840 15 ii surface 1000 20 1.0 ® The factor f = v/vo , where vo is the fall speed of the particle at 1000 mb and OC, is evaluated here for July 1, 1956, but its value is not very de- pendent on the particular air-mass stratification. would be about 5 mm; for graupel particles of specific gravity 0.2, the melted diameter might be as great as 1.2 em. It may be pointed out that scattered hail was reported at the ground, which (from its timing and location) was shown to come from the showers under study. (Hail at the ground is indicated by the arrows on the 5-kft pictures of Figure 2.) Newton [1960] has recently discussed the pres- sure field surrounding a storm moving in a wind field with vertical shear. Considering the storm as a rigid structure moving with the winds ap- propriate to its middle levels in a typical case, he finds ahead of the storm an excess pressure near its base, and a pressure deficit near its top. On this basis, Newton concludes that enhanced lifting, and so formation of new cloud, should take place at the leading edge of the storm. Con- versely, at the rear of the storm the pressure field is modified to lead to downdrafts and conse- quent cloud decay. These conclusions are not in agreement with the more common notion that the strongest activity is near the trailing edge of the storm. But cloud development near the leading edge and remaining separate from the rest of the storm could account for the plumes observed by us. For when this cloud reaches the layer of high winds, it would presumably be ecar- ried away from the storm in exactly the same way as the plumes described. On this model, the plume would not be the result of storm erosion, though erosion may well play an important part in maintaining the storm upright in severe wind shear. Such cloud moreover would surely com- pete severely with the main storm for the mois- ture supply which the storm draws in to an ap- preciable degree from its leading edge. Yet another interpretation of plumes was given by Imai [1957] who made observations by PPI as well as by RHI (vertical) radar sections. His beautiful records of bright-band forming in the falling plume allowed him to identify the plume particles as ice, origimating in the storm. On the basis of his somewhat sparser records he concluded however that the radar plume comes into being only after the decay of the convection, and that it consisted entirely of very small crys- tals. The only fall speed quoted is 40 em sec™. It is noteworthy that our observations and analysis do not require the existence of cloud par- ticles in the plume. Conceivably cloud is also swept out by the wind, but remains undetected PLUME FORMATION IN THUNDERSTORMS 101 of® (2000 — —— | 1gOmin — — 120 MILES Fic. 9—Derivation of plume pattern in the vertical, along bearing 340°; shaded area at left is a see- tion through a typical storm core; solid lines represent projections of particle trajectories in the 340° 160° plane (variation of fall speeds with temperature and pressure was taken into account); dashed lines are isochrones, drawn 15, 30, 60, --- min after the beginning of pluming; positions of trajectories and isochrones are shown relative to storm (two-fold vertical exaggeration) by the radar. At the other extreme, particles falling faster than those mentioned may also ex- ist in the shower at high level, and be moved by the wind, but would remain unidentified by the radar, since such particles would fall very close to, or within, the intense core of the storm itself. This point is among those borne out by Figure 9 which is a theoretical reconstruction of a plume in vertical section, the way the eye might see it. The lines sloping down to the right are the trajectories of particles of various fall speeds, all originating at 35 kft. The fall speeds are in meters per second, and are all corrected to stand- ard temperature and pressure. To the extent that the plume has texture, e.g. unevennesses or characteristic knobs or holes, it would give the appearance of developing relative to the mother storm, in the direction of these trajectories. The dashed lines are isochrones, and indicate size and extent of the plume after 15, 30, 60, and 90 min from the incidence of pluming. The earlier stages are in excellent agreement with observa- tion. The 90-min line would indicate a rather broader base to the plume than we observed, but it is at such later times, and in the altitudes be- tween 25 and 15 kft, that evaporation effects, neglected here, are especially important. Espe- cially noteworthy is the separation of the par- ticles in the plume according to their fall speeds. For the case of snow-generating cells and the ‘continuous’ precipitation resulting from them, such sorting of the particles was studied in detail by Gunn and Marshall [1955]. Acknowledgments—It is a pleasure to ac- knowledge the interest in this work of J. 8. Mar- shall, who as co-author of a method of analysing snow trails, suggested that a similar approach might work for plumes. J. L. Galloway con- tributed a carefully documented analysis of the synoptic weather pattern of the day referred to. Though his painstaking work has not been quoted explicitly, it is he who has provided confi- dence in the validity of the hodograph. This work was performed under Contract AF19(604)-2065 with the Geophysics Research Directorate of the Air Foree Cambridge Research Center. REFERENCES Dovctas, R. H., K. L.S. Gunn, ann J.S. MARSHALL, Pattern in the vertical of snow generation, J. Met., 14, 95-114, 1957. Gunn, kK. L. 8., anp J. S. Marsuaut, The effect of wind shear on falling precipitation, J. Met., 12, 339-349, 1955. Imat, I., Radar study of a dissipating thunder- storm, Papers in Meteorology and Geophysics, Met. Res. Inst., Tokyo, 8, 81-97, 1957. LANGLEBEN, M. P., The terminal velocity of snow- flakes, QM. J. R. Met. Soc., 80, 174-181, 1954. LANGLEBEN, M. P., anp W. D. Gauerty, An optical system for automatic synthesis of constant- altitude radar maps, McGill University Tech. Note MWT-3 under Contract No. AF19(122)- 217 with Air Force Cambridge Research Cen- ter, 1957. Liapa, M. G. H., The horizontal motion of small precipitation areas as observed by radar, Wea. Radar Res. Tech. Rep. 21, Mass. Inst. Tech., 1953. MarsHat., J. 8S. Precipitation trajectories and pat- terns, J. Met., 10, 25-29, 1953. Newton, C. W., Hydrodynamic interactions witb ambient wind field, as a factor in Cumulus de- velopment, Contribution, Ist Conference on Cumulus Convection, Wentworth, N.H., Mav 12-15, 1959. Also Morphology of thunderstorms and hailstorms as affected by vertical wind shear, this volume, pp. 339-347, 1960. WeIcKMANN, Hetmut, A nomogram for the calcu- lations of collision efficiencies, Artificial Stimu- lation of Rain, Pergamon Press 1957, 427 pp., 1955. DISCUSSION Discussion Dr. H. Dessens—Was this storm with or with- out hail? Dr. W. Hitschfeld—There was hail in the plume, but very little. Hail was observed on the ground, but it was small and insignificant. We do not get much hail in Montreal. Dr. E. Kessler—Do you think that the evapo- ration of parts of the plume, and therefore the cooling of the top of the layer immediately below and its destabilization might contribute to the observed structure in the base of the plume? Dr. Hitschfeld—Yes, indeed. In this connec- tion I might mention again the work of Imai in Japan, who had RHI pictures showing some mamatus at anvil base. Mr. C. E. Anderson—Your paper bears out some ideas that I have. I feel that by watching how a cloud dies, one can learn a lot about the dy- namics of the cloud, because the manner in which it dies gives a clue as to how it has lived. You showed that you had a continuous production of particles at 35,000 ft which sent down streamers with the wind for an hour. This we have noted also in anvils in the southwest, and we could only interpret this to mean there was some type of continuous updraft within the cloud producing the plume. Sometimes we noted new cloud devel- opment in the plume away from the core of the main cloud as it moved down stream a bit. Dr. Hitschfeld—At what height are your plumes? Mr. Anderson—These would vary, sometimes 25,000 ft, but usually higher. Dr. Hitschfeld—This, I think, is vital because as I am showing elsewhere (McGill University Report MW, July 29, 1959) if the plume is warm enough to be supercooled water, there is no reason why there should not be new generation of precipitation im it. But in the plumes I was emphasizing here, I know this was not the case because the temperatures were much, much too low. Dr. H. Weickmann—Do you have any indica- tions of differences of lifetimes between storms with strong wind shear and storms with little wind shear? Dr. Hitschfeld—No. Dr. Weickmann—I am asking because by car- rying away the anvil the high-level jet may alter the life history of the storm as determined by cloud physical processes. From the Byers- Braham thunderstorm model we know that the developing state is followed by the mature state and this by the dissipating state. The mature state is characterized by updrafts prevailing throughout the cloud, whereas the dissipating state is characterized by downdrafts throughout the cloud and by an increasing predominance of the ice phase in the cloud. Byers and Braham have pointed out a mechanism by which down- drafts form in the upper parts of the cloud. These downdrafts will counteract the bouyancy of the rising cloud air and may thus mark the beginning of the dissipating state. If these downdrafts are displaced away from the original cloud by the ac- tion of a strong wind shear, they may not initiate the dissipating state and the cloud may stay alive in the mature state. Dr. Hitschfeld—In spite of the fact that the system is being deprived of water all the time? Dr. Weickmann—Yes, because it is only de- prived of water which has spent already its en- ergy for the cloud, whereas new moisture can continuously be fed in at the base, depending on the depth of the moist layer, inflow velocity, and migration velocity of the storm. Mr. Jerome Namias—I would like to ask a question of you or the audience which has puz- zled some of us for 20 years. Over the southern plains of the United States in the summer we have a condition in which an upper-level anti-cyclone develops and moisture flows around it in the form of great moist tongues. In the Great Lakes area rain falls from the warm front, as this moisture is forced over colder air, and much thunderstorm activity takes place. In many of these cases there is a very strong vertical wind shear so that the southwest surface flow from the Bermuda high is overrun by northerly components. As a re- sult, these thunderstorms move southward in clusters. In earlier studies I showed (Bul. Amer. Met. Soc., 19, 1-14, 1938) that the moisture pumped up by these thunderstorms is carried by the wind and in some way sets off chains of thunderstorms that move in the fashion indi- cated. In the 1930’s we tried to explain this on the basis of radiational cooling from the cloud tops or perhaps lack of entrainment. Have you some new explanation to suggest; namely, a DISCUSSION 103 physical mechanism explaining how thunder- storms form and move in the manner I de- scribed. Dr. Hitschfeld—In the other study to which I have already referred, Report MW29, we at- tempt to re-interpret Dennis’ (J. Met. 11, 157- 162, 1954) observations of seeding trails as plumes. Such plumes can travel considerable dis- tances and thus can disseminate nuclei widely. It is possible that this might account for Mr. Namias observation that a favored direction of storm propagation 1s that of the high-level winds. The Structure of Minute Precipitation JOHANNES GRUNOW Deutscher Wetterdienst, Meteorological Observatory Hohenpeissenberg, Germany Abstract—Continuous measurements with a raindrop recorder over a period of four years were used to study the unknown range of diminutive and minute amounts of pre- cipitation. Nearly half of individual rainfalls belong to this class. Frequency distribu- tions of amount, droplet size, and intensity in logarithmic scales are presented. Introduction—The range of minute precipita- tion below 0.2 mm amount is still nearly un- known. With regard to climatological or hydro- logical applications this range is without interest. But in biological respects and above all in precipi- tation physics this range has a practical and the- oretical importance. The limiting value of 0.2 mm is used because such an amount of precipitation is necessary to wet the rain gage before the first drop is recovered out of the sampling pot. The measurement of minute precipitation is only pos- sible by continuous raindrop recordings as also suggested by Bowen and Davidson [1951] with a raindrop spectograph and, in intervals of some minutes, by Blanchard [1953, 1957] and Lamp [1958]. The Hohenpeissenberg device (Fig. 1) is of a similar principle: the raindrops fall through a2 10 = 20 em’ opening on a prepared paper band. An electric synchron-motor transports the band with a velocity of 2, 5, or 10 cm/min. After exposure the paper is dried by a resistance- wire heater below the table which guides the paper band. The role of paper has a length of 100 m, ample for a continuous record of 3Y% days. Spot records of raindrops impart an in- structive insight into the structure of rain, both droplet size, intensity, duration, and amount. It is laborious to measure many thousands of spot-diameters but there is no other way to this day to record all these characteristics simulta- neously. For the range of minute precipitation it seems to be the only method. The evaluations related to this range cannot be measured with the normal methods of precipitation-measure- ment. Frequency distribution of precipitation amounts—Comparing the records of a normal rain recorder with the raindrop recorder more than 40% of each single rainfall was not meas- ured by the usual method. In addition to the frequency distribution of the amount of pre- 104 cipitation derived by the records of a Hellmann recorder, the spectrum is extended in the range of diminutive and minute amounts the maxi- mum of which is reduced to an amount of 0.03 to 0.04 mm (Fig. 2). The dotted lines take the wetting and evaporating effect within the rain gage into account. The presentation of this fre- quency distribution is only possible by using a logarithmic scale of the frequency ranges as sug- gested for meteorological, particularly precipita- tion, analyses by Guss [1955], Schneider-Carius [1957] and Hssenwanger [1960]. The frequency distribution is made up by part collectives the exact analysis of which would be possible with the procedure of Hssenwanger {1954, 1957]. The part collective of Class 7 (1.6-2.5 mm) for instance is found on the thun- derstorm showers in May and June. The insta- bility in August favors the part collective of the range of 0.3-0.6 mm. The assumption that the minute precipitation amounts are originated only by drizzle or fine rain is not right. The most evi- dent part collective of 0.03 mm results from in- stability showers in June, July, and August, while there are scarcely months of transition in this class. There are drop-showers coming out of con- vection cloudiness, but also the fringe areas of more heavy showers at nearby localities. Duration—The duration of precipitation (Fig. 3) ascertained with a normal precipitation re- corder is found with the frequency maximum at 50 to 200 min, those ascertained with raindrop recorder at 3 to 30 min. Therefore the frequency maximum of duration for all single rainfalls shifts to the range of 40-76 min. The relatively high quota of minute precipitation with a longer dura- tion originates in certain weather situations: on the edge of a high pressure area, where air masses of different characteristics are adjoining, stabilizing weather in the rear of a depression and drizzle within moist-warm air together with a shght upslope circulation along the Alps. THE STRUCTURE OF MINUTE PRECIPITATION 105 z V Zeitmorke {min \ Strepler @z or O : = f H “N “ + vorrat Aufapulen Synchron- Uhr Terminwerte Hohergeissenberg , Mai Nov. 1954 - 1955 mit Auagleich des Bonetzungaseffertes durch Tropfenregistrie- rungen belegt Fie. 2—Percentual frequency distribution of precipitation-amounts; the hatched range is veri- fied by raindrop records 3a|sle[7]ej\o | Pa 8 Niederschlagsdauer Prozentuale Haufigkeit Hohenpeissenbarg 1954/55 und 1957/58 sem. nach Registr Hellmann 2-e-- kileinste Ndschlage c alle Niederschlage davon durch Tropfen- registrierung belegt Haufigkeit 1060 2050 3920 7650 Stufenwerta der Dauer in min Fic. 3—Relative frequency of duration of precipitation; (a) normal precipitation recorder; (b) rain- drop recorder; (c) all precipitation amounts; and (d) part of all amounts derived from raindrop records 106 JOHANNES GRUNOW Tropfendurchmesser (mm) 1A 1.5 1.6 1.7 1.8 Prozentuale Haufigkeit Hohenpeissenberg , 1957/58 | AN re) a © ~ a ) = = 3) 9) © t © t © © nN - - Sgr te Ro oe tS os no Of Sine es ie) ° ie) {e) ° fe) a = Ww n 0 o st fe) Tropfenvolumen (mm?) Fic. 4—Drop sizes of minute precipitation derived from raindrop records MW vi Vil x y Prozentuale Haufigkeit Hohenpeissenberg , 1957- 58 x! XII 70 fe.) fo) 0.0003 0.0039 0.006 0-010 0.016 0.025 0.040 0.065 0.103 0.167 O 267 0.426 oO 681 t (mm/min) ow Stufenwerte der intensit 0 90010 0.00017 Fic. 5—Rainfall intensity, derived from normal precipitation records i] ! 13 —— 8 ——7 13 —— 10; -—— 20 IV Vv 7 Vil vin H } * =7 Jae 4 ly x Prozentuale Haufigkeit x! Hohenpeissenberg , 1957 - 58 Xil — 17— 13 — 18 = () (a) wo v fe) o wo Oo oO nt KR o rr fo) fe) QF ~ Ee rs ey. Sk Se we Onno i 2 looks OF Sao om Om 19 SROR Os Fo. oO OL Opi Oa ate Pe CR ope Oem On eo mum Ou OF Vo iG OmrGu > ro Om Oesoge Ono |e ie) Oo ORG (oy) [@) fe) Stufenwerte der Intensitat (mm / min) Fie. 6—Rainfall intensity of minute precipitation, derived from raindrop records Niederschlagsdauer / Intensitat Alle Niederschlage 1 (einschl. Tropfenregistr. ) Hohenpeissenberg , 1954 - 58 ! Zahlen Anzahl der Falle fe ¢ § 287 N 8 SUN 3) 2) N 146 ' i] cS 71, a 2 76 : 7 ° 5 1 3 45 E 39 l : A 3 20 & =} = Ww Si oO wT ww a mM OW (oO wm sq rm mM ft OF mM OF OR = ete C2) ing nO) — uN Manisha) FLOUR INS Gui Og | cag ities. OR ORM ORM OM NOM oeto eo | (Ol ONO OU Mo Sa EOL So ORO OOM OL Vo 1 Ol Os (ONE Ol GS OF OmEo Shc) TOMLoMO(e 2 1679S 1G S On sO) 10), 10 Stufenwerte der Intensitat (mm / min) Fic. 7—Relationship between duration (ordinate) and intensity (abscissa) of precipitation, demon- strated by isolines of equal frequency; all amounts of precipitation, derived from normal precipita- tion records 107 Kleinste Niederschlage Daver der Stufenwerte 0.00010 0.00017 0.00023 000046 000077 0.00026 0.0021 00035 0.0058 0.0096 nach 0.016 JOHANNES GRUNOW Niederschlagsdauer / Intensitat Tropfenregistrierungen Hohenpeissenberg 1954 -58 der Falle hy Ro SN 6) 0.026 0.043 0119 0197 0.325 0.54 0.89 Stufenwerte der Intensitat (mm/min) Fig. 8—Relationship between duration (ordinate) andintensity (abscissa) of precipitation, demon- strated by isolines of equal frequency; minute amounts, derived from raindrop records Drop size—The drop sizes of minute precipita- tion (Fig. 4) lkewise demonstrate some part collectives in the curve of frequency-distribution : diameters below 0.5 mm, originating from drizzle; a more marked maximum between 0.6 and 0.9 mm originating from lability showers and a wide range from 1.0 to 2.0 mm diameter as effects of heavy showers near the station. The effect of wind shear, however, which spreads the various drops in the spectrum not only in the direction of motion of the source but also at right angles to it [Blanchard, 1957], will bring more drops of smaller size-ranges in this case. The dominat- ing range of 0.6-0.9 mm, evident in the summer months, therefore seems to shift to smaller ranges than is the case for precipitation of higher amounts. Intensity—The ranges of intensity shift in the same manner from higher values in case of the total collective (Fig. 5) to smaller values in case of minute precipitation (Fig. 6). The differences between the ranges of diminutive intensity and of higher ones are more conspicuous than be- tween other factors of the structure. The minute precipitation amounts in the summer months, however, demonstrate a secondary maximum in the range of 0.0010 to 0.0030 mm/min, originating from less abundant shower precipitation. The dependence of intensity on duration is shown on Figures 7 and 8 which illustrate clearly the ranges covered by the cases of minute pre- cipitation. They shift to smaller values of both, duration and intensity, the angle of inclination of the mean line of this relation decreases from 42° to 35°. These ranges seem to be of interest in re- spect to artificial stimulation of rain. Therefore further studies of selected cases ought to clear the generating conditions of this minute pre- cipitation. Conclusions—At the beginning of the paper attention was called to the laborious work in evaluating the raindrop recordings. To accom- plish that, the Observatory Hohenpeissenberg has designed two instruments for recording the structure of rain. The one records the duration of precipitation of any amount im minutes based on the dual principle: precipitation or no precipi- tation; the other records the intensity based on DISCUSSION the method of counting the drop flowing out of a sampling funnel each minute. I hope these means will bring further insight in the structure of precipitation, including that of more abun- dant precipitation such as showers and steady rain. REFERENCES Buancuarp, D. C., Raindrop size distribution in Hawaiian rains, J. Met., 10, 457-473, 1953. BiancHarD, D. C., Discussion of raindrop distribu- tions made during project shower, Hawaii, 1954, Artificial Stimulation of Rain. (Helmut Weick- mann and Waldo Smith, eds.) Proc., First Conf. on the Physics of Cloud and Precipitation Par- ticles, Pergamon Press, pp. 213-223, 1957. Bowen, E. G., anp K. A. Davipson, A raindrop spectograph, Q.J.R. Met. Soc., 77, 445-449, 1951, 109 Essenwancer, O., Neue Methode der Zerlegung von Hiufigkeitsverteilungen in Gauss’sche Nor- malkurven und ihre Anwendung in der Meteo- rologie, Ber. Deut. Wetterd., 1, no. 10, 11 pp., 1954. Esspenwancer, O., Tafeln zur Haufigkeitszerlegung mit, Anwendungsbeispielen, Ber. Deut. Wetterd., 5, no. 39, 13 pp., 1957. Essenwancer, O., Frequency distributions precipi- tation, this volume, pp. 271-279, 1960. russ, H., Uber die Bildung typischer Mittel- und Schwankungswerte in der Klimatologie, An. Met., 7, 126-133, 1955. Lamp, R., Das Tropfenspektrum in Niederschlagen und die Radar-Reflektivitit nach fremden und eigenen Messungen, Beitr. Phys. Atm., 30, 223- 245, 1958. Scuneiper-Carivs, K., Zur Frage der statistischen Behandlung von Niederschlagsbeobachtungen, Zs. Met., 9, 129-135, 193-202, 266-271, 1955. Discussion (Note: Discussion of this paper is combined with that following the next paper.) The Productiveness of Fog Precipitation in Relation to the Cloud Droplet Spectrum JOHANNES GRUNOW Deutscher Wetterdienst, Meteorological Observatory Hohenpeissenberg, Germany Abstract—On Mount Hohenpeissenberg in Upper Bavaria (975 m NN) the atmos- pheric offer of fog precipitation is measured by a cylindric net of wires of 0.1 mm diam- eter, for which a nearly constant relation of deposit amount to wind velocity is found. The amount of deposited fog precipitation depends on (1) locality and exposition of the gage, and (2) weather situation. The efficiency of polar cold air, characterized by dominating small diameters of cloud droplets from 2 to 15 u, is seanty. Increasing pro- ductiveness results, when maritime warm air masses from temperate or subtropical zones pass. The cloud droplet spectrum is then characterized by a broader range of 4 to 25 w diameter, with a maximum frequency from 8 to 14 uw. The deposits are heaviest with amounts of 2 to 3 mm/hr when persistent cloud decks form on the windward side of the Alps. The air masses have then often degenerated by continental influence. The droplet spectrum indicates a wide range from 5 to 60 » with a maximal frequent diame- ter of 12 to 18 uw. Introduction—Cloud air streaming against an obstacle precipitates a part of cloud droplets. The deposit on trees is known as fog drip or in freezing weather is visible as rime. In flat land the fog deposits are just sufficient for wetting needles and leafage. But in mountain regions, which rise at times into the cloud space, and in coastal mist belts, where moist-warm air passes from sea to land, considerable amounts of additional water by fog drip can be expected. Measuring method—The atmospheric poten- tial of fog precipitation can be comparably meas- ured with a specific fog gage as suggested by Tabata and coworkers [1953] for the research of sea fog on the coast of Hokkaido, Japan, and by the author [Grunow, 1952] for studying the pro- ductiveness of fog precipitation in mountain forests. Both types of fog collectors use the same principle, a system of wires. The Japanese pat- tern is that of a cylindrical wire screen; the Ger- man pattern that of a cylindrical wire net (Fig. 1). The effect of these gages is found in the theory of the dust filter derived by Albrecht. The amount M of deposit on cylinder, in case of the fog gages on each single wire, is given by M = FvWtC It depends on the diameter and length of the wires through the factor F’, velocity of wind v, water content of fog W, time of deposit t, and an efficiency factor C which is influenced by the diameter of the wire, the diameter of droplets, and the wind velocity. The most favorable re- Fic. 1—View of the Hohenpeissenberg fog- collector; the cylindrical wire-net is mounted on a normal rain gage 10 cm in diameter 110 PRODUCTIVENESS OF FOG PRECIPITATION 30 © | mM! g/mh Se} W= 0,20 g/m? J =20 0 20 111 6 8 lo v m/sec Fic. 2—Dependence of the amount of water deposit M’ on the wind- velocity v, for various wire diameters at a cloud-droplet diameter of 20 lation of fog droplet collection to possible amount in clouds is obtained when the diameter of the wire is a minimum. The condition of constant relation of deposit amount to wind velocity is nearly attained with wire-diameters of 0.1 mm (German pattern) and 0.12 mm (Japan pat- tern) (Fig. 2). Factors influencing the amount of deposit— The amount of deposited fog precipitation, aside from the efficiency of the wire system, depends on (1) the locality and exposure of the gage, and (2) the weather situation. The locality factor is specified by the height above sea-level, the con- tinentality (distance from sea), and the exposure to the fog-producing air currents, especially on windward slopes. These effects are demonstrated for several mountains of Germany in Figure 3 [Grunow, 1958]. The measurements on Table Mountain (Tfb) South Africa, very critically evaluated by Nagel [1956], showed rainfall of 1940 mm and additional fog precipitation amount of nearly 3300 mm in 1954. The fog precipitation was 170% of the rainfall. Increasing amounts of fog precipitation are dependent on the weather situation. It is not only the direction and velocity of the depositing air current, but also the origin of the operating air mass, which influences the production of fog precipitation. The heaviest deposits occur where maritime warm air-masses from temperate or Nebelzuschlag JOHANNES GRUNOW (n, Dreyling Nebelbereitschaft bel SW-W-NW-Winden 1000 ae 1200 1300 1400 m Seehéhe Fie. 3—Dependence of the excess of fog deposit on height above sea level and continentality 2 Suan one 718'S910 1520 30 4050 #* % 20 420 3747 110 12.10. e 10.55 A Fria. 4—Types of the cloud droplet spectrum in dependence on the origin of the depositing air mass subtropical zones are in action, if a zonal circula- tion is predominant. The deposits are moderate or scanty, if the air masses originate in polar or arctic zones. This variable affects the value of W, the water content, of our formula. Record of cloud-droplet spectrum—A relation- ship between the amount of deposit and the cloud-droplet spectrum was established using the record of the droplet spectrum of cloud air for different air masses. According to the method of Diem [1947] cloud droplets were collected be- tween two oil layers of different viscosity, the PRODUCTIVENESS OF FOG PRECIPITATION upper being a thin film of paraffin oil placed above a base of heavier castor oil. The finding was immediately recorded by microphotography. The samples were taken under various fog situ- ations, without any consideration of the de- posited amount. Altogether 25 tests were evalu- ated, each consisted of an average of 12 samples with each several hundred or thousand droplets. Types of droplet spectrum—tThe derived fre- quency distributions of droplet diameters can 115 be classified according to the types of droplet spectrum, as seen in Figure 4. Each of these types presents obvious relations to the existing air mass and through it to the productiveness of fog pre- cipitation. Polar cold air is characterized by dominating small diameters (Types a and b), in case of maritime origin, Type a with a range up to 10 to 12 » and a remarkable part of diame- ters smaller than 2 »; in case of continental origin Type b from 2 to 15 w with a maximum number Fic. 5—Microphotographic record of cloud droplets from polar cold air; small amount of fog precipitation 114 JOHANNES GRUNOW Fria. 6—Microphotographiec record of cloud droplets from degenerated maritime subtropic air mass; heavy amount of fog precipitation PRODUCTIVENESS OF FOG PRECIPITATION at 8 to 9 ». The efficiency of fog precipitation is scanty. Types e¢ and d are maritime warm air masses from moderate (Type ¢) or subtropical (Type d) zones. The droplet spectrum then indi- cates a broader range of 4 to 25 » and a most fre- quent diameter of 8 to 14 1. Fog precipitation be- comes more and more productive. The deposits are heaviest with amounts of 2 to 8 mm/h in case of non-raining cloud decks formed on the wind- ward side of the Alps. The air masses are often degenerated by continental influences and the droplet spectrum indicates a wide range from 5 to 60 » with a maximum number at 12 to 18 p. This result conforms with investigations of Mahrous [1954], who established the increase of droplet sizes as typical evidence of degeneration in the dense coastal fog in England. In the case of a narrow spectrum with smaller diameters of droplets a meridional circulation exists whereas the broad spectrum predominantly shows up with zonal circulation. Selected cases of these two types are demonstrated, with the microphoto- graphic records of droplets in Figures 5 and 6. Water content of samples—The different pro- ductiveness of these types of fog precipitation classified according to the droplet spectrum is easy to understand if the water content of each sample is caleulated from the product n-7/6-D*. With increasing droplet diameter D the water 115 content grows rapidly even if the concentration n of these droplets is small. Integrated over the whole spectrum, the results for the samples are: Type a, bie, di se Total water content* 3 23 76 105 473 * Unit is 10° mm’. Even this rough estimate indicates that the pro- ductiveness of fog deposit in case of a broad spec- trum is a direct consequence of the microphysi- cal structure of the clouds. REFERENCES Dirm, M., Messungen der Grésse von Wolkenele- menten, Met. Rdsch., 1, 261-273, 1947. Grunow, J., Nebelniederschlag: Bedeutung und Erfassung einer Zusatzkomponente des Nieder- schlags, Ber. Deut. Wetterd. US-Zone, 7, no. 42, 30-34, 1952. Grunow, J., Vergleichende Messungen des Nebel- niederschlags, Assn. Int. Hydrol. Sci.. IUGG, Publ. 44 Gen. Assembly, Toronto, II, 485-501, 1958. Manrovs, M. A., Drop sizes in sea mists, Q. J. R. Met. Soc., 80, 99-101, 1954. Nace, J. F., Fog precipitation on Table Mountain, Q. J. R. Met. Soc., 82, 452-460, 1956. Tapata, T., T. Huztoxa, anp N. Matsumura, On a recording fog meter, Studies on fogs in relation to fog-preventing forest (T. Hori, ed.), Tanne Trading Co., Sapporo, pp. 169-173, 1953. Discussion (Relating to the two immediately preceding papers) Dr. C. E. Junge—Figure 3 of the paper just presented showed the increase of precipitation. This was the total increase plotted against area where there is no fog precipitation, is that right? You had figures of 200 to 300%. Dr. J. Grunow—The figures represent only the additional fog precipitation amount deposited on the wire net of the gage at different mountain stations, without any consideration of rain or snow. Dr. Junge—#. Eriksson, for instance, found that in Scandinavia the total amount of sea salt which is deposited from the atmosphere is approximately three times higher than can be accounted for by precipitation. The mountains in this area are often within clouds and the in- crease of precipitation by fog drip may be con- siderable and may explain the increase in sea salt deposit. Dr. Grunow—At some places in higher alti- tudes, for instance, on the mountain station Wasserkuppe we have found the same result. The most interesting point where measurements were made with this type of gage, is Table Moun- tain in South Africa. In January 1955 the ad- ditional fog precipitation was tenfold the rain precipitation. In the annual average the unit with fog gage received four to fivefold the catch of the rain gage. According to the very critical evaluations of Nagel there was an assured excess of 1.7 fold of rain, derived only from days with fog without drizzle or rain. The best conditions for deposit are given if fresh maritime air masses are in action. Dr. Junge—One more question: These 200 to 300% resulted from measurements with the 116 wire screen. Did you make any estimates of how much the precipitation is increased by fog drip in a normal forest in a location similar to yours? Dr. Grunow—In order to test the effective deposit on natural obstacles we have made meas- urements with a normal rain gage and with tubs under trees which acted as a natural fog meter, and in an open area with the fog gage, all at the same time. In case of fog without rain we found a reduction factor of 0.5 to 0.8 within the forests and of 3.2 on the edge of a forest. The reduction factors thus found depend on kind, form, and size of the trees and of the density of the woods. Therefore the reduction factor is only correct for the place at which these measurements are made. Dr. H. Weickmann—You had pine trees? Dr. Grunow—Yes. Dr. Weickmann—They would have a higher collection efficiency than trees with leaves. Dr. Grunow—The pine trees stand before our door. It is true, conifers have a higher efficiency than broad leafs, but more important is the situation of a forest in relation to the fog-bear- ing current of air. The highest amounts will be caught at the edge of the woods, but also within the forests a deposit of fog takes place. I re- member, too, the work of Hori in Japan. He has also found considerable amounts within a forest. Dr. W. E. Howell—With reference to your first paper, I recall that some time ago, C. K. Stidd (Cube-root-normal precipitation distribu- tions, Trans. Amer. Geophys. Union, 34, 31-35, 1953), when he was considering a possible repre- sentation of frequency distribution of rainfall amounts found zero, limited at dry stations for weekly or monthly rainfall amounts. Apparently there is a straight line relationship of the cube root of the fall amount broken down for very small amounts, and I presumed this was due to the fact that amounts less than one millimeter or at some stations less than one hundredth of an inch were not properly recorded. It occurs to me to wonder whether the measurement that you have made of the minute rainfall amounts would verify Stidd’s presumptions that the cube root relationship holds down to very close to the zero line. I think it might be of interest of investiga- tion. Dr. Grunow—Thank you for this reference. In our further investigations we will investigate this relationship. I think this range of minute pre- cipitation, although the monthly amount is not modified by this with regard to climatological DISCUSSION and hydrologic applications, is worthy of con- sideration with respect both for theoretical and practical purposes, especially for agricultural meteorology and for artificial stimulation of rain. Dr. B. J. Mason—When you are considering the collection efficiency of the fog catcher, do you regard this in terms of the collection efficiency of the individual wires? Dr. Grunow—Yes. Dr. Mason—When much fog is coming past the cylinder, do the pores, the spaces between the wires, become filled with water? Dr. Grunow—In winter with riming, yes, but in summer we have found that is not of sig- nificance. This can be deduced from the nearly linear relationship between the amount deposited and the velocity of the wind. Dr. Mason—Nagel in South Africa got rather unreasonable results because when he deduced the water content of the clouds from the collec- tion efficiency of the single wire and the velocity of the cloud air which had gone by, he was out by a factor of 5 to 10, I think. This may have been because the spaces in between the wires were be- ing filled. Then it is no longer possible to regard the cylinder as a number of individual wires. I would not say you should go so far as to regard it as a solid cylinder, but it may have approached that. Dr. Grunow—Nagel assumed a water content of approximately 1 g/m’, and this is a very high amount. The efficiency of a wire net cylinder is higher than that of a solid cylinder, because in the latter case, with increasing wind velocity, the current lines are more conducted around the profile. But the effect is less than the theoretical factor because some spaces will be closed by water. But, more important, the efficiency factor is nearly independent of wind velocity. We can observe the behavior of the cylinder in each weather situation because we have the instru- ments before our door, and we found that at low wind velocity there are no more spaces between the wires filled with water than at high velocity. However, measurements with our fog gage are proposed for determination not of the water con- tent of clouds but of the additional fog precipita- tion, deposited in the same manner as by natural hindrances, and for this purpose we can use any efficiency factor. Mr. Aldaz—At Mt. Washington Observatory we do some collection for the Atomic Energy Commission. We use a frame with no more than DISCUSSION twenty bars, very solid and rigid, with diameters of the order of three millimeters, and we collected enormous amounts of water which reach the order of a quart, on many occasions, in about two hours. The frame is about two feet by one foot. The fog on Mt. Washington is sometimes very thick. Dr. Weickmann—What we have just heard may have important applications to anyone who is interested in or in charge of conserving the water in regions where the mountains often reach into the base level of clouds. No trees should be cut from the tops of these mountains, because 117 these trees are important collectors of other- wise unprecipitated water. Dr. Bergeron—\ wonder if anybody of those present has visited that wonderful place on a small mountain in Portugal named Cintra*. It has a castle on top of it. On the top, which is small and isolated, one is in a tropical rain forest. One looks down on the desert toward Lisbon. Fog drip must be the explanation for its rich vegeta- tion. * Serra da Cintra, rugged mountain mass, north of Lisbon. Highest peak Cruz Alta (1772 ft); castle is Palacio da Pena—Ed. Horizontal Distribution of Snow Crystals during the Snowfall Uxicutro NAkAyA AND Ketst Hicucut Faculty of Science, Hokkaido University, Sapporo, Japan Abstract—Simultaneous observations of the shape of snow crystals were carried out at 14 points in an area of about 5200 km* in the Ishikari Plain, Hokkaido, in the period from January 20 to February 28, 1959. The horizontal distribution of snow crystals and its time sequence on four days; namely, January 20, January 30, February 10, and February 16 are analyzed in detail. From these results, it was confirmed that a depend- ence of shape of natural snow crystals on temperature in the upper atmosphere was in reasonable agreement with that of artificial snow crystals. On the other hand, it was found that the area where the same shape of snow crystals was observed might have some relation to the isothermal lines in the upper atmosphere. Introduction—In the recent researches on nat- ural snow crystals, the relationship between the shape of snow crystals and meteorological condi- tions was studied by many workers. It was con- firmed by Gold and Power [1954], Murai [1956], and Kuettner and Boucher [1958] that a de- pendence of shape of snow crystals on tempera- ture in the upper atmosphere was in reasonable agreement with that found in the laboratory by Nakaya [1954, p. 249]. On the other hand, Weick- mann [1957, pp. 239-241] observed the time se- quence of snow-crystal forms during continuous precipitation, and suggested that the snow crys- tals could be used as an aerological sonde. How- ever, there have been no studies on the horizontal distribution of snow crystals during a snowfall. The influence of the area where the same shape snow crystals are observed will be one of the im- portant problems in the research on precipita- tion systems. From this standpoint, simultane- ous observations of snow crystals were carried out at 14 points in an area of about 5200 km’. The results from these observations will be described in this paper. Observational procedures—Simultaneous ob- servations of the shape of snow crystals were car- ried out at 14 points in an area of about 5200 km? in the Ishikari Plain, Hokkaido, in January and February, 1959. A map of Hokkaido is shown in Figure 1, in which the observation area is indi- cated by a square surrounding Sapporo; the lo- cation of Hokkaido is shown in the upper left corner. The topographical map of the observation area is shown in Figure 2, where the observation points or stations are numbered 1, 2, ete. Station 2 is in Sapporo, where aerological data are ob- tained using Rawinsonde by the Sapporo Me- teorological Observatory at O9h OOm and 21th 00m JST (Japan Standard Time) every day. The observation of snow crystals was requested of the teachers of senior or junior high schools at stations noted above. The observations at Station 2 were made by the Sapporo Meteorological Ob- servatory, and those at Station 13 by the Iwami- zawa Weather Station. Since the observers had no experience in the observation of snow crystals, such methods as the use of microscope or replica or shadow photograph could not be employed. Therefore, observations were made with the naked eye or a magnifying glass. The shape of snow crystals was recorded by graphic symbols of the practical classification of Nakaya [1951, p. 311], in which the snow crystals were classified into the following eight classes: (1) plates O, (2) stellar crystals ¥, (3) columns O, (4) needles «, (5) spatial dendrites ©, (6) capped colums -, (7) irregular ‘crystals x), and (8) graupel X . The period of observation was 40 days from January 20 to February 28, 1959. The time of ob- servations was at 09h 30m, 10h 30m, 11h 30m, and 12h 30m, JST on each day that snowfall oe- curred. Since the aerological observation by Ra- winsonde at Sapporo is carried out at 09h 00m as noted above, such times of observation are reasonable for studying the relation between the shape of snow crystals and meteorological condi- tions. Besides the shape of snow crystals, it was re- quested that observers record the qualitative in- tensity of the snowfall and the occurrence of snow flakes. 118 HORIZONTAL DISTRIBUTION OF SNOW CRYSTALS ity) PACIFIC g OCEAN ep | 100KM mifewe Lu Fre. 1—Map of Hokkaido Results of observation—In the 40 days of the drites were observed widely and continuously period of observation, there were six days when snowfall was not observed at all observation points. On all other days, snowfall was observed at one or more of the stations. It can be said, therefore, that snowfall occurred in the observa- tion area almost every day in the period of ob- servation. Snowfall was observed at all stations on 4 days; namely, January 20 and 30, and Feb- ruary 10 and 16. The horizontal distribution of snow crystals and its time sequence observed in these four days will be described in the following. On January 20, the snowfall was associated with the continental monsoon system. Sea-level and 700-mb charts at 09h 00m are shown in Fig- ure 3. As seen in Fig. 3a, the snowfall area was the northern part of the Japan Sea Coast of Ja- pan. The amount of precipitation on this day was 1.7 mm at Sapporo and 3.4mm at Iwamizawa. The horizontal distribution of snow crystals at 09h 30m, 10h 30m, 11h 30m, and 12h 30m is shown in Figure 4. In these figures, the observed shapes of snow crystals are indicated by the graphic symbols of the practical classification. The graphic symbol shown at the observation point indicates the shape of snow crystal observed most frequently; the graphic symbols in paren- theses indicate those observed less frequently. In these figures, no graphic symbol is shown at some observation points. This does not mean, however, that snowfall did not occur at that place, but that the observation of snow crystals was not carried out. The open circle indicates that snowfall had stopped at the time of observation. As seen in these figures, the stellar crystals and spatial den- during the period of observation. Plates were ob- served in the southeast region indicated by P. At 09h 30m, needles were observed in the east region indicated by N. The sounding curve at O9h 00m is plotted in Figure 5. In the left part of this figure, the full line indicates the relative humidity with re- spect to water, and the dotted line indicates that with respect to ice. In the right part, the broken lines indicate the wet adiabatic lines. The wind aloft at 0.5 km intervals is shown at the left, where the long wing indicates 10 m/sec and the short one indicates 5 m/sec. These notations are also used in the figures that follow. From the C 10 KM 4 Fic. 2—Topographical map of the observational area firp } of e {CHITOSE } SURF ACE : 700 mb 0900 JST 0900 JST Jan.20,1959 Jan.20,1959 V Fig. 3—Sea level and 700-mb charts, 09h 00m, January 20, 1959 N N 12 1. 12 e e A® (HO) FB) Ms °% (km) i ° y ° 2 2 9 oF, ox@®) *k(®) 2 OK) “4 2@0) 0(@xko) 4 ox ox P 5 11 ° 5 “XO 0930 JST S 1030 JST 2 (®) Jan.20,959 oe | [Jan.20,1959 Se N "3 aa a 3 ees Fo® (KH) ae pw a a : 9 ok ~ e Ok) 7 2xBO) i x@® 14 *x Ay ee . Soo ere Jan.20,1959 SS Jan.20,1959 ae Fic. 4—Horizontal distribution of snow crystals from 09h 30m to 12h 30m, January 20, 1959 120 HORIZONTAL DISTRIBUTION OF SNOW CRYSTALS 500 600 121 500 N ° ° 600 1 1 ! 1 + 4 \ ao So fo} 700 PRESSURE (mb) 4 900 800 PRESSURE (mb) 1000 900 80 90 100 110 HUMIDITY (%) -20 -10 ce) TEMPERATURE (°c) Fic. 5—Sounding curve at Sapporo, 09h 00m, January 20, 1959 sounding data, the relation between the air tem- perature and the supersaturation with respect to ice was plotted on the Ta-s diagram [Nakaya, 1954, p. 249] from the study of artificial snow crystals, as shown in Figure 6. The broken line in this figure indicates a line giving the saturated vapor pressure with respect to supercooled water. On the basis of the experimental results with ar- tificial snow crystals, it will be expected from Figure 6 that column (capped column), plate, dendritic, and scroll crystals would occur in such atmosphere aloft as shown in Figure 5. This ex- pectation agrees quite well with the results of the actual observations as shown in Figure 4. The plates observed in the southeast region are con- sidered to form in the warmer layer of Region II, since the plates formed in the cold layer of Region II would develop into dendritic crystals in the layer of Region I. On the other hand, the needles observed at 09h 30m in the east region cannot be explained from the sounding data, and so it will be local snowfall. As seen in Figure 4, it is noteworthy that the southeast region where plate crystals were ob- served did not change position during the period from 10h 30m to 12h 30m. This suggests that the meteorological condition suitable for the forma- tion of snow crystals continues for several hours during a snowfall. On January 30, the snowfall was due to the up- glide motion associated with the warm front. Sea- level, 850-mb, and 700-mb charts at 09h 00m are shown in Figure 7. As seen in the sea-level chart, the rain area reached the southern end of 140 rr) ° Ss ° SUPERSATURATION WITH RESPECT TO ICE (%) to) =-§ -10 -15 TEMPERATURE (°c) =201 =25 SAPPORO, O9OOJST, Jan.20,1959 Fic. 6—T,-s diagram for the sounding at Sap- poro, 09h 00m, January 20, 1959; Region I, den- dritic; II, sector and plate; III, needle; IV, scroll or cup; V, irregular needle; VI, spatial plates; and VII, column Hokkaido, and snowfall occurred in the area northward from there. The amount of precipita- tion on this day was 28.5 mm at Sapporo, and 1.5 mm at Iwamizawa. The difference in the amount of precipitation between these two places can be explained as follows. The horizontal distribution of snow crystals at 850 mb 0900 JST Jan.30,1959 SURFACE | w WY 0900 JST Jan. 30,1959 EN so(KH) 0930 JST 8. 5.cK0) Jan.301959 N o is) 1 eee eo ew 2 OP (*) 3 en eo 11 Pyar ° aocK) ° (MBOnISil S600) ee: 1230 JST Been) Jan.301959 a | [Jan.301959 ——— Fic. 8—Horizontal distribution of snow crystals, 09h 30m to 12h 30m, January 30, 1959 122 HORIZONTAL DISTRIBUTION OF SNOW CRYSTALS 123 500 500 2 ee Ny ae ih X ay N 600} <9 a v a 600 i a m a j \ zs a \ t . — £ 700 a A Ss - 700 ~ Ww ie i NS ie = i Ne \ im w ' bX \, wn ! : N my & 800 ' <— | 800 & a 1 XN r 5 \ t | x 900 Sk | : 900 o- H | bse, 1000 : 1000 go 90 100 110 120 -20 -10 ) HUMIDITY (%) TEMPERATURE (°c) Fre. 9—Sounding curve at Sapporo, 09h 00m, January 30, 1959 09h 30m, 10h 30m, 11h 30m, and 12h 50m was as shown in Figure 8. As seen in these figures, the peculiar characteristic of this snowfall was that needle crystals were observed in the southern half of the observation area, indicated by N. On the other hand, snowfall was not observed in the northern half of the observation area, except that plates were observed at 09h 30m and 10h 30m at some stations. The sounding curve at 09h 00m is shown in Figure 9, and Ta-s diagram for the sounding data is shown in Figure 10. It will be expected from Figure 10 that column (capped column), plate, dendritic, scroll, and needle crystals would occur in such atmosphere aloft as shown in Figure 9. As seen in Figure 8, this expectation agrees with the result of observation in the southern half of the observation area. The predominance of the occurrence of needles can be explained from the existence of the deep layer warmer than —10°C where needles form, as seen in Figure 9. As indicated by N and § in Figure §, the area where needle and stellar crystals were observed is limited by an east-west line. This direction was not parallel to the direction of wind aloft, but parallel to the direction of the isothermal line in the upper air, as seen by the middle and right- hand charts of Figure 7. This seems to be a sug- gestive observation for further research on the system of snowfall. The reason why the snowfall in this case was limited to the southern half of the observation area cannot be explained now, but will be investigated in the further analysis. At 09h 30m and 12h 30m, the area where stel- 140 SUPERSATURATION WITH RESPECT TO ICE (%) -5 -10 =1/5 -20 =25) TEMPERATURE (°C) Fic. 10—T,-s diagram for the sounding at Sap- poro, 09h 00m, January 30, 1959 lar crystals were observed most frequently existed northeast of the area where needle crystals were predominant, as seen on the 09h 30m and 12h 30m charts of Figure 8. This situation may be ex- plained by the drifting of snow erystals by wind aloft. As seen in the left part of Figure 9, the direction of wind aloft was SE and SSE at the altitude from 1.0 to 2.5 km, where needles formed. Therefore, the needles are considered to have drifted to the NNW by the wind aloft. On the other hand, since the direction of wind aloft SURF ACE \ 700 mb 0900 JST 0900 JST Feb. 10,1959 Feb. 10,1959 5 ox eO(KO) 8 | e@®(KO) u eK (6) 9 2 9 (2) ex Ox ex® x@®) S@wa =f s0@) 80 14 $x *(®) ox * 8x@O) sk 80 2 X(O) $x 1030 JST Feb. 10,1959 0930 JST Feb. 10,1959 1230 JST. Feb.10,1959 Feb.101959 Fie. 12—Horizontal distribution of snow crystals, 09h 30m to 12h 30m, February 10, 1959 124 HORIZONTAL DISTRIBUTION OF SNOW CRYSTALS was SW at the altitude from 3.5 to 4.0 km where dendritic crystals formed, the dendritic crystals are considered to have drifted to the NE by the wind aloft. On account of such difference of the direction of drifting, it will be reasonable that the area of stellar crystals existed to the north- east of the area of needles. On February 10, the snowfall was due to the passage of the cold front. Sea-level and 700-mb charts at 09h 00m are shown in Figure 11. The snowfall area was the northern part of the Japan Sea coast of Japan. The amount of precipitation was 15.5 mm at Sapporo, and 1.7 mm at Iwami- zawa. The horizontal distribution of snow erystals at 09h 30m, 10h 380m, 11h 30m, and 12h 30m is shown in Figure 12. As seen in this, the character- istic of this snowfall was the transition from the state of predominance of stellar crystals at O9h 80m to that of needles at 12h 30m. The sounding curve at Sapporo at 09h 00m is shown in Figure 13, and Ta-s diagram for those sounding data 1s shown in Figure 14. It will be expected from Figure 14 that spatial plate (spa- tial dendrites), plate, dendritic, scroll, and needle crystals would occur in such atmosphere. This expectation agrees with the actual observation re- sults shown in Figure 12, excepting the occurrence of column crystals. The layer suitable for forma- tion of dendritic crystals was from the altitude of 2.5 to 2.8 km; this was in concordance with surface observation of clouds, reporting that there was Altostratus [Kuettner and Boucher, 1958] at 3 km at 09h 00m JST. The layer suitable for for- mation of needles was from the altitude of 0.9 to 1.3 km, which is im concordance with the data of surface observation, reporting that there was 500 500 600 O = —j 600 E é ~ 700 700 w w § 3 n 2) 7) wn & 0 & ee 800 80) er 900 900 1000 1000 80 90 100 110 120 HUMIDITY (%) -20 -10 te) TEMPERATURE (%) Fic. 13—Sounding curve at Sapporo, 09h 00m, February 10, 1959 140 130 120 110 SUPERSATURATION WITH RESPECT TO ICE (%) 100 95 =1'5 TEMPERATURE (°c) = 5 =O =20) =25 Fia. 14—T,-s diagram for the sounding at Sap- poro, 09h 00m, February 10, 1959 Fractonimbus at 0.9 km in the period from 09h 00m to 12h 00m. As indicated by N in Figure 12, the area where needles were observed expanded in the period from 09h 80m to 12h 50m. At 09h 30m, the stel- lar crystals were predominant, while needles were observed only at Station 2 (Sapporo). At 10h 80m, the area of needles moved westward, needle crystals being observed at Stations 8 and 13. At 11h 30m, the area of needles expanded in the longitudinal direction, while snowfall stopped in the areas other than this area. At 12h 30m, the area of needles expanded more than that at 11h 30m. The reason for this transition cannot yet be explained. It must be noted, however, that the ex- panding direction of the needle area was parallel to the direction of the isothermal line in the upper ar, as seen in the right-hand chart in Figure 11. This result was the same as that of January 30, and is very interesting. On February 16, the snowfall was due to the passage of the trough in the upper atmosphere. Sea-level and 700-mb charts at O9h 00m are shown in Figure 15. The snowfall area was in Hokkaido, and the rain area was over the north- 126 NAKAYA AND HIGUCHI SURF ACE og00 JST Feb.16,1959 12 eax(O *) eK@BioOX) ex Q(CO¥) 60x 200 (14) *3o(0*X) J 2 x0) 4 200 * X(OH0) 230 @ 00) 4 OK) Ok) en 0930 JST A 1030 JST Feb.16,1959 —— Feb. 16,1959 11 eB(OK) SOKO ox 1230 JST Feb. 16,1959 Feb.16,1959 Fie. 16—Horizontal distribution of snow crystals, 09h 30m to 12h 30m, February 16, 1959 HORIZONTAL DISTRIBUTION OF SNOW CRYSTALS 127 ern half of Japan. The amount of precipitation was 0.0 mm at Sapporo (Sta. 2), and 2.4 mm at Iwamizawa (Sta. 13). The horizontal distribution of snow crystals at 09h 30m, 10h 30m, 11h 30m, and 12h 30m is shown in Figure 16. The characteristic of this snowfall was that plate and column (capped col- umn) crystals were observed widely in the ob- servation area. The sounding curve at 09h 00m is shown in Figure 17, and Ta-s diagram for these sounding data is shown in Figure 18. It will be expected from Figure 18 that spatial plate, plate, and col- umn crystals would be the main shapes in this snowfall. Besides, dendritic erystals may form in Region I, but will not be so predominant, since the supersaturation with respect to ice was 110%, that is, nearly the critical value for transition from a plate to a dendritic form. These expecta- tions agree with the results of observations, as seen in Figure 16. The snow-crystal form recorded as irregular crystals by observers is considered to be spatial plate. From Figure 18, it may be con- sidered that column crystals formed in the warmer layer of Region VII, but that was not the case. Since the capped column was observed at some observation points, the column should form in a layer higher than a layer suitable for den- dritic or plate, that is, in a colder layer of Re- gion VII. However, no colder layer responsible for the generation of crystals of Region VII was observed by the sounding, as seen in Figure 18. This discrepancy must have been due to the hori- zontal difference of supersaturation in the upper layer. In this snowfall, the areas where the same shape of snow crystal was observed could not be 500 500 600 600 z @ = 700 700 ~ ¥ ¥ = =] 2) w u w w w & 800 800 & a a 900 900 1000 1000 ew 80 90 100 110 12 -20 -10 fo) HUMIDITY (%) TEMPERATURE (°c) Fic. 17—Sounding curve at Sapporo, 09h 00m, February 16, 1959 140 130 120 SUPERSATURATION WITH RESPECT TO ICE (%) 100 95: 25 = 5) =O p15) 1-20 TEMPERATURE (°c) Fre. 1S—T,-s diagram for the sounding at Sapporo, 09h 00m, February 16, 1959 decided, since the mixing of snow crystals was ob- served at many stations. Concluding remarks—Simultaneous observa- tions of the shape of snow erystals were carried out at 14 points in an area of about 5200 km* in the Ishikari Plain, Hokkaido. Though this inves- tigation was a preliminary one, it was found that areas where the same shape of snow crystals are to be observed can be detected by observations in an area as wide as in this case. However, a wider area of observation will be necessary for fully understanding the snowfall caused by the large-scale motion associated with frontal zones. Therefore, further observations in the winter of 1959-1960 will be carried out over a wider area, and by the use of more precise methods, such as plastic replica or shadow photograph. In conclusion, the authors express their hearty thanks to C. Magono for his criticism through this work. The authors are much indebted to A. Ichikawa for his kind assistance in carrying out this work, and to the Sapporo Meteorological Observatory, to the Iwamizawa Weather Station and to the Hokkaido Scientific Education Society for carrying out the observations of snow erys- tals. 128 DISCUSSION REFERENCES Gop, L. W., anp B. A. Powrr, Dependence of the forms of natural snow crystals on meteorolgical conditions, J. Met., 11, pp. 35-42, 1954. Murat, G., On the relation between natural snow crystal forms and the upper-air conditions, Low Temp. Science, ser. A, 15, 13-32, 1956, in Japan- ese, with English resume. Kuertner, J, P., anp R. J. Boucuer, A study of pre- cipitation systems by means of snow crystals, synoptic and radar analysis, Mount Washing- ton Observatory, 1958. Naxaya, U., Snow crystals, natural and artificial, Harvard University Press, 510 pp., 1954. Wercxmann, H. K., Physics of precipitation, Me- teorological Monographs, 3, no. 19, 226-255, 1957. Naxaya, U., The formation of ice crystals, Com- pendium of Meteorology, Amer. Met. Soc., pp. 209-220, 1951. Discussion Dr. Helmut Weickmann—How reliable are your humidity measurements? Dr. Nakaya—These measurements are made with a hygrometer developed by Dr. Kobayashi of the Central Meteorological Institute in Tokyo. He has a ten-year experience with such measure- ments and succeeded in developing an instrument which is superior to other hygrometers. Dr. B. J. Mason—If there is an isolated cloud with nothing above or below, any crystals which are collected come from just this layer. Then one can deduce its temperature and perhaps the hu- midity. I am doubtful of this deduction, if there Fra. 19—A three-layer cloud is a deep cloud system where there is a large tem- perature range. In England, I generally observe in 90% of the cases a mixture of crystals of all sorts which come from a deep cloud layer system, and everything is mixed up and it is impossible to make any useful observations. I should like to ask Dr. Nakaya if he agrees with this, and ask him if he belleves that one can only make this kind of an analysis when in fact, you have rather well defined thin cloud layers from which the crystals fall? Dr. Nakaya—That I expected. This is a very interesting and important problem. If the clouds had three layers (Fig. 19) A, B and C, and snow crystals come down in the vertical, we must ex- pect on the ground three types of snow; C, C plus B, C plus B plus A. If A is plate, B is dendritic, and C is needle, we can expect needle, dendrite with needles, plate with dendritic extensions with needles attached; something like that. But it was not thus. Sometimes we observed the combined type, but usually simple type of erystal corre- sponding to each layer of the clouds was observed. In this year’s observations we found that when the upper-air condition is layered A, B and C, the upper type A or the middle type B was observed on the ground. They appear to have escaped layer B or C. This is against our simple assump- tion of vertical fall, and we must develop the theory to explain this phenomenon. This is a fu- ture problem, but anyhow when we observe three or four kinds of crystal types on the ground we see that three or four corresponding layers are in the upper levels of atmosphere. The only ex- planation at present is that the atmosphere has a cellular structure or is in the turbulent condition and is not made up of horizontal strata. In this case a certain type of erystal can come down to the ground without passing through the stratum beneath. So this is a problem of the microstruc- ture of the atmosphere. Dr. Weickmann—(answering Dr. Mason) In fact, your observations of various kinds of snow crystals were interesting because it indicates that you have a deep and vigorous cloud system. If you observe only one type of crystal, the cloud system underneath the generating layer is not vigorous enough to produce its own crystals, it is just able to nourish the crystals which fall through, but in other more vigorous cloud sys- tems you may get the crystals initiated in several levels, and then you observe several types; and this seems to be the case in the systems you ob- served. Mr. L. Aldaz—During the winter of 1956- DISCUSSION 1957, on Mount Washington on the contract sponsored by Dr. Weickmann, we found as did Dr. Grunow and Dr. Nakaya, a very good corre- lation between the synoptic situation and the ice crystals. We made three kinds of analyses: (1) radar, (2) synoptic, and (3) ice-crystal analysis; the last I did myself. It is quite surprising how well one can determine the conditions aloft. Now, I would like to offer a word of caution. The main problem arises not from the mixture of ice crystals, but from the Nakaya diagram in which there is a duality of identical forms coming out on both sides of the diagram. In many oc- casions, for example, we have the occasion of hol- low needles or long columns which one does not know exactly where to place. The same thing hap- pens with plates; only with dendrites, there is no problem. Dr. Horace R. Byers—I notice in Dr. Nakaya’s data that the clouds seemed to be entirely below the 800 millibar surface; therefore, there are not great multiple layers involved. This is true also of the systems which produce snow on the exposed sides of the Great Lakes; therefore, you do not have there this multiplicity of crystal types. Augmenting what Dr. Weickmann said in re- gard to even those clouds which are very thick, it is my experience in observing them in Chicago or elsewhere, without lake or other special in- fluences, that one almost never gets a mixture of types. It is usually one type. The type may change during the course of a storm, but at any given instant there will be usually just one type. Dr. R. List—Regarding the comment of Mr. Aldaz, I can show you a dendrite that was found in a cloud with temperatures above about —4°C. It appears to have been grown at —15°C, but we know it was grown at temperatures higher than —4°C. Mr. Aldaz—How do you know? 129 Dr. List—Our institute is on the top of a moun- tain, and we can see the top of the clouds very well. Dr. C. L. Hosler—Two winters of observations of snow and activity in central Pennsylvania sel- dom got mixtures, and snowflakes were about 80% dendrites. We did not observe mixtures at all. Dr. C. J. Grunow—In the cases of February 10 and 16, the behavior of columns is in con- tradiction with the results found in your labo- ratory investigations. We found the same: the conditions of growth for columns must be some- what other than defined in the Nakaya diagram. Also the observations of Dr. Weickmann in natu- ral Cirrus clouds suggest the beginning of growth for columns at a lower temperature. Considering results of Kobayashi, it follows that not only the temperature and the state of saturation but also the ambient vapor density is an essential factor of growth. In the Kobayashi-diagram the column dominates in a range of little ambient vapor den- sity independently of any temperature ranges. Can the named doubtful cases in the behavior of columns be explained by this effect ? Dr. Nakaya—I admit that my diagram is now almost 20 years old and it must be revised by the advanced technique of experimentation in this field. Mr. Kobayashi is now working on this prob- lem in the Low Temperature Institute of our University. The problem exists not only in the point of the ambient conditions but also in the point of the definition or classification of the type of crystals. The columns are the most embarrass- ing type. Short needle, sheath type, column with thinner wall and the ordinary column belong to the same category; growing more in the direction of principal axis and less in the direction perpen- dicular to it. More detailed studies must be car- ried out for distinguishing one type of crystal from the other belonging to this same category. Snow Crystal Analysis as a Method of Indirect Aerology JOHANNES GRUNOW Deutscher Wetterdienst, Meteorological Observatory Hohenpeissenberg, Germany Abstract—Observations of form and size of snow crystals, whose conditions of growth are widely known from laboratory investigations, were compared with the synoptic situation. The qualitative analysis obtained by a general survey of all forms appearing at the same time imparts an insight to the structure of the atmospheric layers in their temporal and spatial succession. A quantitative analysis is developed to derive the thickness of layers and to reconstruct cross sections of temperature and state of satura- tion, based on rates of fall and rates of growth as known from laboratory investigations. The results show satisfying agreement with the cross sections derived from aerological soundings for layers up to —20°C. From measurement of numerous shadow photos, it was possible to derive frequency-sections and spectra of the distribution of sizes for some crystal forms that permit statements concerning the structure of the precipitating cloud system. From evaluation of water droplets attached to snow crystals, spectra of the diameters of droplets for different air masses were derived. Even simple observa- tions of snow crystals from different altitudes made by the visual method show char- acteristic differences of form and size of the crystals. Thus the suitability of the snow crystals as aerological sonde is confirmed by many single manipulations. Introduction—During the past decades the study of the ice-phase in the atmosphere has yielded important insights in fields of cloud phys- ics and in the formation and release of precipita- tion. With this knowledge, investigations of snow crystals on the ground, particularly on mountain stations, have proven to be useful as can be seen from the work of Weickmann [1957ab] on Mt. Hohenpeissenberg, Germany (located in the northern foreland of the Alps) and Kuettner and others [1956, 1958] on Mt. Washington, N. H. The form and size of snow crystals, whose condi- tions of growth have been widely known from nu- merous laboratory investigations, allow conclu- sions concerning the structure of the precipitation cloud system and upon the temperature and hu- midity within the upper air layers. In order to check these results under different climatie con- ditions and to complement the observations in the upper air layers with aerological measuring de- vices during the IGY, consecutive records of snow crystals by photographic methods, as shadow- macro- and microphotography, and by replica technique, were made on Mt. Hohenpeissenberg during the winter of 1957-1958 [Grunow and Huefner, 1959]. The conclusions drawn from the form analysis of snow crystals with respect to the state of the upper air layers were compared with the synoptic situation as determined by the data obtained by the usual sounding procedure. 130 Qualitative analysis—The manifold forms of snow crystals with their innumerable variants depend upon the atmospheric conditions, particu- larly upon temperature and state of saturation, that prevailed during their formation and along the path of fall. The ranges of temperature and humidity are demonstrated in the diagrams of Nakaya [1954], Aufm Kampe and others [1951], and Weickmann [1957a]. Nakaya chooses as or- dinate units of the relative humidity as a measure of the supersaturation with respect to ice, while Weickmann uses the vapor-pressure difference between water and ice saturation. Recent in- vestigations by Kobayashi [1957, 1958] on the habit of snow crystals artificially produced at low pressures show a relationship of the shape of crystals to the ambient vapor density. There- with the necessary conditions for the growth of each crystal type are known, namely, the ranges of temperature and the variation of humidity (state of supersaturation and ambient vapor pressure). It is possible to deduce from the suc- cessively grown parts of a snow particle that has fallen through the atmosphere, the conditions of the air layers during its passage. This statement about the structure of the atmospheric layers in their temporal and spatial succession we define as qualitative analysis. Such a qualitative analysis requires a general survey of all forms appearing at the same time, and their arrangement according to a detailed SNOW-CRYSTAL ANALY Temperature °C 1 -25 to -30°}30 to -55° -20 to -25°C x [S) & = i # -15 to Li kp Special forms 0700 0800 0900 §=1000 N0O 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 GMT Fria. 1—General survey of observed snow crystals according to Weickmann, showing distribution on March 21, 1958 (Operation 27), Hohenpeissenberg, Germany physical classification, which also includes their temporal variations. A method for such a repre- sentation was used by Weickmann [1957a]. An example for this method is given in Figure 1. Of the two columns of the ordinate the first contains typical forms that require only shght ice super- saturation for their growth. The second column, however, comprises forms whose growth occurs at or close to water saturation. The diagram shows two periods, where the precipitation clouds reached up into upper layers of the troposphere. A cloud layer with water saturation existed in the —15 to —20° C temperature range in agreement with the aerological cross section. During the forenoon such a layer existed also between —10 and —15° C discharging malformed plane crys- tals. Also the disappearance of the upper pre- cipitation clouds during the evening hours can be seen, Quantitative analysis—If the rate of fall and the rate of growth for each crystal type are also known, these facts in connection with the size of the grown erystal type allow calculation of the thickness of layers through which the particle fell and in which these conditions were met. With this supplementary statement the qualitative analysis is extended to a quantitative analysis. From the arrangement of these originating zones a cross section of the isotherms and isohumes can be constructed. For both quantities, the rate of fall and the rate of growth, Nakaya’s values were used. The rate of fall proves to be nearly constant for all dimensions of plane and spatial dendrites as well as of powder snow. For erystals with droplets and even more for needles and graupels the rate of fall increases with their size. The degree to which the rate of fall depends upon the density of air, is not known and cannot be considered. The great- est influence, however, should be exerted by the vertical air transport. But the appearance of up- ward currents is limited to certain weather situa- tions with a character of instability. For the com- putations here average values of the rate of fall 152 JOHANNES GRUNOW were used. In the rate of growth of different types of crystals (such as dendrites and needles) differ- ences exist because of variations of the vapor pressure along the path. Assuming a constant mean value for the rate of growth, as it was done here, the determination of the thickness of layers becomes somewhat doubtful, but is unavoidable. Losses of substance by evaporation in case the erystal passes through possibly existing dry lay- ers, however, can be seen by the degenerated shape of the crystal. Those particles remain un- considered. By picking out the largest of each type from among all crystals, with a sufficient to- tal number of the same, it can be assumed that the size thus found presents a characteristic meas- ure for the thickness of the layer within which the crystal originated. With the rate of fall V, the rate of growth W, and the size of the crystal AG, the thickness of layer H is thus calculated, AH = (V-AG/W) (m) After analysing the different snow crystals con- tained in the snow sample for each observation term according to this procedure, the ranges ob- tained for the temperature and the thickness of Fic. 2—Construction of a height cross section of temperature and humid- ity; March 20, 1958, O8h 34m GMT (Operation 26) SNOW-CRYSTAL ANALYSIS AS INDIRECT AEROLOGY 500 lise chase ueenteteb sb dcicdon ta te tea 0751 0825 0855 1000 1015 1100 1200 1215 1345 1445 GMT Fra. 3—Diagram of temperature ranges derived from snow crystal analysis as basis of a temperature- height cross section, March 21, 1958 (Operation 27); thickness of layers are in meters the layers are taken as basis for the construction of a height cross section. As starting-point it is necessary to have a reference value, for which the relation temperature to altitude is taken from other facts of observation, for instance, from ground observations. The construction is then carried out in two parts (Fig. 2): (1) The thickness of temperature ranges in meters is entered in an equidistant scale of tem- perature for each observation time (above left). If several different types of crystal appear in one observation, as it is the rule in most cases, the diagram of the stratification can be further se- cured by comparisons of the single-layer thick- nesses determined from different snow particles. Thus, uncertainties of using average values for the rate of growth in relation to the state of satu- ration can be partly eliminated. (2) The temperature scale, derived from the analysis of the different crystals, is entered in the diagram with equidistant scale of altitude (above right). This operation is done in several steps, as explained in detail m Fig. 2, below. The state- ments about humidity are added at the right of the altitude-scale. These values obtained for all observations of one operation were put in a row (Fig. 3). A cross sec- tion for temperature and humidity constructed by the snow crystal analysis as derived according to the procedure described here is shown in Fig- ures 4 and 5. A comparison between the results from the snow-crystal analysis with the aerological state measured by soundings indicates (1) the aecord- ance in the existence of layers of defined qualities, especially the state of saturation combined with a defined temperature range and the structure of precipitation clouds (qualitative analysis), and (2) the quality of a quantitative analysis, espe- cially the question whether in spite of some nec- essary simplifications with respect to the use of mean values for the rate of growth the results are suitable for a fairly exact calculation of the thick- ness of defined layers. The results are as follows: The growth conditions of a crystal form, known from laboratory investigations, allow con- clusions regarding the temperature range and the state of saturation of the atmospheric layers in which the erystal originated. The qualitative crystal analy from consecutive observations during snowfall shows excellent agreement be- tween crystal types and synoptic development. Quantitative analysis for deriving the thickness of layers and for reconstruction of cross sections, based on rates of fall and rates of growth, as measured in laboratory experiments, show satis- fying agreement with the cross sections derived from aerological soundings for Jayers up to the —20° C level. Determination of the stratification for the upper atmospheric layers becomes more and more uncertain, as the rate of growth for columns and the upper temperature boundary for their origin seem to be doubtful. As the agreement of the reconstructed analysis- sections with the values from aerological measure- ments is best near the time of sounding, it can be 5. -23 837 290% 92 JOHANNES GRUNOW HH KES KR OR ee OE 0 0 0000 0400 0800 00 0) © ; 9 0 O 05930000: 00 0090: 0: 1200 1600 2000 2400 GMT Fic. 4—Cross sections of temperature and humidity; above: derived from aerological soundings; below: derived from snow-crystal analysis, Hohen- peissenberg, March 20, 1958 (Operation 26) concluded, that the analysis of snow crystals pre- sents more details of the synoptic development than the aerological soundings that, because of their 12-hour intervals, often do not show these details. Frequency analysis—The analyses of shape and size of snow crystals were also correlated with special studies on their frequency of occurrence. Frequency analyses have manifold significance in problems of cloud physics. They present infor- mation in connection with the intensity of pre- cipitation and its dependence upon certain quali- ties, for instance, as carrier of atmospheric electric charges, radioactive fission products, and so on. They give also information as to the quan- tity of freezing nuclei contained in an air layer SNOW-CRYSTAL ANALYSIS AS INDIRECT AEROLOGY 0400 0800 135 =6::73 1600 2000 2400 GMT 0000 0400 0800 1200 1600 2000 2400 GMT Fic. 5—Cross sections of temperature and humidity; above: derived from aerological soundings; below: derived from snow-crystal analysis, Hohenpeissenberg, March 21, 1958 (Operation 27) of certain characteristics that did not form ice- crystals before coming into this layer. Crystals fallmg from a higher layer through the whole depth of a second layer may expect an approxi- mately equal increase of their rate of fall, and their rates of growth are nearly the same. The size spectrum of these crystals or their appen- dices, respectively, will show only a narrow fre- quency culmination. If these crystals were formed in the second layer, however, they would show quite different sizes. In this case the size spectrum will be broad. The frequency curve ought to in- dicate the form of a gaussian distribution. In the case of a broad spectrum several frequency-cul- 136 minations are to be expected that correspond to different part-collectives. Best qualified for the frequency analysis are the shadow-pictures, as they furnish a great num- ber of single individuals in each photo. Frequen- JOHANNES GRUNOW cies of individual crystals were put down in a table showing for each observation the share of each form in accordance with the International Snow Classification expressed in percentage (Fig. 6). The predomination of forms that originated BANNER Ss oe a Se, 1500 1600 1700 1800 1900 Explanation (International Classification) aS Spatial plates (irregular crystals) TC _sColumns, bullets & © Piates, sectors, broad branches =| Plates with dendrites Spatial dendrites Capped columns and bullets HE dendrites, stellare, dencrites with plates Unknown Forms Fie. 6—Frequency analysis of observed snow crystals derived from shadow pictures; percentages of observed crystal types according to the International Snow Classification; Hohenpeissenberg, March 21, 1958 Soee Sip ie BAEC SS5 NG NN SJ <4 G a= aa \U 7 0. 0700 oeo0 0300 1000 1100 1200 1300 BANNNS Byy> > Fra. 7—Percentage of frequency of dimensions of snow crystals; crystal group: plates, sectors, broad branches, Hohenpeissenberg, March 21, 1958 (Operation 27) SNOW-CRYSTAL ANALYSIS AS INDIRECT AEROLOGY at temperatures < —20° C coincides with the ap- pearance of high precipitation clouds that are verified by aerological soundings. The prevalent occurrence of supersaturation forms points to the predominating production of precipitation in lower, nearly water-saturated layers. From the alternating occurrence of certain forms the sink- ing or rising or a cell-like structure of the pre- cipitation clouds can be deduced. Thus this dia- gram is in conformity with the general survey according to the method of Weickmann. The variations of the size of certain crystal types with time is given in isolines of relative fre- 137 quency of the diameter. An example is given for the Operation 27 in the group of plates, sectors, and broad branches (Fig. 7). Frequency of the particular forms, the most frequent diam- eters, width of spectrum, and size of the maxi- mum of the spectral curve, respectively, do not run parallel to each other. A relation seems to be indicated, however, in such a manner that a small variety of forms of one type corresponds to a rela- tively narrow spectrum, that few appearing forms thus show nearly similar dimensions. On the other hand with a large percentage of one form the di- mensions vary a great deal. The size spectra can 607% = nna 56 mul HELA 52 ry TT 48 | | it eet ttt tity ete 40 id bul By +4 ies eee hed BY ea HH _|.] 2 Se a JI 28 ub 2% oo 1 | I 20 nad il a 1 tala leas n Cree | i manne a re TTT I TT oh 02 0a «605 07) 10 20 «30 50 7,0 H Ht TTT oH 204% 14 Ls ri aa 2 oan rt HH HY | CLL S RERIIMOIIIE son Pe an AE cea a + ett 12 | | te E + LL eH HA ITI ae ERIE LL }- 8 Li LH aa yi 02 03 05 07 10 20 3050 7.0 iT ae t | | 10 LN all CUT atl a TTT 10 ' oy Q2 03 05 07 10 2p «40 50 70 0 Fig. 8—Dimensions of single crystal forms; frequency of their occurrence expressed as percentage; Hohenpeissenberg, March 1958 138 JOHANNES GRUNOW 22 at 10 1,0 20 «39 50 70 ey Ww 2 30 » D 05 07 1p 20 59 70 10 Fie. 9—Dimensions of single crystal forms; frequency of their occurrence expressed as percentage; Hohenpeissenberg, March 1958 be narrow as well as broad, the probability curve more pointed or flatter, and the most frequent diameters smaller or larger. With that, also the frequency curve depends upon the momentary structure and the characteristic of the layers and thus presents another means for the indirect aero- logical analysis. Dimensions of crystals—Supplementary, the dimensions of all measured crystals of the same type were compiled as frequency curves, showing the dimensions of single crystal forms expressed as percentage (Fig. 8 and 9). These curves were not smoothed. Their form of a probability curve expresses that under given climatic conditions and altitude, dimensions can be expected that have characteristic sizes for the different types of crystals. Other material based on exact measure- ment of a sufficiently large number of individuals of erystals is only known for Sapporo, Japan, near the sea-level and, for only few forms, for Mt. Tokachi, 1060 m above sea level. The typical values found on Mt. Hohenpeissenberg, 1000 m above sea-level, mostly show smaller dimensions than the ones ascertained in Sapporo. The differ- ences are relatively small with those forms grow- ing in upper layers at a temperature of about below —20° C. But they are great for the forms SNOW-CRYSTAL ANALYSIS AS INDIRECT AEROLOGY 139 1956 Hohenpeissenberg 341 Observations Zugspitze 237 Observations 1957 Hohenpeissenberg 162 Observations Zugspitze 215 Observations Hohenpeissenberg 427 Observations Zugspitze 302 Observations Plates Stellar Columns Needles Spatial Capped Irregular Graupel Ice pellets Sectors Crystals Dendrits Columns Crystals Fra.10—Results of visual snow crystal observations; frequency of shape and size; simultaneous obser- vations Hohenpeissenberg (975 m) and Mt. Zugspitze (2962 m) 1956-1958 140 JOHANNES GRUNOW on =) a | | a | 5 10 15 20 Bb 30 = 50 55 3 20 45 60 Fia. 11—Percentage frequency distribution of diameters of cloud droplets attached to snow crystals, Hohenpeissenberg (dendrites, needles) that grow within the lower layers of the troposphere, their growth being fa- vored by the maritime climate of Hokkaido which has excessive humidity. Also the maximum size of dendritic forms found on Mt. Tokachi is 3.0 mm, still considerably higher than the value 1.8 mm of Mt. Hohenpeissenberg with nearly equal elevation but with a more continental cli- mate. Differences of the same kind were also found by simultaneous snow-erystal observations of Mt. Hohenpeissenberg and Mt. Zugspitze with the visual method according to the International Classification of Snow (Fig. 10). Three years of additional observations by the meteorological ob- servers of these stations have demonstrated the suitability of this scale discussed at the Confer- ence of Woods Hole in 1955. On Mt. Hohenpeis- senberg those types prevail by number and size that need only moderately low temperatures and nearly water saturation for their growth, for in- stance, stellar crystals, needles, and graupel. On Mt. Zugspitze those forms dominate that origi- nate in upper precipitation clouds, and at much lower temperatures, and are erystals of Class 7 (irregular crystals) which mostly prove to be spatial plates if viewed under the microscope. Thus even with application of simplest observa- tion methods the snow erystal as indirect aerolog- ical sonde is capable of furnishing valuable refer- ences. Dimension of cloud droplets—Finally a num- ber of microphotos of rimed crystals were used to measure the diameters of water droplets attached to snow crystals in order to obtain their size spec- trum. It was found that these derivations show parallels to former investigations, with which the abundance of fog precipitation was put in rela- tion to the spectrum of droplets of different air masses (Fig. 11). The individual frequency curves are composed of different part collectives, but the total number is not sufficient for their exact anal- ysis, for instance, by the procedure of Hssen- wanger [1954]. Arctic cold air is characterized by a narrow spectrum with small diameters, warm air and degenerated air masses by a broad spec- trum with larger diameters. Conclusions—The suitability of the snow crys- tal as aerological sonde is found confirmed by many single manipulations and it is expected that the further evaluation of this observation ma- SNOW-CRYSTAL ANALYSIS terial will still give more information on the physics of cloud. Acknowledgments—This_ research has sponsored in part by the Office, Chief of Research and Development, U. 8. Department of Army, through the European Office, under Contract No. DA-91-508S-EUC-286. An expanded version of this report is given in the Final Report to this contract, February 15, 1959. been REFERENCES Aura, Kampen, H. J., H. K. Wetckmann, Ano J. J. Katty, The influence of temperature on the shape of ice crystals growing at water saturation, J. Met., 8, 168-174, 1951. Essenwancer, O., Neue Methode der Zerlegung von Hiiufigkeitsverteilungen in Gauss’sche Nor- malkurven und ihre Anwendung in der Meteoro- logie, Ber. Deut. Wetterd., 1, no. 10, 11 pp., 1954. Grunow, J.. AND D. Hurrner, Observations and analysis of snow crystals for proving the suitabil- ity as aerological sonde, Contract No. DA-91-508- EUC-286, Final Report, 1959. Kosayasut, T., Experimental researches on the AS INDIRECT AEROLOGY 141 snow crystal habit and growth by means of a dif- fusion cloud chamber, J. Met. Soc. Japan., 75, 38-42, 1957. KosayasuHt, T., On the habit of snow crystals arti- ficially produced at low pressures, J. Met. Soc. Japan., ser. 2, 36, 193-204, 1958. Kuettner, J. P., R. Honxata, anp R. J. BoucHer, Results of ice crystal observations during the pas- sage of cyclones, Contract No. DA-36-039 SC- 64671, Final Report, 1956. Kuerrner, J. P., L. Avpaz, and R. J. Boucuer, Study of relationship between snow-crystal type and weather phenomena; a study of precipitation sys- tems by means of snow crystal, synoptic and ra- dar analyses, Contract No. DA-36-039 SC-73153, Final Report, 1958. Nakaya, U., Snow crystals, natural and artificial, Harvard Univ. Press, 510 pp., 1954. WeitckMmann, H., The snow crystal as aerological sonde, Artificial Stimulation of Rain, Proc. First Conf. on the Physics of Cloud and Precipitation Particles, Pergamon Press, pp. 315-325, 1957a. WeickMann, H., A nomogram for the calculation of collision efficiencies, Artificial Stimulation of Rain, Proc. First Conf. on the Physics of Cloud and Precipitation Particles, Pergamon Press, pp. 161-166, 1957b. Structure of Snowfall Revealed by Geographic Distribution of Snow Crystals Cuost Macono Hokkaido University, Sapporo, Japan Abstract—The Cloud Physics Group of Japan made observations of snow crystal forms by various methods at five points which were distributed vertically from eleva- tions of 100 m to 1000 m at Mt. Teine, Hokkaido, through the period January 26-31, 1959. Aspirated psychrometers and rawinsondes were mainly used to measure the air temperature and humidity. The results are summarized as follows: (1) Nakaya’s T,-s diagram represents fairly well the growth of natural snow crystals. The crystal forms observed at the Earth’s sur- face are mainly affected by the temperature and humidity of air layers at altitudes lower than 2000 m. (2) It seems that sometimes dendritic snow crystals grow at a hu- midity very near to ice saturation, or at least at a lower humidity than water saturation. (3) The necessary conditions for the formation of large snowflakes are the existence of a thick moist atmospheric layer and of air temperature higher than —10°C. Introduction—The relation between the snow- crystal forms and the meteorological conditions was studied by Nakaya in laboratory experi- ments, and his theory was proven by Gold and Power [1954], Murai [1956], and Kuettner and coworkers [1958] using aerological sonde data obtained during snowfall. As for the growth of natural snow crystals, however, there are no available observational data. In order to be able to observe the rate of the growth, observations were made at several points distributed verti- cally. The Cloud Physics Group of Japan made the observation of natural snow crystals by various methods at five observation points distributed vertically at Mt. Teine in January 1959 and measured the form and size of snow crystals of almost all types. Methods employed—As one sees in Figure 1, Mt. Teine is located about eight miles north- west of Sapporo where rawinsonde soundings were carried out by the Sapporo Meteorological Observatory at O09h00m, 15h00m, and 21h00m each day during the period of the observations. Since the predominant wind direction during the period was from the northwest, the observing points are located on the windward side, there- fore the atmospheric conditions measured by the aerological sounding may differ somewhat from those above the mountain except for the case of large uniform snowfall. The horizontal distribution and vertical dis- tribution are shown in Figures 2 and 3. The ob- 14 servation points at altitudes 1023 m, 800 m, 560 m, 300 m and 100 m are called Point 1000, Point 800, Point 500, and so on, respectively, in this paper. The upper three points are close together, but the lower two points are somewhat far from the upper points; accordingly, snow crystals ob- served at the lower two points were sometimes not recognized as belonging to the same cloud system. Frequently no snowfall was observed at the lower points even when moderate snow showers were observed at the upper points. This discrepancy is considered to be due to orographie effects. The observers and their work during the ob- servation are listed in Table 1. The work of the observer at Hokkaido Uni- versity was to identify the clouds over Mt. Teine from outside of the observing area. This work was very useful, because the observers located at the mountain often could not observe the clouds by which they were surrounded. Among the methods employed in observing snow crystals, the securing of replicas and microscopic photo- graphs were most useful. As for the measure- ment of humidity, Assmann’s aspirated psy- chrometer was most reliable. The observations at the five points were car- ried out simultaneously, every ten minutes dur- ing three hours after the rawimsonde sounding times (09h00m, 15h00m, 21h00m) from Janu- ary 26-31, 1959. Results—The time cross section obtained us- ing aerological sounding only is shown in Figure STRUCTURE OF SNOWFALL AND SNOW CRYSTAL DISTRIBUTION 143 Sea of Okhotsk HOKKAIDO Sapporo oO A Mt Teine Pacific Ocean Fria. 1—Location of the observations 4. Solid lines show isothermals and dashed lines represent relative humidity with respect to ice saturation. The thick solid line shows espe- cially the isothermal of —15°C around which snow crystals grow rapidly to form dendritic type. In general, moist air existed at the —15°C level on the 26th and night of 27th when light snow showers were observed at ground level. Early in the morning of 30th a cyclone passed through Hokkaido as shown in Figure 5 and warm moist air flowed into the observing area and brought heavy snowfall. This snowfall was on a large scale and the observation points were located to the lee of the mountain, so in this case the data obtained by rawinsonde sounding are considered to be reliable. Continuous snowfall was observed at Point 1000 during the period of the observation except on the 29th, but the moist-air occurrence at the Point 1000 was limited to a few short periods. This strange phe- nomenon is considered to be the result of con- densation of orographie ascending air, because the observed condensation level was always lower than the altitude of Point 1000 as shown on Figure 4. In addition to that, several small erystals of initial stage were almost always ob- served at the upper points. Therefore, the data obtained by the aspirated psychrometer were taken as the condition at al- titudes below 1000 m. As for levels higher than 1500 m, the data obtained by rawinsonde were accepted as they were. The conditions at the in- termediate level between 1500 m and 1000 m were interpolated. The time cross seetion ob- tamed thus is represented in Figure 6 in which the layer lower than 3000 m is shown. The al- titudes of the five observation points are repre- sented by horizontal short thick lines on the or- dinate. The type of representative snow crystals observed at Point 1000, Point 500 and Point 100 Fic. 2—Horizontal distribution of the observa- tion points Pt 1000 10 Pt.800 ° Pt.500 fo} Pt.300 ° =e 2 3 4 HORIZONTAL DISTANCE IN KM oe ° Fic. 3—Vertical distribution of the observation points 144 CHOJI MAGONO Tasie 1—The data-gathering organizalion | Observation points Altitude Terms of observation Observer = = Point 1000 1023 Chief | Choji Magono Daisuke Kuroiwa Point 1000 1023 Humidity Kazuhiko Itagaki Humidity, temperature _ Shoichi Koenuma Close-up photographs Katsuhiro Kikuchi Microscopic photographs Replicas of snow crystals / Tsutomu Takahashi : \Tsutomu Nakamura Point 800 800 Humidity, temperature {Tsutomu Takahashi (Tsutomu Nakamura Point 500 560 Replica Se eae : Shadowing photographs { Soup stave Close-up photographs | : Microscopic photographs | Jiro Muse Humidity, temperature Tadashi Kimura Point 300 300 Humidity, temperature {Keitaro Orikasa Replicas \ Ken-ichi Sakurai Point 100 100 Humidity Close-up and microscopic photo- | Teisaku Kobayashi graphs Replicas Toshiichi Okita Shadowing photographs Goro Walahamal Humidity, temperature Hokkaido University 30 Replicas \ Muasahilco Sivenide Cloud photograph{ Sapporo Meteorological 30 Rawinsonde Sapporo Meteorological Observatory Observatory at each three-hour interval is shown at the upper part of the figure schematically. The first type shown on each of the top lines means the type of snow crystal which fell most frequently. The re- gion of humidity higher than ice saturation is shown by shaded area. Cloud bases are shown only when ascertained. From the figure it may be seen that moist atmosphere layers (hatched areas), exist near or above Point 1000 always when snowfall is observed at Point 1000. The only exception is on the night of 28th. This is im- portant; it will therefore be discussed later. According to Nakaya’s 7,-s diagram, a tem- perature of —15°C is suitable for dendritic snow crystals to grow, while at a temperature of —5°C snow crystals grow to needle form. From an in- spection of Figure 6, note that from the 26th to 28th when the —15°C isotherm existed near or above the top of the mountain, dendritic snow erystals were predominant, and on the 30th when the —15°C isotherm had descended to this alti- tude, only thin hollow columns or needles were observed. One may understand that Nakaya’s diagram agrees very well with the type of natu- ral snow crystals. This fact leads to the con- clusion that the type of snow crystals is con- siderably influenced by the temperature of the air layer lower than 2000 m. It is well known that in the 7',-s diagram the region of column and plate type is distributed symmetrically around the dendritic region: that is about —15°C. How- ever considering the time cross section it is possi- ble that the snow crystal type falling naturally is mainly affected by the warmer region of two tem- perature regions of crystal formation. This is con- sidered to result from the fact that at the higher level the vapor density is small as is the air density. The absolute vapor content is small even if the air of the upper level is saturated because the air is colder than that at the lower level. Ac- 145 AND SNOW CRYSTAL DISTRIBUTION STRUCTURE OF SNOWFALL SUOT}RAIISGO ay} JO potsed ayy FuLMp UOrzooS ssoad OWI P—f “OY 6GB6L “ueL ISLE WOE Yt 67 Yt BTS UELG GOL? 0060 OOLZ? 0060 OO! Z 0060 OOLZ 0060 OOL? ane) ee NOILVSN4ACNOD faen : Vd 7 7 ~ Ys y OO bey” / 4 Wee Hy ~~ if V f > YS > (NOILVANLVS JD)%O0L %OZ1 %001" ¢ A | ‘ %09 % OO! 0060 OT O0LS 0060 OOO! 006 008 OOL 009 00S OOV (WY) (QUI) 146 CHOJI MAGONO cordingly, if any crystals are born at a com- paratively higher level, they do not grow rapidly until they fall into lower layers. As for the relatively dry regions above the mountain on the 30th and 31st as seen in Figure 6, it is not clear whether those regions have any connection with crystal forms observed or not. At time Sections A(21h40m, 27th), B(21h00m, 28th), C(11h20m, 30th), D(21h380m, 30th), and E(16h10m, 31th) in Fig. 6, marked snowfalls were observed. For each time section, some de- scriptions should be offered in detail. Time Section A: After 21h00m on the 27th, large snowflakes were observed (Fig. 7); snow- flakes began to form at the Point 1000 level. The magnification factors of three pictures in the figure are common to all. It seems also that the snowflake formation began when snow crystals fell into the layer warmer than —10°C [Magono, 1953]. This fall of large snowflakes was accom- panied by the occurrence of a thick moist air Fic. 5—Synoptic 850 mb map for 09h 00m, Jan. 30, 1959 layer as seen in Figs. 6 and 7. ane Ca ee ee *8 | | o MEK] Pr.1000 P1000) est T*hOe [One# Y Mee eee ex | Br Sa ae he i eit tis ‘ si 8 —— * 3 ¥ HK Pr 500 *_ —— * 8 fh 44 —— # BBII I } 500] KE OU FRED UH 8 i HF te eis 3 | Bm % ae he OOS | # > x | | Fs Pee «| ae al et ae - eee oo * | 2 | FM D5 Pr. 100 Pr 100 cial ial 2 ek WORK | | 8 0 A em | A B D *E }AO% 60% 100% (ICE SATURATION) | A = £ He — Pr.1000 2 1 ean S Hi — Pr. 800 t 4, — Pr. 500 = 300 - Ni Pr. . — Pt 100 70 90 03900 2100 0900 2100 0900 2100 0900 2100 0900 2100 og00 2100 26 th 27th 28th 29th 30th 31st Jan., 1959 Fria. 6—Time cross section considering the observations at Mt. Teine; crystal types observed at each point are shown in the upper part STRUCTURE OF SNOWFALL AND SNOW CRYSTAL DISTRIBUTION 147 2000 S Lo) IN M ALTITUDE $00 -10 ~5 (°C) TEMPERATURE | 80 90 100 (%) REL. HUM.(ICE SAT.) | Fia. 7—Growth of snowflakes 21h 30m—21h 50m, Jan. 27, 1959 Time Section B: On the 28th, snow crystals of dendritic type continued to fall. It cleared off about 15h00m but the crystals continued to fall although it was a light fall. The snow crys- tals were of very beautiful plane dendrites form. The vertical distribution of air temperature and humidity at 21h00m is shown in Figure 8. There existed a thick layer of —15°C near Point 1000 actually. It is notable that the air was not satu- rated and there were no clouds nearby; however perfect snow crystals fell and grew as shown in the left-hand part of the figure. The size dis- tribution is shown in Figure 9 starting with a erystal diameter of 0.5 mm. It is noted that the mean diameter of the snow crystals observed at Point 500 was markedly larger than that at Point 1000. The mean diameter of snow crystals at Point 100 is about the same as that at Point 500, resulting from the fact that the air layer between Point 500 and Point 100 was dry. The tips of the branches of snow crystals observed at Point 100 were, to some extent, changed to sector form. The observational fact that dendritic snow erystals grew in air not saturated with respect to ice may be thought to be strange. Concerning the fact, the error of the humidity measurement should be considered first. The error of the psy- chrometer was +0.05°C. The error margin cor- responds to about +2% at —15°C, therefore the air whose humidity was lower than around 95% as seen in Figure 8 should be considered to be not saturated to ice. At least it is sure that the air was not saturated with respect to water. Generally it is considered from laboratory ex- periments that dendritic snow crystals grow in 148 CHOJI MAGONO _ 2000 | | 1500 © 1000 | 7a = fal a =) =] = =] + 500+ | 5 -10 eG | TEMPERATURE 60 80 100 % REL.HUM. (ICE SAT) ~ Fig. 8—Growth of plane dendritic snow crystals observed at point 1000 and point 500, 21h 00m—21h 10m, Jan. 28, 1959; shading in column shows the temperature region of snow crystal growth for the crystal type indi- cated Nd i=) 3 0 i} 2 3 4 5 DIAMETER OF SNOW CRYSTAL IN MM Fig. 9—Size distribution of plane dendritic snow crystals observed at three observation points, 21h 30m-21h 50m, Jan. 28, 1959 highly supersaturated humidity which requires the existence of cloud droplets in air in the nat- ural case. But if the air contains cloud droplets, the snow crystals will collect and cannot be called ‘beautiful crystals.’ It therefore appears that beautiful plane dendritic snow crystals grow in air of humidity lower than that assumed from laboratory experiments, in other words, they grow at the humidity very near to ice saturation. In this case, the existence of cloud droplets is not necessary. Time Section C: It was characteristic here that the lapse rate of the air temperature was very small and the atmosphere was saturated from near surface to altitude 6000 m as shown in Figure 4. The air layer with temperatures ranging from —5°C to —8°C was very thick. This condition is suitable for the growth of thin STRUCTURE OF SNOWFALL AND SNOW CRYSTAL DISTRIBUTION 149 ~ aN so Occ TEMPERATURE 80 100 % REL.HUM. CICE SAT.) Fic. 10—Growth of snow crystals of thin hollow column type, 11h 20m— 11h 30m, Jan. 30, 1959; shading in column shows the temperature region of snow crystal growth for the crystal type indicated hollow column and needle type crystals. As as- sumed, it was observed as shown in Figure 10 that the snow crystals of hollow column grew moderately between Point 1000 and Point 500, but below Point 500 the erystal type changed to needle. The layer between the lower two points also was dry, as seen in Figure 10. Dur- ing daytime on the 30th, snow crystals of thin column or needle type were observed predomi- nantly; also various stellar forms occurred. This fact means that at a level colder than —S°C no snow crystals formed. This may be caused by the relatively dry region above the mountain seen in Figure 6. Time Section D: From about 15h00m on the 30th, the temperature of the whole atmosphere fell, and rimed dendritic snow crystals were ob- served simultaneously with those of needle type (Fig. 11). Snow erystals of needle type grew to some extent and the dendrites began to form snowflakes near the level of Point 1000 where air temperature was about —8°C. Time Section E: Near the end of the observa- tion period, the process of the formation of graupel of cone-type was observed in detail as seen in Figure 12. It seems that the graupel of cone-type originates from a rimed branch sepa- rated from a rimed snow crystal as pointed out by Barkow [1908]. Acknowledgments—The writer wishes to thank sincerely the Cloud Physics Group and express his best thanks to the Hokkaido Broadcasting 150 DISCUSSION S S M ALTITUDE IN =e) 0 (°C) TEMPERATURE 90 100 110(%) REL.HUM. (ICE SAT.) i —2 Fic. 11—Formation of snowflakes and growth of snow erystals of thin hollow column, 21h 30m-21h 40m, Jan. 30, 1959 Company (HBC) whose transmitting station is at the top of Mt. Teine. The HBC offered many facilities for the observations. REFERENCES Barkow, E., Zur Entstehung der Graupeln, Met. Zs., 25, 456, 1908. Gop, L. W., anp B. W. Power, Dependence of the forms of natural snow crystals on meteorological conditions. J. Met., 11, 35, 1954. Kuertner, J. P., AND coworkers, A study of pre- cipitation system by means of snow crystals, synoptic and radar analysis, Final Rep. to US. Army, Signal Corps Eng. Lab., Contract No. DA-36-039, SC-73153, 1958. Macono, C., On the growth of graupel, Scz. Rep. Yokohama ser. 1, No. 2, 18 pp., 1953. Mural, G., On the relation between natural snow crystal forms and the upper air conditions, Low Temperature Science, Ser, A, 15, 14, 1956. Naxaya, U., Snow Crystals, natural and artificial, Harvard Univ. Press, 1954. snowflakes and National Univ., Discussion Dr. C. J. Grunow (communicated)—Dr. Ma- gono concludes from his very interesting observa- tions, that the crystal forms observed at Earth’s surface are mainly affected by the meteorological conditions within the layers lower than 2000 m. As shown by his observations of January 30, the upper layers (>2000 m) also cooperate if upper cloudiness is present. Otherwise the growth of columns and capped columns would not be ex- plicable. It is true the rate of growth in the DISCUSSION 151 S 3 ra) IN-M pe) ALTITUDE 500 CLOUD BASE 2-1, -10 -5 (°C) TEMPERATURE | 80 90 100 (%) 110 REL.HUM. (ICE SAT.) J Fre. 12—Formation of graupel, 16h 10m—16h 20m, Jan. 31, 1959 upper layers is much less than in the lower layers where the ambient vapor density is higher. On Mt. Hohenpeissenberg we have observed many snowfalls where, during a long period, the col- umns dominate, falling doubtless from upper layers. Observations on Mt. Zugspitze (2962 m) prove that snow crystals of each type, from nee- dle and scroll to dendrite and column, occur also at this height. Instead of a limit of altitude it would be better to use a limit of temperature; for example, —20°C. I think the maritime climate of Hokkaido is decisive for the predominance of den- dritic forms there observed. Dr. Ch. Magono (communicated)—As for the limits in which the snow crystals of various types develop the description by temperature is better and more general than by the altitude, as you mention, but I would like to take —15°C instead om 20°C, tively warm temperature region. The The snow-crystal form except capped columns observed at Mt. when the cloudiness extends to rela- reason is as follows. Teine always seems to be affected by the meteor- ological conditions of the air layer warmer than the —15°C layer which varied from 1000 m to 3500 m. This phenomenon appears elevation to be strange, but it will be understandable if the following facts are considered. (1) The snow-crystal form is classified by the shape of its branches, so the shape of the origi- nal small portion, in other words, the portion formed in upper air layers, is usually neglected in the determination of the classification. (2) Usually the vapor air layers is much greater than that of the higher density in the lower layers perhaps owing to the maritime climate of Hokkaido, as you note. (3) Considerable numbers of small snow crys- tals are produced in the lower layers (warmer air layers) at the orographic precipitation. It is true of course that the snow-crystal form observed at the high elevation is affected by the air of the upper layers. Operation and Results of ‘Project Pluvius’ Tor BERGERON Royal University of Uppsala, Uppsala, Sweden PI PI The results of all my work on orographic and other precipitation distributions showed that the official network in no country was dense enough. So I had to construct an ‘instrument,’ which, of course, is not a laboratory instrument in the ordinary sense; but after all 1t 1s compara- ble to an instrument, because it is exceedingly complicated, consisting, during the summers of 1955 and 1956, of not less than a thousand rain gages of the type shown in Figure 1. Thus we had to use very cheap ones; in fact, the present cost is only one dollar for this ‘automatic rain gage Pluvius.’ We used it to build our rather complicated measuring ‘instrument’ in order to find out something more about the real distribu- tion of precipitation. I am accustomed to having a lot of questions concerning this instrument and how it works, and about its possible errors. I am prepared to answer them in the discussion. As to regions to select for our ‘instrument’-— that is, for this special network of gages—when starting our project during the autumn of 1953, we thought that one ought to test the whole set up in three different respects. (1) How the in- strument would work in the field. (2) If it were possible to get enough observers evenly distribu- ted and working without pay. (3) We also wanted to get some knowledge as to the interior structure of different kinds of rain mechanisms, for in- stance, the warm-front rain and the cold-front rain, when not disturbed by orography. So we selected an area 20 by 20 miles around Uppsala that was easy to reach, and which, I thought, was so flat that there would be no appreciable oro- graphic effects. The measurements went on for six weeks (in October and the first part of Novem- ber). Unfortunately, we had only a few big rains, but it turned out that they were very suitable after all. On October 14-16, a front lay across southern Sweden with a stationary rain area and northeasterly winds on its northern side. Figure 2 shows the results of the measurements during the first 12 hr of this period. Notice that it is the night and not the day period, so there would be very little convection. When we first got the figures, I thought they did not show much, but when plotted on an appropriate map showing the regions with forest (green on the original base map), and those without, a most surprising con- nection appeared between the shaded areas and much precipitation, and the white areas and a minimum of it. See Figures 2 and 3 where wood- land is indicated by the legend. Now, I must spend one minute on other proj- ects of a similar kind. You might, for instance, Fia. 1—The automatic rain gage Pluvius, with a cork-float lifting the measuring rod; ratio col- lecting area to cylinder area = 5; cost $1 OZ OPERATION AND RESULTS OF ‘PROJECT PLUVIUS’ 17°30'E_Gr ITs 2 Yi AK 4 G 3 hs Cog ROT} 1730’ E Gr Rainfall mm ASQ Woodland S7T7™ Isohyetal of 5 mm s == Shore line Lu One night: 14.X.18z- 15.X.06z, 1953. oat Town of Uppsala i Station reporting 51 mm rain Ground >40m ab s-l Min. Minimum of rainfall Fre. 2—Orographie rainfall maxima and minima around Uppsala, Sweden, during one night within a stationary and continuous frontal upslide rain area, as shown by a meso-scale network of Pluvius gages; the arrows show the wind direction think that one could use the data from the Thunderstorm Project in the United States for the same purpose. However, they had only be- tween 50 and 60 stations, and their areas pre- sented no marked orographic features. As early as 1953 we had 150 stations, and later, in other parts of Sweden, we had up to 800 stations. So, we could cover a much greater area, having an interesting orography, whereas the Thunder- storm Project did not have these requirements. On the other hand, evidently, the Thunderstorm Project and other similar projects had a much better instrumentation at each individual sta- tion. We could not afford that. The official meas- uring instrument of the Swedish Weather Bu- reau costs twenty times as much as the ‘Pluvius,’ and we had the choice between 1000 of this type and 50 of the former type. We had to choose the ‘Pluvius.’ Then also the data from the different American and other projects were generally not accessible to us, as you will understand. In Figure 2 one rain maximum lies to the lee of Uppsala, and one might think of a precipita- tion release caused by certain nuclei produced in this town, or by the convection released through the heating effects of Uppsala; all sorts of other explanations may pass your mind. One might also think that this was just a chance distribu- 154 17°30' E Gr TOR BERGERON ea SO peso Ra 7 , Oey 1730’ E Gr. Rainfall mm. rs } Woodland —=—> Shore line 157/77) \sohyetal of 15mm (es One night: AY Town of Uppsala 1s! Station reporting 15.1 mm rain ” « 5 15.X.18z - 16 X.06z, 1953. Ground >40m ab. s.-l. mn. (tenths unknown) m } Minimum of rainfall ——— Fic. 3—Orographic rainfall maxima and minima during the following night under the same general conditions as in Fig. 2 tion; but the next night, skipping the interven- ing 12 day hours, we got much greater amounts, but practically the same distribution (Fig. 3) with the same stationary rain, and almost the same wind direction. The wind had shifted a little more to NNBE, but notice that in both eases the proportion between maximum and minimum was three to one. (Here it is about 20 to 7, on the previous map it was 7 to 242.) During the intervening and following day-time periods there was a similar pattern, but not so regular. This may be explained by the fact that in daytime, even at this high latitude and so late in the year, there will be some convective effects. Some heat will pass through the cloud, heat the ground, and disturb the cloud sheet. As seen from Figures 2 and 3, in this case the highest elevation of the country from the sur- rounding plain is about 50 m; one cannot ex- pect an increase of the rain to the double or the three-fold only by a lifting of 50 m. With a high condensation level that would hardly give any precipitation at all. True enough, if the low lay- ers are moist, clouds may form even over small hills. But if higher layers are cloudless, these low cloud caps will be colloidally stable and sym- metric, giving practically no precipitation, since there is no upper releaser cloud. Moreover, OPERATION AND RESULTS OF ‘PROJECT PLUVIUS’ 15% within a small and shallow cloud cap there is no possibility of getting warm-cloud precipitation release, because the lifetime of the droplets will be too small. Therefore, I suggest the following explanation in such cases as this. The cloud base was either low from the very beginning, or the air below the Nimbostratus base was moistened through these 100 hours of rain. Then, orographic cloud caps with more or less intense condensa- tion, colloidally stable in themselves, formed over those regions that were higher and clad with forest, because of the great increase in friction and its stemming effect on the flow. At last, the general rain from the frontal cloud system swept down through the cloud caps and ascertained a very good release of precipitation within them. For the next project, July—-October 1954, we selected an area between the great Lake Vinern and Lake Vittern in southwestern Sweden partly shown in Figures 4 and 5, representing an inter- esting orography (plains, dislocations, forests, shore lines, ete.). Here we had 750 gages; in ad- dition in 1955 we had 150 stations in the central part of the region measuring the wind direction and velocity (the latter with a cheap pressure- tube hand anemometer). The two rainfall maps RAINFALL mm. One day: 27. Vil. 06-18z, 1954. ou 1954 (cold- front) and for August 7, 1954 (warm-front), both with a general current from south-southeast. In the cold-front case, obviously, orography has had very little effect on the distribution; the expla- nation evidently being that the cloud base was high, since it was summer, and the stratification chosen as examples are for July 27, was unstable. Thus, no low feeder clouds would form above the low hills or plateaus of the area, and there were, instead, convective cells moving with the direction of the gradient wind, giving streaks of precipitation parallel with that di- rection. Now I may remind you of the Figure 23 of my first lecture (see T. Bergeron, ‘Problems and Methods of Rainfall Investigation,” p. 28, this volume, 1960), where I underlined that two main patterns may be superimposed on most precipitation distributions, owing to two main mechanisms, the convective cell mechanism, and the stationary lee-wave mechanism. Figure 4 1s an example of the Case 1, and Figure 5 of Case 2 with alternating maxima and minima. There is even a minimum occurring where you would expect a maximum because of the passage of the air over the table mountain and so on. e Rainfall station === Shore -line “133m alt. (400 ft.) VATTERN SROs N 7B. 1954 Fic. 4—Instability pattern of rainfall (cold-front with SSE wind aloft) shown by a meso-scale network of Pluvius gages in a region with plains and plateau hills between the two great lakes of southern Sweden 156 RAINFALL mm. One ni DISCUSSION e Rainfall station === Shore-line 133m alt. (400 ft.) 266m alt. (800 ft.) aN Fig. 5—Stability pattern of rainfall (warm-front with SE wind aloft) in the same region as Fig. 4 Another situation from the same year, October 19 (not shown here), also with a warm-front rain and south-southeast gradient wind, showed practically the same rainfall distribution. From these examples you may see what forecasters have to cope with! They should be able to tell that, in such a situation, there will be heavy precipitation (25-35 mm) during 12 hours near the shore of Lake Vattern, but only a few milli- meters at the shore of Lake Vianern, that is, one fifth as much. This whole area is as big as the station ring on an American weather map, at the scale of one to ten millions. So, you see what we are up against; and you may take my word that these differences are even stationary with cer- tain wind directions. Discussion Mr. Jerome Namias—You described the al- most local character of regional differences in precipitation. If I remember correctly you had two very low precipitation areas and also rather high zones, the high being over a forest. You mentioned friction and some other factor as causes. I wonder if you could repeat your ex- planation. Dr. Tor Bergeron—Well, first of all you no- ticed in those first cases that there was a maxi- mum to the lee of Uppsala, and people hearing of or seeing these maps have suggested that nu- cleation from Uppsala might have something to do with it, and also convection raised by the heating. Uppsala is rather small, 70,000 mhabi- tants and some industry; therefore I think the main cause will be the friction. I think these great differences which are constant would prob- ably correspond to different kinds of precipita- tion efficiency; that is to say, over the plains you will have rather great evaporation of the from the whereas over the forest regions you will have perhaps a precipitation efficiency of nearly 100 percent and then in addition also the water con- precipitation falling Nimbostratus, tent of those local cloud caps. That might ex- plain the very great differences in the amount DISCUSSION 157 of rain compared to these small differences im space. I may also say that we are now going to have a much denser network around Uppsala than the one I showed you. Dr. C. W. Newton—The hills around Stock- holm are about the same as those near Uppsala, 40 to 100 m in height. While we were in Stock- holm, F. H. Ludlam made time lapse movies of cloud formations and we were very much im- pressed when we noted that Altocumulus clouds were very strongly influenced by these 40-m hills. I wonder if, even with such low hills, ordi- nary orographie lifting can be ruled out. Dr. Bergeron—I did not mean to rule out that kind of lifting which goes on the theory of lee waves, observable at heights surpassing that of the obstacles by a factor of 10 to 20, as we know. I did allow for that first of all, and secondly on an obstacle with forest, 40 m high, friction would perhaps increase the effective height. I did consider those two things, but I am very thankful for the remark. Efficiency of Natural Rain Raymond WEXLER Allied Research Associates, Inc., 45 Leon Street, Boston 15, Massachusetts Abstract—The efficiency of cloud in utilizing the water made available by the up- draft for precipitation may be derived from a steady state equation involving storage and horizontal advection. The efficiency is greatest in the middle of widespread rain and least in individual thunderstorms. The microscale features are evaluated in the initiation of precipitation. Observations indicate that large drop sizes, adequate for growth by the accretion process, are present in many clouds which do not precipitate. The important factor is the product of the mean effective liquid water content and the cloud depth, which has a critical value of about 3 g m™* km. Introduction—The efficiency of the rain mech- anism is of importance not only for the evalua- tion of artificial ram production but also for the understanding of natural rain processes. An ini- tial analysis was made by Weickmann [1958] who showed that the influence of particle concentra- tion on the rate of rainfall is of secondary im- portance. The particle size adapts itself to the available concentration. The primary factor in- fluencing rainfall rate is the updraft. Weickmann distinguished between a releaser cloud in which there is no storage of cloud liquid water and a spender cloud in which there is storage. In the former case the water vapor made available by the updraft 1s deposited directly on the precipita- tion and no artificial increase is possible. In the latter case an increase in particle concentration could cause a temporary increase in the rainfall rate at the expense of precipitation downstream. In the initiation of rain, probability is a factor both on the meso and microseales. On the meso- scale, probability enters in the favoring by the convergence mechanism of a more vigorous or longer lasting updraft in one Cumulus cloud over another. On the microscale, the passage of a few large drops through regions of relatively high liquid content is a probability problem. Prob- ability also enters in the appearance of freezing nuclei in sufficient concentration in cold clouds. The question arises as to the critical conditions on both scales for the initiation and maintenance of precipitation. It is assumed here that the macro or mesoscale features largely control the cloud extent and depth (although it has been claimed that the sudden release of latent heat in the freez- ing of the upper portion of a Cumulus cloud can cause precipitous growth). In this paper the eriti- 158 cal cloud depth for initiating or maintaining rain is analyzed in conjunction with the microphysical features. The important parameter in the production of precipitation from a cloud is the product of the mean liquid water content Z and the effective cloud depth H which may be defined by mf where V is the fall velocity of the precipitation, w is the updraft and # is the efficiency of catch. The integration in this equation follows the ascent and descent of a drop within the cloud. Accord- ing to the equation, for equal geometric depths, warm clouds should be more effective than cold clouds in producing rain because of higher L. In addition the relation between the updraft and the fall speed of the precipitation has a marked effect. For updrafts of the same order as the fall speeds effective cloud depths may far exceed geometric cloud depths; this effect is important in the pro- duction of rain or hail from shower clouds as well as the production of snow from thin Stratus clouds. Initiation of precipitation—In clouds over the tropical ocean, the percentage of warm rain in- creases from near zero for a cloud depth of 5000 ft to 100% for a cloud depth of about 10,000 ft [Battan and Braham, 1956]. At intermediate depths, wind shear and the humidity of the en- vironment probably have considerable influence on cloud liquid water content (hereafter LWC) and thus the formation of rain. The observations suggest that under the most favorable circum- stances a 5000-ft cloud depth provides sufficient LWC for large cloud drops to reach raindrop size. EVL V-—w (1) EFFICIENCY OF NATURAL RAIN 159 Assuming an efficiency of catch of 0.8, a large cloud drop released at the cloud top could at- tain a diameter of 1.1 mm at the base of the cloud. Over the land, the critical cloud depths are about 10,000 ft in central United States and 12,500 ft in southwestern United States. With colder cloud temperatures the maximum mean LWC is about 2.5 g m™® but evaporation caused by greater turbulent mixing with an environment of lower humidity could easily cause a 50% re- duction in the effective LWC. Under such condi- tions a drop diameter of 1.5 mm could be attained at the base of the cloud. The important factor for rain formation is the product of the mean effec- tive LWC and the cloud depth, which the ob- servations indicate to have a critical value of about 3 g¢ m® km. Cloud duration of about an hour is required in order for the drops to rise from the cloud base to top and then to descend again. It has been observed over land and ocean that cloud drop sizes in Cumulus are somewhat greater in Cumulus clouds which subsequently develop echoes (rain) than those which do not [Battan and Reitan, 1957]. For example, at concentra- tions of 100 per liter the drop diameters in echo- producing clouds over the ocean was 67 pas com- pared to 64 » in non-echo producing clouds; over the land the respective drop sizes were 62 p and 58 ».. However, it may easily be shown that only several meters of fall im a cloud containing 1 g m* would suffice for the 64 drops to grow to 67 » or for the 58 » drops to grow to 62 yp. It is apparent, therefore, that it is not for the lack of large drops that the non-echo clouds failed to produce rain. It appears more likely that mesoscale features controlling the duration and strength of the updraft are responsible for the favoring of one cloud over another in the subsequent development of rain. As for the oc- currence of rain from clouds of smaller depth over the ocean than over the land, drop size again is evidently not the deciding factor since clouds which did not develop rain over the ocean had a greater concentration of large drops than clouds which did develop rain over the land. The critical depth for the production of pre- cipitation via the ice phase in Cumulus clouds is smaller than that using the water phase in warm clouds. There are numerous instances of snow over the Great Lakes from Cumulus clouds less than 5000 ft in depth. Evidence from the radar indicates the existence of snow from gener- ating cells, 2000 to 4000 ft deep and wide, with vertical velocities of the order of 1 m see-’. Many instances of precipitation involving the ice phase from a cloud with top warmer than —12°C sug- gest that when the depth and duration of the updraft is sufficient, growth of precipitation somehow occurs either by the sublimation proc- ess initiated from freezing nuclei or by the ac- cretion process followed by the freezing of drops when they are sufficiently large. Drizzle has been observed to fall from layer clouds about 3000 ft in depth. The important factor in the production of drizzle is the dura- tion of the cloud, or rather the duration of the up- draft, so that drops aided by turbulent motion have a path length sufficient to accrete to a size of a few hundred microns. The efficiency of rain—The efficiency of rain production #, may be defined as the per cent of water produced by the updraft that falls to the surface JS pwdq R where p denotes the density of the air, qg is the specific humidity and R the precipitation rate. Integration is from the top to the base of the cloud. A steady state equation for the continuity of moisture in a cloud may be written as follows oR oq ol (a) (a) + w =w-—-4 u +u Oz Oz Oz Ox oy Er = (2) (3) z xs Ou av (L + NM) + NM (# a *) Ox oy where R = NM (V — w) is the precipitation rate, N the number of drops of mass M/. The second term on the left-hand side is the rate at which liquid water is provided by the updraft. On the right-hand side, the first term represents storage of cloud liquid water, the second is hori- zontal advection (which may include evaporation due to the mixing of the cloud with drier air), and the third represents changes in the concen- tration of the precipitation due to the vertical wind shear (from the equation of continuity). It is readily seen that a measure of the efficiency of rain defined by (2) can be derived from this equation. In the middle of a widespread uniform rain, where the fall speeds of the precipitation particles are large compared to the updraft, all the terms on the right-hand side of (3) may be neglected except the first. In this case it is found [Wealer 160 and Atlas, 1958] that storage in the form of cloud represents less than 5% of the amount of water produced by the updraft, and that the precipitation efficiency is about 95% (neglecting evaporation from the upper surface of the cloud, which should be small). For hght precipitation the entire cloud above about —5°C is a re- leaser cloud (no liquid water or icing), although for heavy rain, storage of cloud liquid water may extend to much higher levels. In the opposite extreme is the thunderstorm in which the precipitation efficiency was found to be about 20% [Braham, 1952]; 45% of the avail- able moisture was evaporated in downdrafts and 35% evaporated from the cloud sides or remained in the cloud after the cessation of rain. From this analysis it 1s evident that most of the loss of water is dynamic so that, once the precipita- tion has begun, little increase can be obtained by increased particle concentration; the greatest opportunity for artificial rain production is in the initial stages of the cloud when storage of cloud liquid water is high. From the point of view of the efficiency of rain production per unit depth of cloud, stratiform 280° HI GAIN 1033 E H! GAIN 1035 E RAYMOND WEXLER clouds are relatively inefficient since a cloud deck some 20,000 ft thick gives a rain of a few mm per hour, while much higher rainfall rates come from Cumulus of smaller depths. Most effi- cient from this viewpoint is the case of a Cumu- lus cloud imbedded in a stratiform deck. An outstanding example is the frontal precipitation of October 1, 1958. Radar photographs showed that the widespread light rai on both sides of the front originated as snow with echo top near 24,000 ft. The heavy rain with a peak of about one inch per hour in a narrow region along the front had an echo top at about 10,000 ft (Fig. 1). Since the bright band was at 12,000 ft the growth of the heavy rain occurred entirely from the water phase. The occurrence of heavy rain over land from a convective cloud mass of less than 10,000 ft thick is unusual. In addition to the smaller loss of available liquid water by evapora- tion, it is reasonable to suppose that drops at least the size of drizzle from the surrounding light rain were carried into the base of the cloud by the strong updrafts, which from the rainfall amounts were calculated to be about 2 m sec™* over the extent of the cloud. The presence of such drops 280° LO GAIN 1033 E 310" LO GAIN 1035 E Fic. 1—RHI’s Blue Hill CPS-9 radar, October 1, 1958; the frontal rain is at a distance of about 5 miles EFFICIENCY OF NATURAL RAIN would greatly accelerate the accretion process. The gap between the echoes of the upper light rain and the heavy rain in Figure 1 indicates that the drops from the light rain did not descend into the heavy rain cloud. Conclusion—The efficiency of cloud in initiat- ing rain increases with cloud depth, LWC, and duration. At a critical depth of about 5000 ft for warm Cumulus, without unfavorable wind shear and mixing with the environment, sufficient liquid water content is established for cloud drops to grow to raindrop size. It is doubtful that clouds fail to rain because of the lack of large drops be- cause observation indicates that some clouds over the land produce rain while some clouds over the sea with more numerous larger drops fail to pro- duce rain. Critical depths and liquid water content for precipitation formation via the ice phase are smaller than in warm clouds. For the formation of drizzle in stratiform clouds critical depths are also smaller but critical durations are probably greater. The efficiency of cloud in utilizing available water is greatest in the middle of widespread 161 precipitation and least in the individual thunder- storm. Rain amounts in Cumulus are greater per unit depth of cloud than in stratiform clouds. Very efficient from both viewpoints is the case of a Cumulus cloud imbedded in a stratiform deck. The author is indebted to Helmut Weickmann for suggesting the topic and for many helpful suggestions, and to Edwin Kessler III for use of the October 1, 1958 radar data. REFERENCES Barran, L. J. anp R. R. Branam, A study of con- vective precipitation based on cloud and radar observations. J. Met., 13, 587-591, 1956. Batran, L. J. anp C. H. Rerran, Droplet size meas- urements in convective clouds, Artificial Stimula- lation of Rain, (Helmut Weickmann and Waldo Smith, eds.), Pergamon Press, pp. 184-191, 1957. Branam, R. R., The water and energy budgets in the thunderstorm. J. Met., 9, 227-242, 1952. WeickMaNn, H., The efficiency of natural rain and its determination, USASRDL Tech. Rep. 1973, 14 pp., 1958. Wexter, R. anp D. Attias, Moisture supply and growth of stratiform precipitation, J. Met., 15, 531-538, 1958. Discussion Mr. R. D. Elliott—I feel that in treating any precipitation mechanism it is necessary to inte- grate over the entire mechanism, and when we consider a major storm, it is necessary to con- sider more than a vertical column. In extending the consideration to the outer boundaries of the storm it is necessary, to put two more terms into that equation: (1) The horizontal transport which may have a relatively small magnitude in the column, but when integrated over a storm, becomes important; and (2) An evaporation term which may be very small in the particular column where all the rain is falling, but out on the boundaries of the storm and on the for- ward edge and possibly the top, can be large. It would appear to me that in the studies of a large scale precipitation mechanism it would be necessary to sample over the entire storm and get a complete water budget. Dr. R. Wexler—I quite agree with you. There is no doubt that the advection term is important. In the case treated previously, I was concerned with the stratiform case in which one could reasonably leave out the horizontal advection terms. In a thunderstorm or any precipitation from a cumuliform cloud, one cannot. Dr. B. J. Mason—I would like to take up a point concerning the time and space requirements for the growth of a raindrop, which Dr. Wexler raised. Clouds over the tropical maritime ocean of little more than a kilometer thick may pro- duce precipitation. Over England we get coales- cence rain from a cloud perhaps five thous- and feet deep. In both cases, if one tries to follow the history of a raindrop, one finds that the time for which the cloud exists is a very important parameter. Assuming a uniform updraft, it is quite impossible in the space available in the cloud and in the time available to get a raindrop out. This means one must have a much more complicated picture of the vertical motion, and one way to do this is by means of successive thermals. It may be the last thermal which is very important, and indeed my theoretical analy- sis shows that this must be the case, if one wants to get a shower out of a cloud only one kilometer deep. If you take the exact same parameters, but a homogeneous updraft speed, nearly two 162 kilometers of cloud depth is needed, and a little longer time, too. Even in this very simple case, the actual pattern of the motion is important. The motion is important, and the time span is important. Dr. H. G. Houghton—I am sure Dr. Wexler agrees with this. Dr. J. Smagorinsky—It would seem that the question of efficiency not only arises in the trans- formation from cloud particles to precipitation particles, but also enters into the formation of condensed particles from water vapor. I think one rarely finds that the entire mass is cooling at the moist adiabatic rate. If one is to consider the budget for the entire water content, that is water vapor, suspended liquid water, and pre- cipitating water, the question of the efficiency should be considered in each transformation. Dr. Horace R. Byers—I was very glad to see Dr. Wexler give a definition of efficiency. I think this is something that has been used in too loose a sense by many people. I hope that those of us who are called upon to review papers for jour- nals and other publications insist that the au- thors very carefully define what they mean by efficiency and use terminology that will not fur- ther confuse the issue. Dr. Helmut Weickmann—As I feel Dr. Wex- ler’s lecture has a very important bearing on the problem of rain making, I may be permitted to elaborate a little on my own thoughts on this particular subject. Figure 2 shows another ex- pression of the water-budget equation with the terms on the left side representing the water source, and those on the right side representing the water sink. Of course, the growth processes, condensation and coalescence of the precipitation particles constitute the water sink; the updraft and water storage in the cloud constitute the water sources. Note that the number of the pre- -———_ SOURCE WATER SUPPLIED BY SINK WATER STORED| WATER EXTRACTED FROM CLOUD WEATHER MECHANISM| IN CLOUD | BY PRECIPITATION MECHANISM | do i) KoWV dane w 27K 2 anes + N400r (= Apr

6 > 0.17 w. Carefully cleaned (xylene), polished chromium foils were used exclusively. Since the aerosol concentration was several hundred times larger than that encountered in nature the micro- photometric analysis could be used although the exposure time was but one to two minutes. The short residence in Cz is the apparent reason for a certain instability of the size distribution during the brief sampling period. To compensate for these, each time two spectra were taken under identical conditions and analyzed for the same 32 L values, and then differentiated by deter- mining (AS) over intervals of Ad = 0.025 uw. The mean of each pair of AS/Ad was then plotted versus d. Adjacent points of this derivative curve were averaged again to minimize the unavoidable inaccuracies of this semi-graphical procedure. The systematic displacement of the 6-value so caused is (6 = 0.0125 wu) and was considered negligible for this type of experiment. Each size distribution curve in Figure 11 is thus based on 74 original S determinations and 31 points derived from them. Figure 11a pre- sents four spectra of a dehydrated aerosol Ty = 0° C after contact 72 = 5 sec with an air stream of a relative humidity varying between 14 and 80%. The size distribution, typical for the nebu- lizer under the particular operating conditions used, is closely similar to those found in nature (Fig. 9) though for a maximum at a higher value (0.30 p > ds > 0.27 p). At a relative humidity of about 50% the hu- midity is slightly larger than in C,, hence any GOETZ AND PREINING effect on the aerosol, while in C2, is unlikely except for a possible small additional adsorption of moisture on the nuclei. The curve 0—50-0° shows a distinct maximum at 0.29 u > d, > 0.25 w and a steady decline toward larger sizes. If the air flow is drier (0-33-0° and 0-14-0°) than in C; this maximum decreases with decreas- ing humidity in C2 concurrent with a slight fre- quency increase (as C'S’) for ds > 0.35 uw. This can be tentatively interpreted as an increased rate of coagulation of the (numerically very dense) small particles into fewer conglomerates of larger sizes, due to electric disturbances, caused by the desorption of residual moisture layers known to exist on dehydrated nuclei [Orr, and others, 1958b]. (It was assumed as a first approxi- mation that the original nuclei d; form conglom- erates of closest packed spheres d, , the number N required for forming a particle of the size d. is (w/6)(d,./ds)’. A decrease of, for instance, 30% of original particles of d; would thus result in a 7% increase of conglomerates for d, = 2d; and only in 1.4% for d. = 3d, , ete.; qualitatively compatible with the experimental indication in Figure 11a.) The distribution is drastically altered when the relative humidity in C2 is larger than critical, that is, when the nuclei are being hydrated (O-80-0°). This causes a general shift to larger particle sizes. The interval 72, for contact with the moisture of the air stream is insufficient for the complete hydration of all nuclei, indicated by the partial remainder of the first maximum, similar to the type of marine aerosols in Figure 9b. Figure 11b shows the effect of partial dehydra- tion of the hydrated aerosol (0-50-24°) by brief contact with an air stream of (rh ~ 50%) in comparison with the corresponding distribution curve (0-50-0°) in Figure lla. As is to be ex- pected, the dehydration, while far from being complete due to the short contact time, is suffi- cient to cause the shift of the maximum toward smaller 6 and the indication of a maximum re- maining at the 6 value of the hydrated aerosol. The variations of the distribution do thus essen- tially agree with the hydration pattern for hygro- scopic aerosols found by other authors previously for individual nuclei. The curves of Figure 11lcdef show the effect of organic traces T added in C2 with the air stream in comparison with the distribution in their absence. Figure 1le represents the hydra- tion pattern of a dehydrated aerosol (T—80-0°) AEROSOL SPECTROMETER AND ITS APPLICATION 181 in the presence of 7, which latter retards sig- nificantly the hydration of the smaller particles (d; < 0.35 w) as indicated by the partial preser- vation of the distribution of the unaltered de- hydrated aerosol (Fig. 11a, 0-50-0°) while a second maximum at dy, ~ 0.6 wu is indicated. The curves of Figure 1lde indicate the effect of T on dehydrated nuclei which is predictably negligible as the rh in C,; remains virtually un- changed (Fig. lle). However, a small increase of (rh) in Cy, that is, adsorption on the nuclei, appears to increase coagulation rate (decrease of small particles and small increase of larger sizes) for 7'-50-0°, similar to the effect of desorption from the nuclei in the absence of 7 in Fig. 11a. Figure 11f compares the dehydration of a hy- drated aerosol with 7 and without (7—50-24°). Obviously 7 increases sharply the number of smaller particles when contacting an increased humidity below the hydration level (rh), , con- trary to its effect on an already dehydrated aerosol (7-50-0°). These preliminary leave but little doubt about the marked in- fluence of organic traces in nuclear condensa- results tion phenomena. A detailed interpretation of these findings, in spite of their fair reproducibil- ity, appears premature and will be postponed until more detailed data are available. ConcLusIon The size-distribution spectra of natural and artificial aerosols in the submicron range appear realistic because the process of separation should interfere less with the airborne habitude of the particle than that of most methods available in the past. Moreover, the method permits discrim- ination between hydrated and dehydrated NaCl particles, because of the relation of the Stokes’ diameters, independent from the state of the nuclei after precipitation. The size-distribution spectra can thus be used to determine changes occuring among airborne nuclei by interaction with their gaseous environment, such as adsorp- tion or desorption, hydration and dehydration. It appears that, whenever such changes occur, the coagulation rate of the particles is affected and that organic traces in general delay these processes, possibly in analogy to the well-known ‘nhibition’ of freezing nuclei [Birstein, 1957; Poppoff and Sharp, 1959]. This hypothesis satisfies also the pattern of the marine aerosol spectra. They show two maxima ds, dy, whenever a source of their generation, such as foam on wave crests [Blanchard and Woodcock, 1957], was within a few miles from the sampling site, most distinctly in the vicinity of sources of organic matter (kelp beds). At sub- stantially larger distance from such aerosol sources, the marine as well as the mountain aerosol spectra showed one maximum only. Nat- ural aerosols are probably rarely, if ever, free from organic traces, hence the persistence of hydrated fractions of the nuclei present under conditions of decreasing humidity could well be caused by such temporary protection against dehydration and vice versa. One has to realize that, contrary to such dispersions in the labora- tory, these aerosols represent mixtures of particles airborne for largely differing time intervals avail- able to them for attaining equilibrium states prior to precipitation in the A.S. Independent of the validity of the above in- terpretation the aerosol spectra, so far available, seem to definitely indicate the significance of gaseous organic traces in the atmosphere with regard to the rate of nuclear condensation, that is, to the formation of fogs and hazes as well as to certain phases of air pollution. It thus appears that a systematic research effort which combines size distribution studies of natural aerosols with their well defined synthetic replicas in the labora- tory promises a new chapter in the understanding of our immediate atmospheric environment. Acknowledgments—The work presented is part of a general investigation program on the Syner- gistic Properties of Aerosols supported by Re- search Grant (No. RG-6743) from the National Institutes of Health, U.S. Public Health Service. The authors wish to express their appreciation to the Instrument Development and Manufactur- ing Co., Pasadena, for putting an aerosol spec- trometer at their permanent disposal; also to Aerometric Research, Inc., Santa Barbara (R. E. Kerr, Jr. and E. Hovind) for contributing the wind-trajectory maps for the times and localities of the off-shore sampling sites. Furthermore they wish to give full credit to members of the re- search staff: to M. L. Warrick, Jr., for applying his mechanical skill to the construction of the micro-analyzer and to numerous other items of special equipment; to A. F. H. Goetz for his capable and conscientious assistance in the field and laboratory, particularly in the analy the aerosol spectra; and to Mrs. L. Hauck for her untiring clerical collaboration. sis of 182 REFERENCES ArcHer, R. J., anp V. K. LaMenr, The effect of monolayers on the rate of evaporation of water, Annals N.Y. Acad. Sci., 58, 807-829, 1954. Barus, C., Condensation of vapor as induced by nuclei and ions, Carnegie Inst. Wash. Publ. 62, 1907. BirsTEIN, 8. J., Studies on the effects of certain chemicals on the inhibition of nucleation, Arti- ficial Stimulation of Rain, Pergamon Press, pp. 376-885, 1957. BuancHarD, D. C., anp A. H. Woopcocrk, Bubble formation and modification in the sea and its meteorological significance, T'ellus, 9, 145-158, 1957. Goetz, A., The aerosol analyzer, reviewed in Chem. Eng. News, August 6, 1956. Gorrz, A., An instrument for the quantitative separation and size classification of air-borne particulate matter down to 0.2 micron, Geofis. Pura Appl., Proc. I1, International Symposium Condensation Nuclei, Basel-Locarno, 36, 49-69, 1957a. Goetz, A., AND H. J. R. Stevenson, The aerosol spectrometer: its theory, construction and ap- plication to the analysis of exhaust and atmos- pheric aerosols, APCA Proc. Semiannual Tech. Conf., San Francisco, pp. 228-267, Air Pollu- tion Control Association, Pittsburgh, Pa., November 1957b. Goetz, A., Study of the properties of aerosols, with particular reference to the nature of the air-particle interface, Final Rep., USPHS Res. Cont. SAph-69557, Taft Sanitary Eng. Center Tech. Rep. A58-10, 1958. GOETZ AND PREINING Goetz, A., H. J. R. SteEvENSON, AND O. PREINING, The design and performance of the aerosol spec- trometer, 52nd Annual Air Pollution Control Association Meeting, Los Angeles, Preprint 59-40, 22 pp., June 1959. Junce, C., Atmospheric chemistry, Advances in Geophysics, 4, 1-108, 1958, Acad. Press Inc., NEY Orr, C., Jr., F. K. Hurp, anp W. J. Corsert, Aerosol size and relative humidity, J. Colloid. Sct., 13, 472-482, 1958a. Orr, C., Jr., F. K. Hurp, W. P. HeNpRIXx, AND C. Junar, The behavior of condensation nuclei under changing humidity, J. Met., 15, 240-242, 1958b. Poprorr, I. G., anp G. W. Suarp, Inhibition of freezing nuclei by adsorbed contaminants, J. Met., 16, 288-294, 1959. PREINING, O., H. J. R. SrEVENSON, AnD A. GOETz, The analysis of aerosol spectra, 52nd Annual Air Pollution Control Association Meeting, Los Angeles, Preprint 59-42, 29 pp., June 1959. SILVERMAN, L., aNnp Cuas. I. Brutines, Methods of generating aerosols, J. Air Pollution Control Assn., 6, 76-83, 1956. Twomey, 8., The identification of individual hy- groscopic particles in the atmosphere by a phase-transition method, J. Appl. Physics, 24, 1099-1102, 1953. Vonnecut, B., F. W. Went, anp A. Gorrz, in Summary of Adirondack Conference on Atmos- pheric Nuclei, Schenectady & Speculator, N.Y., October 1957, (not published). Wasser, E., Das Widerstandsgesetz kleiner Ku- geln in reibenden Medien, Physikalische Zs., 34, 257-268, 1933. Discussion Dr. C. E. Junge—As I understand you, you evaluate the particle concentration using the microphotometer by which you measured the to- tal scattering? Dr. A. Goetz—We determine the surface scat- tering microphotometrically each time over an area of 6 X 10% cm® progressively along the spiral of the deposit pattern. Dr. Junge—In other words, you evaluate the particle concentration on the screen optically? Dr. Goetz—Yes, that is for the artificial aerosols T described. Dr. Junge—I would like to caution a little bit. If the same aerosol is deposited for instance in the absence and then in the presence of organic vapors, the aerosol droplets may spread on the foil surface with different contact angles. This will influence the light scattering characteristics of the individual particles which in turn would influence the analysis. The question of particle spreading is a complex one and I wonder how you took that into account. Dr. Goetz—In the micro-analyzer which I have briefly described individual counts can be taken over an area of 10-4 cm? along the deposit with reference to a reticule in the eye piece. Deposits which are dense enough to allow reliable scatter- ing determination are too crowded for counting, hence it is in general not possible to evaluate the same deposit in both ways. For comparison a brief and long exposure of the same aerosol are taken. This has so far been applied to a few cases only for the artificial NaCl aerosols with and without organic trace. Hence their general quan- titative interpretation in terms of numbers is not yet possible. These comparisons indicated that the presence of the organic trace definitely changed the numerical size distribution as in- dicated qualitatively by the scattering, however, it may also have affected the specific scattering DISCUSSION 183 power of the particles. The detailed relationship will require much future work. Dr. Bernard Vonnegut—1 would like to ask about the pressure drop across the centrifuge. The thought occurs to me that because of these spirals, the air that is taken through the centri- fuge is experiencing a pressure change. Dr. Goetz—The average pressure in the chan- nels should not be different from the atmospheric because the flow restriction (the locus of the pressure drop) is at the exit of the channel. The air in the channel will, however, experience a shght compression because of the impeller action of the spinning helix prior to expansion in the jet when leaving the channel. Tests under stationary con- ditions indicated a maximal pressure difference of 5 em H.O, that is, 0.5% of one atmosphere. There should exist also a radial pressure gradient, analogous to a barometric variation of the pres- sure between the inner and the outer channel walls. Because of the small radial depth of the channels (0.63 em) this pressure difference should amount at 25,000 g to about 2% if the centrifugal force were constant across the channels. Since it is less at the inner than at the outer wall (about 40% at inlet decreasing to 16°% at the outlet due to the conical rotor shape) this radial pressure difference should be even smaller. Dr. Vonnegut—How nearly adiabatic is the expansion? A change of pressure of this sort would amount to a very substantial change in the tem- perature, were it adiabatic. If this were so, the humidity might be considerably changed. Dr. Goetz—Because of the velocity distribution across a laminar flow a substantial fraction of the particle trajectories will pass a slow moving, al- most resting gas layer prior to deposition on the outer wall. This layer must be in thermal equi- librium with the rotor. Hence we believe that the minute radial compression would be closely iso- thermal rather than adiabatic with respect to the equilibrium conditions of the particles. Differences in Coalescence Tendencies in Computed Condensation Cloud Droplet Spectra‘ W. A. Morpy International Meteorological Institute, Stockholm, Sweden Abstract—Four numerically computed cases of the growth of a population of cloud droplets by condensation are analyzed in terms of coalescence tendencies. Following the suggestions of Hitschfeld, 1957; Telford, 1955; and Welander, 1959, particular atten- tion has been given to the stochastic influence on the coalescence-produced cloud- droplet spectrum. The evidence taken from the numerically computed cases strongly supports the contention that collisions between small droplets readily produce a wider spectrum than the condensation-produced spectrum. The transition time for a conden- sation-produced spectrum to change to a predominantly coalescence-produced spectrum depends strongly on the maximum supersaturation and resulting cloud droplet concen- tration produced at cloud base. In a recently published paper [Jordy, 1959] the writer described a theoretical investigation on the effects of vertical motion and condensation nucleus spectra on cloud droplet spectra. The purpose of the present paper is to evaluate the differences in cloud droplet spectra which resulted in these cases in terms of some important factors which lead to the subsequent changing of these spectra by the coalescence of droplets. The coalescence of droplets is mainly depend- ent on three factors. These factors are the size spectrum, the concentration, and the coalescence (collision times collection) efficiencies of the drop- lets. An equation which gives the number of con- tacts between two droplet sizes is frequently given as [for example, Telford, 1955 n = EN,Nor(ri + 12)? E (1) collision efficiency between 7, and rz radius droplets Ni, and N» are the concentra- tions per unit vol of the 7 and rz size droplets respec- tively m(r; + 12)? = the area surrounding a drop- let in which a contact could be made v =relative velocity between the 7; and r2 droplets Customarily the coalescence of droplets has been described by following the growth of a larger droplet as it sweeps up smaller droplets in a cloud with certain assumed characteristics of droplet where * Contribution No. 1079 from the Woods Hole Oceanographic Institution. 184 size and vertical velocity [Houghton, 1950; Mason, 1957; Bowen, 1950; Ludlam, 1951; Langmuir, 1948]. The growth of the larger droplet in these cases is assumed to be continuous, that is 1 dn p at lr 4rr8 = Sane = ExNAn + To)2v = (2) where 7; and rz are the radii of the collecting and collected droplets respectively. In fact of course it is discontinuous, each unit of growth being one cloud droplet. If one adopts the practice of thinking of the coalescence of cloud droplets as in (2) above, then it is the initial drop size spectrum which largely determines the initial and subsequent relative velocities between the droplets. Thus droplets which are initially slightly larger, will remain larger throughout the coalescence process and there will be no tendency for smaller droplets to overtake them, except that they may follow different trajectories in the cloud [Bowen, 1950]. Such reasoning has been followed in the work of Houghton [1950], Woodcock [1952], Fournier ad’ Albe [1955], and others. In this line of thought Wood- cock has reported measuring a correspondence between the size distributions of sea salt particles and raindrops measured in the same localities and at the same time. As exceptions to the above treatment of this problem there have been three very interesting investigations to date [Telford, 1955; Hitschfeld, 1957; Welander, 1959], which study the impor- tance of statistical aspects of the coalescence process. This statistical process in its simplest form may COALESCENCE TENDENCIES IN CLOUD DROPLET SPECTRA be illustrated by the following example. Suppose a group of 100 large droplets is falling through a cloud of randomly spaced, uniform size, small cloud droplets. Because of the random spacing of the cloud droplets, each of the large droplets will have a different collision experience with the cloud droplets and after some time will represent not a uniform-size group but a spectrum of drop- lets located at different levels in the cloud. If such reasoning is applied to an initial spec- trum of cloud droplet sizes instead of an initially uniform-size group, a question arises as to whether, after some time has elapsed, the result- ing drop size spectrum is more dependent on this statistical process than on the initial drop size spectrum. In other words one may ask the ques- tion; do more of the large droplets present repre- sent initially large nucleus droplets or do collisions between the smaller sizes of droplets ultimately produce more large droplets? A complete mathematical investigation of this problem has not been made but the evidence offered by the three investigators above indicates that the statistical nature of the problem is very important. One way of approaching this question is to examine the differences in drop sizes and drop concentrations which may result from condensa- tion with a view toward assessing their coales- cence tendencies, that is, how will n (the number of first collisions) change in (1) as r grows by condensation? It seems that the assumptions which are necessary to make such an appraisal are not too gross to prevent an examination of important aspects of this process. As a model for such investigation, assume a constantly rising current of air containing a given frequency distribution of salt particles. The con- densation conditions attending are then fixed by the initial conditions such as temperature, pres- sure, rate of rise, and the above assumptions such that, until the process of coalescence becomes im- portant, we can describe the cloud droplet spec- trum at each time and altitude above base [Mordy, 1959]. We shall then investigate, as time elapses, the characteristics of these changing spectra which are conducive to coalescence. We shall therefore look first at the way n varies with time or height if the growth of the particles is controlled only by the condensation conditions. The fall velocity of the drops we consider is satisfactorily described by Stokes law (that is, for r < 40y) so that 2gpr? v= = kr? (k = constant) gn If the above expression is substituted in (1) and the terms rearranged the equation can be written n = EnxNiNok(r, + r2)3(r — re) (3) Only that part of the condensation process that occurs above the zone of maximum super- saturation (where NV, and N» are determined in this model) need be considered here so that wN\N2k may be considered as a constant. The variation of # is uncertain and therefore for the moment will be included in a new variable n = n/#. If the In n’ is differentiated with respect to time the equation becomes 1 dn’ 3 n' dt iS d(ry + 12) m+ re dt (4) 1 d(r, — 12) ri + 12 dt The time derivatives of the radii can now be obtained from the equation for drop growth by condensation. Here we shall for the moment con- sider only droplets which have grown until they are dilute enough to neglect the hygroscopic ef- fect of the nucleus. We shall see in the discussion below that this makes very little difference in the conclusions we draw from our results. If a@ is the ratio of the radius 7; to rz or 7; = are (= ar, see (6b) below) the drop growth equations for the two drop sizes which appear in equation (4) can be written [Jordy, 1959] dry a 5 ina (asF — A) ' (5) arg a aileron A dt Te e ) where s = (e — es)/es = supersaturation _ eel2DJe 1 | jin epRITE eL’DJe kR?T3 = const ~ 8 X 1077 egs at 800mb, 10° C A = 2cT/JLp = capillarity term coefficient ~1.7 K 10-® cgs T = temp of drop 186 We = surface tension mech equiv. of heat = latent heat of water = density of water heat diffusion coefficient lta te He | ll = vapor pressure s = saturation vapor pressure When (5) is substituted in (4) the equation be- comes 1 dn’ 2a1 A(2a — 1) = SS = | Spa = 6) n’ dt ria | ‘ v a(a + 1) | The objective now is to see how the terms in oo FD ll 10.5 63+ (g/m3) © Condensed woter 42 217 Fic. 1—The concentration of liquid water on droplets growing by condensation on a spectrum of different size condensation nuclei; the spectrum was characteristic of spectra measured by Wood- cock at cloud base over the open sea in a Beaufort Force 4 wind; note how quickly the liquid water is concentrated on the smallest one or two size categories of droplets; the mean radius derived from the total liquid water content therefore does not differ much from the minimum droplet radius as used in the present calculations [Mordy, 1959] A. MORDY (6) vary as time proceeds. In the writer’s previ- ous study it was shown how the bulk of the liquid water lies in the smallest one or two categories of cloud droplets in such a model (see Fig. 1), hence the mean volume radius will represent nearly the radius of droplets which contain the largest part of the liquid water. It will serve as a good index, therefore, for this discussion to consider collisions between this volume mean radius (7) and larger or smaller droplets in the spectrum. The volume mean radius is defined by 4en7%p = Mm ; (6b) = mean mass of the droplets In the model we are considering, the liquid water is very nearly equal to a constant times the height above cloud base, which is to say Vv a dz ou l a TPL asi aa (7) where dx/dz = the change in mixing ratio in a moist adiabatic expansion (~2 X 10-* egs at 800mb and 10°C) z = ht above cloud base N = X(N, + Nz ---) = const. By differentiating, (7) can be written A)p = (8) where z = vt in the model. The term containing (s* — A) here has been substituted from the condensation growth equa- tion (5). If these expressions in (7) and (8) are used to replace 7? and (s* — A) in (6) the equa- tion becomes: adn’ _(2\ (AY, , n' dt \8a t when it is assumed that p = 1 If the two equations for drop growth (5) are subtracted the following equation may be ob- tained in quite an analogous way 1 dn — 7) -1 i 1 — FT dt sat Now putting A(2Qa — 1) 4raN (9) a(a + 1) cv acv AdmaN | (10) cv LS eA and Ar =m — 7 COALESCENCE TENDENCIES IN CLOUD DROPLET SPECTRA and combining (9) and (10) the following equa- tion is obtained. 1 dn’ —2 dAr L4 3 ni dt Ar dt 1 (11) 1+ -} (ay — 1) a Note: ¢ = dx/dz (see Eq. 7); A is defined in (5). Values of y are given in Table 1 for cases from the writer’s previous condensation study. Choos- ing four representative values of y and computing the value of the coefficient in (11) for all radit larger than one half the mean radius one can see that a good approximation for this quantity is y’ = 2 + 6/y for the given values of y. Hence the time dependence of a can be rather safely neglected in integrating (11). Putting 3 y = 2) 1+ Tae iNGean as ( + ‘) (ay — 1) a when 60 > y > 4, (11) may be integrated to give Aro \Y’ n! = no! (=) ay) < 275) (12) r Rq. (12) indicates that if Ar remains 1/ay that Aro/Ar varies approximately as ¢-"/®, In this range all values of Ar are converging. By the time that 300 sec have elapsed Ar has a time constant of more than 1000 sec. In fact when one includes the effect of the salt nuclei in the drops this time constant is appreciably lengthened so that Ar may be treated as nearly constant in the time interval of 1000 see or so which we consider here. If variations of two in the values of Aro/Ar are allowed for, an error in the estimation of n’ by a factor as large as 16 may occur. We shall see, however, that this variation is small compared to the several orders of magnitude variation in n’ computed in the cases of different droplet spectra. Eq. (12) shows effectively that the most im- portant factors (mo, y) which determine n’ are determined very near the cloud base and are in- 187 TaBLe 1—Values of y for various nucleus distributions and vertical velocities om rertical No. of cu Case velocity) diovs (W) ee Ea cm/sec I-100 100 2.5 X 107 56.2 II-15 | 15 Fee 10? 4.57 III-5 | by 165% 107 4.47 1 I1I-100 100 4X 108 10,2 TaBLE 2—Case III, 100 cm/sec N 7 n’ a 108 lhc LL. 8: | | 3 x 107 2a | 6760 | 0.98 107 12.3 3930 0.96 3 x 108 12.4 | 1780 0.958 10° 12.6 835 0.945 9 X 105 12.9 1167 0.922 7X 10° 13.3 1495 0.895 5 xX 105 13.8 | 1581 0.862 3 xX 10° 14.4 | 1407 | 0.826 9 xX 10! 15.7 870 | 0.758 Be 08 | Siser | 943 | 0.636 9 X 103 | 20.0 | 376 0.595 2X 103 | 24.0 | 211 | 0.496 TaBLE 3—Case II, 15 cm/sec N ip | n’ | a 3 xX 107 | ys | 107 | 17.85 | 3760 | 0.980 3x 106 | 18.10 2005 | (0.966 108 ei ged 1000 0.951 4 X 105 18.7 578 0.935 2.5 X 105 19.2 563 0.911 2 xX 105 19.9 698 0.880 105 20.8 570 0.841 fluenced by the strength of the vertical current and the nucleus distribution on which the drop- lets form. If Ar is considered a constant then with the aid of (7), 7 is known and the spectrum of condensa- tion produced droplets can be estimated at each altitude (or liquid water content). Once the spec- trum is determined an estimate can be made from Kq. (3) of the number of ‘potential’ first collisions (n’ = n/E) per unit time between any size cate- gory and the mean radius. Such calculations of n’ are given in Tables 2-5 for four cases from the condensation study. The drop size distributions for these cases are shown in Figure 2. The calculations were made for a cloud liquid water content of 1g/m* which by (8) 188 W. A. MORDY TaBLE 4—Case I, 100 cm/sec N r n’ a 1.28 X 107 21.2 6.4 X 107 22.2 2710 0.954 3.2 X 105 22.4 1950 | 0.946 1.6 X 10° 22.7 1195 | 0.933 8X 105 | 23.2 730 0.912 4X 10° 23.6 436 0.897 2x10 | 24.2 285 | 0.875 105 25.2 203 0.840 5X 10! | 26.2 134 0.809 2x10! | 27.3 70 0.790 3X 10° | 29.9 | 18 0.708 verte || Seer 3 | 0.628 10 38.6 1.8 0.548 TaBLe 5—Case III, 5 cm/sec N 2 n a 107 24.6 | 3 X 106 26.1 232 | «0.943 10° | 27.0 133 0.910 9 105 “9 28/0 7 4175. Fy 0.878 7 xX 105 29.2 197 | 0.842 5x 10° | 30.6 | 199 0.803 3 X 105 33.1 192 0.748 determines 7. Because of the very skew nature of the droplet distribution the mean radius and the minimum radius were assumed to be the same, an assumption which could lead to an error of a few per cent in the estimate of n’ at most. The four cases chosen were representative of the range of differences in nucleus spectra which resulted from different nucleus distributions and vertical velocities. In all of these cases except one there is a mark- edly higher number of potential collisions among the smallest cloud droplets. The exception is the case where there is an extremely slow rate of rise, 5 em/see, and a dense nucleus distribution (which was taken from Woodcock’s data as characteris- tic of the distributions of salt particles produced at cloud base by a Beaufort Force 7 wind at the sea surface). The fact that there are a higher number of potential collisions between small droplets, how- ever, is not enough to determine whether colli- sions between the smallest droplets are of compa- rable importance to those between the larger and smaller droplets. It must be determined whether in a reasonable time a comparable number of larger droplets are originating by combining smal- ler droplets as from condensation on large salt par- ticles. To test whether this is true the resulting radius and number of the droplets produced by the combination of the smallest droplets in a reasonably short time, must be compared with the total number of condensation produced drop- lets which have about the same radius as the com- bined droplets (r = 2!87 = 1.26r). If these fig- ures are close to the same value then one must assume that collisions between the smaller drop- lets are more important than between large nu- cleus drops and small drops. The larger droplets are then being increased in number at a suffi- ciently rapid rate so that the number of originally large particles is relatively insignificant. A useful index therefore as to the importance of these collisions is the time of replacement of large nucleus droplets (droplets formed on large nuclei) by smaller coalescing droplets. If this is computed for the cases in Table 6 one finds that the number of coalescences between the smallest two categories of droplets replace 1-100 E 7 \ | C3 | mS x 10° —J- |\ + -= PX | 10?- - we | N tN 10 - { | | Om 20p 304 ; 4p Radius Fic. 2—The distribution of cloud droplet sizes used in the computations; these distributions are derived from Mordy [1959] and represent the ex- treme differences in droplet concentration and spectrum width obtained in the different assumed cases of nucleus spectra and vertical velocities; the spectra represent the sizes of droplets expected if the liquid water content is 1g/m’ and is assumed constant (see text); the figures at the top give the distribution type and the vertical velocity in em/sec COALESCENCE TENDENCIES IN CLOUD DROPLET SPECTRA 189 TaBLe 6—Values of T for the four cases parison between the two smallest categories of a ues — ] droplets and the number of existing, condensa- Distri- | 83 ae dros | n/E |p-=ay/iv/z) tlon-produced droplets which have a radius bution | 3S |with r = 27 roughly equal to that of the droplets produced ~ by combining the two small droplets. Actually cn, al Sc07 Se it would be better perhaps to compare all coales- lee alov 3 ; et ae | 3x ine i . Ce cences between the smallest categories having a 3.8 26. ; Ill 53x 105| 2.3 xX 102 1.3 % 193 ‘tadius not more than about ten per cent larger | 6.7 X 10 | 60. than the minimum value with the number of Il 100 | 4 X 105 ! | condensation produced large droplets. If this is done, values of T are decreased by a factor of 3 those with a radius r = 2! = 1.26r in periods — to 5. ranging from less than one second for the dis- If these computations are made for a larger tribution Case I at 100 cm/sec to more than 1000 liquid water content then the collisions between sec in the distribution Case II at 5 cm/sec. These the small droplets become relatively more im- values for the four cases are given in Table 6. portant. To see how this proceeds a useful dia- The values for T in Table 6 only give a com- — gram can be constructed as in Figure 3. Here the 7 = 9 10 15 20 30 40 50 60 70 80 90 100 (2%+Ar) Fic. 3—The number of potential collisions n’ per unit time between two size categories of droplets of radius (7) and (7 + Ar) as computed from Eq. (13); as 7 increases the points in the curves move along the diagonal lines (rkNiN2Ar = constant) hence tend to line up vertically as Ar/7 + 0 and thus demon- strates the increasing importance of collisions between the smaller size categories as 7 increases with time or liquid water content; curve AB becomes A’B’ as 27 + Ar increases; the curves marked C and D represent two cases computed in Table 6 and demonstrate how different the collision expectancy can be for the different condensation conditions assumed. 190 W. A. MORDY terms in (3) have been expressed as Ing= In. 3 = InwN,Ne2kAr + 3 In (2F + Ar) (13) where 7, = 7 Tr, = i + Ar Ar = const Since for any pair of droplet sizes NN» is con- sidered constant in the model, then the variation of In n’ depends only on no’ and 7. Hence if one plots the number of collisions between two cate- gories of droplets as given in Tables 2 to 5 it is possible to extrapolate how the relative number of collisions change with time or with different liquid water contents. As Ar/r becomes small the points representing the number of collisions tend to line up more vertically as the points move along the diagonal lines (curve 4B becomes curve A’B’) showing that as time elapses the relative impor- tance of the small droplet collisions increases. The diagram also shows how important the ini- tial droplet spectra radii are in determining the relative importance of large and small droplets, for these show up as the separation of points in the curves in the diagram. When satisfactory in- formation about F# is available as a plot of In F vs. In (27 + Ar) and Ar, this will allow a more com- plete diagrammatic treatment. The calculations and reasoning in this paper have been made with the assumption that the collection efficiency of the droplet was 100%. Research and theory on the collection efficiency of droplets unfortunately does not yet converge on values which can be substituted into these equations to provide more conclusive arguments. However, if one follows the reasoning of Hocking [1959], it seems that few if any collisions occur before the droplets reach radii of 18 or more. At this point the collection efficiency rises rapidly to values exceeding unity. If these values were to be inserted in the present study an almost ex- plosive effect on the numbers of droplets coalesc- ing should occur at the point where the mean drop size exceeds this value, independently of whether one has a wide spectrum of cloud condensation produced droplets or not. Here the most impor- tant consideration would be the concentration of droplets per unit volume. This is largely fixed by the supersaturation conditions and nucleus con- centrations at cloud base. With different droplet concentration, considerable differences in liquid water content or cloud depth are required to pro- duce the large mean droplet size which Hocking states is necessary for coalescence. Acknowledgments—The writer wishes to ac- knowledge with thanks the helpful discussions of the work described in this paper with B. Bolin, P. Welander, and most especially with Mr. Claes Rooth of the International Meteorological Insti- tute in Stockholm. The work has been supported by the U. 8. Office of Naval Research and the Woods Hole Oceanographic Institution. REFERENCES Bowen, E. G., The formation of rain by coales- cence, Austr. J. Sci. Res., A 3, 193-212, 1950. FournNIeR D’ALBE, E. M., A. M. A. Lateer, L. I. Rasoot, anp I. H. Zatp1, The cloud seeding trials in the central Punjab, July-September 1954, Q. J. R. Met. Soc., 81, 574-581, 1955. HirscHreLp, WALTER, Size distribution generated by a random process, Artificial Stimulation of Rain, Pergamon Press, pp. 224-229, 1957. Hocxine, L. M., The collision efficiency of small drops, Q@. J. R. Met. Soc., 85, 44-50, 1959. Houeuron, H. G., A preliminary quantitative analysis of precipitation mechanisms, J. Met., 7, 363-369, 1950. Lanemurr, I., The production of rain by chain reaction in Cumulus clouds at temperatures above freezing, J. Met., 5, 175-192, 1948. Lupuam, F. H., The production of showers by the coalescence of droplets, Q. J. R. Met. Soc., 76, 52-58, 1951. Mason, B. J., The Physics of Clouds, Oxford Univ. Press, 481 pp., 1957. Morpy, W. A., Computations of the growth by condensation of a population of cloud droplets, Tellus, 11, 16-44, 1959. Te.rorp, J. W., A new aspect of coalescence theory, J. Met., 12, 486-444, 1955. We.anper, P., A theoretical power law for the distribution of small particles or drops falling through the atmosphere, Tellus, 11, 197-201, 1959. Wooncock, A. H., Atmospheric salt particles and raindrops, J. Met., 9, 200-212, 1952. Discussion (Note: The discussion of this paper is combined with that following the next paper.) Computations of the Growth of Cloud Drops by Condensation Using an Electronic Digital Computer M. NEIBURGER AND C. W. CHIEN Department of Meteorology, University of California, Los Angeles, California’ Abstract—The growth of cloud drops by condensation was computed for four cases involving three different assumptions concerning the manner of cooling and two differ- ent size distributions of hygroscopic nuclei. All cas show that the smallest nuclei grow fS) only until the maximum supersaturation has been reached, and then shrink slowly, while the larger nuclei continue to grow rapidly, resulting in a gap in the size spectrum between the cloud drops and the imactivated nuclei. In the cooling models correspond- ing to Cumulonimbus and trade-wind Cumulus a sufficient number of large drops are formed to initiate drop growth by coalescence and warm-cloud precipitation. List of symbols—The following symbols are used in this paper. a Cunningham constant c Average molecular velocity c Specific heat of cloud drop D (Dz ,Dre ,Dr) Coefficient of molecular diffusion Dy Thermal diffusion coefficient e Vapor pressure e, Vapor pressure at surface of drop of radius 7 e; Saturation vapor pressure e, Ambient vapor pressure in air parcel Fy, Flux of mass of water vapor F, Flux of heat g Acceleration of gravity H Heat K Coefficient of thermal conduction k Boltzmann’s constant L Latent heat of condensation M_~ Mass of drop m, Mass of water vapor molecule No Number of cloud drops per unit volume Number of drops per cm’ larger than r; (cu- mulative frequency) n Number of molecules (of all kinds) per unit volume P Pressure R, Gas constant of water vapor r Radius of drop ro Equivalent radius of nucleus 8 Parameter introduced by Rooth T Temperature (°K); T,, T,,, values of T at drop surface and in environment t Time, seconds w Vapor mixing ratio wy, Liquid content a Accommodation coefficient T Consolidated hygroscopic factor Y Parameter introduced by Frisch and Collins 6 Fractional difference between temperature of drop and ambient temperature 1U.C.L.A. Department of Meteorology, Contri- butions to Meteorology No. 40. 191 Ratio of molecular weights of water vapor and dry air (0.622) n Fractional frequency of cloud drops N Molecular free path m Molecular viscosity of air Pa Density of air pr Density of nucleus ps Density of cloud drops p» Density of water vapor; por , pr. , Values at drop surface and in distant (undisturbed) environment Drop-size frequency function o Surface tension nm 6 Introduction—It is a remarkable fact that meas- urement of drop-size distribution in all sorts of clouds at various locations throughout the world almost always shows a mode, or most frequent size, in the range of 5 to 10 microns radius [Diem, 1948; Netburger, 1949; Weickmann and aufm Kampe, 1953]. Methods of measurement which are able to count the very small droplets show that there are in addition a large number of sub- micron droplets and nuclei in the clouds [Eld- ridge, 1957]. We undertook the study we are re- porting on here to see whether drop growth by condensation alone could explain the remarkable uniformity of the drop-size distributions in clouds formed under quite different conditions, and also explain the development of bimodal size distri- butions from the uni-modal distributions which are almost always found in nucleus counts. In addition, we were interested in seeing whether drop growth by condensation on the observed wide range of nucleus sizes would give enough large drops to initiate the growth of precipitation by coalescence. The problem of the growth of drops by con- densation involves two transport processes in the 192 air parcel: (1) the transport of water-vapor mole- cules towards the surface of the drop, and (2) at the same time the transport away from the sur- face of the drop of the latent heat released during condensation. The problem has been considered successively by various investigators who took into account more and more nearly the actual conditions which prevail in the atmosphere. Thus Houghton [1933] derived the equation for drop growth neglecting curvature, hygroscopicity, and heating caused by release of latent heat; Langmuir [1944] took cur- vature and heat transport into account but neg- lected hygroscopicity; while Howell [1949] and Best [1951] took all three factors into account. Even Howell neglected some terms and treated the problem as an equilibrium problem. In addi- tion, as pointed out by McDonald [1953], Howell made an error in his treatment of the hygroscopic effect. The differential equation for drop growth is too complicated to integrate by analytical means. Howell resorted to numerical and graphical tech- niques for its solution. He treated three cases involving various nucleus distributions and rates of cooling. With the availability of the electronic digital computer it is possible to deal with the equation in a somewhat more rigorous form than that used by Howell, in addition to using the cor- rect value for the hygroscopic factor. In addition we thought it would be desirable to try other as- sumptions regarding nuclei distributions and rates of cooling. As will be discussed subsequently, it turned out that the equation which Howell used is an adequate approximation, but that even with the electronic digital computer, the integra- tion of this equation is extremely time consuming. The equation of drop growth—The solution of transport processes in a system with nonuniform distribution of concentration of molecules and temperature must come from the kinetic theory. The theory is fully treated by Chapman and Cow- ling [1952]. The main development is based on the knowledge of the function giving the distri- bution of molecular velocities and of the effects of molecular encounters on this function, and ul- timately on the solution of Boltzmann’s equation for the velocity distribution. From this solution the transport processes in the system can be de- termined. In applying the theory it was necessary to make the following assumptions to reduce the com- plexity and thus decrease the mathematical diffi- culties. NEIBURGER AND CHIEN (1) A binary mixture of gases is considered, water vapor and dry air, and both constituents are treated as perfect gases. (2) The air parcel is considered a closed system with respect to mass. No exchange of matter is allowed between the parcel and its surroundings (that is, no entrainment), while exchange of en- ergy is permitted. (3) Drops in the air parcel do not affect each other, so that the field around each drop is con- sidered to have radial symmetry. (4) Condensation takes place only on nuclei, and these nuclei behave as though all are com- posed of the same hygroscopic substance, taken to be NaCl. (5) The gas that is immediately in contact with each drop is in equilibrium with the drop, so that the temperature and vapor pressure over the drop are completely determined by the properties of the drop. In Chapman and Cowling’s treatment it is shown that the flux of one substance, in our case water vapor, through another, that is, the ‘dry’ air, is given by Fur = —DVp» — mynD7V T/T (1) and the flux of heat is given by Fy = —KVT + nkT(C, — ©) Dr/D (2) The second term on the right in each of these equations is small compared with the first for the case of dilute mixtures such as water vapor in air. For the case of spherical symmetry, the trans- fers of mass and heat to the surface of a drop of radius r are obtained by integrating the above equations from the drop surface to infinity, giving dM 4rDr [fe er — = 4rDr(pr, — por) = a 3 7 Dror per) R, (= =) @) = 4rKr(T,, — T+) (4) The law of diffusion treats diffusion as a con- tinuous process, implying that the individual dis- placements of the molecules are of infinitesimal length. When the mean free path is longer than the radius of the droplet, the question arises whether the same diffusion law can also be ap- plied. The problem is further complicated by the fact that at the iquid-vapor boundary molecules are evaporating as well as being condensed. Langmuir [1944], based on an equation used for calculating the rate of evaporation of sub- GROWTH OF CLOUD DROPS BY CONDENSATION stances in high vacuum, introduced a compen- sated diffusion coefficient of the form ope see ec eat fa Peo 2 | Dir + ax) | or R.T to take account of these effects, where a, the Cun- ningham constant, is about 0.7, and \ is the mean free path. Frisch and Collins [1952], in their investigation of the growth of aerosol particles, examined the boundary condition at the surface of the droplet appropriate for the solution of the diffusion equa- tion. A modified boundary condition was intro- duced which, when applied to the diffusion co- efficient, gives Dre = Dir/(r + y)] The parameter y is defined as y = (1/a)(¥/d) where \? is the mean square free path of the diffus- ing molecules, and @ is the probability that a molecule striking the droplet is absorbed. Rooth [1957] obtained a modified diffusion co- efficient of the form Dr = Dr/(r + 8) The thickness s of the layer through which mo- lecular diffusion acts is given by the relation 8 = (D/a)V/2r/R,T When this expression for s is substituted into Langmui’s compensated diffusion coefficient, D, takes a form similar to Dg or Dre: 2) | The actual value of y or s is subject to con- siderable uncertainty. Anderson [1957], based on some experimental cloud chamber data by Barrett and Germain [1947], suggests a value of y of the order of two microns. The value of s is taken by Rooth to be five microns at 10°C and 1000 mb, based on the value of a = 0.036 ob- tained by Alty and Mackay [1935] by measure- ments of the rate of evaporation of drops. As Rooth points out, if the true value of a were larger, then y or s would be proportionally smaller and its effect would then soon approach the limit of meteorological insignificance. Because the correct values will remain uncertain until accurate data 193 regarding the exchange of water molecules across a liquid-vapor interface are available, modifica- tion of the diffusion coefficient as well as similar modification of the thermal conductivity has not been included in this study. The heat which must be transferred from the drop surface consists of the latent heat released by the condensation and the heat produced by friction of the drop falling through the air, less the heat stored in the drop and the energy re- quired for increasing the surface area of the drop lH We 8 rrég?ps(ps — pa) _ CH penne 2p sea 7’ps\Ps — p dt dt 27 mn (5) 4 e al, 3 dr 3 TT’ ps6 al omor at It is readily shown that all the other terms are very small compared to the first term on the right in (5). Neglecting them and combining (4) and (5) we obtain 3 eeran/gt 20 == CI =46) (6) K where 6 = (psLr dr/dt)/KT, . The vapor pressure of a small drop containing a soluble nucleus is given by 20 Tpnro® p>, = €s(T',) | ex 1 iC er = s( (esp tz) ( sis ) (7) where the second factor expresses the increase of vapor pressure due to the curvature, and the third factor the reduction due to the effect of the solute. It is convenient to replace the drop tempera- ture T,, by the ambient temperature 7’, in (7). This is accomplished using (6) and the Clausius- Clapeyron relationship. The result is Meer pi ee als ereciees) ’ 20 1 Tpnto? ee rR Tans) per’ Substituting this expression and M = 4zr%p;/3 in (3) and dropping the subscript » we have Rypsr dr e e(T) Lé = exp = D dt T TQ-+6) R,TQ + 4) : 20 1 Tpnro? &xP arRaT( + 8) par (8) (9) 194 NEIBURGER AND CHIEN For usual rates of drop growth 6 does not exceed 10-° and thus may be neglected in comparison to unity. The growth equation is thus Lé — eT) | exp —— es( E ml ; 20 1 Tp,70° eRe par’ It is to be remembered that dr/dt occurs in 6, so that this is an implicit equation for the rate of drop growth. If the exponential terms are ex- panded in series and the terms higher than the second are neglected this equation is practically identical with that used by Howell. Langmuir’s equation for small drops is obtained by omitting the last expression in the square brackets; for large drops he also omitted the second (curvature) factor. Houghton’s equation is obtained by neg- lect of all three factors in brackets. To test the validity of these various approxi- mations, dr/dt was computed for various-sized drops grown from various-sized salt nuclei, using (1) Houghton’s equation, (2) Langmui’s large drop approximation, (3) Langmuir’s small drop approximation, (4) Howell’s equation, with the correct expression of the effect of solute, and (5) Eq. (9), and assuming constant temperature and relative humidity (5°C and 101%). The results are shown in Table 1. They show that the neglect of the difference in temperature of the drop from that of the air leads to large errors for all sizes of drops and nuclei. The neglect of the curvature term leads to errors of less than ten per cent for drops larger than about one micron; whereas the size at which the effect of hygroscopicity influ- ences the growth rate by less than ten per cent depends on the size of the nucleus; it appears to be roughly the size for which (ro/r)* is about 0.0005. Howell’s equation gave growth rates within three per cent of that given by (9) for all the cases tested. The method of integration—So far only the growth of a single drop has been considered. The simultaneous growth of drops of different sizes is more complicated, as the distribution of sizes at each instant must be taken into account. Let ¢(r)dr be the fraction of the drops in the size range r to r + dr. Then at all times dr D f Siam ae (10) ie) [ o(r)dr = 1 (11) J0 Suppose that at time f, the fraction of the drops in the range ra to ri + Ara is 7; , and that time t. the r;-sized drops grow to rj2, and the ri + A ra-sized drops grow to rj. + A riz. Since the nature of the growth process is such that a given- sized drop never overtakes a larger one, at time tz the fraction in the range rjz to rig + A riz will still be ;, that is rratArie it o(r) dr = +2 rec (12) = i o(r) dr = ny = constant Ch Thus biAri = GirAriz or g2 = dndrin/Arie (13) The procedure in this treatment will be to divide the initial nucleus distribution into size groups A rj, of average frequency ¢io . The average frequencies ¢;, at each time ¢ will be computed by (18). An approximation of the continuous size dis- tribution at any time is arrived at by graphical interpolation. It was found that the interpolation could be best approximated by dealing with the cumulative distribution, that is, the variation of the number larger than each given size. If No is the total number per em’, the number N,; larger than r; , called the cumulative frequency, is e) 2 aN Nine = No / d(r) dr = | a dr (14) rT; T? i where dN = Nod (r)dr is the number in the size range r to r + dr. The values of N,; were computed for each group at selected times and plotted against r on log—log graph paper. Then a smooth curve was fitted for each time, keeping the physical process of drop growth in mind in establishing the relative posi- tions of the various interpolated curves. The slope of the curves for N, were computed to obtain the frequency per unit size interval, dN/dr = Nod(r), which is called the differential frequency. In interpreting the results it is important to keep in mind the distinction between the definite results of the computations and the results indi- cated or suggested by the curves interpolated be- tween the computed values. In treating cloud development in the atmos- phere it is assumed that the temperature of an GROWTH OF CLOUD DROPS BY CONDENSATION 195 TasiEe 1—Comparison of rate of growth of drops (micron/sec) at various sizes for given initial conditions dr/dt (micron/sec) (roir)? EES) , F | Fa Houghton | quaSdrop) | (email drop) Howell Ea) | For ro equals one micron 0.5 1.26 0.7810 0.3704 0.3486 19.2854 19.9134 1.083 0.1 2.51 0.6484 0.3073 0.2924 4.0349 4.1553 1.0380 0.05 2.71 0.5428 0.2574 0.2440 1.8525 1.9063 1.029 0.01 4.64 0.3321 0.1575 0.1536 0.3540 0.3642 1.029 0.005 5.85 0.2679 0.1270 0.1245 0.2055 0.2114 1.029 0.001 10.00 0.1558 0.0739 0.0730 0.0825 0.0848 1.028 0.0005 12.60 0.1237 0.0587 0.0581 0.0619 0.0636 1.028 0.0001 25.14 0.0724 0.0843 0.0841 0.0846 0.0355 1.028 0.00005 27.14 0.0575 0.0272 0.0271 0.0273 0.0281 1.028 0.00001 46.42 0.0836 0.0159 0.0159 0.0159 0.0164 | 1.028 0.000005 58.48 0.0267 0.0126 0.0126 0.0126 0.0130 1.028 0.000001 100.00 0.0160 0.0074 0.0074 0.0074 0.0076 1.028 For ro equals one-tenth micron 0.5 0.126 | 7.810 3.704 1.533 190.974 197.219 1.033 0.1 0.251 | 6.484 32073" || 1.578 39.032 40.166 | 1.029 0.05 0.271 5.428 2.574 | 1.524 17.579 18.090 1.029 0.01 0.464 3.321 1.575 1.181 | 3.181 3.270 1.029 0.005 0.585 2.679 1.270 1.006 1.808 1.859 1.028 0.001 1.000 1.588 0.739 0.652 0.745 0.768 1.028 0.0005 1.260 1.237 0.587 0.532 0.569 0.586 1.028 0.0001 2.514 0.724 0.343 0.325 0.329 0.3388 | 1.028 0.00005 2.714 0.575 0.272 0.260 0.262 0.270 1.028 0.00001 4.642 0.336 0.159 0.155 0.156 0.160 | 1.028 0.000005 5.848 0.267 0.126 0.123 0.124 0.127 1.028 0.000001 10.000 0.160 0.074 0.073 0.073 0.075 1.028 For ro equals one-hundredth micron 0.5 0.0126 78.10 37.03 —174.16 1726.04 1784.69 1.034 0.1 0.0251 | 64.81 30.73 —115.44 256.03 263.45 1.030 0.05 0.0271 54.28 25.74 —T77 .22 83.05 85.51 1.029 0.01 0.0464 33.21 15.75 —23.11 —2.88 —2.96 1.029 0.005 0.0585 26.79 12.70 —12.26 | —4,24 —4.37 1.028 0.001 0.0100 15.58 7.39 —1.22 —0.27 —0.29 1.028 0.0005 0.1260 12.37 5.89 0.48 | 0.80 0.83 1.028 0.0001 0.2514 7.24 3.43 1.56 1.61 1.65 1.028 0.00005 0.2714 §.75 PARA 1.55 1.56 1.61 1.028 0.00001 0.4642 3.36 1.59 1.19 1.19 1.23 1.028 0.000005 0.5848 2.67 1.26 1.01 1.01 1.04 1.028 0.000001 1.0000 1.60 0.74 0.65 0.65 0.67 1.028 air parcel containing a given amount of water creases the vapor mixing ratio w decreases vapor decreases either isobarically (fog and 4 Stratus) or by adiabatic expansion (Cumulus and — paw + wp = paw + 3 >), Piper? BAN; Cumulonimbus). The temperature is thus a given ; function of time ee 4 C IN, ae ate “= pa) (t) (15) 3 T. > PioPnt ATO = paWo The total amount of water substance must remain where wo is the water vapor mixing ratio before constant, so that as the liquid content wz in- condensation begins. 196 The ambient vapor pressure e at the time when the drops have grown from 7; to 7; is thus Pw iP: Bs DY Fipsri®Ary 4aN = Wo = 3 = > FiopariArio € € 3pa This value of e is used in the growth equation (10). For the numerical integration of (10) on the electronic digital computer the method of Runge- Kutta was chosen. It was found that the equa- tion was subject to great computational insta- bility, so that very small time steps had to be used at first. A method was devised for testing when it was feasible to increase the time steps. Even with this procedure the machine time re- quired was very large. It had initially been hoped that it would be possible to carry out computa- tions for a number of cases in which the various parameters (size distribution and composition of nuclei, manner of cooling, etc.) were varied, but = e 10° 10? 10' +— — — 10° o = < ° 2 et —io0’ « eo | - € ° 5 3 i s © —_——__+— —jloe 2 = 3 . ° = & oO ry £ e ° so 2 il aa Cae aS = « | a c = 2 | it © wot = is az a 3 |e $ S | 2 Seio3\—— +— —i0® §& co) E | 2 2° o [= cS 2 —e - | 3 3 i} J = 04 + \0e © = 3 = 2 10°} —— ‘ io! oS _1L LL Pid 1 piu 10'¢ 10° 10? 10'cm oo! oO! 100 1000 microns Nucleus Radius Fic. 1—Assumed distributions of sizes of nuclei (solid curves, cumulative distributions, dashed curves, differential distributions) NEIBURGER AND CHIEN the machine time required was so large that only four cases were computed, representing three rates of cooling and two distributions of sizes of nuclei. The nuclei distributions used—The measure- ment of particulate matter in the atmosphere has been carried out by various means, each capable of counting particles in a portion of the range of sizes which occur. For a long time most counts were of the range called Aitken nuclei (<0.1 micron) on which condensation occurs only at high supersaturation. Recently it has become recognized that the ‘large’ (0.1-1 micron) and ‘giant’(>1 micron) nuclei are the only ones which participate in cloud formation. Size distributions in the various ranges have been summarized by Junge [1952, 1953], Gilbert [1954], Woodcock [1952, 1953}, and Lodge {1955}. Their data were combined into two idealized size distributions, shown in Figure 1. The difference between the two hes in the larger concentration of large and giant nuclei in Type B distribution. In the figure are shown both the concentrations of each size per unit size interval and the cumula- tive concentration of all nuclei greater than a given size. In Type A distribution there are 1030 particles per cm# larger than 0.01 micron, 115 per cm? larger than 0.1 micron, about 1.5 per liter larger than one micron, and much less than one particle per cubic meter larger than ten microns. In Type B distribution the same numbers are re- spectively 1120, 135, 50, and 14. The models of cooling—The models of cooling were selected to simulate in a general way the conditions of formation of Stratus cloud or fog, Cumulonimbus, and trade-wind Cumulus. For the two Stratus cases it was assumed the cooling proceeded at constant pressure at a rate of 6°C per hour. The initial temperature was taken to be 288°K, and the initial relative hu- midity was about 75%. For the first Stratus case the Type A distribution of nucleus sizes was as- sumed, and for the second, Type B. Correspond- ingly, these cases will be called Stratus Case A and Stratus Case B. The pressure was assumed to be 1000 mb. For the Cumulonimbus model we assumed a distribution of vertical velocities based on the measurements of the Thunderstorm Project [Byers and Braham, 1949}. The initial temperature was taken to be 299.2°K, and the relative humid- ity about 75% at about 1000 mb pressure, and adiabatic cooling was assumed. Figure 2 shows the assumed variation of vertical velocity and GROWTH OF CLOUD DROPS BY CONDENSATION 197 1200 20 sooo 15} #00 -5 Fie. 2—Assumed variation of TIME (MINUTES) vertical velocity and corresponding changes of temperature, pressure, and height with time, Cumulonimbus Case; at top, temperature difference between cloud and environment height and the corresponding changes of tempera- ture, pressure and height with time. The Type A nucleus distribution was assumed. The temperature difference between the cloud and the environment, computed from the vertical acceleration, is shown at the top of Figure 2. In the lowest part of the cloud the assumed accelera- tion corresponds to only a small fraction of one degree, and even in the upper part, in which the vertical velocity increases rapidly, it corresponds to the cloud being only about one-half degree centigrade warmer than the environment. In the trade-wind Cumulus model the vertical velocity distribution was based on the observa- tions by Malkus [1954]. The temperature and relative humidity at 1000 mb were assumed to be 301.7°K and about 75%, and the cooling was assumed to be adiabatic. Figure 3 shows the as- sumed variation of vertical velocity and the corresponding changes of temperature, pressure and height for this case. For the trade wind Cumu- lus case the Type B nucleus distribution was as- sumed. The assumed acceleration corresponds to a larger temperature difference between cloud and environment in the lower part of the trade wind Cumulus than in the Cumulonimbus (see upper portion of Fig. 3). The deceleration near the top corresponds to the cloud becoming 1°C colder than the environment. Properly, in computing the cooling the release of latent heat should be computed directly from the amount of liquid condensed at each step. J. E. MeDonald has pointed out that in the early stages of drop growth the difference between this and the assumption of saturation adiabatic equilib- rium might lead to significant differences in the cut-off point between the nuclei which grow to cloud drops and those which remain small. In a future computation it is planned to examine this point. For the computations presently being re- ported the decrease in environmental tempera- ture was assumed to be that resulting from satura- tion adiabatic cooling. The Stratus cases—The variation of the relative humidity during the isobaric temperature decrease (Stratus Case A) is shown in the upper portion of Figure 4, and the variation in size of the differ- ent droplet groups in the lower portion. Satura- tion with respect to a plane water surface is reached after about 2650 sec. Until about 2400 sec the hygroscopic nuclei all increase slowly in size; from then to the time of maximum super- saturation, about 2700 sec, all groups grow more and more rapidly; after that the degree of super- saturation decreases, and the smallest two groups of drops decrease in size, while the groups growing on nuclei of 0.1 micron or larger continue to grow rapidly. By 2800 sec all the growing groups exceed four microns, while the non-growing nuclei re- #0030 Jao 25 20020 100 \5 oO SS b - se TIME (MINUTES) x Sie Fig. 3—Assumed variation of vertical velocity and corresponding changes of temperature, pressure, and height with time, Trade Wind Cumulus Case; at top, temperature difference between cloud and environ- ment 1003 —_—_,—__—.. 1002 —t 100 I} 1000 100 90} Relative Humidity (%) Radius (cm) | [e} 1000 2000 3000 4000 5000 6000 Time (seconds) Fic. 4—Variation of relative humidity and growth curves for various drop-size groups, Stratus Case A 198 GROWTH OF CLOUD DROPS BY CONDENSATION 10 Ti —, A | [ 158000 sec 10° = \ BI \ | 10' rat = | 4 = \ ° \ | € | < \ \ (S ' - +1 + —4| g Ti 3 if | 5 Wd a io! =| | | : | = | | a) \ | © vi 5 0° ry | 2) ° c Vi z fi! SS ICH a) \t 4 ic = a © Ff ee ee | tes 2 F Heathen eal H\\ | ie Hil | 10° ——--+ ———+——. a \ 4 7 AM F \N\y rat ber ara oS 1 Li piiiii meen 10% 10° 10" 10° 10? 10' em 2101 eit 10 10 100 1000 microns Drop Radius Fie. 5—Cumulative drop-size distributions after various elapsed times, Stratus Case A main smaller than 0.2 micron. Thus the separa- tion between the cloud droplets and the non-grow- ing nuclei is established. To see what this droplet growth means in terms of numbers of drops, the cumulative distribution curves are shown for various times in Figure 5. At 2400 sec there is only about one droplet per cm} larger than one micron; by 2700 sec this num- ber has increased to about 250, and there is al- ready almost one per em* larger than four microns; and at 3000 sec there are around 300 per cm’ larger than four microns, and about ten per liter greater than 10 microns. Thus the develop- ment from no cloud to a dense cloud occurs in a very few minutes. However, even after an hour, only one per liter has grown to 20 microns, where it might be expected, by the Langmiur theory, to start colliding with other drops. The development of the cloud, as distinct from the increasingly dense haze, is shown by the differ- ential frequency curves in Figure 6. While the computations for the relatively small number of groups do not establish these curves uniquely, the interpolation of the cumulative frequency curves 199 is sufficiently definite to indicate their general character. The initial nucleus distribution has a mode at about 0.03 micron. At 2700 sec there is just a slight suggestion that a second mode is developing at about two microns. By 3000 sec the mode is well established at 5.4 microns, and the gap between the cloud drops and the inacti- vated nuclei is conspicuous about three microns. The development of the second mode and the gap between the two modes is due to the fact that all the drops forming on nuclei above a criti- cal size (between 0.032 and 0.1 micron) grow, while those forming on smaller nuclei do not grow or actually shrink. This results in a decrease in number, and eventually development of a fre- quency minimum in the vicinity of the critical size. As the cooling continues the mode moves to larger values, reaching 12 microns at 6000 sec, and the gap appears to have moved upward to include seven microns. The nature of the gap is made clear if it is noted that between one and four microns at 3000 sec there are 90 drops, while between four and seven microns there are 310. At 6000 seconds there are 50 drops between two 10 o ao 10' aI = t= 2400 sec 3 \ o 10" ‘ : SNS eroo ne 8 Vi Tes |. 3000 sec = ee \) ie HIE \ [\ 717 8000 see 3 le Noi! i” Sani \\ Ma & Ee Nei 5 & i = als \ = | ‘e 10" | I = £ E \ | | § lit ink rH 3 a orale | et § 10' = \o lia ilies = Sy wt fe | \ \ 10! —- Vey id e ; yi E heaeeice 1 Jed tii itil Jot tit a A \ tot tii 10® 10° 10* 10° to? 10'cm fone) | oO! 10 10 100 1000 microns Orop Radius Fie. 6—Differential drop-size distributions after various elapsed times, Stratus Case A 200 NEIBURGER AND CHIEN 3 Ttelsitinn) ti titi Liquid Content— 1 = 010 micron 0 | | ‘of Sane eel Liquid Content (Grams m7>) fo} 03 Visual Range (Meters) y-Nisual Ronge 2000 3000 Time (Seconds) 4000 5000 Fie. 7—Variation of liquid content and visual range (for light of wave- lengths 4000 and 7000 A), Stratus Case A; thin lines show liquid content in various drop-size groups and eight microns, and 360 between eight and 14 microns. The rapid development of the visual cloud is shown by Figure 7, in which the visual range com- puted from Koschmieder’s formula and the liquid content are shown as a function of time. The visual range drops from 5 km at 2400 see to 50 m at 3000 sec, a change to one per cent of its earlier value in ten minutes. In the same interval the liquid content increases from 3 X 10-4 grams per m*, to 0.3 grams per m*, a factor of one thousand. In the unrealistic conditions postulated (rapid cooling and no fallout) the visual range drops below ten meters and the liquid content rises al- most to three grams per m*. The thin curves in Figure 7 show the contributions of the various size groups to the liquid content. Almost all of the liquid content is due to the 0.1 micron and 0.32 micron groups, with the former accounting for about five-sixths and the latter about one- sixth of the total. This is because the larger nuclei are so much less frequent and the more frequent smaller ones do not grow. The growth curves in Stratus Case B, in which the same cooling rate was used but with many more large nuclei, are shown in Figure 8. Satura- tion with respect to a plane water surface is reached a little later than in Stratus Case A, the peak supersaturation attained is slightly lower, and the amount of supersaturation remains lower throughout the drop growth. However, there is very little change in the rate of growth of the various-sized drop groups, so that the change in the humidity curve reflects almost entirely the additional water required by the growth of the larger number of large drops. GROWTH OF CLOUD DROPS BY 1003 100 2 = ———IE : | 100.1 100.0 100 Humidity (%) Relative x @ wo ooo CONDENSATION 201 fo) 55 Radius (cm) 1034 3000 4000 5000 Time (seconds) Fic. 8—Variation of relative humidity and growth curves for various ity g drop-size groups, Stratus Case B In Case B, in order to determine more closely the separation between the nuclei which do not grow and those which are ‘activated,’ an addi- tional group was inserted, with average equiva- lent radius of nucleus 0.056 micron. It turned out that this group also was activated, so that the boundary between non-activation and activation for this rate of cooling lies between 0.032 and 0.056 micron. In Figure 9 are shown the cumulative distri- butions for Case B. As might be expected, the main difference between these and those for Case A lies in the ‘tails’ of the curves, representing the largest drops. Thus at 3000 see the number greater than four microns is 330 per em’ compared with 300 in Case A, but the number larger than ten microns is 230 per liter, compared with ten per liter in Case A, and 2.3 per liter are greater than 20 microns. At 6000 sec about 50 per liter are greater than 20 microns in radius, compared with one per liter for Case A. Since in light rain there may be from two to 60 raindrops per liter, it will be seen that for the cooling rate assumed the Type B nucleus distribution might be expected to produce drizzle or light rain within a short time (from 5 to 50 minutes) after the cloud formed. As in the cumulative frequency curves, the differential frequency curves for Case B (Fig. 10) show little difference from those of Case A except that the tails show the larger number of large drops. The modes are nearly the same. Similarly the visual range and total liquid content curves are almost identical (Figure 11), since the larger drops are not sufficiently numerous to affect them. The bulk of the liquid content is due to the same range of sizes as in Case A, but the subdivision of this range into an additional group emphasizes the fact that the 0.1 micron group is responsible for the bulk of the liquid content even though T SS | | | ING ee | N A _—— A | TAN Te \ 2400\ 2700", 3000 4] 1-0 \sec \ sec \ “sec | 1=6000 sec = = ats “| it Nae | | | s e E SIE i © ° = 2 E} oO ib S 4 ° = a7 ° iva c — © = oO c ° = s ° o © oO ry 2 € 3 2 | post td oe UIT} 10° 10° 10" 10° 10? lovcm 0.01 (o 10 10 100 1000 microns Drop Radius Fie. 9—Cumulative drop-size distributions after various elapsed times, Stratus Case B the more numerous 0.056 micron group also con- tinues growing. The Cumulonimbus case—The more rapid cool- ing due to the vertical velocity distribution as- sumed in the Cumulonimbus model results in saturation being reached much more quickly than in Stratus Case A (1180 vs 2650 sec), and a slightly higher supersaturation being attained (0.16 vs 0.14 per cent, see Figure 12). Neverthe- less the separation between the activated and the non-activated groups of nuclei is the same; the 0.1 micron group grows rapidly to 100 times its original radius and continues growing, while the 0.032 micron group reaches less than eight times its original radius at the maximum supersatura- tion and then gradually shrinks as the degree of supersaturation goes down. By 1760 see (less than ten minutes after satura- tion) the average radius of all the growing groups exceeds ten microns, and by 3450 sec they all have grown to more than 20 microns. Thus, as shown in the cumulative distribution curves (Fig. 13), there are about 150 per em larger than ten mi- NEIBURGER AND CHIEN crons (although only 12 per 10° cm larger than 20 microns) at 1800 sec; at 2400 sec the number larger than 20 microns has increased to about one per liter, and by 3600 seconds it exceeds 60 per em’. It should be noted that the numbers per unit volume are altered as the air parcel rises because of the expansion of the volume of the parcel with decreasing pressure as well as because of the drop growth. Assuming that the growth by accretion would become significant when the drop radii exceed 20 microns, precipitation development by the warm- cloud process would begin at about 2400 sec (20 min after saturation) when the parcel has reached 2300 m (7500 ft), with a temperature of 12°C. The 0°C level (4750 m) is reached at 3180 sec, and the —10°C (6400 m) at 3400 sec. Thus there would be more than 15 min during which the warm process (collision and coalescence) would be active in producing raindrops before the ice- erystal process could begin, and radar echoes might be expected at about 2500 m (8000 ft). Drop Concentration (cm~>) per Centimeter Interval of Radius ; \ 10'cm 1000 microns Drop Radius Fia. 10—Differential drop-size distributions after various elapsed times, Stratus Case B GROWTH OF CLOUD DROPS BY CONDENSATION 203 10° Lit 3, ® Liquid Content (Grams m°>) & Visual Range (Meters) 0056+} 010 Visual Ronge 0" 2000 3000 5000 Time (Seconds) Fic. 11—Variation of liquid content and visual range (for light of wave- lengths 4000 and 7000 A), Stratus Case B; thin lines show liquid content in various drop-size groups These figures may be compared with the data of Bowen, Smith, and Styles and Campbell cited by Mason [1957] for non-freezing showers in south- eastern Australia. Four of the six cases with radar data had echoes spreading downwards from levels between 7000 and 10,000 ft, and all of the six cases for which radar data was not available had clouds extending above 8500 ft. Mordy and Eber [1954] reported that rain occurred in the cases they studied of the orographic rainfall in the Hawaiian Islands whenever the cloud extended more than 5000 ft above the cloud base of 2000 ft. While the clouds in the cases cited were differ- ent than the thunderstorm Cumulonimbus for which the assumed vertical velocity distribution is typical, the correspondence of the height of radar echo or the thickness of precipitating clouds with that required in the model for development of drops large enough to initiate the warm cloud precipitation process suggests that the general magnitudes involved in the computation have some relationship to natural processes. With the more rapid cooling, the cloud develop- ment occurs more rapidly in the Cumulonimbus case than in the Stratus cases. At 1200 see (Fig. 14) the second mode in the differential frequency curves is just beginning, at about 0.5 micron; less than two minutes later it is well developed at 5.4 microns, with a conspicuous gap at about four microns. The mode moves rapidly to larger sizes exceeding ten microns after five more minutes and reaching 20 microns by 3600 sec. The rapid de- velopment of the cloud is shown likewise by the liquid content and visual range curves (Fig. 15). i) i=) rs Relative Humidity (%) % 3g yee 8 BB 4 Radius (cm) ° 600 1200 1800 2400 3000 3600 Time (seconds) Fic. 12—Variation of relative humidity and growth curves for various drop-size groups, Cumu- lonimbus Case The change in liquid content from 3 Xx 1074 to 0.3 grams per m* occurs in three minutes in this case, compared to ten minutes in the Stratus cases. By ten minutes after saturation the liquid con- tent has reached 1.6 grams per m*, and at 3400 see it reached a peak value of 6.8 grams per m°. The subsequent decrease is due to the expansion of the ascending air parcel, which begins to over- balance the condensation at that time. As in the Stratus cases, the 0.1 micron group is responsible for most of the liquid content. The decrease in visual range in the Cumulonim- bus is likewise more rapid, and the visual range reaches lower values, with a minimum of 7.2 m at 3300 sec. Except insofar as it might affect the condensa- tion process, the development of drop growth by collision and coalescence would not affect the liquid content if we assume that the parcel re- NEIBURGER AND CHIEN ceives as many of the larger drops from above as fall out of it. The visual range, however, would be influenced considerably, for the removal of smaller drops would reduce the scattering area much more than the growth of the larger drops would increase it. The Trade-Wind Cumulus Case—In the Trade- Wind Cumulus Case the large vertical velocities assumed for the lower portion of the cloud (see Fig. 3) resulted in saturation being reached ear- her than in the Cumulonimbus Case; namely, at 816 sec; and a higher maximum supersaturation, 0.24 per cent at 835 sec, being attained (Fig. 16). The second maximum in relative humidity, which occurs near the level of maximum vertical ve- locity, has no significance in terms of activating new nuclei. Because of the higher maximum supersatura- tion, not only is the additional nucleus group at 0.056 micron activated (as in the Stratus Case B), but so is the 0.032 micron group. This, together with the larger number of giant nuclei in the as- sumed initial distribution, results in larger num- E “RSs Ea | N Sige 11300 sec ‘i pas aS TS Sy, 1=|BOO sec ae = a Seta ete2400'sec ——" =I E \ } Valine | E 120 \te1150 \ | \tsi200} 11 p-1= 3600sec JE sec sec | i \ \ eal i Oe ee \ ee TM TT a TTT Number Greater than Given Radius per Cubic Centimeter 10? — —}— = E OE =e =: Ir le = } 10 al ——— 1 oh 10° 10 10° 10? 10' cm ool ol 10 10 100 1000 microns Drop Radius Fig. 13—Cumulative drop-size distributions after various elapsed times, Cumulonimbus Case GROWTH OF CLOUD DROPS BY CONDENSATION 205 bers of droplets of all sizes near the cloud base in the Trade-Wind Cumulus Case than in the Cumu- lonimbus Case (Fig. 17). Table 2 shows the rela- tive values at two corresponding levels above the cloud base. The modal sizes for the Trade-Wind Cumulus Case are taken from the differential frequency curves in Figure 18. At 130 m above the cloud base the trade-wind Cumulus has more drops in all size groups larger than four microns than the Cumulonimbus. How- ever, because of the larger number of small nuclei which are activated, the mode is smaller even at this height. By 800 m above the cloud base this greater competition for the available liquid has resulted in smaller numbers of drops larger than nine microns in the Cumulus Case than in the Cumulonimbus, and a modal size of eight microns as opposed to 11. At the top of the trade-wind cumulus the modal size is 11 microns, and there are about ten per liter greater than 20 microns in radius. Thus it would appear that also in this case precipitation initiation by the warm process 129 ———_+— -—}— - — | | | 1= 1150 sec Ne il | KXA\Q 11200 see —+— =| AX NN \ 1=1300 sec ~ ” = a=) ° iva ° ° = = " = of feat = 1 ‘a i 1=1800 sec — ' i] © TDA SS eee E nt 1= 2400 sec | : WG © 5 Avct-liy) Fo -ts 3600 sec ye NG! ] NS 9 er | . whi | z NP | 1 < Ve | 4 ‘ | IN, \- E 10 \ \ ry i — | \| ey tj § Wait = Yond 2 \ \ | ey What S$ peat $ \lie | s Wat | & Vit a | Li \ 2 io* wd Ln vie oer a fs) \ inn yy | ype Mid it) it 10' Vas Vit \ yi | \ v\y | yout | ; Lut Pani reve OTT OTT 108 10° 10° 10° 10? 10'cm oo! oO! 10 10 100 1000 microns Orop Radius Fic. 14—Differential drop-size distributions after various elapsed times, Cumulonimbus Case 10! Liquid Content 7.20.10 micron 10° 10° 10" a 7 ’ E 2 . E = 5 = 2 see = 10 10° : a & x ° v J =] & i-7 > a 10° 10? 10* 10! 10° | e 10 1200 1800 2400 3000 3600 Time (Seconds) Fic. 15—Variation of liquid content and visual range (for light of wavelengths 4000 and 7000 A), Cumulonimbus Case; thin lines show liquid con- tent in various drop-size groups could be expected, with the possibility of light showers reaching the sea surface. The liquid content in the Trade-Wind Cumulus Case (Fig. 19) increases faster than in the Cumu- lonimbus Case, and the visual range decreases more rapidly. The values at corresponding heights above the cloud base are shown in Table 2. The maximum liquid content in the trade wind Cumu- lus, however, reaches only 2.7 grams per m’, less than one-half that in the Cumulonimbus, because of the continued ascent in the latter case, but the minimum visual range is a little lower because of the larger total number of activated droplets in the Trade-Wind Cumulus Case. Because the 0.032 micron group is activated in Radius (cm) ° 300 600 300 1200 1500 Time (seconds) Fig. 16—Variation of relative humidity and growth curves for various drop-size groups, Trade- Wind Cumulus Case this case the very large number of nuclei in this group makes it the largest contributor to the liquid content. Conclusions—All four cases for which computa- tions were carried out, representing three widely differing rates of decrease of temperature and two different nucleus distributions, showed the tend- ency for the separation of cloud drop sizes from the inactivated nuclei. While the number of groups used in the computation is not sufficient to define it uniquely, it appears definite that a mode in the cloud drop sizes is established shortly after saturation occurs, and that this modal size increases as cooling continues. The mode is in the same general size range as in observed cloud drop distributions, but tends to move with time to larger sizes than in the observed distributions. On the other hand, there are fewer very large drops in the computed distributions than in size distri- NEIBURGER AND CHIEN butions observed in Cumulus congestus and Cu- mulonimbus [Diem, 1948, Weickmann and aufm Kampe, 1953). Since the initial conditions and rates of cooling for the observed cases were doubtless not the same as those assumed for the computations, the com- puted distributions cannot be expected to corre- spond closely to the observed. Nevertheless it is interesting to note that the processes neglected, namely coalescence and in the case of the Cumu- lonimbus the ice-crystal (three phase) process, would tend to keep the modal size small and in- crease the number of very large drops. As an example of the comparison of the com- puted distributions with observed values, Table 3 gives the drop-size distributions observed for three cases of Stratus off the coast of California, taken by blimp (lighter-than-air ship) in the sum- mer of 1945, and the data for the Stratus Case B computation for 3000 and 6000 sec, as taken from Figure 9. The 3000-sec data correspond in a gen- eral way to the observed cases, but even this dis- 10 Sel | Tee ata NN I (Ne i ast 19 E- 7 ‘ - 11200 sec dat C -0 \6o oo} 12900 sacl |} 171800 sec F ce al o Si S =| 1 ao 3 fe R 10" ae = = |e is] & E BSE 6 = 2 \ $ 10° —— \- ———) HE $ WW ae ven bee E 10 E wil it Fi \ \\\ \\\th 10° =! ee i Vi] \ \\ \ Mi We 108 1 u eli 11 1o® 10° 10* 10° 10? 10' cm oo! ol 10 10 100 1000 microns Drop Radius Fic. 17—Cumulative drop-size distributions af- ter various elapsed times, Trade-Wind Cumulus Case GROWTH OF CLOUD DROPS BY CONDENSATION TaBLe 2—Comparison of relative values at corre- sponding levels above cloud base for the Cumulo- nimbus and Trade-Wind Cumulus Cases Distance above cloud base Item | 130 m 800 m Cloud type Cb Cu Cb Cu Time of rise, sec 1300 900 1800 1200 No. of drops per em? larger | than: 20 microns 9X PSE AN bee Ga [ne eg 10-6 10-4 O54, |) L0e3 14 microns | 1.7 X 6 xX 9X | 5X 10-4 1078 10-3 | 10-2 Symicrons, | 15 $< | 14 || 158 100 10-2 1071 4 microns 220 570 | 200 550 1 micron 350 680 | 310 620 Modal size, mi- 5.4 4.3 11 8 cron Liquid content, 0.29 0.4 | ilke7/ 2.6 g/m$ Visual range,m | 45 30 15 8 AEM 10° 4 * t*600 sec 3 1 i a sec s 10 a ~ Ni SoD sec zimra eal 3 XN i eal 1200 sec 5 rT aN iy eee 2 tn lif fF t = ol . 4 ° at aH & F an > Np | Ii ' 10" + Li a: } o 1 aE E i; + |! + 8 £F \hh | e 10° \ ° F | i | \\ E \\\ ‘ " 10 —\,\\ + FE hak | - /\ \N\ | A Pere 1 \ feeeurn| 10® 10° 10° 10° 107 10'cm 0.oO1 oO! 10 10 100 1000 mrom Drop Radius Fic. 18—Differential drop-size distributions af- ter various elapsed times, Trade-Wind Cumulus Case — os Liquid Content (Grams m~>) Visual Range (Meters) af 900 1200 Time (Seconds) 10° '800 1500 Fie. 19—Variation of liquid content and visual range (for light of wavelengths 4000 and 7000 A), Trade Wind Cumulus Case; thin lines show liquid content in various drop-size groups tribution has the modal radius somewhat larger than the observed distributions, and in the 6000- sec distribution the modal radius is more than twice as large as the observed modes. An explana- tion of the difference probably lies in the rapid rate of cooling assumed in the computations. The coastal stratus forms by slow cooling, during which the large drops may tend to settle out of the cloud. Another factor which may contribute to the small modal size in the observed distribu- tions is the fact that the observations were made in the daytime, when the clouds were tending to dissipate. While the initial nucleus distributions and ver- tical velocities used by Howell were quite differ- ent than those we used, his results are quite simi- 208 TABLE 3—Comparison of computed distributions and observed values for Stratus, number of drops per cms Observed (Stratus B) Size range r Case | Case | Case | 3000 | 6000 1 2 3 sec sec micron 1.5-2.9 14} 66; 47} 35) 40 3.0-4.3 70 | 120 | 142 25 20 4.4-5.7 66} 60 | 210 | 230} 10 5.8-7.0 17 17 | 59] 90 5 7.1-8.1 12 9 18 9 5 8.2-9.1 6 2 7 1 5 9.2-10.5 3 0 0 0 5 10.6-11.7 1 6 3 205 11.8-12.8 1 2 7 90 12.9-14.1 1 2 3 28 14.2-15.0 0 0 0 1 15.1-16.0 0 2 0 il i lar to ours. In his cases also the nuclei smaller than one-tenth micron did not grow while the larger ones did. This shows that the general nature of the results is not sensitive to the initial con- ditions, nor even to the error he made in the ap- plication of Raoult’s law. It is planned to undertake computations of the growth of drops by the combined effects of con- densation and coalescence, and subsequently to take account of the three-phase process as well. For this purpose accurate collection and coales- cence efficiency data are needed. At present the uncertainty, particularly with respect to the efficiency of collection of nearly equal sized small drops, would leave the validity of the results of such computations considerably in doubt. Nevertheless the computations may give a con- siderable insight into the precipitation process. Simplified computations have already contributed to the clarification of the problem (Houghton, 1950; East, 1957]. The computations using the electronic digital computer should provide further enlightenment. Acknowledgments—The computations were car- ried out on SWAC, the electronic digital com- puter operated under a contract with the U. 8. Navy Office of Naval Research by the Numerical Analysis Research Group of the Department of Mathematics, University of California, Los Ange- les. Time on the machine was provided without charge, and our gratitude to the Numerical Anal- ysis Research Group and the Office of Naval Re- search is hereby acknowledged. We wish to thank the staff of the Numerical Analysis Research NEIBURGER AND CHIEN Group also for suggestions and assistance in pre- paring the problem for the computer. REFERENCES Auty, T., ano C. A. Mackay, The accommodation coefficient and the evaporation coefficient of wa- ter, Proc. R. Soc. London, A149, 104-116, 1935. ANDERSON, C. E., Diffusion growth problem in cloud physics, Artificial stimulation of rain, Pergamon Press, pp. 153-160, 1957. Barrer, E. O., anp L. 8. Germain, Growth of drops formed in a Wilson cloud chamber, Rev. Sci. Instr., 18, 84-86, 1947. Best, A. C., The size of cloud droplets in layer- type cloud, Q. J. R. Met. Soc., 77, 241-248, 1951. Byers, H. R., anp R. R. Branam, The Thunder- storm, Report of Thunderstorm Project, U. 8. Government Printing Office, Washington, D. C., 1949. CHAPMAN,S., AND T. G. Cow1ina, The mathemati- cal theory of non-uniform gases, Cambridge Univ. Press, Cambridge, 1952. Diem, M., Messungen der Grésse von Wolkenele- menten, II, Wet. Rundschau, 1, 261-273, 1948. East, T. W. R., An inherent precipitation mecha- nism in Cumulus cloud, Q. J. R. Met. Soc., 83, 61-76, 1957. Evpripar, R. G., Measurements of cloud drop-size distributions. J. Met., 14, 55-59, 1957. Friscu, H. L., anp F. C. Coutirns, Diffusion proc- ess in the growth of aerosol particles, J. Chem. Phys., 20, 1797-1808, 1952. GILBERT, J. Y., Condensation nuclei of the Los An- geles region, Research Rep., Dept. of Met., Univ. Calif., Los Angeles, 1954. Houcuton, H. G., Evaporation of small drops, Physics, 4, 419-424, 1933. Hovuaurton, H. G., Preliminary quantitative anal- ysis of precipitation mechanisms, J. Met., 7, 363-369, 1950. Howe t, W. E., The growth of cloud drops in uni- formly cooled air, J. Met., 6, 134-149, 1949. Junag, C. E., Gesetzmissigkeiten in der Gréssen- verteilung atmosphirischer Aerosole tiber dem Kontinent, Ber. Disch. Wetterdienst U.S. Zone, 35, 261-277, 1952. Junas, C. E., Die Rolle der Aerosole und der gas- formigen Beimengungen der Luft im Spuren- stoffhaushalt der Troposphire, Tellus, 5, 1-26, 1953. LanemurrR, I., Super-cooled water droplets in ris- ing currents of cold saturated air, Rep. RL-223, General Electric Research Laboratory, 1944. Lopaer, J. P., A study of sea-salt particles over Puerto Rico, J. Met., 12, 498-499, 1955. Ma xus, J. 8., Some results of a trade-Cumulus cloud investigation, J. Met., 11, 220-237, 1954. Mason, B. J., The Physics of Clouds, Oxford Univ. Press, London, 1957. McDonatp, J. E., Erroneous cloud physies appli- eation of Raoult’s law, J. Met., 10, 68-70, 1953. Morpy, W. A., AND L. E. Esper, Observations of rainfall from warm clouds, Q. J. R. Met. Soc., 80, 48-57, 1954. DISCUSSION NerpurGer, M., Reflection, absorption, and trans- mission of insolation by stratus cloud, J. Met., 6, 98-104, 1949. Rootn, C., On a special aspect of the condensation process and its importance in the treatment of cloud particle growth, Tellus, 9, 372-877, 1957. WEICKMANN, H. k., ano H. J. AurM Kamps, Phys- 209 ical properties of Cumulus clouds, J. Met., 10, 204-211, 1953. Woopcock, A. H., Atmospheric salt particles and rain drops, J. Met., 9, 200-212, 1952. Woopcock, A. H., Salt nuclei in marine air as function of altitude and wind force, J. Met., 10, 362-371, 1953. Discussion (Relating to the two immediately preceding papers.) Dr. Helmut Weickmann—Did you use in your computations nuclei distributions that had ac- tually been measured? Dr. M. Neiburger—This certainly would be desirable. I should have mentioned that when we started we were not very particular about the conditions we chose, because we did not realize what a big job it was for the electronic digital computer. We decided we would start with a composite using Junge’s size distributions for the small ones and then some different values of Lodge or Woodcock for the big ones for a rough mean of a continental aerosol. But since there is never any individual aerosol which is actually like any of these models we used, it would make more sense to use some real ones. The trouble is that nobody has taken simultaneous measure- ments over the whole size range from the very small nuclei to the large ones. It is simple to in- corporate measured size distributions into the pro- gram, if they are available. Dr. Weickmann—Is it important to know the size distribution down to the Aitken range of about 10~-® microns? Dr. Neiburger—Yes, it affects the size in which the cutoff occurs, because there are so many of those. They do pick up water until the critical supersaturation is reached which is then deter- mined by the larger sizes. Dr. A. Goetz—What determines the size of the second maximum? You had it between ten and twelve microns. What parameter would have to be changed in order to shift its size, decrease it, or increase it? Dr. Neiburger—The rate of cooling is one fac- tor which is very important which would mean the vertical velocity in this case; others are rela- tive numbers of large and small nuclei. Dr. W. E. Howell—I realize that it is extremely hard to predict from the initial nucleus distri- bution what kind of cloud one is going to end up with. I remember I failed completely on that point. But I would like to raise the question whether the initial conditions that you have chosen do actually conform with the trade Cumulus and the Cumulonimbus. I believe you started with updraft velocity of 130 cm/sec in the condensa- tion layer of the trade Cumulus; but going back to Dr. Malkus’ paper, I find an estimate of 40 cm/sec from the flight that went exactly through the base of a trade Cumulus, and 108 cm/sec on the flight that went 130 m above the cloud base; and these were the velocities in the center of the updraft, not average across the whole base of the cloud. I think a reduction in the velocity would make a considerable change in the computation, tending toward a much smaller drop number and larger drop size for the trade Cumulus. Alterna- tively with the Cumulonimbus, where you have used an updraft velocity of 30 em/sec, it seems from our experience in flying light aircraft for water seeding of clouds that 200 or 300 cm/sec in the updraft at the base of the cloud would be more realistic. Again the change would be in the direction of reversing the difference that you com- puted between the trade Cumulus and Cumu- lonimbus, giving the Cumulonimbus a much higher droplet number at least in the initial con- densation stage. What happens later on, when coalescence takes over, may be different, of course. Some of us are more interested in the liquid water content as a function of the drop size than we are in the drop number as such, for studying icing, for example. I think you can transform your graphs to show liquid water content by drawing the base line as a line of slope minus 6 on those graphs, which immediately transforms your double mode to a single mode which corre- sponds to the volume median drop size. Dr. Netburger—Taking the last point first, I do not know whether I got them into the version of the figures projected here, but we have some diagrams in which there are curves showing the 210 variation with time of the contribution to the liquid content by the various droplet groups in addition to the liquid content for the whole cloud. The droplet group just a little larger than the modal size is the one that contributes most to the liquid content in most cases. Returning to the question of initial conditions, what I said previously applies as well to the verti- cal velocity as to the nucleus distribution. I would like to do the computations with a case in which the vertical velocities were actually observed si- multaneously with observations of the nucleus size distribution, rather than the one we assumed as ‘representative’. In arriving at the choice we made Mr. Chien plotted from the tables in Dr. Malkus’ papers the vertical velocities for various positions with respect to the cloud base, drew some lines through them, and showed the result to me, and I said, ‘‘Let’s use this line as a sort of compromise among them.” Now, there must have been one or more measurements of a meter and a half or so per second, or our curve would not have been drawn so far over down at the cloud base; but it may be that most of the measurements really gave lower values, and I am inclined to agree that this may have been an unfortunate choice. Dr. Tor Bergeron—I would like to connect the results especially of the papers by Dr. Neiburger and Mr. Mordy with certain things which are known to synopticians and those who observe clouds. Especially I would like to connect it with visibility observations that I have made during 25 summers up in the Swedish mountains, at latitude of 63 1/2° N. I am very pleased to see that gap in the size distribution, that gap between the inac- tivated nuclei as Dr. Neiburger calls them, and DISCUSSION the nuclei that really grow. Because in those lo- calities of which I spoke, from April to September in different months and different years, I had al- ways a gap in the spectrum of visibility ranges. Visibility could be less than one or two kilometers because of fog or mist; but it could never be be- tween two and twenty kilometers. Remember that we were rather far from the origin of the nuclei, that is, from the ocean, and from any industrial pollution also. So we had evidently very little amount of hygroscopic nuclei. Then we have had the visibility from 20 up to 500 km, the latter cor- responding to practically pure air. And those visibilities, of course, occurred in the presence of inactivated nuclei; that is nuclei with sizes gener- ally less than 0.1 micron. At those sizes, the amount of scattered light will be roughly propor- tional to the fourth power of the diameter. In order to get a haze by inactivated nuclei of that size whose visual range could be comparable with that of fog their number should be between 10° and 10° times as numerous as the activated parti- cles. According to Dr. Neiburger’s diagram, as far as I can see, they were more numerous, but only 10 to 100,000 times perhaps. This then will explain that gap in the visibility spectrum; a gap the existence of which has been absolutely im- possible for me to get the continental colleagues in Europe to understand. Therefore any discus- sion in the International Synoptic Commission, and other places, of scales of visibility and such things was always doomed to fail, because Central Europe, England, Eastern United States, and even the coasts of the ocean, would all have rather plenty of big hygroscopic nuclei that grow with increasing relative humidity. The Relation between Cloud Droplet Spectra and the Spectrum of Cloud Nuclei P. Squires AND 8. Twomny Division of Radiophysics, Commonwealth Scientific and Industrial Research Organization, Sydney, NS.W., Australia Abstract—Observations of cloud droplet spectra in various kinds of clouds have shown that the microstructure of clouds very largely determines the efficiency of the coalescence process in forming rain. They have also suggested that the observed differ- ences in microstructure must be primarily explained by differences in the spectra of cloud nuclei in different air masses. This hypothesis has now been confirmed by simul- taneous observations of the spectra of cloud nuclei and cloud droplets. Introduction—In a classical paper, Houghton [1950] discussed the significance of the various processes leading to the formation of precipita- tion. He showed that sublimation onto ice crys- tals could quickly give rise to the formation of particles equal in mass to a droplet of several hundred microns diameter, and that, given a cloud droplet spectrum which was broad enough, raindrops could form by coalescence. The caleu- lations were based on the collection efficiencies computed by Langmuir [1948] and it appeared that only those clouds which had very broad spectra and very large median droplet diameters could form rain by coalescence in a sufficiently short period of time. Telford [1955] has drawn attention to the fact that only a very small frae- tion of the ‘most fortunate’ droplets in a cloud grow to raindrops, and that consequently it is necessary to consider the statistical fluctuations in the growth time of individual drops, arising from the random and discrete nature of droplet growth by collision. In one example, he showed that one large (collector) cloud drop in a hun- dred thousand would experience its first ten col- lisions in five minutes, whereas the average large cloud drop would require 33 minutes to grow to this extent. This kind of consideration makes the production of rain by coalescence somewhat easier, but it still seems to be possible only in clouds with quite broad spectra and large aver- age and maximum drop sizes. Howell [1949] carried out computations of the growth of cloud droplets starting from assumed distributions of cloud nuclei and reached the con- clusion that, as a result of the quadratic law of growth, condensation tended to produce rather uniform droplet spectra. A study of the condensation phase of droplet 9 4 11 growth [Squires, 1952], aimed specifically at find- ing those conditions which could bring about the formation of large droplets, led to the recogni- tion of a kind of threshold effect: The size of the cloud nucleus has relatively little influence on the growth of a cloud droplet once it has grown through the critical activation region. Its influence is largely restricted to determining whether, with a given maximum supersatura- tion in the cloud-forming region, the droplet shall grow unstably or remain in the stable ‘haze’ stage. This simplification of the role of the nu- cleus made it possible to discuss the conditions leading to the formation of only a restricted number of cloud droplets, apparently a neces- sary and certainly a sufficient condition for the production of relatively large droplets. If the number of droplets formed is to be restricted, the nucleus spectrum must be such that only a small number of nuclei become activated; since a nascent cloud in which this has happened has only a relatively small absorptive power for water vapor, the supersaturation tends to rise to relatively high values; if, therefore, the few nuclei already activated are to continue to mo- nopolize the supply of water, all the remaining nucle: must be appreciably smaller than they. Slow upward movement in the cloud-forming region obviously tends to keep the supersatura- tion low and so to help the processes tending to produce few and large droplets. However, a semi-quantitative analysis indicated that the var- lations in the spectra of cloud nuclei from one air mass to another were probably the dominant factor in determining the size of droplets pro- duced by condensation; on the basis of the fact that Aitken counts are higher over the conti- nents than over the oceans, this view appeared 212 to be consistent with the observed predominantly maritime oceurrence of warm rain. The most significant conclusion was that observations of the spectra of both cloud droplets and cloud nu- clei would be required in order to resolve these basic questions in the physics of warm rain. Measurements of droplet spectra—Cloud droplet spectra have been measured by several observers, but generally without any specific reference to the problems mentioned above. Ob- servations were begun near Sydney in 1950 and evidence quickly appeared which seemed to be consistent with the suggestions drawn from the distribution of the occurrence of warm rain and the characteristic difference in Aitken count between oceanic and continental air; there ap- peared to be a significant difference in micro- structure between Cumuli in maritime and conti- nental air masses. Maritime Cumuli contained both fewer and larger droplets. The picture was, however, confused by other effects: as Zaitsev [1950] found, there is a tendency for the drop- let concentration to decrease upwards in clouds. Furthermore, large Cumuli tend to have smaller average droplet concentrations than small ones. It so happened that among the earliest observa- tions, the maritime Cumuli sampled were signifi- cantly larger than the continental Cumuli, and furthermore, the sampling runs in the former, for operational reasons, had not been evenly dis- tributed throughout the vertical extent of the 3250 ft 50 4250 ft Nn o PERCENTAGE OF DROPLETS 10 DROPLET DIAMETER P. SQUIRES AND 8S. TWOMEY clouds, but were mostly taken in their upper regions. It seemed therefore that some or all of the apparent difference between maritime and conti- nental Cumuli could have been due to these two factors: (1) cloud size, and (2) the height of the sampling run above cloud base. In 1953 it was found that there was a serious deficiency in the method then in use for measuring droplet diameter, although the droplet concentrations were not affected. This difficulty was not finally solved until 1954. Further observations in con- tinental clouds in southeastern Australia and of maritime clouds off the Australian coast, as far south as latitude 42°S, and off Hawaii in lati- tude 19°N left no doubt that the suspected con- trast between maritime and continental Cumuli was real. The median droplet concentrations found were 45 and 228 droplets em™ respec- tively. These results are in very good agreement with those of Battan and Reitan [1957] who found median droplet concentrations over the central United States and over the Carribbean which are very close to the medians quoted above for continental and maritime clouds re- spectively. The observations taken in 1954 and later yielded drop sizes as well as concentrations, and confirmed the expected result that a strong negative association exists between droplet size and concentration. Figure 1 shows typical drop- let spectra found in a maritime Cumulus, and 20 40 (») Fie. 1—The mean droplet spectrum at four levels in a trade-wind Cumulus off the east coast of Ha- wali on October 23, 1954; cloud base was at 2200 ft, cloud top at 9500 ft; there was some light rain in parts of the cloud, and turbulence was moderate; droplet concentrations (n) per em# and liquid water content (w) g per m3: 3250 ft, n = 74, w = 0.50; 4250 ft, n = 51, w = 0.53; 5250 ft, nm = 27, w = 0.50; and 6250 ft, n = 30, w = 0.42 CLOUD DROPLET SPECTRA AND THE SPECTRUM OF NUCLEI Figure 2 shows those found in a continental Cumulus of similar size. Interpretation of measurements of droplet spectra—This result was of course quite consist- ent with the observed distribution of warm rain. Indeed, when account was taken of other ob- servations such as those taken on the orographie cloud of Hawaii [Squires and Warner, 1957], there were five groups of clouds, namely ‘dark Stratus,’ Hawaiian orographic cloud, maritime Cumuli, Cumuli in transitional air masses, and continental Cumuli, arranged here in order of in- creasing median droplet concentration: this proved also to be the order of increasing col- loidal stability, as measured by the depth of each cloud type which normally yields rain [Squires, 1958]. The recent calculations of Hocking [1959] on collision efficiencies indicate that the presence of a few relatively large collector drops is not sufficient to permit the coalescence process to proceed efficiently; it is essential that a signifi- cant amount of liquid water should be present in the form of relatively large drops, for only large drops can be efficiently collected. The ex- amples given in Figures 1 and 2 show that in the continental case there is practically no cloud water in the form of drops larger than 20 mi- crons diameter, while in the maritime case, the greater part of the liquid water is in the form of drops larger than 20 or even 25 microns diam- eter. The relationship between the colloidal stabil- ity of clouds and their microstructure seemed therefore fairly clearly established; it remained to be seen whether the difference in microstruc- ture between maritime and continental Cumuli could be explained in terms of the factors con- trolling the initial formation of the clouds. The suspicion mentioned in the introduction, that such contrasts in microstructure could only be explained in terms of differences in the popula- tion of cloud nuclei could not be directly con- firmed, since no method was available for meas- uring this small but important fraction of the Aitken nuclei, which becomes activated at very small supersaturations (rather less than one per cent), and consequently is effective in cloud for- mation. The only alternative was to examine the other possible factors which could influence the microstructure of clouds to see whether any of them seemed adequate to cause the observed dif- ference between maritime and continental Cu- muli [Squires, 1958]. Thus a comparison of flight notes of turbulence experienced in the two kinds 213 9800 ft 605 8200 ft 11200 ft 9100 ft PERCENTAGE OF DROPLETS 8 Ss Oo 10 20 0 10 20 0 10 20 0 10 20 DROPLET DIAMETER (W)) Fic. 2—The mean droplet spectrum at four ley- els in a continental Cumulus over the Blue Moun- tains northwest of Sydney on November 2, 1956; cloud base was 7200 ft, cloud top at 12,000 ft; drop- let concentrations n per em* and liquid water con- ent wg per m*: 8200 ft, n = 490, w = 0.35; 9100 fits 7 — 270s — 0.29; 9800itts 7, — 250, w' =. 0:31; 11,200 ft, n = 350, w = 0.48 of clouds indicated that over the clouds which had been sampled, the updraft velocities were on the average much the same, so that this fac- tor could not be responsible. Further, assuming equal updrafts, it could be deduced from ob- served droplet spectra that the supersaturation in the body of the cloud was higher in maritime than in continental Cumulh, despite the effect of giant sea-salt nuclei in reducing the supersatu- ration in the former. Thus there seemed little possibility that these giant nuclei caused the dif- ference in microstructure by depressing the max- imum value of the supersaturation and reducing the number of nuclei activated. A rather sur- prising confirmation of this latter point was given by simultaneous measurements of spectra of droplets and of giant sea-salt nuclei, made in southeastern Australia, 200 to 600 mi inland. Suppose for the moment that the cloud nu- cleus spectrum, that is, the largest few hundred nuclei, per em’, is invariant, apart from fluctua- tions in the giant sea-salt nucleus content (usu- ally less than one nucleus per em*). Then it seems possible that in air masses which are rich in giant nuclei the supersaturation may be de- pressed by their great absorptive power for wa- ter. This effect, if large enough, could lead to a negative correlation between sea-salt nuclei and cloud droplet concentration, such as is suggested by the continental-maritime contrast. If, as in- 214 10,000 1000 N m-3 160 0 100 200 aS 300 400 nocm Fic. 3—Seatter diagram showing a positive cor- relation between the concentration of cloud drop- lets in inland Cumuli (7) and that of giant sea salt nuclei (NV), near cloud base level; corresponding points for maritime Cumuli would fall in the hatched area dicated by the theoretical analysis quoted above, the effect of the giant nuclei is not great enough to achieve this, one would expect to find no cor- relation between the concentrations of sea-salt nuclei and cloud droplets. In fact, observations taken to test this hypothesis showed a strong positive correlation between sea salt and cloud droplet concentration as shown in Figure 3 [Squires and Twomey, 1958]. While emphatically indicating the absence of the negative correla- tion, and so confirming the theoretical conclu- sion that the giant nuclei are not responsible for the maritime-continental contrast, these ob- servations indicated a positive association in- stead of a random scatter and so raised other questions which will be discussed later. These indirect considerations, although fairly conclusively disposing of alternative explana- tions, could never establish in a final manner whether variations in cloud nucleus spectra were really the major cause of variations in cloud microstructure. For this purpose, there is no sub- stitute for direct measurement of the spectrum of cloud nuclei. Measurements of cloud nuclei—The formidable P. SQUIRES AND 8S. TWOMEY difficulties in the way of this measurement need little emphasis. While it is a simple matter to produce a small expansion instead of a large one, it is not easy to be sure of the desired initial condition of saturation with the accuracy required, which was estimated from the cloud spectra data as being equivalent to a few thou- sandths of a degree C. Again, droplet growth at small supersaturations is naturally quite slow, so that a new problem appears: that of maintaming the supersaturation for periods of minutes. This problem is made the more difficult by the fact that even apart from the inevitable wall effects, the mere growth of the droplets tends to reduce the supersaturation. These problems were first overcome by Wie- land [1956] using a series of diffusion chambers, the top and bottom of which were held at slightly different temperatures, so that a region of small supersaturation was established, and maintained, in the centre of the chamber. Twomey [1959a] used diffusion between a water surface and a dilute aqueous solution of hydrochloric acid to establish and maintain a small supersaturation in a closed chamber. Using this method, Twomey [1959b] established that there are large and sys- tematic differences between the cloud nucleus populations of maritime and continental air masses, at ground level, and was able to show that a representative surface nucleus spectrum, assuming an updraft speed of 1 m see”, would produce a cloud with a droplet concentration of around 500 em™ in continental air and of about 60 em“ in maritime air. (Observed median drop- let concentrations, 228 and 45 respectively.) This result seemed to leave little doubt that the difference in the cloud nucleus population was indeed the main cause of the difference in cloud microstructure. The fact that the com- puted values lay somewhat above the observed ones could be explained if, as would seem likely, the surface layers were richer in cloud nuclei than the air entering the bases of Cumuli. Simultaneous observations were needed to re- solve this question, and these were taken late in 1958, mostly about 200 mi inland from Sydney. The result, comparing observed mean droplet concentrations found on one flight with those computed from the cloud nucleus spectrum ob- served in air sampled below cloud base, is shown in Figure 4 for an assumed updraft speed of 1 m sec’, and in Figure 5 for a speed of 10 m see’. As will be seen, updraft has little effect; CLOUD DROPLET SPECTRA AND THE SPECTRUM OF NUCLEI the agreement is slightly better for the rather more realistic assumption of 1 m see. The surprisingly small effect of updraft speed on the computed droplet concentration is ex- plained by the shape of the observed spectra of critical supersaturations of cloud nuclei. In most eases these spectra could be represented by an equation of the form Neus" where N is the number of nuclei, per unit of vol- ume, with critical supersaturations less than S, and C and k are constants. On the basis of this equation, it has been shown [T’womey, 1959b] that the computed droplet concentration just above the activation region near cloud base is proportional to V"’°"® approximately, where V is the updraft speed. The observed spectra were fitted by values of k ranging from 0.2 to 0.4. Thus the computed cloud droplet concentra- tions were proportional to a power of V between 0.14 and 0.25. The conclusion of some authors that updraft speed has a more considerable ef- fect on cloud microstructure than is indicated by Figures 4 and 5 is essentially due to assuming cloud nucleus spectra which correspond to values of k much greater than those which have been found to fit measured spectra. While observed cloud nucleus spectra are occasionally found which rise steeply over a portion of their range, 1000 800 600 400 200 No. cm? (observed) 100 60 60 100 200 400 600 800 1000 No. cm3 (computed, for V=1m /sec ) Fic. 4—Comparison of mean droplet concentra- tions observed in cumuli with those computed from observed spectra of cloud nuclei, with an assumed updraft speed of 1 m sec’; the dashed line repre- sents exact agreement between observed and com- puted values 1000 600 600 400 200 No. cm73( observed) 60 100 200 400 600 800 1000 No. em™3 (computed, for V=10m/sec ) Fic. 5—Comparison of mean droplet concentra- tions observed in Cumuli with these computed from observed spectra of cloud nuclei, with an as- sumed updraft speed of 10 m sec™!. The dashed line represents exact agreement between observed and computed values the use of values of & of the order of 1 or 2 is unrealistic. In some instances the empirical law of Junge [1953] for nucleus size distribution has been invoked to deduce a supersaturation spec- trum for cloud nuclei. This corresponds, for soluble particles, to k = 2. However, Junge’s law was not intended to represent the supersatu- ration spectrum, but the size distribution of the heterogeneous natural aerosol particles down to 0... The critical supersaturation of a nucleus is influenced by its chemical composition and surface properties, as well as by its size. Even micron-sized particles will remain unactivated at the shght supersaturations occurring in clouds if they are at all hydrophobic. Conclusion—These latest observations seem to provide definite confirmation of the view that cloud microstructure is primarily determined by the spectrum of cloud nuclei. It appears that some continental surfaces at least are source regions of cloud nuclei, so that Cumuli forming in air masses which have passed over them have large droplet concentrations and consequently consist of small droplets. They are therefore relatively inefficient in releasing warm rain, which can form only by the coalescence process. In the light of this result, a tentative ex- planation may be offered for the positive corre- lation observed between cloud droplet concentra- tions and sea-salt content found at places some 216 hundreds of miles inland. It has been observed that the most continental clouds, that is those with the highest droplet concentrations, occur during dry weather. In such weather also, the highest counts of cloud nuclei have been ob- served; unfortunately, simuitaneous observa- tions have not been obtained in these conditions. The salt content of an air mass moving inland is redistributed by vertical mixing during dry weather, so that the concentration in sub-cloud levels is somewhat reduced; but in wet weather the greater part of the salt is washed out. Thus when the air mass concerned has not rained since leaving the coast, there may be a tendency for both the salt and cloud droplet concentrations to be high. As regards the association between dry weather and high cloud nucleus and cloud droplet concentrations, it may be noted that dry weather would favor the formation of nuclei from fires or perhaps by the drying out of soluble salts [Twomey and McMaster, 1955]. It seems almost self evident that the release of particles into the atmosphere from the land surface would be most efficient in dry weather. For when the surface is dry, and evaporation slight, the surface temperature rises to very high values during the day, so that the surface of the soil and the air layer above it are very dry, while the lowermost layer of the atmosphere is strongly unstable. REFERENCES Barran, L. J., anp C. H. Rerran, Droplet size meas- urements in convective clouds, Artificial Stimu- lation of Rain, Pergamon Press, pp. 184-191, 1957. Hocxine, L. M., The collision efficiency of small drops. Q. J. R. Met. Soc., 85, 44-50, 1959. DISCUSSION Houcuton, H. G., A preliminary quantitative anal- ysis of precipitation mechanisms, J. Met., 7, 363- 369, 1950. Howe tt, W. E., The growth of cloud drops in uni- formly cooled air, J. Met., 6, 184-139, 1949. Junce, C., Die Rolle der Aerosole und gasférmi- gen Beimengungen in der Luft im Spurenstoff- haushalt der Troposphire, Tellus, 5, 1-26, 1953. Lanomutr, I., The production of rain by a chain reaction in Cumulus clouds at temperatures above freezing, J. Met., 5, 175-192, 1948. Squires, P., The growth of cloud drops by conden- sation, pt I: General characteristics, Aust. J. Sci. Res., Ser. A, 5, 59-86; pt II: The formation of large cloud drops, /bid, 5, 473-499, 1952. Squires, P., The microstructure and colloidal sta- bility of warm clouds, Tellus, 10, 256-271, 1958. Squires, P. anv S. Twomey, Some observations re- lating to the stability of warm Cumuli, Tellus, 10, 272-274, 1958. Squires, P., anp J. Warner, Some measurements in the orographic cloud of the island of Hawaii and in trade wind Cumuli, Tellus, 9, 475-494, 1957. Tevrorp, J. W., A new aspect of coalescence the- ory, J. Met., 12, 436-444, 1955. Twomey, 8., Condensation nuclei at low super- saturations, pt I: The chemical diffusion method and its application to atmospheric nuclei, Geo- fisica pura e applicata, 1959a (in press). Twomey, S8., Condensation nuclei at low supersatu- rations, pt Il: The supersaturation in natural clouds and the variation of cloud droplet con- centration, Geofisica pura e applicata, 1959b (in press). Twomey, S., anp K. N. McMaster, The produc- tion of condensation nuclei by crystallizing salt particles, Tellus, 7, 458-461, 1955. Wretanp, W., Die Wasserdampfkondensation an natiirlichem Aerosol bei geringen Ubersittigun- gen, E.T.H., Ziirich, Promotionsarbeit 2577, 1956. Zaitsev, V. A., Water content and distribution of drops in Cumulus clouds, Glavaia Geofiziche- skaia Observatoria, Trudy, 19, 122-132, 1950. Discussion Dr. C. E. Junge—This paper seems to me a very important one and I would like to con- gratulate the authors for their work. I would like to comment on two items: (1) Concerning the supersaturation spectra, the reason for the difference in these spectra in continental and maritime air is the difference in the size distribution of the condensation nuclei. The relationship between supersaturation and size can be calculated on the basis of the well- known growth curves of salt droplets. This rela- tionship is somewhat influenced by the chemical composition of the nucleus but not too much as long as a good portion of the nucleus consists of soluble salts. This relationship was recently con- firmed indirectly by measurements of the growth curves of nuclei with relative humidity down to sizes of about 0.01, radius (Ord, Hurd, Hendrix, and Junge, The Behavior of Condensation Nuclei under Changing Humidities, J. Met., 15, 240- 242, 1958). The relationship between supersatu- ration and size can therefore be regarded as re- liable and can be used to convert nuclei size spectra into supersaturation spectra. In our measurements of the size distribution of nuclei, which were confirmed by others. we DISCUSSION found a profound difference between ocean and continent. Figure 6 gives the essence of these ob- servations. Whereas the difference in concentra- tion is comparatively small for the giant par- ticles larger than 1p radius, there is an increasing lack of nuclei over the ocean when approaching 0.1, radius. Unfortunately, there are no data below 0.1 for the ocean, but there is some indi- cation for a secondary increase as indicated by the part with a question mark. Now, the nuclei between 1 and O.1p are the most important ones for cloud-droplet forma- tion. In Figure 7 we converted these size dis- tributions into supersaturation spectra and com- pared them with the observed supersaturation spectra of Twomey. It can be seen that the agreement is good considering the fact that the two sets of data were obtained in completely different geographical locations. The fact that CONTINENT PARTICLES / Cm> —» 0.01 O.l 1.0 —-+ RADIUS OF NUCLEUS Fic. 6—Size distribution of aerosols (1) over land, and (2) over the ocean; the curves give, in contrast to earlier presentation, the total number of particles larger than the indicated value of the radius (cumulative figures) Op PARTICLES / Cm3 0.1% SUPERSATURATION — 1.0% 10 % Fic. 7—Supersaturation spectra, (1) calculated from Curve (1) in Fig. 1; (2) calculated from Curve (2) in Fig. 2; measurements by Twomey over Australia: (3) drought conditions; (4) conti- nental air masses; (5) maritime air masses; the curves give the total number of particles active above the indicated supersaturation our maritime curve is still lower than the cor- responding values of Twomey may indicate some continental aerosol residues in the Australian maritime air where the data were obtained. Two- mey’s data were taken from a manuscript sub- mitted to the Geofisica Pura et Applicata, which Dr. Squires made available to me. (2) The role of sulfate as a substance of con- densation nuclei in areas which are normally considered completely unpolluted, and a pos- sible difference between the southern and north- ern hemispheres. We found that about 50% of the atmospheric sulfur in the northern hemi- sphere is due to industrial activities. Since we know that sulfate is an important constituent of the condensation nuclei, it may be that during the industrial development within the last 100 218 years a gradual increase of condensation nuclei oceurred which may have had some effect on cloud and precipitation physies along the lines Dr. Squires has indicated. The importance of sulfate for the composition of condensation nu- clei in remote places is for instance well demon- strated by the recent finding that in Greenland ice the concentration of sulfate is higher by one order of magnitude than that of all the other constituents, including sea salt. If it is true that the northern hemisphere is, as a whole, polluted to such an extent as indicated, it may be that the difference between ocean and continent with respect to nuclei concentration is more pronounced in the southern hemisphere where this pollution must be negligible, and the original natural conditions still prevail. This should result in a corresponding difference with respect to cloud behavior. I wonder if anybody has thought about this interesting problem? Dr. P. Squires—I am very happy that there are some observations in the northern hemi- sphere which confirm this. Dr. L. J. Battan—lIt is true that the concen- trations measured by the University of Chicago were similar, but there is one thing which I wanted to ask about. As you know, in the mari- time distribution there was a bimodality which was evident after averaging as well as in vir- tually every individual observation. There was one maximum in frequency at a radius of about 15 microns and another at about 5 microns. I wonder if there is anything in your discussion which would suggest that there should be a dif- ference in the shape of the curves as well as in the concentration. Dr. Squires—The methods we have used are not good below five microns. The crux of the matter, however, is how many drops share the liquid water effectively, and the ones down around four or five microns are perhaps not im- portant. Mr. Jerome Namias—The problem of drought, on which I have been working for some 25 years, is very fascinating. Its incipience over the United States in summer is associated with the large- scale features such as I described earlier; namely, the presence of the upper-level contmental anti- cyclone with its neighboring anticyclones in the Atlantic and Pacific. If the continental cell van- ishes, it does so only temporarily so that it re- curs persistently. This happens so frequently that a forecast rule is: ‘All signs fail in times of drought.’ Some recent studies of mine dealing DISCUSSION with the problem of its maintenance suggest some influence of the condition of the soil below. (Discussed in the paper Persistence of Mid- Tropospheric Circulations between Adjacent Months and Seasons, to be published in the forthcoming Rossby Memorial Volume, Stock- holm, 1959.) But the only way I guessed this influence could operate was through a thermo- dynamic mechanism involving the availability or non-availability of the latent heat of vaporiza- tion, depending on the dryness or wetness of the underlying soil. Dryness would perpetuate the upper anticyelone through thermal heating. However, I am intrigued by the possibility im- plied by Dr. Squires that under very dry con- ditions rain might be inhibited because the clouds, once formed, contain too many nuclei and perhaps of an unfavorable kind. It could be that this is one of the feedbacks of nature to provide a sort of memory for long-term situa- tions. Certainly if we isolate the other factors such as I mentioned, and are able to do this quantitatively, the nuclei factor should receive consideration as a feedback. Dr. R. Wexler—Admitting the importance of the nuclei count, other factors may also cause considerable differences between land and sea clouds. The greater moisture content of the air over the sea should cause a greater liquid water content per unit depth of cloud than over the land. Entrainment of drier air into the cloud over the land may inhibit ram development. Measurements in Cumulus over both land and sea, reported by Battan and Reitan in the last Woods Hole conference, show only slight differ- ences in cloud drop size between those which de- veloped echoes and those which did not. Hence, the failure of ram to develop from these clouds cannot be ascribed to the lack of large drops. Dr. Squires—In this series of measurements, the liquid content was perhaps 20 to 30% higher in the maritime clouds. This shght difference would not go far towards explaining the radically different ability of maritime and continental clouds to produce rain by the coalescence proc- ess. Some much more drastic effect, such as Hocking’s calculations suggest, seems to be called for. The differences which cause some clouds to rain while others in the same air mass do not are probably too minute to be observed. At the present stage of knowledge, we merely wish to contrast continental clouds, which are so re- luctant to form rain by the coalescence process, DISCUSSION with maritime clouds, which are so ready to do so. Dr. W. E. Howell—There seems to be a real difference here between conclusions as to the effect of vertical velocity. Computations by Neiburger and myself, among others, seem to show that different nuclei spectra produce clouds in which the difference is much less marked be- cause of the compensating effect that, if there are few nuclei, the supersaturation is forced higher, and a larger proportion of them is ac- tivated. These computations in general led to clouds more uniform than are found in nature, while your figures show the computed droplet concentration more disperse than the natural ones. I am led to wonder whether new classes of nuclei were brought into your computations at close enough intervals to follow the natural process. Dr. Squires—The compensating effect noted by Dr. Howell certainly exists; with a maritime spectrum of nuclei, the supersaturation maxi- mum is twice or three times that computed for a continental spectrum. However, the observed nucleus spectra show a much slower increase in accumulated number with increasing supersatu- ration than has usually been assumed in ecaleula- tions of the condensation process. As a result, an increase in the supersaturation consequent upon an increase in the assumed updraft speed does not result in so large an increase in the number of activated nuclei. The form of the ob- served nucleus spectrum is such that the com- puted cloud droplet concentration increases only as about one-fifth power of the updraft speed. As regards the last point, the droplet concentra- tions were estimated by an analytical method which gives an upper and a lower bound. The starting point was, of course, a curve fitted to the observed nucleus spectra. Dr. Howell—I would also like to question further your assumption that vertical velocities are roughly the same in maritime and continen- tal Cumulus. Malkus has shown that maritime Cumulus are generally rootless, without convec- tive currents extending below the cloud base, the energy for the convection being supplied by the condensation within the cloud and the convec- tive currents becoming stronger as they rise farther above the cloud base; whereas with con- 219 tinental Cumulus the convective currents origi- nate near the ground and, especially in small Cumulus, often deerease in intensity above the cloud base. Even within the cloud, convective currents in maritime Cumulus are generally cited as being weaker than in continental Cumulus. Finally it is my experience that the character- istic differences between maritime and continen- tal clouds appear even within one and the same air mass between clouds that form over the sea and those that form nearby over small tropical is- lands, where vertical velocities are perhaps the principal differences involved. At Mount Washington we have found nearly the same differences in droplet concentration be- tween maritime and continental trajectories that you cite, namely, about 300 per em* in west winds and 60 per em* in east winds; but meas- urements of cloud thickness and liquid water content seem to show that the high concentra- tions occur in clouds formed by slow warm- front lifting. And so I do not think that vertical velocity differences should be ruled out yet as a major factor in determining the droplet concen- tration in clouds. Dr. Squires—It is probably true that up- drafts are somewhat stronger in continental Cumuli than in maritime clouds of the same ver- tical extent. Our maritime clouds were, on the average, a little deeper than the continental ones. In any case, a comparison of subjectively clas- sified turbulence is an extremely crude way of comparing updraft speeds. However, because of the slight dependence of droplet concentration on updraft speed, this matter is not one of great significance. Thus, if the average updraft speed were ten times greater in continental Cu- muli, the nucleus spectra being the same, the ratio of droplet concentrations (continental/ maritime) should be about 1.5; the observed ratio is about 5. Concerning Dr. Howell’s observations of clouds over and near tropical islands, the appearance of a cloud and its chance of producing rain both depend, no doubt, on the pattern of convection below and within it, as well as on its micro- structure. It is relevant to point out that, with the exception of one point, all the data of Figures 4 and 5 were obtained one to two hundred miles inland. A Statistical Study of Cloud Droplet Growth by Condensation Crags Rootru International Meteorological Institute, Stockholm, Sweden Abstract—A droplet spectrum is defined in terms of the moments of its frequency distribution, and equations are derived for the rate of change of these moments. Effects of dissolved salt are not considered; this limits the application of the theory to regions well above cloud base. It is shown that the supersaturation adjusts itself towards a quasi-steady value within a time given by C(N7)~! where N is the number of droplets per cm, 7 is the average droplet radius in em, and C is a coefficient of size order one cm-?. The basic parameter used to characterize the cloud development is the average growth rate of droplet mass. For very slow rates the droplet size spectrum has a tendency to widen, but at higher growth rates a contraction of the spectrum occurs. In the limit the linear width of the spectrum is inversely proportional to the average radius and the standardized form of the spectrum is invariant. Introduction—The development of droplet spectra has long been a major concern of people engaged in cloud-physics research. Several inves- tigators have constructed computation schemes for studying in detail how a droplet spectrum is formed on a specified nucleus population con- tained in a parcel of humid air, as the air is cooled past its point of saturation. The causal chain in such a model is depicted in Figure 1. One may divide the variables of the system into two classes, characteristic of the mesoscale and the microscale of the development. We shall refer to the meso- scale group all those properties of the bulk air, which have to do with the hydrodynamical de- velopment on the scales of convective elements, that is, pressure, temperature, vertical velocity, and content of water in liquid and in vapor state. To the microscale we refer the details of the drop- let size distribution and the chemical properties of the aerosol, as well as any turbulence on scales that may interfere directly with the coalescence process. It is evident from the work of previous investi- gators that, except at the very onset of the cloud formation, the rate of change of the liquid water content of the cloud is almost exactly that which corresponds to complete utilization of the avail- able water vapor. In other words the turnover of water is very large compared to the amounts re- quired to effect what changes in supersaturation that may occur [Howell, 1949; Mason, 1957; Mordy, 1959; Squires, 1952]. Since the warming of the bulk air by released latent heat and the total amount of supported liquid water are the only feedback effects from the condensation proc- 220 ess on the mesoscale dynamic processes, a de- tailed knowledge of the microphysics is not re- quired for the study of these scales. On the other hand the concept of complete utilization of the available water vapor provides an integral con- straint on the development of the droplet spec- trum, which can be formulated in terms of the mesoscale development. If a system is governed by integral constraints, this forms an ideal basis for an attempt to study its development in some suitable statistical terms. The present paper is an example of such an ap- proach applied to a simple system with some re- semblance to what occurs in natural clouds, namely, a droplet population with negligible salt content, embedded in an air parcel subject to steady cooling. The basic model—Consider a parcel of humid air containing a nearly uniformly distributed pop- ulation of cloud droplets. Let the size distribution of the droplets be defined by a frequency distri- bution n(r), such that Vn(r)6r is the number of droplets in the size range r to r + 6r, to be found in an air sample of volume V. We shall denote averages taken with respect to this distribution by a bar (for example, 7). Let us further introduce a normalized size variable x, defined by TAQ i= ee) r (1) The distribution n(r) is completely defined by its moments N,, poo | r’n(r) dr (v = 0, 1, 2, -:: 0 Ny = (2) Our goal is to be able to describe the develop- CLOUD DROPLET GROWTH BY CONDENSATION ment in time of these moments. We shall however find it convenient to use the equivalent set of variables No , 7, @’(v > 1), with x defined by (1). The time derivative of an average of a function of r will depend in part on the rate of growth of the individual particles, and in part on any changes in the distribution that may occur be- cause of turbulent transfer or settling of particles, or by coalescence. We shall assume that particles are conserved in our air parcel, hence only the particle growth by condensation is considered. In that case the operations of averaging and differ- entiation with respect to time are interchangeable in order, so for any differentiable function f(r) | (Gh: = ; LES TES (3) f@) = ai” The growth equation and the basic integral con- straint—The equation governing the growth of a cloud droplet in a cloud of moderate droplet con- centration can be stated in the form dr A 8} #4 (s_ 2) (4) The definition of the different symbols is briefly discussed in Appendix I. In order to simplify the arithmetic operations / is neglected. This step may also be defended on the grounds that recent ex- perimental work by the author (unpublished) in- dicates that its value is less than 2 * 1074 em, which limits its effects to the initial stage of cloud development. So our basic equation is dr A ( 2) eee eal (ic eee a dt r r Our next aim is to see how the supersaturation S is coupled to the cooling rate. The total rate of production of liquid water in a unit volume of cloud is (4a) q -/ ndnr? (5) 0 dt Substitution for dr /dt from (4a) yields q = 4rnNoA (SF — B) (5a) The rate of change of the supersaturation is de- termined by the combined action of temperature change and water consumption. Denoting the mixing ratio of vapor to dry air by w, and satura- tion conditions by subscript s 1 dw ws dt we dt ds d w— ws dt dt Ws 7 w dws (6) 221 Microscale Mesoscale Fic. 1—An example of the logical intereonnec- tions between the variables in a model cloud; mesoscale variables steer the development on the microscale, but they are not influenced by the de- tailed behavior of the microscale variables Now —pa ~ where pz is the density of the dry air, is clearly identical with q in Eq. (5). Further- more w, is a function of pressure and temperature, and since the system we consider does not ex- change heat with its surroundings, it is a function of the pressure and of the total amount of con- densed water. So (6) may be rewritten as dS —4rN,A(ST — B) w dt Pas we dw,dp — dws dw op dt dw dt w dws | 4rN oA - E dee (St — B) Ws OW Pals w dws dp w? dp dt (6a) We observe that dw,/dw < 0 anddw,/dp > 0, so that (6a) is of the form dS/dt = —(1/r)[S — g(p, w)dp/dt]} (7) where 7 and g are positive definite functions of p, w, and #, and dp/dt is prescribed by the particular mesoscale system of which our air parcel is thought to be a part. The time constant 7 is seen to have the form ¢c/Nor, where the coefficient ¢ is a function of p and w. Its evaluation is discussed in Appendix II. We find that its magnitude is about 1 sec/cm? for fairly typical conditions ob- tained in low clouds. Hence our time constant will normally be much less than one minute, while the convective processes in a cloud generally have time scales of several minutes or more. It follows 222 that the actual supersaturation should be very well approximated by S = g dp/dt (8) Since the supersaturation is so sensitive to the actual rate of condensation, we may conclude that the water vapor will be condensed as fast as it is being made available by the cooling. The total rate of condensation is thus a function of the ex- ternal influences on our air parcel, and essentially independent of the details of the condensation process. If we denote this rate by qo, then from (5a) SF — B = qo/4rN 0 (9) This relation holds as long as the implied varia- tions in S are slow in a time scale defined by the time constant T. The development of the droplet spectrum—The growth equation for a single drop as stated in (4a) can be transformed into a set of equations for the statistical parameters of the droplet spectrum by the following procedure. First we introduce the variables 7 and 2, as defined above, cet ks ene: d B qe aa aN sea) We shall limit ourselves to cases where r < 27, that is, the upper limit for the droplet size is twice the mean radius. In that case the fractions in (10) can be developed in geometric series (10) dee ee dt ; dt M (10a) AS AB = en) se 22) Ol See) Tr p=0 T p=0 After rearrangement of terms (1 + 2) dr r3 dz 3A dt A dt * (10b) = > [Sr — (1+ »)B](—2)# u=0 Averaging all terms in (10) yields dr? Ss SS SB SA dha s (11) + (esr = @ tw Ble# p=2 This equation is used to eliminate d7*/dt from (10b). If now the equation is multiplied through with an arbitrary power x” of 2, and averages CLAES ROOTH are taken again, then the following expression is found for the rate of change of any a” et dx = 2SF 3B)x™ ates aii ae 24 + > (-pelsr — 1 + Bl 2 iz = [gmt aa ze(am + zmt)| It was shown above that the expression Sr — B is a function of the enforced average rate of mass growth. We shall introduce the notation Si —B=oB in (11) and (12), and so, with some transforma- tion of the derivatives, our system of equations is re diln7 £2 a =o+ » (—1)'e — px AB dt ro Fara ee ae is In (z")1m = — (26 = 1) (13) 8 , gmth — gh(gm + amt) > Stes ) ———_ SF fzS ( ) ( K = This is an infinite set of equations, each con- taining an infinite number of terms. The possi- bility of deriving solutions to the system depends upon the rate of convergence of the series. Some conclusions may be drawn however, without ac- tually going to the problem of solving the equa- tions. It is first of all clear that the condensation process is a powerful agent for changing droplet spectra only when the droplets are small. All rates are inversely proportional to 7*. It is further evi- dent that spectra of the same shape, in the sense that the set of a” is identical between them, will develop in the same way if subject to the same forcing in terms of the specific growth rate o. A doubling, say, of the mean radius, will carry with it the same change in spectral shape irrespective of whether it means growth from 2 to 4, or from 20 to 40 microns. The time scale would differ by a factor 1000, however. We shall now have to consider the actual values of the parameter o. Figure 2 shows how it is re- lated to vertical velocity and total number of ac- tive particles, for the pressure 900 mb and tem- perature 10°C. The relation is rather insensitive to variations in p and 7 within the range of me- teorological interest. It is obvious that values suf- ficiently low to change the sign of the leading terms in (13) would hardly occur. Points corre- CLOUD DROPLET GROWTH BY CONDENSATION sponding to cases studied by Howell [1949] and Mordy (1959) have been entered in the diagram. It is interesting to note that Howell’s Case 3 gives a value of o = 1.5, which brings it near to the critical value. This case, somewhat inexplicably, according to Howell, produced a very wide droplet spectrum. The condensation nuclei were considered in his computation, and they would obviously tend to widen the resulting droplet distribution, but it seems obvious that the param- eter o should be of comparable importance also in case the dissolved salt in the droplets is considered. The fact that the parameter o normally is ex- pected to be much larger than unity lends support to the concept that (13) might be approximated by retaining only the first term on the right-hand side in each equation. The equations can then be solved, to give the relations 7 = F(t = 0) + 3ABat z(t) \t/n F(0) \ee-/¢ a(0)) ra) The variable x was normalized with respect to F. If we replace it by another variable £, defined by g= t// x2 = (r — 7) /+/ (r — 72 then (14) gives em (ft) \1lm 2(0)\12 fet) \ tie se ea = =1 (16) en(0) x°(t) x(0) that is the standardized distribution is invariant within this approximation, and the linear width of the spectrum, as represented by the standard deviation of r from its mean, is proportional to Fate. (14) (15) It may seem surprising that the capillarity term in the growth equation should play the same role irrespective of the size of 7, but this is explained by the fact that the supersaturation is inversely proportional to 7, and so is the capillary term. If the ambient supersaturation is high, then the difference in growth rates between various mem- bers of the droplet population is controlled by the factor r in the growth equation. But if the supersaturation is low, then the capillary term may overcompensate the effect of this factor. The influence of the parameter o on the individual droplets is seen clearly if we write the growth equation (4a) in the form rar: GSE 1 1 (17) ABdt fr r 99° ase ] | Howell | x | Mordy | | a 100 Mardy |» | Mordy III] © w, cm/sec Fic. 2—The growth forcing functions as a func- tion of particle number and vertical velocity; the points marked represent conditions in computa- tions made by Howell [1949] and Mordy [1959]; lines connect points representing identical nucleus spectra Differentiation of the right-hand side with re- spect to ¢ gives the result that the growth rate is largest for the droplet size r = 27/(¢ + 1). It is interesting to note that the condition for contrac- tion or expansion of the linear width of a fairly narrow spectrum is identical with the condition that the radius of maximum growth rate be smaller or larger than the mean radius. Possibilities for further development—The model considered in this paper is very simple. The re- sults are equally simple and straightforward. It seems possible, therefore, that the present formu- lation of the problem of droplet growth by con- densation could be used as a starting point for more sophisticated studies of cloud development. It is my opinion, that such extended models should not attempt to treat this particular prob- lem in greater detail, but that one should build up the more complicated system by blocks repre- senting its different aspects, each of them being simplified in similar extent as the present study. The cloud base problem, that is, the question of finding the most economic treatment of the initial cloud formation and the question of which char- acteristics of the nucleus spectrum one should use, in order to describe its behavior in clouds in the most pregnant way, seems to be one that should be attacked along these lines. In the coalescence problem the obvious approach is a generalization of the ordinary ‘basic-cloud-versus-growing-rain- drop’ approach by consideration of a basic cloud droplet population, described essentially with the method advanced here, and a population of drop- lets growing by coalescence alone. One would also like to approach the problem of whether drop 224 size distributions exist that are stable in a sta- tistical sense, like the spectral-energy distribution in statistical turbulence theory. Acknowledgments—The approach used in this paper was inspired by the lectures on statistical methods in hydrodynamics given by Phil D. Thompson at the International Meteorological Institute in Stockholm in 1958-59. Numerous dis- cussions about problems in cloud physics with Wendell A. Mordy, of the same Institute, pro- vided the stimulus necessary to complete it. APPENDIX I The Growth Equation The equation for droplet growth by condensa- tion has been discussed extensively by several au- thors. We shall only briefly state the results, a more thorough discussion with references is found in the paper by Neiburger and Chien in this vol- ume. One considers the spherically symmetric case of diffusion of water vapor onto a droplet of radius r. The steady state provides a satisfactory ap- proximation for natural cloud conditions. The boundary conditions are given by the vapor den- sity in the surrounding air, taken to be valid at infinite distance from the drop, and the equi- librium value at the droplet surface, with due ac- count taken of the capillary effect, and of the heating of the drop by the condensation. In ad- dition one has to consider the vapor-pressure jump at the phase boundary. In the case where the exponential influences of heating and surface tension can be linearized equation (4) becomes (nuclei neglected) dr _ Dps 1 27M dt i MI2Dp; r + I RTr KRT? where the symbols used are D diffusion coefficient for water vapor in air K heat conductivity of air L latent heat of condensation for water M molecular weight of water R universal gas constant DISCUSSION degree of supersaturation absolute temperature vapor pressure jump parameter droplet radius surface tension of water ps vapor density at saturation SL ya ttc) APPENDIX II Evaluation of the Time Constant in Eq. (7) The time constant 7, that occurs in (7) for the rate of adjustment of the supersaturation in a cloud, is defined by 1 Od In ws | 4rN AF -=/1 w T ow PaWs If we substitute for A from Appendix I, and transform the partial derivative inside the brack- ets, then 1 | d In ws =a 4rN FD -= 7p. == SS > T oT ow ML?Dp; KRT? But (T/dw), = —L/c, and (0 In w,/OT), = ML/RT*, so il MLw 4arN TD -= 1 +t —— ee eee T Cale 1 ML?Dps KRT? At p = 900 mb and 7 = 283°K a 0.5/N oF REFERENCES Howe tu, W. E., The growth of cloud drops in uni- formly cooled air, J. Met. 6, 134-149, 1949. Mason, B. J., The Physics of Clouds, Oxford Univ. Press, 470 pp., 1957. Morpy, W. A., Computations of the growth by condensation of a population of cloud droplets, Tellus, 11, 16-44, 1959. SaqurreEs, P., The growth of cloud drops by conden- sation, I, General characteristics, Austr. J. Sct. Res., 5, 59-86, 1952. Woopcock, A. H., Salt nuclei in marine air as a function of altitude and wind force, J. Met., 5, 362-371, 1953. Discussion Dr. M. Neiburger—I do not want to pretend that I followed the details of the computation, but I think this approach looks like the sort of thing to which we will have to turn. Now, I am not sure I see how the variations with time of the shape of the spectrum are taken into account, or how one goes back to the variations of shape from the time spectrum if the spectrum has to be char- DISCUSSION acterized by an increasing number of modes be- cause of the change in shape. But I do agree, as in the case of Dr. Mason and his colleagues in their paper in the Transactions of the Faraday Society, that we have to go to some representation of the spectrum other than the complete details. [had thought of the possibility of using some sort of other representation in the computation we did, to see changes in the results these had with time. Dr. Claes Rooth—The change in time of the spectrum shape is given by the relative changes in magnitude of the moments of the distribution. The indication here is that any such changes ‘xaused by condensation alone would be very slight. The formation of bimodal or more compli- ‘ated distributions has to be attributed to mixing and differential settling, and to the partition of the nucleus spectrum into an actively growing part and a population of stable nucleus droplets. Such a partition will always occur at cloud base, but the nucleus droplets would normally be very difficult to observe because of their small size, and most observed cases of bimodality do not fall into that category. As to the number of moments that have to be considered, it would obviously have to be quite large, if an accurate description of something like the shape of a bimodal distribu- tion is desired. But the situation might be differ- ent if we want to apply our model to the develop- ment of a physical property of the spectrum other than shape, since a property like average mass or scattering power is defined by one or a few of the moments of relatively low order. Dr. W. Hitschfeld—I would like to comment on the particular method you chose for represent- ing the distribution. You chose an average over number. I think this may be mathematically at- tractive, but physically such averages are not very attractive because the distributions we know and measure are always incomplete, notably at the small-radius end. Any ignorance there would lead to serious difficulties in evaluating a ‘mean radius.’ Mean radii, weighted by particle mass, surface area, or scattering power, or in fact any power of the radius higher than the first are largely free of this defect. Dr. Rooth—Vhe set of zero-centered moments of the distribution function, as defined here, is equiv- alent to the set of mean radii derived with an ar- bitrary power of the radius as a weighting func- tion (see Eq. (2)). If one wants to study the time variation of a property like the scattering power, he has to make use of the proper moments of the distribution. If the physical property with which he is concerned involves the radius taken to a power equal to or higher than that involved in the basic averaging process, then he is all right, otherwise he is certainly worse off than if he had included the moments of lower order. Take, for instance, the supersaturation. It is seen to be in- versely proportional to the linear mean radius. Now this fact is a consequence of the physical model used, and not of the particular method of mathematical analysis applied to it. If we have available a measured droplet spectrum, together with data on the cooling rate and other pertinent factors, then our best estimate of the ambient supersaturation in the cloud would obviously be founded on the observed mean radius, in spite of the fact that this is less well defined than any of the weighted averages suggested. So I do not go along with the direct implications of your com- ment, but if I may interpret it as a warning against the pitfalls of uncritical combination of mathematical method and physical reasoning, then I would support it wholeheartedly. The Nucleation and Growth of Ice Crystals B. J. Mason Imperial College, London, England Abstract—Experiments to test the ice-nucleating ability of a wide variety of natural mineral dusts suggest that kaolinite is probably the main source of atmospheric ice nuclei, and that a number of silicate nuclei may be preactivated. The nucleating prop- erties of artificial ice nuclei, mamly morganic compounds, are discussed in relation to their solubility, crystal structure and, especially, their surface structure. It is shown that nucleation occurs preferentially at steps and other special sites on the substrate surface. A particular nucleating substance has a critical temperature above which it may act only above water saturation but below which it may act as a sublimation nucleus pro- vided the air is supersaturated relative to ice by a well-defined critical value. Ice crystals growing as hexagonal plates on the surface of covellite show interference colors which give a measure of their thickness. Colored growth layers may be seen spreading across the crystal surface, careful measurement of which provides new infor- mation on the mechanism of crystal growth. The growth of snow crystals in a diffusion-cloud chamber shows that, over the tem- perature range 0 to —50°C, the crystal habit undergoes five changes, and these are con- trolled primarily by the temperature and not the supersaturation of the vapor. Their habit changes are not affected by the pressure and nature of the carrier gas, or by the presence of aerosols, as reported by Japanese workers. Natural and artificial ice nuclei—In an at- tempt to discover the nature and origin of at- mospheric ice nuclei, we have tested the ice- nucleating ability of various types of soil particles and mineral dusts. Of the 80 substances tested, 16, mainly silicate minerals of the clay and mica groups, were found to produce ice crystals in supercooled clouds at temperatures of —15°C or above, and of these, seven were active above —10°C (see Table 1). The most abundant of these is kaolinite with a threshold temperature of —9°C. Ten natural substances, again mainly silicates, were found to become more efficient ice nuclei having once been in- volved in ice-crystal formation, that is, they can be pre-activated or ‘trained.’ Thus, ice crystals grown on kaolinite nuclei, which are initially active at —9°C, when evaporated and warmed to near 0°C in a dry atmosphere, leave behind nuclei which are thereafter effective at —4°C. Particles of montmorillonite, another im- portant constituent of some clays, and which are initially inactive even at —25°C, may be pre-activated to serve as ice nuclei at tempera- tures as high as —10°C. It is suggested that although such particles can initially form ice crystals only at Cirrus levels, when the ice erys- tals evaporate they will leave behind some ‘trained’ nuclei which may later seed lower clouds 226 at temperatures only a few degrees below 0°C. On this hypothesis, the fact that efficient nuclei are occasionally more abundant at higher levels would not necessarily imply that they originate from outer space. Indeed, in view of our tests on particles of stony meteorites, produced both by grinding and by vaporization, which show them to be ineffective at temperatures above —17°C, it appears that atmospheric ice nuclei are predominantly of terrestrial origin, with the clay minerals, particularly kaolinite, being a major source. This work is described m greater detail by Mason and Maybank [1958]. Although a good deal of work has been ear- ried out in different laboratories on the ice- nucleating ability of a wide variety of chemical compounds there has been little agreement in the results. Careful tests in our laboratory indi- cate that many of the published results are spurious because of the presence, in the air or the chemicals, of small traces of silver and free iodine, leading to the formation of silver iodide. If all such trace impurities are removed, many of the substances that have been suggested are found to be quite ineffective. The first six substances listed as artificial nuclei in Table 1, all being practically insoluble, are active to the extent of about one particle in 10* producing an ice erystal at the indicated NUCLEATION AND GROWTH OF ICE CRYSTALS 227 TaBLE 1—Substances active as ice nuclei Natural nuclei Artificial nuclei ———_ — 2s ae | | j Threshold Substance | Crystal symmetry areca Substance Crystal symmetry fem: | cc | | IP Se Covellite | Hexagonal | —5 | Silver iodide Hexagonal | —4 Vaterite | Hexagonal —7 | Lead iodide Hexagonal | —6 B-Tridymite Hexagonal | —7 | Cuprie sulphide Hexagonal —6 Magnetite | —8 | Mercurie iodide Tetragonal —8 Kaolinite | Triclinic | —9 | Silver sulphide Monoclinic —8 Glacial debris —10 | Silver oxide | Cubie —11 Hematite | Hexagonal } —10 | Ammonium fluoride | Hexagonal -9 Brucite | Hexagonal —11 | Cadmium iodide | Hexagonal | —12 Gibbsite | | —11 | Vanadium pentoxide | Orthorhombic —14 Halloysite | Monoclinic —13 | Iodine Orthorhombic —14 Voleanic ash | —13 | Dolomite Hexagonal } Sane | Biotite —14 Vermiculite Monoclinic | —15 | Phlogopite | ls Fic. 1—A deposit of oriented, hexagonal ice crystals growing on special impurity sites on the surface of a single crystal of silver iodide; whole field = 300u Fig. 2—An epitaxial deposit of ice crystals growing only at the steps of a hexagonal growth spiral on cadmium iodide threshold temperature when introduced into a supercooled water cloud in either a diffusion- or mixing-cloud chamber. They also cause highly purified bulk water to freeze at these same tem- peratures. Ammonium fluoride, cadmium iodide, and iodine, being soluble in water, are inactive in a water-saturated atmosphere but produce ice crystals in an environment maintained between water and ice saturation, at the temperatures indicated. In effect, small particles of these sub- stances act as sublimation nuclei, but on enter- ing a water-droplet cloud, they go quicky into solution and lose their ice-nucleating ability. In addition to the substances shown in Table 1, whose nucleating ability increases steadily as the temperature is lowered beyond the threshold value, we find a number of metallic oxides (for example, oxides of copper, cadmium, manganese, and tin) are slightly active at temperatures be- tween —6 and —10°C but show no appreciable increase in nucleating ability at lower tempera- tures; again, these appear to act as sublima- tion rather than freezing nuclei. Although there is a tendency for the more effective nucleators to be hexagonally symmetri- cal crystals in which the atomic arrangement is reasonably similar to that of ice, Table 1 shows that there are a number of exceptions; but, for all the substances which are active above —15°C, it is possible to find a low-index crystal face in which the atomic spacings will differ from those in either the basal or prism faces of ice by only a few per cent. However, there is not, in general, a high correlation between the threshold nuclea- tion temperature and the degree of misfit between the ice and the nucleus structures, indicating that nucleating ability is only partly determined by simple geometrical factors. Full details of our work on artificial ice nuclei are given in a paper by Mason and van den Heuvel [1959]. Detailed study of the epitaxial growth of ice crystals—In an attempt to investigate the nu- cleating mechanism in more detail we have studied the growth of ice on well-defined faces of single crystals of various nucleating agents under carefully determined conditions of tem- perature and supersaturation. Oriented deposits of ice crystals have been observed on hexagonal crystals of silver iodide, lead iodide, cupric sul- Fra. 3—A time sequence of photographs showing the orientation and growth of thin hexagonal ice plates on a single erystal of covellite, taken at about 30-sec intervals; left to right from the top fr eet ses Load t Syeer NUCLEATION AND GROWTH OF ICE CRYSTALS 229 phide, cadmium iodide, and brucite, and also on freshly-cleaved muscovite mica, mercuric 1odide, iodine and calcite. This study has revealed the great influence of the surface structure and topography of the host erystal. The ice crystals show a marked tendency to form at special sites on the surface, particularly at the edges of growth or cleavage steps. This is illustrated in Figures 1 and 2. Crys- tals will appear at these preferred locations un- der ice-supersaturations of order ten per cent but much higher supersaturations exceeding per- haps 100%, are required for nucleation on the very flat, perfect areas of the substrate surface. Some very striking colored effeets, which re- veal a good deal about the detailed mechanism of ice-crystal growth, have been observed with ice crystals growing on a blue erystal of natural cupric sulphide (covellite). Figure 3 shows the crystals viewed in reflected white light. Being only a few thousand angstroms high, the hexag- onal plates show interference colors which give a measure of their thickness. Inspection of four parts of Figure 3 taken at about 30 sec intervals, reveals that some crystals grow considerably in diameter with no discernible change of thick- ness. This suggests that molecules arriving on the upper surface of the crystal are not assimi- lated but migrate over this surface and are built in at the edges. The crystals generally thicken after meeting a cleavage step on the substrate or when they contact a neighboring crystal. This is shown very well by the line of five crystals which rapidly change color (thickness) after contact, with colored growth fronts spreading across their surfaces. These ‘accidents’ probably set up dislocations in the crystals from which growth fronts can emanate. There is a marked tendency for the ice crystals to cluster along cleavage steps on the substrate. A erystal setting astride a step may be of different thickness on either side as indi- cated by the two-tone effects of certain crystals in Figure 3. In order to investigate the nucleating prop- erties of these single crystalline surfaces in more detail, careful measurements have been made, at different temperatures, of the minimum vapor supersaturations required to produce oriented deposits of ice crystals. The results for silver iodide are as follows. At temperatures above —4°C only water droplets were deposited. As the temperature was lowered from —4°C to —12°C, increasing numbers of ice crystals formed on selected sites provided that the air surpassed saturation relative to liquid water. At tempera- tures below —12°C, however, crystals appeared when the air was sub-saturated relative to water but supersaturated relative to ice by at least 12%. The observations suggest that between —4 and —12°C the initial deposit may have been liquid water, perhaps in droplets too small to be seen before they froze, while at tempera- tures below —12°C erystals may appear by sublimation direct from the vapor phase. Very similar results have also been obtained for lead iodide, cupric sulphide, and cadmium iodide, with shghtly different critical tempera- tures and supersaturations in each case, and also for an aerosol of silver iodide introduced into a diffusion cloud chamber in which the supersaturation could be accurately determined. These cloud-chamber experiments show that, even at temperatures above —12°C, it is not necessary for a silver iodide particle to enter a supercooled droplet in order to produce an ice crystal; it can act by adsorbing a film of liquid water. Full details of the work deseribed in this section appear in a paper by Bryan’, Hallett, and Mason [1960]. The growth forms of snow crystals—Ore of our most fascinating problems, and one of great importance to the crystal physicist, concerns the remarkable variety of shapes exhibited by natural snow crystals. In order to discover the factors which influence the crystal form, and in the hope of discovering the exact nature of the controlling mechanism, we are growing artificial snow crystals under very carefully controlled conditions. The crystals are grown on a thin fiber running vertically through the center of a diffusion cloud chamber in which the vertical gradients of temperature and supersaturation can be ac- curately controlled and measured. The results of many experiments covering a temperature range of 0 to —50°C and supersaturations vary- ing from a few per cent (in the presence of a water-droplet cloud) to about 300% (in very clean, droplet-free air) consistently show that the crystal habit varies along the length of the fiber in the following manner: 0 to —3°C Thin hexagonal plates —3 to —5°C Needles —5 to —8C Hollow prisms —8 to —12°C Hexagonal plates 2 tor —16r© —16 to —25°C —25 to —50°C Dendritic crystals Plates Hollow prisms This scheme is very similar to that which we obtained in earlier experiments in which crys- 230 tals were grown in small-scale supercooled clouds, and on metal surfaces, but the simul- taneous growth of all the crystal forms on the same fibre has revealed the sharpness of the boundaries between one habit and another. For example, the transition between the plates and needles at —3°C, and that between hollow prisms and plates at —S8°C, oecurred within temperature intervals of less than one degree. Crystals having an almost identical variation of habit with temperature have also been grown from the vapor of heavy water but with the transition temperatures all shifted upwards by nearly 4°C, corresponding to the difference be- tween the melting points of H.O and D,O. These experiments, reported by Hallett and Mason [1958], appear conclusive in showing that very large variations of supersaturation do not change the basic crystal habit as between prism and plate-like growth although, of course, the growth rates are profoundly affected. On the other hand, the supersaturation appears to govern the development of various secondary features such as the needle-like extensions of hollow prisms, the growth of spikes and sectors at the corners of hexagonal plates, and the fern- like development of the star-shaped crystals, all of which occur only if the supersaturation exceeds values which correspond roughly to saturation relative to liquid water. The effect of suddenly changing the tempera- ture and supersaturation of the growth form of a particular erystal could be observed simply by raising or lowering the fiber in the chamber. Whenever a crystal was thus transferred to a new environment, the continued growth as- sumed a new habit characteristic of the new conditions. For example, when needles grown DISCUSSION at about —5°C were lowered in the chamber to where the temperature was between —12°C and —16°C, stars grew on their ends. In a similar manner it has been possible to produce combination forms of all the basic crystal types. Such radical changes in the crystal shape could not be produced by varying the super- saturation at constant temperature but, in some cases, were produced by only a degree or two change in temperature at constant supersatura- tion. The growth habit of ice crystals is not es- sentially altered by growing them in hydrogen or air at reduced pressure as recently reported by Japanese workers. The exact nature of the growth mechanism by which only a degree or two variation in tem- perature can completely change the crystal shape and which, furthermore, allows the habit to be reversed four times in a temperature range of only 25°C, is still something of a mystery. However, our current studies of the detailed evolution of the various crystal forms, in relation to their surface properties, are yielding some valuable clues. REFERENCES Bryant, G. W., J. Hatverr, anp B. J. Mason, The epitaxial growth of ice on single-crystalline sub- strates, Physics and Chem. of Solids, 1960 (in press). Haier, J., anp B. J. Mason, The influence of temperature and supersaturation on the habit of ice crystals grown from the vapour, Proc. R. Soc., A 247, 440-453, 1958. Mason, B. J., anp J. Maypanx, The ice-nucleating properties of some natural mineral dusts, Q. J. R. Met. Soc., 84, 235-241, 1958. Mason, B. J., np A. P. vAN DEN Hevuvet, The prop- erties and behavior of some artificial ice nuclei, Proc. Phys. Soc., 1959 (in press). Discussion Dr. C. L. Hosler—How did you measure the supersaturations ? Dr. B. J. Mason—This is a very important question. In a diffusion chamber one can not measure the supersaturation if one disturbs the air. So what I tried to do and what worked out to be almost too good to be true, was to insert two parallel sheets of ice, one at a temperature level 7, and the other at a temperature level T.. Knowing the temperature profile, one can actually caleulate what the supersaturation will be at any level in terms of the upper or lower temperature, and so on. One can check it be- cause one can arrange that the supersaturation at one particular level, according to theory, would be just 100 or 98% or whatever value one wants to take. Now put im a source of nuclei, say sodium chloride; let it settle down in this region and observe optically. For in- stance, if it started to grow where the humidity was 78% and that coincided with the theory, one would be quite happy about the theory. DISCUSSION 231 That is the way you check it. That is the way in which we essentially measure the supersatura- tion over this very wide range from zero to 300% relative to ice. Mr. C. E. Anderson—lf I understand, you have also examined the influence of low pres- sure, and have found no influence? Dr. Mason—That is right except the erystals grow faster; the shape is completely unaltered. This is in conflict with the Japanese work. Dr. H.-W. Georgii—Would you suggest there is a relation between the misfit and the special nucleating temperature for any given mineral? Dr. Mason—TVhere are really two threshold temperatures. There is the highest temperature at which ice crystals appear at water saturation, —4°C in the case of silver iodide, and —12°C, below which crystals appear in a sub-water saturated atmosphere providing the supersatu- ration relative to ice exceeds 12%. One can ex- press the nucleating ability in terms of the supersaturation or of the temperature. Dr. Georgii—lIs it a specific value? Dr. Mason—Yes, for a specific subject. Dr. W. Hitschfeld—I would like to ask, in connection with your table of ‘activation tem- peratures’ whether you agree that there is no sharply defined temperature at which a given nucleus becomes active, but rather there is a range in temperature in which activation is pos- sible with varying likelihood. Dr. Mason— Activation temperature’ means the highest temperature at which one gets one ice crystal from 10,000 particles of seeding agent. If you want 1 in 100 for most of those sub- stances, take two degrees away from those figures. Dr. Hitschfeld—Closely associated is the ‘time of activation.’ In earher papers from Dr. Mason’s laboratory (for example, Bigg, Proc. Phys. Soc. B, 66, 688, 1953), time was accorded an important place. But in some of the current work, one feels that not enough emphasis 1s always placed on it. Recent experiments at MeGill University (Barkhe and Gokhale, Part Ill of Scientific Report MW-30, Stormy Weather Group, July 1959) have clearly shown that the probability of a freezing occurrence is an approximately lear function of the time, and so the possibility arises that nuclei can become active at relatively higher temperatures if you wait long enough. This is a factor which meteorologists need to take most carefully into account when they apply the nucleation infor- mation which is becoming available. Dr. R. Weaxler—You mentioned kaolinite. Is this common on the ground and in the at- mosphere ? Dr. Mason—It comes in very small particles, and, in fact, in nature is hard to find in particles greater than oné micron, and so it is in very finely divided form. It can not be very abundant. Most soils containing kaolinite tend to have a good vegetation cover, but obviously wherever this is disrupted it gets into the air. I would also say that voleanic ash when weathered produces kao- linite. So, I think, there is a reasonable amount in the atmosphere, but not too much. The only di- rect evidence that we have is that of the Japanese workers who often detect kaolinite particles in snow crystals (K. Isono, Jap. J. Geophys., 2, no. 2.1959). Dr. H. Weickmann—I am very happy about your paper because it is closely connected to the questions which I had posed in my letter of invitation: Can we prove that true sublima- tion nuclei do not exist and that AgI acts only as a freezing nucleus? There remains, however, a problem which is still unsolved: How does nature achieve the formation of ice at 0°C? So far in controlled laboratory tests this has not been achieved, not even with the best known freezing nuclei. It appears however that our experiments with freshly cleaved mica come closest. It would be very interesting if Dr. Mason would repeat those using his well con- trolled diffusion chamber. In our experiment breathing against the mica plate caused the formation of a very thin film of water on the mica plate recognizable only due to the for- mation of Newton interference rings. The crys- tallization of this film is easily visible. It started either at the very thin edges or at steps and irregularities in the mica plane. Crystalliza- tion occurred between 0° and —1.0°C wet bulb temperatures, that is, at room temperatures well above freezing! Erroneously we had assumed a practically perfect match between the geo- metric similarity of the cleaved plane and the base plane of an ice crystal but later we found out that the lattice structure of the cleaved plane is that of quartz and that it should —12°C. This ex- periment seems to indicate that we have to differentiate between the crystallization of a thin liquid film and that of bulk water, and nucleate at best at around 232 that perhaps here les the answer to the aston- ishing performance of nature. Dr. Mason—Yes, indeed, that is right. Dr. U. Nakaya—My diagram was obtained in the case of mixing or convection and in your case the crystal is produced by diffusion of vapor. The experimental procedures are dif- ferent, still both diagrams are quite similar, al- though a little different im some portions. The most characteristic type of snow crystal, the dendritic crystal, appears in the same tempera- ture range in both diagrams. One thing to be mentioned is that the meaning of supersatura- tion in our case is different from the ordinary definition. In the case of mixing, usually minute fog particles are abundantly produced in the atmosphere where the crystals are made. We measured the total water content (minute drops plus vapor) by the gravimetric method, and calculated the degree of supersaturation. Our supersaturation, therefore, means the sum of water vapor and minute drops. It is very in- teresting that these droplets behave just like water vapor when they are very small, say, the order of one micron in diameter. Watching the process of growth of a snow crystal through a microscope, it is observed that the minute drops DISCUSSION spread over the surface of the snow crystal without leaving any trace of the drop shape. Ii the drops are larger, say, several microns in diameter, they freeze in a drop shape on the surface of snow, thus giving the rimed snow crystal. Dr. Mason—I think the mechanism respon- sible for the habit changes of ice crystals must be a surface phenomenon, because otherwise one might expect some difference between heavy and ordinary water. This one does not get; in fact, I can produce all shapes by adding in- creasing but still very small quantities of al- cohol. It must be a question of the properties on the surface, and changing the surface prop- erties. It can not be a question of the structure of the ice itself. This is one thing one has to worry about; if there is a minute amount of impurity, the experiment can come to grief. Dr. Nakaya—We must be very careful in this point. Sometimes a very small amount of impurity changes the shape of crystal com- pletely. We have the experience that an inde- tectable amount of silicone vapor changed the erystal shape completely. Dr. Mason—This I would expect. The Influence of Climate and Weather Elements on the Activity of Natural Freezing Nuclei Hans-WALTER GEORGIL Department of Meteorology and Geophysics, University of Frankfurt, Frankfurt, Germany Abstract—The paper presents results of parallel measurements of freezing nuclei and condensation nuclei. The results gained at different places on the European continent in different altitudes and under purely maritime conditions are compared. They clearly show the effect of various weather conditions and the influence of certain trace sub- stances in the ground layer of the atmosphere on the freezing-activity of the aerosol particles. Introduction—During the past years simul- taneous investigations on condensation nuclei and ice nuclei were carried out by the author in order to gain a deeper understanding of the mechanism of heterogeneous phase transition in supercooled clouds. The experiments on conden- sation nuclei were performed on the basis of the results gained by Junge [1952] on the size distri- bution and the composition of the atmospheric aerosols. Our studies led to the detection of cer- tain relations between the freezing nuclei and the aerosol particles of certain size ranges. The present paper will deal mainly with three problems: (1) What is the difference between the results gained under different weather conditions and at places with different climatic conditions? (2) In what way does the altitude at which the measurements are performed influence the activity of the freezing nuclei? (3) How is the activity of natural freezing nuclei influenced by the presence of certain trace substances and pollutants? The freezing nucleus measurements were per- formed in an 865-liter mixing cloud chamber which was described in detail elsewhere [Georgii, 1956]. The following places were chosen for the investigations: (a) at Frankfurt am Main as base station, (b) on the Taunus ridge in an al- titude of 800 m, 20 mi from Frankfurt (Taunus Observatory, Mt. Kleiner Feldberg), (c) on the summit of the Zugspitze at 3000 m altitude, and (d) on Valentia Island off the west coast of Ire- land as maritime station. On the Irish west coast westerly winds prevail supplying a constant rate of fresh maritime aerosol particles. Before dealing in more detail with the prob- lems mentioned above, some earlier results of our research will be briefly summarized. The concentration of freezing nuclei active within the temperature range 0°C to —30°C shows a di- urnal trend with a minimum in the early after- noon and a maximum during the night. This diurnal fluctuation runs parallel to that of the large condensation nuclei. It is most pronounced in summer and on days with calm sunny weather. The measurements taken on the Zugspitze show an inverse trend, namely, maximum in the after- noon, minimum during the night, indicating that the diurnal fluctuation of the numbers of ice nuclei is caused mainly by vertical convective mixing. The evaluation of the parallel measurements of freezing nuclei and condensation nuclei (the latter were measured in three size ranges sepa- rately, Aitken nuclei, ‘large’ nuclei, and ‘giant’ nuclei) revealed that there definitely exists a re- lation between the concentration of freezing nu- clei active above —30°C and the number of large condensation nuclei. This result was confirmed at all three continental stations and could be supported by direct methods, namely, by filtra- tion of particles of definite size from the air sample to be checked on ice nuclei. On the other hand it could be proved that the Aitken nuclei are ineffective as freezing nuclei above —80°C. A detailed description of these investigations is being published [Georgii, 1959]. Influence of weather elements—The evaluation of the daily measurements showed a considerable fluctuation of the concentration of freezing nu- clei from day to day. The great number of counts made at Frankfurt permitted an analysis of the relation between the occurrence of certain weather phenomena at the time of the measure- ments and the concentration of freezing nuclei 233, HANS-WALTER GEORGII 400 350 300 250) 200 150 100 1956 — Monthlyaverage © radiation days 7 days with showers | . days with continous rain = ground fog in evaporation = days with high wind speed in 700 mb level 1957 Fic. 1—Influence of certain weather-conditions on the freezing nucleus concentration at Frankfurt am Main active above —30°C. Figure 1 shows the aver- age monthly freezing nucleus concentration com- pared with the concentration on such days when a certain weather situation prevailed. It can be seen in Figure 1 that the concentration of freez- ing nuclei is above average: (a) During and af- ter showers as well as at the time of a strong vertical mixing. The shower activity causes a down draft of a great number of highly active freezing nuclei into the air layers close to the ground, especially of such particles which have already participated in the formation of the shower in higher levels of the atmosphere. Some- times, such ice particles still preserve an ice-like structure on their surface which enables them to become effective once again at temperatures only slightly below the freezing point (preactivated or ‘trained’ nuclei). (b) During evaporation of fog droplets. Very high values of freezing nuclei were always found on days with ground fog, es- pecially when the fog was in a state of evapora- tion. The activation of the nuclei may be ex- plamed in connection with drying of their surface. Possibly electric phenomena at the sur- face of the nuclei occur in connection with the evaporation which may also be partly responsi- ble for the increased freezing activity [M/viihlei- sen, 1958]. (c) When there are high wind speeds in high altitudes. The strong upwinds are mostly connected with high wind velocities near the ground thus removing the air pollution in the Rhein-Main basin. The concentration of freezing nuclei in the ground-layer of the atmosphere is remarkably low: (a) On summer days with intensive solar radiation. The convection causes an up-current of the aerosol particles while the air sinking down by continuity reasons has a small aerosol content. (b) On days with continuous precipita- tion leading to a wash-out of freezing nuclei. The influence of the different weather ele- ments on the concentration of freezing nuclei active above —30°C is summarized in Figure 2. The annual average value of the 308 measure- ments carried out from May 1956 to May 1957 at Frankfurt was used as 100%. The other aver- ages refer to this value subject to the above de- scribed meteorological phenomena taking place. It can be recognized that on days with evaporat- ing fog, showers, and advection of fresh air masses in higher levels the concentration of freezing nuclei was higher than normal and amounted respectively to 138, 127 and 109% of the annual average. On the other hand the con- centration on days with rain and on days with calm radiation weather reaches respectively only INFLUENCE OF WEATHER ELEMENTS ON FREEZING NUCLEI 235 80 and 84% of the annual average. The mean fluctuation of the individual values was also eal- culated and entered in Figure 2, showing that the quantitative interpretation is representative. The evaluations entered in Figures 1 and 2 in- dicate the effect of different weather factors on number and activity of freezing nuclei. It is now of interest to compare the Frankfurt analy- sis with those gained at the other locations. Influence of climatic elements on the concen- tration of freezing nuclei—As already mentioned in the introduction of this paper the investiga- tions were extended to three continental and one maritime location. A summarizing survey of the results is shown in Figure 3. The mean numbers of freezing nuclei, and large and Aitken nuclei at Frankfurt were set equal 100 and the average values of the measurements at the other loca- tions were related to the Frankfurt average. Fig- ure 3 presents an interesting result. Compared with the Frankfurt average the freezing nucleus concentration found at Mt. Kleimer Feldberg is 63%, on the Zugspitze 80% and at Valentia Is- land 27%. Referring however to the very active freezing nuclei agitating ice nucleation above —20°C, the picture becomes still more amazing since the absolute concentration of these freezing nuclei is higher on Mt. Klemer Feldberg than at Frankfurt (125%). For Valentia Island we found 65% and for the Zugspitze 44%. The distribution of the condensation nuclei shows a considerable deviation from these re- sults. For the large nuclei (r above 0.2 ».) the numbers found at Mt. Klemer Feldberg amount to only 18%, on the Zugspitze to only 4%, the corresponding values for the Aitken nuclei are 9% and 4% of the Frankfurt concentration. With regard to Valentia Island large nuclei could only be measured during a short period of time and are therefore not included in the summary given in Figure 3. The number of Aitken nuclei was only 2% of the Frankfurt mean number. This low number of Aitken nuclei at a maritime site is in good agreement with the findings of other investigators. The concentration is of the same order of magnitude as given in the survey by Landsberg [1938] in which the results gained at 21 different maritime locations are compiled and it Is In agreement with the assumption by Mason and Moore [1954] that all Aitken nuclei found over the oceans are of continental origin. A full account of the investigations on Valentia Island had been given by Georgii and Metnieks [1958]. The vertical decrease of the particle number 140 130 120 10 100 90 80 7, 70 60 50 Relative number of freezing nuclei 40 30 20 Fie. 2—Annual summary of the evaluation of the weather effect on the freezing nucleus con- centration at Frankfurt am Main of the atmospheric aerosols as measured by us at the three continental stations at 100 mtrs, 800 mtrs and 3000 m altitude corresponds closely to former investigations not only as far as the trend is concerned but also with respect to the absolute concentration. In this connection attention is di- rected to the investigations by Weickmann [1957] on Aitken nuclei or the investigations by Dreis- bach [1956] on the vertical distribution of large nuclei. During 1955 and 1956 Reiter [1955] con- ducted measurements of Aitken nuclei on the Zugspitze to supplement his air electric measure- ments and found values very close to our own results. While our investigations confirm the strong vertical decrease of condensation nuclei of all sizes they show also clearly that the number of freezing nuclei (particularly the most active) decreases much slower. This means that the properties responsible for the phase transition 236 freezing nuclei 140 y 20 130 DNe 0 120] 100 Relative concentration (eZee) continental = mar. continental mar. continental HANS-WALTER GEORGII continental mar. Fre. 3—Comparison of the concentration of freezing nuclei at different locations (concentration at Frankfurt am Main equals 100%) (1) Frankfurt; (2) Taunus Observatory; (8) Zugspitze; and (4) Valentia Island liquid to solid improve with altitude in the atmosphere. This fact can be caused by the following reasons: (1) The particles of indus- trial and anthropogeneous origin in the ground layer of the atmosphere are poor ice nuclei. The concentration of these pollutants decreases rather rapidly with increasing altitude. (2) The high concentration of certain trace gases in the Frankfurt area causes an inactivation of the surface properties of the nuclei. In the free at- mosphere the concentration of these gases is neg- ligible. (8) Although the majority of our meas- urements including these at the high altitude station were carried out at outside air tempera- tures above the freezing level the influence of preactivated nuclei cannot be fully disregarded. The effect of an increased activity of freezing nuclei shows up also in the phenomenon de- scribed above, namely, the occurrence of very active freezing nuclei in the ground layer after showers. In a recent paper of Kassander and others [1957] the presence of preactivated nuclei in the free atmosphere is also indicated. During flights over the southwestern United States air samples from ice clouds were taken and warmed above freezing level in a cloud chamber. Later the air samples were cooled once more and pro- duced ice erystal concentrations of 100 per liter at only —10°C. Laboratory tests finally suc- ceeded in conserving the efficiency of the ‘trained’ nuclei after they had kept above 0°C for several hours [Mason, 1959]. Inactivation of freezing nuclei by surface re- actions—In order to clarify the problem of in- activation of freezing nuclei as a first step, parallel measurements of the concentration of certain trace gases in the atmosphere of the heav- ily industrialized Rhem-Main Basin were taken. Applying the methods of trace-gas analysis by Junge we sampled SO., NH;, and NO., gases which were thought to be able to act as surface poisons. Table 1 gives a survey of the relation between the concentration of each of these gases and the activity of freezing nuclei. The latter is expressed as activity quotient, being the ratio of the number of large condensation nuclei and freezing nuclei active above —30°C. High fig- ures of the activity-quotient stand for low ‘qual- ity’ of the freezing nuclei. The figures indicate clearly that the increasing concentration of the three gases in question de- teriorates the activity of the freezing nuclei. However these parallel measurements of freez- ing nuclei and trace gases do not give an un- equivocal answer which of the three gases is the most effective in inhibiting the ice nucleation although it seems according to Table 1 that the nuclei react rather sensitive on the ammonia INFLUENCE OF WEATHER ELEMENTS ON FREEZING NUCLEI concentration. In most cases the fluctuations of the three gases listed in Table 1 run parallel and are regulated by the actual weather situation. In an attempt to study the poisoning effect more in detail we have started a series of tests of the freezing nucleus concentration in an air sample to which a known volume of the trace gas is being added. In addition to each ice-nuclei count a second run in a sample of untreated out- side air is made to give information of the nor- mal conditions in the atmosphere at that time. It may be mentioned that in the course of these experiments the method of counting the ice erystals in a dish containing concentrated sugar solution was applied which was first invented by Bigg [1957]. The results with this counting method agree quite well with our usual pro- cedure of counting the ice crystals in a parallel light beam, the diameter of which can be nar- rowed by shutters when increasing ice-crystal numbers afford it. Figure 4 shows the results of a first series of 20 inactivation tests using NH, as poisoning agent. In order to exclude the natural fluctua- tion of the absolute number of freezing nuclei on the different days when the samples were taken, the numbers found in normal outside air above —18°C and —21°C respectively were set equal 100. The numbers of freezing nuclei ac- tivated in an air sample containing 1500 ppm TaBLE 1—Relation of various gases to the activity of freezing nuclei onan te toe Activity quotient | Number of cases Ammonia 0-8 93 6 8-16 133 58 16-32 143 8 32448 210 3 72-88 235 3 Nitrogen dioxyd 0-5 | 92 | 15 5-10 135 60 10-15 158 | 13 15-20 175 | 4 Sulfur dioxyd 0-160 tosh |) a0 160-320 134 34 320-480 174 5 237 ~ \ a b a 5b Fie. 4— Inactivation of freezing nuclei by adsorption of NH; within the tempera- ture ranges 0 to —18°C and 0 to —21°C, respectively; (a) freezing nucleus concentration in normal outside air equal 100; (b) freezing nucleus concen- tration after addition of 1500 ppm NH, to the air sample NH,, the ammonia concentration during these experiments, is a proportion of 100. It can clearly be recognized that the presence of this amount of ammonia reduces the number of ac- tive freezing nuclei remarkably. This first series of tests applying a rather high concentration of NH;, much higher than can be expected nor- mally in the atmosphere, was intended to present a rough estimate on the effect of NH, as surface poison. An extension of these measurements with lower concentration of NH, and with the addi- tion of other trace gases 1s under way. The results of these experiments can be con- sidered to be in this first stage as a confirmation of the investigations by Birstein [1954] on the inhibition of ice nucleation of silver iodide par- ticles by certain chemicals. Testing the effect of NH,, Birstein started with a partial pressure of 0.1 mm increasing it in stages up to 7 mm. The ice-nucleation ability decreased consequently. At a partial pressure of 7 mm no ice crystals were observed above —20°C. The most effective chem- icals to inhibit ice nucleation were amines, methylated and ethylated amine. From Bir- stein’s results the conclusion must be drawn that 238 the inactivation of the particles is irreversible, meaning that the trace substance is not only loosely adsorbed but more firmly bound to the particle by chemisorptive forces. The parallel measurements of condensation nuclei and freezing nuclei carried out at different places prove that besides the importance of ch- matic conditions the threshold temperature of ice nucleation of a given particle is not only a function of the constitution and size of the par- tiele but is also influenced by environment con- ditions. The presence of certain trace substances and their concentration will effect the activation of the particle within a wide range of tempera- ture. Preactivation of the nucleus extends the temperature range for ice formation to higher values than normal while surface poisoning will drop the threshold temperature to lower values. The factors will most certainly affect the op- eration of the mechanism of the rain formation process as postulated by Bergeron and Findeisen. The investigations reported in this paper have been sponsored in part by the Geophysics Re- search Directorate, ARDC under contract AF 61 (514)-927 through the European Office. REFERENCES Biaa, E. K., A new technique for counting ice-form- ing nuclei in aerosols, Tellus, 9, 394-400, 1957. Birste1n, 8S. J., Adsorption studies of heterogeneous phase transitions, Geophysical Res. Papers 32, 1954. DreissacH, K., Die vertikale Verteilung der grossen Kkerne in der unteren Troposphire und ihr Zu- sammenhang mit dem elektrischen Potential- DISCUSSION gefille, Archiv Met. Geophys. Biokl. A 9, 36-53, 1956. Georcu, H-W., Eine neue Mischwolkenkammer fiir wolkenphysikalische Untersuchungen, Be- richte Met. Geophys. Inst. Frankfurt, 6, pp. 25- 30, 1956. ; Groreu, H.-W., Uber die Eiskeimbildung in unter- kiihlten Wolken in ihrer Abhdangigkett vom at- mosphdrischen Aerosol, Habilitationsschrift Uni- versitat Frankfurt, 110 pp., 1959. Georcit, H-W., ann A. L. Merninks, An investiga- tion into the properties of atmospheric freezing nuclei and sea-salt; nuclei under maritime condi- tions at the west coast of Ireland, Geofis. Pura e Appl. 41, 159-176, 1958. Junar, C., Gesetzmissigkeiten in der Gr6dssenver- teilung atmosphirischer Aerosole tiber dem Kon- tinent, Berichte Dt. Wetterd. US Zone, 35, 261- 277, 1952. Ikassanper, A. R., L. L. Sims, anp J. McDownatp, Observations of freezing nuclei over the South- western United States, The artificial stimulation of rain (H. Weickmann and W. Smith, eds.) Pergamon Press, pp. 392-403, 1957. LanpsperG, H., Atmospheric condensation nuclei, Ergebnisse Kosm. Physik, 3, 155-252, 1938. Mason, B. J., Recent developments in the physics of rain and rainmaking, Weather, 14, 81-98, 1959. Mason, B. J. anp D. J. Moorr, The concentration, size distribution, and production rate of large salt nuclei over the oceans, Q. J. R. Met. Soc., 80, 583, 1954. Miutersen, R., Elektrische Ladungen auf Kon- densationskernen bei Wasseraufnahme und Ab- gabe, Naturwissenschaften, 45, 34-35, 1958. Rerter, R., Ergebnisse luftelektrischer Messungen auf dem Zugspitzplatt, Geofis. Pura e Appl., 30, 155-169, 1955. Weickmann, H., Recent measurements of the verti- cal distribution of Aitken nuclei, Artificial Stim- ulation of Rain (H. Weickmann and W. Smith, eds.) Pergamon Press, 81-88, 1957. Discussion Dr. Bernard Vonnegut—I am very much in- terested in the observation that the effectiveness of ice-forming nuclei tends to increase with con- vective activity suggesting that these particles may be brought down from aloft. I think this observation might shed some light on the ex- perience of my colleague, Charles Moore in bal- loon flights in thunderstorms over New Mexico. He observed on two flights that the exterior of large thunderstorm clouds was covered by a very thin mass of ice crystals that were not present in the interior. This observation, I think, suggests that air on the outside of the clouds, being pulled down from aloft, is high in nuclei content. In connection with ammonia and its ef- fect on nuclei, it is worth mentioning Reynold’s work of some years ago, in which he found am- monia had a very strong effect on silver iodide in the reverse direction; it appeared to increase the activity of silver iodide quite remarkably. Dr. 8. Birstein—With respect to inhibiting, it is gratifying to find that Dr. Georgii reports these effects. I gave a paper at the last Woods Hole Meeting, and I have another paper this afternoon on this subject. I think there is a lot more that can be said about it after that paper. Dr. B. J. Mason—We all agree that Dr. Georgii’s investigation is a very welcome one, DISCUSSION and I agree with nearly everything he says; I just want to raise the problem of contamination, to see how important that is. There is some advantage of living in a filthy atmosphere! If one takes an absolutely clean silver surface and puts it in the London air, for a few minutes, it absorbs enough iodine or sulfur to form patches of silver iodide of silver sulfide on which oriented ice crystals may be formed. If one irradiates silver iodide with ultraviolet, one finds in the first five minutes that its nucleat- ing properties actually improve because its irradiation removes certain impurities; but thereafter its nucleating effectiveness decays log- arithmically. So, this shows that impurities can work in either direction, and I think it is im- portant to bear that in mind. Dr. H. Weickmann—I would like to call at- tention to the observation regarding the increase of nucleating ability when sub-cooled droplets are in the state of evaporation. This may apply to Georgii’s observations in radiation fogs as well as to Vonnegut’s observation in the exterior layer of a thunderstorm cloud. Two processes 239 seem to act: (1) the one which we mentioned before (see discussion of Dr. Mason’s paper) and which seems to indicate that a thin film of water crystallizes easier than bulk water, and (2) an observation which I made in the labora- tory when making ultramicroscopic studies of the melt water of cirrus crystals. Insoluble par- ticles in the interior of these drops migrated dur- ing the evaporation, driven by Brownian motion, to the edge of the drop. Here the water sur- rounding the nucleus may only have the thick- ness of a thin film and nucleation starts. Dr. H.-W. Georgii—The mechanism of evap- oration effect is not quite clear to me yet. The in- crease of the concentration of freezing nuclei is also present if the fog is at temperatures above freezing without any supercooled droplets in the outside air, Dr. C. J. Todd—On one occasion we were counting freezing nuclei and watching rain with a vertical radar, and as the rain changed from warm-cloud precipitation to ice precipitation, there was a very marked increase in the nuclei count that we measured on the ground. Recent Observations of Freezing Nuclei Variations at Ground Level Dwicut B. Kune U.S. Weather Bureau, Washington 25, D. C. Abstract—Daily observations of freezing nuclei in the vicinity of Washington, D. C., during the period January 11—-March 31, 1959, using a rapid-expansion technique, show indications of appreciable differences with respect to air-mass history. There was evi- dence of a pronounced tendency for the unusually high counts to occur in air with a recent marine fetch, while air with an extended continental trajectory characteristically showed lower concentrations of ice-forming nuclei in the subfreezing temperature ranges warmer than about —25°C. Some exploratory tests indicate that ocean water could be a source of freezing nuclei, as measured by the expansion technique. Introduction—Only a few sustained series of observations of the natural variations in freez- ing-nuclei concentrations in the atmosphere ex- ist. The tedious nature and other practical difficulties associated with obtaining reliable freezing nuclei observations together with un- certainties regarding current measuring tech- niques pose serious difficulties in this field. Pres- ent indications are that, although discrepancies of at least factors 2 to 4 in measured values may exist between different methods [Fenn and Weickmann, 1959], relative fluctuations are probably delineated by careful use of most techniques. There seems to be general agree- ment that variations in the number of natural freezing nuclei per unit volume span several orders of magnitude, that increases and de- creases seem fairly abrupt, and that the major anomalies may last from only a few hours to a day or so, seldom longer. The sources and nature of the responsible natural aerosols remain in doubt, as do their connection with meteorological parameters. Rau [1954] concluded that his measurements in Ba- varia showed appreciable differences with re- spect to airmass types, and that the more active nuclei were of polar-marine rather than recent continental origin. An analysis of an extended series of observations at Mt. Washington, N. H. [Schaefer, 1954], suggested that the higher counts were associated with air trajectories from the western semi-arid regions of the U. S., and Isono and others [1959] reported an association between abnormal counts and the arrival of loess dust particles from the Asiatic mainland and also voleanic eruptions in Japan. Mason and Maybank [1958] found a substantial amount of laboratory evidence that various forms of 240 siliceous materials were active nuclei. Some di- rect, but fragmentary, evidence of such particles at the center of snowflakes exists from electron microscopy techniques [Jsono, 1955]. The ef- fluents of certain industrial processes also ap- pear to contain active components [Soulage, 1958]. The meteoritic-dust hypothesis advanced by Bowen [1953], although presenting seemingly insurmountable physical difficulties according to most existing astronomical and meteorological concepts, nevertheless continues to pose some interesting questions. A summary of January data [Kline and Brier, 1958] indicated some sta- tistical support for the hypothesized singulari- ties in freezing nuclei during this month, but anomalies in the succeeding two months at Washington, D. C. in a 1958 series of data could not be associated with any known meteor showers. There was a tendency for the abnormal counts with the mixing-chamber technique used to coincide with the intrusion of air with at least a limited marine fetch. Georgu and Met- nieks [1958] reported evidence of parallel trends in ice-nucleation activity and the concentrations of large and giant condensation nuclei, but there was an absence of direct evidence of a maritime origin in a limited summer series of data on the coast of Ireland. On the other hand, laboratory experiments by Birstein and Anderson [1953] yielded positive indications that sea salt in- duced nucleation to the ice phase beginning at —15°C, but the role of water-soluble substances in the range of typical natural cloud nucleation temperatures remains in a somewhat contro- versial status. The purpose of the following discussion is to outline the trends that appear to be emerging from a recent series of daily observations in the FREEZING NUCLEI AT GROUND LEVEL Washington, D. C., area and some related test results using a rapid expansion technique. Be- cause of existing uncertainties regarding the quantitative interpretation of measurements in this field, the data should tentatively be con- sidered as relative rather than absolute in na- ture. The time factor in the activation of ice nuclei is such that the rapid-expansion tech- nique may result in the detection of fewer nu- cle: than mixing-chamber or constant-tempera- ture methods. However, the rapid-expansion technique has the extremely desirable feature of permitting replicated observations over a wide range of cloud-chamber temperatures with- out unreasonable time requirements. The data presented here were collected primarily to gain further insight into the observational problem, and were obtained with a prototype model of a refrigerated expansion chamber intended for a sustained observational program at a number of sites (planned by the U.S. Weather Bureau as a joint effort with and supported in part by the National Science Foundation under Grant Gl-29 with the assistance of a number of co- operating groups). Observational procedure—The observations during the period January 11—March 31, 1959, were made about eight miles west of Washing- ton, D. C. in an area removed from any known local sources of industrial pollution. At least two sets of data consisting of replicated tem- perature-spectrum runs from the threshold value (the appearance of one crystal per ten liters) to about —30°C were obtained on most days. The equipment used is similar in basic de- sign to that described by Warner [1957], the primary difference being the addition of an electrically operated air pump for both purging and pressurization. The technique depends on the creation of a supercooled fog during an adiabatic temperature drop on expansion from a normal operating wall temperature of —10° to —12°C. Resulting ice crystals settle into a removable tray coated with a thin layer of sugar solution which is placed at the bottom of the ten liter chamber. The crystals subsequently grow to visible size in 30 to 60 sec, and the total number is then counted visually. Estimat- ing procedures were used when the number of crystals exceeded 150 to 200 per ten liters by limiting exact counts to known fractional areas of the trays. All observations were made with the equipment located out-of-doors whenever practicable to reduce the risk of misleading re- 241 sults caused by possible contamination with un- representative inside air. Counts at —20°C (the primary ‘reference temperature’ used here) were augmented to some extent by extra readings, particularly during variable conditions. The data from each set of observations covering a range of expansion temperatures were plotted and mean-temperature spectrum curves con- structed. At least 10 to 15 separate observations were usually considered necessary to define a temperature-spectrum curve with reasonable confidence. Results and discussion—Approximately 2950 individual measurements comprising 172 sets (mean temperature spectrum runs) were ob- tained during the 80-day period under con- sideration. The variety of weather patterns together with the abruptness with which airmass changes frequently occur during the winter months in the Washington, D. C., area offers an opportunity to evaluate the trends in freez- ing-nuclei observations in relation to synoptic weather features with perhaps less ambiguity than at locations farther inland or in more uni- form climatic regimes. Typically, the number of nuclei activated with decreasing temperature shows an exponential type of relationship such that a tenfold increase occurs with roughly a 5°C drop in temperature. However, as shown by several examples in Figure 1 there are considerable variations in 3-4,000 a th / t Lae 26MARCH,1959 Ti 0804-0913 EST iA rey ? 27MARCH,1959 i 823.1934 EST i 24MARCH,1959 j (1813-1917 N 28MARCH,1959 1726-1805 EST NUMBER OF CRYSTALS IN 10 LITERS = 2 —25 TEMPERATURE °C —35 Fie. 1—Examples of freezing nuclei data ob- tained in the Washington, D. C., area; ordinate scale is VV + VN + 1, where N is the number of ice erystals 242 DWIGHT B. KLINE 1000 FEB 11,1959 06120727 EST CONTINENTAL POLAR AIR 600 400 200 FEB 10.1959 18071856 EST a MARITIME TROPICAL AIR ae 100 50 NUMBER OF CRYSTALS IN 10 LITERS 1 25 —30 let eee ees 1 =10 —15 —20 TEMPERATURE °C ili b Fic. 2—Temperature-spectrum concentrations of freezing nuclei measured before and after a pro- nounced airmass change in the Washington, D. C., area the slope of the mean curves. A few observa- tions have indicated maximum values in the range of —20° to —25°C with no appreciable increases with decreasing temperature. Figure 2 illustrates the rather spectacular changes that were usually observed with pro- nounced airmass changes. In this instance the evening observations were in a_ well-defined maritime tropical airmass preceding the arrival of the leadig edge of continental air of polar origin which dominated the area by the follow- ing morning. This example displays a feature commonly observed during the January-March period, namely, the strong tendency for air of continental fetch to have appreciably fewer freezing nuclei active at expansion temperatures warmer than roughly —25°C, but higher con- centrations as the —30°C temperature value is approached. Examples such as the foregoing indicated that a more detailed examination of air trajectories might profitably be undertaken. In the initial study, 12-hour trajectory estimates were de- rived by examination of the 6-hourly surface weather charts most nearly synoptic with the mid-period of each set of freezing nuclei ob- servations. The stratification of the data was according to the quadrant from which the sur- face air arrived at Washington, D. C., using streamline flow estimates rather than geo- strophic computations. This preliminary analy- sis indicated that the stratification could be simplified according to whether or not the air trajectory was entirely continental, of a mari- time tropical nature, or was such that air moved into the Washington area from the northeastern and southeastern quadrants with a resulting high probability of a recent marine fetch. Tem- perature-spectrum data applicable to each of these three categories were averaged to obtain the mean threshold temperature values and ice crystal concentrations at —20°, —25°, and —30°C, as shown in Figure 3. On the average, air with a recent marine trajectory contained about an order of magnitude more particles ac- tive as freezing nuclei at —20°C than air with an extended continental history, while mari- time tropical air with several hundred miles of overland fetch showed intermediate values. How- ever, there were too few cases in the later cate- gory to conclude that this difference is repre- sentative. The average daily counts at —20°C from January 11-March 31, 1959, and the variations between individual sets of freezing nuclei observations on each day are shown in Figure 4 with respect to airmass history. Two features in particular are evident: (1) the con- siderable amount of variability on many days, and (2) the strong tendency for the higher counts to occur in marine air with the most abnormal values in airmasses with a probable recent marine trajectory. Of 17 sets of obser- vations indicating concentrations in excess of 1000F ar a / / RECENT MARINE TRAJECTORY / 61 OBS. ON 33 DAYS 7. 600 i ’ 400+ : MARITIME TROPICAL AIR 19 OBS ON 10 DAYS AVERAGE NUMBER OF ICE CRYSTALS IN 10 LITERS 100}- CONTINENTAL T 50 9208S ON SSDAYS. 20) 10 5 J. AA etre eh ares Eo Sn Mnreerasiat an ann —10 —15 —20 —25 —30 —35 TEMPERATURE °C Fig. 3—Mean values of freezing nuclei measure- ments with respect to air trajectory observed in the Washington, D. C., area from January 11- March 31, 1959 FREEZING NUCLEI AT GROUND LEVEL 243 100 crystals per ten liters at —20°C, all but one occurred during such airflow regimes while 67 out of 84 observations in the range of 0 to 10 crystals per ten liters were in continental air masses. Figure 5 shows a more detailed presentation of this trend. The incidence of the unusually high counts in excess of 500 per ten liters on February 9, March 14, and March 26 was in air with an overwater fetch from the northeast. The sparsity of meteorological observations a i=] Ss a So i=] T @ CONTINENTAL TRAJECTORY @ RECENT MARINE TRAJECTORY @ MARITIME TROPICAL AIR MASS NUMBER OF CRYSTALS IN 10 LITERS AT -20°C (afi Keren ea ee S 30 20 JANUARY ,1959 600}- 400- iL, e jc are VS (hr ees sl Bs Cota 15 10 n Aidt 15: 20 25 30 FEBRUARY 1959 1000; 600; NUMBER OF ICE CRYSTALS IN 10 LITERS AT -20 °c 400;- 200}- ee A Fac 2 St a eae ar eee ree es Za y 10 15 MARCH 1959 Fic. 4—Mean daily values and variations in freezing nuclei counts at —20°C with respect to air trajectory BO}- 60}-- oO! 0-10 11-100 NUMBER OF OBSERVATIONS. | Fic. 5—Number of cases in which specified values of freez- ing nuclei active at —20°C oc- curred with respect to airmass categories 101-1000 NUMBER OF ICE CRYSTALS/10 LITERS AT -20 °C off-shore prevents a detailed examination of possible upwind factors. There was no obyious correlation with wind speed or probable extent of over-water fetch. However, there were some indications that low-level instability and wide- spread precipitation were associated with the freezing nuclei anomalies. If so, this may provide a clue regarding the conditions most favorable for the generation and transport of the respon- sible aerosols. The existence of a recent marine history alone does not appear to represent both a necessary and sufficient condition, since, as shown in Figure 5, there were several instances of low concentrations in such flow regimes. In view of the highly suggestive nature of these empirical results, samples of ocean water were obtained from the Rehoboth, Del., coastal area. On the assumption that the bursting of bubbles at the sea surface would be the most likely mechanism for the natural production of aerosols from oceanic sources, the expansion chamber was purged and pressurized with air ingested from a few inches above the surface of agitated ocean-water samples. These tests have been conducted a number of times with similar results. Two examples are shown in Figure 6 in which the background counts were compara- tively low. While there is considerable scatter in the results, there appears to be little doubt of a positive response with the expansion cham- ber technique. Whether the responsible particles are solely the soluble components of ocean water or substances in colloidal suspension can- 244 1000f- vioev ® BACKGROUND C TS MARCH 18,1959 @ BACKGROUND C S MARCH23,1959 YCOUNTS WITH MARCHIB 19 ACCOUNTS WITH MARCH23.,) 600+ NUMBER OF ICE CRYSTALS IN 10 LITERS Fic. 6—Comparison of temperature- spectrum counts of freezing nuclei at —20°C in air drawn from near the sur- face of agitated ocean water and exist- ing background values not be stated at this time. The threshold nu- cleation temperature of the sea-water aerosols has consistently been in the neighborhood of —14° to —16°C, in close agreement with the results of Birstein and Anderson [1953]. Trial runs with solutions of NaCl and MgCl, as well as other soluble substances appear to give posi- tive responses of comparable magnitude, while carefully distilled water shows a null effect. Concluding remarks—These results appear to offer strong circumstantial evidence, but not proof, of a marine source of aerosols active as freezing nuclei in the Washington, D. C., area. This evidence seems at variance with the ex- perience of others in this field, and raises some provocative questions regarding the physical na- ture of at least some of the freezing nuclei in the atmosphere. It is of course possible that the explanation for these results may reside in the inherent nature of the rapid-expansion tech- nique wherein soluble substances could initiate the freezing process before going into solution, but not in the slower condensation rates more representative of atmospheric processes. On the other hand, the mixing-chamber technique used in the earlier 1958 series of observations in the Washington, D. C., area showed similar ten- dencies for anomalous conditions to occur in air with a marine trajectory. The possibility of local sources of freezing nuclei cannot be ruled out completely. Hovsever, a series of ob- DWIGHT B. KLINE servations at various locations within a ten mile radius of the metropolitan area on 15 separate days yielded no evidence that this might be the case. These results plus recent work of Papée [1959] pointing toward activation phenomena in soluble substances such as NaCl which may facilitate their role as a sublimation nucleus raises some intriguing and rather crucial ques- tions regarding the role of hygroscopic particles in atmospheric chemistry and cloud nucleation. They may have a bearing on the limited number of aircraft observations [Coons, Jones, and Gunn, 1949] indicating a tendency for the oc- currence of ice crystals in clouds at warm sub- freezing temperatures In marine air. Acknowledgments—The assistance of Gilbert D. Kinzer, Glenn W. Brier, and DeVer Colson in certain experimental and analysis phases of this study is gratefully acknowledged, along with help by Thomas H. Carpenter and Fred- erick Van Cleef in the laborious and tedious process of maintaining a daily freezing nuclei observational program. REFERENCES Birsteqn, 8S. J., anv C. E. Anpgrson, Preliminary report on sea salt as an ice nucleus, J. Met., 10, 166, 1953. Bowen, E. G., The influence of meteoritic dust on rainfall, Australian J. Phys., 6, 490-497, 1953. Coons, R. D., E. L. Jones, anp R. Gunn, Fourth partial report on artificial production of precipi- tation, Cumulus clouds, Gulf States, 1949, Bul. Amer. Met. Soc., 30, 289-292, 1949. Fenn, R. W., anp H. K. Wertckmann, Some results of aerosol measurements, Geofis. Pura Appl., 42, 53-61, 1959. Grorcu, H.-W., ano A. L. Merniexs, An investi- gation into the properties of atmospheric freez- ing nuclei and sea-salt nuclei under maritime conditions at the west coast of Ireland, Geofis. Pura Appl., 41, 159-176, 1958. Isono, K., M. Komasayast, AND A. Ono, Volcanoes as a source of atmospheric ice nuclei, Nature, 183, 317-318, 1959. Isono, K., On ice-crystal nuclei and other sub- stances found in snow crystals, J. Met., 12, 456- 462, 1955. Kurz, D. B., anp G. W. Brikr, A note on freezing nuclei anomalies, Mon. Wea. Rev., 86, 329- 333, 1958. Mason, B. J., ano J. Maysanx, Ice-nucleating properties of some natural mineral dusts, Q. J. R. Met. Soc., 84, 235-241, 1958. Paper, H. M., Activated salt surfaces in ice nu- cleation and growth, and the formation of drop- lets, J. Met., 16, 217-218, 1959. Rav, W., The ice-nucleus concentrations of various air masses, Met. Rundschau, 7, 205-211, 1954. DISCUSSION Scuarrer, V. J., The concentration of ice nuclei passing the summit of Mt. Washington, Bul. Amer. Met. Soc., 35, 310-814, 1954. Sounace, G., Contribution des fumées industrielles a Venrichissement de l’atmosphére en noyaux 245 glacogénes, Bul. Obs. dw Puy de Dome, pp. 121- 124, 1958. Warner, J., An instrument for the measurement of freezing nucleus concentration, Bul. Obs. du Puy de Dome, pp. 33-46, 1957. Discussion Mr. D. Blanchard—I think I would be one of the last to discourage any work related with phenomena of the air-ocean interface, but I think a word of caution might be in order. One produces aerosols by bubbling or spraying. Any way in which one produces aerosol from sea wa- ter or distilled water means this aerosol will come from the surface. This means any surface contamination on this water will end up in the aerosol, and if one has any surface active con- tamination, this may be what you are actually measuring. I think these experiments certainly should be carried out using very clean condi- tions, perhaps using artificial water. Mr. D. B. Kline—We have tried distilled water. Carefully distilled water did not give a response. Tap water, however, did. We have tried sodium chloride, magnesium chloride, and calcium sulphate solutions and we consistently got a response. Dr. H.-W. Georgii—In January 1957 we had very marked peaks at about the same dates at which Dr. Bowen had them. At that time, I did not yet know of Bowen’s work. We believe, as does Mr. Kline, that they are connected with the large-scale flow pattern of the atmosphere, and perhaps the change from zonal to meridional circulation that we had at this time in 1957. Dr. Tor Bergeron—I thought our freezing nu- clei measurements in January 1959 were of very little value; but I shall now be very glad to have them compared with yours. Mr. Kline—I am very glad to establish this contact and I am very interested in the data. Dr. Choji Magono—A group in Japan under Dr. Isono at Tokyo University made observa- tions like you, using different methods. They found that peaks of concentration of freezing nu- clei agreed very well with volcanic eruptions in Japan. This was derived using the trajectory method. Mr. Kline—I was interested in the report that the freezing nuclei concentration was not only correlated with voleanic eruptions, but could also be traced back to the latest dust storm in northern China (see reference to Jsono and others im my paper). Mr. Jerome Namias—In the synoptic situation for maritime flow in the Washington, D. C., area, there is usually a very strong vertical wind shear, so that fresh maritime air is seldom ob- served up to high elevations. It is a warm-front condition in which if the air flow is fresh from the ocean in the lowest levels, it changes to a continental flow aloft. Frequently the precipita- tion mechanisms develop in the higher layer, so that this type of stratification should be con- sidered in regard to these observations. Mr. C. BE, Anderson—I wonder whether or not measuring ice nuclei at the surface is of any real value in getting an estimate of what the ice nu- clei activity is likely to be aloft. Since there is not only a question of separation of trajectories with height, but also the influence of contamina- tion at the surface. Mr. Kline—All we can do to attempt to get around the problem is set up our network to in- clude high altitude stations. Dr. C. L. Hosler—What are the short-period variations in these ice-nuclei counts? The data you presented is the result, I presume, of a number of counts. How many and over what period of time? What would happen if you waited an hour longer, would this result in a greater variation from day to day? Mr. Kline—It takes about 60 to 90 min to run through a spectrum such as is presented in Fig- ure 3. Durmg that period we normally have variations only within roughly a factor of two or three. Reproducibility is usually good; but we do encounter periods where there is con- siderable variation. Dr. H.-W. Georgii (communicated)—In the course of our own measurements off the Irish west coast we also found a relatively high num- ber of freezing nuclei active above —20°C. The absolute number of freezing nuclei within this temperature range was even higher than on the Zugspitze and equally as high as in Frankfurt. However, at lower temperatures (between —20 246 and —30°C) the freezing nucleus concentration in Valentia Island, Ireland, increased only very slowly, while at the three continental places a very sharp increase was observed. We assume that in the very clean maritime air around Val- entia Island an inactivation of the aerosol parti- cles by adsorbed trace substances does not occur while in Germany this is more or less everywhere DISCUSSION the case because of the overall effect of air pollu- tion. We are therefore also inclined to suggest that the relatively low concentrations of freezing nuclei which Kline observed in air masses com- ing from the interior of the country are also caused by a partial inactivation of the particles by pollutants which is not the case when the air is coming from the ocean. Studies on the Effect of Chemisorbed Impurities on Heterogeneous Nucleation Seymour J. BrrsTern Geophysics Research Directorate, Air Force Cambridge Research Center, Bedford, Massachusetts Abstract—Studies have been made on the effects of the chemisorption of ethyl amine in lead iodide insofar as they affect the nucleation of supercooled water. It has been found that concentrations on the order of one part per two million of ethyl amine in the carrier gas will decrease the temperature of nucleation by seven degrees. Higher concentrations cause an even greater temperature change. The implications of these results in terms of atmospheric phenomena are discussed. Introduction—Previous work on the inhibition of ice nucleation by ethyl amine has shown that in a dynamic system it is possible to inhibit lead iodide nucleation of supercooled water by chemi- sorbing ethyl amine on the surface of the lead iodide [Birstein, 1957]. These results showed that it is possible to lower the temperature of water nucleation by 17° by passing the lead iodide nu- clei over a saturator filled with ethyl amine held to a vapor pressure of approximately 0.2 mm at a standard flow rate and nuclei generator setting. Higher vapor pressures of the amine gave greater degrees of inhibition of the nu- cleation process (Fig. 1). Because this work was done in a dynamic system the question arose concerning whether equilibrium conditions were reached between the nuclei and the nuclei inhibitor. The following series of experiments were run to study the re- action under equilibrium conditions to determine whether it is possible to inhibit nucleation of wa- ter droplets with traces of impurity approaching that of trace contaminants in the atmosphere. Experimental—The apparatus used in this work consisted of our standard nuclei generator (Fig. 2) described in previous publications |Birstein and Anderson, 1955], connected to an especially designed cryostat (Fig. 3). The eryo- stat was essentially a block of lead in which was imbedded a copper coil. Liquid nitrogen was circulated through the coil to bring it to a de- sired temperature. The block was insulated with styrofoam. A Tag controller-indicator regulated the flow of liquid nitrogen through the coil. The ‘Tag, in turn, was controlled by a thermocouple set within the cryostat. Two glass tubes were located in the cryostat. One tube was filled with 247 ethyl amine and held to a given temperature which could be interpreted in terms of the vapor pressure of the amine at that temperature. The second tube was the control and, therefore, was empty. These tubes were connected to flasks lo- cated outside of the eryostat and the flasks, im turn, were connected to the nuclei generator through a three way stopcock. All ground glass joints and stopcocks were ungreased to prevent contamination by the extremely reactive ethyl amine. In making a run, the Tag was set for the de- sired cryostat temperature and the liquid nitro- gen flow was started. When the ethyl amine was at the set temperature the nuclei generator was started and nuclei samples prepared in a nitro- gen atmosphere were collected in both flasks. The flasks were then opened to the thermo- statted tubes in the cryostat and the system was allowed to come to equilibrium. Preliminary ex- periments to determine the equilibrium time showed that fifteen minutes was sufficient. A nuclei sample was then removed from the control flask and injected into the cold chamber to de- termine whether nuclei were present in the sys- tem. This was next repeated with the nuclei sample in the flask exposed to the ethyl amine vapor. The cold box temperature was lowered and nuclei injection was repeated until the temperature was reached at which ice crystals were first formed with the lead iodide sample treated with the nuclei ‘poison.’ These experi- ments were repeated until the nucleation tem- perature for the lead iodide had been obtained after exposure to ethyl amine vapor at pressures corresponding to the amine vapor pressure be- tween —75° and —171°. 248 =—26 -28 ae -120 aC -100 -90 Poison temperature, °C Cloud temperoture A ed i) ° 1 ao - Fic. 1—Inhibition of lead iodide nucleation of supercooled water by ethyl amine SEYMOUR BIRSTEIN Fig. 2—Nuclei generator Fic. 3—Cross section of the eryostat The cold box used in these experiments (Fig. 4) was of conventional design and it, too, was designed in this laboratory [Birstein, 1954]. It consisted of a dewar flask L filled with methanol in which was suspended a brass cylinder M closed on one end and covered on the other with a removable plexiglas lid. Ice crystal formation was monitored by shining a beam of parallel light through the transparent top. The chamber N ries 4— Cold box was cooled by circulating refrigerated methanol through a copper coil immersed in the dewar. The temperature of the cold box J and K, too, was controlled by means of a Tag controller- indicator T whose thermocouple was suspended in the cold box to sense the temperature and, therefore, control the flow of refrigerant through the valve D. Discussion—From Figure 1, it can be seen that even in a dynamic system the effect of ethyl amine on lead iodide nucleation of supercooled water is quite marked. A comparison of the data from the dynamic system with those obtained from the static tests under known equilibrium conditions shows that there is, in general, good agreement between the two sets of data. While the static tests were quite interesting, because of the nature of the apparatus used, it was only possible to run the tests at relatively high partial pressures of ethyl amine. The system used in- volved the passing of a nitrogen stream contain- ing the nuclei over a saturator filled with the amine. The lowest temperature which could be reached in the saturator was approximately —110°. At —105° the vapor pressure of the ethyl amine is on the order of 0.1 mm or approxi- mately 0.0001 atmosphere. With the cryostat used in the static measurements, it was possible to reach a temperature approaching the boiling point of the coolant. In the case of liquid nitro- gen which boils at —196°, the cryostat tempera- ture could be lowered to approximately —180°. The vapor pressure curve for ethyl amine is shown in Figure 5. The curve for the plot of log vapor pressure as a function of temperature can, for all practical purposes, be assumed a straight line in this range. The results of the static runs are given in Table 1. The cryostat temperature ethyl amine vapor pressure, and nucleation CHEMISORBED IMPURITIES AND HETEROGENEOUS NUCLEATION (mm) ai 0.01 VAPOR PRESSURE OF ETHYL AMINE ° ° 2 | | | 0.0001 “100 140 -180 TEMPERATURE °c Fic. 5—Vapor pressure curve of ethyl amine temperature for the supercooled cloud are given for each series of measurements. The results, in terms of ice nucleation temperature for lead iodide as a function of cryostat temperature, are given in Figure 6 and the results in terms of ice nucleation temperature as a function of vapor pressure of ethyl amine are given in Figure 7. When one examines Figure 6, the curve for nu- cleation temperature as a function of eryostat temperature, it appears exponential. The plot of nucleating temperature as a function of log va- por pressure of ethyl amine, however, appears to be a straight line, indicating that the nucleating temperature bears the same relationship to va- por pressure of the ethyl amine as the vapor pressure has to the temperature of the ma- terial. An analysis of the data obtained in the static tests shows that the lower limit of measured change is a decrease in nucleation temperature from —6° to —13° when the partial pressure of ethyl amine was approximately 0.0004 mm. This corresponds to, at one atmosphere, one part of ethyl amine per two millon parts of air. Going up towards the higher partial pressures of nuclei poison, a partial pressure of 1.1 mm of amine will lower the freezing point of supercooled water to —33°, a change in nucleating temperature of 27°. This latter pressure, however, is quite high; it corresponds to better than one part per thou- sand of ethyl amine and is unrealistic when one is thinking in terms of atmospheric contami- "Cc TEMPERATURE OF ICE NUCLEATION ° [a | ta | WRN | -60 -100 -140 CRYOSTAT TE MPERATURE °C Fic. 6—Inhibition of ice nucleation as a function of cryostat temperature (mm) TUTTI 0.0iL VAPOR PRESSURE OF ETHYL AMINE °o 8 0000! | | iL 10 -20 -30 -40 TEMPERATURE OF ICE NUCLEATION °C Fre. 7—Inhibition of ice nucleation as a function of ethyl amine vapor pressure TaBLE 1—Results of static runs 249 Cryostat Vapor pressure Nucleation temperature ethyl amine temperature 2 mm BG —81 ileal —33.4 —101 0.19 —28.2 —120 0.033 —25 —129 0.016 —22 —139 0.006 —20 —171 0.0004 —13.4 nants. One part per million of the contaminant will lower the freezing point of supercooled wa- ter droplets in the presence of lead iodide to —15°, and one part per hundred thousand to —20°. Conclusions—W hile the above data were taken in the laboratory on lead iodide, an artificial nu- eleating material, certain conclusions can be drawn which are directly applicable to the at- mosphere. The concentration of ethyl amine used in these experiments was purposely kept low in order that the lower end of the curve of partial pressures would approximate that of atmos- pheric pollutants. If one thinks in terms of con- centrations up to one part per hundred thou- sand, the nucleating temperature is lowered by 14°. Although these data were taken on lead iodide, work done in the past [Birstein, 1957] has shown that it is possible to inhibit ice crystal formation by natural nuclei through treating the air sam- ple with methyl amine before it is brought into a cold box. These experiments showed that with a sufficient amine concentration it is possible to prevent so-called ‘spontaneous nucleation.’ We were able to reach —52° in one experiment be- fore ice-crystal formation took place. Ethyl amine acts in a manner similar to methyl amine but is slightly more effective because of the longer carbon chain on the molecule [Brueheman and Verhoek, 1948}. If we accept the following type of reaction as being the cause of the loss of effectiveness of the lead iodide nucleus [Biltz, 1922] PbI + 2C.H;N He os Pb(C2H;N Hs)oI5 DISCUSSION we see that this is the simple formation of coordi- nation complexes on a metal salt. It is an ex- tremely common type of reaction and would be expected to occur with many compounds other than amines. Hundreds of other type reactions are also possible with other particulate matter which may be responsible for ice crystal forma- tion in the atmosphere. While these experiments were not designed to pinpoint the exact mechanism by which ice- crystal formation may be inhibited in the at- mosphere, they do show that the concentrations of industrial wastes present in an air mass are certainly sufficient to make marked changes in the ice-nuclei spectrum in the air mass. REFERENCES Birtz, W., Ueber die Ammoniakate der Bleihalo- genide, Stammverbindungen und Mischverbin- dungen, Zs. anorg. allgem. Chem., 124, 230-247, 1922. Brrstern, 8. J., Adsorption studies of heterogene- ous phase transitions, Geophysics Research Pa- per No. 382, Air Force Cambridge Research Center, December 1954. Brrster, S. J., Studies on the effect of certain chemicals on the inhibition of nucleation, Arti- ficial Stimulation of Rain, Pergamon Press, pp. 376-385, 1959. BirsteIn, S. J., AnD C. E. Anprrson, The mecha- nism of atmospheric ice formation, I, the chemi- cal composition of nucleating agents, J. Met., 12, 68-73, 1955. BruEHEMAN, R. J., AnD F. J. VerHork, The basic strength of amines as measured by the stabili- ties of their complexes with silver ions, J. Amer. Chem. Soc., 70, 1401-1404, 1948. Discussion Dr. James P.. Lodge, Jr—yYour use of very low temperatures to obtain low partial pressure of contaminants is a very difficult one. We have used the apparatus of Stephan to obtain low con- centrations by means of diffusion through tubes (A. P. Altshuller and I. R. Cohen, “The Apph- cation of Diffusion Cells to the Production of Known Amounts of Gaseous Hydrocarbons,” pa- per presented at the 136th National Meeting, American Chemical Society, Atlantie City, Sep- tember 18, 1959). In this manner we can obtain concentrations of one part per million and less in a dynamic system. Mr. 8S. J. Birstein—I agree that this approach is a rather difficult one. Dr. F. W. Van Straten—It would seem that there is something of a conflict between the re- sults of this work and the work of Dr. Mason, because according to Dr. Mason’s paper there seemed to be a preferential nucleation on, shall we say, the active lines of the host crystal. If this is true, in that case, you could not expect poisoning to be a linear function of the concen- tration of the poison. It should first affect the host crystal on the most efficient sites, then drop off very sharply to the point where the other surfaces of the erystal begin to nucleate. Dr. B. J. Mason—I think it is important that you saw the ice crystals, in my cases, growing on the dislocation steps. It is at these that the DISCUSSION poison will be absorbed first. It is because the nucleation occurs only on these steps that such a small amount of poison ean do the trick, because if you put a monomolecular layer of poison all around the steps, it still covers only very little of the surface. As Dr. Van Straten says, the poison affects the steps first, and the amount of material required to poison the steps is very small mdeed. We certainly have evidence that the small traces of poison do, in fact, kill nucleation sites at these very steps. Dr. Walter Hitschfeld—I think this is ilus- trated quite well on Figure 1. Here the relation- ship of the poison concentration to temperature is shown to be linear. But obviously it cannot re- main linear down to zero concentration. So if one goes beyond Mr. Birstein’s data to zero concen- tration, one knows he has to get to the tempera- ture usually called ‘activation temperature.’ There is thus necessarily a non-linear region m the relationship. This is precisely what Drs. Van Straten and Mason require. Dr. H.W. Georgii—lt is right to assume from your results that the process of the poisoning 1s not only absorption but a chemisorption ? Mr. Birstein—On the lead iodide, I would call it reversible chemisorption. On the silicate it would probably be physical absorption of some sort. However, what it does in the activity, I could not begin to say. Dr. Georgii—Can the poisoned particles re- cover their activity ? Mr. Birstein—It can recover its activity, but not easily. Dr. Roscoe R. Braham, Jr—Perhaps some of you did not see a paper that bears on this, al- though not critically, when it was published. Back in 1949 or 1950, in work we were doing at 251 the Institute of Mining and Technology, we felt that thunderstorm electricity had its origin in freezing of water, according to Workman and Reynold’s work on freezing potentials. It had been found in the laboratory that water very shghtly contaminated with ammonia (1 to 10° to 1 to 10") gave freezing potentials which were just reversed from those of normal water. We felt we had a straight-forward experiment that was ideal. All one had to do was release quantities of ammonia into potential thunderstorms; and it would be ‘flipped upside down’ and simultane- ously we would have proven the Workman-Rey- nolds effect. But it turned out when we loaded a B-17 with all the ammonia it could carry and stocked tanks of ammonia on the ground, so we could release it up underneath the thunder- storm, we were completely unable to observe any effect whatsoever on the electrical structure of this storm. We certainly were releasing quantities of ammonia into these particular storms, but Nature has a way of disposing of this material as though it were never released. This was un- doubtedly real, and I would like to suggest that many times Nature does not know about many of the things we do. Mr. Birstein—We have been doing some work in clouds inhibiting ice-crystal formation, and the results thus far have not been too great; but we seem to have gotten limited success in de- creasing the ice-crystal concentration. We hope to do some work of this sort in Flagstaff in the summer of 1959. Dr. M. Neiburger—Did you stop the rain from falling? Mr. Birstein—This is one thing we are inter- ested in determining. Some Observations of Chloride-Sulfate Relationships in the Atmosphere and in Precipitation JAMES P. LopGE Robert A. Taft Sanitary Engineering Center, U. S. Public Health Service, Cincinnati, Ohio Abstract—A series of measurements, including the determination of chloride and sulfate in particulate matter, were made at a U.S. Coast Guard weather ship midway between Honolulu and San Francisco. Even in this extremely isolated location, the sulfate concentration frequently exceeded the chloride. In the light of this finding, chloride-sulfate relationships were examined for a number of other remote stations; published data in the literature have also been studied. The chloride-sulfate regression lines were found to vary markedly in slope and intercept. There appears to be a definite relationship between chloride and sulfate concentrations; however, the nature of the relationship varies markedly with location. An interpretation is offered, based upon a three-source model. Introduction—Among the salts circulating through the atmosphere are sizable quantities of chlorides and sulfates. Both species are of im- portance in precipitation physics, since they form soluble particles which are extremely effective as cloud or precipitation nuclei. Both are of in- terest in air pollution, since man liberates them, or their precursors, in quantity by his activities. The levels contributed by nature thus constitute a background to the urban levels measured in air-pollution studies. On the other hand, the hu- man contribution constitutes a sort of ‘noise level’ on the natural concentrations, considered from a global geochemical viewpoint. For several years the U. S. Public Health Service has had in progress a small study of natural levels of substances which are considered pollutants when they are found in urban areas. In collaboration with the California Department of Public Health, measurements of these natural levels were made at a number of remote coastal sites [Harrison and Lodge, 1959; Holzworth, 1959]. Subsequently two series of measurements were made during the summers of 1957 and 1958 at Weather Station November, the weather ship located approximately midway between San Francisco and Honolulu [Lodge and_ others, 1959]. When it was discovered that nearly all of the particulate samples from this operation con- tained more sulfate than chloride, a statistical study was made of chloride sulfate relationships, from both the coastal sites and from those data available in the literature. The data—In addition to two sets of measure- ments from Station November which were tested for homogeneity and pooled, the California study made available air data from Southeast Farallon Island, Point Piedras Blaneas, San Nicolas Is- land, and the top of Mount Hamilton. Also uti- lized were the excellent precipitation analyses of Larson and Hettick [1956] from central Hlinois, and analyses of air or precipitation or both from four selected stations of the Swedish network [Egner and Eriksson, 1955, and quarterly reports by a variety of authors in Tellus}: Kinnvika, Spitsbergen; Valentia, on the west coast of Ire- land; Edinburgh, Scotland; and Bonn, West Germany. The statistical analysis was not as complete as might be desired, either as to the depth of the treatment or as to the number of stations coy- ered. It would be desirable to extend the analysis to all of the stations of the Swedish network and to other historic sets of air and precipitation analyses, to see if it would bear out the tenta- tive conclusions of this paper. The Swedish data are reported in terms of the amount of mineral matter brought down by pre- cipitation per unit area. However, since total precipitation is also recorded, it is possible to convert the units given into concentration m the rain water. For convenience, the former figures will be referred to as ‘rainout’ data, and the latter as ‘precipitation’ data. It seems hkely that rainout should be a more valid measure of the concentration of materials aloft, since it is substantially independent of the intensity of pre- 252 CHLORIDE-SULFATE RELATIONSHIPS IN THE ATMOSPHERE 253 cipitation. It will, however, be in some degree de- pendent on the frequency of precipitation. The findings of Byers and others [1957], among others, make it clear that particulate matter sampled near the surface of the Earth may not be representative of that aloft. It is more likely to represent local influences, and less likely to show marine influence, than sam- ples taken at higher altitudes. Thus raimout, rep- resenting as it does the mean concentration in a layer of air some thousands of feet thick, may differ markedly in composition from surface air; it should be more representative of the atmos- phere as a whole. This is especially apparent im the two sets of urban data in the present study. The interpretation—The data, with sulfate ex- pressed as sulfur equivalent, were fitted to best regression lines on logarithmie paper by the method of least squares. Thus all the regres- sions had the form (Cl) = .a(s)? (1) where (Cl) is the concentration of chloride in appropriate units, (S) is the concentration of sulfate computed as sulfur in the same units, and a and b are constants. Table 1 gives the values of a, 6, and the correlation coefficient 7 for all cases in which significant correlations were obtained. A particular sample of airborne particulate matter, however taken, will contain chlorine and sulfur compounds of very local origin, together with substances which have traveled great dis- tances. A reasonable physical model is that of the atmosphere as a great reservoir, charac- terized by a certain mean ratio of chlorine to sulfur. At any point within this reservoir, how- ever, local perturbations may result in a sam- ple composition very different from the mean. However, from the viewpoint of a particular sampling location, it is perhaps simpler to con- sider the mean atmosphere and the various local influences on an equal footing. This mathemati- cal model of the sample as the result of a num- ber of ‘sources’ has the advantage for purposes of this paper of involving less prejudgment con- cerning the over-all mechanism. Further study should be made before a mechanism can be set forth with confidence. Thus three ‘sources’ will be considered: the oceans, the mean atmosphere, and human activity. The direct marine contribution contains chlo- ride equal roughly to 21 times the mass of sul- TaBLe 1—Summary of regression data; order of increasing a Site ey | Nei r 3 | E | Champaign, Illinois | 0.401 .11|0.77| P Mt. Hamilton, California | 0.60)0.63 0.62) A San Nicolas Island, Califor- | 1.22)1.02)0.57) A nia | Station November 1.85/0.73/0.47| A Bonn, Germany 2.12|0.55)0.55) A Valentia, Ireland 2.82/1.30/0.91) R Point Piedras Blancas, Cali- | 6.20)1.20/0.71) A fornia South East Farallon Island, | 6.241.050.57) A California Valentia, Ireland 1.7 (1310.90) Kinnvika, Spitsbergen 28.6 |0.92/0.92) A 61.5 (0.54 0.59) R «Type of analysis: P = rainout; A = air. precipitation; R = fur. Thus its composition may be represented as (Cl) = 21 (5) (2) The total atmospheric loading has been deduced by Eriksson [1959]. From his figures, one obtains (Cl) = 148 (S) (3) for the chlorine-sulfur relationship. The third component, man’s own products, contributes, for practical purposes, only sulfur to the atmos- phere. It may thus be taken as a relationship of the form (Gh =k (4) that is, for a given station, the chloride level will be relatively constant, as fixed by that en- tering the area, but sulfur is indeterminate and independent of chloride. Thus the mean chloride- sulfate relationship for any locale will reflect all three ‘sources.’ (It should also follow that the world-wide average of all such determinations should be identical with the above ‘mean atmos- phere’ relationship (Eq. 3), within the accuracy of Eriksson’s figures.) Turning to the actual data, it can be seen that Kinnvika (Fig. 1) is the most truly ‘maritime’ station. Both air and rainout figures are for practical purposes identical in composition with sea water. The precipitation itself varies so much less than that of most stations that 1t may well be constant within the errors of the measure- ments. Station November (Fig. 2), in contrast, is Legend 4 = RAINOUT,mg m= O= AIR, ug m3 O = PRECIPITATION,mg li"! CHLORIDE 6 ° SEAWATER 30h al 25 —| 20 4 ist =| 3 [ee | | SS hea as ee | 1 15 2253 4 5 678910 15 20 2530 40 5060 80 100 SULFUR Fic. 1—Regression of chloride on sulfur for air, rainout, and precipitation at Kinnvika, Spitsbergen SEAWATER CHLORIDE ,pq m-3 MEAN ATMOSPHERE 1 5 2.25.35 4 .5. 6 .7.8.910 is SULFUR, yg m™ 2255 4 5678910 Fic. 2—Regression of chloride on sulfur for air at Weather Station November much closer to the mean atmosphere than to sea water. Presumably this reflects the relatively calm weather of the mid-Pacific summer when little sea-spray is generated and the aerosol col- lected was predominantly that of the general atmosphere. Kinnvika, on the other hand, in an area of higher winds and generally less temperate climate, should show a much greater contribu- tion of marine aerosol. Woodcock (private com- munication) has pointed out that a great deal of minute marine aerosol is generated when snow falls into water; this may constitute an addi- tional source at some seasons. Bonn (Figs. 3 and 4), with numerous local JAMES P. LODGE sources of sulfur compounds, shows the far greater scatter to be expected under these cir- cumstances. The rainout shows a very pro- nounced flattening of slope as predicted by (4) above. The air regression has a greater slope which may or may not be significant, but most analyses lie farther to the right of the mean-at- mosphere line than do the rainout points, indi- cating higher relative sulfur concentrations. This confirms the thesis that local influences are shown more strongly by surface air analyses than by rainout. Similar effects are shown by the other stations considered. It is also worth noting that at Va- SEAWATER o | CHLORIDE rr [] D> oD is} [eT | es || MEAN ATMOSPHERE 4 RAINOUT, mg m-2 20f/— © PRECIPITATION, mg li-! x 107 (a el 20 25 30 ee es ee ee 40 50 60708090100 150 200250300 400500600 600 100 SULFUR Fic. 3—Scatter diagram for rainout and pre- cipitation at Bonn, Germany; the line is a visual fit SEAWATER CHLORIDE ,UNITS - pg m7> MEAN ATMOSPHERE 1 LS TU2pe 2S us: 4 5 678910 15 20 2530 40 50 60708090100 SULFUR, UNITS-pg m-> Fia. 4—Regression for air at Bonn, Germany DISCUSSION 255 lentia, in contrast to Kinnvika, rainout and precipitation gave lines of identical slope. Cham- paign, Illinois, lies well to the right of the mean- atmosphere line, because of added sulfate from the continent, but this addition increases with higher chloride loadings, so that the line remains nearly parallel to the mean atmosphere line. Probably this can be explained by the absence of large nearby sources. It may also reflect the role of aerosols in the oxidation of the lower valence states of sulfur to sulfate. Summary—Examination of chloride-sulfate re- lationships in air and precipitation at a number of sites has led to the postulation of a three- source model for the composition of atmospheric particulate matter. It would be highly desirable to study all available data, in order to shed more light on these important correlations. It is possible that an index of the relative contribu- tion of urban and maritime sources can be de- vised, based upon the chloride-sulfate ratio of the environment. REFERENCES Byers, H. R., J. R. Stevers, anp B. J. Turrs, Dis- tribution in the atmosphere of certain particles capable of serving as condensation nuclei, Arti- ficial Stimulation of Rain (H. Weickmann and W. E. Smith, ed.) Pergamon Press, pp. 47-70, 1957. Eener, H. ano E. Ertksson, Current data on the chemical composition of air and_ precipitation, Tellus, 7, 134-139, 1955. Eriksson, E., On the geochemistry of chloride and sulfate, The atmospheric chemistry of chlorine and sulfur compounds (J. P. Lodge, ed.), Geo- phys. Mono. 3, Amer. Geophys. Union, pp. 124— 127, 1959. Harrison, W. K., Jr. ano J. P. Lopcr, Jr., Some measurements of oxidant levels at remote Cali- fornia sites, J. Air Poll. Control Assn., 8, 341- 345, 1959. HotzwortH, G. C., Atmospheric contaminants at remote California coastal sites, J. Met., 16, 68- 79, 1959. Larson, T. E., anp I. Herrick, Mineral composi- tion of rainwater, Tellus, 8, 191-201, 1956. Lopcg, J. P., A. J. MacDonatp, anp E. Viuman, A study of the composition of marine atmospheres, Tellus, 1960, in press. Discussion Dr. R. M. Schotland—Is there any possibility of stack gases from the ship contributing to the sulfur content of the samples taken at Station November? Dr. Lodge—I think not. We were simultane- ously measuring sulfur dioxide and found very little of it at any time. Dr. C. E. Junge—To me it was very interest- ing that you found these industrial sulfurs over the Pacific. I think I did not make my point very clear this morning when I spoke about the two hemispheres. Industrial sulfur, having only a lifetime of a few days, can therefore neither penetrate to the arctic areas nor into the tropi- eal regions. So it will normally remain in mid- dle latitudes, and was therefore found at Station November in the Pacific. The sulfur which we found in Greenland was natural, that is, we are pretty sure that the sulfur is primarily present as H.S which is oxidized and then washed out. This agrees with our findings that the residence time of the total sulfur which includes a natu- ral component, is much longer than ten days, which is approximately the residence time of the industrial component (SO.). Dr. M. Neiburger—In connection with this it would be very desirable to know the lifetime of the pollutants which go into the atmosphere. How many times around the Earth will they travel before they are washed out? My frank opinion is that industrial sources still are affect- ing Station November even though the aerosol will have to come all the way from Europe or with easterly winds all the way around from the United States. It seems to me this is also of in- terest in terms of the organics that might be acting as inhibitors to the freezing nuclei. It would be very valuable if somebody could make an attack on that question. Dr. Junge—1 definitely think this material circulates around the northern hemisphere once or twice before most of it is washed out. We have now a number of residence times from various sources which are not too accurate, but they give an approximate picture. We know that the lifetimes are of the order of 30 days in the tropo- sphere. They are shorter for some other pollu- tants, like sodium chloride formed from sea spray. Estimates show that they may be of the order of five to ten days. Of course, the water cycle has a ten-day turnover, so actually it looks as if most of the material which is readily washed out has approximately the same residence time 256 as water. Some may remain two to three times longer depending on the kind of washout mecha- nism. I would say with a residence time of 10, or 20, or 30 days it can go once or twice around the world and even in the center of the Pacific you will get quite a bit of contamination from the continents. Dr. A. Goetz—The analyses were all for sul- fur only, not for sulfate? Dr. Lodge—The samples were analyzed for sulfate, but it was computed as sulfur, the way the Swedish group reports it. Dr. Goetz—The industrial SO, would require DISCUSSION a fairly long time before it is converted into sul- fate, whereas the ocean could probably only yield sulfate. Dr. Lodge—A substantial percentage of these data were obtained from filter samples, and were not oxidized during the treatment; this would be sulfate. I am a little less certain of the Swedish data, which may include some SO. . Dr. A. H. Woodcock—Since it is fairly well established that chloride varies with the wind force over the sea, it would be interesting to know whether or not sulfur is also related to wind force. Preliminary Results on the Aggregation of Ice Crystals R. E. HauucGren anp C. L. Hosier Pennsylvania State University, University Park, Pa. * Abstract—A brief description of the experimental apparatus and procedure is given. Preliminary results of measurements of the collection efficiency of a 170-micron sphere as a function of temperature show a decrease of collection efficiency with tempera- ture from 0.17 at —4°C to 0.04 at —20°C. The results are discussed with reference to growth of snowflakes, charge separation in thunderstorms and the bright band. Introduction—The study of the mechanisms involved in the growth of cloud particles into precipitation particles has been one of the most important phases of cloud physics. The growth of water drops by condensation and coalescence has been treated extensively both theoretically and experimentally. Although all of the investi- gations are not In complete agreement and more work is needed for the smaller drops, one can make a reasonable estimate, from existing in- formation, of the time required for a small drop to grow to the size of observed precipitation particles. In addition, the growth of ice crystals by sublimation has received considerable atten- tion; however, the importance of the aggrega- tion or conglomeration of ice crystals has been grossly neglected. In this case, in addition to the aerodynamic considerations, it 1s necessary to establish the environmental conditions in which two ice crystals will actually stick together. The results of field experiments by Cunning- ham and Atlas [1953] indicated that in some storm systems the ice phase accounts for as much as two-thirds of the precipitation. It appears that a considerable amount was caused by the aggregation of ice crystals; however, it is quite difficult to separate the growth by sublimation and by aggregation in this particular experiment and to specify the conditions which are most conducive to aggregation. Several radar studies also indicate the importance of aggregation. In particular the attempts to justify the change in the echo intensity above the zero degree isotherm by sublimational growth alone seems to require unreasonable rates of growth of the ice crystals, *The research leading to this paper was sup- ported by the National Science Foundation grant G-3477. “Contribution No. 59-55, College of Mineral In- dustries. 257 and it appears that the aggregation of ice erys- tals must make an important contribution to the change in intensity of the echo. Very elaborate studies at MeGill University [Douglas and oth- ers, 1957] of snow generating cells using verti- cally pointed radar, which gives a height-time record of snow echoes from which the terminal fall velocity of the particles could be determined, have shown that aggregates of ice crystals exist at very low temperatures. They found aggregates at temperatures as low as —34°C. In the cases they studied they found no preferred tempera- ture at which snow cells form, but did find that the aggregation generally occurred within the first few thousand feet above a frontal surface. Preliminary laboratory experiments carried out by Hosler and others [1957] have shown that the aggregation of ice crystals may be important at temperatures lower than had been expected, and that the temperature and the vapor pres- sure are extremely important in determining whether or not a collision between two ice par- ticles will result in aggregation. They carefully manipulated two ice spheres together and meas- ured the force required to pull them apart after being in contact for one minute. The force re- quired to separate the spheres as a function of temperature and at ice saturation is reproduced in Figure 1. These measurements, although not realistically simulating two small ice crystals, in- dicate that aggregation should not be very im- portant at ice saturation at temperatures below —25°C. Their measurements at near water satu- ration gave only a slight decrease with tempera- ture in the force required to separate the spheres. With this in mind, we have developed an ap- paratus in which a small ice sphere could be fixed in a flow of ice-crystal-laden air, and the growth of the sphere observed at various tem- peratures and vapor pressures. 258 HALLGREN AND HOSLER Environment saturated with respect to ice. Curve A. Environment dry Curve B. FORCE REQUIRED TO SEPARATE SPHERES(IN DYNES) -80 -25 -20 1h} -10 -5 ie} TEMPERATURE , °C. Fra. 1—Relationship of mean force required to separate the ice spheres to temperature Experimental apparatus—An overall view of the freezer, apparatus, and control panel is shown in Figure 2. The apparatus is mounted in a commercial freezer approximately 2 X 2 ft and 6 feet high. The temperature can be varied from room temperature to —26°C, with the temperature difference from the top to bottom of the freezer kept to approximately 1°C or less by a mixing fan located at the bottom of the freezer. A schematic of the basic components of the apparatus is shown in Figure 3. It is, basically, a variation of the techniques used by Kinzer and Cobb [1956, 1958] in their studies on small wa- ter drops. Region A represents an inner chamber with a 4-ft® volume in which an ice-crystal cloud is formed by means of a regulated flow of satu- rated vapor and subsequent seeding by dry ice. The concentration and form of ice crystals vary with temperature in the usual manner. The aver- age diameter of the ice crystals is between 8 and 20 microns being in general larger at higher temperatures and smaller at lower temperatures. The cloud is slowly transported up to the mouth of the vertical tube (2-inch inside diameter) con- taining the sampling device by a negative pres- sure created by a pump. The crystals are then transported through the smaller tube (34-inch inside diameter plastic tube) in which the veloc- ity can be varied from 0 to 100 cm/sec by vary- ing the voltage applied to the motor of a blower which in turn varies the negative pressure cre- ated at the top of the tube by the Venturi ef- fect. A rack gear at B permits the insertion of an ice sphere into the center of the tube. The ice sphere is mounted on the end of a fine rabbit hair or on a spider silk and is observed through a microscope. Immediately below the observa- tional area is a sampler with which we measure the concentration of ice crystals passing through the test section. It permits a section of the tube to be shifted out of the flow, and subsequently the crystals contained in the volume precipitate onto a cover glass covered with a one-percent solution of Formvar and placed at the bottom of the shifted section of the tube. The height of the sampling section is two inches, and the cover glass is placed on a holder and then inserted into the center of the tube. Since the cover glass is located in the center of the tube, losses to the Fic. 2—Overall view of freezer, control panel, and apparatus AGGREGATION OF ICE CRYSTALS 259 walls and by impingement do not affect the ac- curacy of the sample. From samples taken only a few seconds apart, it appears that this method of sampling is reproducible and that the accu- racy is very good. Another attempt to sample in the smaller tube immediately above the observa- tional area has proved unsuccessful although we still have some hope of resolving the difficulties with this particular sampler. The method currently being developed for maintaining varying degrees of supersaturation with respect to ice is to mix air at a known flow rate, temperature, and dewpoint with the ice- saturated air. The rate of flow of air is measured by means of a sensitive flowmeter. This method appears favorable for varying the vapor pres- sure with reference to ice saturation and water saturation, but will be limited in the sense that we will not be able to determine absolutely our position above ice saturation due to deposition on the walls of the tube and the ice crystals. Experimental procedure—A cloud is formed within the inner chamber by a continuous source of vapor and then the cloud is slowly lifted through the larger tube. A period of ten sec- onds is required for the cloud to travel the length of the tube. During this time a small ice sphere is inserted into the observational area and the motors turned on so that the ice crystal cloud is carried past the ice sphere at a known velocity. The width and height of the aggregate is measured several times throughout the period of the run which in the cases reported here var- ied from three to six minutes. The cloud is sam- pled at the middle and end of the run. Immedi- ately prior to sampling, the cloud is stopped in order to prevent impingement of the cloud on the tube. A cover glass is then removed from the plastic solution, placed on a holder and inserted at the bottom of the volume to be sampled. The section is then shifted and the run continued. In the case of the final slide of the run, the tube is not shifted, but a known volume is closed and the cover glass inserted. Several minutes are allowed for the ice crystals to precipitate onto the cover glass. The cover glass and holder are then re- moved and left to dry. A complete analysis for concentration, size distribution, and type of ice crystal is made from the slide. From the con- centration, velocity in the tube, length of run, and the average area of the aggregate (actually the area of a circle of the diameter of the aggre- gate), we obtain the number of ice crystals for which collision was possible. At the end of the COMMERCIAL 4 cu. ft. Cloud volume Mixing fon Fie. 3—Schematic of the apparatus run the aggregate of ice crystals is melted and the diameter of the drop is again measured. From the increase in size, the mass can be determined, and using the average volume of the crystals counted, we obtain the actual number of crystals that adhered to the sphere. The volume of the crystal is determined by measuring the diameter of the ice erystal and from average measure- ments of the thickness obtained from a side view of the erystal through the microscope. At pres- ent a technique is being developed so that the thickness can be determined by shadowing the replicas and measurements made from electron photomicrographs. With the two, we define the ratio of erystals collected to the total number of crystals in the path of the collector. Preliminary results—A summary of the aver- age measurements of some of the parameters necessary to compute the ratio is shown in Ta- ble 1, along with the ratio at several tempera- tures. All of the measurements reported here 260 HALLGREN AND HOSLER TaBLe 1—Average values of measurements | | Ratio: Increase , Final Size of crystal crystals Temperature | Hangth | im mass [Density of diameter Crpetal co" ype of crystal collested sphere | gate | crystals Volume Radius in path XO} sec 108 g | gm/cm* micron cm-3 | micron’ micron —4 197 3.2 0.05 450 | 3050 Needle | 1170 6.3 X 39 0.17 —8 147 2.0 0.04 435 8100 Plates | 320 8.7 | Columns |" Gr3) ie 0.12 —12 175s || Oral 0.038 740 14700 Plates 350 | 9.0 Columns 0.07 — 20 297 2.07 0.02 570 7300 Plates 425 10.5 0.04 were taken with a sphere with an initial diameter of 170 microns. The increase in crystal concen- tration with decreasing temperature accounts for the manner in which the amount of mass col- lected on the ice sphere and the final diameter of the aggregate vary. If reduced to a common crystal concentration and length of run, the mass collected and the final diameter is actually much less at the lower temperatures. The ratio of erys- tals collected to erystals in the path of the collec- tor decreases with decreasing temperature. The decrease with temperature is quite uniform, be- ing 0.17 at —4°C and 0.04 at —20°C. Whether or not the factor of four between the collection efficiency at —4°C and —20°C represents en- tirely a change in the number of ice crystals that stick after a collision is open to some question because of the method utilized in estimating the area swept by the aggregate. Actually, since the density of the aggregate is less at lower tempera- tures than at higher temperatures, one would expect that an ice crystal would have a better chance of actually being within the area and still not having a collision with another crystal at the lower temperatures. We are currently at- tempting to obtain a more realistic estimate of the actual area. However, the type of growth we observe probably is similar to that occurring in clouds since our densities are approximately the same as the density of snowflakes. Therefore, the results are satisfactory for computations of the growth of aggregates within clouds. Although we did not measure the charge accumulated by the aggregate, the studies of Reynolds and others [1957] indicate that it should be negligible since the cloud used in these particular runs contained only ice erystals and no supercooled droplets. It is interesting to note that the area pre- sented to the flow by the collector increases quite rapidly because the initial growth is quite open and results in a rapid decrease of the density of the aggregate. This could very well lead to a particle of sufficient size to reflect a radar signal in a rather:short period of time. Observations of an aggregate growing in our chamber show ex- tensions growing out from the sphere a consid- erable distance before any appreciable ‘filling in’ occurs. For example, in Table 1 we see that while the increase in mass was only sufficient to increase the diameter of the 170 micron sphere shghtly at —4°C, the final diameter of the ag- gregate was on the average 450 microns. Simi- larly, at —8°C the average final diameter of the aggregate was 435 microns, at —12°C the final diameter was 740 microns and at —20°C the final diameter was 570 microns. Actually, the in- crease would be more pronounced if the con- centration of ice particles had not increased with decreasing temperature. In addition, the average length of the run increased with decreasing tem- perature. It seems to be true when observing growth of an aggregate that the final size of the aggregate is considerably larger with larger ice crystals. In other words, the extension grows much more rapidly with the larger ice crystals (our crystals are largest at —4°C) and results in a much lower density growth initially than with smaller crystals. However, it is, at least with the present information, extremely difficult to make any estimate of the time required for the particle to grow to a particular size because the relation between the length of the extension and the size of the crystals has not yet been established. The rapid growth of the extensions could ex- plain the recent observations of Vonnegut and Moore [1958] which indicate that the initial echo on the radar scope is in the form of an inverted cup and that the echo develops very rapidly. This, combined with their observation of a veil AGGREGATION OF ICE CRYSTALS of ice crystals surrounding the core of the cloud, might be explained in the following manner: Drops grow in the core of the Cumulus to a di- ameter that cannot reflect a radar signal, say 40 microns, and upon arriving in the layer of ice erystals surrounding the Cumulus grow quite rapidly by means of the extensions to a size that can be detected by the radar. Unfortunately, present airborne sampling techniques do not en- able us to detect the presence of such small ag- gregates. These extensions would only make an impor- tant contribution to the area swept out by the aggregate when the collector is rather small. It seems reasonable that there is some critical di- mension after which the ‘fillmg in’ would pro- ceed at the same rate the extensions are grow- ing. For some time there has been a good deal of speculation as to how much of the increase in the radar signal above the bright band can be attributed to aggregation and how much to sub- limational growth of the ice crystal. With the above results, one can see that even at ice satu- ration considerable growth could be achieved through aggregation down to temperatures lower than had been thought. The above results also have some important implications with reference to charge separation in clouds. The graupel process, as it has been developed by Reynolds and others [1957], re- quires the separation of the charge by means of frictional contact between the larger ice parti- cle and the ice crystals in the cloud. In the ex- periments of Reynolds, which were carried out in an ambient temperature of between —12 and —17°C, with the growing graupel particle being three or more degrees warmer, one would expect a large number of the ice crystals actually to ad- here to the graupel particle. If one assumes that the 0.17 measured at —4°C represents 100% col- lection after collision, then even at temperatures down to about —15°C approximately one-half of the crystals adhere after collision even at ice saturation. In addition Reynolds and others [1957] observed the maximum charge generation in a cloud near water saturation which is where Hosler and others [1957] report only a slight change with temperature in the ability for ice crystals to adhere, and therefore, places the as- sumption (made by Reynolds) of the amount of charge separated per collision by assuming that none of the crystals adhered, in error by a con- 261 siderable amount. Our contemplated investiga- tions should elarify this particular point. It is interesting to speculate upon the role collection efficiencies of ice pellets in an ice or mixed cloud may play in charge separation m thunderstorms. Should the collision between a graupel or hail pellet and an ice crystal, without collection, be a necessary prerequisite to the rapid separation of charge, then a pellet falling through an all ice cloud at the lowest possible temperature would yield the largest charge sepa- ration. This is due to the observation that fewer crystals are collected at ice saturation than at higher vapor pressure, and that the lower the temperature, the fewer ice crystals that are col- lected. This would not agree with Reynolds and others [1957] observations, but it might well ex- plain the increased lightning in thunderstorms where cloud seeding has been employed to trans- form a greater proportion of the clouds to ice [Battan and Kassander, 1960]. If Reynolds’ ob- servations are correct, then in light of our ex- periment, another charge separating mechanism must be operative. However, it may be that the charges generated in Reynolds’ mixed clouds were due to the small amount of bounce-off that occurred and had he performed the experiment at high erystal concentrations in an all-ice ecrys- tal cloud he would have measured even more charge generation. With our projected measurements at ice super- saturations, we also hope to explain the result of some radar studies of snow generation cells carried out at MeGill [Douglas and others, 1956]. These observations indicated that the majority of the cells occurred just above a frontal sur- face where the uplift of the front would be most intense. Combined with the general uplift that was occurring under the situations studied, one would expect these stronger regions of uplift to be supersaturated with respect to ice, thereby making aggregation possible at all temperatures. In these studies the conditions were always such that the atmosphere was supersaturated with re- spect to ice, and for the several observations that indicated generating levels at very low tempera- tures, it appears the area was also somewhat unstable at the generating level, which would create convection and higher supersaturations with respect to ice. REFERENCES Bartan, L. J., anp A. R. Kassanper, Jr., Artificial nucleation of orographic Cumuli, this publica- tion, pp. 409-411, 1960. 262 Cunnincuam, R. M. anv D. Attias, Growth of hy- drometers as calculated from aircraft and radar observations, Proc. Toronto Met. Conf., R. Met. Soc., pp. 276-289, 1953. Doveuas, R. H., K. L. S. Gunn, ano J. S. Mar- SHALL, Patterns in the vertical of snow genera- tion, Sci. Rep. MW-21, MacDonald Physics Lab., McGill Univ., 153 pp., 1956. Hoster, C. L., D. C. Jensen, anp L. GoLtpsHuLaAK, On the aggregation of ice crystals to form snow, J. Met., 14, 415-420, 1957. Kinzer, G. D., anp W. E. Coss, Laboratory meas- DISCUSSION urements of the growth and collection efficiency of raindrops, J. Met., 11, 295-801, 1956. Kinzer, G. D. ann W. E. Cobb, Laboratory meas- urements and analysis of the growth and collec- tion efficiency of cloud droplets, J. Met., 15, 138- 148, 1958. Reynotps, 8. E., M. Brooks, anp M. F. Gowtry, Thunderstorm charge separation, J. Met., 14, 426-436, 1957. Vonnecut, B., anp C. B. Moore, Thunderstorm study, Mt. Withington, New Mezico, unpub- lished memorandum, A. D. Little, Inc., 9 pp., 1958. Discussion Dr. U. Nakaya—How do you measure these ice crystals? Dr. C. L. Hosler—We have a man who sits there eight hours a day and measures these erys- tals. We have made replicas in Formyar. We have spent a year and a half trymg to measure the actual number and size of the crystals in our cloud. It has been our most difficult problem to make sure we had a representative sample and to know what we had in the test section. We had inserted a collection device above and below the test section. We are finally fairly con- vinced we are actually measuring the population of test erystals going through our section. The process of collection of individual crystals is observed by means of a microscope attached to the test section. Their thicknesses and lengths are determined throughout the test. In addition, we have these samples collected by actually ro- tating out a section of the tunnel and by gravi- tational settling collecting them in a Formvar solution and making plastic replicas. Dr. W. Hitschfeld—I think these are very beautiful data, but I am still surprised to find that the collection efficiencies you measured are so low. Dr. Hosler—Do not put too much weight on these efficiencies because we computed them using an average cross-sectional area. In reality, they present weird-shaped aggregates with a lot of holes in them. Maybe one-half of this average area is actually occupied by ice and one-half is holes. Dr. Hitschfeld—So you could double these collection efficiencies ? Dr. Hosler—Yes, now we are trying to meas- ure the true area of these crystals, but we have not accomplished it yet. Dr. B. J. Mason—Those values on the right in Table 1 really do not represent ‘sticking’ alone, because they are really partly due to aggregation and partly due to sticking. The imterpretation of exactly what those figures mean will be diffi- cult because the hydrodynamics of the problem is changing all the time depending on the shape of the erystals one is using. But, nevertheless, what you are measuring is the overall thing which meteorologically is important. Of second- ary importance perhaps is whether you noticed any major difference, even in a qualitative way when you changed from needles, say, to plates. Dr. Hosler—One observes very interesting things. The bigger the crystals are, the more quickly this aggregate assumes a greater area. Some detailed observations appear to be quite important: We were afraid, for instance, when long extentions would build out, that they would break off and fall away. Instead, they build out to a certain length and then fold right back into the aggregate. Then it merely fills in and gives a graupel-type buildup. Dr. Helmut Weickmann—I have the impres- sion that your experiment is a good analogy to what really happens in nature during the ag- gregation in a convective cloud layer. Such a layer has a little convective activity with up and down draft velocities of one-half to one meter per second. This is enough to support some of the crystals. The ensuing small-scale turbulence cre- ates a much better chance to aggregate than if they just meet each other during a straight fall. If they go up and down, veering left and right, they meet each other much more frequently. Dr. Hosler—In addition to this, when falling through a cloud layer a water film may form on the crystals which greatly assists the sticking. DISCUSSION 263 Dr. Choji Magono—As the crystal type is very important in the formation of snowflakes; what type did you use in the experiment? Dr. Hosler—We had plates, columns, and needles but because of the temperature range along our wind tunnel it was difficult to control this. However, we can work with plates or nee- dles by just changing the environment we are creating. Dr. Magono—Did you use dendritic types? Dr. Hosler—No, we were unable to obtain them in our small chambers. Perhaps the Swiss can get dendrites. In ours, we must wait a long time before we get dendrites. Dr. Magono—In nature we find that snow- flake formation begins at an air temperature warmer than —10°C. Dr. Weickmann—(communicated) Dobrowol- ski in his fundamental but little-known work on snow-crystal observations in the Antarctic (A. Dobrowolski, La neige et le givre—Rapports Scientifiques; Résultats du voyage du 8.Y. Bel- gica en 1897-1898-1899; La Météorologic, 1904) gives the following table on the dependence of snowflake occurrence from the ambient tempera- ture: Snowflake Temperature occurrence +1.0 to —5.0°C 83% —5.1 to —10.0°C 9% >—10°C 8% Growth by Accretion in the Ice Phase R. H. Doveuas Meteorological Service of Canada, and McGill University, Montreal, Canada Abstract—The growth of spherical ice particles of various densities by sublimation and accretion is considered. The less dense the particle, the greater the mass it must achieve by sublimation before accretion becomes the dominant growth mechanism. Once this stage is achieved, however, growth rates of particles of the same mass are relatively insensitive to particle density, the cloud water content exercising the major control. With low water content (0.1 gm m™) such as in stratiform clouds and in the dilute peripheral regions of cold Cumulus, the precipitation products are essentially sublimation elements rather than graupel. In four gm m™* Cumulus, low-density grau- pel can grow to millimeter size within six minutes and to centimeter size within ten minutes, much denser particles requiring only a few minutes longer to reach the same sizes. These times are comparable with the observed elapsed times of about 15 min be- tween the detection of the first radar echo and the first appearance of hail at the ground. Introduction—The accretion process is im- portant to the production of graupel and hail; there is a need for study of the initial growth of the primitive ice particle and its transforma- tion from a sublimation to an accretion element. The appearance of graupel seems to be related to the development of electrical fields in Cumu- lus [Fitzgerald and Byers, 1958]. While the Thunderstorm Project [Byers and Braham, 1949, p. 48] reported very few flight encounters of hail in thunderstorms, this may have been due in part to the localization of hail within the storm; identification of graupel would likely be diffi- cult from an aircraft. However Kuettner [1950] claims that graupel is the most frequently ob- served hydrometeor in thunderstorms occurring over the Zugspitze (at 10 kft), beg always as- sociated with high electric fields; large hail was found to be a rare and by no means a neces- sary occurrence in the 125 storms which he studied. Thus, while hail may not accompany every thunderstorm, it appears that graupel does. For a small frozen droplet, growth proceeds mainly by sublimation until a critical size is reached, following which accretion predominates; it has usually been particles above this critical size whose growth has been studied, Ludlam’s [1952] study of the development of ice parti- cles and their role in shower initiation being a noteworthy exception. Also, the graupel prob- lem involves densities which may be as low as 0.04, according to Magono’s [1954, p. 38] data, and relatively few studies have considered den- sities even as low as 0.1; the present paper ex- amines the growth of spherical particles (such as frozen droplets) of densities from 0.05 to 0.9, by sublimation and accretion occurring together. Growth rates—Sublimational growth at a rate (dm/dt), supplies heat to a growing spherical particle at a rate Q, = L, (dm/dt), = L. 4rSCDAp where L, = latent heat of sublimation, S = par- ticle radius, C = ventilation factor, D = dif- fusivity of water vapor in air, Ap = excess of ambient vapor density over that at the crystal surface. Growth by accretion at a rate (dm/dt). supplies further heat at a rate Q: = L, (dm/dt). L, being the latent heat of fusion. Heat is lost to the environment at the rate Q; = 4crSKCAT where K = thermal conductivity of the environ- ment and AT = excess of temperature at the crystal face over that of the environment. In the steady state, Q: + Q. = Q;, whence Ko Ly ee] Apa _ 1 AT, ~ DE: |) 4aKSCAE in which the subscripts a on the left hand side indicate the presence of accretion. The physical significance of Ap./AT. is shown in Figure 1 in an environment which is saturated with respect to water, such as would exist in the supercooled 264 GROWTH BY ACCRETION IN THE ICE PHASE 265 water cloud in which accretional growth would occur, Now K/DL, = Ap./AT., for sublimation alone [Marshall and Langleben, 1954], so that a Aps dm 7m ease 1 — 2, || eK SCAT) AT a AT; diac and since AT is positive, the crystal being warmer than the air, it follows that Ape/ATa < Ap:/AT,, the difference being proportional to the accretional growth rate. Thus the effect of accretion is to increase the temperature excess of the growing particle, and so to reduce its va- por density excess which in turn reduces the sub- limational growth rate. The total growth rate, then, is the sum of the sublimation-only and ac- cretion-only components, the former reduced by a term which is proportional to the latter. At 700 mb and —10°C the reduction term is ap- proximately three per cent of the accretional growth rate; it increases with temperature and with pressure to about six per cent at 1000 mb and 0°C. Considering all other possible sources of error in growth calculations, 1t appears rea- sonable to ignore this relatively small reduction, and to consider the total growth rate as the sum of the two components, sublimational and ac- cretional. Density of particle and of accreted material— The density of the particle is important in de- termining its terminal speed, and may of course vary during growth. Densities of hailstones are usually estimated to be about 0.7-0.8 [see, for example, Weickmann, 1953, p. 129]. Densities of graupel have been measured by Nakaya [1954, p. 115] who reports a value of 0.125, invariant with particle diameter, over a range of 1.5 to 6 mm. Magono [1954], theorizing on the terminal speed of graupel, finds agreement with observed values when the density is of that order, but presents observational data indicating densities as low as 0.04. That the density of the accreted material is dependent upon the ambient temper- ature and liquid water content is suggested by riming data of Clark [1948] and by the results of Melcher’s [1951] experiments [see Weickmann, 1953], also by the riming data of Langmuir [1944; see Ludlam, 1958, p. 55]. Generally speak- ing, the warmer the temperature, the higher the cloud water content, and the greater the velocity of impact, the denser is the accreted material. Thus, for the smallest particles on which accre- tion is just beginning, a relatively low density Fig. 1—Curves show schematically the equilib- rium vapor density with respect to water p, and to ice p; as a function of temperature; at the face of an ice erystal, growing by sublimation in water- saturated air, the temperature exceeds the ambi- ent value by A7’, , and the growth rate is propor- tional to the vapor density excess Ap;; accretion increases the former to A7’, and reduces the latter to Apa of acereted material is reasonably to be ex- pected; with increasing size and fall speed, this density should increase, and Magono’s [1954, p. 38] data do indeed show a roughly linear increase in density from 0.04 to 0.17 as graupel diameter increases from 1 to 6 mm. Therefore, in consid- ering the growth of particles, particularly in the early stages, consideration must be given to rela- tively low particle densities. In the present study, growth has been treated arbitrarily at constant density. When a particle of initial mass mo, and density oo accretes mate- rial of density o., then the particle density be- comes g when it has grown to mass m according to the equation (o — oa)/(oo — oa) = M/m, Thus, as the particle mass increases tenfold, the density difference between the particle and the accreted material decreases to one-tenth its imi- tial value. It will be found (Fig. 2) that this density change can be accomplished within a few minutes. Growth calculations—Growth rates were com- puted for spherical particles of densities 0.05, 0.2 and 0.9, representative of the range from Magono’s [1954] least dense graupel to dense hailstones. Terminal speeds were determined on the basis of Langmuir’s [1948] work. Sublima- tional growth rates were calculated on the basis MASS (pgm) 10° --- 00:05 o-2 1o'b 14 0-9 Coalescence 8 Ob 2 #4 TIME (min.) 6 18 20 Fic. 2—Mass of a spherical ice particle as a function of time; the coalescence curve shows the growth of a liquid droplet in 4 gm m-*Cumulus; cross-marks on the 4 gm m“$ curves indicate parti- cle diameters of 1 cm and (on the coalescence curve) of droplet radius 50u; open circles indicate masses at which the sublimational and accretional growth rates are equal (in the As case, growth is predominantly sublimational within the range of the figure) of a water-saturated environment at 700 mb and —15°C. Accretional growth rates were cal- culated by means of the growth equation am IP (S + r)UEW, d —= 2 uh dt i" us 7 T where S = particle radius, 7 = droplet radius, U = velocity of particle with respect to the droplet, Z = collection efficiency of particle with respect to the droplet, W,dr = liquid water con- tent contained by droplets of radius 7 to (r + dr). Droplet growth by condensation and coa- leseence has been treated at length by Hast [1957], whose derived cloud droplet distributions appropriate to 1 and 4 gm m™* Cumulus were used in the present work; for stratiform cloud of low water content, Diem’s [1948, p. 261] dis- tribution for Altostratus was used. For convenience in comparing the collection R. H. DOUGLAS characteristics of various particles in various environments, it is useful to consider an ‘effec- tive collection efficiency’ H’, the fraction of the liquid water content, contained within the swept volume, which is accreted. Thus H is defined by the equation dm/dt = 2S°v,.E’W where v, = terminal speed of the collecting par- ticle, and W = liquid water content. In this way EH’ incorporates the effects of droplet size dis- tribution and of relative speeds. Figure 3 shows EY’ as a function of mass, for particle densities of 0.05, 0.2, and 0.9, in 1 and 4 gm m™® Cumulus and in Altostratus. The improvement in collec- tion as particle density increases, and as one proceeds from Altostratus to increasingly dense Cumulus, is clearly dicated, as also is the ap- proach, for large particles, toward a maximum value. However an extension of these curves to even larger masses tends to show a decrease in EY’; such a decrease at large radii is evident in Langmuir’s [1948] Table 4 and in Gunn and Hitschfeld’s [1951] Figure 1. Figure 4 shows the growth rate as a function of particle mass, obtained by the addition of the sublimational and accretional rates. The parti- cle masses at which these two rates are Just equal, when the particle density is 0.9, are indi- cated by the arrows; for densities of 0.2 and 0.05 the critical masses are displaced to higher values by factors of about 3 and 8, respectively. Thus the denser the particle and the higher the cloud content, the smaller the mass, and the ra- dius, to which growth must proceed before ac- cretion becomes dominant. Considering cloud of low liquid water content, it is seen that particles of mass greater than 10° to 10° »gm may be ex- pected to exhibit riming. This is in general agree- ment with observations of (unrimed) spatial dendrites and of crystals with droplets attached; of these erystal types, the largest observed by Nakaya [1954] had masses in the range 300-500 pgm. Particles of masses greater than these were in the form of graupel [see Nakaya, 1954, Fig. 224). Also shown in Figure 4 is the growth curve, by accretion only, of a 0.9-density particle in 4 em m™ cloud. This particle density is nearly enough equal to that of a liquid droplet that this curve may be used to describe droplet growth by coalescence, and to compare droplet growth with graupel growth. GROWTH BY ACCRETION IN THE ICE PHASE 267 —CU 4gm m-> —CU Igm m$ --AS 107 io" 10° 10! 10? 0° 10* MASS (x. gm) Fic. 3—Effective collection efficiency H’ as a function of particle mass for spheres of densities 0.05, 0.2, and 0.9 in Altostratus and in Cumulus of 1 and 4 gm m“$ 77) CU 4gm m* 1o* --- 00:05 ra 02 09 to! od Coalescence GROWTH RATE (pgm sec!) Gl 10° 1o* MASS (pgm) Fic. 4—Growth rate of a spherical ice particle by sublimation and accre- tion, as a function of its mass, for various particle densities and in various clouds; the coalescence curve shows the growth rate of a liquid droplet in 4 gm m*Cumulus; particle masses (density 0.9) at which the accretional equals the sublimational growth rate in the various clouds are indicated by the arrows 268 R. H. DOUGLAS The most striking feature of these growth- rate curves is the relative insensitivity of growth rate to particle density. For any given mass, variation of density by a faetor of 18 results in a variation of growth rate by a factor of only 3 or less; for a given mass, a reduction in den- sity tends to increase the swept volume, but re- duces the effective collection efficiency by an al- most equivalent amount. The major control of growth rate is clearly the liquid water content. At the upper ends of the curves, the growth rate is proportional to the 5/6 power of the particle mass. Curves showing particle mass as a function of time are given in Figure 2. Initial particle mass was taken to be 10° pgm, but the individual curves can be used for any greater initial mass. Also included is one curve for growth by accre- tion only, of a particle of density 0.9 in 4 gm m™ Cumulus, which may be considered to represent droplet growth by coalescence; this curve begins at droplet radius 20u, below which growth pro- ceeds entirely by diffusion. Results—Houghton [1950] has compared drop- let growth by coalescence in 1 gm m™ cloud with the sublimational growth of ice crystals, and found the latter to be more rapid for masses up to about 10 pgm (melted radius 130 p), a result in substantial agreement with the present caleu- lations when the coalescence rate in 1 gm m~® cloud is compared with the low-density sublima- tion rate. But the present study provides the means of comparing growth of liquid drops with growth of frozen drops by sublimation and ac- cretion, and over a wide range of density. Considering growth in 4 gm m™ Cumulus, the frozen droplet will have the advantage over the unfrozen one for masses up to about 1 pgm (melted radius 60 ,) (Figs. 2 and 4). In 1 gm m~ cloud the advantage persists for masses up to 10 pgm (melted radius 130 »), and in Alto- stratus of 0.1 gm m™, up to masses of at least 10* pgm (melted radius > 600 »). The less dense accretion particle has a slight advantage over the more dense one (Fig. 4). If liquid drops freeze at smaller sizes than those noted above, they will continue growth more rapidly than their unfrozen neighbours, but if freezing is postponed until larger sizes are reached, the frozen particle loses most of this advantage. Hast [1957] shows that the initiation of the all-water coalescence precipitation process follows closely upon the appearance of 50 p», radius droplets in 4 gm m™ Cumulus. But if droplets of lesser radius should freeze before any have reached 50 p, these frozen particles can compete vigorously with the un- frozen remainder, and _ precipitation growth through the ice phase is competitive with that through the all-water process. This applies only to summer Cumulus of the temperate regions, in which cloud water contents of 4 gm m™ are at- tained above the freezing level. With higher cloud contents such as may be achieved in warmer Cumulus, the advantage of the all-ice growth process over coalescence may be greatly reduced, since accretion ‘cuts in’ at a smaller particle size the greater the cloud water content. The effectiveness of the growing particles in removing the cloud water content is best defined as the mass collected per unit distance fallen. While Figure 4 shows the approximate equality of growth rates (within a factor of 2) at various particle densities, the less dense particle, falling more slowly, collects more cloud water per unit distance fallen. Thus, in falling through a unit depth of cloud, the less dense particle sweeps up more cloud water than a denser particle of the same mass. In the three types of cloud considered here, particles of density 0.05 may in this sense be up to six times as effective as those of den- sity 0.9; thus low density accretional growth 1s the more potent cloud-consuming process. In cloud of low water content (0.1 gm m™*) growth to the stage where accretion becomes the dominant mechanism requires times in excess of half an hour, and cloud depths from 3000 to 8000 ft for low- and high-density particles, respec- tively. Unless cloud exists in such depth, the emergent precipitation particles will be more of the nature of sublimation elements (snow) rather than graupel; with cloud layers of rea- sonable thicknesses, only the lowest density eraupel is likely to emerge. As cloud water con- tent increases, and accretion is increasingly favored, the likelihood of accretion elements in- creases, and conditions for significant higher- density growth improve. In cold Cumulus, the dense undiluted core may be favorable for graupel growth, while the dilute cloud bound- aries will yield sublimation elements, or snow; such precipitation of both graupel and snow is occasionally observed from small Cumulus dur- ing the cold seasons of the temperate regions. In denser cloud of 4 gm m™, accretion becomes predominant at masses of the order of 1 pgm, which may be achieved within the first four min- utes of growth; particles of 1 em diameter are grown within an additional twelve minutes. Ob- DISCUSSION servations of radar echoes and of hail occurrence indicate that, at times, hail may reach the ground within fifteen minutes of the first ap- pearance of echo. In 4 gm m™* Cumulus, coales- cence will produce a 50 » radius droplet within about ten minutes, at approximately which time the first echo will be detected [Hast, 1957]. Fol- lowing detection, the droplets may freeze and continue growth in the ice phase, or may grow further by coalescence before freezing, depend- ing upon the temperature. Caleulations made (from Fig. 2) of the times required for the growth of graupel or hail of 1 em diameter, starting with a 50 » ra- dius drop, and varying the size at which the liquid drop froze. Even considering drops freez- ing over a wide range of sizes, and subsequent growth over a wide range of particle densities, the times to reach 1 em diameter varied only from 9 to 16 mins, the shorter time being for the low-density growth. These times are com- parable to the 15-min interval observed between echo detection and appearance, at the ground, of the first hail. The growth rates and times involved, as dis- cussed above, are only applicable until depletion of the cloud content becomes significant, and so may be relevant only to the first ‘burst’ of hail. The shape of the primary graupel nucleus is not known, and may not be spherical. It is not known whether dense hail begins as graupel or as a frozen drop, and it may grow in supercooled rain; high density growth by collision with rain drops has not been considered, and undoubtedly should be. Reliable data on stone structure, and on the laboratory growth of various types of particles in various environments, are urgently needed to clarify these pomts of uncertainty. Acknowledgments—The author is on assign- ment to the Stormy Weather Group, MeGill University, the assistance of whose members is gratefully acknowledged. Participation in this research, and publication of the above, is with the permission of the Director, Meteorological Service of Canada. This paper constitutes a revision and exten- sion of work reported earlier in Stormy Weather were 269 Group Scientific Report MW-26, Growth of Pre- cipitation Elements by Sublimation and Accre- tion, May 1957. The present results are consid- ered more reliable than in the earlier work. REFERENCES Byers, H. R., anp R. R. Brauam, Jr., The thunder- storm, Govt. Print. Off., Washington, D.C., 287 pp., 1949. Cuark, V., Icing nomenclature, Harvard—Mt. Washington Icing Res. Rep. 1946-1947, Air Force Tech. Rep. 5676, pp. 415-481, 1948. Diem, M., Messung der Grosse von Wolkenele- menten, II, Met. Rundschau, pp. 261-273, 1948. East, T. W. R., An inherent precipitation mecha- nism in Cumulus clouds, Q. J. R. Met. Soc., 83, 61-67, 1957. Firzceratp, D. R., anp H. R. Byers, Aircraft ob- servations of convective electrification, Recent advances in atmospheric electricity, Pergamon Press, pp. 245-268, 1958. Gunn, K., anp W. Hirscuretp, A laboratory in- vestigation of the coalescence between large and small water drops, J. Met., 8, 7-16, 1951. Hovuauton, H. G., A preliminary quantitative anal- ysis of precipitation mechanisms, J. Met., 7, 363- 369, 1950. Kuerner, J., The electrical and meteorological conditions inside thunderclouds, J. Met., 7, 322- 332, 1950. Lanemuir, I., Supercooled water droplets in rising currents of cold saturated air, Gen. El. Res. Lab., Schenectady, N.Y., 1944. Lanemutr, I., The production of rain by a chain reaction in Cumulus clouds at temperatures above freezing, J. Met., 5, 175-192, 1948. Lupuiam, F. H., The production of showers by the growth of ice particles, Q. J. R. Met. Soc., 78, 543-553, 1952. Lupuam, F. H., The hail problem, Nubila, 1, 1-96, 1958. Macono, C., On the falling velocity of solid pre- cipitation elements, Sci. Rep., Yokohama Nat. U., sec. 1 no. 3, pp. 33-40, 1954. MarsHat., J. S8., anD M. P. Lanciesen, A theory of snow-crystal habit and growth, J. Met., 11, 104— 120, 1954. Mevcuer, D., Experimentelle Untersuchungen von Vereisungserscheinungen, Zs. fiir Angew. Math. Phys., IT, p. 421, 1951. Naxkaya, U., Snow crystals, natural and artificial, Harvard Univ. Press, 510 pp., 1954. WEICKMANN, H., Observational data on the forma- tion of precipitation in Cumulonimbus clouds, Thunderstorm Electricity, Univ. Chicago Press, pp. 66-138, 1953. Discussion Dr. R. List—Have you taken into account the Nakaya-Higuchi observations of drops which are caught by the erystals, and which are rolling over their surface. I think that this may give a greater rate of growth than that by the normal sublimation which is taken into account here. 270 Dr. U. Nakaya—ULast year we made a movie film which shows the mechanism of a small drop- let captured on the surface of ice; these ice sam- ples are polished and are exposed to the air for some time. We place a very small water droplet (one or two microns) on the surface. This drop- let does not freeze to the surface of the ice but it rolls over the surface getting smaller and smaller and, finally, it vanishes. That means this DISCUSSION droplet as a whole freezes onto the surface, but does not give a rimed crystal. It spreads out over the surface evaporating very quickly within 0.01 and 0.1 second. Dr. Hitschfeld—Obviously, this has not been taken into account, but I doubt that it would change Dr. Douglas’ results very greatly if it had. Frequency Distributions of Precipitation Oskar ESSENWANGER National Weather Record Center, Asheville, N. C. Abstract—Considerable difficulty is involved in the physical interpretation of the frequency distribution of precipitation. Such distributions usually do not follow the law of a gaussian distribution in a linear scale. This brings up the question for trans- formation to normality. The problem is rendered more difficult as the usually ob- served data have to be considered as truncated on the dry side. The author suggests the use of a logarithmic scale. A frequency distribution of annual precipitation generally consists of one collective, while in monthly values and shorter amounts the mixture of the rainfall processes becomes obvious. A sample for the frequency distribution of daily amounts at Asheville, N.C., is discussed. The col- lective of excessive daily rain in autumn could be explained in connection with hurri- canes on the east coast of the United States and the movement of extratropical cyclones through North Carolina. A two-dimensional analysis of intensity and dura- tion for single rainfalls in Braunlage (Germany) is also discussed. The sample demon- strates that it is necessary in order to read more details from the precipitation amount either to spht the rainfall data into intensity groups (such as convective and ad- vective types) or to keep the observational interval as short as possible. Hourly data may be sufficient. Introduction—The physical interpretation of the observed data is one of the primary topics of climatological work. If it were possible by some method to determine all physical processes of rainfall a priori, and collect the data into sepa- rate and distinct groups, then probably most of the following discussion would not be necessary. However, the basic physical processes leading to precipitation have not been completely investi- gated as yet and in many cases the set of ob- served data available consists of a complex of physical events which we call weather or climate. This mixture exists also for other meteorologi- cal elements, for which interpretation may be easy. Considerable difficulty is involved, how- ever, with frequency distributions of precipita- tion. In a linear seale they usually do not follow the law of a gaussian distribution and represent a mixture of different processes of rainfall, at least in the form of hourly, daily, monthly, ete., amounts. The kind of distribution we may expect from daily and shorter periods of observations is well known. It shows a maximum in the class of smallest precipitation amount and decreases to- ward higher amounts. A typical sample is illus- trated by Schneider-Carius [1954], who smoothed the frequency distribution in taking four German stations (Berlin, Bremen, Karlsruhe, and Mu- 271 nich) and all months of the year together (100,- 000 values). This summation merely serves to demonstrate the type of frequency distribution or to derive an average rainfall probability for an area, though its applicability for climatological de- tails is very limited. Data in linear scale—Using a linear seale for frequency distributions of precipitation, several statistical approaches may be made. The best fit, to date, under the limitations discussed be- low, may be obtained by applying an incomplete gamma function though the possibility also exists to employ a hyperbola, e* function (= also the limiting form of incomplete T function) or the negative binomial. The hyperbola or a form e-* may solve prob- lems of rainfall probability, but furnishes practi- cally no physical result. Wanner [1939] tried to use the negative binomial series for curve fitting in recognition of the persistence involved in me- teorological elements. However, this applies a discrete function to continuous data and the au- thor [Hssenwanger, 1956a] has previously dis- cussed the difficulties connected in arranging pre- cipitation data in discrete form to meet the requirement of the negative binomial distribu- tion. Besides this, the persistence for rainfall data is not a constant. This may be proved for 272 TaBLeE 1—Persistence factor f for various amounts of precipitation, Hamburg area, Germany, winter Limits Dry |Traces| 0.01 vats Lene i ze inch Dry 1.46 0.89) 0.79) 0.68) 0.59) 0.44) 0.33 Traces to | 0.71} 2.09| 1.77} 1.31] 1.21} 0.94] 0.73 0.01 0.02-0.03 | 0.72] 1.17] 1.27] 1.28] 1.21] 1.32] 0.58 0.04-0.09 | 0.58] 0.81) 1.24) 1.33) 1.40) 1.53) 1.48 0.10-0.40 | 0.55] 0.72) 0.91] 1.06] 1.45) 1.72) 2.19 >0.40 | 0.45] 0.68} 0.26) 0.71] 1.36) 2.16] 3.81 daily precipitations. Table 1 shows a persistence factor f, which is the observed frequency of oc- currence divided by the expected value without persistence (discussed in detail by the author [Essenwanger, 1956a]) . This factor is listed for several classes of daily amounts and it is easy to see that this is not a constant for the different rainfall groups. Thus, departures between theory and observation may be expected from this result, even when it would be possible to establish an adequate discrete scale. The parameter of persistence d, which can be derived from this negative binomial theory may perhaps lead to some climatological rela- tions, although in general, the result is influenced by the discrepancy mentioned above. This leaves the incomplete T function, which has been successfully applied by Barger and Thom [1949; Thom 1958, 1957ab]. This fune- tion renders good fits for amounts of approxi- mately five days and more [Barger, 1957] de- pending on the proportion of near zero rainfall days, while for shorter periods the application is restricted to special collectives like the storm series [Thom, 1957ab]. Therefore, the question is still open: How should we treat precipitation data for periods shorter than five days? Before giving some answers to this problem, a few facts about transformation of scales for precipitation data should be discussed. Transformation of scales—The author dis- tinguishes between two sorts of transformation. In the first case one applies a pure formal math- ematical function, developed to reduce the data into the desired form, such as a gaussian dis- tribution. In the second case we derive the trans- formation function from the physical back- ground. Either may be justified for particular purposes; the second one should be considered OSKAR ESSENWANGER at least, as not every physical law renders a lin- ear relationship. By formal transformation any curve can be reduced into a normal distribution. For example, when the data follow an incomplete gamma function, one may transform them as is illus- trated by the lower curve of Figure 1. The ordi- nate is the probability scale of a normal dis- tribution, and the accumulated frequency has to be a straight line when it follows the gaussian law. The lower curve in Figure 1 shows the storms for Santa Barbara in February 1931-1950, [Thom, 1957a] transformed from an incomplete gamma function. The data follow a fairly straight line when we neglect about five and ten per cent at the upper and lower ends, respectively. This seems permissible. The upper curve is constructed for observed daily precipitation sums at Asheville in Septem- ber (1907-1956) in a linear scale. Suppose we are interested in computing the transformation function which reduces the curved line to a straight line. Taking the smallest possible class interval (0.01 inch) the first interval includes 12% of the total observations and for the range from 0.01 inch to 3.20 inches we would have to take more than 300 class intervals into account. By this method we would have to assume that 12% follow the same law which we derive for the other S8% of the observations (0.01 inch is the least measurable amount recorded). If we would take 0.1 inch as the first class, in order to save the laborious work and reduce the values to 30 class intervals, then we do not consider more than 40%, which is remarkably high. In practice it has been found that those small amounts do not fit well in the theoretical curve derived for the larger amount. Further discus- sion follows in connection with Figure 2. As the frequency in those lower classes in- creases, the shorter the time period of measure- ment becomes, such as hourly totals, it is natu- ral that the formal transformation is not strictly valid for the whole curve. This may be demon- strated by Figure 2. It represents the frequency distribution of daily precipitation December- February at Munich for a cubic scale. The theo- retical normal distribution and the observed values agree fairly for sums =>1.0 mm (= 0.04 inch). However, the part less than 1.0 mm is drastically different. This is the part in the small precipitation amounts. In the accumulated frequency the part in the hatched area is com- pensated at the 40th percentile. 02 04 06 08 10 5 20 25 30 32 INCHES 99.99 9999 Accumulated sum of daily 999 Precipitation amount Asheville, 999 998 September 1907-1956 (N=458) 998 99 99 98 98 95 95 90 90 80 80 70 70 60 60 50 50 40 40 30 30 Transformed incomplete I tunction to 0 20 normality (accumulated frequency) for lo Santa Barbara storms (February 1931-1950 10 5 5 2 2 \ \ 05 os “18 -15 -10 -15 fo} 05 10 15 20 23 (a) Fig. 1—Accumulated rainfall frequency in probability scale; abscissa seale for Santa Barbara storms at bottom, for daily precipitation amount for Asheville at top 500; Cubic Scale 400 S Frequency ——» —~ Sy | OR pacha g Q06 051 173 410 800 B8 220 328 47 640 mm Q22 100 273 563 6 76 270 393 589 14.7 Fie. 2—Comparison of observed frequency distribution for daily pre- cipitation amount at Munich in December through February 1880-1950 with theoretical frequency in a cubic scale 273 500 OSKAR ESSENWANGER 400 300 Frequency ——e Ss "A ok” No 002 00 O Logarithmic Scale 25 063 158 aah we 398 10 257 631 1 006 016 040 100 251 631 68 398 wou™™ Fie. 3—Frequency distribution of daily precipitation amount at Munich in December—February 1880-1950, logarithmic scale In some instances, where the small amounts are unimportant or negligible, we may be satis- fied with such an approach. For a physical in- terpretation usually we have to deal with both great and small amounts. The transformation for physical reasons is based on the physical law involved in the proc- ess. Therefore, it is not based on the good fit for a part of the material but includes everything from a general point of view. The logarithmic scale—Now return to the treatment of precipitation data of shorter time intervals. For these, the author suggests the use of a logarithmic seale which has been applied in hydrology for a long time. Wischmeier and Smith [1958] established a logarithmic law for the ki- netic energy of rainfall. Schneider-Carius [1954] classified the rainfall process as autochthonous and also came to the conclusion that a logarith- mic law may dominate the rainfall process. The writer [Hssenwanger, 1956b] discussed some other facts pointing to a logarithmic law. The theory for the log-normal distribution by Chow [1954] and others indicate that any log- arithmie scale is suitable. Schneider-Carius [1955] and the author [EHssenwanger, 1959] have pub- lished some proposed scales which proved to be convenient for meteorological data. The daily data for Munich, December through February, previously shown in a cubic scale (Fig. 2) are now arranged in a logarithmic scale (Fig. 3). First we consider the total frequency only. The graph shows a mode at 2.51 mm. The frequency for the small amount is left open. This incom- plete part on the dry side is justified. Grunow [1956] has studied this problem thoroughly at Observatory Hohenpeissenberg. To summarize his result, a large percentage of the dry days may be reclassified as days with rainfall by eare- ful consideration of the precipitation amount, either not recorded or given under ‘traces.’ Therefore, rainfall records of shorter time pe- riods such as daily amount and less are truncated on the dry side, which almost eliminates any type of formal mathematical transformation. The detailed analysis of the data in Figure 3 renders three partial collectives, each one a nor- mal distribution in a logarithmic scale. Under collective the author understands the definition used in many statistical books, a random sample for homogeneous conditions of the same physi- cal process. They are also submitted with Fig- ure 3, while a detailed discussion of the process and problem is given below. Frequency distributions and their analysis— In many cases meteorological events are defined FREQUENCY DISTRIBUTION OF PRECIPITATION Asheville, N.C 1893-1956 20 24 29 35 42 5O INCHES 18 Madras, India 1813 —1900 2 27 34 4 SI 63 78 95 INCHES Fic. 4—Frequency distribution of annual precipitation amount for Ashe- ville, N. C., and Madras, India a priori and then a frequency distribution for those defined groups is established. This is an expeditious way to present climatological sum- marizations. The author feels that in cases where the various basic processes are not com- pletely known, we should try the reverse way and analyze the total material to find out how many and which subgroups may appear. This approach is elucidated in the following discus- sion. In the previous sections the author has sug- gested the use of the logarithmic scale. We start now the analysis with annual amount of pre- cipitation. Figure 4 demonstrates for two dif- ferent stations and climates (Asheville, N.C., and Madras, India), that for the annual amount, in general, the various rainfall processes become effaced. We obtain one collective, following one normal distribution in a logarithmic scale, ex- cept for locations in a pronounced desert climate. In the consideration of monthly amounts, the mixture of the rainfall processes becomes obvi- ous [Hssenwanger, 1959]. This means that these frequency distributions cannot be considered any more as one collective and the problem is one of how to separate those frequencies into the indi- vidual parts and to investigate the physical basis for the partial groups. As a demonstration sam- ple the daily precipitation amounts for Ashe- ville may serve. First a frequency distribution (in logarithmic scale) has been arranged for each single month and then the frequencies have been split into partial collectives, each one a gaussian distribution. The author [Hssenwanger, 1954, 1957] has developed an objective method for this resolution. The survey (Table 2) shows TaBLE 2—Asheville daily precipitation, 1907-1956 (50 yr); analysis of frequency distribution in logarithmic scale Excessive I, Heavy II, Moderate III, Slight 3 Month = Xm || NV o tm, || NN o tne Ne o ten N o Lom INT 1.0 inch 41 36 38 115 Thereof in Group I* 4 6 3 13 (heavy) Caused by hurri-| 15 | 17 | 10 42 canes Cyclones 20 | 16 26 62 Others 6 3 2 11 The second line is included in the count of the first line and serves merely to compare with the last line. More details in text. four groups of which the last group to the right is the subject of further interest. We find that the collectives overlap, but that there is also a part where mainly one collective prevails. We may now take those ranges for the limits im our study of the physical basis of the rainfall process for the excessive group. The investigation com- bines these groups in the months of August through October. Precipitation 21.0 inch for all three months was determined as the limit where the excessive collective appears almost uninfluenced. From Table 3 it is seen that from the total of 115 cases with amount = 1.0 inches, 13 belong to the adjoiming group (heavy daily rainfall). The 115 cases were examined using synoptic weather maps and the reason for the precipitation determined. One-third of the total sum and between 40 and 50% in August and September is caused by hurricanes which is not a surprising result. Fall is the main season for these phenomena and Asheville lies in the region of their influence. Most of the remaining parts were typical bad-weather conditions, where ex- tratropical cyclones moved through North Caro- lina. Eleven cases had to be listed under mis- cellaneous such as other frontal or air-mass rains. From the theoretical analysis we expected that 13 values are part of the adjoining collective with another basis of rainfall. Therefore, the 11 FREQUENCY DISTRIBUTION OF PRECIPITATION 277 Duration 213 %o 196 Min. I71 Ko mm a020 aaa Intensity Fre. 6—Schematical demonstration of two dimensional analysis of single rainfalls for Braunlage, Germany in June through August 1935-1950 cases which do not belong to the hurricane rains or cyclonic rains are in good agreement with the theory. The detailed investigation of the group with excessive daily rain shows clearly two reasons for the produced rain and demonstrates again the complexity involved in rainfall sums. Refinement of analysis—The rainfall amount originally contains two parameters: intensity and duration. The recorded data are available in most instances for a predetermined constant duration such as hourly and daily sums. Very seldom a study is made which examines single rainfalls. Fortunately such a tabulation was available for Braunlage, Germany, in summer- time for the period 1935-1951 with approxi- mately 1000 values. A frequency analysis for both duration and intensity (in logarithmic scale) was made and the analysis exposed three partial collectives in both intensity and duration. About 20% have an average duration of 3% hr (log-normal distribution), the main part, in- cluding almost 50%, is just short of an hour, and the remaining 30% have an average of 4 hours. This may differ for other climatological regions, of course. The group division for the intensity proves to be slightly different as the parts are almost equal. One group is a little less with 0.009 mm/min, (3.10 inch/min) while the other two show an average of 0.02 mm/min (10° inch/ min) and 0.063 mm/min (2.5.10° inch/min). In a two-dimensional analysis, the amount should now yield nine groups. But the analysis rendered three groups only. Hence, we may conclude that some of the groups may have been combined. Figure 6 demonstrates this fact. This is exactly similar to the result discussed for the daily precipitation amounts in Asheville in the preceding section where we discovered two physical processes in one group. Hence, a refinement of the analysis would be to separate the data by intensity and then split them into duration groups or vice versa. This takes for granted the knowledge of the various kinds of in- tensity or duration groups. Also a preparation of the observations in the form of single continuous rainfalls would be necessary. This is very diffi- cult, laborious and costly and there is little hope of accomplishing it. The alternative to the above-mentioned re- cording of data is to split the material into in- tensity groups by observation which means 278 classification as to advective or convective types. Dr. Bergeron, at the opening of this conference, has outlined some possible schemes. Another way could be to keep the duration for the summation short so that we may be able to comprehend the intensity groups. Hourly sums may be close to the goal. Literally, it means to cut off parallel strips in Figure 6 which dem- onstrate the two dimensional analysis. Conclusion—The author has tried to discuss some of the difficulties we have to face with commonly available sources of data for precipi- tation, when we are interested in the mterpreta- tion leading to the physical basis of the rainfall process. Besides the statistical techniques avail- able for a linear scale, it could be demonstrated that the logarithmic scale may also be employed. How to study frequency distributions for in- vestigations of the physical basis of the rainfall process has been demonstrated on the example of daily precipitation amounts in Asheville for the time of August through October. For the selected collective of excessive daily rainfall, de- rived by theoretical analysis, the connection to the generating process of rainfall can be ex- plained. The result differentiates between rain- fall from hurricane appearance on the southeast coast of the United States and extratropical cy- clones through North Carolina as the possible reasons. This shows that collectives selected by using daily precipitation amounts may not be completely uniform in the physical origin. Therefore, the question is justified. Is the pre- cipitation amount an adequate parameter for the interpretation of the rainfall process? A two- dimensional analysis of intensity and duration for single rainfall data in Braunlage, Germany, points out the limitations we have to expect. If they can be accepted, the material in the present form is sufficient. For refinement of the analy- sis, however, it is necessary to do more research on rainfall intensity data which may be aided by radar analysis. We may study the classifica- tion groups of convective and advective type. Using the duration as parameters in the pres- ently convenient form of equal time intervals, we may find that probably the daily amount is the upper limit needed to study the physical processes involved. A shorter time interval would be preferable. Hourly precipitation values have OSKAR ESSENWANGER been prepared by the U. 8. Weather Bureau on a routine basis for several years at a number of stations and might be sufficient. However, much more study has to be done on this subject before final recommendations can be made. REFERENCES Barcer, G. L., ano H. C. 8. THom, Evaluation of drought hazard, Agronomy J., 41, 519-526, 1949. Barcer, G. L., Preliminary report to Technical Committee on Relation to Weather on Agricul- ture (NC-26), unpublished manuscript, Iowa State College, October 11, 1957. Cuow, Ven Tr, The log-probability and its engi- neering applications, Proc. Amer. Soc. Civ. Eng., 80, 536, 1954. Essenwancer, O., Neue Methode der Zerlegung von Haeufigkeitsverteilungen in Gaussche Nor- malkurven und ihre Anwendung in der Meteor- ologie, Ber. Dtsch. Wetterd. 10, 1954. Essenwancer, O., Wahrscheinlichkeitsansteckung und Erhaltungsneigung beim Niederschlag, Met. Rundsch., 9, 13-25, 1956a. Esspnwancer, O., Zur Verwendung eines Logarith- mischen Maszstabes bei der Niederschlagsstati- stik, Met. Rundsch., 9, 197-206, 1956b. Essenwancer, O., Tafeln zur Haeufigkeitszerlegung mit Anwendungsbeispielen, Ber. Dtsch. Wetterd., 39, 1957. Esspnwancer, O., Linear and logarithmic scale for frequency distribution of precipitation, 1959. Geofis. Pura e Applicata, in press. Grunow, J., Zur Erfassung und Statistik der klein- sten Niederschlaege, Geofis. Pura e Appl., 33, 251-261, 1956. Scunerwer-Carius, K., Der Wirkungszuwachs in statistischer Betrachtung, Arch. f. Meteor. Geoph. u. Bioklim, 6, 22-35, 1954. Scunerper-Carius, K., Zur Frage der statistischen Behandlung von Niederschlagsbeobachtungen, Zs. Met., 9, pp. 129, 193, 266, 299, 1955. Tuom, H. C.S., A note on the gamma distribution, Statistical Laboratory, Iowa State College, 1948, manuscript (manuscript of the U. 8. Weather Bureau, 1958). Tuom, H. C.S., A statistical method of evaluating augmentation of precipitation by cloud seeding, Advisory Committee on Weather Control, vol. II, pp. 5-25, 1957a. Tuom, H. C. S., An evaluation of series of oro- graphic cloud seeding operations, Advisory Com- mittee on Weather Control, vol. II, pp. 25-45, 1957b. Wanner, E., Ueber die Frequenz der taeglichen Niederschlaege, Verh. Schweiz. Naturf. Gesellsch., p. 27-00, 1939. Wiscumerer, W. H., ano D. D. Smrru, Rainfall energy and its relationship to soil loss, Trans. Amer. Geophys. Union, 39, 258-291, 1958. DISCUSSION 279 Discussion Mr. C. J. Todd—t like Dr. Essenwanger’s idea of looking for discontinuities in the probability distribution and using them as a lead in the search for a physical cause. Some years ago I was interested in Los Angeles hourly precipita- tion and probability functions, and I found out it rained nine per cent of the hours. I plotted the cumulative frequency of this nine-per-cent tail starting at 91% on linear probability paper, and got a very nice straight line. Dr. O. Essenwanger—There are several ways to approach accumulated frequency amounts. As shown in hydrology hourly precipitation may fol- low a straight line in the log probability paper quite well, if they are from a homogeneous popu- lation. If we have different types of physical processes, depending on the regional climate, then it might be that this is practically a formal approach. The result is caused by the fact that one is missing the small precipitation amounts. The frequency distribution is practically trun- cated. Dr. Tor Bergeron—I was very impressed to see what you could achieve just only by statistics of precipitation frequencies. From my experience with precipitation maps of all sorts, of all scales, and in many countries, I have always been look- ing for maps containing what I call a one-factor rain, and it has always been very difficult to find typical one-factor rains from daily precipitation measurements. We would like to have precipita- tion observations twice a day, as in the tele- graphic reports. There is not a sufficiently large number of stations, but we would be so much better off. The 12-hour period often manages to take a one-factor rain. The 24-hour period does not. I have no figures, just general experience, and I would like to invite Dr. Essenwanger or somebody else to look into this matter. If the figures could be produced, then this could per- haps be recommended and carried through in the WMO. Although, as you know, it is generally easier for the observers to measure once a day in the morning upon arising. Dr. Essenwanger. I can support Professor Bergeron’s remark absolutely, because this is just what I wanted to say. Our daily amount is probably not sufficient for a subdivision into physical collectives. I rather would like to see very short periods like hourly amounts and then everybody who works in this field can analyze the period he likes. But this is probably not pos- sible, at least on a world-wide basis. Dr. Bergeron—Hourly amounts one can get in the United States, but you can not get them anywhere else. That 1s why I propose twelve hours. Some Aspects of the Optics of the Rainbow and the Physics of Rain Frreprich E. Vouz Blue Hill Meteorological Observatory, Harvard University, Milton, Massachusetts Abstract—It has hitherto usually been believed that the classic rainbow theories of Descartes and Airy for spherical drops completely satisfy the observations. However the well-known deviations of large falling drops from a spherical shape require changes in the rainbow angle, especially for scattering in the vertical cross section of the drop. Flattened raindrops of different radii cannot form a perceptible bow; this may explain why the interference bows are more visible at the top of the bow than towards the base, although their spacings do not change. Preliminary investigations on the oscillations of large fallimg raimdrops have been made. Such oscillations can result in blurring or washing out the rainbow. Rainbow in- tensities for measured drop size distributions have been calculated from the Airy theory. Since drops with radii larger than 0.2 to 0.6 mm are flattened and oscillating, they contribute little to the rambow. Analysis of the rainbow can therefore only give information about the spectrum of the smaller drops. Studies of the rainbow have found little place in modern investigations into the physics of rain; and yet this beautiful natural phenomenon is by no means as lacking in interesting problems as it may seem to be. The well-known classical Airy theory requires much modification before it can be applied to actual atmospheric conditions. Few meteorologists may know that the super- numerary or interference bows (if they can be seen at all) gradually fade as we go from the vertex of the bow to the horizon, but without any change taking place in the displacement from the main rainbow. Also there have been only two recorded observations in the past of vibrations in the rainbow caused by thunder. As this paper will try to demonstrate, the first phenomenon is probably connected with the deformation of any large raindrops, while the Fig. 1—A rainbow photographed by Clarke [1920] showing how the inter- ference bows vanish from the apex to the foot of the bow (Permission of Constable and Co., Ltd., London) 280 OPTICS OF THE RAINBOW AND THE PHYSICS OF RAIN second raises the question of the oscillations of falling raimdrops. Other developments in rain- bow theory concern the effect of actual drop size distributions and the comparison of calculated and observed rainbow brightness. Further details may be seen in a review article [Volz, 1960}. The unusually fine photograph by Clarke [1920] (Fig. 1) illustrates well some of the im- portant results of the Airy theory [see Pernter and Haner, 1922; van de Hulst, 1957]. The pri- mary rainbow, and some secondary bows caused by interference, can be seen. The distance of a rainbow in monochromatic light from the anti- solar point depends upon the refractive index of water and therefore slightly upon the wave- length; consequently, the rainbow shows colors in natural light. The overall width of the in- tensity distribution depends upon the radius of the raindrops (proportional to (\/1°/°). Small drops give a broad rainbow with well separated —> 1 (mm) 4 2 SEAS r6m 8) On LS 3.4 516 uD b/o 1-0 — x OmolS = 09 ioe OE MEASUREMENTS : qo og L BLANCHARD b/o > 20s iS 5 MAGONO b/o // EQ\ yo 30° O & f= 07 MAGONO single drops -e =0° 5 \ O¢(H=0°) « UPPET half of drop —\ on 06 lower eT pCeCr ORG \l a x 0.5; THEORY : IMAL I O4F sPILHAUS SP | Fic. 2—Deformation of falling raindrops; ratio of the vertical to the horizontal axis from both measurements and calculations Fic. 3—Path of through a falling raindrop of 2.4 mm radius, scat- tered in the vertical plane horizontal incident light 281 210° 180° ° 150 ts b x 20 5 > A: 120 a Ho Ss fo) 90° 7) 5 2 ead 60 wy oe = 30° 5 z2 a joa 10D Go. DISTANCE OF RAINBOW FROM ANTI-SOLAR POINT LARGER=— -—*SMALLER +10° O Fic. 4—Variation of the rainbow angle ¢o with the angle x between the incoming light and the major axis respectively, the solar height H; for a drop with the cross section of (a) an ellipse, by Moebius [1907]; (b) a flattened raindrop (vertical plane), measured by the author on a similar shaped water stream supernumeraries. The close supernumeraries of larger drops are washed out by the divergence of the Sun’s rays. Only rain consisting of small and very uniform drops can give a rainbow such as that shown in Figure 1. The supernumerary bow—The disappearance of supernumerary bows towards the foot of the rainbow is a long-established result [Poey, 1863] clearly to be seen in some modern color photo- graphs. It might be supposed that this phe- nomenon is caused by increasing drop size be- cause of collisions and evaporation during fall. However, it seems that this cannot be the prin- cipal reason because the spacing between the mean bow and the supernumeraries is constant. Furthermore the calculations of Rigby and Mar- shall [1952] show no significant change of drop size distribution by collision with low rainfall intensities. Another possibility which must be in- vestigated is the shape of the falling drops. Drop shape and the rainbow—The Airy the- ory assumes that the raindrops are spheres, and yet we know from the experiments [Lenard, 1904; Laws, 1941; Blanchard, 1950; Magono, 1954] and the calculations [Liznar, 1914; Spil- haus, 1948; Imai, 1951 and McDonald, 1954] that falling drops flatten more and more as the size increases (Fig. 2). The path of horizontal incident light through a drop of 2.4 mm radius is shown in Figure 3. The rainbow angle has de- creased to 25° from 42° for a sphere. It is also important that now some rays suffer total im- ternal reflection while in a spherical drop only partial reflections are possible. Probably such a rainbow is much less intense than that of spheri- cal drops. Figure 4 shows calculated changes of rainbow angle for an elliptical cross section [Moebius, 1907] and measurements of this angle for a flattened drop as a function of the angle between the major axis of the drop and the incident light. From these results it is clear that flattened FRIEDRICH E. VOLZ drops with a low Sun will lead to rambows whose radii at the apex decrease as the drop size in- creases. This distortion of the rainbow is im- portant for drops greater than 0.25 to 0.6 mm radius (Fig. 2). Larger drops of different size can contribute nothing to the rainbow of small droplets. For sideways scattering, however, the drops have a circular cross section and hence the rainbow angle at the foot of the bow is the same regardless of the drop size. These statements agree well with the observations (Fig. 1). Raindrop oscillations—Of great imterest both to the physics of rain and to the theory of the rainbow is the problem of drop oscillations. Early photographie observations by Lenard [1887] show that drops falling down a tube os- cillate between vertically elongated and flattened ellipsoidal shapes, in addition to the flattening mentioned earlier. The oscillations of the drops —. DROP RADIUS r (mm) Sane u 1.0 i520 3.0 40 50 60mm 270 600 |1000 pre—- 2000 3 Tie © at EDDY FREQUENCY _>>~_ (RIGID SPHERES) . ~ x . \ BLANCHARD —* DROP DIAMETER (cm) 04 06 Ale) (4 3 4 6 8 |Ocm 6 4 Vy = S= 5 V,{cm sec™'] 2 7 INTERRUPTION WAVELENGTH { 10% TERMINAL 6 FALL VELOCITY A a a 2 Ww | i 10 10 102 Wa Yea — > DROP MASS (mg) Fic. 5—Some properties of raindrops plotted against the drop size and the drop mass; upper part: oscillatio n frequency v by Rayleigh, and eddy frequency f behind a sphere by Moeller as a function of the Reynolds’ num- ber Np of falling water drops; lower part: terminal velocity vr of water drops, and spacing s = v;/y of interr uptions in raindrop illumination OPTICS OF THE RAINBOW AND THE PHYSICS OF RAIN 283 Fic. 6—The natural oscillations of raindrops; part of an enlarged photograph (which were about 6 mm in radius) were strongly damped, decaying to 1/10 amplitude in one second. Moreover, Blanchard [1950] re- cently found other types of oscillations in drops suspended in an upward-directed jet, which was presumably turbulent. He and Lenard roughly confirmed the theoretical law of Rayleigh [1879] (Fig. 5) 1 / Qo Ds = ,/ | ee tg 4/ b6r3 (=3.84r-3? for distilled water) where a = surface tension, and p = density. Here we may recall two earlier observations by Poey [1863] and Laine [1909]. These observa- tions noted that the rainbow (particularly the more sensitive secondary bow) showed vibrations with each peal of thunder. It is quite likely that this indicates droplet oscillations excited by the intense sound waves. Almost nothing is known however about the oscillations of freely falling raindrops. Earlier, Lenard [1887] and Schmidt [1913] carried out a few experiments at night but they recorded only a very small fraction of drops in oscillation. Some preliminary results of a new investiga- tion indicate that most of the larger raindrops are oscillating. If the fallimg raindrops are il- luminated with a reflector bulb, and we look in the direction of the divergent beam, observations or photographs (Fig. 6) near the rainbow angle show bright traces of raindrops. Oscillating drops show traces broken by equidistant dark spaces. The distance between dark spaces (s = v;/y, where v, is the fall velocity) les visually be- tween 0.5 and 10 em, and photographically be- tween 2 and 10 em. Using Rayleigh’s formula this gives droplet radii between 0.4 and 1.4 mm or between 0.6 and 1.4 mm for photographic images. Analysis of a photograph taken in shower rain of medium intensity, gives a radius distribution for the oscillating drops (Fig. 7, top). There are many physical problems about these oscillations which have yet to be solved. Are the oscillations maintained by eddies generated in 284 Ss ] 2.4 6 8 lOcm XN 10 eat Nrel SIZE DISTRIBUTION 3 OF OSCILLATING RAINDROPS 3 10 r=1mm N{&m-3] dr=Imm_ 9 RAINDROP SIZE 10 DISTRIBUTION BEST 1950 10! i 5mm/h 10° n 1 (ao fe) 0.5 1.0 15 20mm —> RADIUS r Fie. 7—Size distribution of oscillating rain- drops, evaluation of a photograph, compared with averaged size spectra 105 Ww 4 S$ o : 10 4H BEST LENARD S = tmm/h Nr.133.6mm/h = S : 5Smm/h Nr. loa = Ss 4 asec 25mm/h Netoey 20m M/A fldiy m z| “dr E ° = s a wi02 2 10 a % o (=) 3 10! wl z a a a 9 & 0 10° a ° 0.5 FRIEDRICH E. VOLZ As the drop size increases, eddy frequency in- creases rapidly while the oscillation frequency of the drop falls. Only the questionable as- sumption that the proper vibrations of drops larger than 0.6 mm may excite turbulent eddies of the same frequency can lead to a source of eddying energy which may maintain the damped droplet oscillations. It is possible that small- scale atmospheric turbulence can excite the os- cillations. In this case the amplitude and number of oscillating drops should be influenced by the factors which control the Austausch coefficient. Depending upon the orientation of the os- cillations, the rainbow can be affected in a way analogous to that caused by the flattening, dis- cussed previously. With the Lenard type of os- cillation (ellipsoidal with elongation and flatten- ing in the vertical) and the Sun near the horizon, 3 6 LAMB 1°, Shower Thunder4 storm Cold Front Warm Front RELATIVE EFFICIENCY FOR RAINBOW INTENSITY ie) 0.5 1.0 LS 2.0mm 1.0 1Smm r Fra. 8. (a) and (b)—Measured size distributions of rain drops; (c) relative efficiency of drops for rain- bow intensity the wake of the drops, or are they excited by atmospheric turbulence which exists independ- ently of the falling droplets? How large are the oscillations and what is their form ? The eddy frequencies behind rigid spheres falling in water were measured by Moeller [1938] for varying Reynolds’ numbers (Vz). In Figure 5 the frequencies for raindrops are shown using the relation between Reynolds’ number and drop size given by Gunn and Kinzer [1949]. In Moel- ler’s experiments regular eddies first appear for Np = 400 to 600; only in this region, when the droplet radius is near 0.6 mm the frequencies of eddies and drop oscillations are equal. This agrees with sideward shipping of drops of 0.5 mm radius observed by Gunn [1949] and with the observed lower limit of 0.4 to 0.6 mm for oscillating drops. the rainbow will not be affected m a sideways direction, but it will be broadened or missing at the top thus reinforcing the effect of droplet flattening. Raindrop size distribution and the rainbow— Up to now relative intensities of color distribu- tion in the rainbow have been calculated only for uniform drop size. However we know that raindrops range in size from 0.2 to 1.5 or even 3 mm. Figure Sa shows average size distributions for various rainfall intensities by Best [1950] and Figure Sb shows distributions for typical kinds of rain measured by Lamb [1958]. In the following we will take the raindrops to be spheri- eal, thus neglecting flattening and oscillations. The results are therefore only valid for the rain- bow near to the horizon. OPTICS OF THE RAINBOW AND THE PHYSICS OF RAIN 285 |\Omm imp 20 0.63 OTe eae mie =| (0) | a 3 4 Fic. 9—Theoretical monochromatic rainbow intensities, (a) for the Airy theory, single drop size; (b) line I for a rain with a Gaussian size distribution; (c) line II for shower rain, III for warm front rain, and IV for drizzle (see Fig. 8 b). For the mean rainbow: z = 0.63 (2r7ro/d)?3(@ — go), yo = 0.5 mm for model II to IV, and ¢) = geometric rainbow angle Because the intensity of the rainbow increases with drop size (geometric scattering intensity ~r, Airy intensity ~7"/°-\7'/°) the efficiency of drops for rainbow intensity is very broad and has a weak maximum near 1.0 to 0.6 mm (Fig. 8 a’ and b’). The rainbow intensities in Figure 9 were cal- culated corresponding to various raindrop dis- tributions. These rainbows have almost entirely lost the secondary Airy bows. The divergence of the sunlight would destroy the secondary bows even more. Calculations of the absolute intensity of rain- bow are shown in condensed form in Table 1. If we neglect the extinction of light by the rain it- self the intensity of the rainbow should increase with the rain intensity. However the extinction of a sereen of falling raindrops also increases TasBLe 1—Erxtinction of rain and brightness of the rainbow | Rainfall rate (mm/h) }) al 5 25 Drop numbers (em~? Km) 34.5 |50.0 |205.0 Extinction coefficient (Km!) 0.19) 0.45) 1.338 Visibility range (Km) ZION 820 ||) .30 Brightness of rainbow* (unit: 1076 Sun disk brightness) | without extinction 6.4 | 9.4 | (38) with extinction Sel aeono! (Od) * Rain falling from 1 km height, Sun altitude and angle of view to the horizontal 21°; no rain between Sun and observer. with rainfall intensity and, as a result, rainbow brightness for normal conditions is nearly inde- pendent of the rain intensity. In green light the principal rainbow maximum is roughly three times as bright as the clear-sky brightness. REFERENCES Best, A. C., The size distribution of raindrops, Q. J. R. Met. Soc., 76, 16-36, 1950. BuancHarp, D. C., The behavior of water drops at terminal velocity in air, Trans. Amer. Geophys. Union, 31, 8386-842, 1950. Crarke, G. A., Clouds, Constable, London, 160 pp., 1920. Gunn, R., Mechanical resonance in freely falling raindrops, J. Geophys. Res., 54, 383-385, 1949. Gunn, R., anp W. Kinzer, The terminal velocity of fall for water droplets in air, J. Met., 6, 243-248, 1949. Imat, I., On the fall velocity of raindrops, Geophys. Mag. Tokyo, 21, 60-63, 1951. Larve, V. J., Der Einfluss des Donners auf die Regentropfen, durch eine seltene Regenbogener- scheinung ermittelt, Phys. Zs. 10, 965-967, 1909. Lams, R., Das Tropfenspektrum in Niederschligen und Radarreflektivitiat nach eigenen und fremden Messungen, Beitr. Phys. Frei. Atmosph., 30, 223- 232, 1958. Laws, J. O., Measurements of the fall-velocity of water drops and rain drops, Trans. Amer. Geo- phys. Union, 22, 709-721, 1941. Lenarp, Pu., Ueber die Schwingungen fallender Tropfen, Ann. Phys. Chem., 30, 209-243, 1887. Lenarpb, Pu., Ueber Regen, Met. Zs., 21, 248-262, 1904. Liznar, J., Die Fallgeschwindigkeit der Regen- tropfen, Met. Zs., 31, 339-347, 1914. Macono, Cu., On the shape of water drops falling in stagnant air, J. Met., 11, 77-78, 1954. 286 McDonatp, J. E., The shape and aerodynamics of large raindrops, J. Met., 11, 478-494, 1954. Moestus, W., Zur Theorie des Regenbogens und ihrer experimentellen Priifung, Diss. Leipzig, 1907; Abhandl. Kgl. Ges. Wiss. Sachsen, Ma- them-Phys. Klasse, 30, 35 pp., 1907. Moeuter, W., Experimentelle Untersuchungen zur Hydrodynamik der Kugel, Phys. Zs., 39, 57-80, 1938. Pernter, J. M., ano F. M. Exner, Meteorologische Optik, 2. Aufl., 907 pp., Braumiiller, Wien and Leipzig, 1922. Pory, A., Sur l’existence A la Havane des ares su- pernuméraires et sur les arc-en-ciels observés en 1862, C.-R., Paris, 57, 109-114, 1863. RayiercH, Lorp, On the capillary phenomena of DISCUSSION jets, Proc. R. Soc., 29, 71-79, 1879; see also A. Gyremant, Kapillaritit, Handb. Physik (Geiger- Scheel), 7, Kap. 6, 343-410, Springer, Berlin, 1927. Riapy, BE. C. ann J. S. Marsuatyi, The modification of rain with distance fallen, McGill Univ. Sci. Rep. MW-3, 32 pp., 1952. Scumipt, W., Die Gestalt fallender Wassertropfen, Met. Zs., 30, 456-457, 1913. Spinuaus, A. F., Raindrop size, shape and falling speed, J. Met., 5, 108-110, 1948. Van ve Hurst, H. C., Light Scattering by Small Particles, John Wiley, 470 pp., 1957. Vouz, F. E., Der Regenbogen, Handb. Geophys., 8, Physik der Atmosphdre 1 Kap. 14, III, Liefg. 6, Borntriger, Berlin, 1960 (in press). Discussion Mr. C. E. Anderson—I am sure most of us had not been aware of the importance of the rainbow as a possible means of getting informa- tion on raindrop sizes and on oscillations of the drops. Dr. Bernard Vonnegut—I think it is possible that raindrops and rainbows may be affected not only by shock waves but also by the sudden changes in electric field caused by lightning. The raindrop shape should be altered by an electric field, and it would be most helpful if we could use the rainbow as a tool for measuring the elec- tric field. The usual measurements of the electric field in thunderstorms are complicated by the fact that most instruments profoundly modify the field being measured. If we could use the rain itself as an indicator of the electric field it would be an ideal measuring device. Dr. F. Volz—But this vibration of the rain- bow is not synchronized with the lightning, but rather with the thunder. Dr. C. L. Hosler—My next-door neighbor is from Berlin and several times when there was fog he observed a variation in brightness that seemed to coincide with the 16-cycle alternating current of the electric overhead powerline. There was no visible discharge anywhere from the powerline to the ground. Can you explain this to me, so I might explain it to my neighbor? Dr. Heinz Kasemir—This phenomenon is well known and can be observed at any railroad sta- tion where steam engines are operated and elec- tric locomotives are fed from an overhead line. As soon as the steam from the steam locomotive comes into the neighborhood of the powerline, which usually runs on a very low frequency (1624 eps at Munich, Germany) the steam cloud shows an oscillation in brightness in synchronisa- tion with the frequency of the powerline. This problem was studied by G. Escherich of the Technische Hochschule, Munich, and the results are published (see review of this paper by A. Schmauss in Meteorologische Zeitschrift, 57, 83-85, 1940). The steam droplets, contaminated by soot particles, form an electrical dipole and oscillate with the alternating electric field. The optical impression is that of a periodic variation in brightness. A Possible Effect of Lightning Discharge on Precipitation Formation Process BERNARD VONNEGUT AND CHARLES B. Moore Arthur D. Little, Inc., Cambridge, Massachusetts Abstract—The electrical effects caused by lightning strokes within clouds may cause a rapid and effective drop coalescence process. It is suggested that the lightning stroke intensely electrifies cloud drops in its immediate vicinity. These drops acquire a charge opposite to that carried by the rest of the cloud and under the influence of electrical forces move rapidly away from the stroke, colliding and coalescing with the unaffected droplets. Introduction—Atmospherie electrical measure- ments show that the great majority of precipita- tion-producing storms are accompanied by rather intense electrification even though they may not produce lightning. It follows that the precipita- tion-forming processes often occur in the pres- ence of electrical activity. It is well known that electrical effects are of great importance in determining the stability of emulsions and suspensions and there appears to be good reason to believe that atmospheric elec- trical activity may play a significant role in de- termining the stability of clouds. Various work- ers have approached the problem of the effect of electric fields on precipitation growth both ex- perimentally and theoretically and in general they conclude that strong electric fields can ac- celerate coalescence phenomena. With few exceptions these investigations have been confined to considerations of the effect of steady electric fields and have not dealt with the transient effects that might occur when a light- ning stroke occurs. It is the purpose of this writing to offer some speculations on the nature of a lightning discharge in a cloud and its effects on the formation of precipitation. Nature of lightning discharge within cloud— An understanding of the effects that a hghtning stroke has on precipitation growth processes is obviously dependent on knowledge of the details of the discharge within the cloud. Unfortunately we presently know very little of these details, for this portion of the stroke is always screened from view. In this discussion it is therefore necessary to make some guesses concerning the nature of the stroke. It is generally agreed that a large part of the electric charge is carried on cloud particles. Since 2 to 87 a lightning stroke obviously serves as the mecha- nism for the release of the electrical energy ac- cumulated in a cloud, it is frequently assumed that the lightning discharge neutralizes electri- fied precipitation and cloud particles. Atkinson [1887] has considered the effect of lightning on the coalescence process in the light of this idea, that the lghtning removes the charge from the cloud droplets. He says, “The small drops which were before kept apart by mutual repulsion from being highly charged and of the same potential now coalesce and form the large drops, which being too heavy to be sus- tained in the atmosphere, fall.” While it is undoubtedly true that some of the electrified particles in a cloud are neutralized by a lightning stroke, we question that this occurs generally. We prefer instead a somewhat differ- ent picture based to a large extent on the ap- pearance of the lightning-like patterns that are results of the dielectric breakdown of electrified, methylmethacrylate plastic blocks. Gross [1958] has described an interesting phenomenon which he produced by irradiating plastie with high en- ergy electrons from an accelerator until the elec- trie field within the plastic became sufficiently large to cause a spark quite similar to hghtning. The pattern produced within the plastic by the electrie discharge is shown in Figure 1. This phe- nomenon is in many ways analogous to a light- ning stroke within the cloud, for here we have a charged region in a dielectric that produces sufficiently high electric fields to cause a spark discharge. Because the plastic is quite trans- parent, it is possible to see the fine details of how the discharge behaves within the highly charged region that gave rise to it. An examination of Figure 1 shows that the VONNEGUT AND MOORE Fic. 1—Lightning-like pattern produced by dielectric breakdown in charged methylmethacrylate block spark pattern is a treelike system that extends throughout the region of high charge density. There is no question but that the electric dis- charge has greatly reduced the high potential within the plastic and that from a gross point of view the charge within the block was neu- tralized almost instantaneously by the discharge. However, if we look at the fine structure of the pattern with a microscope we see that it is not infinitely subdivided. The successive branches become smaller and smaller and finally termi- nate. We see that between the tendrils of the discharge there is transparent unaffected plastic, whose volume is considerably larger than the volume affected by the spark. Since a large frac- tion of the charged plastic is unaffected by the discharge it is reasonable to conclude that the spark did not neutralize a good part of the charge within the plastic but merely balanced this negative charge with an equal and opposite positive charge that was distributed in the dis- charge pattern. Our picture of the nature of the lightning dis- charge within a cloud is based on the assumption that it is similar to what we believe takes place in the plastic. If this is true, the lightning does not neutralize the charged cloud particles but merely introduces a treelike pattern of approxi- LIGHTNING DISCHARGE AND mately equal and opposite charge into the charged region. According to this view the light- ning discharge would produce a flow of current that would greatly reduce the potential differ- ences within the cloud but would not cause com- plete neutralization such as occurs when a spark jumps to a charged metal electrode. This view of what may happen in the cloud has been arrived at largely on an extrapolation of what happens in the pastic, but it seems rea- sonable from another point of view. Before a lightning stroke can oceur a large volume of charge, of the order of 10 or 20 coulombs must accumulate within the cloud. When the discharge begins, large voltages and high currents are avail- able to supply the large energies required to form and maintain the intensely ionized path. As the stroke progresses and the flow of current con- tinues, it is clear that the initial large reservoir of charge steadily decreases and along with it the potential gradients and electric currents. Finally a point is reached at which the energy required to form the ionized path is greater than the available energy. It seems likely that this happens long before the discharge proceeds to each electrified cloud particle. Effect of discharge on precipitation particle growth—The lightning discharge as envisioned above would suddenly introduce a large quantity of concentrated charge into the cloud that would cause neutralization on a gross scale. Following the stroke, neutralization on a much finer scale would occur by the migration of ions through the cloud. It appears that this final stage of neutralization following the stroke could result in a rapid and effective coalescence process. The largest part of the length of the disrup- tive discharge pattern in the plastic is in the form of the rather fine terminal branches of the discharge. Similarly the greatest length of the lightning structure in the cloud is probably also in the form of the branch sparks, which are far smaller in diameter than the main stroke. When a discharge into a cloud takes place, we can imagine that these smaller branches penetrate into the charged region and suddenly deposit along their path a localized intense electric charge of approximately equal magnitude and opposite sign to that in the charged region. This intense charge introduced by the lightning creates an intense local electric field. Initially this charge is doubtless in the form of fast ions, and under the influence of the electric field these ions move rapidly away from the stroke. PRECIPITATION FORMATION 289 We have no knowledge of the intensity of the local electric field in the region of the stroke just after 1t occurs but it is unquestionably high, per- haps approaching the dielectric breakdown strength of air. If this is so we may expect that the fast ions move outward with initial velocities of the order of 20 to as high as 100 m/sec. The heat released in the immediate region of the stroke is probably sufficient to vaporize the cloud droplets so that initially the ions may move in clear air. After moving only a short distance away from the stroke the ions will en- counter cloud droplets to which they will become attached and impart their charge. The intensity of charge acquired by the cloud droplets near the lightning stroke depends on the ion density and electric field, both of which are probably quite high. It appears hkely that in the im- mediate vicinity of the stroke the droplets will acquire sufficient charge to raise the fields on their surface to values approaching dielectric breakdown. A rough estimate shows that if this occurs, these highly charged droplets will move outward in the local intense field with initial velocities that may be as high as 100 m/sec. The process visualized above would be exceed- ingly effective in causing coalescence. The highly charged droplets would move rapidly away from the stroke out into the unaffected region of the cloud where they would collide with the other cloud particles. If we assume that the droplets in the region of the stroke are charged to values approaching dielectric breakdown this is equiva- lent to a space charge density of about two or three orders of magnitude greater than the av- erage values one might expect in a thunder cloud. If this is true, the highly charged droplets pro- duced by the hghtning stroke will collide with hundreds or thousands of the oppositely and far less strongly charged cloud droplets in the sur- rounding cloud before their charge is neutralized. By the time the highly charged droplet has lost most of its charge by collision, its mass will probably be so large that it will have an ap- preciable rate of fall and gravitational forces will begin to play a part in its growth. Discussion—If lightning does indeed cause a rapid coalescence of the sort suggested here, one would expect to observe an increase in precipi- tation shortly after a lightning stroke. Tt has been observed that gushes of heavy rain frequently follow a lightning stroke. Weickmann [1953, p. 111] has stated, “The precipitation left the cloud base regularly at those places where 290 one half to two minutes earlier a cloud-to-ground stroke had come out of the cloud base.” In our observations on Mt. Withington, New Mexico we observed a similar sequence repeated six times on one day in which heavy rain with 3 mm drops appeared on the summit about two minutes after nearby cloud to ground strokes. On this oceasion the cloud base was well below the summit. The time that elapses between the stroke and the appearance of the rain appears to be sufficiently large that the phenomenon could be explained on the basis of accelerated coales- cence. Alternatively it is possible that the rain gushes that were observed may have been the cause of the hghtning. Measurements made at close range with a sensitive radar to determine whether or not an increase in reflectivity precedes or follows the stroke should determine which of these possible explanations is correct. If such observations show that the lightning occurs first they will indicate that the stroke is effective in promoting pre- cipitation formation. Whether or not this hap- pens in the way that is proposed or by some other mechanism will require sufficient detailed knowledge of the nature of the discharge and the electric fields and ion densities that it pro- duces so that quantitative calculations can be carried out. It is worth noting in this discussion of the pos- sible effects of lightning in thunderstorms that a possibly related phenomenon has been ob- served in connection with volcanic electricity. In describing the electrical discharges that some- times accompany voleanic eruptions, Guest [1939] references Beyersdorfer [1922] and Boning [1927] and states, “These dark clouds of finely divided particles of ejected matter are often brightened by vivid flashes of lightning dis- VONNEGUT AND MOORE charging through the cloud to the rim of the crater. At such times a sudden agglomeration and precipitation of dust may follow... .” Laboratory experiments are another approach that may shed some light on the possible effects of lightning in promoting particle growth. It should be possible to produce high voltage spark discharges in aerosols that simulate conditions in the thundercloud and to determine what ef- fects occur. Conclusions—It is concluded that the sudden redistribution of electric charge caused by light- ning in a cloud may significantly accelerate the formation of precipitation. In order to evaluate this effect, radar measurements, laboratory ex- periments, and investigations of the lightning discharge are required. Acknowledgment—This work was made pos- sible by the support of the Office of Naval Re- search, Bureau of Aeronautics and the Atomic Energy Commission under Contract Nonr 1684(00). We wish to thank High Voltage En- gineering Corp. of Burlington, Massachusetts, which organization irradiated the plastic blocks for us. REFERENCES Arxinson, P. (translator), Ganot’s Physics, Wil- lam Wood & Co., New York 1255 pp., 1887. Bryersporrer, P., Sugar-dust explosions, Zs. Ver. Deut. Zucker, Inc., 72, 475-523, 1922. Bontna, P., Dust electricity, possible explanations, Zs. Tech. Phys., 8, 385-398, 1927. Gross, B., Irradiation effects in plexiglas, J. Poly- mer Sci., 27, 135-143, 1958. Guest, P. G., Static electricity in nature and in- dustry, Bul. 368 U. S. Bureau of Mines, 98 pp., 1939. WerckMann, H., Precipitation in Cumulonimbus, Thunderstorm Electricity, (H. R. Byers, ed.) Univ. Chicago Press, 345 pp., 1953. Discussion (Note: Discussion of this paper is combined with that following the next paper.) Estimates of Raindrop Collection Efficiencies in Electrified Clouds C. B. Moore anp B. VonNEGUT Arthur D. Little, Inc. Abstract—Observations of thunderstorms , Cambridge, Mass. from the summit of Mt. Withington, New Mexico, with a sensitive 3 cm radar indicate heavy rainfalls from electrified clouds a very short time after the initial detection of a radar echo. Estimates of the drop collec- tion efficiency necessary to fit the observed depending on the asumed liquid water conte time sequence give values of 200 to 500% nt of the cloud. These deduced values for raindrops in electrified clouds are 4 to 10 times greater than the mean collection efficien- cies determined by Kinzer and Cobb for drops in the absence of an electric field. It is suggested that electrification im clouds may greatly enhance the accretion and coales- cence processes and thus can be a causative factor in the formation of precipitation. INTRODUCTION 3.2 During the summer of 1957 a sensitive 3.2-cm RAI radar was operated on the summit of Mt. Withington, New Mexico, in conjunction with a meteorological and atmospheric-electrical ob- servatory. The primary purpose of the study was to relate the time and location of the first pre- cipitation formed to the development of electri- cal activity in the stationary clouds growing over the mountain. It was found that in general the potential gradient within the cloud reversed and increased greatly in the negative direction sev- eral minutes prior to the appearance of the first radar echo. These results have been reported in detail elsewhere (Moore and others, 1958, Von- negut and others, 1958; 1959). The subject of this paper is the short time interval between the appearance of a precipitation echo overhead and the collection of large raindrops at the mountain summit. EXPERIMENT We designed an experiment to extend the ear- her work of Reynolds and Neill [1955] and Rey- nolds and Brook [1956] aimed at determining the initial precedence of organized electrification and precipitation in thunderstorms. We did this by increasing the sensitivity of the radar detec- tion of precipitation and by making the poten- tial gradient measurements in the cloud as close as possible to the electrical activity. Radar—The primary components of the APQ- 13A radar we used were made available to us by Marx Brook and were those that he and Rey- nolds had used in their earlier work. We in- creased the sensitivity of the radar for the de- 291 tection of initial precipitation by (1) bringing the equipment much nearer to the cloud by in- stalling it on a mountain summit beneath the cloud being studied, (2) changing the antenna mount to give a zenith sean, and (3) carefully adjusting the radar components. New, low-noise 1N23E crystals were used so that a measured receiver sensitivity of —1l05dbm was attained repeatedly. TR tubes with a recovery time of 4 microsee or less (to within 3db of full sensitivity) were used so that precipitation could be detected at ranges as small as 2 or 3 km. During the summer of 1957 we used the stand- ard 76-em (30-inch) diameter parabolic antenna furnished with the set, modified only to permit a zenith scan. This scan took 8 see and was pre- sented as a range-height indication. In addition the plane of the scan was rotated slowly about a vertical axis, completing one-half revolution every 2 min. This arrangement permitted radar Inspection of the hemisphere overhead once every 2 min. In 1958, we replaced the original antenna with a larger parabolic reflector 152 em (5 ft) in di- ameter. The beam width produced by the new antenna was 1.4°, as compared with about 3° for the smaller dish. The larger antenna was mounted to give either zenith or azimuthal scans as desired, thus permitting RHI or PPI presen- tation of any echoes. Our estimates of the smallest raindrops that could be detected in these clouds during 1957 indicate that the initial precipitation echoes could be caused by raindrops with a median di- ameter for reflectivity no larger than 100 mi- crons at 2 km ranges. 292 10* T n lor i "E £ TG cm DISH 5 ¢ | IN 1957 E 1 n (>) w E 2 $ 10" l 3 \ 152 cm DISH IN 1958 10" l) \ 10 fie ee 1 A | 10 100 RANGE (KM) Fic. 1—Plot of computed Zmin , minimum de- tectable cloud-reflectivity factor for 3.2-cm radar, versus target range for APQ-13A sets used in 1957 and 1958 1000 | To cm. DISH IN 1957 do nin (microns) al 152 cm DISH IN 1958 ees a | { 10 100 RANGE (KM) Fic. 2—Estimates of minimum detectable median-volume drop diameter versus target range for APQ-13A radar sets used in 1957 and 1958 on Mt. Withington, New Mexico In 1958 the radar sensitivity was determined by use of 10-cm spherical metallic reflectors sup- ported on captive balloons 6 or more km dis- tant. From these measurements, estimates were obtained for the minimum detectable cloud re- flectivity and for the minimum detectable me- dian-volume cloud-drop diameter as a function MOORE AND VONNEGUT of distance. Plots of these estimates are shown in Figures 1 and 2. The pertinent data on the APQ-13A radars used are given in Table 1. The curves of Figure 1 were derived from cali- brations of the radar with metallic reflectors carried on captive balloons. Assuming that the path to the minimum detectable target lies through cloud, we applied appropriate correc- tions for cloud-droplet attenuation. These curves are based on the relationships summarized in Mason [1957]. The lower limit on the usable range is imposed by the time required for re- covery of the TR tube after the transmitter pulse. The curves of Figure 2 were estimated from the data in Figure 1, by use of relationships derived by Atlas [1954]. For this we assumed a cloud liquid-water content of 0.5 gm m™*. We feel that these estimates of minimum drop size detectable are of the right magnitude, for with the 152-em-diameter parabolic antenna, we re- peatedly obtained properly shaped echoes from nonprecipitating Stratocumulus clouds. Other instrumentation—We increased the sen- sitivity of the detection of the initial electrifica- tion by supplementing measurements made on the summit with potential-gradient measure- ments made within and above the cloud. Radio- sondes modified to measure the vertical compo- nent of the potential gradient were suspended in the cloud from a tethered balloon. Most of the radiosonde field measurements were made with apparatus employing three radioactive probes. (These will be described in detail elsewhere.) To supplement the data obtained with this appara- tus, several tethered balloon flights were also made with a newly designed passive electric field meter devised by Roy Hendrick of Cornell Aero- nautical Laboratory. The operation of this field meter was difficult because of the conditions within the cloud. Nevertheless, we obtained sey- eral comparative measurements with this instru- ment and the potential-gradient measuring ra- diosondes employing radioactive probes. Since the measurements with the two instruments were in substantial agreement, we gained some con- fidence in the radioactive probes when used alone. Measurements directly above the top of the cloud were made with a P-88 aircraft equipped for measuring the component of the potential gradient normal to the plane of the aircraft wings. (The participation of James Cook, owner and pilot of the airplane, was made _ possible through the co-operation of the United States RAINDROP COLLECTION EFFICIENCIES IN ELECTRIFIED CLOUDS Weather Bureau and the Office of Naval Re- search.) This airplane was also used to obtain time-lapse motion pictures of the cloud tops and to make temperature and humidity soundings. To determine the nature of the precipitation, the airplane made several flights through the cloud according to radioed instructions from the radar observer. OBSERVATIONS During a typical summer day in the moun- tains of New Mexico, the early morning sky is usually cloudless. Under the influence of solar heating small Cumulus clouds begin to form over the mountains and after a few hours these clouds grow in size and become thunderstorms. Figure 3 shows how the cloud grows with time and the sequence of cloud electrification and radar echo formation on August 13, 1957. On this day an isothermal stable layer about 200 m thick at about 7 km limited the early convection; thus, several episodes of cloud activity were studied. The sequence seemed to be as follows: A new cell rose at about 4 m sec™*. When the top rose beyond 6 km or so, negative charge concentra- tions appeared in the lower portion of the cloud. In two minutes or so, precipitation was detected by radar as a cup echo above the upper radio- sonde, which still reported fair-weather polarity. The precipitation echo spread, and the vigorous updraft ceased. The electrification then vanished. In five minutes heavy rain and small hail fell to the surface. In 15 minutes or so the rainfall di- minished, a new updraft appeared, and the entire sequence was repeated. In situations where the wind speeds aloft were low, we found that quite commonly the first ra- dar echo in a developing Cumulus is in the form of a hollow inverted cup that changed in appear- ance quite rapidly. Initially the cup echo is dis- tinetly hollow. However, in a matter of several minutes it increases in reflectivity and fills in. As the echo grows and moves downward, virga makes its appearance beneath the cloud and on occasions when the cloud is directly overhead rain falls on the mountain summit. Cook in his instrumented P-38 airplane played an important part in our study by making ob- servations directly over the tops of the growing cloud. On several occurrences we were lucky enough to observe simultaneously an initial, hol- low echo and the echo of his airplane as he flew a few feet above the top of the visual cloud. When this happened, we determined that he was 293 TasBLe 1—Characteristics of the APQ-138A radars used on Mt. Withington Item | 1957 1958 Magnetron frequency | 9875 me | 9363.8 me Nominal wavelength 3.2cm | 3.2 cm Peak power 40 kw | 40 kw Receiver sensitivity —103 to} —105_ to —105 —107 | dbm dbm Ratio: Measured sys- 1/30 1/3 tem sensitivity /Com- puted theoretical | sensitivity Antenna diameter 76 em 152 em Beam width to !g power) 3° 1eaS points Pulse duration ly usec | 0.65 psec nominal Pulse repetition rate 850 sec"! 850 sec"! TR tube recovery time | about 3.5 usec to within 3db of full 4 psec sensitivity of the order of 500 to 700 m above the initial echo and established that in these cases the ini- tial echo was well below the cloud top. Although we made several attempts we were unsuccessful in directing Cook into the initial hollow echo. Passes made through some of these clouds during later stages in their development showed that the precipitation was liquid water even when it was considerably above the melting level. The phenomenon of the first precipitation echo in the form of an inverted cup was observed over quite a temperature range. In some cases the temperature at the top of the echo was as low as —17°C, while in other cases the tops of the echo were below the freezing level. Rapid appearance of rain from clouds in New Mexico—One of the most striking features of the thunderstorms in New Mexico is the rapidity with which the clouds frequently develop and the great speed with which electrification, rain, and lightning make their appearance (see Fig. 4 and 5). As we have pointed out in earlier work, the available evidence suggests that the first rain is formed by a coalescence process. It is therefore of some interest to make estimates of the collec- tion efficiencies of the drop growth process in these clouds. Regarding Figure 4, closely associated with a strong updraft at 09h 58m MST, the potential gradient within the base of the cloud went off seale at —20 V em™. At 10h 00m MST, a hollow precipitation echo appeared 2 km away at about 6 km altitude. By 10h 02m MST the echo had 294 MOORE AND VONNEGUT 0730 0800 0830 0300 0930 1000 (030 | POTENTIAL GRADIENT MEASURED OVER CLOUD FROM P-58 ‘ n POTENTIAL GRADIENT (V CM) + i So o a g 3 i te =f CONVECTIVE CELL es 8 ISOTHERMAL STABLE PS SV ae Si ——— LVER 200M. DEEP mn A Ea wW G re] = 5 32 Xs ey t 5 ALTITUDE ra =z 4 = 40° TERRAIN : a ALTITUDE .Z8 AT UPPER RADIOSONDE Bz POTENTIAL GRADIENT 5 IN CLOUD 5 AT LOWER RADIOSONDE - Vv Oz o a ol z a je Nae LLL ™. > B g : : 55 gS POTENTIAL GRADIENT B 3 4 500) AT SUMMIT es 10 8 3 re) at o eB + = z wn 3 2500 SPACE CHARGE 2 ‘ie AT SUMMIT 2 Fé 22 as 0730 0800 (000 MOUNTAIN STANDARD TIME s Se ses 3 3 TEP 3 2 Z329 2 on § ZESS"22 & S32 S zedguds & ee HES gzz 2 beg THEE 5 Fa & 23983*9 = 7 Fig. 3—Development of convection and electrification August 1: wo ets) i ALTITUDE (KM) {O15 MST \ KM (O\T MST Fie. 4—Precipitation echoes formed subsequent to two different episodes of cloud electrification at 09h 58m MST and 10h 183m MST, August 13, 1957 (these echo photographs have been retouched to re- store the images as they appear on the original film) ALTITUDE (KM) Wie Ye MST WS MST W23 MST Fie. 5—RHI radar sequence showing growth of precipitation echoes on August 16, 1957 (these echo photographs have been retouched to restore the images as they appear on the original film) erown to the size shown. With the formation of rain, the vigorous updraft in the cloud ceased, and the electrification relaxed back to fair- weather values. The top of the cloud turned to ice and disintegrated while heavy rain fell to the eround. A new convective cell was formed over- head at 10h 11m MST, and negative charge con- centrations again appeared within the base of the cloud. A new hollow echo (see Fig. 4) ap- peared in this cell at 10h 15m MST. With the development of the precipitation echo, the up- draft in the cell ceased, and the electrification disappeared. Starting at 10h 20m MST, tor- rential rain and small hail fell to the mountain; no further electrical activity occurred until new convection appeared. A new cell 4 km to the south produced the first lightning at 10h 41m MST. Regarding Figure 5, at 1lh 16m MST the first echo appeared almost overhead, at a slant range of about 2 km and just below the freezing level. It had the cross section of an inverted hollow cup. The threshold median drop size for detection may have been less than 100 microns with the high radar sensitivity at this short range. The radiosonde echo was to one side of the first precipitation echo. The first rain ar- rived at the summit as 3-mm drops at 11h 20m MST. The rainfall became torrential by 11h 24m MST. From several considerations, the initial rain was probably formed by a coalescence mechanism. Close examination of the original film showed that until 11h 45m MST there was no ‘bright band’ in the precipitation echo at the melting level, where it first appeared on the out- skirts of the echo. The data of Table 2 and the Appendix were obtained when organized electrification in clouds was observed to precede closely the detection of a precipitation echo overhead [Moore and others, 1958] followed by a burst of rain falling to the summit. COMPUTATION OF APPARENT RAINDROP CoLLECTION EFFICIENCIES IN ELECTRIFIED CLoups With these data and the usual simplified rain- drop growth model we can compute apparent collection efficiency, liquid water content prod- ucts [suggested by Atlas, 1955] for these clouds assuming that each raindrop is independent of the others. According to this model, the growth of a falling raindrop by accretion is a function of its horizontal cross-sectional area, the dis- tance it falls relative to the cloud, the cloud’s liquid water content, and the raindrop collec- tion efficiency. dM = pwaterdV = chLAdz = chAvdt (1) where bo Ko) Oo MOORE AND VONNEGUT TaBLe 2—Data on two electrified clouds August 13, 1957 August 16, 1957 Item Initial echo Initial echo Second echo 09h 58m MST 10h 00m MST 10h 12m MST 10h 15m MST 11h 14.5m MST 11h 16.5m MST | Potential gradient reversal in cloud Time of echo detection overhead Estimated threshold median drop diameter 70u 70u 70u for reflectivity at detection (for 0.5 gm liquid water content) Altitude of lowest portion of initial echo, 4.3 km 4.5 km 4.5 km MSL Altitude of 0°C isotherm within cloud 5.4 km 5.4 km 5.2 km Altitude of cloud base, MSL 3.7 km 3.7 km 3.5 km Time rain arrived at level of summit (3.1 km altitude) 10h 03m MST 10h 17m MST 11h 20.3m MST Mean diameters of first raindrops collected unknown 3.0mm 3.2mm M = drop mass g = gravitational acceleration V = drop volume C, = drag coefficient of resistance for c = collection efficiency spheres which may vary between 0.30 L = cloud liquid-water content and 0.21 in the size range between a A = drop cross-sectional area 0.5-mm and a 3-mm diameter. v = drop velocity em For our calculation we take the minimum p = density To eliminate the effect of updrafts within the cloud we use the observed time between the de- tection of an echo and the collection of rain at the summit, and the fall velocity of the drops at the observed altitude. We assume that the drops have the shape of an oblate ellipsoid to take the case of drops with the largest collection cross section. Thus the horizontal cross-sectional area for collision is 7a and the drop volume is (4/3) za*b, where a and b are the ellipsoid ma- jor and minor semiaxes, respectively. (This neg- lects the contribution made to the drop col- lection area due to the size of cloud droplets located at the edge of the raindrop path. This as- sumption is discussed below.) For convenience we assume also that 6 = ha, where h is a con- stant <1, a function of the eccentricity of the ellipsoidal drop. Therefore cLvdt = dowaterhda = dowaterdbd (2) From Spilhaus [1948], the terminal velocity v of fall for such an ellipsoid is dp b 1/2 jae (3) 3pa Co (0.9h — 0.01) where value for C,, which will give the smaller value of collection efficiency. Substituting for v and clearing we get Saune 2 db cL di = 2| =**\C,(00h — 001)" ee) g pie and integrating 3 mys 1/2 cL =4 Ee C(0.9h — von | g (5) (bilan — Dinitian) At Now 1, the radius of the equivalent spherical drop, equals bh** by definition. From Magono [1954], A for a 3-mm drop is about 0.87; thus = 0.91r and b°” = 0.95r'” Using pwater = 1.0 gm cm™ par = 0.79 X 10° gm cm™ at a 4-km altitude Ca— 021 we obtain 12 (rfinal cL = 2.5 X 1073 =: rinitial) ay (6) at a 4-km altitude From (3), the fall velocity at 4 km of 3-mm RAINDROP COLLECTION EFFICIENCIES IN ELECTRIFIED CLOUDS (equivalent diameter) raindrops is computed to be about 11 m sec’. On subtracting the mini- mum fall time through the clear air beneath the cloud from the observed total time interval, we estimate that the maximum fall time within the cloud is 140 see and 65 sec for two echoes on August 18, 1957, and 180 see on August 16, 1957 for the lowest part of the echo. Evaluating (6) for these days from the minimum radius de- teetable to the observed size on collection, for the maximum time of fall within the cloud, we get cL = 55 gm m”“, August 13, 1957, 10h 00m MST (3-mm drops estimated) cL = 12.5 gm m*%, August 13, 1957, 10h 15m MST (second echo) cL = 46 gm m™, August 16, 1957, 11h 16m MST (We let 7min = 50 microns for this computation. The median cloud-drop diameter for reflectivity was estimated to be about 70 microns.) Discussion OF CALCULATIONS From the soundings for these days, the maxi- mum liquid water content possible (assuming no dilution) from the cloud base (at about 3.5 km) to the lowest portion of the first echo (at 4.5 km) is about 2.0 gm m™ before the first pre- cipitation is formed. This calculation then sug- gests that drops in these clouds may have net collection efficiencies in excess of 200% after the appearance of a high potential gradient within the cloud. Use of the more realistic mean liquid water content in the layer from the cloud base to the initial echo leads to values in excess of 400% for the computed collection efficiencies. It should be noted the simplifying assumptions have been made that no dry air is entrained into the cloud and that evaporation beneath the cloud has not decreased the raindrop radius. Our estimated values of the collection efficiency would be still higher had these factors been taken into account. A solution of (6) for various assumed initial drop diameters is given below using the fre- quently observed 3-mm drop diameter as the final size and three minutes as the drop fall time within the cloud. The computed reflectivities Z which would arise from these initial sizes are shown in Table 3 for raindrop liquid water con- centration of 1 gm m”™. From this it can be seen that the computed 297 TaBLeE 38—Computed collection efficiency—water content products required and cloud reflec- tivity as a function of the assumed initial drop diameter Assumed initial drop | diameter | Required cL | Z at detection ‘ : mm i. ah ea - 7 ae - 0.07 | 4.5 1 0.1 4.4 Dates 0.3 3.8 750 0.5 | 3h2 350 1.0 D2) | 2500 5 | 1.6 | 4000 2.0 | eal 20000 high value of the cL product is not a critical function of the initial drop size chosen but the reflectivity and hence the detectability of the cloud is very sensitive to drop size. Therefore, even if the initial drop size used in the calcula- tion were in error by a factor of 10 (so that the threshold of detection for the radar was 1/1000th as sensitive as we believe it is) the computed collection efficiency would only be decreased to unity. We believe that the sensitivity of the radar approached the design performance so that we place some credence in these indicated high values of raindrop collection efficiency. Consider these results from another point of view. Under these conditions in New Mexico it has been observed that the rate of rainfall be- came ‘torrential’ (50 mm hr” or greater) two minutes or so after the first drops arrived at the summit and only four to eight minutes after the echo was first detected. High rates of rainfall so soon after detection of the echo indicate that these first echoes did not rise from a low con- centration of very large drops but from many drops in the cloud. It follows from the low initial reflectivity of the echo at detection (and the sub- sequent rapid increase in intensity) that these first drops must have been small in size but grew very rapidly. These deduced collection efficiencies are quite remarkable if they are to be believed. The ob- servations of which we are quite sure are the initial altitudes and the repeated short elapsed- time intervals between the detection of a radar echo in these electrified clouds and the collec- tion of 8-mm raindrops on the mountain summit in a gush of rain. If our estimates of the thresh- old drop size for detection were in error by a factor of 10 (so that we could not detect rain- drops less than 1 mm in diameter at a 2-km 298 T ———s— 4 1.0 2.0 3.0 RAIN DROP DIAMETER, mm Fic. 6—Experimentally determined collection efficiencies for raindrop falling through artificial cloud of 5- to 10-micron-diameter droplets [after Kinzer and Cobb, 1956] range overhead), the computed collection ef- ficiency of unity required would still be greater by a factor of 2 than the collection efficiencies observed in the laboratory. Kinzer and Cobb [1956] made laboratory observations of the col- lection efficiency of water drops supported by an upward flow of a cloud of known properties, in the absence of any external applied electric field. The collection efficiencies they reported are shown in Figure 6. It can be seen that for drops 0.1 mm to 3.0 mm in diameter falling through a cloud of small droplets, the mean collection ef- ficiency is less than 50%. To a first approximation, a raindrop falling through a cloud of water droplets has the op- portunity of coalescing only with those cloud droplets lying at least partly within the vol- ume that it sweeps out. If, however, we consider the finite size of the small droplets it is apparent that the rain drop might coalesce with small drops just tangent to its path. Accordingly to be rigorous the effective radius for collision should be that of the raindrop plus that of the cloud droplet. For simplicity this consideration has not been included in (2); instead, a solution was made for the apparent collection efficiency in natural clouds as a coefficient for comparison with collection efficiencies determined in a labo- ratory cloud by Kinzer and Cobb [1956] who used the same simplifying assumption for When the growing drop becomes much larger than the droplets that are captured, the correc- tion for the size of the droplets becomes very MOORE AND VONNEGUT small, much less than the high collection ‘coef- ficients’ indicated. Discussion OF COALESCENCE An observer of the convective clouds in New Mexico soon notices that rain falls abruptly from these clouds as though a valve had just been opened or some trigger mechanism had been activated. Here the initial rainfall does not start slowly indicating slow droplet growth or an or- derly process of rain formation. A cloud may float around producing no rain for an hour (or for as little as 15 min); then, closely associated with a burst of convection, there is an abrupt change in the cloud, with vigorous production of rain in a transient gush. The calculations above were an effort to de- termine the collection coefficients necessary for initial raindrops in these clouds to fit the ob- served time sequence. The effective values found for the collection of actual raindrops are ap- preciably greater than collection efficiencies ex- perimentally determined in a laboratory. There are several possible explanations for the sur- prising fact that our observations give collection efficiencies greater than unity. It may be that unwarranted assumptions have been made in the model of drop growth that we and others have used. This model probably is a fairly good deserip- tion of the growth process when a large drop falls through a cloud of small droplets. When large numbers of big drops have formed and the precipitation process is well underway, more rapid drop growth can also occur by interactions between large drops. These interactions are more complicated and probably not well described by the model. It is possible that the high collection effi- ciencies we obtain may arise from large drop interactions that are not properly accounted for by the model. We discount this possibility, how- ever, for our observations concern the first drops to fall from the cloud during the beginning of the precipitation process. At the time of our ob- servations the concentration of raindrops was quite low (possibly 0.3 drops m™), and the con- centration of rain water was but 0.005 that of the cloud-hquid water content. It is doubtful that interactions between big drops are im- portant during this period and it appears to us that the assumptions of the model are justified. We believe that the high collection efficiencies indicated by our observations may arise from the RAINDROP COLLECTION EFFICIENCIES IN ELECTRIFIED CLOUDS action of the electric fields we observed to appear shortly before the formation of rain [Moore and others, 1958]. From our observations, the appearance in a cloud of electrical activity above some threshold of perhaps 30V em seems to destroy the col- loidal stability of the cloud. Precipitation echoes appear very shortly after the electrification within the cloud; these echoes increase rapidly in intensity and extent despite the subsequent disappearance of the electrical activity. A gush of rain falls from the cloud for several minutes then ceases slowly. We then observe only drizzle type rain until after there is another episode of electrical activity whereupon the sequence re- peats itself. Effects of electric field on colliding water drops—Both laboratory and theoretical investi- gations indicate that electrical fields may have a very appreciable effect in speeding up the coa- lescence process in clouds. Laboratory experi- ments performed by Fuchs [1856], Plateau [1873], and Rayleigh [1879] have shown that even a rather weak field will cause colliding wa- ter drops to coalesce instead of bouncing off each other. Tn his well known book on surface tension phe- nomena, Boys [1911] discusses the action of electricity to cause coalescence of two impinging jets of water. He wrote, “A piece of sealing wax rubbed on (a) coat is electrified. ... The sealing wax acts electrically on the different water drops, causing them to attract one another, feebly, it is true but with sufficient power where they meet to make them break through the air film between them and join. To show that this is not imagi- nary, I have now in front of the lantern two fountains of clean water coming from separate bottles, and you can see that they bounce apart.” “To show that they really do bounce, I have colored the water in the two bottles differently. The sealing wax is now in my hand; I shall re- tire to the other side of the room, and the in- stant (the wax) appears the jets of water coa- lesce ... These two bouncing jets provide one of the most delicate tests for the presence of elec- tricity that exist. You are now able to under- stand the first experiment. The separate drops which bounced away from one another and scat- tered in all directions, are unable to bounce when the sealing wax is held up, because of its electrical action. They therefore unite, and the result is, that instead of a great number of little drops fallmg all over—great drops, such as you see in 299 a thunderstorm, fall on top of one another. There can be no doubt that for this reason the drops of rain in a thunderstorm are so large. This ex- periment and its explanation are due to Lord Rayleigh.” Electrical effects can be expected to increase not only coalescence (by preventing bounce-off) but also the frequency of collisions between drop- lets. From theoretical considerations, Sartor [1957] calculated that a field of 30v em™ might produce ‘collision efficiencies’ of 400% for neutral raindrops falling through a cloud of 10-micron droplets, and that larger fields in thunderstorms could produce ‘collision efficiencies’ of 10,000% or more. The electrostatically induced increase in collision efficiency arises from the force of attraction between the dipoles induced on the water drops in an electric field. This force varies with the square of the external field, the radius of the drops, and in a complex manner with the distance of drop separation. Sartor noted that this effect applies to all droplets, charged or uncharged, and that most of the droplets affected are those for which the computed efficiencies are very small. He con- cluded that “the electrostatic field, even when very small, plays an important role in the initia- tion and growth of precipitation, at least in warm or supercooled clouds and that the electri- cal manifestations of the thunderstorm are not merely its by-products but form an integral part of the precipitation mechanism.” Formation of rain by coalescence—The rapid growth in the intensity of initial radar echoes in convective clouds by coalescence has been noticed by Battan [1953] and other observers. The phe- nomenon is worthy of further study so that coa- lescence mechanisms in clouds may be evaluated more properly; from computations with ex- isting models, these mechanisms seem too slow to account for the observed production of precipi- tation. For example, Houghton [1951] (who early sug- gested that coalescence and accretion should be important precipitation forming mechanisms) calculated the time required for the growth of a raindrop by coalescence (using collection ef- ficiencies computed by Langmuir) and found that a 100-micron-diameter drop falling through a cloud of 20-micron drops (with a liquid water content of 1 gm m™“*) would require 24 min to grow to a diameter of 500 microns, and another 7 min to grow to a diameter of 1 mm. (By Houghton’s caleulations, an initial period of 92 300 minutes would be required for a 30-micron di- ameter drop to grow (by accretion and coa- lescence under the same conditions) from this size to a 100-micron diameter.) It can be seen that there is a considerable discrepancy between these computations and the period of 3 min or so elapsing from the time a radar echo overhead is detected by a sensitive radar and 3-mm drops are collected at the mountaim summit. A further discrepancy is that initial echoes were observed several times in vigorous clouds 20 min or less after the clouds first formed and rain fell from these clouds a few minutes later. From the appearance of these echoes it would seem that they formed by coalescence mecha- nisms, since a bright cup echo was observed, with no change in intensity at the melting level and some of these echoes first appeared below the level of the 0°C isotherm. Application of col- lection-efficiency computations based on aero- dynamic and geometric assumptions would indi- cate that the drops need a much longer period from the time the cloud is formed to grow by coalescence to the size at which radar echoes might be detected (possibly more than 100 min) or to fall from the cloud as rain (possibly 30 min more). Our observations of appreciable electric fields within the clouds during this period of rapid drop growth suggest that electrical enhancement of coalescence may actually oecur. The disap- pearance of the electrification within the cloud as the rain developed and as vigorous convection was observed to cease makes it difficult to sup- port an argument that the precipitation causes the electrification. The characteristic cup shape of many initial echoes [Vonnegut and others, 1958] may be a significant connection between the coalescence and the distribution of electric fields within a convective cloud. The cup shape may arise from a coalescence process and may depict the distribution of a region of high po- tential gradient within these clouds. CoNCLUSION Our observations of the rapid appearance of rain from clouds in New Mexico support the ideas that electrical effects appreciably accelerate the coalescence process. We have examined our data for days when the first rain formed overhead and find that in the more vigorous clouds of New Mexico, rain echoes sometimes appear (within electrified clouds) in as little as 19 min after the cloud is first formed. MOORE AND VONNEGUT In these Cumuli the rate of increase of cloud reflectivity is quite remarkable; sometimes 3- mm-diameter raindrops fall in as little as 8 min after an initial echo appears. On computing ef- fective collection efficiencies for drops in these cases we obtain values several times unity. On the other hand, computations with present coalescence models of the time required for un- electrified drops to grow from 0.1 mm to 1 mm diameter suggest that about 30 min would be re- quired for such a size change and that two hours may be required from the time the cloud appears until rain is formed. Since both the formation of an echo and the arrival of rain (sometimes apparently formed by coalescence) from the Cumuli in New Mexico occur much too rapidly to be described properly by present coalescence ideas, the possible effects of the observed cloud electrification must be con- sidered. It appears desirable to carry out further studies that will provide a detailed picture of the precipitation growth process from which more defensible collection efficiencies can be com- puted. Another experimental approach that may shed light on the coalescence process is to determine whether high precipitation growth rates such as we observe ever occur in clouds that have not become electrified. The examination of raindrop growth rates in warm clouds should be of ex- treme interest. Acknowledgments—This work was made pos- sible by the support of the Office of Naval Re- search, Bureau of Aeronautics, The Atomic En- ergy Commission and The National Science Foundation under Contract Nonr 1684(00). REFERENCES Atuas, D., The estimation of cloud parameters by radar, J. Met., 11, 309-317, 1954. Atuas, D., Radar measurements of precipitation growth, summary of doctoral dissertation, Met. Dept., Mass. Inst. Tech., 11-12, 1955. Battan, L. J., Observations on the formation and spread of precipitation in convective clouds, J. Met., 10, 311-324, 1953. Boys, C. V., Soap bubbles, 1911 (republished, Dover Publ., New York, pp. 75-77). Fucus, A., Verhandlungen des Vereins fiir Natur- kunde zu Presbourge, first issue, 1856. Hovucuton, H. G., On the physies of clouds and precipitation, Compendium of Meteorology, Amer. Met. Soc., pp. 176-177, 1951. Kryzer, G. D., ano W. E. Coss, Laboratory meas- urements of the growth and collection efficiency of raindrops, J. Met., 13, 295-301, 1956. Macono, C., On the shape of water drops falling in stagnant air, J. Met., 11, 77-79, 1954. RAINDROP COLLECTION EFFICIENCIES IN ELECTRIFIED CLOUDS Mason, B. J., The Physics of Clouds, Clarendon Press, Oxford, pp. 378-417, 1957. Moors, C. B., B. Vonnecut, anp A. T, Borxa, Re- sults of an experiment to determine the initial precedence of organized electrification and pre- cipitation in thunderstorms, Proc. 2nd Conf. on Atmospheric Electricity, New Hampshire, Perga- mon Press, 1958. Piareau, J., Statique experimentale et theorique des liquide soumis aux seules forces moleculaires, Article 486, p. 434, Gauthier-Villars, Paris, 1873. Raytercu, Lorp, The effect of electricity on collid- ing water drops, Proc. ee Soc. London A28, 406- 409, 1879. Reynoups, 8. E., anp M. Broox, Correlation of the initial electric field and the radar echo in thun- derstorms, J. Met., 13, 376-880, 1956. Reyno.ps, 8. E., anp H. W. Netty, The distribution and discharge of thunderstorm charge-centers, J. Met., 12, 1-12, 1955. Sartor, J. D., The force and electric field between cloud drops in a uniform electric field, Trans. Amer. Geophys. Union, 38, 405, 1957 (abstract). Sprpuaus, A. F., Raindrop size, shape, and falling speed, J. Met., 5, 108-110, 1948. Vonnecut, B., anv C. B. Moore, A study of tech- niques for measuring the concentration of space charge in the lower atmosphere, Final Rep. un- der contract AF 19(604) 1920 to Air Force Cam- bridge Research Center, and report to Office of Naval Research under Contract Nonr 1684(00), Arthur D. Little, Inc., Cambridge, Mass., 163 pp., 1958. Vonnecut, B., C. B. Moorr, anp A. T. Bora, Pre- liminary results of an experiment to determine initial precedence of organized electrification and precipitation in thunderstorms, J. Geophys. Res., 64, 347-357, 1959. 301 APPENDIX Data describing the first raindrops collected on August 16, 1957 between 11 h 20 m and 11 h 22 m MST Collection surface: Whatman *1 filter paper (31 em dia) treated with methylene blue dye (see Fig. 7). (a) Drop data: 30 drops collected in 120 see (b) Distribution of drop sizes: 2 drops 3.8 mm diameter Piet 3.6 to 3.7 mm diameter 6 3.4 to 3.5 iG 3.2 to 3.3 ie 4 3.0 to 3.1 3) 2.8 to 2.9 1 2:6: to 2.7 4 2.4 to 2.5 1 2.2 mm diameter (c) Drop concentration: The rain collection area was 760 em* and the approximate distance fallen in two minutes was about 1.2 km, so that the 30 drops came from an air volume of about 90 m*. The mean drop concentration was 0.3 drop m™*. (d) Rainfall rate: The water contained in the 30 drops amounted to 0.5 em* over a 760 em? area. This is a rainfall rate of 0.2 mm hr™. (e) Liquid water concentration in the first rain: 5 X 10° gm m™® (ie. the mean liquid water content in the lower portion of the cloud is enriched by 1 part in 200 by this first rain). Via. 7—Photograph of filter paper stained by first raindrops, August 16, 1959 302 DISCUSSION Discussion* (Discussion of the two immediately preceding papers.) Dr. B. J. Mason—The first thing that im- pressed me when Dr. Vonnegut showed his field records, was that his field variations fit very well the thunderstorm model of C. T. R. Wilson. If the thunderstorm is some distance away, then the electrical field at the point of observation is certainly controlled by the positive cloud dipole and one gets a positive field. Lightning dis- charges may cause excursions of negative sign for short periods. But if the thunderstorm ap- proaches the point of observation, the influence of the negative charge in the base of the cloud becomes predominant, and the field changes to the negative sign. The small positive charge pocket in the base of the cloud, in passing di- rectly over the observation poimt, might again cause a short positive excursion. I find nothing really very unusual about these field records since they are exactly what one would expect. Now the other important pomt is whether or not one can deduce the charge of precipitation in the cloud from precipitation charge measure- ments at the ground. A large concentration of negative drops in the cloud will cause a strong negative field which in turn produces point dis- charge at the ground. The point discharge will send a stream of positive ions up to the cloud, which the negative raindrops, falling to the ground, have to pass. By this passage the rain- drops may pick up enough positive ions to re- verse their charge. This is the commonly ac- cepted explanation for the ‘mirror image effect,’ which recognizes that the sign of the electric field and the sign of the precipitation current are inverted. So I would be very very reluctant to make any firm deductions about the pre- cipitation charge in the cloud from measure- ments on the ground. Dr. B. Vonnegut—I agree with Dr. Mason that because of point discharge it is difficult to ascertain from ground measurements what charge is carried by the rain within the cloud. However, I pointed out that occasionally we had * At the conference Dr. Vonnegut presented a condensed and slightly different version of the two immediately preceding papers. It is because of that reason that some of the discussion-remarks do not seem to have an immediate bearing to the papers as published. As the discussions are, however, of general interest and importance, they have not been omitted. Ed. rain arriving on the summit while the field was too low for point discharge. Under these condi- tions the rain was observed to transport only a very small current. It is quite possible that al- though the rain appears to carry little charge during these intervals it may become highly charged later on. If one is free to make whatever assumptions one chooses concerning the amount and polarity of charge carried by the rain in the cloud and to vary these assumptions at will, it is quite possible to account for the observed data. If rain is mdeed responsible for the pri- mary electrification process it is surprising, how- ever, to find that it generally carries such small currents. If we assume that the excursion of the electric field to negative values associated with the rain gush is caused by the falling of charged precipitation, this still leaves us with the prob- lem of explaining the very similar excursion also accompanied by a wind that we observed near the end of the storm, without any precipitation. Gunn’s observations, as Dr. Mason points out, indicate that the raindrops in thunderstorms are very highly charged. However, I think we should be somewhat cautious in accepting his findings for he himself acknowledges the difficulty of making these measurements and the possibility that some of his points may be appreciably in error. On the occasions when the cloud base was below the mountain top and we were in the cloud we found the currents carried by the rain were quite small. Even when the fields were large enough to give point discharge, the rain current was perhaps an order of magnitude smaller than that we measured with the cloud base some dis- tance above us. Dr. C. Magono—lI have been very happy to know your opinion concerning these observations because I am interested in field changes during rain and snowfall, and we made some observa- tions at Sapporo. We were wondering which is the origin: is the change in charge on raindrops the origin of field change, or the field change the origin of the change in raindrop’s charge. We carried out simultaneously the observation of field change, charge on raindrops and rainfall intensity. The result is given in Figure 8. The abscissa shows time, the ordinate shows field. The solid line indicates the field change. The charge on raindrops is given by the circles and dots along the field line. We find negative charges above the zero potential line and posi- +800 DISCUSSION 303 = ee ae a= ie az een rx fa’ POTENTIAL GRADIENT (Yn) -800 o --> POSITIVE CHARGE @--+NEGATIVE 4 Fig. 8—Atmospheric field change, charge on raindrops and rain fall intensity during rain fall, Nov. 10, 1958 tive charges below the line. The rate of rain is shown by the dashed line. Dr. Vonnegut—I think this is a very interest- ing observation. I am curious to know the magni- tude of the electric fields involved. Were these high enough so that point discharge was oc- curing or not? Dr. Magono—Observations were made on or- dinary rainfall not thunderstorms, so that the field was about a thousand volt per meter. Dr. Vonnegut—This value of the field is on the borderline so it is difficult to know whether or not point discharge was taking place. Dr. H. Kasemir (communicated)—I think I can give an explanation for the mirror effect and all the questions connected with it, which are brought up in the paper and discussion. Ob- servations such as reported here where the mirror effect has been observed in the presence of low fields apparently require that we abandon the old theory, as outlined by Dr. Mason, that the original precipitation charge is identical with the negative charge in the base of the cloud. We postulate a charging mechanism whereby the precipitation fallmg through the lower part of the cloud assumes a positive charge leaving nega- tive ions behind. These negative ions attach themselves to the cloud elements and thus they lose their ability to wander away. They are re- sponsible for the negative charge in the base of the cloud but not the precipitation. As long as the precipitation does not reach the ground, the net charge of the cloud elements and of the pre- cipitation are the same amount but of opposite sign. The electric field generated by the positive precipitation charge will almost be cancelled by the reverse electric field of the negative cloud charge. But as soon as the raindrops reach the ground, they get discharged and their charge is withdrawn from the picture. From there on the net charge of the precipitation remains at a constant value while the cloud charge continues to accumulate. A few minutes after the first rain- drop hits the ground the cloud charge becomes so predominant that the field reverses its sign and becomes negative while the rain charge re- mains positive. The negative field increases rap- idly until the discharging induction current bal- ances the charging effect of the precipitation. If for some reason the precipitation charge re- verses its sign and becomes negative then posi- tive charge is left behind in the cloud and after a short transient period the field also changes to positive values and we observe the mirror effect, that is, that field and precipitation charge usu- ally have the opposite sign. This picture explains all of the observed facts: (1) that we have the mirror effect with and without point-discharge ; (2) that the mirror effect exists even in the cloudbase itself, as the measurement of Dr. Vonnegut and others (Kuettner on Zugspitze, Israel and Kasemir on Jungfraujoch) have shown; (3) that we observe the mirror effect also, if the cloudbase is several kilometers above the ground. There are cases, where precipitation charge and field have the same sign. Also the precipita- tion may lose some of the charge on its way to the ground passing through ion clouds of oppo- site sign. But we have to consider these as sec- ondary effects while the basic mechanism works as outlined above. Dr. Vonnegut (communicated)—While Dr. Kasemir’s suggestion may explain the mirror ef- 304 fect under the conditions when the electric field is quite low, I question that the process he de- scribes is usually the dominant one. He ascribes the field changes primarily to the discharge of electrified rain when it falls on the ground. It appears to me that a serious objection to this idea is the general fact that the current density resulting from the falling rain is usually only a fraction of that measured for point discharge. Accordingly, since field changes are the result of current flow, it would appear that the precipita- tion current plays a secondary role. Another ob- jection to this postulated mechanism is our ob- servation that the changes of the electric field associated with the falling of precipitation often begin a minute or more before any precipita- tion has reached the ground. Dr. James P. Lodge (communicated)—Dr. Vonnegut has noted, as numerous previous in- vestigators have done, that an energetic light- ning discharge is frequently followed by a marked increase in rainfall intensity. He asso- ciates this as, respectively, cause and effect. Is it not more likely that the cause and effect are instead reversed, that in fact the lightning dis- charge simply used the descending rain sheet as a low resistance path to the ground so that the lightning flash merely appears to precede the rain because the final air gap is bridged while the rain is still a few hundred meters above the ground? It seems to me that the increased rain DISCUSSION usually arrives only seconds after the hghtning flash, which is much too short a time for in- creased rain to be generated as a result of the lightning stroke and to fall all the way from the cloud. Dr. Vonnegut (communicated)—The gush of rain frequently observed after a lightning stroke is probably quite a complicated phenomenon that may arise from several different causes. The alternative suggestion proposed by Dr. Lodge seems quite reasonable and may indeed account for some observations of this kind. I believe there may be some question concerning the validity of Dr. Lodge’s main premise that the lightning uses the descending rain sheet as a low resistance path. My own observations of thunderstorms lead me to doubt that lightning prefers the rain sheet. I have frequently been struck by the fact that the lightning often de- scends from the cloud base through clear air where no rain is falling even though a heavy rain sheet is nearby. The lightning appears to have little affinity for the rain and seldom either fol- lows a path through or terminates in the rain sheet. Quite possibly Dr. Lodge may have in mind a situation that is somewhat different from the sort we have discussed, for the rain gush that we observed followed the lightning by a minute or two instead of only seconds after the lightning flash, as Lodge describes. The Mechanism of Hail Formation RAYMUND SANGER Swiss Federal Institute of Technology, Zurich, Switzerland Abstract—Critical considerations of the Ludlam model for producing large hailstones are presented. In connection with the results of the work on turbulence by Kolmogoroy, von Karman and Heisenberg, it is questionable whether the procedure of how the water content of supercooled droplets is transported onto neighboring ice particles occurs ac- cording to the laws of molecular diffusion. The significance of the Bergeron-Findeisen mechanism for producing precipitation 1s mentioned and referred to the newest ex- perimental finding on the structure of hailstones. In a recent article Ludlam [1958] goes very thoroughly into the problem of hail formation and comes to the conclusion that the formation of large hailstones is due exclusively to droplets present near the base of Cumulus clouds and having a radius of 20-30 », particularly when these are very sparsely scattered with an inci- dence of less than 10°/em*. These particles, which lie at the large end of the drop spectrum, are therefore to be regarded as the initial par- ticle or embryo of the large hailstones. Ludlam bases his observation on a model of the way showers are produced, which in all essentials cor- responds to the all-water precipitation process of the kind most recently employed to explain the origin of warm rain where the solid phase of the water does not appear at all. Since the fundamental features of all such models are de- rived from theoretical considerations, idealizing isolated aspects of a natural process and there- fore representing only an approximation to re- ality, there is always the danger that conclusions may be drawn on which too much reliance is placed. And precisely the inference already re- ferred to, namely, that large hailstones owe their origin entirely and only to the sparse pres- ence of relatively large droplets around the cloud base, should properly be treated with some scepticism. By introducing thermals into the pattern of air currents, Ludlam has overcome the difficul- ties which arise in explaining the production of showers by means of the air-parcel theory and the related concept of air columns existing in- side Cumulus clouds in the form of a steady up- draft. At the same time it also becomes possi- ble to understand the discrepancy between the values for temperature and liquid-water con- tent measured inside the clouds, and the values 30 calculated in accordance with the parcel theory as an adiabatie process. (The origin of these vortex motions Ludlam sees principally in lo- cally conditioned increases in temperature or in instability accompanying an atmospheric front.) Cloud particles of initial radius 20-30 p, may, if they are favorably placed at the start, grow to such an extent while they are within the thermal (reaching a radius perhaps of 150 ,) and gather such a speed of fall (1-2 m/sec), that they escape the general erosion of the ther- mal which sets in when it reaches the top of the cloud; and they are then caught up in the course of falling by the following thermal, and continue to grow into precipitation particles or drops of water. In this way the particles of pre- cipitation have time to pick up the necessary amount of water despite the usual deficiency (in fact) in the fluid-water content by contrast with the adiabatic values, yet without having to climb to any considerable height and thereby run the risk of reaching the —40°C level where spontaneous glaciation prevents any further growth. In the mechanism of shower formation which has just been described, the initial particles are already of such a size that growth can in prac- tice only take place through coalescence with other particles, while the condensation of water vapor on the particle is only of secondary im- portance. (We shall return later to the diffu- sion of water vapor in the Bergeron-Findeisen process.) For this mechanism of shower forma- tion it is unimportant whether and where the particle, during its growth into a particle of precipitation, undergoes freezing, which may be initiated by the presence of some foreign ice particles or ice-forming nuclei. Nor is it of any consequence in this connection whether the rc f3) 306 cloud particles which have coalesced and been caught up are supercooled or not. If there is no glaciation, then we are dealing purely with a shower forming as warm rain (by the all-water process). If on the other hand there is glacia- tion, then the particles of precipitation, which have now solidified, can sometimes grow into huge hailstones through contiued aggregation with supercooled droplets. The fact that it makes no difference in this mechanism whether the coalescing droplets are supercooled or not, has led understandably to less importance being attached than formerly to the Bergeron-Findeisen process of rain forma- tion. There may, however, be grounds for ask- ing, whether the disparagement of the Bergeron- Findeisen process has not perhaps gone too far. At all events we should at least check whether, if glaciation were to take place in the growing particle later, after an initially pure all-water process, this would not bring about an increase in the amount of precipitation produced. Firstly, here are a few basic considerations. The introduction of thermals into the general movement of upward currents of air within a Cumulus cloud is merely a first approximation to suggest the turbulent character of atmos- pheric movements. The fundamental works of Kolmogorov [1941] and the theoretical reflec- tions of von Karman [1948] and Heisenberg [1948], which follow on Taylor’s [1922] enquiries into statistical-isotropic turbulence, have led to an appreciable clarification of the inner struc- ture of turbulence. What is above all relevant to our present discussion is that a successful dem- onstration has been made, on a statistical basis, to show that a law of energy distribution exists, which in the case of meteorology is valid for an extremely wide spectral range of vortex ele- ments. It is in accordance with this law that the energy contained in the largest vortex elements in the atmosphere, which may be several hun- dred meters across, is successively transferred to others of smaller dimensions until it finally disappears in vortices of almost molecular size. Two questions are to be raised in this connec- tion. (1) When Ludlam uses a mathematical de- scription of the amount of aggregation to cal- culate the growth of hailstones, relying entirely on Langmuir’s [1948; Langmuir and Blodgett, 1948] concept of collection efficiency, which in practice is equated to unity, is sufficient allow- ance made for the turbulent character of the RAYMUND SAN GER air stream, particularly in view of the fact that during ice formation additional heat is liber- ated? (2) In the mathematical account of how the water content of supercooled droplets is trans- ported onto neighboring ice particles, is it enough to take into consideration only the mo- lecular diffusion process? In discussing the prob- lem already mentioned of the effect which the Bergeron-Findeisen mechanism has on the pro- duction of precipitation, we shall have to pay particular attention to this second point. With regard, finally, to the admissibility of a sta- tistical approach to turbulence phenomena, it should be pointed out that thereby a variation is tacitly included in the product of the growth processes, and this may reveal itself in a con- siderable multiplicity of size and shape in the precipitation particles. It is generally acknowledged that, if the ma- jor part of the supercooled droplets in a cloud were to freeze, this would impair the further growth of a solid particle of precipitation through coalescence and stop the development of hailstones. Ludlam has calculated that for this the density of ice-forming nuclei would have to be 10/em*, and Weickmann [1953] arrives at a similar value by an analogous argument. It is a high figure for the density of icing nuclei and it could never be realized artificially, for im- stance, through seeding the atmosphere, by any economically feasible methods. Ludlam’s calculation of the nucleus density necessary to bring about a sufficient glaciation of the supercooled parts of a cloud to prevent coalescence, is based, as I have suggested previ- ously, on the same theoretical ideas that under- lie the Bergeron-Findeisen mechanism. And here the transference of the water from the super- cooled droplets onto the precipitation particles, which have themselves solidified into ice under the influence of ice-forming nuclei, occurs ac- cording to the laws of molecular diffusion. Since the freezing process releases considerable quan- tities of heat, however, and thereby initiates pro- nounced turbulent intermingling, the following experimental enquiry is suggested: May not a closer approximation to reality be reached if, m the expression for the movement of water from the fluid droplet to the ice particle, the constant D of molecular diffusion (D = 0.45 em*/see in Ludlam’s calculation) is replaced by a constant more in keeping with turbulent diffusion? The conception of this constant (which cannot, for THE MECHANISM OF HAIL FORMATION 307 obvious reasons, be the same) may be justified on the basis of Prandtl’s considerations aimed at a better quantitative description of the ex- change of ponderable matter brought about by turbulence. It may be remarked in passing that Sutton [1947] has made successful use of this concept in deriving his formulas for the spread of atmospheric dust. By adopting such a pro- cedure, a density would be obtained for ice- forming nuclei, which would turn out to be mark- edly smaller in order of magnitude than that given by Ludlam. This density could clearly of- ten be realized in nature at temperatures less than —10°C, and there would also be no great difficulty in producing it artificially. These suggestions make it evidently necessary to say, that the possibilities of precipitation be- ing produced according to the Bergeron-Findei- sen process should not be rated so low as has sometimes been done more recently. This view is supported ultimately also by the Final Re- port of the U.S. Advisory Committee on Weather Control which states that it has been proved statistically with a satisfactory degree of certainty, that in orographic conditions an increase in rainfall amounting to between 10 and 20% may be expected from artificial seeding with silver iodide by means of ground generators. Also the results of the first two experimental years of the Swiss Hail Suppression Project, in which a randomized ordinance has been con- sistently adhered to, likewise give indications for believing that a surprisingly large increase in precipitation can be effected by seeding; a re- port on this is, however, being presented in a separate paper. Dessens [1958] points out in a short article, in which he takes up the ideas propounded by Ludlam, that the effects known to be produced in clouds by seeding with ice- forming nuclei could never be observed in clouds seeded with condensation nuclei. And in a work published recently Schaefer and Dietrich [1959] have also confirmed in an impressive manner the influence on supercooled clouds by seeding with silver iodide particles. Finally, the excellent experiments designed by Schaefer must be re- ealled, in which, within a few seconds after dropping dry-ice particles through supercooled clouds, centimeter-broad dark bands appear along the sides of the threads of small ice crys- tals; after approximately another 30 sec the whole picture becomes blurred as turbulence sets in. These comments on the significance of the Bergeron-Findeisen mechanism have been put forward less to provide a more solid foundation for hail-prevention experiments by silver iodide seeding than to indicate from the point of view also of these experiments what kind of problems are involved in constructing any theoretical model to represent some part only of a weather process. It is important to stress here with par- ticular clarity that only experiment can provide the ultimate answer. This is no less true when it is a question of clarifying the processes which lead to the formation of hail, than im the practi- cal field of hail prevention. Recently List [1958] has published two arti- cles on investigations into the structure of differ- ent types of graupels and of large hailstones col- lected at different places in Switzerland in the years 1953 to 1957. The structural analyses have been carried out by means of techniques for producing very fine cross sections, which have been developed to a degree of great proficiency at the Swiss Federal Institute for Snow and Ava- lanche Research, Weissfluhjoch-Davos. This In- stitute houses also one of the research centers of the Federal Commission for the Study of Hail Formation and Prevention and it is here that for the last few months the Swiss Research Hail Tunnel has been operating, about which a sepa- rate report is presented as the next paper in this volume by the supervisor of the tunnel experi- ments. On the basis of pictures which have been made of the structure of actual hailstones, List ar- rives at the view that the hailstones which were examined and had dimensions of several centi- meters, all possessed in their original form as growth centers (to use the author’s own term) some type of rime or frost graupel, which may well in certain eases have come about through snow crystals entering a graupel phase. A par- ticularly pertinent example is offered by the hailstone 57.7 (see Fig. 1 and 2), of which struc- tural photographs are reproduced. There can be no doubt that this argument is entirely correct in this case, and above all his claim that the initial graupel cannot have developed from a drop of water which subsequently froze. Thus we are able to make a statement, which is certainly confirmed by experiment, but contradicts Lud- lam’s suppositions regarding the growth of hail- stones, as we described them at the beginning of this paper. Figure 3 is a picture of a fine cross section of a graupel which has reached such RAYMUND SANGER Fig. 1—Conieal center of the hailstone 57.7; = real length of the figure, 2.2 cm Fic. 2—Cross-section of center of hailstone 57.7 (polarized light); real length of the figure an advanced stage of development that the original particle, namely, a snow crystal, can now only just be recognized. In conclusion, a remarkable finding should be mentioned, which has already resulted from in- vestigations made with the Hail Research Wind Tunnel. It appears that large ice particles, which contain imprisoned within themselves consider- able quantities of still liquid water, can be pro- duced relatively easily by coalescence with sub- , 22 cm cooled droplets. This immediately raises the question, whether the bigger natural hailstones could not also carry enclosures of water. This possibility would allow us to understand how growth may take place in a considerably shorter time than is generally assumed nowadays. In order to find out, investigations would have to be carried out immediately after the hailstones had fallen, and might therefore prove especially difficult. For there can be no question of pre- THE MECHANISM OF HAIL FORMATION 309 Fic. 3—Top of a graupel indicating residuals of a snow crystal (star); real length of the figure, 0.43 em serving the hailstones by any form of refrigera- tion, since this would lead to a change in strue- ture. REFERENCES Dessens, H., Recherches sur la gréle, Bul. Obs. du Puy de Déme 148, 1958. Hetsenserc, W., On the theory of statistical and isotropic turbulence, Proc. R. Soc. A, 195, 402- 406, 1948. Kotmocorov, A. N., Doklady Akad. Nauk SSSR, 32, 19-21, 1941. Lanemuir, I., The production of rain by a chain reaction in Cumulus clouds of temperatures above freezing, J. Met. 5, 175-192, 1948. Lanemurr, I., anp K. B. Bropcerr, A mathemati- cal investigation of water droplet trajectories, Army Air Forces Technical Report 5418, 68 pp., Washington D.C., 1946. List, R., Kennzeichen atmosphirischer Eisparti- keln, 1, Graupeln als Wachstumszentren von Hagelkérnern, Zamp 9a, 180-192, 1958; 2, Hagel- k6rner, Zamp 9a, 217-234, 1958. Lupuam, F. H., The hail problem, Nubila 1, 12-99, 1958. ScuHaeFer, V. J., AND J. H. Dierricn, The seeding of Cumulus clouds by ground-based silver iodide generators, Zamp 10, 174-188, 1959. Sutton, O. G., The problem of diffusion in the lower atmosphere, Q. J. R. Met. Soc., 73, 257- 281, 1947. Taytor, G. I., Diffusion by continuous movements, Proc. London Math. Soc., 20, 196-212, 1922. von Karman, T., Progress in the statistical theory of turbulence, Proc. Nat. Acad. Sci., 34, 530-539, 1948. WeickMann, H., Entstehung und Bekimpfung des Hagels, Met. Rundschau, 6, 175-180, 1953. Discussion (Note: Discussion of this paper is combined with those of the two following papers at the end of the second following paper.) Design and Operation of the Swiss Hail Tunnel Rouanp List Swiss Federal Snow and Avalanche Research Institute, Weissfluhjoch, Davos, Switzerland Abstract—An acceptable theory on hail formation should be based on the general physical conditions prevailing within thunderstorm clouds and in particular on the proc- esses of nucleation and growth of ice particles. An attempt has been made to approach this problem from the experimental side by means of a vertical wind tunnel offering a wide range of airconditions. In this paper the Swiss Hail Tunnel as it has been built in the Laboratories of the Federal Snow and Avalanche Research Institute, Weissfluhjoch, Davos is described and discussed. It is shown that in the tunnel stationary and variable conditions can be reproduced similar to those to be expected in a natural hail-pro- ducing atmosphere. Introduction—The hail tunnel was designed and built in order to grow hailstones experimentally in the laboratory. For it was felt that compara- tive observations of these with natural hailstones would enable conclusions to be drawn as to the conditions in which hail forms in nature. Experi- ence gained over a number of years at the Swiss Federal Snow and Avalanche Research Institute in investigating thin sections, when applied to soft hail (graupel) and hailstones [List and de Quervain 1953, List 1958ab], showed that here too the key to any explanation of how these nat- ural ice particles arise must lie in an interpreta- tion of their physical structure. It may be ex- pected that specific structural zones in iced-up particles of precipitation are a direct consequence of specific growth conditions in a cloud: that the structure of a particle is essentially the product of the conditions in which it originates. The experiment has thus to clarify the connec- tion between conditions of growth and the re- sultant ice build-up on a nucleus particle. The hail tunnel is the plant which permits this experi- mental aim to be carried out. It consists basically of a wind tunnel which is vertical in the section where measurements are made, has a closed cir- cuit and an adjustable climate. When formulating the problem it must be clear that, as a result of the many parameters of the experiment, it is not possible in every case to classify a certain ice formation under a particular set of growth conditions. This is especially true of different growth phases built up in time at the same place. The final conclusions are also com- plicated by the multiplicity of forms which occur in natural hailstones [List, 1959a]. Before designing a hail tunnel, it is important to elucidate the extent to which the conditions concerning temperature, humidity, air speed, air pressure, impurities in the air, electrical effects, etc., such as may be found in a hailcloud, can in fact be imitated in the experiment. Enquiry into these factors gives a positive answer on all counts. It would in itself be desirable to reproduce vari- ations in pressure, but here the financial expense is disproportionately high, and so experiments have to be designed at constant pressure and the results transformed by suitable rules of similarity [List, 1959b]. In addition it was decided when planning our wind tunnel not to try to check and influence the electrical conditions, on the prelim- inary assumption that they are only of secondary importance. The possibility still remains, how- ever, of elaborating the plant in this respect or of otherwise improving its capacity. The construction of the hail tunnel—The basic construction of the hail tunnel can best be seen in Figure 1. The blower a generates the necessary air-speed relative to the object b suspended or floating in the measuring section. (The direction of the air stream is counterclockwise). In the position ¢ next to the blower is the air cooler or vaporizer. Ammonia vaporizes in its ribbed tube system, is compressed in the refrigerating com- pressor d (or Fig. 2) and is then cooled and con- densed in the condenser e by means of air from the atmosphere (since the plant stands at 2665 m above sea level there is no supply of cooling wa- ter). A heater f with a capacity of 0 to 19 kw, which can be engaged immediately at any level, makes possible rapid periodic changes of tempera- ture as well as the eventual warming of the ex- 310 SWISS HAIL TUNNEL 311 wayyy Ws IC aN — Vjstthts em SS SS SASSASSSASSA ASS SSASSSSSSS yyy 0403; Qs, ) shal ia N IS pad, VAIO LD» My aS eee vA 2077777 VOM harhanhehhchhorhohked 'MLOIT TOOT OTM LLZZZ AL Fic. 1—General diagram of the hail tunnel; (a) blower; (b) test object; (¢) air-cooler or vaporizer; (d) refrigerating compressor; (e) ammonia condenser; (f{) heater; (g) electrostatic filter; (h) point where humidity and ice-forming nuclei are injected; (1) section where the flow achieves homogeneity; (I) measuring section; (1) control panel; (m) liquid separator; (n) aleohol-water cooler for cooling the cold compressor perimental atmosphere. The electrostatic filter g, which has particular advantages with regard to ice-forming nuclei, serves to purify the air. (The special characteristics of the electrostatic filter have been discussed, for instance, by List and de Quervain (1956].) At the point h, humidity is con- tinuously added to the air which since leaving the blower has been dried, cooled, and cleaned. It is a matter of choice whether the humidity is intro- duced via a steam generator (Fig. 3), an air-water compressor (Fig. 2), or a rotor atomizer (Fig. 4). By varying the method of producing the droplets their size can be altered to quite extreme limits. At the same point in the tunnel h, nucleating sub- stances are added (Fig. 4), after having been va- porized in a high-temperature oven. The next ver- tical section of the tunnel i, which follows the humidity injection point, allows the air current to become less turbulent and the temperature of the droplets to adjust to the temperature of the air about them. The air which has been climatically conditioned in this way now flows into the actual measuring section k, where its ice-forming capacity is ex- amined through the growth of a test object. Various measuring probes are also installed in the measuring section, and the test object can be il- luminated and observed at any time through plexiglass windows. In this connection it should be noted that the measuring section has in prin- 312 Sets. Fic. 3—Blower and steam generator for produc- ing drops ciple to be specially adapted for each series of experiments. The remaining parts of the tunnel serve only to allow the air to expand slowly and to bring the circulation back to the blower. ROLAND LIST Fig. 4—The injection of humidity and ice- forming nuclei The whole plant is supervised and run from the control panel (marked as | in Figure 1). Here the object under investigation can be directly ob- served at the same time that all the values which an be regulated are set on the panel. All the important values, whether of temperature or some other electrical scale, are simultaneously recorded on three compensation recorders. The apparatus for regulating temperature is housed independently; the gages for measuring pressure and humidity are likewise located close by the measuring section (Fig. 5). From this description it will be clear how, in the part of the tunnel below the measuring sec- tion, a cloud is continuously produced more or less subcooled according to need; it does not cir- culate more than once, however, as drops of water are deposited at the latest in the air cooler and any particles of ice on the electro-filter. The whole tunnel is constructed of separate components, which can easily be taken apart and changed. The main substance from which it is built is a cellular, slightly spongy plastic called Polystirol; it combines lightness of weight (y = 20 kg/m*) with insulating properties similar to those of cork, and has by comparison the advan- tage of an even lower thermal capacity relative to the unit of volume. These characteristics all guar- antee minimal losses of heat with minimal ther- SWISS HAIL TUNNEL mal inertia. External surfaces are additionally protected by a coating of aralidite, which pre- serves a certain elasticity even at very low tem- peratures. THE PERFORMANCE OF THE Hath TUNNEL During stable operation—The operation of the tunnel is very complex, in particular with regard to the regulation of the temperature. The various factors which have to be observed for the general case may therefore be listed as follows: (1) The basic temperature of an individual experiment is given by the lowest temperature in the tunnel, that of the air-cooler: ty . (2) On the way to the measuring section the temperature of the air is raised as a result of cold losses by conduction to the outside and also of indirect heat generated by the blower: values which depend on the temperature of the tunnel itself and on the air speed. (3) The tunnel temperature is further influ- enced by the excess energy injected through the medium of the humidity. Fic. 5—The measuring section of the tunnel, the gages for pressure and the control panel 313 (4) Ice-forming nuclei may also influence the temperature according to their activity in trans- forming energy, as freezing processes take place in the subcooled cloud, before it reaches the measuring section. The sum of these influences determines the actual temperature in the measuring section, which is the effective temperature of the experi- ment, ty. To regulate it by means of the com- pressor acting on the vaporizer temperature is extremely difficult and quite impossible where there is any sudden alteration in humidity. The procedure adopted was therefore to produce in each experiment always more cold in the vapor- izer than was actually needed. The surplus cold is then destroyed by the heating element, whose output can be altered almost instantaneously; so that a maximum temperature adjustment can be achieved by hand control, or alternatively be regulated automatically. The efficiency of the tunnel with regard to temperature and humidity input is a function of the vaporizer temperature as well as of the air- speed, which helps to determine the amount of the losses from the system. The effective per- formance available for a particular experiment can be ascertained directly, by observing the fol- lowing procedure: the refrigerating compressor is allowed to run at full capacity while the air- speed and heat-setting are constant. With time the stable vaporizer-temperature ty develops, and once this is arrived at it provides an operational point which describes the connection between vaporizer temperature, effective refrigerating ca- pacity (which equals heating capacity), and air- speed. The group of curves in Figure 6 were given by the sum of such measurements. They show | ] Fic. 6—The effective cold output LZ; available for the experiment, at different air speeds vy, , as a function of the vaporizer temperature ty 314 y ty) 0 -40 -30 -20 -10 °C Fic. 7—Correlation of the vaporizer tempera- ture ¢y with the measuring-section temperature ty , at different air speeds vy , and as a function of the energy value Qj), added between the vaporizer and the measuring section through hu- midity or heating that the performance of the tunnel decreases as the vaporizer temperature goes down, but tends toward a higher value as the air-speed falls. For this procedure it is tacitly assumed that the energy added through humidity is equivalent to, and interchangeable with, the energy added through heating. Although the vaporizer temperature is decisive for regulating the system, we are interested here rather in the measuring-section temperature ty. The conversion of these two values is done ac- cording to the expression Qvar + Oru ty =ty + = = (1) = : pi Py-Va-er The meaning of the individual symbols is as fol- lows: tw = the temperature in the measuring sec- tion, °C ty = the temperature of the vaporizer, °C Qian = the energy which is added to the air in the tunnel between the vaporizer and the measuring section through heating and humidity, keal/h Onn = cold losses between the vaporizer and the measuring section, keal/h px = the density of the air, kg/m Fy = the sectional area of the tunnel in the measuring section, mm? vm = the air speed in the measuring section, m/h cy, = the specific heat of the air, keal/kg® ROLAND LIST The value Qya can be measured experimen- tally, so long as the value Onn is not involved. Corresponding values are entered in Figure 7 as mean values for the air speeds in question. This presentation shows the connections in accordance with Eq. (1); it is used especially when the oper- ational point for the compressor, that is to say, an appropriate vaporizer temperature has to be determined on the basis of a desired measuring- section temperature ty, a given energy value Om present in the tunnel as a result, for example, of humidity, and a certain air speed vy . In prac- tice, one starts with the energy value (Onn and finds the point of intersection with the line rep- resenting the chosen speed (Fig. 7). What is then given is principally the degree to which the mea- suring-section temperature diverges from the va- porizer temperature. Additional choice of a ty value allows the operational point in the (ty , ty) —diagram to be fixed and the vaporizer tem- perature ty to be read off which is appropriate to the particular experiment. Before an experiment calculated in this way can be practicably carried out, it is necessary to establish whether the assumed amount of added energy can in fact be produced for the re- sultant vaporizer temperature. This information is given in Figure 6. Figure 8 shows the maximum performance of the tunnel as a function of the air speed with the parameter ty, , while Figure 9 gives similar cor- relations for the maximum water injection. (It was assumed here that the added water has a temperature of +10°C.) The effect of the heating apparatus provides other possibilities beyond improving our control over the tunnel. It enables the water content of the air in the measuring section to be substan- Lid reese ] 2 mis Fig. 8—The maximum effective cold output Ly available for the experiment as a function of the air speed in the measuring section vy and at different measuring-section temperatures fs SWISS HAIL TUNNEL tially reduced for evaporation measurements, with the vaporizer elements then serving as an air dryer. The moisture content in the measuring section corresponds in this case to the moisture content of the atmosphere at saturation point relative to the vaporizer temperature as com- pared with ice. Suitable diagrams could easily be worked out from the data given earlier. The behavior of the tunnel during unstable opera- tion—In nature relatively rapid changes in the conditions of growth play an important part in the way hail forms, as is seen from hailstones having a layered, or ‘onion-coat,’ structure. In order to clarify the possibility of effecting some equivalent imitation, the flexibility of the atmos- pheric conditions in the measuring section of the tunnel was also investigated. The greatest obstacle in the way of rapid alter- ations in the operational conditions, and particu- larly in temperature, lies in the large mass of the air cooler. As a result of its large heat capacity (corresponding to 1200 kg of iron) the quickest changes of temperature that can be achieved in either direction are in the order of 1.5 to 2°C /min. At first, these values appeared to be inadequate. They can, however, be very considerably im- proved by the use of the 19-kw heater, although the temperature changes thus produced are al- ways upwards, making the tunnel air warmer. In creating periodic variations the basic temper- ature ty is arranged so that it remains constant, with the cooling compressor set at a fixed out- put-level. The maximum rise in temperature with the heating switched fully on is accordingly dependent only on the air speed, and it goes up as the volume of air put through decreases. The rapidity with which this rise in temperature shows up in the measuring section is dependent on the heat inertia of the tunnel between the a =F =50) -10 -20 -40 -50 a Fic. 9—The maximum possible water injection Wym as a function of the measuring-section tem- perature ty and at various air speeds vy 917 old 4ty 10 1S 20 20 10 a 2 4 6 8 10 min Fic. 10—The maximum increase of temperature At which can be produced in the measuring section by switching the heater full on, expressed as a function of time and for various air speeds vi (showing the heat inertia of the hail tunnel at a constant vaporizer temperature fy) He 20} 10 | 5 20 a | | | 2 10 ! Tamin | | | | | | eee ee ta | | VM 5 ite) 15 20 20 m/s Fie. 11—Behavior of the hail tunnel under periodic changes of temperature: maximum double temperature amplitude 2A as a function of the air speed vy, and for different period times 7’ 4 heater and the measuring section. Figure 10 shows these relationships, observed for various air speeds as a function of time with maximum heat- ing. If, moreover, the refrigerating compressor is stopped at the moment when the heating is switched on, increases in temperature result which are on an average 20 to 40% higher than the values shown in Figure 10. Since we have been able to observe that heat- ing takes as long as cooling, we are in a position to estimate the double periodic amplitude 2A (which equals the maximum temperature increase) as a function of the period time; (this is shown in Figure 11). These periodically induced changes of temperature are, however, subject to some limitation from the capacity of the refrigerating plant in the lower temperature ranges. Here care must be taken that the heat setting for the lowest temperature wanted does not exceed the requisite cold output, otherwise the compressor cannot adjust itself to this operational point. Similar 316 considerations are called for when extra humidity is injected. From these particulars it may be seen how the cold output which is too high during stable oper- ation makes possible large periodic temperature changes during unstable operation of the tun- nel.—To what extent, however, the variations brought about in our experimental atmosphere may suffice to simulate the growth of natural hailstones, is a question which can only be prop- erly answered by experiment and appropriate comparison. PROBLEMS OF MEASUREMENT That subcooled water clouds may be produced in the way we have shown, does not, of course, solve the problem of how the relevant conditions are to be measured. For measuring the tempera- ture alone a great variety of methods is therefore being tested and used according to need; and as the state of research shall dictate, new types of measurement can be tried out and new measuring apparatus built into the tunnel. PROSPECTS The performance of a plant has also to be judged from the point of view of how far it broad- ens our knowledge of known phenomena or helps us to discover new instances of regularity and law. In the latter connection the first experiments with particularly high water contents (up to 20 g/m’) have indicated the following interesting effects: (1) It ean easily be shown that a close relation- ship must prevail between the conditions in which hailstones arise and their shape. But since differ- ent growth phases become overlaid the connec- tions are sometimes noticeably complicated. (2) A number of authors have assumed, when postulating a hail theory, that no more water can ROLAND LIST accumulate on a hailstone than can become frozen as a result of the warmth generated by freezing escaping into the surrounding air. The surplus water would then be carried away by the air cur- rent. These assumptions have proved to be quite arbitrary, since this surplus water can to a large extent be incorporated into the ice structure of a hailstone. This fact suggests a basic revision in the way the origin of large hailstones is explained. At the same time it also becomes obvious that nature produces hailstones of density greater than that of ice [List, 1959c]. The hail tunnel was planned and built under close cooperation with the firm Sulzer AG, Win- terthur, as part of the research program of the Swiss Commission for the Study of Hail Forma- tion and Prevention. I should like to express my particular thanks to my distinguished Principal, M. de Quervain, under whose helpful guidance I have been able to design, build and run the wind tunnel. The plant was paid for by the “Schweiz. Nationalfonds.” REFERENCES List, R., anp M. pre QureRvatn, Zur Struktur von Hagelkérnern, Zs. angew. Math. Phys., 4, 3-6, 1953. List, R., anp M. pE Quervarn, Untersuchung liber die Wirksamkeit eines elektrostatischen Filters gegeniiber kleinsten Silberjodidteilchen, Helvetica Physica Acia, 29, 424-426, 1956. List, R., Kennzeichen atmosphiarischer Eisparti- keln, 1. Teil, Zs. angew. Math. Phys., 9a, 180- 192, 1958a. List, R., Kennzeichen atmosphirischer Eisparti- keln, 2. Teil, Zs. angew. Math. Phys., 9a, 217- 234, 1958b. List, R., Zur Aerodynamik von Hagelkérnern, Zs. angew. Math. Phys., 10, 143-159, 1959a. List, R., Der Hagelversuchskanal, Zs. angew. Math. Phys., 10, 381-415, 1959b. List, R., Wachstum von Eis-Wassergemischen im Hagelversuchskanal, Helvetica Physica Acta, 32, 293-296, 1959¢. Discussion (Note: Discussion of this paper is combined with those of the preceding and following papers at the end of the following paper.) Growth and Structure of Graupel and Hailstones Rowuanp List Swiss Federal Snow and Avalanche Research Institute, Weissfluhjoch-Davos, Switzerland Abstract—Interpretation of the structures of air bubbles and single ice crystals makes it possible to show that the growth of hailstones on graupel and small hail particles fol- lows certain laws of symmetry. For the present a number of general qualitative state- ments concerning corresponding glaciation conditions can be made, which explain these facts. INTRODUCTION The elucidation of the structure of natural ice particles is fundamental for an understanding of their growth. This principle takes precedence over any theoretical consideration, since in the case of atmospheric freezing processes, only ob- servation of the natural ice particles covers the full range of variation in shape, structure, and growth potential. An attempt is here made to give some coherent order to all the facts which have thus far been established from graupel and hailstones at Weissfluhjoch. Of course, so far it has not been possible that every type occurring in nature has been taken into account. Further observations or equally intensive parallel studies in other places will perhaps give more complete results. In particular what will be shown is the way in which the growth of graupel or hailstones is to be characterized and by what structural fac- tors this suggests. For specialized information reference may be made to the more detailed publications [List, 1958ab]. Tue THIN-Section TECHNIQUE The structural analysis of graupel and hail- stones is based primarily on the thin-section technique as it was developed by de Quervain [1950] for snow. His method enables, in particu- lar, layers 0.3-0.4 mm thick to be sawed out of ice particles of low density (0.1-0.7 g/m*), with- out the ice structure being disturbed. The layer obtained in this way provides us with knowledge of the amount of air contained in the ice and of the arrangement of the individual air bubbles. The use of polarized light shows up the crystal- line structure of the ice and indicates the ar- rangement and size of the individual single erys- tals. 317 The structural picture is strongly influenced, of course, by the zone and direction in which the section is taken from the graupel or hailstone. Normally the plane investigated should run through the growth center, the original nucleus of the particle, the growth directions of the in- dividual crystals bemg contained in this plane. This is called a main section; other sectional planes may be taken for special examination. Tur FUNDAMENTALS OF GROWTH IN ATMOSPHERIC Ick PARTICLES Crystallographic considerations—The crystal- lographic main axis, the c-axis of the individual ice crystallites, is as a rule approximately verti- cal to their direction of growth. This results from the speed of growth bemg dependent on direction; this determines the selection of start- ing points for new unit crystals. A further conse- quence of this characteristic is that the unit crystals, growing out symmetrically from the center like rays, exhibit a pyramidal or trun- cated pyramid form. Lengthwise sections are therefore generally triangular or trapezoidal, while sections taken at right angles to the di- rection of growth are rather polygonal. With practice all intermediate cuts can also be recog- nized distinctly. The arrangement of the crys- tallites yields a certain symmetry for which conclusions can be drawn as to the manner of growth. It is, for instance, possible in every hailstone to determine the center of growth, the oldest part of the whole particle, on the basis of the form and arrangement of the single crys- tals. So long as this center comprises the growth directions of the first generation of single crys- tals, it is regarded as symmetry-center I. It con- tinues to occupy this role so long as the condi- tions of growth, the type of glaciation, the shape of the particle, and its aerodynamics all remain 318 ROLAND LIST Fig. 1—Thin section through center of hailstone 57.15 under polarized light; real length of the figure, 2.1 cm practically constant. If the fallmg particle, how- ever, should change its relative direction of fall, begin to rotate or be arrested in its initial rota- tion, then normally a new center of symmetry (Il) is formed and a second generation of unit crystals become oriented about this other point. Frequently different generations of this kind are interrupted by a so-called intermediary phase which consists of relatively much smaller crys- tals. A single hailstone may exhibit a third or even more centers of symmetry. Figure 1 gives a par- ticular example of a hailstone core having three centers of symmetry. Changes of symmetry, equivalent to changes of growing conditions, are happening over a whole intermediate surface of a growing hailstone and can be recognized later in the thin sections. This fact helps us to con- clude from the variations of symmetry to earlier shapes which the hailstone has passed through. In the case of hailstone 57.15 (Fig. 1 and 2), for instance, we can recognize a conical structure which turned into an ellipsoid (symmetry-center I). Continued growth led to a rotary ellipsoid (symmetry-center II) and afterwards reached the final shape of a triaxial ellipsoid compressed along the line of the smallest axis (svmmetry- center IIT). The causes leading to the formation of new crystallites are unknown. The assumption that there is some connection with the incorporation of additional freezing nuclei [List, 195S8ab] can- not be maintained, as these would have to be active at approximately 0°C. The whole mecha- nism follows, however, an apparently strict pat- tern, as can be seen from the structural pictures, and further research should throw hght on its causative principle. Bubble structures—Analogous conclusions may be drawn from the arrangement of air bubbles contained in the ice: bubbles arranged in lines indicate the direction of growth; an inner shell of bubbles indicates an earher form of the hail- stone. Zones of equal density may, with certain exceptions, be taken to indicate zones where the same growth conditions prevailed. Figure 2 shows the same section from hailstone 57.15 as Figure 1 but seen this time by translucent light. From this picture it is clear that the intermediary phase I-II has resulted from a change in the conditions of growth, causing a shell of bubbles to form partially around the growth zone I. As GROWTH AND STRUCTURE OF GRAUPEL AND HAILSTONES 319 Fic. 2—Thin section through hailstone 57.15 under translucent light; real length of the figure, 3.0 em a result the particle developed different aero- dynamic behavior and this led to the establish- ment of a new center of symmetry. It may be remarked here that growth in one place may be the result of two different phases, the one ‘overlaying’ the other. This oceurs when a primary ice formation produces a loose ice framework, air capillaries of which become filled with liquid water at a later stage; this then freezes either entirely or in part. It is this ‘overlaying’ process which gives us a generally better picture of the original center than of the later phases, contrary to the views of Dessens [1959]. As an example, Figure 1 may again be referred to. We know that normally a graupel acts as the basic particle of a hailstone. Hailstone 57.15 indicates by the conical sym- metry of the initial particle that the graupel was also conical. Since, however, the shape of this central zone is ellipsoidal, this means that the graupel has absorbed slow-freezing water into its cohesive system of caverns. This has brought about its transformation into a small hail particle with the surface tension of the wet surface leading to a roundish shape. Such over- layings cannot be so well recognized in later phases. ICING NUCLEUS ICE CRYSTAL rapid freezing Sublimation Increase in volume Ww x= o c : 5 GRAUPEL is a i FS (soft hail) = eo a wo fe w ° c = o|s & ° WW - slow freezing c S a | ° = > o r|s ain ry i = 5 Vl gz < SMALL HAIL t+ (= > E slow or rapid freezing < eo “” o Y 2 HAILSTONE 2 ——— ———————— Fic. 83—Characteristics of the growth of a hail- stone GrowTH FROM Icr-FormMInc NucLEus To HaILsToNE On the basis of observations made between 1953 and 1959 on graupel and hailstones the 320 diagram given in Figure 3 can be used to repre- sent the various stages in the development of a hailstone. On the left the type of growth is given, whether by sublimation or accretion of drops, and on the right the main growth phase. This may consist either of an increase in volume or of an increase in particle density. Figure 3 also shows whether the accreted drops freeze slowly or quickly. While there is no need to give a definition of freezing nuclei and ice crystals, the other par- ticles may be characterized as follows: Graupel (soft are white opaque particles, resembling sectors of spheres, roundish or irregular in shape, and with a diameter rarely exceeding 7 mm. Origin: through the accretion of hail)—Appearance: Graupel Graupel originate cloud drops on an initial ice crystal which has grown by sublimation. Water caught up in this way freezes relatively quickly at the point of contact. ROLAND LIST Small Hail—Appearance: Small hail particles are particles having generally rounded surfaces, but of conical, spherical, or irregular shape. They appear white and opaque in parts; certain zones of their surface are glassy or wet. Their diameters rarely exceed 7 mm. Origin: Small hail originates through aceretion of water drops on graupel. Freezing takes place slowly, so that the floating water has time to spread out and penetrate the air capillaries on the original graupel. It may freeze entirely or in part. Hailstones—Appearance: Hailstones are trans- parent or partially opaque particles with a di- ameter of about 5 to 150 mm or more. The num- ber of shapes which are met with is extremely large; the structure is most frequently ‘onion- skin’ with alternating clear and opaque (white) layers. Larger hailstones often contain liquid water in a system of connected caverns. Origin: Hailstones originate from small hail through ac- Fia. 4 Thin section of a graupel under translucent light; height, 4.5 mm GROWTH AND STRUCTURE OF GRAUPEL AND HAILSTONES 321 Fie. 5—Thin section of a small hail particle under polarized light; diameter, 4.5 mm cretion of water drops which then freeze par- tially or entirely. (Small hail particles are, in fact, essentially graupel which have already reached a higher stage of density. To call them small hail makes sense only according to this manner of charac- terization, for there is otherwise no_ possible means of distinguishing small hail from hail- stones.) Figures 4-7 show thin sections of a graupel, a small hail particle (these are wet as a rule and freeze together before examination, with the re- sult shown in Fig. 5), and of a hailstone. With regard to Figure 3 note that in all cases observed there was no indication that graupel arise from frozen water drops. This possibility may, however, exist in nature; this would neces- sitate a corresponding modification of the model. The color pictures, Figures 8-11, should give an impression of the real appearance of a thin section under polarized hght. The range of variation in color is given by the thickness of the ice, where the brown tone sections corre- spond to 0.3 mm; the other ones are thicker. As the limits of the single crystals are much sharper the thinner the section, it is better to cut the ice slices as thin as possible, perhaps con- trary to the aesthetic point of view. The comparison with black and white repro- ductions of thin sections under polarized light (see Fig. 7 and 11 which were taken of the same thin section) show that the impression of the ar- rangement of the single ice crystals and the symmetries is more evident in the color pictures. CoNcLUDING COMMENTS The information which can be inferred from analysis of bubble arrangements and crystalline structure is of crucial significance but only qualitative. Our improved knowledge should, on the one hand, prevent us from carrying out calculations concerning layer formations on the basis of entirely untenable assumptions [J/ason, 1958], and on the other hand encourage research which will yield quantitative results. It is to this end that investigations are to be carried out with the Swiss Hail Tunnel, which aims at explaining natural ice structure by creating similar struc- tures by artificial means. Whereas a year ago it seemed possible to understand growth behavior perfectly with the help of structural investigations, laboratory 322 ROLAND LIST Fig. 7—Thin section of hailstone 59.1 under polarized light; diameter, 4.0 cm 10 Fic. 8—Thin section through hailstone 57.50 under polarized ight; diameter, 5.0 em Fic. 9—Center of hailstone 57.A under polarized light; diameter of the center, 2.2 em; large single crystals surrounded by smaller ones Fre. 10—Thin section of hailstone 57.10, under polarized light; diameter, 4.1 em Fic. 11—Thin section of hailstone 59.1, under polarized light; diameter, 4.0 em DISCUSSION measurements have established that not only are there growth phases which in places become over- laid, but that many times a water layer forms that is stabilized by a subsequent ice framework; it is this which, together with the action of capillary forces, is responsible for maintaining the fluid phase where it is [List, 1959]. This phase, which is apparently of such prime im- portance, means that even the usual and seem- ingly reasonable classification that rapid growth produces opaque ice layers must be given up. Very rapid particle increase may be connected with a two-phase ice-water addition, with the water involved only able to freeze at a later stage, when it forms a frequently clear zone in conjunction with the original ice framework. A technique for estabilshing such distinctions after the event has not yet been found, although the requisite comparative experiments are in progress. REFERENCES Dessens, H., La Gréle, Association d’études des moyens de lutle contre les fléaux atmosphériques, no. 7, pp. 3-17, 1959. pe Quervarn, M., Die Metamorphose des Schnee- kristalls, Verhandlungen der Schweiz. Naturfor- schenden Gesellschaft, pp. 114-122, 1950. List, R., Iennzeichen atmosphiirischer Hisparti- keln, pt. 1, Zs. f. Angew. Math. Phys., 9a, 180- 192, 1958a. List, R., Kennzeichen atmosphirischer Hisparti- keln, pt. 2, Zs. Angew. Math. Phys., 9a, 217-234, 1958b. List, R., Wachstum von Eis-Wassergemischen im Hagelversuchskanal, Helvetica Physica Acta, 32, 293-296, 1959. Mason, B. J., The Physics of Clouds, Clarendon Press, Oxford, 481 pp., 1958. Discussion (This discussion relates to the three immediately preceding papers.) Dr. C. L. Hosler—Do the thin sections elimi- nate the possibility that a large portion of the growth is due to the collection of the ice crystals rather than entirely to supercooled water? Mr. R. List—We have not yet made experi- ments which could show very clearly that that would not be the case. But our experiments show that it is not necessary to have snow crys- tals which can aggregate. Dr. Hosler—My picture would be one of ag- gregation of crystals; then filling in of the spaces by water of the supercooled droplets. Mr. List—Only when the surface is wet can ice particles aggregate. When the particles, big or small, are dry they bounce off. Dr. Choji Magono—The pictures shown by you are actual hail stones? Mr. R. List—Yes, and the center of natural hailstones can be recognized in 80% of the cases as graupel. Mr. D. Blanchard—I would like to take ex- ception to a statement Dr. List made about liquid water being shed from the hail pellet itself. You said that the liquid water is itself absorbed into the hail stones or is shed. At the first meeting here at Woods Hole, I presented a paper (The Supercooling, Freezing, and Melting of Giant Waterdrops at Terminal Velocity in Air, Arti- ficial Stimulation of Rain, pp. 233-249) report- ing on some experiments I did. One day, I tried the reverse process, taking an ice sphere, sus- pending it in the wind tunnel, to see what hap- pens when the ice melts. When the melting oc- curred, a water ring would form around the center of the sphere. Of course, eventually water will be shed, but first there will be a horizontal ring around the center. Mr, List—Horizontal rings can be observed when the rotating axis of the growing stone is stable. That means the form of hail stones de- pends on the icing conditions. When the water freezes slowly, it has time to soak into the in- terior and finally to form corresponding to the aerodynamic pressure distribution a ring around the rim of the stone. Then one finally arrives at plates which can rotate about the vertical axis. One can see this rotation also in the frozen water droplets. They are arranged around the vertical axis. From the floor—Do we know enough about what a frozen water drop looks like when it is freezing? I wonder whether your analysis would indicate whether the center of the stone was formed by the particle which Ludlam talks about, that is, by freezing of a water drop having a radius something of the order of 30 to 50 microns. If this froze because of a violent collision of two such drop sizes, or because of the crystallization of a single water drop or if the center was formed from the conglomeration of a number of frozen particles which resulted from 324 growth caused by sublimation, I wonder whether from an examination of the frozen center of hail stones one could differentiate these processes. Mr. List—I think I can answer that last ques- tion, but not in an absolute manner. Since our institute lies S000 ft above sea level, we can ob- serve these graupel stages 20 to 30 times a year. We find not many graupel with what is prob- DISCUSSION ably a frozen droplet in the center, but in about 40 or 50% we are sure that the center is an originating snow crystal. I would say it is not necessary to have frozen droplets. Dr. Helmut Weickmann—How much did the tunnel cost ? Prof. R. Sdnger—It cost about 600,000 Swiss franes or $200,000. Hailstorm Structure Viewed from 32,000 Feet Rosert M. CunNINGHAM Aerophysics Laboratory, Geophysics Research Directorate, Air Force Cambridge Research Center, Bedford, Massachusetts Abstract—Photographs taken near Cheyenne, Wyoming, on a high-altitude flight from the cloud-studies aircraft of AFCRC show hail thrown out of the side of a large organized thunderstorm. A small vortex is visible at one edge of the hail shaft. The re- lation of the hail region to other regions of the cloud is clearly evident. The cloud and hail patterns, revealed after mapping the clouds from the photographs, suggest a hori- zontal cyclonic circulation of the whole storm. While studying the effects of local topography on the cloud patterns east of the Denver area, aerial photographs were taken of a well-de- veloped large hailstorm. This paper will discuss these photographs and the measurements made from them. On the afternoon of September 11, 1958, the AFCRC C-130 Hercules aircraft, equipped with cloud-probing and large mapping cameras (T- 1l’s) flew along a SSE-NNW line some 80 mi east of the Front Range of the Rockies. Small showers and thunderstorms had produced a gen- eral chaotic cloud mass over the Rockies. Figure 1 shows the tops of these clouds as they descend and evaporate in the westerhes flowing down from the mountains. The photograph was taken looking toward the west. A west-east lne of cumulus is visible at a lower altitude. These mountain thunderstorms have not developed into self-propagating storms; presumably at least on this day they cannot survive passage through the downdraft region east of the Front Range. In contrast to the poorly organized thunder- storms over the mountains, large well organized hailstorms were photographed east of our flight path (Figs. 2 and 3). These storms were self- propagating, lasting until after midnight. Moun- tain wake circulations may be of importance here; that is, the large storms first develop in and under a region of general upward motion in the first downstream wave beyond the mountain. Once started over flat terrain, these storms, on drifting eastward, can apparently become or- ganized enough to outweigh the effects of the farther downstream portion of the mountain wave. The surface and upper-air conditions can be described as follows. A thin layer of moist hot air was moving at moderate velocity from the 325 south and southeast over the region just east and north of Denver and Cheyenne. Tempera- tures reached into the upper eighties (all surface readings in °F) in this region and dew points were recorded at Akron, Colorado, in the lower fifties, and at Scotts Bluff, Nebraska m the lower sixties. The surface air at Denver, however, was part of the direct flow down off the mountains as the dew point fell in the afternoon to the upper thirties, the temperature reached the up- per eighties, the wind was light and variable. Cheyenne recorded light southeast winds with surface temperatures in the lower eighties, dew points near fifty. The vertical thermal and wind structure of the atmosphere is shown on a skew T, log P diagram, (Fig. 4). The features to note are the following: (1) The thinness of the sur- face layer of southeast wind with slowly increas- ing westerly wind above, and the strong west northwest winds above the isothermal layer at 33,000 to 35,000 ft. (2) The difference in the moisture structure over Denver and over Scotts Bluff; the air at Denver below 23,000 ft is relatively homogeneous with a nearly constant potential temperature and small range in mois- ture content, suggesting again that this air is well mixed and comes from the higher terrain to the west. The air at Scotts Bluff, on the other hand, is moist in the lower layers and very dry above 15,000 ft. (3) The isothermal layers, a minor one at 22,000 ft, a major one at 33,000 to 35,000 ft. This latter layer is perhaps a remnant of a more northerly tropopause. The sharp tropical tropo- pause appears at 51,000 ft. The hailstorms to be discussed were, it ap- pears, surrounded by an atmosphere close to that measured by the Scotts Bluff radiosonde. The maximum temperatures during the day in the storm area reached as high as 91°F (33°C). A Fic. 1—Right T-11 Photo 122, looking west 2— Right T-11 Photo 91, looking east northeast 326 HAILSTORM STRUCTURE VIEWED FROM 32,000 FEET 327 Fie. 3 more representative temperature sounding for mid-day (radiosonde released one to two hours after time of maximum temperature) would lie in between the Denver and Scotts Bluff curves in the lower layers. A dry adiabat drawn from the point of intercept of the storm cloud base (15,000 ft MSL, 600 mb by measurement from the photographs) and the Scotts Bluff sounding reaches the surface at a temperature of 34°C. The moist adiabat from the cloud base intercept crosses through the isothermal layer at 34,000 ft (266 mb). With the structure of the ambient atmosphere in mind, a closer look will now be taken of the large storm masses that developed during the afternoon of the 11th. In the upper middle part of Figure 2, a large storm is just beginning to produce rain at the ground. Almost the whole perimeter of the cloud shadow can be seen, in- dicating only a few hydrometeors below cloud base. This storm has grown, however, to above 40,000 ft and a large volume of cloud and other hydrometeors have been blown downstream in the strong upper winds to form a large anvil with maximum horizontal spreading at the upper iso- Left T-11 Photo 107, looking east thermal layer (33,000-35,000 ft). Another sim- ilar storm appears in the upper left but is largely obscured in this picture by lower, nearer Cumu- lus. A third storm, the one to be studied here in detail, appears on the right side of Figure 2. A more complete view of the western end of this storm, (Fig. 5), shows several interesting features. (The dark vertical line in the upper part of the picture is one blade of the aircraft propeller.) Figure 6 should be referred to when studying Figure 5. Figure 6 was traced from photographs with the use of a Canadian grid tech- nique and by triangulation from several pictures. Note that because of the varying distances from the flight path, this tracing is divided into three parts with three different scales. The upper and left parts are from Photo 90, the lower right from Photo 89. The features of interest will be discussed from the top down. The portion of the cloud above flight and cirrostratus level reaches some 10,000 ft into stable air; individual cloud elements (bub- bles) do not greatly outrun their neighbors, giv- ing the whole cloud a rather rounded top. The Jy) bo (0/0) ROBERT M. CUNNINGHAM UPPER WINDS DENVER SCOTTSBLUFF —l0Ombs j2097 ABOVE ts VT {Ith lakh DENVER —__- '200Z I|SEPT 58 Fie. 4—Skew T log P plot lack of distinet individual turrets at the top sug- gests that the storm is characterized by a large region of fairly continuous upward velocity with a narrow velocity spectrum, in contrast to many Cumulus systems where the velocity spectrum is wide and individual turret production is a major feature. Much of the cloud material that reaches these heights gains momentum from the ambient air and spreads downstream in the anvil. This feature is best seen in the young cloud in the upper middle of Figure 2. The Cirrostratus layer at flight level (Figs. 5 and 6), may be caused by the upwind spreading of that portion of the upper cloud material that has lost its up- ward momentum, is relatively cold, and descends against the ambient wind down to the isothermal layer. More hkely, however, this upstream Cir- rostratus is formed by an uplift of the ambient air flowing around the storm. The horizontal, thin protrusions on the north side of the storm, pictured best in Figure 3 at about 27,000 ft and 22,00 ft, may be caused by this blocking action forcing the ambient air to ascend. That portion of the protrusion at 22,000 ft, visible on Figures 5 and 6, appears rather to be caused by motions within the storm. Mammatus formations mark the lower portion of this protrusion, suggesting that small precipitation particles and clouds are flowing down and out of the main cloud and evaporating into the ambient air. The most interesting feature shown on Figure 5 and sketched on Figure 6 is the great fall of hydrometeors into the sunshine below the marked protrusion. The bright portion of this fallout is presumably a region of snow, snow pellets, and hail (S + A). The dimmer portion, rain and hail (R + A). The brightest portion in these two regions may be shafts and bunches of falling heavy hail. The level at which most of the small frozen particles have melted is 8000 to 12,000 ft or at +20 to +8°C ambient air temperature; the more relevant local air and wet bulb tempera- ture in the precipitation is unknown. To the right of the precipitation is a large TH LEN WER, RE 6210 Fie. 5—Right T-11 Photo 89, looking east northeast ALTITUDE K FT S| 3 p pe) (eo) (12 MI DIST) Fia. 6—Two vertical cross sections west end of hailstorm parallel to flight path; scaled from Photos 89 and 90 329 330 region of Cumulus and Cumulus congestus seem- ingly leading into the storm, the cells growing larger the nearer to the storm mass they are. These clouds and their relation to the main storm are also seen in Figure 3. At the juncture of the western edge of these clouds with the area of precipitation a dark sloping line is visible, bor- dered by two bright lines. This configuration is assumed to be the result of a vortex circulation, ROBERT M. CUNNINGHAM the precipitation particles being concentrated on the perimeter of the vortex. This apparent vortex was short-lived; it is not visible on Photo SS (taken one minute previous) ; and it appears about double the size but very faintly on Photo No. 90 (taken one minute later). One may im- agine that the Cumulus cloud material on the right is streaming into the storm while the pre- cipitation is flowing out and that the region of Gad Enlargement of part of Photo 89 HAILSTORM STRUCTURE VIEWED FROM 382,000 FEET oe strong shear between these flows spawns eddies, some of which develop sufficiently to show up as a long vortex such as the one visible on Figure 5. Figure 7 is an enlargement of the region in which the vortex is visible. Close inspection of the ground shading in Figures 2 and 5 reveals the pattern of rain cover- age from the nearby storm. The darker ground leading to the left of the storm is the ground wet by the heavy rain and hail. The spots of white on the upper side of this dark area are patches of hail left by the storm. According to W. B. Beckwith (private communication) hail on the ground that falls with little rain will show well from the air but when accompanied by heavy rain it will be washed into the vegetation and gullies and will not show. Hail, therefore, could have fallen throughout the precipitation area but only show on the ground where it separated from the other hydrometeors, descending along a dif- ferent trajectory because of its greater fall ve- locity. Many of the features discussed above are SCALE Gaamtmem eo os 10 stat. mi +0 == WHITE HAIL PILES ON GROUND <> © AREA OF WET GROUND Laas Oo 1 \ < 6 \ + 3/1 + « \ Ww I aaa ii 2 H + & =a5=4e ! i. ° \ i Reet + (Owe, ‘ PEN =; . o ——_+—1—r zo i ry 60 400 140 180 220 300 MAXIMUM WIND VELOCITY ykm/h Fre. 1—Frequency distribution of wind speeds at high levels for 38 days with heavy destructive hailstorms (full line) and for 38 control days with thunderstorm but without significant damage by hail (broken line) diagram, we have included also (broken line) the frequency distribution of wind speeds for an equal number of days during the same season of the year (April to September) and the same period (1951-58), these 38 control days were days without significant damage due to hail, al- though thunderstorms did occur over the region. A comparison of these two frequency distri- butions shows clearly the correlation between the wind velocity at upper levels and the degree of damage caused by hail. It is probable that the correlation between wind speed and the in- tensity of the hailstorms is actually closer than indicated on Figure 1. In effect the correlation is probably somewhat reduced by the fact that the radiosonde observations are often made at places distant both in space (that is to say, up to 250 km) and in time (up to 12 hr) from the hailstorms. It is worth mentioning in addition, that although on five days, winds of more than 90 km/h were observed without wide-spread destructive hail. On four of these days, heavy hailstorms did in fact occur but the damage done was not very great because they were very limited in extent. Finally, to sum up, on a total of 76 days with Cumulonimbus activity, there is only one case in which the maximum wind- speed exceeded 90 km/h without bemg accom- panied by destructive hail. In conclusion, it appears that the presence of a jet stream, or at least a very strong wind at upper levels, is the factor which determines whether or not a thunderstorm situation will transform itself into a heavy destructive hail- storm. A suggested structure for the hailstorm—In air masses with relatively little variation of horizontal wind speed with height, the ascend- ing currents in Cumulonimbus are approxi- mately vertical. The air in the ‘chimney’ up- draft takes its energy from the instability of the atmosphere, perhaps increased locally by differential heating of the soil and from the latent heat of condensation and of freezing; this energy is liberated mainly in the lower part of the ascending air column. Therefore chimneys are fed from the low end and receive no im- portant energy at high levels; furthermore, if air is not removed from the top, then the ‘chim- ney’ may fail to draw. Chimneys therefore tend to be short lived, depending, as they do in this ease, on the hazards of local conditions and particularly on the nature of the terrain over which they travel, under the influence of the HAIL STORMS TEMPERATURE °C HEIGHT IN km 0100 200 500 ASSOCIATED WITH STRONG UPPER WINDS 99r 2090 WIND SPEED kmh Fie. 2—A suggested structure for the hailstorm: (left) wind velocity versus height; (right) the chimney inclined to the vertical prevailing wind. In the cloudy edifice, a chim- ney is born, develops, and quickly dies to give place to another. Such sporadic activity is not favorable to the formation of large hailstones [Weickmann, 1953]. On the contrary, under conditions of strong windshear, as in Figure 2, the chimney is in- clined to the vertical. On the right side of Figure 2 is included a chimney of very restricted transversal dimensions, in accordance with the observations of Wichmann [1951]. It is certain that in a case such as this, a part of the air rising in the chimney is entrained horizontally at the top of the chimney at a speed of the order of SO m/s. Therefore I envisage a coupling taking place above 6000 m between the updraft in the chimney and the very strong horizontal current and that this current tends to stabilize and prolong the life of the chimney, which now receives, in addition to the energy of thermo- dynamic origin at low levels, kinetic energy of the strong wind at high levels. The chimney may, in fact, be considered as forming the lnk between these two main sources of energy; the lifetime of an individual chimney appears to be prolonged under these conditions for periods of more than 30 min sufficient to make possible the formation of very large hailstones. Arguments in favor of the suggested struc- ture—In addition to the data which led me to suggest this structure of the hailstorm, there is the following argument in its favor. It is the correlation, which has been observed, between the maximum size of hailstones and the maxi- mum wind velocity between 6,000 and 15,000 m. DIAMETER ,mm w ) VELOCITY ,m/s Fic. 3—Correlation between diameter and _ ter- minal velocity (curves after Wichmann) of hail- stones and the maximum wind velocity between 6,000 and 13,000 m (crosses) Figure 3 shows the correlation between these two parameters for seven hailstorms which oc- curred in the region within a 200 km radius of Bordeaux. The curves showing the variation of terminal velocity of hailstones with height and with diameter are taken from Wichmann. The fact that the crosses representing observations lie fairly close to the curve corresponding to 11,000 m, shows that the maximum velocity of the updraft tends to approach that of the hori- zontal wind as measured outside the storm- cloud. Thus the maximum size of the hailstones would appear to depend on the velocity of the horizontal wind. It is because of this that a hailstone cannot remain indefinitely within the ascending chim- ney when this is inclined to the vertical; and therefore we can obtain from this picture of the hailstorm a forecast of a maximum size which 336 the hailstones may reach. The value of such a forecast hes im the fact that in general the up- per air winds have already been present for several hours at least before convective activity becomes important. This last paragraph and Figure 3 represent only a preliminary version of the suggested hailstorm structure. It is to be hoped that the different studies at present beimg pursued in various parts of the world will enable us in the near future, to reach some more definite conclusion as to the value of this suggestion. On the other hand there is need for a theoretical explanation of the fact that the strong hori- zontal wind at high levels tends to accelerate and stabilize the updraft m Cumulonimbus clouds. REFERENCES Dessens, H., Sur l’apparition des particules glacées dans les Cumulus, Bul. Obs. Puy de Dome, pp. 20-23, 1953. DISCUSSION Dessens, J.. Niveau de congélation des nuages convectifs équatoriaux, Bul. Obs. Puy de Déme, pp. 73-80, 1959. Donatpson, R. J., Analyses of severe convective storms observed by radar, J. Met., 15, 44-50, 1958. Lupa, F. H., The production of showers by the coalescence of cloud droplets, Q. J. R. Met. Soc., 77, 402-417, 1951; also Nubila, no. 1, pp. 12-96, 1958. Sounace, G., Réponse A la note de E. K. Bigg: Freezing nuclei in the atmosphere, Bul. Obs. Puy de Dome, pp. 80-85, 1956. Soutace, G., Influence de l’aérosol atmosphérique sur la formation de la gréle. I—Pouvoir gla- cogene de lair & proximité d’orages A gréle, Bul. Obs. Puy de Déme, pp. 125-146, 1958. WeIcKMANN, H., Observational data on the forma- tion of precipitation in Cumulonimbus clouds, Thunderstorm Electricity (H. R. Byers, ed.), Univ. Chicago Press, pp. 66-138, 1953. Wicumann, H., Ueber das Vorkommen und Ver- halten des Hagels in Gewitterwolken, Ann. der Met, 4, 218-226, 1951. Discussion (This discussion pertains to the two immediately preceding papers.) Dr. Helmut Weickmann—I call attention to the fact that another plausible explanation exists as to why there occurs little or no hail in the tropics. It has been found (Fawbush and Miller, Bul. Amer. Met. Soc., 34, 235-244, 1953) that no hail falls from hailstorms which have a wet-bulb freezing level above 11,000 ft, be- cause then even the biggest stones melt before they reach the ground. I suspect that this is the case in these tropical hailstorms. Dr. H. Dessens—I think that the greater height of the O0°C level cannot explain the scarcity of the hail in the equatorial regions. In France, in summer, the 0°C level is near 3500 m, and the top of the hailstorms near 14,000 m; at this top, the temperature is about —55°C. In the Congo Basin, the 0°C level is near 4500 m, and the top of the thunderstorm near 17,000 m; at this top, the temperature is about —so°c. In both of these regions, during the heavy showers, the temperature near the ground is of the same order: +17°C. Thus, the difference in the 0°C level is of the order of 1000 m. The time of fall of big hailstones through this layer is shorter than one minute. This time seems inadequate to melt the hailstones noticeably, the more so as the mean temperature between the 0°C level and the top of the cumulonimbus is much lower near the equator than in the temperate regions. Mr. Jerome Namias—In the United States one of the atmospheric characteristics looked for in the prediction of severe storms or tornadoes is the existence of a mid-tropospheric jet. No one has yet given a satisfactory explanation for this association. Nevertheless, it 1s a pretty good indicator, provided the lower thermody- namic air-mass structure is conducive. I would like to suggest two points which may have something to do with this. Springtime is the most favorable for tornadie activity. Then we frequently have conditions which lead to the development of deep layers of very dissimilar air masses—very cold air from the Pacifie over- riding moist and warm, tropical gulf air. This differential flow often leads to convective in- stability and, simultaneously, the presence of jets which are found in the middle troposphere. Perhaps there is something about the circulation in and around these jets that might encourage convection; this would be enhanced by the thermodynamic instability. DISCUSSION 337 Dr. J. Smagorinsky—It might be possible to explain the convective instability underneath a jet as a gravitational shearing instability. Dr. Weickmann (communicated)—I may make an attempt to explain this phenomenon from purely cloud-physics reasons. We know from the Byers-Braham thunderstorm model that a storm’s life span can be subdivided into a developing stage, a mature stage, and a dis- sipating stage. The dissipating stage begins with the development of a downdraft in the rain area which slowly gains momentum and extends upward in altitude. Downdrafts also develop aloft and within the cloud because of entrain- ment of drier outside air. In conditions of great instability the updraft velocities in the inner core of the storm may be sufficiently high as to prevent even larger particles from descending against the updraft. They too end up in the anvil where the updraft finally ceases. The particles, however, continue to grow until they are large enough to descend against the powerful updraft and to initiate the downdraft mechanism. The hailstones thus formed have a conical shape in the ideal case. Suppose now the existence of a strong jet in the upper levels. It will displace the anvil down- wind from the mother cloud, so that large par- ticles cannot fall back into it and cannot stimu- late the formation of downdraft which would lead eventually to the dissipating stage. Of course, from the downwind spreading anvil large particles will fall mto other up-coming clouds and may form hailstones in these. The lifetime of the original mother cloud depends now only on the correct adjustment of external factors, such as inflow characteristics, migration velocity, and air consumption in the updraft. The in- creased lifetime of this updraft may be a deci- sive factor for tornado formation as it will per- mit the encounter with an already existing micro-low, or it will even assist in the organiza- tion of the correct low-level cyclonic circulation. Then the tornado may form. Dr. W. E. Howell—Of course, in the tropics there are very seldom high-level winds of ve- locities that are anywhere comparable with mid- dle latitude high-wind velocities. However, on the Pampa de Junin, the high plain in central Peru, there is often a strong easterly wind at high levels across the main range of the Andes while the Pampa lies, protected, between two ranges. Here the air is relatively slow moving and in fact often undergoes a reverse circulation so that there is a west wind near the ground beneath the east wind aloft. On this Pampa it is not unusual to have rather strong showers of graupel. Of course, since the elevation of the ground is 14,000 ft, there is much less depth of cloud in which hail could grow, but we do have the first phase that Mr. List has shown. Dr. E. Kessler—Referring to this problem in a purely intuitive way, I have been struck also, as many others have, with the association of thunderstorms and high winds aloft, and their occurrence together in the spring. In Corpus Christi, Texas, where I used to live, numerous severe thunderstorms occur in the spring; later, in the summer they are not as severe. I have thought at times, that the explanation for this may he in the transport of heat away from the region of active convection by the strong up- per-level winds, which are weak or absent in summer. The unstable thermal stratification which is associated with the development of the springtime storms may then persist locally for a comparatively long time, with a correspond- ingly long time available for an organized, strong circulation to develop in the lower troposphere. Dr. D. Swingle—I just have a quick question for Dr. Cunningham. Do you have proof this is the same storm that made hail near Cheyenne? Dr. R. M. Cunningham—I do not know ex- actly what you mean by proof, but the track of the storm is right for that conclusion, shall I say. Dr. Swingle—You do not have the continuity that actually ties it back? Dr, Cunningham—Radar showed it coming from that area, but I do not believe we have the radar echo right over Cheyenne. Mr. Alan Faller—I would like to ask if the hail was falling through the zone of strong shear from the region of high winds into the lower region where the wind is not so strong? Dr. Cunningham—The visible hail coming out of the side of the cloud was all lower than the strong winds. The strong winds are up in the Cumulus part of the cloud and the hail was down where we only had a wind of 20 knots. Of course, I do not know where it came from inside. Dr. Tor Bergeron—Concerning Dr. Dessens’ paper, I must confess that I on the whole agree with the first remark made by Dr. Weickmann. On the other hand, it is not my intention to deny the possible effect of the shear. But I want to remind you of the fact that in the United States you have the maximal thunderstorm frequency in summer with one maximum over Florida and the other over New Mexico, the first being characterized by practically no hail, but by much rain and low cloud base. In the other maximum you have rather little precipitation reaching the ground, with the cloud base more than 3500 m ab. s.-l. I think, on an average the cloud base is generally higher than Mount Sandia at Albu- querque, and yet hail reaches the valley, which is 1500 m ab. s.-l. My explanation, when I tell my students about these things, is that in Florida the hailstones exist probably high up in the cloud, but they melt before reaching the ground because there is constant condensation on them all the time, almost down to the final melting. In the New Mexico region they fall through dry air. They may evaporate, but they do not melt beeause they keep cool. Those principles would DISCUSSION probably, on the whole, apply to all the storms in the tropics, and I thought it was generally recognized that there was no hail within the equatorial region. The really devastating hail is in central Europe, in Switzerland, and certain parts of the United States, but not in Florida. And then as to the shear and the high winds aloft, in Florida there are no such high winds aloft in summer. The jet may reach down to the northern part of New Mexico, which has a higher latitude. So jet and hail may have a com- mon basis, but there need not be any direct con- nection between them. Dr. C. J. Todd—F. H. Ludlam pointed out (Nubila, 1, p. 1, 1958) that the fall velocity of hailstones of radius of one centimeter or larger at O°C is so fast that they should reach the ground with little loss of radius even in hot weather. Morphology of Thunderstorms and Hailstorms as Affected by Vertical Wind Shear Cuester W. Newton Department of Meteorology, Chicago, Illinois Abstract—Within convective clouds imbedded in a current with pronounced vertical shear, horizontal velocities are considerably different (1 to 10 m/sec or more) from environment winds, because of intense vertical transfer of momentum inside the cloud. Pressure fields induced by relative motions tend to promote new cloud growth on the downshear flank of a large convective system containing both updrafts and down- drafts. Physical analysis of the forces, with the aid of experimental analogy, indicates that the induced pressure field is quantitatively capable of triggering convection and that it significantly augments vertical accelerations in the newly formed cells. Possible influences on growth and distribution of large hail relative to the main body of a storm, are discussed with examples. INTRODUCTION Although theories for hail formation differ in important details, it is generally accepted that the vigor of updrafts (or successions of ‘bubbles’) is a major factor in hailstone growth, since this determines the possible effective length of the path swept out by a hailstone [Ludlam, 195s}. It is thus natural that the degree of instability serves as an excellent predictor for maximum hail size. Air-mass structure, however, does not by itself determine the character of the convection. In air masses having much the same thermodynamic structure, small and chaotically-distributed, or very large organized thunderstorm systems may oceur. Particularly in the latter, the distribution of severe convective phenomena tends to be strongly asymmetrical. In the outline for the Woods Hole Conference, H. Weickmann posed the questions: ‘““‘What do we know of hail formation; is it due to a very intensive or persistent updraft?” and “What is the significance of the zones of high winds (jet streams) which appear to be a typical feature of hailstorms?” This paper is designed to suggest how these two questions are related, for certain types of convective storms. This analysis will concern only the effects of vertical shear on the structure of a cloud system, without regard to antecedent conditions for its formation. The latter, as is well known, is strongly influenced by the temperature and moisture ad- vection and by large-scale weak but. persistent vertical motions [Ffulks, 1951], which are most pronounced in the jet-stream region. 339 INTERACTIONS BETWEEN IN-CLOUD AND AMBIENT WINDS As background for comments on the hail ques- tion, it is necessary to review some results of an earlier investigation [Newton and Newton, 1959] which treats, in greater detail, the interactions between convective cloud systems and the wind fields in which they are imbedded. Rainfall and radar observations show that or- unized convective systems, even relatively solid te g squall lines, are composed of distinct agglomera- tions of thunderstorm cells, having average widths in the range 15 to 50 km. Such an aggre- gate, henceforth called a ‘rainstorm,’ is the entity to be discussed here. In a typical organized convective situation where storms are found in the warm sector or ahead of a middle-latitude cyclone, the wind veers with height. Figure 1 shows a rainstorm in such a wind field, V, and V, being the environment winds in upper and lower levels. Large rainstorms are made up of alternate up- and downdrafts which exchange horizontal momentum between upper and lower levels. Complete mixing would result in mean in-cloud velocities as shown by the dashed arrows in the figure. As indicated by the double-shafted arrows, relative motions would exist between ambient winds and in-cloud air. Evidently the right flank (with respect to motion of existing cloud) is most favored for new cloud growth, due to relative in- flow of moist air on that flank in lower levels. Several authors [Desai and Mal, 1938; Hum- phreys, 1940, pp. 353 and 3859; Newton, 1950; U.S. Weather Bureau, 1949] have suggested that 340 CHESTER W. NEWTON Fig. 1—Ambient and in-cloud winds, convective rainstorm imbedded in shearing current; Vp shown by double-shafted arrows triggering of new convection by cold air flowing outward from beneath a thunderstorm is en- hanced if the air brought down in downdrafts has initially high horizontal momentum. In the fol- lowing, an attempt will be made to analyze the broad-scale aspects of this process in terms of the physical forces at work. Induced pressure field and new cloud growth— At a given level in Figure 1, the rainstorm may be regarded as an obstacle in motion relative to the ambient winds. If Vz is the velocity in the undisturbed environment (for example, V, or Vz in Fig. 1), and V. the mean in-cloud velocity, the basic relative motion is Ve = Ve — V-. Hydrodynamic pressure is defined as P= Pp = Dr (1) being the departure from the hydrostatic pressure in the undisturbed environment. Aerodynamics experiments [Goldstein, 1938] show that, in the case of a circular cylindrical obstacle, a positive pressure P = pV,*/2 is induced on the upwind side (with respect to Vr), and negative pressures shghtly larger on the lateral and downwind sides. In Fig. 1, the sign of P is indicated on the right flank at upper and lower levels; the signs are opposite on the left flank. Evidently one effect. of this pressure distribution is to tilt the cloud along the direction of the vertical shear. Substitution of p from (1) into the equation for vertical acceleration gives dv (aT _P | ap dt di dB P Op Here AT is the excess of temperature relative to the undisturbed environment. On the right flank, the second term (not always negligible) is small compared with the third, when averaged through the depth of the cloud. In general, for ‘triggering’ convective instabil- ity, a certain amount of lifting is required to reach a state of free convection (positive thermal buoyancy). During lifting, the air becomes tem- porarily cooler than in its undisturbed state. Eq. (2) shows that lifting can be accomplished by the hydrodynamic pressure force, if there is a strong enough decrease of P with height. On the right flank of the rainstorm in Figure 1, the induced pressure field favors such lifting. Thus, the same pressure field that acts to shear the cloud away from the vertical, tends to promote new convective cloud growth on the downshear side. Radar observations [U. S. Weather Bureau, 1949; Ligda, 1956] show that nonpropagating thunderstorm cells move very nearly in the direc- tion of the mean wind in the cloud layer (or the 700-mb wind). If growth on the right flank pre- dominates, this should show up as a tendency for rainstorms to deviate toward right of the winds. In case studies using hourly rainfall data [Vewton and Katz, 1958] this was consistently observed, rainstorms moving on the average about 25° (10-15 knots vector velocity) to right of the mean wind, in situations where the wind veered mark- edly with height. QUANTITATIVE ESTIMATES Relative motions between cloud and environment —Because the induced pressure field depends on the relative motions, it is essential to establish the probable magnitude of Vz to see whether the process described above can be quantitatively significant. Pressure forces acting horizontally across the cloud (Fig. 1) tend to accelerate it, at EFFECTS OF VERTICAL WIND ON STORMS 341 a given level, from high to low induced pressure, and thus to decrease Vz. The force acting on a unit slice is DAP, AP being the difference be- tween upstream and downstream pressures, aver- aged across the cloud diameter D. The accelera- tion is given by this force, divided by the mass of the slice (prD*/4), being dV. ti 4AaP dt pxD (3) In a coordinate system following the cloud, if advective transfer of momentum across storm boundaries is neglected We Ve FAV, a ah ae On substitution from (3), av. 4AP av. Sie aD ap a ; Pa Oz The in-cloud air can be maintained at a constant mean velocity different from that in the environ- ment, so long as the sum of the two terms on the right is zero. With strong shear typical of spring squall-line situations, it is found [Vewton and Newton, 1959] that for large rainstorms (D ~ 30 km), with modest mean vertical motions (w ~ 1-3 m/sec), balance between the terms in (4) can exist if the in-cloud shear is about 1 that in the environ- ment (the difference between 0V./02 and dV; /dz determines Vz and thusAP, at upper and lower levels). In the cases studied, it turned out that the estimated difference between mean in-cloud and ambient wind velocities was around 10 m/sec in lower and upper parts of the cloud. This proposition may be illustrated by use of observations provided by Malkus and Ronne [1954]. Figure 2 shows a comparison of horizontal velocities of cloud towers, with winds at a nearby station. Cloud turrets penetrating a strong shear layer and entering the subtropical jet stream, had speeds 9-15 m/sec lower than the environment winds. From data tabulated by Malkus and Ronne, the following mean values are estimated for sev- eral towers in the layer 10-12 km: D = 8 km, w = 6 m/sec, Ve = 12 m/sec, p = 0.4 X 10° em/em’, 0V./dz = 3.5 X 10-% sec. At the ap- propriate Reynolds number,AP is about 0.4 mb. Substitution of these values gives, for the first term on the right in (4), 1.6 em/sec?, and for the second term, —2.1 em/sec?. Considering the crudity of our estimates from their data, this is good agreement, showing that vertical transfer of momentum can effectively offset the tendency for the cloud to be accelerated by outside forces. Furthermore, the close agree- ment suggests that the analogy between a vigor- ous cloud tower and a rigid obstacle (for which the laboratory measurements of P are valid) is not a bad one. The expression for form drag used by Malkus and Scorer [1955] is physically similar to that used here. Analogous to (3), their expression would be dV./dt = KV;?. The experimental values quoted above give K ~ 1/(3R), R being the cloud radius. This value for the drag coeffi- cient is several times smaller than that derived by Malkus and Scorer for cloud bubbles. Vertical pressure-gradient forces—Maximum values of P on the upstream and downstream sides of an obstacle being about pV ,?/2, relative motions of the order 10 m/see give a total vertical decrement of P, in a case like Figure 1, of about 1 mb. In a typical large thunderstorm, there is a radial outflow in lower levels of order 10 m/sec, due to thermodynamic processes within the storm. When this is superimposed on the mean relative motions caused by momentum transfer, the total relative motion between ‘in-cloud’ and ambient winds on the right flank is double the amount estimated above. The vertical decrement of pressure can then be 1.5 to 2.56 mb. WithéP = 2 mb in a layer 500 mb deep, the vertical accelera- tion given by the last term of (2) is 4 em/sec?, comparable with the buoyancy acceleration if AT = 1°C averaged through the whole layer. Significance for triggering new convection—Par- ticularly because low-level outdrafts decay rap- idly with height, most of the hydrodynamic pres- sure differential tends to be concentrated in the lowest 200 to 300 mb or less. According to (2), a 200-300-mb layer can be lifted until it is 2-3°C cooler than the undisturbed environment, if 6P = 2 mb. Ina typical mT air mass, the amount of lifting involved is enough to set off the existing potential instability. Lesser lifting, such as provided by the down- draft outflow alone, can suffice to trigger new convection when the air mass is very unstable in lower levels, such as in mid-afternoon. The estimates of Vz and P above are characteristic 342 16 32 48 17.6 16.0 14.4— 12.8 HEIGHT (KM) 9.6 8.0 6.4 16 32 48 WINOSPEED (m/sec) O WIND OBSERVATIONS x TOWER*X-CLOUDTI © TOWER Y-CLOUDI CHESTER W. NEWTON 200 280 360 63,000 57,600 52,500 47,200 42,000 (14) LHOIGH 36,800 31,450 26,200 21,000 DIRECTION (°F ROM N, 360° COMPASS) LEGEND V TOWER Q-CLOUDI O TOWER W-CLOUDL 4 STREAMER- CLOUD ID Fic. 2—Horizontal movements of Cumulus towers near Anegada Island, compared with winds at San Juan, P.R. (120 mi WSW), 15h 00m GCT April 1, 1953; from Malkus and Ronne [1954] of spring situations wherein the vertical shear is strong. In summer, these values would be on the average considerably smaller; on the other hand, the mechanical lifting required is often corre- spondingly less. The significance of momentum transfer lies in the fact that it augments the rela- tive motion due to outflow alone, and that the induced pressures are proportional to V2. Thus, if a relative motion of only 5 m/sec because of momentum transfer with modest vertical shear is added to a relative motion of 10 m/sec due to the outflow field of a thunderstorm, the kinetic energy of relative motion, and the potential for lifting, is still more than doubled. Effects of storm size—Equating the right-hand terms in (4) and noting that AP is proportional to V,2, it is seen that for steady motion of the cloud ( zi) = 1 w D Oz Since 0Vr/dz = OVz/dz — OV./dz, for a given environment shear small 0V./dz is concomitant with large Ve at upper and lower cloud levels. Proportionality (5) then states that for a given intensity of vertical motion and of vertical shear, large relative motions and induced pressures are enhanced by large storm diameter. Thus propagation arising from shear is most favored when a rainstorm is of large size. This suggests a selective growth of large storms at the expense of small ones, which can be more readily sheared off without propagation of new cells on VR? EFFECTS OF VERTICAL WIND ON STORMS their boundaries. This is consistent with the fact that a few large rainstorms tend to predominate (e.g., in squall lines) when the vertical shear is strong. On the lower end of the scale, small trade Cumuli,as shown by Malkus [1949], acquire meas- urable but not great velocities relative to ambi- ent winds. Induced pressures at their boundaries are small and probably have no appreciable effect on cloud growth. For this reason, clouds of the scale treated by Malkus do not propagate in the manner described above. Rather, they appear to grow on the upshear side because [Scorer and Ludlam, 1953] successive towers rising from the same base appear upwind from older towers which have been carried off by the wind. Ackerman [1956] has shown observationally that shear in- hibits production of rain in tropical Cumuli, but that rain may occur with proportionately larger shear when the buoyancy is increased. VERTICAL SHEAR AND Hat The above discussion leads to the following con- clusions possibly applicable to hail occurrence: (a) With strong vertical shear and pronounced veering of wind with height, growth of new con- vection is most favored on the right flank of a rainstorm. Since young cells have most intense vertical motions [Byers and Braham, 1948], large hail should tend to occur predominantly on that flank. The hail track should have restricted width compared with the track of the rainstorm as a whole. (b) The vertical pressure gradient induced by cloud-environment interactions favors, in the newly growing cells, upward accelerations stronger than provided by buoyancy forces asso- ciated with temperature anomaly alone. (c) An additional factor favoring localized strong vertical motions with large hail growth, is that new updrafts growing on the downshear flank are sheltered by the main body of the rain- storm itself (cf. Fig. 1), from the decreased buoy- ancy which would result from entrainment of dry air in upper levels. (d) The above effects should be most evident in vigorous rainstorms of large horizontal extent, and probably not noticeable in small storms. EXAMPLES Heavy hail damage occurs in a variety of cir- cumstances, often in warm sectors or ahead of warm fronts, but more commonly behind cold 345, fronts, in the geographical regions of most fre- quent occurrence [Harrison and Beckwith, 1951; Douglas and Hitschfeld, 1958]. Since we have been unable to find any detailed descriptions of large storms behind cold fronts, attention will be confined to two warm-sector situations where the shear was of the type shown in Figure 1. There is little evidence of asymmetry of the kind described above, in the Alberta hailstorms described in great detail by Douglas and Hitsch- feld {1958}. On the whole, those cases involved storms of small diameter, mostly in weak shear (or with vector shear nearly along the mean wind direction). In one example wherein there was sig- nificant veering of wind with height, the principal hail fall occurred with several cells forming suc- cessively toward right of the individual cell paths. Figure 3 shows a set of observations collected by Harrison {1952], giving the precipitation dis- tribution in the neighborhood of an incipient tornado (stippled track) at Fort Wayne, Indiana, near 19h30m CST on April 28, 1951. As shown by Figure 4, the heavy hail was concentrated on the south edge of a large rainstorm. This storm was located a short distance ahead of the cold @ R+, no hail 4 Light hail 4 Mod. hail a Heavy hail A Pickle shaped, 5"long Baseball size fe) 1 2 3 4 5 al 1 EEE MILES Fig. 3—Hail and rain distribution, Fort Wayne, Indiana, near 19h30m CST April 28, 1951 [Harri- son, 1952] Oo 20 40 60 80 100 NAUT MI Fic. 4—Rainfall near Fort Wayne, Indiana, in hour ending 20h00m CST, April 28, 1951; outer isohyet, 0.01 inch, then 0.20, 0.50 (hatched inside), and 1.00 inch Fig. 5—Winds in Fort Wayne vicinity, April 28, 1951, at 10,000-ft level (light symbols, full barb 10 kt) and vector shear 4000-18,000 ft (heavy ar- rows); solid lines, 700-mb contours; dashed, 850- 500 mb thickness (hundreds of feet) front of a wave cyclone, with SSW-SW winds in the lowest few thousand feet, and winds from W in the upper troposphere. Although no upper- wind observation is available for Fort Wayne, the vertical shear vectors at surrounding stations (Fig. 5) clearly suggest that the hail occurred on the downshear flank of the rainstorm. Successive rainfall maps showed movement of the rain area as a whole toward ESE, somewhat to right of the upper winds. The second example is shown in Figure 6 from Hamilton [1958], who gives a detailed description of the use of radar in tracking the storm and in identifying the hail. First echo appeared at A at 14h40m CST; hail was first apparent at B. Large hail (up to 2-inch diameter, some larger) and high winds occurred intermittently along a narrow track 130 mi long, ending near Bremond prob- CHESTER W. NEWTON ably around 18h380m CST. A tornado occurred at Midlothian (C). The track of large hail was con- fined to the right side of the storm, which pro- duced small hail along with the extensive heavy rain. It is not possible to reconstruct the exact con- ditions in the neighborhood of the storm, but as far as can be determined, the Fort Worth winds of 12h00m CST (inset, Fig. 6) are nearly representa- tive. By 18h00m CST, winds were W to WNW in lower levels. Hamilton quotes a radar report stating that echo movements (individual cells?) were from west, an agreement with the mean winds in the cloud layer in Figure 6, inset. The Fort Worth hodograph, as well as the 850- and 300-mb wind charts (Fig. 7) shows strong veering with elevation. According to the earlier conclusions, pronounced building of new storms should be expected on the SSE side of the rain- storm at a given time, with marked deviation of the storm track to right of the mean winds. The movement of the rainstorm is thus qualitatively in agreement with expectations, although the de- viation to right is stronger than might be ex- pected. Without a detailed analysis on the scale of the storm itself, it is not possible to give a reason for this excessive deviation. In an earlier study [New- ton and Katz, 1958] it was found that rainstorms moved on the average 7 knots slower than, and 25° to right of, the 850-500 mb mean winds in the cases concerned. Individual storms, however, ap- peared to deviate up to 20-30 knots vector veloc- ity from this mean behavior. Such aberrations are to be expected in a phe- nomenon so complicated as a large thunderstorm, where many different processes are at work. The above discussion is obviously oversimplified; for example, a low-level outflow, assumed to radiate uniformly outward from storm center, has been added to a mean in-cloud velocity based on the ambient winds, in arriving at the relative velocity at a given point on the storm boundary [Newton and Newton, 1959]. Very likely other hydrodynamic effects are present which modify the simple conclusions here. Byers [1942] was the first to give a systematic description of the movement of thunderstorm paths to right of the winds. His observations sug- gested a cyclonic rotation within individual storms. Byers explained the storm movements on the basis of the rotor principle (a counterclock- wise-rotating cylinder propels itself to right of the current in which it is imbedded). On the basis of about 30 synoptic situations EFFECTS OF VERTICAL WIND ON STORMS 345 Ae First echo Be FORT WORTH (Radar) MIDLOTHIAN ce waco @ (Radar) STORM MOVEMENT KN Heavy rain, small hail \\ Damaging winds, large hail e@ BREMOND Fig. 6—Path of heavy hail- and rainstorm near Fort Worth, Texas, April 21, 1958, from Hamilton [1958]; (inset) vector storm velocity compared with winds aloft analyzed, the hypothesis presented above appears to account for the gross behavior of rainstorms. That it does not satisfactorily account for all de- tails is shown by the fact that in the second case above, as well as in several published radar ob- servations of tornadoes, the most intense phe- nomena apparently occurred somewhat upwind, rather than on the direct right flanks of the storms concerned. Understanding of such phenomena must come eventually from increasingly detailed observations, interpreted not only in terms of or- dinary thermodynamic processes, but also in the light of the interactions between storms and their environments. Further remarks on other studies—At the time of writing the above, I was not aware of highly pertinent remarks in some other studies. Dessens [1959] (who offers a different explanation) states that “the existence of a jet stream or at least of a very strong wind aloft is the sole factor that we have been able to isolate as very probably re- sponsible for the formation of destructive hail’; the relation to high winds aloft was also brought out by Wichmann [1951]. These studies emphasize that instability by itself does not completely ac- count for large hail formation. Small or medium Fic. 7—Winds in Fort Worth vicinity at 30,000 and 5000 ft, 12h00m CST April 21, 1958 346 hail is common, but large hail is apparently fa- vored by asymmetric storm structure, with con- centration of the most violent convection in a restricted part of the storm as a whole. Weickmann [1953, pp. 108-109] has described a process which fits in very well with the notions above. He emphasizes that the persistence of an updraft column is augmented by the migration velocity of the storm. Weickmann likens a con- vective storm to a snowplow, sweeping up the un- stable layer ahead of it in lower levels and throw- ing the air out in upper levels. The amount of air swept up, and ascending in the updraft, is aug- mented when the storm is impelled to move along through the air mass. REFERENCES AcKERMAN, B., Buoyancy and precipitation in tropical Cumuli, J. Met., 13, 302-310, 1956. Byers, H. R., Nonfrontal thunderstorms, Univ. Chicago Dept. Meteor., Misc. Reps. 3, 26 pp., 1942. Byers, H. R., ano R. R. Branam, Thunderstorm structure and circulation. J. Met., 3, 71-86, 1948. Desal, B. N., anp S. Mau, Thundersqualls of Bengal, Gerlands Beit. z. Geophys., 53, 285-304, 1938. Dessens, H., Severe hailstorms are associated with very intensive wind between 6000 and 12,000 meters, this publication, 333-336, 1960. Douauas, R. H., anp W. Hirscure tp, Patterns of hailstorms in Alberta., Q. J. R. Met. Soc., 85, 105-119, 1959. Fuuxs, J. R., The instability line, Compendium of Meteorology, Amer. Met. Soc., pp. 647-652, 1951. Go.pstEIN, 8. (ed.), Modern developments in fluid mechanics, Clarendon Press, Oxford, vol. 2, pp. 421-424, 1988. Hamiuron, J. W., Some features in the use of radar in forecasts and warnings of heavy hail, damag- ing winds and/or tornadoes, Proc. 7th Wea. Radar Conf., Amer. Met. Soc., H 18-25, 1958. DISCUSSION Harrison, H. T., Notes on certain tornado and squall line features, United Air Lines Met. Circ. 36, 24 pp., 1952. Harrison, H. T., ann W. B. Beckwirn, Studies on the distribution and forecasting of hail in the western United States. Bul. Amer. Met. Soc., 32, 119-131, 1951. Humpureys, W. J., Physics of the air, MeGraw- Hill Book Co., 1940. Liapa, M. G. H., Study of the synoptic application of weather radar data, Final report, Contr. AF 19(604)-573, A. and M. College of Texas, 1956. Lupa, F. H., The hail problem, Nubila, 1, 12-96, 1958. Maukus, J. S., Effects of wind shear on some aspects of convection, Trans. Amer. Geophys. Union, 30, 19-25, 1949. Maukus, J. 8., aNpD C. Ronne, On the structure of some Cumulonimbus clouds which penetrated the high tropical troposphere. Tellus, 6, 351-366, 1954. Matxus, J. S., AND R. 8S. Scorer, The erosion of Cumulus towers, J. Mei., 12, 48-57, 1955. Newton, C. W., Structure and mechanism of the prefrontal squall line, J. Met., 7, 210-222, 1950. Newton, C. W., AND 8. Katz, Movement of large convective rainstorms in relation to winds aloft, Bul. Amer. Met. Soc., 39, 129-136, 1958. Newton, C. W., anv H. R. Newton, Dynamical interactions between large convective clouds and environment with vertical shear, J. Met., 16, 483-496, 1959. Scorer, R.8., anp F. H. Luptam, Bubble theory of penetrative convection. Q. J. R. Met. Soc., 79, 94-103, 1953. U. 8S. Wearner Bureau, Thunderstorm Project, The Thunderstorm, Govt. Print. Off., Washing- ton, pp. 108-114, 1949. WEICKMANN, H., Observational data on the forma- tion of precipitation in Cumulonimbus clouds, Thunderstorm Electricity (H. R. Byers, ed.), Univ. Chicago press, pp. 66-138 (see p. 108-109), 1953. Wicumann, H., Uber das Vorkommen und Verhal- ten des Hagels in Gewitterwolken, Ann. der Met. 4, 218-225, 1951. Discussion Dr. Roscoe R. Braham, Jr.—I have had the ad- vantage of having heard this lecture before, and I think you have left out in the interest of time, one point that needs to be brought out in the discus- sion of the model; namely, the consequence of the dynamic dam created by the vertical transport of momentum and of the hydrostatic pressures being built up on one side. This would lead to the de- velopment of new clouds, as Dr. Newton suggests, off to the right; and in fact I have seen some of his analyses of hourly rainfalls tracing out this kind of storm system. These hourly rain patterns move off to the right from the path of the storm as analyzed from radar records. Mr. W. Boynton Beckwith—I would like to cast a vote for Dr. Newton’s theories on the basis of radar. Although I would not like to generalize on all thunderstorm echoes, I would say three- fourths of the thunderstorms’ echoes observed tend to bear out your ideas. Incidentally, we prob- ably have in our ten years of record, ample rain- DISCUSSION 347 fall and hail records which would give you added material to work on this theory. Dr. Helmut Weickmann—In connection with your paper I would like to recall Finley’s famous analysis of 600 tornadoes. He found that they usually developed on the right side of the path of a big thunderstorm complex, and this would tend to agree with your model, since you also have the main cloud formation on the right side with re- spect to the path. Mr. R. J. Donaldson, Jr.—I would like toadda little observational radar data to the theory. There is some evidence (see my paper in this vol- ume) which indicates that the larger the hail size in thunderstorms, the more the hail is displaced to the right of the high-intensity echo core. Analysis of Hailstorms in the Denver Network, 1949-1958 W. Boynton BEckKwITtH Meteorology Department, United Air Lines, Inc., Denver, Colorado Abstract—Data collected during 225 hail days over the past ten years are investi- gated. The synoptic and thermodynamic conditions associated with hail development are analyzed and comparisons are made between storms of this area and those of the Middle West and Alberta. Upper wind distribution and the position of the tropopause are related to the development and growth of hailstorm-producing cells. Introduction—Since 1949 a cooperative hail reporting network in and around the city of Denver has made possible the collection of suf- ficient detailed hailstorm data to make the be- ginnings of a climatology of this troublesome hydrometeor. Organized first to learn more about the true areal frequencies of hailstorms in this vicinity, and to establish new forecasting tech- niques on the basis of the various parameters that can be measured with a micro network, the project has been a continuing one since then. This paper is an extension of earlier studies [Harrison and Beckwith, 1950; Beckwith, 1956; Douglas and Beckwith, 1958] with respect to hailstorm characteristics and some thermody- namie relationships. Comparisons between the Colorado hailstorms and those of the Midwest and Canada are made on the basis of studies by Stout and others [1959], Douglas and Hitschfeld [1958], Fawbush and Miller [1953] and others. Since 1953 an AVQ-10 radar has been used to monitor with a PPI display, some of the heavier hailstorm developments in the Denver area. Some results of this phase of the investigation have been published earlier [Harrison and Post, 1954; Beckwith, 1956]. The relation of the net- work to the Front Range of the Rockies is shown in Figure 1. The area covered by the cooperative network is shown in Figure 2. Site of the United Air Lines radar corresponds very closely to the position labeled USWB. The actual number of re- porting stations shown in Figure 2 has varied from 12 in 1949 to 30 in 1951 to an average of 50 each year since that time. Time, space, and frequency variations—It has frequently been pointed out that a more correct picture of the incidence of hail for a given area is afforded by network reporting than by point reporting. Hail frequency for the Denver area is shown in Table 1 and is expressed as a ratio to the official point reporting of the Weather Bureau. The Denver network encompasses about 150 sq mi. Even in such a small area as many as five hailstorms have been reported in one day. The 225 hail days shown in the ten-year total represent about 300 individual hailstorms. Many earlier studies have expressed the fre- quency of hail occurrences in ratio to thunder- storm days. This is a useful relation for point summaries, but when area figures are summa- rized some bias is introduced if one reporting station is the basis for thunderstorm day counts. The hail-thunderstorm ratio of Table 2 has been subjected to this bias. Also, the year-to-year ratio has varied widely during the past ten years, a function of the change in hail patterns from one year to the next. An opinion expressed very often by forecasters concerned with the problems of the ‘hail belt’ as well as by trans- port pilots frequenting this region is that nearly every thunderstorm developing off the Rocky Mountains contains hail in some stage of its development. A relationship that has proven more valid than the hail-thunderstorm ratio during the past ten years is shown in Figure 3. For the period April through October, precipitation is almost entirely from shower activity, the exceptions be- ing frontal and upslope developments which are of some importance in April and October. Since this precipitation is shower-generated, a good indicator for hail activity would be expected. The precipitation for 1957 which falls away sharply from an otherwise good scattering, re- fleets the two very wet months of April and May of this year which were characterized by a late heavy snow and a series of cloudbursts. The sharp rise in hail activity in the Denver area in late spring is well illustrated in Figure 4. On the average, activity falls off more gradually 348 B Z Z A A \\ IZ ZI \S KS\ 349 CONTOURS REFERENCED TO Vv z 5 30} fo w ir Le & 20t WwW 5) a WwW * 107 GRAIN CURRANT PEA GRAPE WALNUT GOLF We APPROX A cs aM yy BALL ALL DIAMETER SYA; Vas v2 ¥o4 la 13/4" 21/2 To 2" to 3" SIZE Fic. 6—Size distribution by frequency for larg- est hailstones reported at each observing point, 829 reports over ten years (2) Wind direction on hail days at 500 mb favors WSW. (3) In only four per cent of the hail cases were cold lows found in or near Colorado. Crossings of jet streams within 100 mi of the network occurred on about 15% of the hail days. (5) Surface temperature just prior to onset of hail averaged 71°F. Values ranged for the ten years from 40° to 98°F, (6) The average surface dew point before pre- W. BOYNTON BECKWITH HMB >cor Bate DENVER 1949-1958 0) 10 20 30 40 60 70 80 oe ee is ADR asia cece ee 37 MAY a RRS 249 sunel IA E265 <) UY, | |S SEES 143 ° AUG. J Seiten ZA ———} | 02 a eee LATS 48 3 1 aa, a ee S| Zz##### emAayee RTECS 25 ALBERTA 1957-1958 0 10 20 30 40 60 70 60 90 100% &£ JUNE [TE YA s82 JULY [Prater rete peer nerernennenens UY al 1730 © AUG| [ast LLLLeeeeyyy-Z-— WJZ 829 9 SEPT. MME (5 sxor = Fa] PEA z EZ crare Es] WALNUT E6jcorr Bate Fic. 7—Size distribution by months of largest hailstones reported at Denver during period 1949-1958 and at Alberta during 1957-1958 (by Douglas) ee NUMBER OF CASES sm SH She ee e) I6- 20- 24- 28- 32- 36- 40- 44- 48- 52- 56- 60- 1923) ee tS l, NS5S39' 4310 47 all55) 59) 163) oF Fre. 8—Surface dew-point frequency distribu- tion at Denver during ten-year period; dew point is the value measured at official U. 8S. Weather Bureau station prior to onset of precipitation of any type cipitation began was 46°F. (Figure 8 gives the dew-point distribution for the ten-year period.) One of the most obvious differences in char- acteristics between hailstorms of the High Plains and those of the Middle West is in comparing the surface dew-point distributions in the two regions. Denver dew points above 55°F are rarely measured prior to hailstorms. In contrast, Fawbush and Miller [1953] pomt up the fact that surface dew points for Middle West storms are nearly always in the 60’s and 70’s. A preliminary survey of the Denver RAOBs for 18 hail days selected at random during 1956, 1957, and 1958, shows a temperature and mois- ture relationship in the vertical as illustrated in the mean sounding of Figure 9 and in the data below: Freezing level: 590 mb Wet bulb freezing level: 637 mb Temperature at LCL: 5°C (lifting condensation level) : Tropopause height: 134 mb* * Approximately 45,000 ft In comparing these figures with the mean hail- storm soundings computed by Fawbush and Miller [1953], a similarity is found from 700 mb to 400 mb for stone diameters between one and two inches. The greatest discrepancy lies in the 5000-ft layer above the surface. The High Plains moisture distribution is marked by a low hu- midity at the surface, increasing gradually to about 500 mb and decreasing gradually above this level. The inversion above the moist layer noted by them as a pattern for stones of one inch diameter or larger is also missing in the mean Denver sounding. However, the 0°C wet-bulb temperature is reached at about 7500 ft above the terrain, again in agreement with a consistent parameter for the larger stones. Extending the HAILSTORMS IN THE DENVER NETWORK MB tt 1 1 a = 570) =60) =S0) =40°-30° =20 -=10 fe) 10 20 ~=30' °c Fic. 9—Mean sounding for 18 hail days in 1956, 1957, and 1958; solid line is temperature distribu- tion, broken line is dew point curve, and dash-dot line is the parcel adiabat; mean tropopause height is at 134 mb (approximately 45,000 ft) investigation to the tropopause, it is found that the mean lapse rate of the 18 soundings is steep enough to produce a positive energy area from the LCL to about 35,000 ft. Soundings published by Douglas and Beckwith [1958] for some of the larger hail situations oc- curring in Alberta in 1957 are mainly in agree- ment with this Denver mean except for the tropopause altitude which is lower in Canada in accordance with the normal latitudinal differ- ence. Although no firm conclusions may be drawn on this limited sampling, it appears that on days with hail, the height of the tropopause at Denver is, on the average, lower than on non-hail days. Other work—In the attempt to develop new methods of analysis of hailstorms and in re- viewing the work of others in this field, one can- not overlook the strong suggestion that the 393 make-up of thunderstorms in general and hail- storms in particular, involves an important in- gredient not recognized today. Whether or not this involves space charges, for example, or un- knowns in cloud nuclei is something for the cloud physicists to determine. As of today, the hailstorm remains as a prob- lem for the farmer and for the property owner. In aviation, hail is less of a hazard now, thanks to airborne radar. But the forecaster must con- tinue to be alert for these developments as air- craft now flying near the tropopause appear to be exposed to an even higher proportion of large hailstones than experience up to now would dic- tate. Acknowledgments—The author again wishes to express his gratitude to the corps of unofficial observers who have cooperated since 1949 in the reporting of hailstorms in the Denver area, and without whose help this project would not have been possible. REFERENCES BecxwitH, W. B., Hail observations in the Denver area, United Air Lines Met. Circ. 40, 41 pp., April 1, 1956. Dovcias, R. H., ano W. Hirscureup, Studies of Alberta hailstorms, 1957, McGill University, Stormy Weather Res. Group, Sci. Rep. MW-27, 79 pp., May 1958. Dovatas, R. H., anp W. B. BeckwirH, Hailstorm features determined from studies in Alberta and Colorado, paper presented at American Mete- orological Society Conference on Practical Prob- lems of Meteorology, Sept. 24, 1958, unpublished. Fawsusu, E. J., anp R. C. Minter, A method for forecasting hailstone size at the Earth’s surface, Bul. Amer. Met. Soc., 34, 235-244, 1953. Harrison, H. T., ano W. B. BeckwitH, A re-ex- amination of hail patterns over western United States, United Air Lines Met. Cire. 35, 27 pp., March 15, 1950. Harrison, H. T., anp E. A. Post, Evaluation of C- Band (5.5 em) airborne weather radar, United Air Lines Spec. Rep., 108 pp., March 1, 1954. Strout, G. E., R. H. Brackmmr, 8. A. CHANGNON, AND F. A. Hurr, The hail hazard in Illinois, Prelim. Rep. Ill. State Water Survey, 33 pp., January 31, 1959. Discussion (Note: Discussion of this paper is combined with those of the two following papers at the end of the second following paper.) Some Behavior Patterns of New England Hailstorms Raueu J. Donaupson, Jr., AND ALBERT C. CHMELA Geophysics Research Directorate, Air Force Cambridge Research Center, Bedford, Massachusetts AND CHARLES REEVE SHACKFORD Allied Research Associates, Inc., Boston, Massachusetts Abstract—Radar measurements of New England thunderstorms have been com- bined with reports furnished by cooperative observers during three years. Echo tops in storms releasing hail of less than %4-inch diameter were higher, colder, and penetrated the tropopause more often than tops of rain thunderstorms. The differences are even more striking for storms with large hail (%4-inch or larger) compared with the other two categories. Extreme tropopause penetrations of 10,000 to 15,000 ft occurred on five days, of which all but one were tornado days. A study was made of the histories of 20 hailstorms. Ten of them dropped hail for long periods of time (hail repeaters), the others for less than 20 min and at only one or two locations. All cases of severe damaging winds and tornadoes occurred with the hail repeaters. Within a wide scatter, both echo tops and maximum intensities in the hail repeaters attained higher peaks and remained high for longer periods of time than in the single hail producers. Hail locations in all storms exhibited a slight tendency to appear in the right, rear quadrant of the storm, with the larger hail sizes located to the right of the smaller hail, facmg downstream. Echo areas of various intensities as a function of height were measured in two hail- storms, one just getting under way and the other a well-developed producer of several tornadoes. Computations are made of hail-mass concentration versus height at various times in the two storms, assuming the radar echo is scattered from 1-cm ice spheres. Mean 1-cm hail concentrations in the tornado storm, averaged over the total echo area at the height of the most intense echo, varied from 0.3 to 1.3 g/m*, but the maximum concentrations in the echo core ranged from 9 to 170 g/m*, subject to a possible over- estimate by a factor of 5 due to an unresolved radar calibration error. During two ob- servations of echo tops penetrating the tropopause, the echo volume above the tropo- pause increased rapidly with time, suggesting a progressive modification of the lower stratosphere above the storm. Hailstone information furnished by cooperative observers is summarized. Median values are: maximum diameter, 7 mm; max/min size ratio in a hailfall, 2; number concentration, 0.1/m*; hailfall duration, 3-4 minutes; hailfall started four minutes after heavy rain began. About 75% of hail shapes were divided between spheres and oblates. Introduction—Thunderstorms have been stud- ied in southern New England during 1956 through 1958 by a combination of CPS-9 radar observa- tions taken from Blue Hill, Milton, Massachu- setts, and storm reports received from a network of cooperating observers. This paper is a descrip- tion of some of the characteristics of hailstorms observed during the three years of the investiga- tion. The CPS-9 radar has a 1° conical beam which can be set at any desired elevation angle. A series of antenna rotations about a vertical axis (PPI 354 scan) with successive increases in elevation angle causes the beam to sweep out a volume defined by a cone of revolution with vertex centered at the radar position. All parts of thunderstorms (except those within 25 mi) can be observed con- veniently by this means. The height of an echo volume is given by its range and elevation angle. The heights of echoes within 25 mi were usually measured by means of an RHI sean (a rapid ver- tical slice from near-zenith to horizon, at fixed azimuth). Echo intensity can be determined by means of a calibrated receiver gain control. Er- BEHAVIOR PATTERNS OF NEW ENGLAND HAILSTORMS 355 rors in echo height and intensity measurement have been discussed by Donaldson [1959]. Echo top heights and temperatures—All thun- derstorm echo top heights measured during 1956 and 1957, plus a few from 1958, were classified according to the largest hail size reported within ten minutes before or after the radar measure- ments (+15 minutes for the 1956 data) and within ten miles of the location of the echo top. The heights were grouped into three precipita- tion categories: no hail (rain only), hail diameter less than 34 inch, and hail diameter equal to or greater than %4 inch. If an echo top measurement was associated with several reports of rain with- out hail and only one report of one-inch hail, it was put into the larger hail category. Echo top temperatures were read off the Al- bany, New York, radiosonde nearest in time to the echo height measurement. The tropopause height was also determined, where possible, se- lecting the height above the 300-mb level where the temperature lapse rate first became less than 2°C/1000 ft. The distance by which the echo tops exceeded or fell short of the tropopause was re- corded. For echo tops penetrating the tropopause, an estimate was made of the negative energy re- quired for penetration by measuring the area > O9fF a oer 4 0.7+ | > re re L vy 0.6 =| Ss w « re w O5F 4 = = < a 5 = 0.47 | 5S oe) 0.3F 4 2p x d NO HAIL, 450 OBSERVATIONS| — ——— HAIL SMALLER THAN 3/47 92 OBSERVATIONS HAIL 3/4" AND LARGER OIF : 39 OBSERVATIONS Ove Lo sc H ¢ (oe 1 1 we Hie 10 20 30 40 50 60 THOUSANDS OF FEET Fic. 1—Cumulative frequency distribution of thunderstorm echo top heights - + NOHAIL, 450 OBSERVATIONS ——— HAIL SMALLER THAN 3/4" , 92 OBSERVATIONS HAIL 3/4” AND LARGER, 39 OBSERVATIONS CUMULATIVE FREQUENCY TEMPERATURE IN DEGREES C Fic. 2—Cumulative frequency distribution of thunderstorm echo top temperatures bounded by the sounding, the dry adiabat rising from the tropopause (very nearly equivalent to the moist adiabat at stratospheric pressures), and the pressure surface at echo top. The results are shown in Figures 1 to 4, which show the cumulative frequency distributions of echo tops associated with each of the three precipitation categories with respect to height, temperature, penetration above (or below) the tropopause, and negative energy required for stratospheric penetration. Table 1 summarizes the upper quartile, median, and lower quartile values (in descending order) of these four param- eters for the three precipitation categories. The differences between the ‘all rain’ category and the larger hail category are quite marked, even considering the several sources of error. These errors include the uncertainty as to hail oc- currence and maximum hail size because of holes in the observing network almost certainly larger than significant variations in the character of thunderstorm precipitation. Thus, the proximity of the ‘all rain’ and smaller hail size curves on all four diagrams may be partly attributable to un- observed (or unreported) small hail that falls 356 near an echo top measurement thought to be in the ‘no hail’ category. Another error is inherent in the timing of the ground events relative to the echo-top determina- tion. Douglas [1959] associated echo tops with the appearance of hail or rain 20 min later at the ground, allowing time for the precipitation to 0.9 0.8 0.7 3 20.6 w > Ss w « u | w ce < iy) mol > = > ° a Sei ++. NO HAIL,450 OBSERVATIONS ———— HAIL SMALLER THAN 3/4" 0.1 r 92 OBSERVATIONS HAIL 3/4" AND LARGER * 39 OBSERVATIONS = / ° [ee 6 ee os ee ee ————— —}} -20 -10 ° 10 20 HEIGHT (THOUSANDS OF FEET ABOVE TROPOPAUSE) Fic. 3—Cumulative frequency distribution of thunderstorm echo top penetrations above and be- low the tropopause CUMULATIVE FREQUENCY 12 DONALDSON, CHMELA, AND SHACKFORD fall. The timing used in the present study is a rough attempt to relate hail production to con- vective forces that result in the increase or main- tenance of echo-top height. The optimum timing relationship probably lies somewhere between those adopted by the two investigations. Other errors are randomly distributed. They include echo-top height measurement, with a mean error estimated to be about +2000 ft; un- certainties in a few of the tropopause height de- terminations; and deviations in time and space (up to six hours and 150 mi) of the Albany radio- sonde from conditions at an echo-top measure- ment. Hopefully, the sum of these random errors should tend to zero in a distribution of many cases. The few special cases of extreme penetration are interesting. Echo tops pushed 10,000 to 15,000 ft above the tropopause on five days during the three years studied (two complete years and part of a third). Tornadoes oceurred on four of these five days. The maximum penetrations of the par- ticular tornado storms were 8, 10, 13, and 15 k ft. On the fifth day widespread hail occurred with extremely severe electrical storms (45 houses were struck by lightning in one town alone) ; the maximum penetration on this day, 12 k ft, was related with the fall of one-inch hailstones. The negative energies overcome by the tornado storms ranged from 1.6 * 10% to 3.0 x 10° ergs/gm, or 2 to 5 times the median value for hailstorms with %4-inch or larger hail. The severe lightning storm with one-inch hail had to overcome the greatest negative energy found during the entire study, 34 x 10° ergs/gm. These extreme cases NO HAIL, 450 OBSERVATIONS HAIL SMALLER THAN 3/47, 92 OBSERVATIONS HAIL 3/4” AND LARGER, 39 OBSERVATIONS 20 24 ERGS/ GRAM OF AIR xX 10° Fic. 4—Cumulative frequency distribution of negative energy required for thunderstorm echo top penetration above the tropopause BEHAVIOR PATTERNS OF NEW ENGLAND HAILSTORMS 307 TasiEe 1—Thunderstorm echo top characteristics Maximum hail size Parameter None (all rain) Height (K ft) 42 37 30 Temperature (°C) —60 —51 —38 Height above (+) or below +2 (—) tropopause (Kx ft) —4 —11 Negative energy required for 9X, 10° tropopause penetration 0 (ergs/gm of air) 0 Diameter < 44” Diameter > 34” 48 50 Upper quartile 40 46 Median 35 39 Lower quartile —60 —63 Upper quartile —54 —59 Median —48 —52 Lower quartile +5 +9 Upper quartile 0 Fo) Median —6 +1 Lower quartile 4.6 X 10° 1.4 X 107 Upper quartile 0 6.3 X 105 | Median 0 xX 105 | Lower quartile approach the conditions listed by Vonnegut and Moore [1958] for their category of ‘giant’ thun- derstorms. Their simplified assumption that the updraft speed at the tropopause equals 20 m/sec for each kilometer of penetration shows good agreement with a sample calculation. The re- quired updrafts are incredibly high for these few extremely penetrative storms. However, it is suggested later (under Hailstorm echo areas) that the first penetration of the tropopause ini- tiates a modification of the lower stratosphere, and hence the unreasonably high requirement for updraft speeds is considerably reduced. Composite hailstorm histories—Twenty hail- storms depositing hail one-half inch or larger in diameter were selected from case studies con- ducted during the three years for examination of their common features, if any. A storm is defined as a unique radar echo, in most cases entirely sep- arate from other echoes at maximum radar re- ceiver gain and O° antenna elevation angle. Oc- casionally, the weaker, lower parts of a storm will merge with another storm, but the boundary be- comes clear at slightly reduced gain settings and especially at moderate heights (for example, above the melting level). A storm may have one to five or six well-defined echo cores which be- come visible from the surrounding background as the receiver gain is lowered. The cores, which are very likely related to convective cells, gen- erally have a much shorter lifetime than the total storm duration of two to six hours. Ten of the storms produced hail during a single period of less than 20 min, reported in every case but two from a single location. The others, named ‘hail repeaters,’ dropped hail for periods of up to 35 min continuously and up to 140 min inter- mittently. This classification of storm types may be analogous to that found by Douglas and Hitschfeld [1958] in Alberta hailstorms. They found that the hail usually fell in short bursts but on several occasions there were continuous hail falls of 1/2 hr in a swath 30 mi long. If the New England hail frequencies were increased by closer observer spacing (comparable to the tight Al- berta network) and by accounting for over-all regional differences in hail probability, some of our hail repeater storms might fill in to form continuous hail swaths. One further fact emerged: the single-hail pro- ducers ineluded no instance of severe wind dam- age (uprooting or fracturing of trees, structural damage to buildings, etc.). However, of the ten hail repeater storms, severe wind damage was re- ported in seven of them, including three storms with several tornadoes each and another one with two funnels aloft. Also, the maximum hail size was only 4 inch in four of the ten single-hail pro- ducers; hail of %4 inch diameter or larger was re- ported in all of the hail repeater storms. Inciden- tally, the maximum hail size in the repeaters appeared 10 to 100 min after the time of first hail, with a median separation of 40 min. In the analysis that follows, all times are given with respect to the first appearance of hail. This may be a dangerous thing to do because of the probable incompleteness of hail reports. Of course, the storm classification scheme is subject to the same criticism. However, for all its uncer- tainty, it seemed better to relate events to time PERCENT OF STORMS IN WHICH EVENT OCCURRED DONALDSON, CHMELA, AND SHACKFORD i NN Ea L100] ! 60 I wt TORNADO OR FUNNEL ALOFT. Fic. 5—Frequency of storm events in hail repeater storms during 20-min periods following first report of hail of first hail than to time of first echo, since many first echoes were not observed at all in our sched- ule of radar observations and only nine of them could be stated within an accuracy of five minutes and 13 within 11 min. Figure 5 depicts the hail and severe damaging windstorm events, including tornadoes, during the time following first hail in the hail repeaters. Note the tendency toward a 100- to 120-min periodicity in tornado activity and occurrence of large hail. This is an integrated picture; the seven individual storms in which such changes are ob- served show a periodicity of 30 to 70 min with, at most, three periods apparent. Figure 6 shows the time variation of maximum echo height in all 20 storms. The first echoes are arbitrarily started at a height of 15,000 ft with a maximum rate of height increase of 2000 ft/min. There is a wide variation in time between first echo and first hail (14 to more than 162 min), in maximum height reached by an echo (27,000 to 56,000 ft), and in total height interval covered by the echo tops (always greater than 20,000 ft). Wide variety in echo-top behavior is the rule. Nevertheless, some general trends superimposed on these large variations are brought out by Fig- ure 7, which shows the median and maximum echo-top history of the two storm groups. The echo tops of hail repeaters differ from those of the single-hail producers in the following particulars: They are rising when the first hail falls, they maintain extreme heights for greater periods of time, they attain a higher over-all max- imum, and they have a longer lifetime. These characteristics are similar in certain respects to those discovered by Douglas and Hitschfeld in their sustained hail producers. The most intense radar echo found anywhere in the storm was observed at various times during the life cycle of 17 of the hailstorms, in the man- ner described by Donaldson [1958]. The height of the most intense part of these echoes ranged from near the surface up to 31,000 ft, with half of the observations centered between 13,000 and 24,000 ft. At least part of the reason for the surprisingly high altitude of the most intense radar echo in hailstorms is due to the high attenuation in heavy rain of the 3.2-em waves radiated by the CPS-9 radar. Attenuation by ice is much lower than by the same mass of rain. Other possible causes in- clude high particle concentrations accumulated near the maximum of a non-steady-state updraft BEHAVIOR PATTERNS OF NEW ENGLAND HAILSTORMS fore) 60 50 50 40 40 H max 30 30 k ft 20 20 STORM CLASS Lo HAIL REPEATER 10 —--—- HAIL <20 MINUTES fe) 1 il — f] 1 1 ie) -150 -120 -90 -60 =30 fe) 30 60 90 120 150 TIME AFTER FIRST HAIL — minutes Fiag. 6—The trends of echo top height in 20 hailstorms, related to time before or after first hail; the numbers identify the various storms; storms 1, 7, and 19 each produced several tornadoes 330 i STORM CLA8S H 420 ' HAIL REPEATER H —--- HAIL <20 MINUTES Ki \ 410 ' ‘ 1 [enna rae -150 -120 -90 -60 -30 ° 30 60 90 120 150 TIME AFTER FIRST HAIL —— minutes Fic. 7—The trends of median and maximum echo top height for the two groups of hailstorms, related to time before or after first hail and the attrition of falling hailstone size by melt- sity, at the same range, as the measured echo in- ing and break-up. The maximum echo intensities are expressed as the common logarithm of the maximum value of the equivalent radar reflectivity factor Z. The equivalent Z is defined as SN D®° (or volume con- centration of the sixth power of drop diameters, in mm°/m*) of small spherical water droplets which would return the same radar echo inten- tensity. The water droplets must be small enough to permit the use of the Rayleigh scattering ap- proximation, or about 2 mm or smaller in diam- eter for a radar wavelength of 3.2 em. Further discussion of the meteorological interpretation of equivalent Z is given by Donaldson [1958] Hail returns a considerably lower echo power than would be indicated by computing the Z of DONALDSON, CHMELA, AND SHACKFORD LOGEZimnax 3 STORM CLASS 5x10 HAIL REPEATER ===" HAIL <20 MINUTES | 5x1074 \ =i ue pe a aes oS ET Ses ees ate — I -150 -120 -90 -60 -30 0 30 60 90 120 150 TIME AFTER FIRST HAIL — minutes Fic. 8—The trends of maximum echo intensity in 17 hailstorms, related to time before or after first hail; see text for explanation of log Zmax an assortment of hailstones, for three reasons: (1) the dielectric backscattering factor is lower in ice of unit density than in water by a factor of 4 or 5; (2) hailstone densities may be as low as 0.5 and, of course, are always less than the density of water; and (3) for 3.2-em radar practically all observable hailstones are outside the Rayleigh scattering region and begin the transition through the complicated Mie region toward geometrical scattering which is approximately proportional to the square instead of the sixth power of par- ticle diameter. Figure 8 shows the time variation of log Zmax in the 17 storms in which this was measured. The right-hand ordinate gives the maximum ice con- tent, assuming the maximum echo is scattered from unit density ice spheres of 1-cm diameter. Note the rapid growth in Storm 10, in which Zax measurements were made near the time of first echo. The maximum and median Zmax trends for the two classes of storms are illustrated in Figure 9. Similar to the echo top situation, the hail re- peaters attain a higher maximum and at a later time. Radar echo maximum heights and maximum intensities appear to be conveniently observable indicators of the convective activity within a storm. Although the two parameters are loosely correlated, they reflect somewhat different as- pects of the convective situation, the heights in- dicating more about updraft speeds and persist- ence, and the intensities perhaps more about moisture supply and the efficiency of converting the available moisture to large hailstones. A con- vective index, the product of Hmax and log Zmax , was plotted for the median trends of the two storm groups (Fig. 10). Hmax is expressed in k ft and Zmax im mm‘/m*. The median convective index change with time was also plotted for the three tornado-producing storms, with each tor- nado storm maximum plotted separately. The diagram also shows the range of convective index calculated from the medians and quartiles of two populations of hailstorms and rain-thunder- storms (the Hmax population includes the Zmax population and many more cases besides). Figure 10 is intended to be provocative rather than definitive. Several general features are worth mentioning: (1) the more severe the storm class, the higher and later the peak of convective in- dex; (2) the close association in time (within the seale of time resolution in the original observa- tions) between the maximum convective index in a tornado storm and the time of the most de- structive tornado; and (3) the rapid rise but slow BEHAVIOR PATTERNS OF NEW ENGLAND HAILSTORMS Ol a a a a) ea To T T T ==) mox 7 L =e re Z y mox Oe NS eee mo My) max mox _-- | ue 45 a/m> median “median 5 medion .—_——" 45x10"! LOG Zmox mecton all 45x10? 3p STORM CLASS HAIL REPEATER ~--—) HAIL <20 MINUTES 2 1 4 1 =i 1 n 1 n 4 “150 -120 -390 -60 -30 ° 30 60 90 120 150 TIME AFTER FIRST HAIL — minutes Fic. 9—The trends of median and maximum log Zmax for the two groups of hailstorms, related to time before or after first hail CONVECTIVE INDEX: Hyngy (K ft) X LOG Zmox TORNADO STORM MAX TIME OF MOST DESTRUCTIVE TORNADO 400} STORM IDENTIFYING NUMBER INDEX HAILSTORM 300 “a 4300 HIGH Z aa QUARTILE r z F RAIN TY, PL / x / De y 7 REPEATERS MEDIAN eZ \ A } x fi / \ I aN 200 oy ; Re 200 “i a ; = Low / Peat POUAnTICE ff ‘MEDIAN OF STORMS WITH we a HAIL < 20 MINUTES. / ’ 10 1 L L 1 n 1 n 100 -30 60 =30 ° 30 60 90 120 150 TIME AFTER FIRST HAIL (MINUTES) Fie. 10—Median convective index trends in hailstorms with less than 20 minutes of hail, hail repeater storms, and tornado-producing hailstorms; the convective index maximum and time of most destructive tornado are shown separately for each tornado storm; all times are before or after first hail; at left, medians and quartiles of a large number of rain-thunderstorms and hailstorms are plotted, independent of timing decay of convective index for the median hail re- peater. The position of the leading edge of hail was de- termined relative to the low-altitude echo core in 25 cases where both the timing and location of the hail occurrence were considered accurate within limits of one minute and one mile. The po- sition of the low-altitude echo core was interpo- lated from the available measurements, generally taken two to five times during an hour. The rela- tive hail locations, plotted in Figure 11, seem to have quite a scatter, but closer examination shows that half of all hail and three-fourths of hail larger than ¥-inch falls within three miles of the echo core. There were many hail occurrences for which 362 LOW ALTITUDE ECHO CORE << x (Zp max) MILES DONALDSON, CHMELA, AND SHACKFORD HAIL DIAMETER : DIRECTION OF ECHO CORE Fic. 11—Position of leading edge of hail relative to low-altitude echo core Taste 2—Mean hail locations relative to low altitude echo core Normal to echo core path Along echo core path Maximum hail diameter inch D<% stream) y% 0.9 mi to right All hail 1.2 mi to left (facing down- 0.48 mi to right (84 cases) 1.7 mi behind 1.2 mi ahead 0.4 mi behind 0.16 mi ahead (25 cases) the timing was in doubt but the location exact; for these cases the hail position could be deter- mined normal to the path of the echo core but not along the path. There was similar scatter in posi- tion, but in over half of these cases the hail fell two miles or less to the right or left of the echo core path, or exactly on the path. Table 2 sum- marizes the mean hail locations for various hail sizes. It shows a progressive tendency for the larger hail to be located toward the right-hand side of the core path, in support of the model pro- posed by Newton [1959]. Since these locations are for the forward edge of the hailfall, which has a median duration of three to four minutes (see later under Characteristics of New England hail), the hail path tends to lag the echo core. Thus, the right rear quadrant of the storm (with respect to the echo core) shows a weak tendency to claim the greater part of hail. Hailstorm echo areas—The echo areas at var- ious receiver-gain settings and elevation angles were traced in two of the storms, one in which a first echo was detected (Storm 10) and the other, Storm 19, a producer of several tornadoes. Fig- ure 12 is an example for Storm 10, for three gain settings. The areas enclosed by various values of equiv- alent reflectivity factor Z, as a function of height, were computed for both storms at different times in their history. The areal heights were obtained simply from the height of the echo core at each antenna elevation angle. Similarly, the range of the echo core at each height was adopted as an average range for purposes of computing the BEHAVIOR PATTERNS OF NEW ENGLAND HAILSTORMS ~@' (1.0K FT 15.5 K FT 363 -5.9°C -——25: MI 220K FT -17.3°C 27.0KFT -29.0C 3I1.5KFT ~39.0 C @Mcainit Ccains MWecaing REFERENCE POINT AT INTERSECTION OF GRID LINES JULY 30,1957 Do -—3 MI 36.0 KFT -49.5°C Fie. 12—Echo areas observed in a young growing hailstorm; Gain 1 shows the weakest echo; Gain 9 the strongest; the arrows are not direction vectors; they are for orientation; note the scale change at the highest alti- tude; the reference point denotes the location of hail which fell as the 36 k ft areas were being photographed cy cn Ae! 152 R—-% 1538+ (FIRST ECHO") o—2 1545+ x 91 HEIGHT HEIGHT (Kft) (Km) 20 Ga 3.0 lo or ' 0 Oo -200 AREA (Km?) Fig. 13—Areas enclosed by decade values of Z, as a function of height, in the growing hailstorm ilustrated in Fig. 12. (July 30, 1957, D. storm) equivalent Z of all of the areas at the several gain settings. As many as eight gain settings were used to minimize interpolation errors. Some of the results are shown in Figures 13 and 14. The solid curves in Figure 13 relate to the areas of Figure 12; the observation started at 15h45m and ended at 16h02m. The dotted curve is the first echo, measured between 15h38m and 15h40m. The growth both in area and in inten- sity 1s almost explosive. Note the two regions of 50 Tn rr 1 T_T annys2 * -K 1538+ (SOON X~__ x AFTER FIRST TORNADO) =a He O—® 1730+ (aT cane ~ CONCLUSION OF FINAL TORNADO) aw By | 40F N x 122 Nx \ \ t | I I 30 mi HEIGHT { HEIGHT (K ft) i (Km) 20k Ne dhe lo yi k , oF 430 oO — ey wt (EN Se ' 10 100 1000 AREA (Km?) Fic. 14—Areas enclosed by decade values of Z, as a function of height, at two stages in the life cycle of a tornado-producing storm. (July 11, 1958) maximum intensity in both observations. The lower one rose at the rate of 550 ft/min, the upper one at 620 ft/min, assuming the corresponding regions to be related. The lower maximum rose through the 0°C level at approximately 15,000 ft. The upper maximum rose to a level where the temperature was —39°C. Two of the five area-height measurements of 364 DONALDSON, CHMELA, AND SHACKFORD the tornado storm are depicted in Figure 14. The areas covered by this well-developed storm are much larger than those found in the previous ease. During the development of the storm the maximum equivalent Z aloft increased, while the areas covering the lesser values of equivalent Z increased markedly near the surface but de- creased somewhat in the upper part of the storm. The areas were used to estimate the precipi- tated water of hailstone size as a function of height in the storm. For the purpose of this com- putation, all the precipitated water that contrib- utes appreciably to the radar echo was assumed to consist of ice spheres of unit density and diam- eter 1 em. From Ryde’s [1946] scattering curve for ice, a concentration of 1/m* of 1-em ice would give an equivalent Z of 10° mm*/m* for a radar wavelength of 3.2 em. (An equal concentration of 7-mm water drops would have a slightly larger equivalent Z.) An integration of area by Z at various altitudes in the storm was interpreted in terms of grams of ice per meter thickness of the storm. The results are plotted in Figure 15 for the five times during which areas were obtained dur- ing the life cycle of the tornado-producing hail- storm of July 11, 1958. (The areas of two of these times were shown in the previous figure.) The early echo (but not first echo) case of July 30, 1957 is included for comparison; the areas of this storm were the solid lines of Figure 13. Figure 15 shows a large development at all al- titudes in the mass content of large particles during the half hour preceding the first tornado, which touched down at about 15h30m. During the next two hours there is little further development except a redistribution of some mass from high altitudes to medium altitudes. 50) 40 “3 — EARLY ECHO JULY 30, 1957 The mean concentration of large particles in this storm, averaged over the total area of the radar echo at the altitude containing the greatest mass, ranged from about 0.3 to 1.3 @/m*. (In the ‘early echo’ storm, July 30, 1957, 15h45m-+, the highest mean concentration was only 0.017 g/m’.) These values, somewhat lower than those men- tioned by Weickmann [1953], suggest that the large (1 em) particles, which give the strongest radar echo, contribute only a small fraction of the total water substance. On the other hand, the extremely high values of radar reflectivity in the small echo cores aloft indicate mass concentra- tions of 9, 19, 35, 170, and 125 g/m‘* in the five measurements. Thus, the distribution of large particles is extremely spotty, with a surprisingly large concentration in the echo core, falling off to low concentrations and probably smaller maxi- mum sizes as the storm periphery is approached. A word of caution is advised in interpretation of these water-content estimates. First, all cali- brations of weather radars reveal a systematic departure of the echo intensity by a factor of 2 to 5, approximately, below the value expected on theoretical grounds. Corrections have been made for this factor. If the factor is somehow related to the calibration scheme but is not operative in meteorological observations, then the water con- centrations have been considerably overesti- mated. Secondly, attenuation by thunderstorm rain and water-coated hail, which is not accounted for here, leads to an underestimate of the water concentrations by an unknown amount. Finally, the assumption adopted regarding particle size and state has a marked effect on the water con- centration capable of giving the same intensity of radar echo. For example, the same radar echo 15.2 TOTAL MASS/UNIT HEIGHT ASSUMING | CM. HAIL (GRAMS/ METER ) Fria. 15—The relationship of total precipitated water mass per unit height to height, during five measurements in the tornado storm of July 11, 1958 and one in the growing hailstorm of July 30, 1957 BEHAVIOR PATTERNS OF NEW ENGLAND HAILSTORMS 365 TaBLE 3—T'otal precipitation mass in hailstorms (assuming all radar echo is from 1-cm hail) P J Storm date and type July 30, 1957 ‘first echo’ hailstorm July 11, 1958 hailstorm with tornadoes First Echo, 15h38m-40m Soon after first echo, 15h45m-16h02m (first hail at 16h01m) Developing, 15h03m—05m Stage and time Mass gm 3 X 10° 3 X 10° 6X 104 Mature, 15h38m—43m (first tornado near 15h30m) 4 x 10! Mature, 16h06m-—18m (two tornadoes near 16h00m) 5 1022 Mature, 16h42m~-17h02m (lull in severe weather) 4 xX 10! Peak maturity, 17h80m-39m (final, most damaging <0 tornado 17h15m-30m) TaBLE 4—Tropopause penetration by July 11, 1958 tornado storm (tropopause height = 38,000 ft) Measurement time Echo top height Mean echo area, 38 to 44 Kk ft Mean echo area, 44 K ft to top Echo volume in stratosphere Total penetration energy 15h31m 16h03m 51,000 ft 49,000 ft 310 km? 2000 km? 110 km? 570 km? 800 km# 4500 km? 1.7 X 10% ergs 6.3 X 107! ergs attributed to l-em hail would be returned by three times the mass concentration of 8-mm water drops, about 3 the mass concentration of 4-em hail, and somewhere between 43 and 4 of the mass concentration of a 1l-em particle composed of a mixture of ice and water in equal parts. With these limitations in mind, the total mass of precipitation, assuming it to consist entirely of 1-em hail, was added up for the two storms under consideration and is listed in Table 3. Echo areas near and above the tropopause were measured with reasonable accuracy at two times in the tornado storm of July 11, 1958. In both cases the areas above the tropopause de- creased with height, at first im a linear fashion and then more rapidly near the echo top. How- ever, the second measurement, about one-half hour later than the first, showed much larger echo areas penetrating above the tropopause level. The echo volume in the stratosphere in- creased more than five times, and the energy re- quired for penetration increased by more than a factor of three (see Table 4). The penetration energies were computed in two steps because the specific negative energy from the tropopause at 38,000 ft up to 44,000 ft was relatively small, but increased rapidly above 44,000 ft in a strong temperature inversion. Malkus [1959] has demonstrated the critical role of element size in the penetration of Cumulo- nimbus towers; the lower entrainment rate for the large element size inhibits the dilution of the ‘protected core.’ The echo areas of this tornado storm at the tropopause are much larger than the element areas reported by Malkus for clouds reaching 50,000 ft in Hurricane Daisy of 1958. However, the penetrations above the tropopause were somewhat greater in the case of the tornado storm. The rapid increase in echo volume above the tropopause and in the computed total energy re- quired for penetration of the tropopause, along with a shght decrease in echo top height, sug- gests a progressive modification of the lower stratosphere in such a manner that the actual penetration energy does not increase so markedly with time, or perhaps even decreases. The mixing of the early storm tops with the lower strato- sphere would moisten and cool the region so that subsequent penetrations would require less en- ergy. The vertical exchange of momentum sup- ported by the strong updrafts necessary for pene- tration of the tropopause by particles large enough to give a radar echo would tend to main- tain and enhance the modified region above the main body of the storm. In effect, the tropopause would seem to be bulging upward in the vicinity of the storm, though the authors have no knowl- edge of direct measurements of temperature or humidity which would confirm or deny this pic- ture. Characteristics of New England hail—During 366 ro) in mm % OCCURRENCE /CATEGORY WIDTH a fo} 10 20 30 40 50 60 DIAMETER — mm (he 2" Fig. 16—Occurrence of maximum hail size 100 80 x 60 | > o Zz 40 = CUMULATIVE FREQUENCY OF OCCURRENCE Y OF MAXIMUM HAIL SIZE “ 20 n= 290 10 20 30 40 50 60 70 80 DIAMETER — mm " 2" 3" Fie. 17—Cumulative frequency distribution of maximum hail size three summers, 317 hail reports were received with one or more useful bits of information about the hailstones or their timing. The most frequent maximum size reported (Fig. 16) is %4 inch. The median is 7 mm, and less than five per cent of the reported hail equals or exceeds one inch in diam- eter (see Fig. 17). Hail sizes in New England are considerably smaller than those found to the east of the Rockies by Beckwith [1959] and by Doug- las and Hitschfeld [1958], but are comparable to those observed in Illinois by Stout and others [1959]. Information on size distribution within a given hailfall was received from a limited number of observers who reported maximum and ‘average,’ or maximum and minimum sizes (Fig. 18). The representative size distribution is narrow. A typi- DONALDSON, CHMELA, AND SHACKFORD cal max/min size ratio is 2, with nearly 90% of all distributions within a spread of 3. One should expect the size range to be relatively narrow at the ground because of the greater melting rate of small stones during their fall. Many observers reported hail durations (Fig. 19), but a certain favoritism was evident for multiples of five minutes. A three-minute run- ning mean smoothed out this periodicity some- what. The median hailfall duration is three to four minutes. The five-minute periodicity was also a strong feature of the timing relationship between the beginning of hail and heavy rain (Fig. 20). In a very few cases hail began falling before the heavy rain, but in the median case 100 CUMULATIVE FREQUENCY OF OCCURRENCE OF HAIL SIZE RANG 80 60 40 FREQUENCY — % 20 | 3 5 it 9 I RATIO Fig. 18—Cumulative frequency distribution of size range in a hailfall 50 40- (et) fo} OCCURRENCES n fe} ° 5 10 15 20 25 HAIL DURATION — minutes Fie. 19—Frequeney of occurrence of hailfall durations BEHAVIOR PATTERNS OF NEW ENGLAND HAILSTORMS hail started falling four minutes after the heavy rain began, Hailstone shapes were reported only infre- quently, and are summarized in Table 5. Almost 75% of the reported shapes are about evenly di- vided between spheres and oblate ellipsoids. Some of the observers reported the number of stones left on the ground per unit area, as well as size and duration of fall. Using Ludlam’s [1958] formula for fall speed and his estimates of drag coefficient, the number concentration of hail- stones was found. These are spotted on Figure 21 as a function of diameter. Apparently the two pa- rameters are related only slightly. The median concentration decreases from 0.14 to 0.1 to 0.07/m* in the 5-10, 10-15, and 15-20 mm diam- eter size groups. A few mass concentrations are included. It is interesting to note that the maxi- mum value, 6 g/m", agrees with Ludlam’s state- ment that the concentration of water in the form of hailstones has a maximum value of several g¢/m*. General conclusions—New England hailstorms exhibit a wide variety of characteristics. Some of these features have been presented here, derived from radar measurements and the observations of a network of cooperating observers. The most surprising result, and the least reliable one, is the derivation, from the intensity of the maximum radar echo, of extremely high water concentra- tions in the cores of many hailstorms at medium altitudes. Even if a possible calibration error of a factor of five is taken into account, however, this maximum concentration reaches a value of 34 g/m* at a height of 23,000 ft in a tornado- producing hailstorm. Perhaps the most interesting result concerns the penetration of the tropopause by many storm echoes. The median rain-thunderstorm echo top 40 TIME HAIL BEGAN — TIME R+ BEGAN ow fo) n= 183 OCCURRENCES n ° -20 -10 ° 10 20 30 40 TIME — minutes Fre, 20—Frequeney of occurrence of time be- tween start of hail and heavy rain 367 TaBLE 5—Shape of New England hail (from reports of Cooperative Observer Network during years 1956-1958) avi Number of Characteristic shape reports Oblate 23 Spherical | 22 Irregular 10 Conical 4 Cylindrical 1 Prolate 1 Ratio of maximum/minimum dimen- | sions for oblate hailstones (six ob- servations): 1.25, 2, 2.1, 3, 3, 8 Total | 61 10 T T Trak i- a0 T © 05 9/m> © 08 g/m> 1 a/m Tr . f © 30104 g/m? ie pee = eeereare Serie [ESSN 15 20 DIAMETER — mm Fie. 21—The relationship of the number con- centrations of hailstones to diameter falls short of the tropopause by 4000 ft and the median hailstorm with hail less than %4 inch in diameter has its echo top coincident with the tropopause. However, the median hailstorm hay- ing hail %4 inch or larger penetrates 5000 ft into the stratosphere, and 4 of these storms pene- trate 9000 ft or more. Extreme penetrations of 10,000 to 15,000 ft occurred on five days; four of these were tornado days, with the tornado storms heavily involved. The increase of echo 368 DONALDSON, CHMELA, AND SHACKFORD volume in the stratosphere with time during the course of one of the tornado storms suggests a progressive modification of the low stratosphere in the vicinity of the storm, allowing easier pene- tration by the storm tops during the latter part of the storm life. Acknowledgments—The authors are deeply ap- preciative of the helpful criticism and many sug- gestions furnished by David Atlas. We are also appreciative of the constructive criticism of Ed- win Kessler. We are pleased to record our grati- tude to the volunteer thunderstorm observers of New England, whose many excellent reports have made this study possible. REFERENCES BeckwitH, W. B., Analysis of hailstorms in the Denver network, 1949-1958, this volume, pp. 348— 353, 1960. Donatpson, R. J., Jr., Vertical profiles of radar echo reflectivity in thunderstorms, Proc. Seventh Weather Radar Conf., B 8-16, 1958. Donatpson, R. J., Jr., Analysis of severe convective storms observed by radar, II, J. Met., 16, 281-287, 1959. Dovatas, R. H., Observations of Alberta hailstorms, First Conference on Cumulus Convection, Ports- mouth, N. H., May 19-22, 1959. Douatas, R. H., ann W. Hirscurep, Studies of Al- berta hailstorms, 1957, Sci. Rep. MW-27, Stormy Wea. Res. Group, McGill Univ., 79 pp., 1958. Lupuam, F. H., The hail problem, Nubila, 1, No. 1, Verona, Italy, 96 pp., 1958. Markus, J. S., Recent developments in studies of penetrative convection and an application to hur- ricane Cumulonimbus towers, First Conference on Cumulus Convection, Portsmouth, N. H., May 19-22, 1959. Newton, C. W., Morphology of thunderstorms and hailstorms as affected by vertical wind shear, this volume, pp. 339-347, 1960. Rype, J. W., The attenuation and radar echoes pro- duced at centimetre wavelengths by various me- teorological phenomena, Meteorological factors in radio wave propagation, Physical Society, Lon- don, 1946, pp. 169-189. Srout, G. E., R. H. Brackmer, Jr., 8. A. CHancnon, Jr. ano F. A. Hurr, Preliminary report on The Hail Hazard in Illinois, Illinois State Water Sur- vey, 33 pp., 1959. Vonnecut, B., anp C. B. Moore, Giant electrical storms, A. D. Little Co., Cambridge, Mass., 21 pp. 1958 (unpublished). WeickMann, H., Observational data on the forma- tion of precipitation in Cumulonimbus clouds, Thunderstorm Electricity, Univ. Chicago Press, pp. 66-138, 1953. Discussion (Note: Discussion of this paper is combined with those of the preceding and following papers at the end of the following paper.) Hail Studies in Hlinois Relating to Cloud Physics G. E. Srour, R. H. Buackmerr, anp K. E. Wik Illinois State Water Survey Division, Urbana, Illinois Abstract—Three independent hail studies during the past year have provided con- siderable basic knowledge concerning Illinois hailstorms. Analysis of climatological records from 85 stations indicates marked spatial and seasonal differences in frequency of hailstorms within the State. Considerable variability also occurs from year to year and decade to decade. One hundred eighty days with hail which caused damage to crops during 1953-1957 have been studied using insurance records or crop-loss, radar, and synoptic data. The crop-loss data were plotted to determine the time, location, and areal extent of the hailstorms. Variations in hail intensity (per cent of crop damage) were also examined. Detailed case studies of the most significant hailstorms were made using radar and severe local storm volunteer observer data. It was found that distortions in squall lines corresponded closely with areas of greatest hail and wind occurrence. A case of hail formation in advance of a squall line was examined. Radar and rawinsonde data were used to formulate an hypothesis of the advanced hail formation process. Introduction—Three studies of hail are cur- rently in progress at the Illmois State Water Survey. The first study involves the use of the records of the U. 8. Weather Bureau coopera- tive substations and first-order stations. These records provide data on the frequency of hail- storms throughout Illinois. The data are studied to determine if the climatological differences can be related to physical processes involving the formation and dissipation of hailstorms. The second of these studies, supported by the Crop-Hail Insurance Actuarial Association of Chicago, utilizes insurance company records of paid hail losses. The purpose of this study is to determine whether meteorological parameters can be used to define variations in the hail hazard in Illinois, and, consequently, be em- ployed in establishing hail insurance rates for various areas of the State. The third study, supported by the Air Force Cambridge Research Center (AFCRC), is con- cerned with collecting and analyzing radar data and volunteer observer reports of hail occur- rence to evaluate the utility of radar for identi- fying hailstorms. This paper presents examples of the data used and the types of analysis being performed which are of importance in determining the physical processes of hail formation. Climatological distribution of hailstorms—A study was made of the hail distribution in I- linois on an annual and seasonal basis. The pur- pose of this study was to provide a climatologi- 369 cal description of hailstorms in Illinois in respect to their average and extreme occurrences. Em- phasis was placed on the period from March through August, when most hail occurs in the State. The analysis was based on satisfactory hail records between 1901 and 1950 from 85 stations in Ilhnois including 12 first-order stations [Huff and Changnon, 1959]. Fifty of these 85 stations had 20 or more years of reliable hail records. Annual hail distribution—The average fre- quency of annual hail days is illustrated in Figure 1. In this figure, the average has been expressed in terms of number of days with hail in an average ten-year period. The annual hail maximum occurs in the region west of Spring- field. Secondary maxima are indicated in ex- treme northwest and in southern Illinois. Areas of minimum occurrence are indicated in eastern Illinois and west of Peoria. The areas in northwest and southern Illinois do not have elevations exceeding 1200 ft above mean sea level. The regions are quite rugged locally and the hills rise abruptly from the flat- lands to the south in the path of the prevailing wind flow. Consequently, it is quite likely that the hail maxima in these areas are partially in- duced by the abrupt differences in the local relief. The area of maximum frequency west of Springfield has no pronounced changes in relief in relation to the topography of the land sur- rounding it. The U. S. Weather Bureau [1947] has pointed out that this maximum area, which 370 30 —-7—- » e \ ROCKFORD \ a CHICAGO Serie “4 JOLIN aa MOLINE 21 @ PEORIA @URBANA '8 2i ,24 24 N 24 @MT VERNON CI S — SCALE © 10 20 30 40 50 a) MILES ——— Fie. 1—Annual average hail distribution ex- pressed as number of days with hail per ten-year period is a part of a non-orographic hail belt extending from Oklahoma to Pennsylvania, coincides roughly with a region of strong frontal activity. Summer hail distribution—The average fre- quency distribution of hail days durimg the three summer months of June, July, and August is similar to the annual hail frequency shown in Figure 1. However, the maximum in extreme southern Illinois is not present. Furthermore, the area of highest hail frequency is located in northwestern Illinois rather than in the area west of Springfield. The annual hail minimum west of Peoria appears pronounced in the sum- mer. Months of maximum hail occurrence—In general, the month of maximum hail activity is March, April, or May in the southern portion and April, May, or June in the northern half. Eight days with hail are average for May, six days for April, and between five and six days per month for March and June. The frequency STOUT, BLACKMER, AND WILK of hail days declines through the summer and fall seasons, with an average of four hail days in July, three in August, and between one and two in September and October. Reliability of distribution patterns—Since there was some question whether the hail maxima in northwestern, southwest central, and southern Illinois were persistent or had been induced by a few years of unusually heavy hail oceurrence in these areas, the reliability of the hail distribution pattern was investigated. Hail maps for each of the five decades in the 1901-50 period were drawn. It was found the three maxima areas per- sisted throughout this 50-year period, although some deviations from the pattern of Figure 1 were apparent im the various decades. In general, the five ten-year periods showed patterns similar to the average pattern of Figure 1 with respect to outstanding features. However, some major pattern differences did appear from decade to decade. To illustrate time variability further in the number and distribution of hailstorms in the State, hail occurrence maps for separate years were prepared. It was found, for example, that a relatively large number of hailstorms oceurred over a large portion of the State during 1911. Individual station amounts ranged from zero to nine. In contrast, in 1935 hail was relatively sparse. The maximum number of storms re- corded at any station was four, and the majority of the stations had none or only one storm. In 1936, again relatively few hailstorms occurred with a maximum number of four in northwestern Illinois and large areas of zero or one over the rest of the state. Analysis of crop-hail loss data—Variations in the hail hazard in Illinois are being studied using records of paid hail losses compiled by the Crop-Hail Insurance Actuarial Association (CHIAA) [Roth, 1955]. The purpose of the study is to determine whether or not meteoro- logical parameters can be used to define varia- tions in the hail hazard, and, consequently, be employed in establishing hail insurance rates for various areas. The records of paid hail losses include the year, month, day, and hour of hail occurrence; the county, township, and section (square mile) where hail occurred; the rate or percent of loss caused by the hail; and the type of crop dam- aged. In addition to the hail loss records for the period 1952-57, radar data of the Illinois HAIL STUDIES RELATING TO CLOUD PHYSICS State Water Survey and surface and upper air data of the U.S. Weather Bureau are also being studied. From these various types of data, information has been extracted on the location and extent of hailstorms, the movement of hailstorms, and the intensity of hailstorms in Illinois. Location and extent of storms—Days having greater than 20 paid losses were defined as hail- storm days. The number of hailstorm days from late May to early October during the period studied was 201 and ranged from 21 in 1952 to 49 in 1956 [Stout, Blackmer, Changnon, and Huff, 1959]. Maps showing the location of hail damage to crops on each of these hailstorm days were plotted by marking the section in which hail damage occurred. A color code was used to designate the hour of hail occurrence when plotting the larger storms (greater than 150 paid losses). Examples of the plotted maps showing the time and location of damaging hail are shown in Figures 2 and 3. 371 Figure 2 shows the locations where hail dam- aged crops on August 7, 1953. On this date hail destroyed one per cent of the crops in Illinois insured by CHIAA companies. The storm was widespread enough to affect three per cent of the crops in the state and the average loss to the crops affected was 33%. Areas of relatively continuous hail damage, shown on the map of August 7, 1953, will be referred to as ‘swaths.’ On this date there were six outstanding examples of these swaths, while other swaths which are smaller, or more scat- tered, are discernible. The locations of crop damage during the hail- storm of August 9, 1954, are shown in Figure 3. This storm had the largest number of paid losses during the 1952-57 period and is of particular interest because of the extreme length of the longest swath. This swath is at least 160 mi long, perhaps longer, since it may extend into Iowa. This storm destroyed one-half of one per cent of the crops insured by CHIAA companies in L.. Fie. 2—Loceation of hail on August 7, 1953 STOUT, BLACKMER, AND WILK CHAMPAIGN - URBANA Fie. 3—Location of hail on August 9, 1954 Tasie 1—Areal extent of hailstorms Year Item : | 1952] 1953 | 1954 | 1955 | 1956 | 1957 | “ Percent of crop loss dur- | 0.78) 3.09) 2.46) 0.43) 1.18) 0.22 ing year Number of hailstorm |21 31 40 34 49 26 days Percent of storm days | 81 94 75 74 65 69 with swaths Average number of | 2 3 2 2 2 1 swaths per storm day Average length of swath, |18.0 mi Average width of swath, | 5.5 | 6.0 mi Average spacing be- pe 4) aki 20 20 28 tween swaths, mi Average area of swaths, sq mi Average area of hail re- gion, sq mi 31.5 99 174 = |224 94 116 = |220 18, 000) 20, 000)17 , 000/18, 000/15, 000 Illinois in 1954. It was comparable in extent to the storm of August 7, 1953, since it also af- fected three per cent of the crops. All of the maps showing location of hail for the period 1952 to 1957, inclusive, were ex- amined and information tabulated concerning the number, length, and width of swaths. In addition, the rectangular area necessary to en- close all reports of hail on a storm day was computed. This area is called the hail region. Table 1 presents statistics relating to the areal extent of the storms in various years. The reason for the variations from year to year, as shown in Table 1, has not been in- vestigated but may be related to long-period variations in such atmospheric parameters as zonal wind speed, temperature, and moisture distribution. Detailed information of this type is necessary to define the extent of hail more accurately. Information on the extent of hail provides knowledge of the volume of the at- mosphere which is contributing to the forma- tion of the hail. The need for more detailed data on hail occurrence for use in evaluating radar for identification of hailstorms has led to the establishment of hail observer networks [Donaldson, 1958; Douglas and Hitschfeld, ronan LOSS! ie) Ke Ate; inte aeat pe oe < AAS. i 34 STORMS 7 i 374 1958; Wilk, 1959]. In these networks, however, observers are often spaced so widely that exact definition of the areal extent of hail is impos- sible. Thus, crop-loss records are the best avail- able data for defining the extent of hailstorms in heavily insured areas. Hailstorm movement—The movement of each hailstorm was determined by examination of radar echoes at the time and location of hail occurrence. The direction of movement showed a seasonal change. In May and October, hail- storms moved from directions south of west. In July and August the preferred direction of movement shifted to the northwest quadrant. The direction of movement of hailstorms varies greatly seasonally and annually. Figure 4 shows the percent of hailstorms moving from various directions each year, 1952 to 1957 in- clusive, and also shows the percent of the total damage each year which occurred with storms moving from the indicated direction. The most damaging storm in a given year may cause a high percentage of the total damage. The per- cent of the year’s damage caused by the major storm during each of the six years is indicated beside the damage bar of the direction from which the major storm moved. For example, in ! 1953 [ 31 HAILSTORM DAYS 3.09% OF TOTAL CROP DESTROYED 10 3 PERCENT OF LIABILITY EXPOSED TO STORM a xo) 5 10 15 20 25 30 35 PERCENT OF EXPOSED CROP DESTROYED STOUT, BLACKMER, AND WILK 1953 ten per cent of the storms moved from the west-northwest, causing 44% of the year’s damage. Most of this damage was caused by the storm of August 7, 1953, which produced 43% of the year’s damage. Hailstorm intensity—Variations in hailstorm intensity may be studied using the percent of crop destroyed. This may be done by year, month, day, or hour for the heavily insured areas of the state. In this study, individual hail- storm days have been classified according to the areal extent of the storm and the intensity of the storm. The areal extent is given by the percent of the total insured crop in the state which was exposed to hail on a given day. The storm intensity is given by the percent of the exposed crop which was destroyed by hail. The distribution of storms in 1953 and 1957, clas- sified in this manner, is shown in Figure 5. The figure shows that storms had a tendency to be larger and more damaging in 1953 than in 1957. Local variations in intensity may be studied by plotting the percent of exposed crop in each section which was destroyed by hail. Maps showing intensity variations have been plotted for ten days with hail. Two of these maps are shown in Figures 6 and 7. 10 1957 26 HAILSTORM DAYS 0.22% OF TOTAL CROP DESTROYED PERCENT OF LIABILITY EXPOSED TO STORM ‘ee-0-e—e a ees 5 10 ihe} 20 25 30 35 PERCENT OF EXPOSED CROP DESTROYED Fic. 5—Comparison of 1953 and 1957 storm area and intensity HAIL STUDIES RELATING TO CLOUD PHYSICS 375 PERCENT OF CROP DESTROYED O 0-25 M >25 : at eee | i Fic. 6—Hail intensity on August 7, 1953 Data from only two crops (corn and soy- beans) have been plotted on these maps. By restricting the plotted data im this manner, apparent hail intensity variations resulting from differences in hail susceptibility among crops is minimized. Figure 6 shows variations in hail intensity during the storm of August 7, 1953. Examina- tion of the figure shows that the regions of heaviest damage are scattered along most swaths, except for the one in the center of the map. This swath had relatively heavy damage along a substantial portion of its length, and, according to a newspaper account, hail the size of baseballs and oranges was observed near the end of the swath. The large size of the observed hailstones may indicate that the thunderstorm causing the hail damage along this swath was more severe than the other storms on this date. However, detailed examination of the radar echoes revealed that at least three thunder- storms moved across parts of this hail damage swath during the reported hours of hail oe- currences and that a single thunderstorm could not have produced all the hail. The fact that several different thunderstorms each produced hail in this area and that the areas overlapped in some parts of the swath probably explains the higher rates of destruction in this area. A more detailed study is being made of the radar echoes on this hailstorm day. Figure 7 shows the distribution of crop losses during the storm of August 9, 1954. Most of the hail observed with this storm was the size of marbles according to newspaper accounts. The rates of damage in individual sections with this storm were generally less than with the storm of August 7, 1953. Studies of hailstorm intensities are compli- cated by the fact that there are variations among crops in susceptibility to hail and that a single erop may vary in susceptibility to hail depending on its stage of development. Two methods may be used to overcome this margin of STOUT, BLACKMER, AND WILK PERCENT OF CROP DESTROYED O 0-25 N 25-50 M 50-75 : | v ae sf “ CHAMPAIGN-URBANA od Fra. 7—Hail intensity on August 9, 1954 error. First, losses to a single crop may be used in detailed studies; second, periods when all crops are equally susceptible to hail may be studied. Fortunately, one of the major crops in Illinois, soybeans, does not vary appreciably in susceptibility to hail during its life history. To show that two crops may be equally sus- ceptible, the distribution of various rates of damage were compared for corn and soybeans for the storm of August 7, 1953. This compari- son showed no significant difference in rates of damage to the two crops per unit area. Currently, a study is being made to compare hail intensity with slope of terrain over which the storm is moving. This study is not. suffi- ciently advanced to report at this time. One of the limitations mm studying hail intensity using crop-loss data is the lack of information about the size and concentration of the hailstones. Identical crop damage could result from many combinations of hailstone size and concentra- tion. It is at this point that the networks of volunteer observers become necessary. Analysis of radar and network data—A net- work of volunteer observers was established in central Illinois in the summer of 1958, under AFCRC sponsorship (AF Contract 19(604)- 4940, The Determination of Techniques for Radar Identification of Severe Thunderstorms). Approximately 1000 volunteer observers, lo- cated within a 380-county area and 100-mile range of the radar, furnished detailed reports concerning the time of occurrence, size, and concentration of hail, as well as reports of dam- aging wind, hghtning, and heavy rain. Exami- nation of these data in conjunction with PPI (CPS-9) and RHI (TPS-10) radar data yielded several enlightening facts concerning hailstorm formation. Mid-tropospheric jet penetration—PPI radar display of intense pre-cold frontal squall line activity often exhibits major distortions, or bulges, indicative of zonal acceleration within TO CLOUD PHYSICS STUDIES RELATING HAIL SG61 ‘27% Ang ‘us0yyed VAM OYOS VUIT—g ‘DIY NIVD IVWYON IHY 1S9 2191 odie ovOk o00E 0962 082 oc8e NIV9 Q39Nd3u = Idd 1S9 2291 1S 829) 1S 29! 1S9 O29! 1sd 9/9! Ls 219! 1S9 809! 1S9 209! LS9 89S] NIVD IVWWHON Idd 1S9 2¢9! 1S9 829! 41S9 p2S9i 159 029 1S9 9191 LS digi 1S9 8091 LS9 209 1S9 8sSl the line. A recent investigation [Nolen, 1959] suggests a close association of tornadic activity with this echo pattern. Nolen has appropriately named these line distortions ‘line echo wave patterns, referred to hereafter as LEWP. Two storms in 1958 which exhibited LEWP were well documented by data from radar and network observers. Detailed analyses of the storms were made to determine: the association of hail and strong winds with the LEWP; and, whether the LEWP was a function of echo height. Figure § illustrates the radar display on July 27, 1958, with the LEWP development shown at four-minute intervals on normal and reduced gain. The total time for development was ap- proximately 30 min. The sharp increase in echo intensity along the southern extreme is a normal product of LEWP development. An RHI cross section indicated little or no echo height varia- tion through the LEWP. This suggests that the line distortion was not a result of vertical growth KEY 4 HAIL — WIND DAMAGE 0.1600 CST , 27 JULY 1958 STOUT, BLACKMER, AND WILK into a steering level of higher wind speeds, but rather a consequence of a horizontal discon- tinuity in the wind field, in the form of a nar- row jet penetration. Analysis of the general wind profile, with emphasis on the Peoria rawin- sonde observation, provided support to this con- clusion. Figure 9 is a radar-synoptic schematic of the network, hail and wind reports, the LEWP, and the wind maxima that occurred on July 27, 1958. The wind value of 263°, 58 knots, was observed at 13,000 ft over Peoria at 18h 00m CST. A greater maximum of 245°, 64 knots, was observed near the tropopause at 29,500 ft. The northerly drift of the LEWP suggests that the higher maximum had limited directional control; however, the surface wind observations, as well as the LEWP, are aligned with the di- rection of the lower maximum. The second example, August 7, 1958 (see Fig. 9) supports the LEWP correlation with the hail reports. Post-analysis of surface synoptic b.0830 CST, 7 AUGUST 1958 Fra. 9—Mid-tropospheric jet penetration of squall line HAIL STUDIES RELATING TO CLOUD PPI (00 MILE RANGE 342° PHYSICS RHI 349° AZIMUTH RHI AZIMUTH Fia. 10—Line echo wave pattern, August 8, 1958 08 FREEZING LEVEL 12,200 FT. HEIGHT , THOUSANDS OF FEET MILLIBARS 7 / if TEMPERATURE 5) 7 7 a? 4: a 08 FREEZING PRESSURE , O600 CST PEORIA RAOB 1030 CST RW- 4 INCH HAIL 1200 CST PEORIA RAOB Fic. 11—Profile of a pre-squall line hail shower observations confirmed the stationary front po- sition in northern Illinois at 06h 00m CST and 12h00m CST. The single wind maxima of 299°, 62 knots, occurred at 16,000 ft. Pre-squall line hail shower occurrence—The PPI radar display for August 7, 1958, shown in Figure 10 indicates a less continuous line than that associated with the LEWP on July 27, 1958. It is apparent that further loss of line continuity results in the LEWP becoming am- biguous, as is highly probable in the case of isolated radar echoes associated with weather. Most of the hail occurred simultaneously with the heavy rain associated with the principal thunderstorm cells. However, one detailed re- port was received of hail falling in advance of the disturbance. An examination of the RHI radar data disclosed a unique echo over this severe location. The echo at 349°, as shown in Figure 10, exhibited distinct streamers which gested the existence of hail shafts. The only other echo in proximity was a suspended cell at 342°. Analysis of the Peoria rawinsonde data for 06h 00m CST and 12h 00m CST provided the general airmass temperature and moisture distributions south and north of the LEWP de- velopment. The profile in Figure 11 shows the streamers becoming continuous near the minus five-degree centigrade level, diffusing, and losing their identity near the wet-bulb freezing level. The echo depth decreased below the convective condensation level suggesting that limited evap- oration was occurring. The surface observation indicated very light rain associated with one- fourth inch hail. It was initially assumed that the hail was thrown out from the main thunderstorm. How- sug- 380 STOUT, BLACKMER, AND WILK 4 STO SUPER-COOLED DROPLET % ICE CRYSTAL @ = GRAUPEL & HAIL (GROWING) 40| 4 HAIL (MELTING) O RAIN DROP 35 I * + * * * * * ° @ © oO * * * * °% * * BASE OF ANVIL HEIGHT, THOUSANDS OF FEET 8 a ECHO "A" AT 0933 15}— -~7T N ae “A fice a Oe rZ- ag ege wae sare AZIMUTH , DEGREES 349° 340° ECHO A AT 0938 344° are AZIMUTH , DEGREES ECHO B <—0933cC——| +0938 c —> Fic. 12—Pre-squall line hail shower ever, further examination of the RHI radar data suggests the formation of hail was aided by the auxiliary shower development at 342°. The echo configuration and apparent hail for- mation process is illustrated in the schematic in Figure 12. At 09h 33m CST, echo A was dis- tinguishable from 840 to 347° and sloped up- ward to 15,000 ft. Five minutes later, at O9h 38m CST, echo A was entirely suspended, with the base at approximately 7500 ft and the top entering the cirrus overhang at 26,000 ft. The strong vertical transport ahead of the LEWP had carried the super-cooled droplets along the trajectory (1) into co-existence with the ice crystals in the anvil. The graupel which was formed in this region (2) was released to the lower levels and would have terminated as virga, except for the facet that it was in juxta- position with the origin of echo B. The growth stage of this new cell provided vertical support and droplets for continued particle growth (3) and hail formation. Summary and conclusions—Studies of hail are being made using climatological, crop-hail loss, radar, and volunteer observer data. No single type of data provides sufficient informa- tion to conduct a comprehensive study of hail formation. For example, the crop-loss data ean define the areal extent of damaging hail in re- gions where large areas of insured crops are located, but cannot provide information on hail size or concentration. The radar data ean pro- vide information on precipitation location, ex- tent, movement, and intensity, but radar is not capable at present of definitely distinguishing between rain and hail. The volunteer observer network data are useful in determining the size and concentration of hailstones and the rela- tionship of hail to the occurrence of rain, but do not permit the evaluation of the areal extent of hail. Although the primary purpose of the investi- gations being carried out at the Illinois State Water Survey is the determination of hail dis- tribution and radar detectibility, it is hoped that the preliminary case studies presented in this paper will contribute toward a better un- derstanding of the physical processes involved in hail formation. Acknowledgments—This research is partially supported by the Crop-Hail Insurance Actuarial Association and the Cambridge Air Force Re- search Center. REFERENCES Donatpson, R. J., Jr., Analysis of severe convective storms observed by radar, J. Met., 15, 44-50, 1958. Dovatas, R. H., anp W. Hirscureip, Studies of DISCUSSION 381 Alberta Hailstorms, 1957, Sci. Rep. MW-27, Mc- Gill University, 79 pp., 1958. Hurr, F. A., anv 8. A. Cuananon, Jr., Hail clima- tology of Illinois, Rep. Invest., Ill. Water Surv., 1959, (manuscript). Noten, R. H., A radar pattern associated with tornadoes, U. S. Weather Bureau, RADU, Kan- sas City, Missouri, 1959. Roru, R. J., Crop-Hail Insurance Actuarial As- sociation, Bul. Amer. Met. Soc., 36, 409-411, 1955. Stout, G. E., R. H. Buacker, Jr., S. A. CHANGNON, Jr. and F. A. Hurr, The hail hazard in Illinois, Crop-Hail Insurance Actuarial Association, Chi- cago, Illinois, 33, 1959. U. S. Wearuer Bureau, Thunderstorm Hydromet. Rep. 5, 330 1947. Witk, K. E., Research concerning analysis of severe thunderstorms, Q. Status Rep. 1, Con- tract AF 19(604)—4940, Illinois State Water Sur- vey, 6 pp., 1959. rainfall, Discussion (Relating to three preceding papers by Beck- with; Donaldson, Chmela, and Shackford; and Stout, Blackmer, and Wilk.) Dr. W. Hitschfeld—l think Messrs. Beck- with, Donaldson, and Blackmer have given us three excellent papers in which a great deal of factual material was presented. So, if I may lead off the discussion with Donaldson’s paper, in Figure 10, he plotted the product of height and radar mtensity measured in suitable radar units. I think this is the kind of approach that could be extremely valuable in the discrimina- tion by radar techniques, of rain from hail, and possibly the recognition of tornadoes by radar. Mr. Beckwith showed us some. surprising things. The photographs of the dents that were produced by large size hailstones in aircraft at high levels are strong evidence that four- inch hailstones occur at such enormous levels as 40,000 ft. This may suggest updrafts as high as 30 or even 60 m see, depending on hailstone shape and density. Mr. Blackmer has shown us how one can use insurance records, which (Dr. Douglas tells me) are difficult to get at and analyze; and he has done a lot with them. I only want to sound a word of warning. When one comes to relating these insurance records with storm patterns, one may be in for a surprise. For instance, a 160- mile-long streak of damage, may turn out to have been caused by three or four different storms. Mr. Roy Blackmer—lI have looked a little bit at the radar echoes of that particular storm. It is a little difficult to tell just how much echo development was going on, because the radar beam was a little wide and the place where the echo first appeared was out toward the maxi- mum range of the radar. But there appears to be really good echo continuity along that whole path. Dr. Hitschfeld—One of the nicest features, by the way, is the fact that you have suggested in showing from what square miles you had a right to expect the reports, and from what square miles you did not. The negative infor- mation is Just as important as the positive. With the usual kind of ground observers, the negative information is either not available or very spotty but I think the way you did it gives a lot of credence to the continuity. Mr. Blackmer—With the 1959 data, we can put two different types of observations together: the volunteer observer network gives us the distribution of hail size and accurate time of oceurrence. The crop-loss data will fill in the gaps between those to give the exact areal extent. Dr. L. J. Battan—I am curious about the ob- servation of a thunderstorm that went 12,000 ft above the troposphere. If one sets down the approximate equation and considers an iso- thermal layer, one needs very extreme vertical velocities, in order for a parcel to get very far above the tropopause. As a rule of thumb, Vonnegut has suggested 20 m see per kilo- meter of penetration. This means that the as- cending air must have a vertical velocity of 70 m see or more when it passes the tropopause. Taking into account all the possible errors, what would you say was the accuracy of the height measurement ? Mr. R. J. Donaldson, Jr—Plus or minus 2000 ft average for all of these measurements. Dr. Hitschfeld—How accurate is your meas- urement of the height of the tropopause? Mr. Donaldson—An arbitrary tropopause was taken using the point above 300 mb at which the lapse rate first becomes less than two degrees C per thousand feet. Most of the time it was fairly clearcut. The sounding either became iso- thermal, or bent backwards, indicating a nega- 382 DISCUSSION tive lapse rate. There are some cases where this is not so simple, and I am sure there are errors in trying to decide where the tropopause was. Major Currie S. Downie—Tropopauses in gen- eral are not like a wall or curtain that stay in one position from one sounding to the next. These things can vary considerably over a 12- hour period; time and space variations may be appreciable. Mr. Donaldson—I am sure we can have a possible six-hour error or a 150-mi error from the time it is measured. But the time and space errors probably average out over hundreds of items of data. Dr. R. Wexler—I enjoyed the paper very much, but I want to put in this suggestion about the use of statistics. I have noted that down in the tropics, for example, it is very difficult to tell where rain will develop on the basis of sta- bility alone; even with a very unstable sound- ing no rain may develop. Whenever anybody determines the frequency of hailstorms asso- ciated with large positive energy, I would lke to ask the frequency of clear weather also asso- ciated with large positive energy. Mr. Boynton Beckwith—Forecasters know better than the dynamic meteorologists, that thermodynamic curves are very poor forecast- ing tools by themselves. Dr. Hitschfeld—I agree with you. Positive energy areas are a very poor indicator for hail occurrences both in Denver and Alberta. I nevertheless believe that the Fawbush and Mil- ler criteria are perfectly valid for the region that they are worked out for. I think they have a physical basis and have been verified empiri- cally, but they do not seem to be exportable to Canada or the Rockies. Major Downie—Recently I made a study con- cerning the frequency of occurrence of two-inch hailstones, and find in this country the maxi- mum frequency occurs in the Great Plains re- gion; they almost never occur along the sea coast and only occasionally in the Middle West. I would like to find out if there is an explana- tion for this distribution. How can we explain the fact that practically all the two-inch hail in the country occurs over the land with an ele- vation of 3000 to S000 ft, whereas in southern United States practically no large hailstones are reported. Mr. Jerome Namias—Actually we are here dealing with large-scale dynamic climatology, and a very complex problem. However, there are some points which are fairly straightforward. In the first place very deep layers of unstable air are required for hail and tornadoes whatever way you look at it. These are manufactured especially im spring and early summer in a manner that favors the Middle West. Usually, the deep moist layers are produced this way: As the spring sun begins to warm southern United States and the Bermuda High anticy- clone begins to build, a shallow layer of warm moist air flows northward (see warm moist tongue in Fig. 13). At the same time mid- Fra. 13—Schematic differential flow pattern in spring leading to severe thunderstorms, hail and tornadoes, especially over shaded area DISCUSSION 383 tropospheric wind patterns over the west fre- quently are different during spring (broken lines of Fig. 13). This upper-level pattern, of course, depends on circulations in other parts of the hemisphere. The combination of surface and upper-level patterns results in differential advection over a broad area (especially shaded area). In the low layers we get warm moist air flowing into the Great Plains in the form of great warm moist tongues. At upper levels, 500 mb or so, the air is frequently very cold, having arrived from the eastern Pacifie or even the Gulf of Alaska. The lower warm moist air is shielded by the Rockies, so the cold air over- runs. This cold air has low specific humidity, and it is relatively dry; so that over a large area where this differential flow pattern ob- tains, there is increasing instability, both con- ditional and convective. The lapse rate increases because of the cold air overrunning the warm, and also convective instability increases because moist air from below is being overrun by rela- tively dry air. Also, one of the most favored storm tracks in spring when the polar front moves north is the ‘Colorado Low,’ so that synoptic-seale disturbances which have the vigor to release the energy of this instability are fre- quent. The synoptic activity is favored by geo- graphical considerations. The presence of the Gulf, the cold air from Alaska and the Pacific, and the Continental Divide all fit into the dy- namic climatology of hail and tornadoes. In the East we rarely have such meteorological condi- tions, since this type of differential advection rarely takes place. The rain situations are of a quite different character, and by the time the moist air and trough arrive, there has been a warming, and the conditional and convective instability have been released. There are many factors which make the East climatologically quite different from the standpoint of stability. Occasionally, tornadoes occur when the flow pattern at upper levels stalls so as to permit a moist current from the Gulf to enter below an eastern jet stream and into confluent pattern. After a period with very warm lower air and high troposphere, some storm may rip through and do the job of releasing the pent-up insta- bility. But this is a very infrequent case and most of the time the pattern I earlier described is present. Mr. Blackmer—Recently when looking at var- lations in hail occurrence across the state of Kansas, I plotted a cross section using ten-year mean June soundings for Columbia, Mo., Dodge City, Kan., and Grand Junction, Colo. On this cross section I marked the height of the con- vective condensation level and the height of the freezing level. At Grand Junction, where hail is quite frequent, the low humidity at low levels resulted in a convective condensation level at sub-freezing temperatures. At Columbia the convective condensation level was at a tempera- ture considerably warmer than freezing. Thus the cross section showed considerable change in the thickness of the layer between the cloud base and the freezing level. I believe that the temperature and thickness of the layer between the cloud base and the freezing level is very important in the forma- tion of hail. In humid regions where there is a thick layer of cloud beneath the freezing level, the cloud water will be quite warm. To freeze any of this water it must be lifted considerably and the cloud drops could possibly grow to fallout size before being lifted to the freezing level. In a cloud with a base near the freezing level the cloud water will be cold and will not have to be cooled much more to freeze. The cross section showed that the thickness of the cloud layer between the cloud base and the freezing level varied from zero in western Kansas to 35000 ft in eastern Kansas. Long- period insurance company records show an average crop loss of ten per cent in western Kansas while in the eastern part of the state the loss is about one per cent. Obviously, much more work needs to be done before any definite conclusions can be reached. One very important step would be to obtain long-period average sounding using data only on days with hail. These soundings would pro- vide data which could be compared with in- surance company records of hail loss to learn more about just what conditions are most favor- able for hail. Dr. G. D. Kinzer—In bringing the session to a close, I would like to read to you from to- day’s newspaper, “Eighteen inches of hail falls in Kansas.” “A hail storm battered this small prairie town of Seldon in northwest Kansas for two hours last night covering the town with 18 inches of ice.” I think that is a very remarkable event, and yet in the light of what we have dis- cussed tomight it does not seem unusual. (A re- port on this spectacular hailfall can be found in the Monthly Weather Review, 87, 301-303, 1959, by A. D. Robb, entitled “Severe Hail, Seldon, Kansas, June 3, 1959.”—Ed.) Future Research in Weather Modification Howarp T. OrvILLE Vice President, Beckman & Whitley, Inc., San Carlos, California Abstract—The paper outlines the present status of research in cloud physics and weather modification, and attempts to emphasize the need for expanded research in certain areas of cloud physics. Several suggested outlines for research projects are given. Introduction—W eather modification as treated in this discussion deals with competent research designed to increase precipitation, prevent hail, inhibit lightning, or dissipate fog. Present scien- tifie efforts at weather modification follow quite closely experimental methods and techniques de- veloped by Langmuir and others [1953]. These methods use nucleating agents dispersed into the cloud by ground generators or by aircraft flying over, in, or under the base of clouds to create artificial precipitation or to bring about other changes in state in the clouds. Solid carbon di- oxide (dry ice) or silver iodide are the two most commonly used nucleating agents although oth- ers such as cupric sulphide, hydrogen chloride, and a number of clay minerals are effective as freezing nuclei. Many uncertainties exist as to the exact man- ner in which the nuclei affect the clouds to bring about the change of state from vapor to water or solid form when they are seeded. This, then, brings us to the field of cloud physics. Cloud physics and weather modification— Houghton [1959] recently has reviewed the cur- rent problems in cloud-physics research. One cannot read this excellent review without be- coming singularly impressed with the urgent need for expanding and accelerating the research effort in cloud physics and the precipitation processes. Not to be overlooked are studies of the chemistry and electrical effects in the at- mosphere. Houghton’s review of homogeneous nuclea- tion, condensation nuclei, freezing nuclei, pre- cipitation processes, and natural precipitation mechanisms repeatedly emphasizes the broad gaps in our knowledge. He concludes that there are many challenging problems that only can be answered by both laboratory and field research. He particularly stresses the need for more in- strumentation to measure the parameters of cloud physics. A casual review of the papers presented at this meeting serves to impress the reader with the many unsolved problems of atmospheric proc- esses. Almost every paper reports lack of ob- servational or experimental data. Frequently, assumptions are made to justify later deriva- tions or arbitrary criteria are set up to make it possible to justify the conclusions. It seems to me that many of the assumptions are the same ones used when I was a student 30 years ago. Of course, much progress has been made but in comparison with other fields of science, medi- cine and atomic energy, for example, the prog- ress in understanding atmospheric processes seems quite insignificant. Until more progress is made in our understanding of precipitation mechanisms, efforts at weather modification are limited to our present knowledge. Need for basic research—The Advisory Com- mittee on Weather Control [1957] recommended that encouragement be given for the widest pos- sible competent research in meteorology and re- lated fields. The report pointed out that a vigor- ous research program should be established with adequate provisions to maintain continuity and reasonable stability for long-term projects. It stressed the fact that emphasis should be placed on sponsoring talented men and their projects. A National Institute of Atmospheric Research —The Committee on Meteorology [1958] of the National Academy of Sciences - National Re- search Council has proposed the establishment of a National Institute of Atmospheric Research. This Institute would be devoted exclusively to basic atmospheric research. It recognizes the formidable problems that the meteorologist faces in the field of cloud physics and would establish a research program commensurate with the global importance of weather. The program pro- posed by this Committee deserves the strongest possible support by all scientists having an in- terest in atmospheric research, Cloud physics and planetary research pro- gram—Ackerman [1959] has suggested a two 384 FUTURE RESEARCH IN WEATHER MODIFICATION 385 pronged attack on the problem of atmospheric research. He suggests a cloud-physics program and a planetary program. The cloud-physies program would be con- cerned largely with the problems discussed in this volume: dynamics of clouds, precipitation mechanisms, condensation nuclei, freezing nuclei, and other small-scale phenomena of the atmos- phere. This program would be a long-range one with stable financial support with complete free- dom of action and latitude to scientists in choos- ing areas of research. It would include experi- ments on any appropriate scale to msure orderly research. Such a program, Ackerman thinks, should be conducted by an agency of the gov- ernment separately from those agencies now having meteorological services and heavily com- mitted to day-to-day weather problems. An in- dependent research program, he thinks, would be conducive to essential depth, balance, and originality. The second program, the planetary one, sug- gested by Ackerman is a large-scale, long-range one which would be primarily concerned with global atmospheric circulation problems. It would be heavily weighted on the theoretical and ob- servational basis and would eventually require international scientific cooperation. Guidance for such a global program might well be placed un- der the United Nations with a planning and re- view board made up of eminent meteorologists, mathematicians, physicists, and other repre- sentatives of other disciplines to insure widest possible cooperation. Such a program would pro- vide an opportunity to show scientific leadership which might well play an important role im mitigating the problems in diplomacy. While such a program today might seem visionary, by tomorrow it might have revolutionary economic and military implications. Fiscal problems—lf we are ever to develop a multiphased atmospheric research program to get the answers to the thousands of questions now confronting us, we must present a bold, imaginative, and unified front that will com- mand strong public support. At the present time the entire research effort can be seriously jeop- ardized by the whims of one or two public offi- cials in prominent positions in government. In 1957 many of us saw research funds reduced to a trickle by the adverse decision of economy- minded officials and only the historic launching of Sputnik in October saved this program from almost complete obliteration. Only two weeks ago two very important items were disallowed in the National Science Founda- tion fiscal 1960 budgetary requests, by the House Appropriations Committee. One item was for $500,000 for the initial phases of the estab- lishment of the Institute of Atmospheric Re- search; the other a request for two million dol- lars to carry on the research and evaluation of weather modification as directed by Congress in Public Law 510 [American Meteorological So- ciety, 1958.] Such actions on the part of unin- formed public officials account for the weak, un- coordinated, and halting atmospheric-research effort today. One can cite many more examples where sud- denly funds have been reduced or eliminated and have forced the release of good research teams. Tf and when funds are again granted, the chances of re-assembling a competent scientific team are very remote. Under these conditions, meteorol- ogy is not an attractive field for the young man interested im science. The foregoing problems are given as examples of difficulties which prevent the establishment of a strong stable research program in cloud physics. Without the necessary answers gained from this research, weather modification efforts must necessarily be limited. Research tools—Radar was found to be imval- uable in studying the effects of cloud seeding in Arizona [Battan and Kassander, 1959]. As a re- search tool radar has become indispensable. Since World War II it has played a role of in- creasing importance for operational and research studies of atmospheric phenomena. Color radar combined with an electronic memory system 1s destined to become indispensable in future re- search projects in cloud physics. Instrumented aircraft have been used [Cun- ningham and Atlas, 1954] to study the structure of hail at 32,000 ft as observed from the air- craft. Cunningham’s long experience in obsery- ing frontal systems, thunderstorms, tornadoes, and hurricanes is a strong endorsement for in- strumented aircraft as a research tool for future research. Simpson and others [1958] confirm the value of aircraft observations in studying the structure of hurricanes. Much of the experi- mental data obtained in the University of Chi- cago cloud-physies research program were ob- tained from specially instrumented aircraft. Constant-level balloons, manned and un- manned, have not been mentioned in the present discussions. These large inexpansible polyethyl- 586 ene balloons are, in my opinion, ideal platforms for carrying on very important observations from altitudes of 50,000 to 100,000 ft. Capable of carrying a payload of 2000 lb and remaining aloft for more than 100 hr assures that the bal- loons can be used to track a front continuously across the United States. Radar, television, nu- clei count, and air samples, as well as the usual cloud-physics parameters, can be obtained throughout the life history of a frontal condition. Observations aloft coordinated with lower-alti- tude aircraft observations and a ground net- work of weather stations might give some very important clues into the atmospheric processes. Future research projects should include con- stant-level balloons for atmospheric research. The cost of these balloons would be much less than experimental aircraft and they offer a plat- form to obtain continuous observations at high altitudes for periods of a week or ten days. It would be feasible to use them for global oceanic observation platforms. Present electronic capa- bilities would permit the use of unmanned bal- loons in many areas but eventually all balloon observation stations should be manned with at least two observers. Future research programs—Future research programs in weather modification should plan for and provide the following: (1) An exhaustive cloud-physies program on a continuous basis for a period of five to ten years. The program should be developed by competent scientists so that projects are well de- signed and carefully controlled to yield maxi- mum amount of experimental data. (2) Projects should be established in at least nine areas of the United States: Florida and Gulf Coast, New England, Iowa and South Da- kota (flat lands), Utah and Colorado; Califor- nia and Washington. The location is based pri- marily on orographic and climatic features to provide maximum opportunity for observing all DISCUSSION unmanned constant-level balloons should provide observations on a coordinated basis to supple- ment ground observations. (4) Additional mountain observations should be established to furnish most representative surface observations. High-speed cameras will find increasing use in observing change of state in the laboratory, and eventually their use in field experiments will become an essential part of any future research program. (5) Radar of the latest type designed specifi- cally for cloud-physics observations should be available to each of the research projects. Color radar, magnetic-memory systems, and closed- circuit television should be provided when the science of the art can provide such ultra modern equipment. Funds to implement the entire program out- lined should not exceed 30 million dollars an- nually after the initial facilities have been estab- lished. REFERENCES AcKERMAN, Epwarp A., Resources for the Future, Inc. Forum, January 22, 1959. Apyisory ComMirtEe oN WeraATHER Controt, Final Report, vols. I and II, Superintendent of Docu- ments, Government Printing Office, December 31, 1957. American Merrorouocicat Society, Public Law 510, Bul. Amer. Met. Soc., November, 1958. Barran, Louis, aND R. Kassanper, Artificial nuclea- tion of orographic Cumuli, Institute of Atmos- pheric Physics, University of Arizona, June, 1959. Commirten oN Merteorotocy, Preliminary Plans for a National Institute for Atmospheric Research, National Academy of Sciences, January, 1958. CunnincHam, R. M., ann D. Attas, Growth of hydrometeors as calculated from aircraft and ra- dar observations, Proc. Toronto Met. Conf., Sept. 9-15, pub. 1954. Hovuauton, Henry G., Cloud physics, Science, 129, Feb. 6, 1959. Lanamuir, I., V. SCHAEFER, AND OTHERS, Project Cirrus, General Electric Research Lab., Schenec- tady, N. Y., March, 1953. Smupson, Gentry, AND oTHERS, [st National Hurri- types of weather situations. cane Conference, Miami, Florida, November (3) Instrumented aircraft and manned and 1958. Discussion Dr. Bernard Vonnegut—I agree with you that high-altitude balloons are a very useful tool for meteorological study. One application of bal- loons that should be of value in cloud physics is their use for obtaining time-lapse pictures of cloud development as viewed from above. These observations can be carried out with fairly small balloons as the cameras weigh only 10 or 20 Ib. It is much more instructive to look down on clouds and see how they grow and move than to look up at an uninformative cloud base. Dr. Helmut Weickmann—It is a very good DISCUSSION suggestion to look for areas which are specifi- cally favored for the study of key problems of cloud physics or cloud modification. One is the Olympic Mountains near Seattle, Washington, for a study of orographic rain. These mountains have characteristics of a tropical rainforest on their windward side and desert-like stretches on the downwind side. Another is the downwind shore of the Great Lakes where studies on winter snow showers could be made. They are due to continental polar-air outbreaks across Canada at a time when the Lakes are still unfrozen. The un- stable dry cold air eagerly takes up water vapor from the warm lakes which is readily being dumped on a 20-mile deep strip along the down- wind shores. The Great Lakes region invites another study: large-scale seeding of super- cooled cloud layers. The region produces very persistent Stratus cloud decks during the winter, which can be dissipated through dry-ice seeding. A study appears feasible of the influence of large-scale seeding (areas of 1000 sq mi or more) on weather. This would have to be a cooperative project with the Air Force furnishing ‘flying boxears’ loaded with dry ice and the US. Weather Bureau and other institutions in the area making measurements of meteorological parameters in the air and on the ground, such as, for instance, the variation of net radiation flux, albedo, and of the local windfield before and after seeding. Dr. B. J. Mason—It would be presumptuous for me to make comments on some aspects of Captain Orville’s paper, but nevertheless I would like to express what I feel very strongly about research in this field and the programs. There are three outstanding thoughts in this talk—continuity, stability, and building research around the promising individual. One of the greatest problems we have to face in this field of cloud physics is the shortage of competent peo- ple. There are many more projects than there are good people, and there are certainly many more problems than there are people competent to talk about them. We have spread the avail- able talent far too thinly. This means we must 387 do everything we can to make the maximum use of the people we have available and to recruit people from other physical sciences. This brings me to underline my view on how important con- tinuity and stability are, so you can build up a team around a promising individual, and he can be sure he has funds for the work over a period of years. In my view one can do very much more research if one has ten million dollars over ten years, rather than ten million dollars in one year. There are no problems worth tackling in this field that ean be solved by a crash program in one year. The trivial problems we are not in- terested in anyway. It is this continuity and sta- bility that is so important, and I believe that one does not solve problems by building grandi- ose institutions in the first place, and finding staff afterwards. You have to build the institu- tion around the staff. It is the people that mat- ter and this means, of course, one must plan very carefully. In the long term, it is better to do five things properly than to make a half-hearted job of fifty things. Dr. Douglas K. Lilly—It appears to me that for the most part we are trying to modify the weather after it was largely already quite settled and in order to modify a large convective sys- tem or something of this kind energies are re- quired of any astronomical figure you want to take arbitrarily. I know, however, that in chemi- cal reactions we have very often a situation in which it is necessary for a system to acquire a certain level of energy before it can do some- thing. At this level it can possibly do several different things the results of which may be quite different. But at exactly this peak, the activation peak, it takes really very little additional en- ergy to push it in one direction or another, or in fact, back where it came from. I would like to suggest the possible place to look for a modifi- cation is way back at the beginning when a cy- clone has not even started. There must be a point of indecision in the system at which a very small push in just the right direction could be perfectly enormous in its final effect, and this is something we looked at very little. The Swiss Randomized Hail Suppression Project in the Tessin RAYMUND SANGER Swiss Federal Institute of Technology, Zurich, Switzerland Abstract—The first two years of the Swiss randomized antihail project does not yet allow any statement having statistical weight about the effect of the AgI seedings to prevent hail, neither in a positive, negative, nor indifferent sense. However, the pre- cipitation patterns display indications for a strong increase of the rain as a result of the AglI seeding by ground generators. According to the general design the project will be carried through for the time of five years in the expectation to arrive until then to some definite decisions as to the effects of the silver iodide on hail formation. Since 1957 the Swiss Federal Commission for the Study of Hail Formation and Prevention [Sanger and others, 1957, 1958] has been carry- ing out its Third Hail Suppression Project in the Tessin. The test area hes in the southernmost part of the Alps and covers a region of about 3000 km* having a pronounced orographic char- acter. The project is financed jointly by a Fed- eral Grant from the Department of Public Economy (Division of Agriculture), by the Can- ton Tessin, and by two private firms which have cooperated in the project: Essagra 8S. A., Ba- lerna, and the Oerlikon Machine-Tool Works, Biihrle and Co., Ziirich, the latter maintaining a large agricultural estate in the test area. The seeding of the atmosphere is done from 20 silver iodide ground generators which sur- round the test area at distances ranging from less than one up to 30 km; seven of these are on Italian soil. The output of the generators is in the order of 10"/see of active ice-forming nuclei, measured at a temperature of —10°C, which is in keeping with the figures usual in such experiments. The generators have been made available by the Oerlikon Machine Tool Works, Ziirich, until now two different types have been used, the first a copy of the model de- veloped by North American Consultants, Inc., Goleta, Calif., and the second a new type of con- struction in which the AgI solution is sucked in by the flow of the fuel gas. After some initial trouble the second type well proved its worth, so that from the beginning of the third annual experimental period this year it alone will be used. The experimental period runs from the middle of May to the beginning of October. A strict process of randomization governs the occasions when seeding is to be carried out. Every day at 16h 30m a weather forecast is re- ceived from the meteorologists at the Osserva- torio Ticinese in Locarno-Monti; if they con- sider that there is a danger of thunderstorms on the following day, then this is considered to be a test day. A randomization experiment then determines whether seeding is to be done or not. In this way two groups of test days are ob- tained, for which the observational results can be compared with one another on a statistically satisfactory basis. Seeding always takes place between the hours of O7h 30m and 21h 30m, with the generators working to the rhythm of a ten-minute interval between five-minute operational periods. In ac- cordance with the seeding time the observational or test period runs from OSh 00m to 22h 30m; only hailfalls occurring within this observational period are included in the later statistical evalu- ation. A special network of 29 observation posts, distributed over the entire area of southern Switzerland, has been set up in order to collect the necessary data in sufficiently local detail. In the first two years of the project there were S85 test days, 42 seeded and 48 not. Hail was observed on 15 of the seeded days and on 13 of the unseeded days, but this statement takes no account either of the recorded intensity or of the geographical extent of the hailfalls. It only means that, during the test period, hail was reported at some place in the test area. It must further be noted that thunderstorms were ac- tually observed only on 33 of the 42 seeded days and on 26 of the unseeded days. This allows us to see that the group of seeded days was more heavily burdened with storms than the un- seeded group, so that the latter benefited from a higher rate of false forecasts. Generally speak- ing the amount of hail which has fallen during the first two years has been within modest limits, 388 SWISS RANDOMIZED HAIL SUPPRESSION PROJECT if we restrict our record to the actual test period of the day, and does not permit any analysis in terms of intensity and location. The sparsity of the hailfalls compels us therefore to put aside any idea of an exact mathematical statistical treatment of the observational data, to wait at least for the results of the third test year, and for the time being to insist only that it is not now possible to make any statement having sta- tistical weight, as to the effects, either positive, negative, or neutral, of the AgI seeding which has been done to prevent hail. Two heavy hailstorms in the years 1957 and 1958 which he outside the prescribed observa- tion period deserve to be mentioned. These therefore will not figure in a later statistical 389 evaluation of the test results. They are the hail- storm of August 13, 1957 and that of August 11, 1958. The first occurred on a day for which the forecast had been that there would be no storms (and which was therefore not a test day). In the case of the second hailfall, the storm did not begin until 22h 55m, five minutes after the end of the test period, and cannot consequently, if we are to be correct in our methods, be taken into account in the evaluation, despite the fact that this was a test day when there had been no seeding! Particular interest attaches to the question whether the effect of Ag] seeding may not per- haps be registered in the volume of precipita- tion. Apart from the records of the pluviograph Fic. 1—Daily precipitation in the test region in millimeters, 1957; upper values, seeded test days; lower values, unseeded days 390 in the Osservatorio Ticinese and of two other pluviographs which were put up during the course of the project, the only available figures for the daily amount of precipitation are those of the usual rainfall recording stations of the official Meteorological Service. If one considers, however, that seeding lasts for 14 hrs, that is, for more than half the day, then it is reasonable to expect that, if loading the atmosphere with silver iodide really has a strong influence on the amount of rain that falls, this must show up in the daily amount of precipitation. The values obtained for mean daily rainfall in the years 1957 and 1958, are entered respec- tively on Figures 1 and 2. The upper figure Reckingen 76% mS RAYMUND SANGER written beside the recording stations gives the mean quantity of precipitation for the seeded days, and the lower figure the mean for the un- seeded days. The astonishing result for 1957 (Fig. 1), namely that the increase in precipitation ap- parently caused by seeding is in the order of 100% (though there is some falling off towards the Alpine Divide), led to the enquiry being extended to find out how much rain had fallen in the nearby Italian districts and in the zone south of the Po. The necessary data was most obligingly put at our disposal by the Servizio Meteorologico della Aeronautica Nazionale through the good offices of Ezio Rosini. Since Fre. 2—Daily precipitation in the test region in millimeters, 1958; upper values, seeded test days; lower values, unseeded days 740 2418 Sondrio 0.41 Aosta Perou Mie as gee freee Bisbino 38S jlare Malpensa % 098 Milano 1@ ag 69 Linate are ; Vercelli i an Pracenzd 5 50 Q A ae °ferrara Ys a486@ 0.70 Parma 137 ase, Marina £ Lt Bologna Oi Ravenna Rimini S54 — e Sasso Faltrio 140 O77 170 26s Ancona Frontone Sin AMacerata 0.31 S Fia. —Daily precipitation in northern Italy in millimeters, 1957; ; upper values, seeded test days; lower values, unseeded days Passo Resid, 5.2 $2 188 Ssse Sonario 2.57 567 ® re. Grigna 4.60 posta Peroulaz ase @ Bergamo 264 Milano Malpensa, 4.26 Hone Li joe Milano Linate Vercelli 1.7 2.50 lary 103 @ 1.64 Ferrara 297 Parma Piacenza 003 J ean 0. He Marina d Ravenna Bologna 0.81 0.52 Rimiar 0.72 Sasso Feltrio’ 0.1% 136 —Ancona 0.92 ag 175 a7 Frontone S 9/00 Macerata®?s \— Fig. 4—Daily precipitation in northern Italy in millimeters, 195§ values, seeded test days; lower values, unseeded days 391 ; upper 392 these figures were entirely taken from pluvio- graphs, it is possible to refer the amounts of rainfall exactly to the prescribed test period. In Figures 3 and 4, the results from this source have been assembled. It is extremely surprising to find that, for a majority of the recording stations south of the Po, the mean daily rain- fall is again approximately doubled for the seeded days by comparison with the unseeded days during the test year 1957. This phenome- non was significantly not repeated in 1958. From Figures 2 and 4 it can be seen that in 1958 it is possible only to establish a doubling in the mean rainfall as due perhaps to seeding in the northern half of the Tessin. Yet at the same =o — Reckingen Cevio? 2° Fic. 5—Kolmogorov-Smirnov RAYMUND SANGER time even in the southern half the question of the mean rainfall between the seeded and the unseeded days is still considerably above unity. However, in the case of the Italian recording stations it does show a considerable fluctuation around unity. That the recorded 100% increase in the amount of precipitation on seeded days even (in 1957) at the Italian recording stations south of the Po should have been brought about by the AgI seeding, is a physical impossibility; the observation can be explained in no other way than as the result of statistical scatter. And in- deed these recording stations show a relatively small number of days on which there was any er, 1 \= 2 Disentis Bellinzonm™ test applied to the daily precipitation quantity of the test region, 1957 and 1958; percentage probability P of an error of the first type SWISS RANDOMIZED HAIL SUPPRESSION PROJECT 393 *Sondrio + Pre. Grigna e as Bergamo (50) e (so) Milano Lingte vercelli (30) Piacenza 9) ($0) "parma Ghedi Q e (=) Ferrara. (50) Marina o/ Ravenna e = Bologna (so) (50) Rimini e Sasso Feltrio (50) Ancona (50) (50) (50) Frontone S e Macerata Fig. 6—Kolmogorov-Smirnovy test of northern Italy, 1957 and 1958; per- centage probability P of an error of the first type precipitation, and as chance would have it the seeded days were unduly favored. Statistical treatment of the observational data, which in conclusion we shall now consider, clearly shows that this is, in fact, the correct explanation. The experimental results with regard to rain- fall were evaluated statistically according to the test procedure developed by Kolmogorov and Smirnoy [Darling, 1957]; the evaluation was carried out by P. Schmid, a statistician at the Swiss Federal Institute of Technology. The re- sults of these calculations are reproduced in Figures 5 and 6 for the recording stations on Swiss and Italian territory respectively. The fig- ure written beside the station represents the probability P that there would be at least the same result as regards an increase in precipita- tion if the experiment were repeated, but with- out any actual seeding. At the same time the differences of the values to 100% indicate in some way how much reliance we can place in the recorded increase in precipitation as a sign of the effect of seeding. From Figure 6 it is immediately clear that all the recording stations south of the Po have probability values of more than 50%; thus the amounts of precipitation gathered by these sta- significance from a_ statistical point of view in terms of the possible effects of seeding, a result in keeping with the supposition we have just made. The recording stations in the test area, however, present an entirely different picture; their probability values vary between 30 and 0%, and in no fewer than eight cases the probability is less than 5%. The recording sta- tions involved here all lie in extremely moun- tainous terrain between the Magadino Plain and the central Alpine Massif. From the point of view of physical meteorol- ogy the result of the statistical evaluation is ob- viously more consistent than the earlier figures given for the recorded rainfall. The possibility of effecting an apparently strong increase in precipitation as a result of seeding the atmos- phere by means of AgI ground generators, makes it potentially likely that in similar orographie conditions hail formation can also be interfered with im some way. At all events it may be legiti- tions have no 394 mate to assume that, in the kind of conditions existing in the test area, dispersed silver iodide from ground generators is able to rise to heights where it can have an active nucleating effect. This means that when the experiment has been continued for a sufficient length of time it will be possible to arrive at. some definite decision as to the effects, whether positive, negative, or neutral, of silver-iodide seeding on hail forma- tion. DISCUSSION REFERENCES Darurnc, D. A., The Kolmogorov-Smirnov, Cra- mer-von Mises tests, Ann. Math. Statistics, 28, 823-838, 1957. SAncer, R., Fr. Sprinc, W. Staus, anp J. C. THAMs, Grossversuch III zur Bekimpfung des Hagels im ‘Yessin, Eidg. Kommission zum Studium der Hageibildung und der Hagelabwehr, Abteilung fiir Landwirtschaft des EVD, Bern, Tatigkeits- bericht no. 10, pp. 1-111, 1957 and no. 11, pp. 1- 105, 1958. Discussion Dr. O. Essenwanger—Did 1 understand cor- rectly that you said there is no statistical evalua- tion? Prof. R. Sdnger—We have too little data to undertake an evaluation of the occurrence of hail. Dr. Essenwanger—That is what I wanted to say. The more samples you have, the more pos- sibilities exist to get a significant result. One may get an insignificant result because of the shortness of samples? Capt. H. T. Orville—Were your generator sites exactly the same in 1957 and 1958? Prof. Sdnger—We decided not to change any- thing during the whole period, mainly because of statistical reasons. Mr. Jerome Namias—I do not mean to stick my head into a hornets nest here, but I have often wondered about the question of evaluating rain-making experiments from the rainfall rec- ords themselves. While I think the techniques used are legitimate from the standpoint of sta- tistics, there are two possibilities that I would like to suggest for evaluations of this sort. One is that the synoptic characteristics of the periods be considered. Nature sometimes has a way of defeating our procedures of randomization. It might be that, because of the small number of seeding cases, during one long-period weather regime, the recurrent synoptic situation favors one period with respect to another. The second thought I have to offer is perhaps more contro- yersial. One is often dissatisfied with the knowl- edge that weather forecasting has amassed up to the present. Nevertheless, there is positive skill on the part of the forecaster. I have wondered, therefore, why the forecaster can not be con- sidered as some sort of a control in evaluating seeding effects. If one has sufficient cases over a long period, and the forecaster has positive skill, one can ask him to predict amounts over a long period of time and the discrepancy between his predictions and the observed amounts can be evaluated in terms of the effect of seeding opera- tions. Or it can be done on a ‘post-mortem’ basis. Give him various maps, let him make predictions or hindeasts of what might have happened, and use these as a control. So, I think there are methods other than statistical that might be put to use throughout the world. Prof. Sanger—Every year we prepare a large report including the meteorological situations, but here I present only the statistical part. It is also our intention to discuss the observations made in a manner similar to Mr. Namias’ pro- posal. On the other hand we want to have an evaluation which is completely free of subjectiv- ity. Dr. Fred Decker—Will your future work on this include enough observation on hail so that you establish the area where the hail fell? Prof. Sdnger—We intend to evaluate the hail fall in three areas separately, and also with re- gard to intensity. Our observations have been made according to the international scale of in- tensity. Dr. Helmut Weickmann—I am particularly happy about your comment, Mr. Namias, be- cause it emphasizes the importance of meteorol- ogy in the problem of the evaluation of the seeding experiments. I like to recall the days of the great argument between Dr. Langmuir and the U.S. Weather Bureau on the subject of the generation of a seven-day rainfall period as a consequence of periodic seeding with one Agl generator in New Mexico. In those days the U.S. DISCUSSION 395 Weather Bureau unfortunately did not employ synoptic meteorology analysis to the problem as you Just suggested, but it tried to fight back with Langmuir’s own weapons, with statistical analysis. Here, of course, Langmuir’s genius could not be defeated and in the bombardment of his ever new and different significance tests and correlation factors which however con- tributed so little to the basic physical meteoro- logical argument did the Weather Bureau lose rather than gain ground. Mr. Namias—Could I just make one last re- mark? I meant to point out that in reality this whole problem indicates the extreme importance of numerical forecasting procedures. If we can get an objective rainfall forecasting method, we can find answers and in ways involving much less emotion. A Project for a Formation of Cumulonimbus by Artificial Convection Henri Dessens Observatowe du Puy de Déme, Clermont-Ferrand, France Abstract—The researches on the weather control should not be restricted to the nucleation of the clouds. The convection the formation of the precipitation. After several experiments with great brush fires process plays a first importance part in ’ an experimental installation capable of modifying the local system of convection suf- ficiently to produce rain has been planned. This installation called ‘meteotron’ will consist of a pump serving 100 burners with fuel oil, so that the total consumption will be of the order of one ton per minute. The results of the experiments with great brush fires indicate that the formation of obtained, at least in equatorial regions, by Historical introduction—At the conference in Tueson, in April 1956, Byers recalled the sug- gestions made by Hspy [1841] that it would be possible to stimulate the formation of rain-giv- ing Cumulus clouds by means of large fires. In 1938, 100 years later, Gorog and Rovo [1938], on the bases of some observational data, proposed that gasoline could be burned in large quantities with the same effect. In 1930, Dessoliers [1930] showed how the men should be able to increase rainfall progressively in arid regions ‘‘en créant et multiphant au milieu des terres et des eaux des aires de surchauffe solaire de quelque cent hectares destinées 4 provoquer l’appel, la con- vergence d’énormes masses d’air et leur ascension vers le zénith ou, plus briévement, en créant et multiphant les centres de coordination atmos- phériques.” Preliminary experiments—The first experi- mental trial for the stimulation of convective as- cending air currents consisted in clearing in the equatorial forest a surface of 0.2 km’. In effect, in the surrounding forest the thermal capacity of the vegetation and the high evaporation tended to reduce the daily variation of tempera- ture, in particular to reduce the daily maximum temperature. Over the cleared area, the solar radiation heated the soil to high temperature and the air temperature is also raised. In fact, it was observed that Cumulus clouds did tend to form over the cleared area and the study of these clouds has allowed a theory called that of ‘coupled convection’ [Dessens, 1956]. But it ap- pears that to obtain Cumulus clouds sufficiently developed to give rain, there were also the fol- lowing requirements: (1) the cleared area should artificial thunderstorms will probably be working with the meteotron. be at least 1 km* in extent; (2) it is not sufficient really to clear or to burn the vegetation, but it would be necessary to make use of an uniform artificial covering for the area; and (3) the con- vective effect is only noticeable when low winds are very light. To cover the terrain will be an expensive proposition and the results at least uncertain. For these reasons, instead of following the idea to use only the solar energy, we preferred to have recourse to another source of energy, very much cheaper, for short series of experiments: the energy liberated by the burning of the vege- tation. We were immediately struck by the ease with which, in the equatorial regions, large Cu- mulus clouds can be obtained by this method, on a condition solely that the fire should be started at a suitable time in the day. These fires should be made with careful regard to the me- teorological conditions. When these are favor- able, large Cumulus clouds can easily be stimu- lated. These observations confirm entirely the ideas expressed in the last century by Espy [1841]. Artificial cloud seeding or artificial convection —Since 1955 we have made experiments to at- tempt to increase precipitation on an area of the Congo Basin at Lukolela (1°S, 17°E). Two methods have been employed: (1) the use of rockets to send large sodium chloride particles up to cloud base; and (2) the use of silver iodide emitted by burners situated at ground level. Be- ginning in 1956, we have undertaken these si- multaneously with experiments of artificial con- vection. The preliminary conclusion which we have reached after these two series of experi- 396 FORMATION OF CUMULONIMBUS BY ARTIFICIAL CONVECTION 397 ments, is that the only falls of rain which we can attribute with certainty to our intervention are those which have been stimulated by artificial convection [H. Dessens and J. Dessens, 1956, 1957]. As far as the cloud seeding is concerned, the results are particularly disappomting, because the conditions under which we work seem ex- ceptionally favorable: (1) the base of the Cu- mulus clouds was less than 1000 m above the ground, so that the rockets can easily reach the cloud base. (2) In this region there was a com- plete absence or at most very few natural ice- forming nuclei active at temperatures above —30°C. This was shown by measurements made with an ice-nuclei counter, at ground level, by Soulage [1956], by the photogrammetric study of the clouds themselves by J. Dessens [1959], and also by observations of large subeooled Cumulus over the southern Congo and Rhodesia made by Schaefer [1958]. A third factor in favor of the seeding was the fact that the winds are gener- ally light and of very steady direction, which facilitated the evaluation of the results of seed- ing. The last favorable condition is that the pre- cipitation is principally due to local convection clouds. In contrast with the apparent lack of any ef- fect on the precipitation of the seeding, the evi- dence for the positive effect on the Cumulus of the artificial convection is very striking. Fur- thermore, these first experiments have permitted us to calculate approximately the amount of energy which has been liberated by combustion to trigger the formation of Cumulus or Cumulo- nimbus in definite local conditions in the dry and in the rainy season. The ‘Meteotron’: a brief description—I use the word ‘meteotron’ to describe any experi- mental arrangement capable of modifying the local system of convection sufficiently to form frequently clouds which may produce rain. Our experience with brush fires suggests that the energy to be liberated must be comparable with that received from the Sun, that is to say of the order of 10° kw/km’*. This energy must be im- mediately available and ready for application to take advantage of the meteorological situation; that is, that it is necessary to use some hquid or gaseous fuel. We chose to use fuel oil. Our ‘meteotron’ therefore includes a station for the preparation of the fuel with a pump driven by a diesel motor. The motor drives also a small generator which produces alternating current necessary for automatic firing of the fuel at a distance. We are, at present, thinking in terms of a dis- tribution of 100 burners connected to the cen- tral post by tubes, these 100 burners situated on a circle of approximately 250 m in diameter. Each burner will burn 600 kg of fuel oil per hour so that the total consumption will be of the order of one ton of fuel oil per minute in the whole system. Site of the experiments—The most suitable region for a first trial of this method, would, I think, be between latitudes 5°N and 5°S, in a region of plains during the rainy season. The severe droughts observed in 1958, south of the equator, Justify such an experiment for the eco- nomic point of view. Regions such as the Ma- yumbe, the Niari Valley or the Congo Basin will be very suitable. The relatively light winds, the absence of cyclonic perturbations, the perma- nent presence of a very humid air layer at low levels, the low cloud-base level are favorable factors. It is important to realize these differ- ences between conditions in the tropics and those in temperate regions. Method of use of the ‘meteotron’—The most delicate part of the operation is the choice of the moment to start. Our first objective is mod- est: just before the moment at which the general instability becomes sufficient to permit the natu- ral formation of Cumulonimbus, we must light our burners, that is to say, anticipating the natu- ral formation of Cumulus by a short period. Six minutes after lighting the burners, the first arti- ficial Cumulus cloud appears. After 15 min the development of this cloud is greater than that of the other Cumulus in the region. So that, in- stead of leaving it to chance the location of the first formation of Cumulonimbus over the area, we have chosen and imposed this location. In brief, what we do, is to add a little artificial impulse to the natural instability of the air, which is due to the heating of the soil by the solar radiation of the whole area. This impulse starts half an hour before the time at which the normal Cumulonimbus will begin to form gener- ally over the whole region in radius, say, of 50 to 100 km without intervention. Despite the fact that the experience of previ- ous days gives us some ideas of the moment at which Cumulonimbus will begin to form, it 1s necessary to be able to make, each day, a short- term forecast, in order to know exactly when the ‘meteotron’ should be put in the action. This forecasting for periods less than an hour may be a delicate matter, but various methods are al- ready envisaged to make it more objective. Such methods might include the observation of ‘sfer- ics,’ the use of radiosondes at the critical mo- ments and the study of the intensity of diffused light from the zenith. When the operation started, the experiment will consist of observing low-level conditions, how long it would be possible to go on localizing the convection over the experimental area, and how long it would be possible to continue influ- encing the precipitation over the area. Possible future development of artificial con- vection—From the foregoing discussion, it ap- pears that our first objective would be to try to concentrate the rainfall over a cultivated area, possibly at the expense of a slight deficit of rain- falls over surrounding regions. For example, if we succeeded in increasing the rainfall over 500 km? of cultivated area by 30%, it is possible that we will cause a decrease of 38% over 5000 km*, which we assume will be relatively wild, that is to say forest or savanna. This decrease in the rainfall on the surrounding regions could have no economic disadvantage because it is not cultivated. Before finishing this exposition of this project, I would like to discuss some of the future per- spectives which the artificial convection opens to us and which have much wider application than this that we considered so far. (1) In tropical regions, during the dry sea- son, it is commonly found that the humid air at ground level, is overlain by dry air. It sometimes occurs that this humid layer is not sufficiently deep to permit the natural formation of Cumulo- nimbus. In this ease the artificial impulse given by the burning of fuel, may provoke a local deepening of the humid air layer and thus the very local formation of cloud. In this case, it is possible to imagine, when during a dry season, the cloud formation is not general, that local cloud and precipitation may be produced. We have already succeeded in Africa, by brush fires, in producing some local light rainfall (1 mm) in situations when no natural rainfall occurred in the region. (2) In temperate regions, in situations where instability occurs along a chain of mountains such as the Pyrenees, our intervention at criti- cal moments might result in a concentration of HENRI DESSENS stormy precipitation at higher areas useful to hydroelectric installations. (3) From a study of the very heavy storm rainfall in southern France, sometimes accom- panied by devastating hail storms, this phe- nomenon results from the coupling of the ther- mal energy of low air with the kinetic energy of the jet stream, through quite stable and localized ascending air currents. By analogy, some cou- pling effect might be obtained, in situation with strong jet-stream, with artificially stimulated convection. There would be advantage that, m this case, the location is controlled by the choice of place for the experiments. The ‘solar meteotron—The first experiments have to be made with a ‘fuel meteotron’ because its cost is relatively low, less than $100,000, while the preparation of the surface for the differential heating by the Sun with the proper materials will require a very much higher expenditure. I hope, nevertheless, that some participants at this Second Conference at Woods Hole, will agree that, in the end, it will certainly be necessary to consider either the ‘solar meteotron’ or a ‘mixed meteotron’ in which both solar energy and fuel are used. The real domestication of solar energy will come only with the use of a ‘meteotron’ to provide a rain-giving cloud. REFERENCES Dessens, H., Essai de formation artificielle de Cumulus par utilisation exclusive de l’énergie solaire, Bul. Obs. Puy de Déme, pp. 113-125, 1956. Dessens, H. ann J. Dessens, La formation arti- ficielle de grands Cumulus producteurs de pluie, C.-R. Acad. Sci., 243, 814-817, 1956; Etude pré- liminaire des Cumulus et des pluies obtenus par convection provoquée, Bul. Obs. Puy de Déme, pp. 47-60, 1957. Dessens, J., Niveau de congélation des nuages con- vectifs équatoriaux, Bul. Obs. Puy de Dome, pp. 73-80, 1959. Dessouiers, H., Refoulement dw Sahara, Ch. Beé- ranger, Edit., Paris, 158 pp., 1930. Espey, J. P., The philosophy of storms, Boston (Ch. GC. Little and James Brown), 552 p., 1841. Goréa, H. anp Rové, A., Kisérlet mesterséges esd eloallitasara. Idéjaras, 14, 2-9, 1938. Scuarrer, V. J., Cloud explorations over Africa, Trans. New York Acad. Sci., ser. I, 20, 535-540, 1958. Soutacr, G., Réponse A la note de Bigg, E. K., Freezing nuclei in the atmosphere, Bul. Obs. Puy de Déme, pp. 80-85, 1956. DISCUSSION 399 Discussion Mr. W. A. Mordy—lI lived for a number of years in Hawaii. In the process of harvesting sugar cane in the Islands they set fire to the fields to get rid of the leaves and waste ma- terial before they harvest the cane. They burn 15 to 20 acres of cane at a time. Frequently a cloud forms over these fires. At the appearance of these clouds such as we have seen in Dr. Dessens’ slides, we have occassionally made time- lapse movies. When I first went to the Islands, I heard a report that such a cloud had in fact yielded a half an inch of rain on one occasion. This, of course, was interesting to us, since these clouds were very frequent. They could be seen about fifty times a year. It therefore became a pastime of mine to follow up on these whenever possible. As I traveled around the Islands I did this. And I was very interested to see if I could find another instance when a cloud had, in fact, formed rain. I never found another instance, and I could not confirm the first report either. In ten years we found not a single case when one of these clouds produced rain. Dr. H, Dessens—It is necessary to start the fire under favorable meteorological conditions; these are latent instability and no wind. Both conditions occur in our equatorial regions. Rain has been obtained by us in the first experiments but it was light rain, amounting to less than one millimeter. Dr. Tor Bergeron—l have in fact another project for getting more precipitation in central and northern Africa: the main thing is that one should not let the waters of the Rivers Congo and Nile run out into the sea, but one should use any available source of energy for keeping them inland, and especially within the regions where there is already some vegetation. The second point is that the water should certainly not be used for irrigation in the northern part of the Sahara or lower Egypt, because it will be evapo- rated into dry air without clouds to a great ex- tent. But further south, of course, the project of Dr. Dessens would probably come in very handy. I just wonder if these two projects could not go hand in hand and help each other, and I hope, in fact, we shall have an opportunity to do so, but then I have one question about the possible cost. Dr. Dessens—From the economic point of view this project seems to me more useful than the project of sending rockets to the Moon. Dr. C. E. Junge—I think it is a very good idea to start making use of the huge amounts of energy which are available in an unstable atmos- phere just by initiating the vertical convection by means of bringing in some heat. I think this may really be the first step in a quite new direc- tion of weather modification which should be much more exploited. Major C. Downie—We should also look into the chemistry of this process. Fuel oil during combustion produces about one and one-quarter (14%) pounds of water per pound of fuel, de- pending on the particular hydrocarbon mixture involved. Thus an appreciable amount of mois- ture, in addition to the heat energy, is released into the atmosphere. That both of these factors are important is borne out by the Geophysics Research Directorate study of aircraft condensa- tion trails, another example of artificially pro- duced clouds. Mr. Mordy—We did make estimates on the basis that one adds very much water. One would expect the cloud base in these eases would be different from other clouds in that area. But if you compare the effect of the added water and the effect of released heat, you find the energy added makes the difference. It is not the water. Actually, there are three possible variables: the nuclei, the water, and the energy. Dr. Bernard Vonnegut—In his comments a few minutes ago, Dr. Bergeron hinted at some ideas he had on the control of climate, and he has consented to give us a brief, but more ex- tensive outline of this. Dr. Bergeron—As you know, there are great plans for buildmg a new dam at Aswan, in Egypt. For immediate needs, this dam will be very useful, but not for more far-sighted plan- ning of water resources. In fact, the irrigation water spent in the arid northeast trade region will only be utilized by vegetation to a very small percentage. Part of it will go through plants and be useful once, and then never more. But the rest of it will not even go through plants once; it will go directly up in the air and from there, anywhere. It will not come down again in North Africa, because there are no clouds there. True enough, we should not allow the 400 10 DISCUSSION Z Hot and/or dry trade AA Warm humid monsoon 100~,lsohyetal 100 mm 20° 0° — bw oox a < oO a = » a = fo} uv uw 3 v N 0 Vy) fac K ° Q =) - = N Yi q | Sa Bad Ds : M4 > g AA > S LS g eS A? ow TB.1958 oT 40° heer mee OS Fig. 1—Schematie picture of rain distribution and general circulation in lower troposphere over Africa in July waters of the Nile, Niger, and Congo to reach the ocean. However, they should not only be kept inside Africa, but inside the southwest monsoon, between the two tropical fronts shown in Figure 1. We should use any sources of en- ergy, in the future atomic energy, for distribut- ing it rationally. If the water is spent where we already have vegetation and clouds, most of it will go through plants, and then that humidity will come down again and again. Figure 1 shows the structure of the general circulation over the whole of Africa in July as observed from the ground. This analysis is based on ideas I already had in 1928; part of it was published in 1929, but only in Russian, so nobody here has seen it. The southern tropical front moves down to Rhodesia in January. The northern one hes along 18-20°N in July, and there must be remains of it near the equator at the opposite time of the year. So, it seems as if the southwest monsoon were enclosed between two tropical fronts. The northern one we know very well by now; this was confirmed by the work of Brooks and Mirrless in 1934. The precipitation distribution in Figure 1 is shown by shading. Evidently, the equatorial pre- cipitation is not at all directly connected with the front. It is a pure air-mass precipitation, which falls within the region where this very humid and unstable air mass is deep enough to be able to produce Cumulonimbus. In fact, it forms a flow of air that one may really follow. So far as I know, there is no other place on Earth where you have an air mass that is so well de- fined. You have the even flow of moist air com- ing in from the ocean. It can not pass through the northern tropical front at lower levels, since this front surface is a well-established and marked one. It leaks out above, at the top of the Cumulonimbus clouds, but not so very much, because the temperatures are so low there, and thus amounts of humidity are very small. So, we can use the water of these rivers for impor- tant irrigation projects within the outskirts of DISCUSSION the monsoon region, in the savannas. There, it will go up and down many times before it leaks out east of Ethiopia and aloft, and perhaps also somewhat through the southern front. This pic- ture holds good not only for July, but for all the time from April or May until October. In fact, the tropical front passes Kharthum (15°N.) in the middle of May on its way north, and passes the same place again moving south in the middle of October. In the future, when we have economical atomic energy, we can even have factories evapo- rating sea water, thus enriching the southwest monsoon with humidity, and let the monsoon itself carry and distribute the humidity over the region, if huge irrigation plants prove too costly to construct. Moreover, the present cooling ef- fects within the monsoon area will be intensified both indirectly by increasing cloudiness, shutting off the sunshine, and indirectly by the increased precipitation. Then the northern tropical front will move north a little. How much, we do not know, but it is quite likely to move north until it reaches a position where it can not go further north for reasons of the general plane- tary dynamics. If you now have increased amounts of humidity, this project of Dr. Des- sens is very useful because then it will pay even more to utilize the latent instability for releasing even more showers. So, I think these two proj- ects might be able to cooperate nicely in the fu- ture when we have more sources of cheap en- ergy. Mr. Jerome Namias—It is refreshing to see a man of Dr. Bergeron’s stature becoming inter- ested in weather modification problems. Sup- porting his discussion, I want to bring out a thought which may have been overlooked in dealing with this problem. In the first place, of course, the problem will not achieve a desirable solution until the numerical part of it is solved, so that we know exactly the sequence of events after we have treated weather or cloud condi- tions artificially. Now, in this conference, where all sorts of ideas are set forth, we may consider possibilities which extend further into the fu- ture. Presently, a science is emerging from re- search in extended forecasting which deals with ‘tele-connections, the long-distance interactions of weather regimes where one or more effects in one area affect other areas in a very dramatic way. One of the aims of long-range forecasting is to find such areas which are in resonance with other areas. It appears possible that certain 401 forms of the general circulation exist which are rather precariously balanced, and which might be influenced if man acquires the amounts of energy commensurate with what is believed to be necessary and, of course, knows how and where to apply it. Then those people who have worked many years on these problems, namely, those who have experience in extended long-range forecasting, should be consulted as to the weak spots and precariously balanced states in the at- mosphere; that is, the circulations that are on the verge of doing one thing or another. Here is an example: The weather over the North American continent, and particularly the United States, is greatly influenced by a special type of intense cyclone which often forms in the Gulf of Alaska. If it is there, it tends to bring about one type of weather through its influence on the large-scale circulation over North America; if it is not there, another quite different, meteorologi- cally opposed, type occurs. The development of this cyclone is very explosive. It takes place rapidly, and is sensitive to the general upper-air flow. If this flow comes from Alaska (with ex- treme cold air heated over the Gulf) the rapid heating and distortion by the coastal ranges in- duces strong cyclonic vorticity. Since this ap- pears to be a rather sensitive mechanism, it may lend itself to artificial control. I therefore feel that synoptic studies of the general circulation and its weak spots should be earried on right now, so that if the day comes when commen- surate supplies of energy are available, we will be in a better position to undertake projects of large scale weather modification. Dr. Bergeron—May I just declare that I am more than in agreement with my friend on these points. I have always thought of these critical thresholds in the general circulation, how the pattern may Just jump over from one preferred shape to another; and that there may be rather small quantities of energy needed. And, of course, I am also quite aware that dynamists, the long- range forecasters, and those working with nu- merical computors are the people to take care of certain important sides of that problem. The reason I chose that part of the world (North Africa) was, that down there the problem seems to be even simpler, because you do not need to change very much, just a little increase in the humidity, and that would be perhaps the best region in the world at present where one could utilize the humidity directly without too much los: 7] Physics of Precipitation in Winter Storms at Santa Barbara, California Ciement J. Topp Meteorology Research, Inc., Altadena, California Abstract—The immediate purpose of the physical analysis of storms at Santa Barbara, is to increase the sensitivity of the statistical analysis, (a) by finding physical explanations of as much of the variability between target and control as possible, and (b) by finding physical methods of classifying which precipitation mechanisms are operating in order that the storm periods may be stratified according to a reasonable hypothesis of seedability for a statistical test. Introduction—Meteorology Research, Inc., is engaged in a study using radar and other tools of physical analysis to see what light can be shed on the physics of natural and seeded precipita- tion in Southern California winter storms. The study is in conjunction with the Santa Barbara Cooperative Seeding Project. The Cooperative Seeding Project was designed as a statistical study to evaluate a commercial seeding opera- tion. In the design of the statistical experiment the primary concern is on safe guards against all sources of bias. The seeding operation is as follows: if the commercial operator forecasts the ensuing twelve hour period to be seedable he is instructed to seed or not to seed according to a random pro- cedure controlled by the statistician. The physi- cal observations are all passive. Physics of rain distribution—Probably for a long time to come the best estimate of what would have been the unaffected precipitation over a target will come from the comparison of the actual precipitation in an unaffected control. There have been many attempts to make this comparison more sensitive by stratifying the storms according to synoptic scale types. Our approach is to go to the mesoscale and vertical structure and classify the storms ito short pe- riods that have physical similarity. Operating a 3-cm radar at La Cumbre Look- out on a 4000-ft ridge six miles north of Santa Barbara for the last three years has convinced us that there are several different types of storm periods. The types are apt to persist for several hours at a time and they reoccur in different storms and in different years. The consistency of types is no doubt due to dominance of terrain effects. Only the surface has been scratched in understanding the significant physical causes of the different types, but we have a faith that understanding will come from inquiry. Just scratching the surface has shown that a most pronounced rain anomaly is associated with the height of the stability layer. If it is low with respect to the ridge of the Santa Ynez Mountains, the surface air does not flow easily over the range. It piles up and is forced out to the west, as indicated by strong east surface winds at Santa Barbara. Figure 1 shows a cross section of the February 25, 1958 storm, an un- oap 16P. o4P 16P ao FEB 24-25 ] —TEMP~0.P*C) 1958 —- AIR TEMP: ast 4 L 250MB | | so+ 2et 20°C 20°C 20+ sal ——— 500 STABLE | HEIGHT (THSDS. FT.) A | Sra BED TIME - HEIGHT STORM STRUCTURE Fic. 1—Time-height cross section over Santa Barbara for February 24-25, 1958, a typical low- level stable layer storm; broken lines represent air temperatures in °C; solid lines, the difference be- tween air temperature and dew point 402 PRECIPITATION IN WINTER STORMS IN CALIFORNIA 125) SAN RAFAEL RIDGE o i Sle 2 RK a 2 9 q w el lof 8 + re - ° = ° \ wy SANTA YNEZ VALLEY < i‘ ons’ + de) T hee STABLE +4 N (a) N fe) 6 AS COASTAL RIDGE : ° NY o 4 cls o < ° ° w - + x w KEY oO 2 " © SEEDED 2 N Lok @ + NOT SEEDED =x N HF 2 ° ° S fo) c a 6 WY 0.5 CONVECTIVE \ COAST Fae ° + 4 < i ° A = + =! x INCHES= VI > NY (b) 2 ° | 1 | =x Oo 0.5 1.0 1.5 2.0 N ISLANDS ° Fie. 3—Comparison of island versus target rainfall under stable and unstable storm condi- tions N 2 NN : ISLANDS a ah nets _ue \N sof ees 1 : _—TemP-0.P. 1958 | 6 SS == AIR TEMP °C) | S a 20' ‘22 24 ‘02 ‘o# ‘os’ ‘os i | ee FEB. 24 FEB. 25,1958 HT Fic. 2—Hourly rainfall averaged over oro- ail graphic regions for the low-level stable storm of February 24-25, 1958 complicated example of this structure. Figure 2 shows the hourly rainfall distribution of this storm, over (a) the island control area and four east-west strips of target, (b) the coastal plain, (c) the first ridge, (d) the valley, then (e) the next ridge to the north. The maximum occurs in the coastal plain and the first ridge. These same storm characteristics have been observed in Sweden by Bergeron [1949] and are there dis- cussed in illuminating detail. Figure 3a shows the scatter diagram of the island control stations against the mainland tar- get stations for the stable storms of 1958. The rain pattern is consistent from one stable storm period to another. Figure 3b on the other hand shows the scatter diagram for the unstable storm periods of the same year. Note that the slope of the regression TIME -HEIGHT STORM STRUCTURE Fre. 4—Time-height cross section over Santa Barbara for a typical convective storm of April 2-3, 1958; broken and solid lines as in Figure 1 404 line is markedly different and that the correla- tion has degenerated considerably. The storm of April 2, 1958, Figure 4, is an ex- ample of deep instability. Figure 5 shows hourly rain distribution. Here the lift starts close to the coastal ridge and there is little precipitation on the coastal plain, and the islands are missed com- pletely during long periods of the storm. This might be interpreted to mean that at times cy- clonic component of the storm produces no pre- cipitation while the orographic boost sets off substantial rain. There are many significant phenomena that repeat several times during a season, that we have not begun to tie down quantitatively yet. A distinct frequent and spectacular one consists INCHES 18 20 22 24 APRIL 2 CLEMENT J. TODD of plumes of precipitation that point back to the high points on the ridges of the Channel Islands. There are silver iodide generators on the Chan- nel Islands, and the first year we thought that we had a simple observable effect of seeding. The plumes, however, occur when the generators are off as well as when they are on. Another interest- ing phenomenon which has appeared several times is a plume of precipitation that points back to the channel between the two main islands, ap- parently identical to what Fujiwara [1958] has observed in Japan. Precipitation mechanism—The possibility of discriminating between the condensation-coales- cence and the ice-precipitation processes from ground observations seems good. As reported by SAN RAFAEL RIOGE SANTA YNEZ VALLEY COASTAL RIDGE ISLANDS 04 06 os 10 12 14 APRIL 3,1958 Fre. 5—Hourly rainfall averaged over orographic regions for the typical convective storm of April 2-3, 1958 PRECIPITATION IN WINTER STORMS IN CALIFORNIA MacCready and others [1958], both the drop-size distribution and the potential gradient have characteristics indicative of the precipitation ori- gin. When the radar and vertical cross section indicate that the precipitation must be warm- cloud origin, the drop distribution follows the Blanchard type and the potential gradient shows fair-weather field. When the evidence points to ice-precipitation origin, the drop spectrum fits the Marshall-Palmer distribution and the po- tential gradient goes negative, or fluctuates, and 405 may show discharges [MacCready and others, 1958]. In Figure 6, Drop Samples 1 to 9 are given as dots and show good agreement around the straight line representing idealized Blanchard distribution; while Samples 10 and 11, the broken lines, show marked disagreement. Figure 7 shows samples 10 and 11 agree well with Mar- shall-Palmer distribution line. Figure 8 shows the potential gradient record for the period. Note the change just before 20h 00m. Radar indicated that Samples 1 to 9 were warm cloud 10% == == 5 ae ee 5 ne ae ae 3 2 ot-—4 \ | 5 Jian = 3 ° 2 3 lO iN = BS ee ee “ly Np (M 2MM 2 4 6 8 lo 12 14 16 18 20 2D Fic. 6—Rain with warm-cloud origin is expected to have drop size distribution following the straight line; dots show agreement of Samples 1-9; broken lines show poor fit for Sample 10 and 11 Z Z pu +4 | | | 3 3 4 5 6 AD Fic. 7—Raindrop size distribution expected from ice origin rain is shown by straight line; dashed line shows goodness of fit of Sample 10 and 11 origin and that ice precipitation started just before 20h 00m and is represented in Sample 10 and 11. Figure 4 is a time-height cross section of this storm. The warm cloud precipitation occurs when the top of the moisture layer is lower than —5°C. Ice precipitation starts when it goes above —5°C. Incidentally, this storm was seeded. Ice precipitation becomes general when the top of the moisture layer is above —15 or —20°C. Sometimes the drop size distribution indicates that the two precipitation processes occur to- gether. We have not yet been able to go far enough to separate the artificially induced and natural ice precipitation on anything approaching the DISCUSSION general case. We will have to intensify our phys- ical measurements. Equipment is now on hand, such as vertical radar, electronic raindrop size counters, along with more potential gradient devices and nuclei counters. These did not re- ceive full field application this year due to the history making dry period the latter half of the seeding season. In addition to the above it would be very helpful to make coordinated aireraft ob- servations on top of the storm. Comments—Mesoscale analysis combined with appropriate physical observations will certainly be the backbone of seeding analysis. In order not to use up all available degrees of freedom it is of utmost importance to make intensive use of mesoscale analysis of historical storms. This is especially true here in Southern California where a relatively good network of upper-air soundings provides an extraordinarily good chance of re- lating mesoscale structure and seeding effects, where seeding has gone on for ten years now and where two steel foundries are highly suspected of producing seeding anomalies [MacCready, 1957]. Conclusions—As we become skillful at using our physical tools, we have the possibility of de- veloping greatly increased sensitivity of test, to a degree where we will be able to check hy- pothesis of when, where, how much, and under what conditions seeding is effective. Acknowledgement—This research was sup- ported by the National Science Foundation and the Department of Water Resources, State of California. REFERENCES Bercreron, T., The problem of artificial control of rainfall on the globe, Tellus, 1, no. 3, 1949. Fusiwara, M., Formation of stationary rainbands, Proc., Seventh Wea. Radar Conf. I-33, 1958. MacCreapy, P. B., Jr., T. B. Smrru, C. J. Topp, ann K. M. Bresmer, Nuclei, cumulus, and seedability studies, Final Report of the Advisory Committee on Weather Control, pp., 137-200, 1957. MacCreapy, P. B., Jr., T. B. Surry, anv C. J. Topp, Discrimination between condensation-coalescence and ice-crystal-produced precipitation, Proc., Sev- enth Wea. Radar Conf. A-17, 1958. Discussion Dr. Tor Bergeron—I like this paper very much. Especially, I appreciate the fact that we see here the influence of the orography. That is very much to be appreciated, and of course, you have also used every other means at your disposal for the physical analysis of these precipitation patterns. I would like to repeat what I said in my open- 407 ISSION Ta DISC UOLNLYSIP oZIS payVUIFLIO dot OF Phop WARM [voIdA} WoOIF SoduUBYO UOTYNIIYSIP aZIs doip way [TT pue OT opdueg YIM vAtjesou OF Burs daivys ojou ‘ueye, otaM TT Ysnosy} [ sopdueg usyM WA04s BuLnp vow} \uoIpels [BIyUI}OG—S “D1 BS6! Tindv 2 ore! 0002 ocoz oo1z oeiz oozz oczz ooez nin ae hg r T 408 ing lecture, that I should like to have more con- nection between the different scale ranges from micro over meso to macro scale. In my termi- nology this means from the cloud particles to the individual clouds and from there to the pre- cipitating systems as seen in the synoptic scale. During most of the discussions on radar studies, which were quite admirable in themselves, I could not determine what the general synoptic situation looked like. I think it is important to have this in papers. DISCUSSION Dr. Walter Hitschfeld—I want to know what Mr. Todd meant by the plumes that were con- tinually coming from the island toward the coast? Mr. C. J. Todd—Well, they were streams of echo, like smoke plumes. But they did not start at the island; they would line up in straight lines of precipitation and the extrapolation of these lines would point right back to the ridges on the island. Artificial Nucleation of Orographic Cumulus Clouds Louis J. Barran anp A. RicHarp KASSANDER, JR. Institute of Atmospheric Physics, University of Arizona, Tucson, Arizona Abstract—A brief summary is given of the results of randomized cloud-seeding ex- periments carried out durimg two summer seasons. Orographic Cumuli were seeded with an airborne AgI generator. The results to date have suggested that seeding causes important changes in the physical processes involved. It is planned to continue the experiments. Introduction—During the last two years, the University of Arizona has been carrying out a program of cloud-seeding research directed to- wards the study of the effects of silver-iodide nu- clei on supercooled orographic Cumulus clouds. Clouds over the Santa Catalina Mountains in southeastern Arizona were studied. Since the program is still in progress, this note is a brief summary of some aspects of the research. When the research is completed, the results will be published in the geophysical Jour- nals. Design of excperiment—The design of the seed- ing experiment was evolved with the assistance of K. A. Brownlee and W. Kruskal of the De- partment of Statistics of the University of Chi- cago. Briefly, the procedure involved an objec- tive prediction, made prior to 09h 00m MST of each day, as to whether or not Cumulus con- gestus or Cumulonimbus clouds would form over the Santa Catalina Mountains. The main cri- terion for the prediction was whether or not the precipitable water at Tucson, Arizona, equalled or exceeded 1.10 inches. When this occurred, the day was considered to be suitable for seeding, and an envelope was opened which specified which of two suitable days would be seeded. If more than one unsuitable day separated two suitable days, the first day of the pair was re- jected and a new pair was started. The scheme of randomized pairs was adopted in order to take into account day to day correlations and to assure that there would be an equal number of seeded and not-seeded days. The actual seeding was carried out with an Australian-type airborne silver iodide generator suspended under the wing of a Supercub air- plane. The generator has been made available through the cooperation of the University of Chicago. The flight plan involved repeated passes at about the —6°C-level along a track 409 upwind from the mountain range. The pilot nor- mally started the generator at about 12h 30m MST and continued his flight until all the seed- ing material was exhausted or the burner went out. Normally the seeding period was of the order of four hours. The generator consumed a 20% solution of silver iodide in acetone at a rate of 2 to 24% gal/hr. Observations—In order to permit studies of cloud and precipitation processes the following observations were taken: (1) visual cloud prop- erties were recorded on a pair of carefully cali- brated ground-located K-17 aerial cameras from which accurate estimates of cloud locations and dimensions could be measured; (2) the location and spread of precipitation echoes were ob- served with a vertically scanning 3-cm radar set; (3) rainfall was noted with a network of 29 recording rain gages; and (4) visual observations were made of the time and location of cloud-to- ground lightning strokes. Results—The experiments conducted during the first two years suggest that AgI seeding caused some important changes in the natural cloud processes. During each summer 16 pairs of days were studied. Rainfall—When data from both years were combined it was found that the mean rainfall per gage was 30% higher on the seeded days; however, the probability that the observed dif- ferences in the mean rainfall occurred by chance was quite high, about 0.14. This value was ob- tained from a sign-rank test which made use of a ranking of the differences of the mean rain- fall of pairs of days. A comparison of the ex- treme rainfalls on seeded and non-seeded days showed greater differences, but the statistical confidence of a real difference was still not suffi- ciently high to be acceptable. Heights of thunderstorms—An objective way to measure the relative frequencies of large 410 6 Se 2 He piss Girl Sy mee 32 75 69 47 34 20 " 6 7 2 Jt ay Ea 2 of 2 u 8 NS 36 7 72 38 25 " 12 | 8 100 Veeco — Seeded (320 Clouds) \ --- Not S. (297 Clouds) oi gt Ht 80 q H ' es 4 wn x) nee | Cnn nn I I 2 crs = 2 60 oO WwW se = = = 40 = WwW oO a WwW a , 20 Note: On seeded 7 days 19 clouds and on not-seeded days 13 clouds with T<-42°C. All had echoes. +6 0 -6 -I2 -I8 -24 -30 -36 -42 CLOUD TOP TEMPERATURE °C Fic. 1—Fraction of clouds observed to extend to the indicated temperature levels which con- tained precipitation echoes; data on which the curves are based are shown at the top of the diagram; ten clouds, five in each sample, had temperatures above +6°C and have not been plotted thunderstorms is to take radar observations every 30 min and note whether there is at least one cloud extending above any particular alti- tude. When this was done, it was found that dur- ing the seeded days there were about twice as many echoes extending above 30,000, 35,000 ft, and 40,000 ft. A sign-rank test in this instance showed that the probability that the differences in the number of clouds extending above 30,000 ft occurred by chance was 0.05. Lightning—Lightning observations were not taken in 1957. However, in 1958, it was found that on the seeded days there were about nine times more lightning strokes than on the not- seeded days. A sign-rank test revealed that the probability of chance occurrence of the observed ranking of the differences of strokes on pairs of days was about 0.015. It was interesting to find, that notwithstanding the large difference in lightning frequency, there was little or no dif- ference in the number of lightning-caused forest fires. One might offer the explanation that the higher lightning frequency was offset by more BATTAN AND KASSANDER rain which reduced the likelihood of the forma- tion and spread of fires. Initiation of precipitation—By means of the cloud camera and radar data, it was possible to note the vertical extent of clouds (and thus cloud-top temperatures) and whether or not they contained precipitation. When a sufficient number of clouds have been examined it be- comes possible to speak of the ‘probability of precipitation’ in clouds whose summit tempera- tures are between —12 and —18°C, or any other temperature interval. Figure 1 shows a summary of the observations made during 1957 and 1958. The smoothed solid and dashed curves were drawn in by eye. It is quite obvious that on the seeded days, the likelihood of precipitation was greater than on the non-seeded days. The fairly uniform shift of the curve towards the left lends support to the belief that the effect is real, and that in fact, the AgI seeding caused the forma- tion of precipitation in clouds which would not have precipitated naturally. If the nearly straight parts of the curves are extended to the abscissa (dotted lines) it is found that the ‘not-seeded curve’ intercepts the abscissa at about —17°C. It might be argued that this result is reasonable because observa- tions of ice nuclei in the atmosphere show that in general, the concentrations at temperatures above —15°C are small. As the temperature is reduced the concentration increases. It appears reasonable to assume that the dotted-dashed curve represents clouds in which the ice-crystal mechanism was effective in causing precipitation. An extension of the ‘seeded curve’ shows that it intercepts the abscissa at about —9°C, a tem- perature just below the value at which AglI crystals can be expected to become effective as ice-crystal nuclei. If the interpretations of the significance of the dotted curves are correct, then one is led to the assertion that those precipitating clouds which fall to the left of the projected curves produced the precipitation by the condensation-coalescence process. Summary—In view of the fact that this re- search is still in progress, the authors feel that they are still not ready to draw final conclu- sions. Although the results to date pomt towards the conclusion that seeding produced important effects, it is vital that more data be compiled in order to be sure that the results have not been DISCUSSION brought about by chance. This brief note has been written as a progress report for others working on similar problems. After more data are collected, it is hoped that some of the press- ing questions in the important area of cloud seeding can be given definite and unequivocal answers. Acknowledgments—The authors gratefully ac- 411 knowledge the contributions to this program made by personnel of the central and the Tuc- son offices of the U. 8. Weather Bureau. The main financial support for this work has come from the National Science Foundation and the State of Arizona. In 1957, the research pro- gram was conducted as a cooperative effort with the University of Chicago. Discussion Mr. J. Namias—The evidence looks very in- teresting here, and very convincing at first glance. I would just like to ask about the method of selection. You pointed out, if I understood correctly, that the criterion of whether you would have clouds was determined from the amount of precipitable water? Dr. L. J. Battan—That is correct. Mr. Namias—And then you chose a pair of days with the seeded day determined by the process of randomization. The question is whether you had a bias when you seeded on either the first or the second day. It is therefore very important that the data on which the evi- dence is based is evenly distributed between the first and the second day. Dr. Battan—The data were very well dis- tributed. This was one of the things the statis- ticians looked up right away. Mr. Namias—That would be a rather impor- tant consideration, for if there were any bias, your criterion would imply a certain synoptic situation, the second day of which is not at all independent of the first, so you could have a certain situation that would either augment or inhibit. But if the evidence is evenly distributed between the two days, my point does not hold. I was thinking also of the possible factor in- volving the preceding day’s precipitation and its effect on the surface. As I pointed out earlier, a relationship between thunderstorms occurring in southern Texas on one day and their lack in the same area on the subsequent day has been as- cribed to wetting of the ground the first day. Dr. Battan—This is exactly why we used ran- domization by pairs of days, because if you ran- domized by day, one might be led to seed or not, seed on three or four consecutive days. With the present scheme the most you can get is two con- secutive seeded or not-seeded days. Dr. R. D. Elliott—I might add that the State of California Forestry Service has conducted cloud seeding experiments in the northern part of the State for a number of years to see if lightning could be reduced, and the answer so far seems to be that the hghtning is actually in- creased on the seeded days. The experiments are randomized, but the outstanding factors are that the precipitation is mereased, and this fits very well also with what Dr. Singer said about the Swiss Hail Suppression Experiment. Mr. C. EB. Anderson—I want to raise a point about whether or not these experiments are truly randomized from the seeding-agent standpoint. This would apply to both the Swiss experiment and to the ones you conducted in New Mexico, where you released silver iodide on a particular day for seeding, and then did not seed the next day. I recall the seeding experiment that the Weather Bureau conducted on the West Coast as part of the Artificial Cloud Nucleation Project which the United States Government sponsored some five years ago. During this time we had made some trials in cooperation with Ferguson Hall who was in charge of that project in the State of Washington, with release of zinc sul- phide tracer materials from the aircraft at 15,000 ft. We were quite surprised to find that the zine sulphide turned up (and this was during pre- cipitation at the release level) in the rain gages, not that day, but the next. Therefore I am just wondering whether or not, when you release this in the atmosphere, you can depend on its being removed overnight, so that the next day is truly a fresh sample. Dr. Battan—We do not have measurements, which can dispel this argument; but I find it hard to understand how it can happen. Cloud Seeding in the American Tropics Wauuace E. HowEiu W. E. Howell Associates, Inc., Lexington, Massachusetts Abstract—Cloud-seeding projects that have been carried out in the American trop- ies are described, and evaluation of the results are summarized and discussed in the light of existing models of precipitation formation. A new model based on a field of competition in which convective clouds develop is proposed and discussed to explain the effectiveness of seeding under weather conditions where clouds develop relatively slowly toward the precipitating stage. Introduction—We should hope that an ex- amination of the results of cloud-seeding trials in the tropics will reveal essential agreement be- tween the results observed and the expectations based on observations of the natural mechanisms of rain formation in the tropics and in labora- tory and theoretical studies of natural and arti- ficial mechanisms for the release of precipitation. Most of the trials of cloud seeding in the American tropics have been of a practical na- ture, intended to increase the rainfall for a spe- cific purpose or need, or, in a few instances, to diminish the force of locally destructive winds. The operations have been for the most part conducted by commercial firms and in a few cases by the agencies directly interested. The in- stances of cloud seeding performed by persons entirely uninvolved with the outcome have been with few exceptions incidental to other aspects of the investigation of cloud physics. In no in- stance known to the author have such seedings resulted in data suitable for evaluation to de- termine whether seeding applied for practical purposes could be effective. Up to the present time, no evaluations have been performed by any competent independent agencies of the practical seedings carried on in the American tropics, nor has any specific re- buttal been made to the reports by the cloud seeders of practically successfully results. It would be desirable, perhaps, to limit examina- tion of seeding trials to those carried out under impartial auspices in conformity with certain standards as to seeding agent used, the control of its dispersal into the air or cloud, the ade- quacy of rainfall data, and the objectivity of the procedures of analysis. For the present, how- ever, such a limitation would end our examina- tion at once, and so we must examine what is at hand, and substitute suspicion for the luxury of impartiality. Seeding experiences—A series of commercial projects conducted for the Francisco Sugar Co. is described next because it will serve to illus- trate the conditions under which a majority of the projects were conducted and the manner of their operation. The target covers some 3800 sq mi of nearly flat land for about 20 mi along the south coast of Camagiiey Province in east cen- tral Cuba, and extending 15 to 20 mi inland. It is shown as the two right-hand areas in the map, Figure 1. The climate has been described in de- tail elsewhere [Howell, 1953]. Operations were begun in the summer and fall of 1951, using six ground-based silver iodide smoke generators of the acetone-propane type which dispersed about 50 g/hr of silver iodide. These were located at various points in and immediately upwind from the target at points where instructions for their operation could be given by telephone, and they were operated in groups of two to four at a time on 33 days during a period of three months at the times and places judged appropriate by the field meteorologist on the basis of forecasts and local pilot-balloon observations. Subsequently, in 1952, similar operations were conducted over the same target for 11 months, encompassing most of the dry season and all of the showery season, and during several of these months op- erations were conducted also for the adjoining properties of several neighbors. In subsequent operations a different type of smoke generator was used, which burned string, impregnated with silver iodide, in a propane flame and dispersed silver iodide at a rate of about 10 g/hr, with about 15 generators situated in and upwind of the target. Operations were conducted in 1953 for five months which showed 412 CLOUD SEEDING IN THE AMERICAN TROPICS [o) A Florida a) TARGET AREAS AND metS RAIN GAGES Soke oumMaslON = 204 mis0 > = Scale of kilometers A Camagiey % Vertientes ° fe] Oi ewelts 5° A Siboney ° UES ° Noajasa Oa A y 2 N= ~ Om ° [ ON} pies =r me Santa | XN oe \ M each ea| eno » | ey) ! ° \ ° / a ° Jood iC Francisco 4 od ° oo ° oy et Rone ° CARIBBEAN oe ° gobaboe. eee ° ° SEA 7 , ea Fra. 1—Map showing rainfall stimulation tar- get areas and rain-gage locations in central and southern Camagiiey Province, Cuba a 15% increase in rainfall. In February and March of 1954, experiments were conducted on the spray seeding of warm clouds, but operations were suspended because of adequate field mois- ture. They were not resumed again until May of 1956, because of sugar marketing and milling restrictions, but have been conducted much of the time since then. Operations were somewhat upset by local political disturbances late in 1958, and some of the generators were put to uses other than those intended by the sugar mill, in- cluding perhaps some connection with an iso- lated dry-season shower that bogged down a column of tanks as it was about to close in on a large rebel encampment located within the tar- get. Perhaps some future historian will be able to tell us if this was the first direct use of cloud seeding to discomfit an enemy. There were several rain gages located in vari- ous sections of the Francisco property, and the adjacent properties also each had several rain gages. It was therefore possible to assemble a considerable network of gages, as shown on Fig- ure 1, with at least ten years of record, 1941- 1950, before the start of seeding. The first at- 413 tempt at an evaluation was made after the 1951 season by comparing the percentage of normal rainfall received during the operating period on the target with the percentage normal received on the surrounding plantations, and it was esti- mated that an merease of 26% had been achieved. After the longer operations of 1952 over both Francisco and some adjacent plantations, the evaluation was improved by using a regression analysis using the seasonal total rainfalls for the operated portion of the year for each year of the historical record. This evaluation indicated an increase of 28% with significance for the group of operations well beyond the one per cent level. By this time we had thoroughly scoured the countryside for rain gages, and from then on the composition of the control data was not changed except to drop the Lugareno gages—located un- der the cartouche of Figure 1—when it was found that they had no useful degree of correlation with the target. The evaluation of later years, however, was further refined by basing the re- gression on individual monthly rainfall totals instead of seasonal, and by transforming them to normality. The two evaluations made subse- quently have shown respectively 15% and 25% increases. Figure 2 shows the regression with the results of the 1956 operations. The probabilities of chance occurrence are arrived at by a one- tailed t-test, allowing for the size of the sample and the departure of the control variable from its mean. Where several months of operation of a project have been tested against a single re- gression, the t-tests have been combined into one. Seeding of warm clouds has been carried out, 30F Correlation coefficient r= .92 - 20 Probable error of r f= .029 3 15 r/f = 32 = ae) ihe a 5 °o a8 cz x2 | o> ol 5= j *unseeded month Lge gs © seeded month " Wk (e) " fo) | | 5 10 15 20 30 > X=x3 = Control zone monthly rainfall, May to November Fic. 2—Regression diagram illus- trating the results of cloud seeding at Francisco, Cuba, May to November, 1956 414 WALLACE E. HOWELL TasLe 1—Trials of cloud seeding in the American tropics | Operations Results Location Year = |Area - Category Agent | Duration Increase Probability sq.mi pet Atlantic off Florida 1947 Uninvolved | Dry ice 1 day | Conversion of stra- | tiform super- cooled clouds observed in hur- ricane Honduras 1948 Uninvolved | Water 1 day | Extraordinary rain- fall in dry season Hawaii 1948-49 Uninvolved | Dry ice | 15 days) Some showers thought to be trig- | gered Mexico, Necaxa 1949-592; 800) Practical Agl | 54 mo. +9 0.0001 Bolivia 1951 50) Practical Agl Uncertainty as to smoke trajectory Peru, Rio Chicama 1951-59 |3500) Practical Agl 80 mo +25 0.0001¢° Rio Mantaro 1951-56 |2500| Commercial | Agl 30 mo +20 0.07 Cuba, Francisco (1951 300) Commercial | Agl 4 mo +26 ae Cespedes |1952 100, Commercial | Agl 3 mo +25 0.04 Ermita 1952 50) Commercial | Agl 7 mo +46 0.005 Francisco 1952 300, Commercial | Agl 11 mo +28 Macareno 1952 150, Commercial | Agl 5 mo +35 0.08 Najasa 1952 50| Commercial | Agl 6 mo +33 Hawaii 1952-53 | ...| Uninvolved | Water se ave Cuba, Los Canos 1953 100, Commercial | Agl 3 mo +20 Macareno 1953 150! Commercial | Agl 6 mo +20 Cuba, Baltony 1953 30, Commercial | AgI 3 mo +15 we Preston, Boston 1953 500) Commercial | Agl 3 mo +19 0.002 Francisco 1953 400) Commercial | AgI 5 mo +15 Pe. Puerto Rico, Fajardo 1953 250| Commercial | Agl 2 mo +14 etch Nearby waters 1953-54 | ...| Uninvolved | Water 5 mo ie 0.024 Cuba, Macareno 1954 300/ Commercial | AgI,wa- | 2 mo +61 0.02 | ter Puerto Rico, Fajardo 11954 250,/ Commercial | Agl | 2 mo +13 wate Cuba, Baltony 1955 30, Commercial | AgI | 3 mo +12 0.03 Puerto Rico, Fajardo 1955 250| Commercial | AgI,wa- | 2 mo +27 0.07 ter | Cuba, Francisco /1956 550/ Commercial | Agl 7 mo +25 0.005 Colombia, Santa Marta 1956-57 | 350) Commercial | AgI 12 mo. | 39 decrease in wind damage per stormy day Cuba, Havana-Mantanzas 1956 4000) Commercial | Agl 3 mo +27 0.03 Manati 1956 400, Commercial | Agl 3 mo +9 0.40 Manati 1957 400, Commercial | Agl 8 mo +15 0.21 Puerto Rico, south coast 1957 400| Commercial | Agl 2 mo +42 0.05 Cuba, Baltony 1957 30| Commercial | Agl 2 mo +20 0.06 Hispaniola, Romana 1957 600) Commercial | Agl 4 mo +31 0.10 Cuba, Esperanza 1957 120; Commercial | Agl 2 mo +27 0.06 Los Canos 1957 100| Commercial | Agl 2 mo +21 0.02 Florida, Boca Raton 1957 Uninvolved | Agl No effect of seeding observed Average of all AgI seedings (24 cases) +22 Average of all AgI and water seedings (3 cases) +43 * Excepting 1952. b On commercial basis prior to 1955. ¢ Separate evaluations of runoff showed increase of 35%. 4 Water seeding with coarse spray in tops of trade Cumulus. Probability figure refers to likelihood that seeding caused precipitation in a cloud that would not otherwise have precipitation [Braham and others, 1957]. CLOUD SEEDING IN THE AMERICAN TROPICS in the projects included in this study, by spray- ing either plain water in droplets with a mean diameter about 70 microns or by spraying sodium chloride solutions with a mean droplet diameter about 40 microns. In either case the spray was introduced at or near the bases of the clouds in the updrafts. In the discussion the process has been referred to simply as water seeding. In Table 1, which shows the results of cloud- seeding trials in the American tropics, distinc- tion has been made among three classes of proj- ect: (1) commercial, those conducted by a cloud seeder for a client where the cloud seeder pre- sumably is motivated to show a positive result; (2) practical, those conducted by an agency which is motivated by pecuniary interest to ob- tain an accurate evaluation of the result, either positive or negative; and (3) uninvolved, those conducted by an agency having no involvement other than the search for knowledge. The table is not exhaustive, and I know that there are other trials about which my present information is too meager to make inclusion of them in this examination useful. The individual percentages of increase cited in this table are extremely varied in reliability, some of them seem well founded, others are quite dubious. Hence it is unlikely that great confidence will be placed in the mean increases shown, but it is nevertheless interesting that the combined water and AgI seeding seems to show a clear advantage over AglI seeding alone. Certain among these data are worthy of closer attention, however. They represent the cases where a target-control relationship has been es- tablished, usually subsequent to a first season of seeding; and then the same relationship, un- 415 altered in any significant degree, has been used to evaluate subsequent seedings. There are six such cases, and they are tabulated separately in Table 2. These represent seeding trials where the game has been played according to pre- established rules. It will be noted that the mean increase of 19% among them compares closely with the 22% among all cases. These values, especially the ones representing probability of chance occurrence, should still probably be regarded with reservations. It is conceivable that there are secular changes in the climates of target and control zones that would alter the target-control regression sufficiently between the historical period and the seeding period to affect the value of the test, though such changes remain to be demonstrated, and it is doubtless true that other possible selections of control region or historical period or both would have produced different results. However, it seems that it would take an extraordinary de- gree of prescience on the part of the evaluator to select a control that would at some future time be biased in favor of a false indication of seeding influence. Leaving to the statisticians the question whether the figures tabulated afford reliable proof that the seeding increased the rainfall, one thing nevertheless is clear: a hypothesis that silver iodide seeding is incapable of increasing the rainfall in tropical clouds over land is open to serious doubt. The rest of this paper will be devoted to examining the implications of this statement. Should AgI seeding affect tropical Cumulus ?— The development of precipitation in shower clouds, both in the tropics and in middle lati- tudes, has been the subject of extensive study. TasLe 2—Evaluations of operations conducted after establishment of control area and historical period and evaluated according to established rules of the game >% Sais Location Year Seeding agent a $ Bs Remarks 2g 3> Cie 24 4 a pet Mexico, Necaxa 1950-58 | Agl +9 | 0.0001 | Orographic, maritime air Peru, Rio Chicama 1952-58 | AglI +25 | 0.0001 | Orographic, continental air Cuba, Baltony 1955 Agl +12 | 0.03 Valley location Puerto Rico, Fajardo 1955 AglI, water +27 | 0.07 Windward shore, mostly flat Cuba, Francisco 1956 AglI +25 | 0.005 | Flat, lee shore Cuba, Manati 1957 Agl +15 | 0.21 Flat, windward shore Average +19 416 In a census of tropical clouds Byers and Hall [1955] have shown that over the sea the likeli- hood that a cloud contains rain is related closely to the size of the cloud, and that all clouds were found to contain precipitation before they reached a size that would bring their tops above the freezing level. In clouds over the land, both in Puerto Rico and in the central United States [Battan, 1953], weaker connection was found between the size of clouds and the probability of precipitation being present in them, but it was concluded from the timing and position of ap- pearance of radar echoes in developing shower clouds that the onset of precipitation was due to a coalescence process. A fairly well-developed model for the formation of precipitation by a coalescence process has emerged from the sug- gestion by Houghton [1938] that the few parti- cles at the large end of the drop-size spectrum play an important part and the work of Bowen [1952], Mason [1952], Ludlam [1951, 1952, 1956], Keith and Arons [1954], Hast [1957] and many others in developing quantitative expressions for the growth of droplets by coalescence. These have been used by MacCready and others [1957] to develop graphs which he employed success- fully in Project Shower to predict the time of onset of precipitation and to indicate that this precipitation originated by coalescence rather than by the Bergeron-Findeisen process. It has been widely concluded as a result of these ob- servations and analyses that the presence of ice crystals plays no part in the onset of precipita- tion from most convective clouds and only a secondary role in subsequent developments, and that therefore, although a basis is established for supposing that water seeding may sometimes stimulate Cumulus clouds to produce showers, the supposition that AgI or dry-ice seeding could have such an effect is discouraged. If the appar- ent effectiveness of AgI in stimulating precipita- tion is to be given a reasonable explanation, it must be through the development and verifica- tion of a somewhat modified model of shower formation in Cumulus clouds. Considerations for a new model—Our first survey of cloud conditions in Cuba, undertaken in the summer of 1951, showed the regular oc- currence of convective clouds over the land which reached the freezing level a considerable time, frequently hours, before the first onset of precipitation, and the phenomenon of ‘cirrus pumping’ was also observed which appeared to indicate that some clouds reached even to the WALLACE E. HOWELL level of —40°C temperature where homogeneous nucleation occurred and caused the cloud tops to glaciate without increase of particle size, de- taching themselves and floating off as separate cirrus umbrellas (see Fig. 3). The marked dif- ference in characteristics between the clouds over the land and those over the water was noted, as has later been well documented by Malkus {1958, 1955], with the generally higher level of convective activity in the land clouds. These observations appeared to indicate that considerable volumes of cloud frequently endured for some time in a supercooled state without raining, or before the onset of rain, and led us to believe that AgI seeding had at least a rea- sonable chance of being effective in releasing rain. These and subsequent observations led us to distinguish between two typical sequences of cloud development leading to showers. Sequence I is characterized by the nearly continuous and rapid growth of the cloud from humble be- ginnings, through the congested stage and on to the formation of Cumulonimbus, the entire de- velopment taking place in perhaps half an hour to an hour. Such a sequence occurs typically when the conditional instability of a deep moist layer is released by a definite impulse such as the arrival of a sea-breeze front. As the cloud develops, rudimentary precipitation particles are formed at a much faster rate than they are lost by evaporation at the top and edges of the clouds, and precipitation begins promptly as soon as the first-formed particles are sufficiently aged. The time interval during which artificial influences could operate to speed up the forma- tion of precipitation is extremely short, with consequent small likelihood of any considerable effect being produced by seeding. Rainfall is likely to be widespread in the general region where cloud development occurs. Sequence IT is characterized by a much more gradual increase in the state of development of the clouds, even though convective activity re- mains high all the while. Typically many clouds of nearly the same size may be seen that display great activity of growth in their lower parts and dissipation in their upper parts, the average size of the clouds gradually increasing and their num- ber decreasing. This state of affairs may con- tinue for many hours until it is ended by the afternoon decrease of diurnal heating, or it may be brought to an end by the development of pre- cipitation in one or another of the clouds. When CLOUD SEEDING IN THE AMERICAN TROPICS Fie. 3—Towering Cumulus in tropical air over land, showing umbrella of cirrus recently separated from top of a Cumulus tower which has since dis- sipated under circumstances such as these precipitation does become well established in one cloud, it is hard to avoid the impression that a marked in- crease in the rate of growth of the cloud is often connected with the onset of precipitation, ac- companied by the degeneration of other clouds in the vicinity. New towers rise from the top of the precipitating cloud to much greater heights than formerly and take on the aspect of Cumulo- nimbus; the cloud base darkens; and the im- pression of roiling, tumbling growth-and-dissi- pation activity is replaced by one of swift organization of a large-scale convective cell. The ensuing rainfall, while sometimes heavy, is likely to be much more spotty than that accompanying Sequence I. Both sequences, together with gradations be- tween them, were observed during our seeding activities in Cuba. After the first season’s work we drew daily isohyetal maps [Howell Associates, 1952] and examined them for connections be- tween the pattern of rainfall and the pattern of seeding. It was immediately noticed that about a third of the maps showed good correspondence WALLACE E. HOWELL Generator Scale of kilometers fe) 10 20 Sl —— HODOGRAPH OF WINDS ALOFT Generator 0 10 20 30 a Scale of knots Arrows represent one hour of mean wind travel _30 CARIBBEAN SEA Fra. 4—Isohyetal map of rainfall and hodograph of winds aloft for cloud seeding trial, October 18, 1951 between the areas of rainfall and the positions of the smoke plumes at from one to two hours of wind travel from the generators. Another third of the maps showed some weak connection, and in the remaining third no connection was found. Figure 4 illustrates an exceptionally good con- nection. Furthermore, it was noticed that most of the days when there were isolated heavy showers showed a good connection, while most of the days when rain was more or less general showed weak connection or none at all. The analyses suggested that the seeding was most effective under Sequence II conditions, and it is these conditions that form the basis for a new model of shower development. Although it was not found possible to treat these results rigor- ously, they together with the pilot balloon runs and local cloud observations gave the field me- teorologist a feeling of considerable confidence in directing the seeding effects onto the target. The _ field-of-competition model—We have taken for our model not a single cloud but a portion of the atmosphere, overlying a uniform ground surface, extensive enough to contain sev- eral convective cells. We suppose that heat and moisture are added slowly at the bottom of this atmosphere, creating a ‘moist layer’ of condi- tional instability which gradually deepens through the upward transport of heat and mois- ture by convective clouds. Horizontal transport is presumed sufficient to maintain more or less horizontal uniformity throughout the region. Above the moist layer the air is assumed to be relatively dry and with slight positive stability. This part of the atmosphere constitutes a field within which a number of convective cells compete for the potential energy that they can convert to air motions. At each stage in the heat- ing and deepening of the surface layer there is an optimum size of convection cell that repre- sents a balance between the advantages of larger cell size for drawing energy from more air and the disadvantages of lengthening horizontal transports, the optimum size becoming larger as the surface layer deepens; and all the competing cells will tend to approach this optimum size. Within the field of competition there will there- fore be a number of clouds that in their mature stage are of nearly equal size and in which the probability of precipitation is nearly equal. Following the model developed by Ludlam [1956] and others, we consider the clouds as formed by a series of bubbles or ring vortices that entrain air from their environment, pro- ducing energy in the lower part of the cloud, while at the top and sides of the cloud exchange of air with the environment causes evaporation, cooling, and subsiding motion. The bubbles, while within the cloud, lose water by mass exchange but not by evaporation, but once they reach the cloud top they begin evaporating rapidly, cool- ing and falling back as they dissipate but leaving a moister environment for the next bubble. Cloud droplets form in a variety of sizes depending on CLOUD SEEDING IN THE AMERICAN TROPICS the updraft at the condensation level and on the size on the condensation nuclei, and we may regard some fraction of the largest cloud drop- lets as rudimentary precipitation particles that, if they survive long enough within the cloud, will become raindrops. The rate of formation of rudimentary precipi- tation particles in a given cloud depends on the concentration of giant hygroscopic nuclei, oc- currence of collisions, ete. Survival of them in the evaporating part of the cloud, or if they are thrown out of the cloud, depends upon their being large enough to maintain their existence until they are re-entrained or fall back into the cloud. Ludlam [1956] has estimated that a di- ameter of about 150 microns is critical for drop- lets carried by a bubble out the top of a cloud; those smaller will be lost; those larger will fall back into the cloud and continue growing. The establishment of precipitation, we assume, re- quires the survival of some critical number of rudimentary precipitation particles in the region of the cloud where the liquid-water content is high. Or, to express it another way, the cloud must accumulate a certain quantity of particle seniority in its rain factory. If the operating force is insufficient or the turnover is too high, this necessary quantity of seniority will not be accumulated, and although some few raindrops may fall, precipitation will not be established. But when this critical seniority is reached and precipitation is established, a mass of water that approximates, according to Braham [1952], 20% of the water entering the convective circulation (and probably with respect to the water in the active portion of the cloud a somewhat higher percentage) is removed by the rain and falls from the cloud. This water represents not only a loss of mass from the cloud but also a gain of the heat that would otherwise have gone to re-evaporate this water in the upper branch of the circulation. Both these effects operate in the direction of increasing the convec- tion in the cloud in which rain forms as com- pared with similar clouds nearby. Now, during the time that there are a num- ber of clouds having approximately the same size, the ascending air currents will tend to oc- cupy the maximum area consistent with unsta- ble motion according to the slice method of computing instability. But if one single cloud outstrips its neighbors and grows significantly higher, it will enter a slice of the atmosphere where it is the only rising current present, and 419 hence the instability it experiences will be much greater; its convective circulation will increase rapidly in magnitude and depth. The energy- producing part of the circulation is then able to draw on the whole depth of the moist layer as a source of moisture and energy, whereas for- merly only the lower portion of it was available so. These several effects working in concert cause the precipitating cloud to grow rapidly in size and in the intensity of its circulation, suppressing the unsuccessful competitors. Figure 5, which is a photograph of a Cumulus cloud 13 min after being seeded by dry ice published by Kraus and Squires [1947] and reproduced here through the courtesy of P. Squires, appears to show this ef- feet occurring under conditions similar to those of our model. At any time during the gradual growth of the convective clouds, we may describe their collec- tive approach to the rain stage as a frequency distribution of the property that we have called quantity of seniority in each cloud’s rain factory, which can be represented in the manner of Fig- ure 6 as an ogive of cumulative probability of the seniority having surpassed the value critical for production of rain in some one of the clouds within the model. If there are many clouds in the group, by the time the percentage of clouds surpassing the critical limit rises to a few per- cent (at a ‘seniority’ of about 12 on Figure 6), it becomes very likely that rain will have begun somewhere, in one of the clouds within the field of competition. We then presume that this oc- currence will be followed by rapid growth of the successful cloud and depress the level of conveec- tive activity elsewhere, causing the average sen- lority of the remaining clouds to diminish again. Let us consider the effect on this model of seed- ing one of the clouds with water droplets or hygroscopic particles during the time that the group of clouds is approaching the stage critical for the formation of rain somewhere in the group. The seeding in effect employs in the seeded cloud a large number of pre-aged rudimentary pre- cipitation particles and thereby increases the quantity of seniority in the operating force, and places the seeded cloud somewhat higher on the seniority scale than its neighbors, perhaps only by a few percent, or one unit higher on the arbi- trary scale of Figure 6. But it will be noted that before the group as a whole reaches the point where the formation of rain in it becomes likely, the seeded cloud will have a very good chance of becoming a rain-producer. 420 WALLACE E. HOWELL Fra. 5—Photograph of a Cumulus cloud 13 min after seeding with dry ice (Courtesy of P. Squires) a 3 “ Arbitrary scale of average cloud aging or 'senority ny a roy ° 20 40 60 80 100 Percentage of clouds surpassing critical limit Fie. 6—Ogive illustrating an assumed typical relationship between the mean aging of a group of clouds in the field-of-competition model and the probability of precipitation onset somewhere in the group And now let us consider the effect on our model of seeding one of the clouds with AgI. No effect is to be expected until the top of the cloud reaches a temperature of about —5°C. But when this temperature is reached in the cloud, some ice crystals will appear and some of the rudi- mentary precipitation particles will freeze, either because of infection with AgI or through collision with an ice crystal. The volume of air within which these frozen particles will continue to grow encompasses all that within which the air is satu- rated with respect to ice and therefore is con- siderably larger than that within which the un- frozen particles can grow; and even in dry air the frozen particles evaporate more slowly. Fur- thermore, as Douglas [1960] has shown, the fro- zen particles may enjoy as much as a two-times advantage in growth rate by accretion over their unfrozen neighbors. The result is that the rate at which the cloud loses rudimentary precipita- tion particles is diminished and the rate at which these particles grow or ‘acquire seniority’ is in- CLOUD SEEDING IN THE AMERICAN TROPICS creased. In exactly the same way as with the water-seeded warm cloud, then, the seeded cloud is given an advantage that expresses itself in the form of a much improved chance that the seeded cloud will be the one in the group that will first develop precipitation. It will be noted that this effect of AgI seeding operates through the coa- lescence mechanism and that it is unnecessary to postulate the independent growth of new rudimentary precipitation particles in the form of ice crystals entirely by sublimation in order to account for an effect of the AgI seeding. When the seeding releases precipitation within the field of competition, the ensuing chain of events draws to the seeded cloud the energy from a much larger share of the atmosphere than it could otherwise have reached. In effect, the ‘signal’ energy released directly by the seed- ing is amplified many times over, and the mag- nitude of the output is determined not so much by the strength of the signal as by the energy resources of the system. The outcome will be sometimes the initiation of rain on a day when rain would not otherwise have fallen, in which event the precipitation efficiency of the model as a whole is increased; and sometimes the outcome will be to direct onto the target area the center of shower development that might otherwise have been elsewhere, and to a certain extent to increase the precipitation efficiency of the shower mechanism. Discussion—Of course, natural occurrences present all gradations between the Sequence I and Sequence II types of development described above. On the other hand, certain locations are more suitable for the occurrence of one sequence or the other. For example, we may contrast the situation of the Francisco target, already dis- cussed, where the usual trajectory brings air for some considerable distance over a rather uniform level terrain, with the situation of the Necaxa Watershed in Mexico and with the Boca Raton, Florida, site of the Project Seabreeze studies. In the latter two, strong localized impulses are available to initiate convection, the orography in the Necaxa location and the sea breeze at Boca Raton, so that one might expect more frequently to find Sequence I followed at these sites. In- deed, examination of the plots of cloud top height against time for the Project Seabreeze observations [MacCready and others, 1957] shows that in most cases the clouds more than doubled in height and reached altitudes greater 421 than 25,000 ft within less than an hour. The ef- fect of AgI seeding might therefore be expected to be less at these locations than on the Francisco target. Referring back to Table 2 we note that the rainfall stimulation at Necaxa is indicated to be less than that at Francisco, in accordance with this expectation. It has often been noted that horizontal shear in the wind sometimes decapitates growing Cu- mulus clouds, carrying away the portion of the cloud containing the best-developed rudimentary precipitation particles and thereby preventing or delaying the onset of precipitation. However, shear also contributes to the energy available for convection when the cells reach an appropri- ate size; and if the field of competition is char- acterized by vertical shear, a sudden jump in the growth rate of the clouds will appear when they approach the size at which they can utilize the energy of the shear for their growth. How- ever, this jump will probably appear throughout the field at about the same time, and indeed it may have much to do with the occasional de- velopment of Sequence I clouds causing more or less general rainfall. However, our experience in the tropics suggests that the jump usually does not occur until a cloud has begun precipitating, and that the shear energy then contributes to the selection of the favored cloud for still more vigorous development. The operation of the field-of-competition model suggests that the effects of cloud seeding will be extremely variable, often ineffective but sometimes extremely effective, with an average effectiveness that depends to some extent upon the habitual sequence of cloud developments over the seeded region. These characteristics are in- deed suggested by the data on actual seeding so far accumulated. The model further suggests that, if it is practical to isolate for experimenta- tion those situations characterized by Sequence IL developments, effects of seeding will occur that may be large enough to make their reality immediately apparent. Another implication of the model is that ex- periments performed in clouds situated over lo- calized sources of convective impulses, such as isolated mountain peaks or small tropical islands, while capable of making trial of the physical changes that may be produced within a single cloud by seeding, will tend not to demonstrate to full advantage the significance of the com- 422 petitive advantage that seeding may give to one cloud in relation to others. It is planned for the present to develop fur- ther the model that has been proposed here and to attempt to bring it to the poimt where ex- perimental verification of it can be sought. REFERENCES Batran, L. J., Observations on the formation and spread of precipitation in convective clouds, J. Met., 10, 311-824, 1953. Bowen, E. G., A new method of stimulating con- vective clouds to produce rain and hail, Q@. J. R. Met. Soc., 78, 37-45, 1952. Brana, R. R., Jr., The water and energy budgets of the thunderstorm and their relation to thun- derstorm development, J. Met., 9, 227-242, 1952. Brauam, R. R., L. J. Barran, anp H. R. Byers, Artificial nucleation of Cumulus clouds, Mete- orological Monographs, 2, no. 11, 47-85, 1957. Byers, H. R., anp R. R. Brana, The thunderstorm, Superintendent of Documents, Washington, 282 pp., 1949. Byers, H. R., anp R. K. Haty, A census of Cumu- lus cloud height versus precipitation in the vicinity of Puerto Rico during the winter and spring of 1953-54, J. Met., 12, 176-178, 1955. Dovctas, R. H., Growth by accretion in the ice phase, this volume, pp. 264-270, 1960. East, T. W. R., An inherent precipitation mecha- nism in Cumulus clouds, Q. J. R. Met. Soc., 83, 61-76, 1957. DISCUSSION Hovcuton, H. G., Problems connected with the condensation and precipitation processes in the atmosphere, Bull. Amer. Met. Soc., 19, 153-159, 1938. Howe ., W. E., A study of the rainfall of central Cuba, J. Met., 10, 270-278, 1953. Howe ti, W. E., Associates, Inc., Evaluation re- port of the 1951 rain stimulation program for the Francisco Sugar Company, unpaged, 1952. Keir, C. H., anp A. B. Arons, The growth of sea- salt particles by condensation of atmospheric water vapor, J. Met., 11, 173-184, 1954. Kraus, E. B., anp P. Squires, Experiments on the stimulation of clouds to produce rain, Nature, 159, 489, 1947. Lupuam, F. H., The production of showers by the coalescence of cloud droplets, Q. J. R. Met. Soc., 77, 402-417, 1951. Lupiam, F. H., Artificial and natural shower forma- tion, Weather, 7, 119-204, 1952. Lupuaq, F. H., Shower formation in large Cumulus, Tellus, 8, 424-442, 1956. MacCreapy, P. B., T. B. Smiru, C. J. Topp, anp K. M. Beesmer, Nuclei, Cumulus, and seedability studies, Final Report of the Advisory Commit- tee on Weather Control, pp. 137-200, 1957. Mauxus, J. S., Some results of a trade Cumulus cloud investigation, Woods Hole Oceanogr. Inst. Tech. Rep. 23, 46 pp., 1953. Markus, J. S., The effects of a large island upon the tradewind air stream, QM. J. R. Met. Soc., 81, 538-550, 1955. Mason, B. J., The natural and artificial production of rain, Scientific Journal Royal College of Sci- ence, 22, 1-14, 1952. Discussion Dr. Joanne S. Malkus—I think this is one of the best descriptions of tropical clouds. I have read Dr. Howell’s paper in some detail, and have listened to his lecture, and I like this approach on cloud modification very much. I think this is because Dr. Howell is not just dumping in stuff and making statistical analyses, but he is also asking questions concerning the processes at work. Dr. Bernard Vonnegut—Our observations in New Mexico show that at about the same time that the cloud suddenly grows and gives precipi- tation there is also an extremely rapid buildup of electricity. The electric field frequently dou- bles every minute or two so that in ten minutes it can inerease by two or even three orders of magnitude. I think it would be exceedingly inter- esting in observations of clouds to observe not only the onset of precipitation but also the de- velopment of electrification. Dr. Walter Hitschfeld—I would like to ask a question about the system of organization that you mentioned. You started out with a popula- tion of small clouds; one of the clouds for some reason is able to develop ahead of the others, and then somehow is able to organize the devel- opment of the remainder of the clouds. What is the scale? What is the range over which such an organization could be active; and further, have you any idea of how it might work? Dr. W. E. Howell—First as to scale and range. Dealing with impressions rather than measure- ments, I would say that clouds approaching the critical stage have a depth, typically, of 15,000 to 20,000 ft, and are roughly the same in diam- eter, three miles or so. After passing the critical stage they may grow perhaps five times their horizontal size and to a depth of perhaps 50,000 ft, still guessing. This impression was gained from DISCUSSION 423 repeated flights at 20,000 ft altitude: at that al- titude, you do not seem to be even halfway to the tops of the mature clouds. As to the mechanism, of course the latent heat released by freezing was suggested very early, but I think this may be only a small part of the story and that the more important effect is the removal from the precipitating cloud of the con- densed water that would otherwise cool the air off again by re-evaporating in drier air entrained into the cloud. You might say that precipitation removes latent cold from a cloud and leaves the heat locked in. I think it is an interesting and fruitful field for investigation to study other possible feedback mechanisms. For instance, a cloud, once slightly favored on account of latent heat, will then also have a competitive advantage in utilizing the energy of shear. Also, the down- draft chimneys set up by precipitation shafts may be important in increasing the efficiency of convective overturning. The behavior of the clouds strongly suggests that feedback of some sort is working here, and I do not believe that Dr. Weickmann’s plumbing model of precipitation stimulation can be con- sidered complete without a valve controlling the supply to the spigot that can be operated by the water coming out the holes. Artificial Precipitation Potential during Dry Periods in Illinois RicHARD G. SEMONIN Illinois State Water Survey, Urbana, Illinois Abstract—The macroscale meteorological conditions of the atmosphere were studied during 31 dry periods which occurred in 1953-1955. A dry period is defined as at least five consecutive days with less than ten per cent of the normal precipitation over an area in east central Illinois. The parameters investigated, measured at Rantoul, Illinois, were: precipitable water, low cloudiness, and the Showalter stability index. The upper-air flow, surface tem- perature, and general synoptic conditions were considered in individual case studies. The results indicate that although there is near normal water vapor in the atmosphere during the majority of the dry periods, there was a deficit of low clouds. It is con- cluded from the study that in addition to present cloud-seeding techniques, much re- search is needed to determine means of initiating clouds, since, during dry periods in Illinois, large quantities of clouds desired for seeding are not available. Introduction—Bergeron [1935] postulated nearly 30 years ago that precipitation was the result of microphysical processes in clouds con- taining a mixture of ice particles and subcooled water. However, little progress was made to- ward a better understanding of the precipitation process during the ensuing 20 years. Langmuir [1948] and Schaefer [1948] began to make fur- ther progress in the study of precipitation phys- ics with their laboratory and field experiments in cloud seeding. These experiments definitely illustrated the possibility that man could arti- ficially affect the microphysical processes taking place within clouds. Following these poineer experiments, con- siderable research has been directed toward modifying clouds by attempting to increase the efficiency of the physical processes which initiate or enhance precipitation. While it is of the ut- most importance to determine the physical struc- ture of the clouds, it is equally important to ex- amine the macroscale conditions attending these cloud formations. The President’s Advisory Committee on Weather Control [Orville and others, 1957] re- cently disclosed that the most effective cloud- seeding experiments have been performed in areas where pronounced orographic effects are present. Little evidence has been found for es- tablishing the suecess of seeding clouds to in- crease rainfall in flat-land areas, such as the Midwest. This paper summarizes an attempt to ex- amine some of the more obvious macroscale parameters of the environmental atmosphere, such as precipitable water, low cloudiness, and stability durmg periods when artificial stimula- tion of precipitation is most needed; that is, during periods when the natural precipitation process is either not functioning or is very in- efficient. Analysis and results—The dry periods chosen for study in this investigation consisted of at least five consecutive days during 1953-1955 in which no measurable precipitation occurred at Rantoul, Illinois. To assure that no portion of overlapping wet periods was included in the dry-period analysis, the beginning and ending days of each dry period were deleted from the dry period. Thus, a defined dry period of five days was, in reality, a period of seven days with- out precipitation at Rantoul. Inasmuch as a point observation of rainfall sometimes can be unrepresentative, the dry periods, as determined from the rainfall records at Rantoul, were investigated further on an areal basis. An average areal value was calcu- lated from the precipitation values for seven stations within a 50-mi radius of Rantoul. The dryness of each period was then evaluated by comparing the daily average areal precipitation of the period to long-term daily averages. If less than ten per cent of the average amount was observed, the period was accepted as a dry period. This selection yielded 31 cases for in- vestigation as dry periods. To conduct this study, the Illinois State Water Survey obtained IBM punch cards from the 424 ARTIFICIAL PRECIPITATION POTENTIAL DURNG DRY PERIODS U. 5. Weather Bureau containing upper-air soundings at 12-hr intervals during 1953-1957 at Rantoul, Hlinois. The precipitable water con- tent for the layer from the surface to 400 mb was computed from the punch-card data by a digital computor at the University of Ilhnois. The Showalter stability index was computed in the standard manner for the twice daily ob- servations at Rantoul during the five-year pe- riod. A negative index value indicates unstable conditions and the numerical value is related to the degree of instability. Monthly median values were determined from these computations and are used as normals throughout the remainder of this paper. Cloud data for this study were obtained from a previous study of cloud distributions in II- linois made by Changnon and Huff [1957] of the State Water Survey. The hourly observations of clouds were summed to provide a total number of tenths per day of individual cloud types. In discussing cloudiness during dry periods, only low-cloud data were used since the observation of higher clouds is very dependent on the amount of low cloudiness. Furthermore, cloud seeding techniques to initiate or increase precipitation are more readily performed on the low clouds. The clouds used in this investigation are: Stratus, Stratocumulus, Cumulus, Cumulonimbus, and Nimbostratus. Daily normal values of precipitable water, stability index, and low clouds were calculated and used as a basis for determining the normal- ity of observations obtained during the dry pe- riods. The data obtained for this investigation were studied on an annual, seasonal, and indi- vidual case basis. Table 1 illustrates the median values of precipitable water, cloudiness, and sta- bility for the 31 dry periods during the years 1953-1955. The Table indicates that, although the pre- cipitable water is within ten per cent of normal during dry periods, the cloudiness is well below the normal value. The absence of cloudiness is not a surprising feature during dry periods, but the near normal values of precipitable water in- dicate that a mechanism causing the initiation of clouds is absent. The investigation of the Sho- walter stability index was made in an effort to de- termine some information on the thermodynamic state of the atmosphere during these dry periods. A total of 610 calculations of the stability index were made for the dry periods, and only nine per cent of them were equal to or less than zero. 425 At the same time nearly 80% of the observations were more stable than the five-year median val- ues. Thus, very stable atmospheric conditions, which are unfavorable for the formation of pre- cipitating clouds, are predominant during dry periods. An examination of the 31 cases involved in this study disclosed that in 90% of the dry pe- riods the cloudiness experienced was less than the normal amount. However, in only 71% of the periods was the amount of atmospheric mois- ture below normal. Eighty per cent of the pe- riods investigated were more stable than the five-year seasonal median values of the stability index. In an attempt to determine facts more perti- nent to the problem of weather modification, these data were studied on a seasonal basis. Ta- ble 2 illustrates the results of the seasonal in- vestigation. It is noted in the Table that during dry pe- riods in winter there is considerable more cloud cover than in any of the other seasons, even though the winter dry periods are 31% below normal. The percentage of precipitable water in winter is relatively high, indicating a supply of moisture available for the precipitation proc- ess if it is initiated. However, the stability index is more stable than would be expected for the winter months which have a five-year median of +12.7. Admittedly the meaning of the Sho- walter stability index in the colder months of the year is somewhat dubious, but it does serve to TaBLE 1—Median values of environmental conditions during 1953-1955 Dry Periods Duration | Precip. water® Clouds® | Stability Index ho |- days 8.0 | 90.8 SNe? | EEN * Per cent of normal determined from daily averages. TABLE 2—Seasonal median values of environmental conditions and duration of dry periods Item Winter Spring | Summer Fall Duration, days 8.0 8.0 8.5; 10.0 Clouds, per cent 69.0 | 19.2 | 49.5] 49.3 of normal | Precipitable 81.8 | 76.8] 95.4] 91.0 water, per cent of normal Stability index +16.5 | +8.5 | +4.0 | +8.0 426 illustrate a comparison between the dry periods and the median values obtained from upper-air observations during 1953-1957. The spring months are clearly below normal in cloudiness while the precipitable water is still realtively high with 77% of the normal value. The remaining two seasons have over 90% of the normal precipitable water, but have less than 50% of the normal cloudiness. Since cloud modi- fication practices to initiate or increase precipi- tation are dependent on the existence and amount of low cloudiness, the data presented indicate that investigations on methods of ini- tiating low clouds are equally as important as the seeding of existing clouds. van Straten [1958] recently attempted seeding cloudless air with carbon black to initiate clouds. The results of these experiments are encouraging, and certainly justify more research on the physics of cloud initiation. In all the dry periods investigated, there appears to have been an ample supply of moisture in the gaseous state, but for some rea- son the condensation process was not operating efficiently. It was suspected that the lack of cloudiness was due to the absence of vertical motions which are necesesary to the condensation process. However, an inspection of the individual dry periods does not indicate an absence of the conditions which would support convective ac- tivity m a number of cases. As an example, a ten-day dry period in July-August of 1953 was above normal in precipitable water content, and relatively unstable with a median stability index of +0.5. However, only 383% of the normal low cloudiness was observed. The surface maximum temperatures during the period were above 90°F, and a visual inspection of the thermodynamic structure of the atmosphere did not reveal any unusual, stable layers. Therefore, many of the conditions conducive to convective cloud forma- tion were observed, but the clouds did not form. An examination of the upper-air flow during this dry period revealed predominantly north- westerly flow over Illinois. In view of the fact that the macroscale conditions leading to cloud initiation and precipitation were present, it seems likely that the flow from the northwest was deficient in condensation nuclei. The Illinois State Water Survey, under a grant from the National Science Foundation, is now engaged in an airborne particulate sampling program to de- termine the distribution of nuclei during a wide variety of synoptic conditions. The results of RICHARD G. SEMONIN the particulate sampling research will provide data on the distribution of condensation nuclei during dry periods similar to that described. It is evident from the data presented that, in the majority of the dry periods investigated, the clouds and instability which are necessary for initiation of precipitation were not present and therefore, cloud-seeding practices would not have helped to alleviate the problem. Summary—This study has brought to light some of the interesting features of the conditions of the large-scale atmosphere during periods of little or no precipitation in the Midwest. The study is presently in its initial stages and will be developed more fully, but the preliminary re- sults present some interesting aspects of the problem of weather control. If we are to alleviate drought in the agricultural areas of the Mid- west, it appears that in addition to seeding existing clouds to increase precipitation, meth- ods for initiating clouds must be developed. If Ilhnois is considered representative of the Midwest, a large quantity of clouds desired for seeding are just not available during dry periods. Acknowledgments—The writer wishes to thank Wilham C. Ackermann, Chief, and Stanley A. Changnon, Climatologist, Illinois State Water Survey for their helpful comments, discussions, and careful review of the manuscript. This work was accomplished under the immediate super- vision of Glenn E. Stout, Head of the Meteorol- ogy Section of the Illinois State Water Survey. REFERENCES Berceron, T., On the physics of clouds and pre- cipitation, Proc. 5th Assembly, U.G.G_1., pp. 156- 178, Lisbon, 1935. Cuaneonon, 8S. A., ano F. A. Hurr, Cloud distribu- tion and correlation with precipitation in Illinois, Rep. Invest. 33 Illinois State Water Survey, Ur- bana, Illinois, 83 pp., 1957. Lanemuir, I., Studies of the effects produced by dry ice seeding of Stratus clouds, G. E. Res. Lab., Project Cirrus, final rep., Schenectady, New York, pp. 121-135, 1948. OrvitLe, Howarp T., anv orHers, Final Report of the Advisory Committee on Weather Control, Superintendent of Documents, U. 8. Govern- ment Printing Office, Wash., D. C., 422 pp., 1957. Scuarrer, V. J., The production of clouds contain- ing supercooled water droplets or ice crystals under laboratory conditions, Bul. Amer. Met. Soc., 29, 175-182, 1948. vAN Straten, F. W., Preliminary experiments us- ing carbon black for cloud modification and for- mation, U.S. Naval Res. Lab. Rep. 6235, Wash., D. C., 25 pp., 1958. DISCUSSION 427 Discussion Dr. W. E. Howell—May I speak to this ques- tion from the point of view of rain-making ex- perience. Of course anyone in my position makes 90% of his new contacts during the 10% of the dryest weather. One is always asked the question, “Can you make it rain in the middle of a drought?” I can honestly say that our reply is “No.” However, that is not the end of the mat- ter. These people do not come to us in the first five dry days; they are not particularly ap- palled by any five-day period without rain. It is when they have gone 30 or 60 days with only a fraction of the normal precipitation that they begin to worry about drought. By then, the question is not, “How suitable is a typical drought day for cloud seeding?” but “How fre- quently during an extended drought do seeding opportunities present themselves?” We have made, therefore, a rather detailed study for Louisiana defining a drought situation as a pe- riod beginning with the sixth day after a gen- eral rain, and continuing as long as the cumula- tive amount of precipitation was less than a tenth of an inch a day. In the 39-month period, January 1949-March 1952, we found 400 drought days, covering a trifle over a third of the time, in 37 individual drought periods, mostly of a few days duration; but there were several more extended periods of drought: for instance, Au- gust 26-December 20, 1950; April 28 to June 10, 1951; and November 8 to December 17, 1951. Now, in the longest of these, August 26 through December 20, 1950, there were 31 out of 116 days, about “4, during which small amounts of rain fell somewhere on or near the target. It was similar for the other drought periods. It is our feeling that these occasions that punc- tuate the typical drought are quite good for cloud seeding when the precipitation mechanism almost reaches the stage of rain but does not quite get there; our experience working in this kind of condition is on the whole quite favorable. We feel that we can not actually break a drought, but we also feel that we can considerably di- minish its intensity during certain critical parts of the drought. Mr. Jerome Namias—I would like to say a little about this problem of drought, and also mention a few things about criteria for the for- mation of rain. The criteria Mr. Semonin used were the Showalter stability index and the total precipitable water. Those two indices are cer- tainly not the best criteria for the occurrence of rain. It is well known that the vertical compo- nent of air motion is the central factor in the formation of rain, and Mr. Semonin’s criteria would often not be very wise choices. Also, varia- tions in precipitable water of five per cent have to be considered against the knowledge of the normal variability; and not considered small. We have to know the frequency distribution of it, particularly in the Midwest, where this distribu- tion is extremely important. Now, with regard to the situation Mr. Semonin described; I have tried to look it up, although the precise dates were not mentioned in his abstract. I could get just a broad seale picture, but I have studied that drought period as well as many others. Figure 1 depicts the 700-mb conditions at- tending the great Dust Bow] drought of 1936. It is somewhat similar in nature to the period that arose during the seven-year drought from 1951 to 1956 over Texas and adjacent areas of the southern Plains. The main thing to note in this figure is the great anti-cyclone in the mid-tropo- sphere into which dry air from the westerlies is recurrently injected. A good deal of subsidence takes place, resulting in lack of clouds, and the excess insolation during the daytime raises tem- peratures as much as 10° above normal; this means that temperatures between 100 and 110°F are frequent over the drought area. The two conditions, very hot and very dry, go hand in hand. An important point is that this great drought- producing cell depends in large part on the exist- ence of two neighboring cells, one in the Atlantic and one in the Pacific; both have to be anoma- lously strong, so that they are, so to speak, in resonance. If one or both of the oceanic cells should vanish, the U.S. cell would die. But once this mechanism is set up, there are also some life-sustaining properties for the continental cell which remain to be explained. It might be, for example, that Squires’ suggestion of the differ- ent nuclei counts and kinds in continental and maritime regions might be important here. There are also some other factors which might be raised, such as changes in the characteristics of the underlying surface itself, and presence or lack of water on this surface. In other words, solar heat may be used for evaporation or for DISCUSSION Fra. 1—Mean 700-mb contours for August 1936; note the great anticyclone over the Southern Plains and the companion cells over the Pacific and Atlantic building the upper level anti-cyclone, depending on the character of the surface. Figure 2 shows an isentropic analysis for this particular month (August 1986). This is a slop- ing surface of constant potential temperature (515° A) whose heights are given by the broken lines. Shown also are the circulating moist and dry tongues which are largely responsible for the outbreak or inhibition of showers. You will note in this great drought-producing cell that dry air is frequently flung from the westerlies over Canada, around the cell, finally entering into the central portion of this great anticy- clonic eddy. At the same time, this dry air moves from higher to lower elevations as it spins into the cell. The dry subsiding air inhibits the forma- tion of clouds. As a matter of fact, if Cumuli do form, when they penetrate this dry layer a sort of entrainment takes place, so that they are dis- sipated quickly, by the mixing with this dry air. Now, in the southern part of Illinois it is ex- tremely dry. There are deficits on the order of two to four inches in the Plains area of the United States. In some areas there is no rain at all, and the rain is confined to the left-hand por- tion of the moist tongue, where the air is to some extent forced up slope. A similar case was ob- ) served during August 1955, and Figure 3 shows DISCUSSION AUGUST - 1936 429 Fic. 2—Isentropic chart for the 315°A surface for August 1936; solid lines are isopleths of mixing ratio in grams per kilogram, broken lines represent in meters the height of the isentropic surface, moist and dry tongues are labeled M and D, respectively; insert shows departure from normal of precipitation for the month in inches, shaded areas showing excess, and unshaded areas deficit the mean 700-mb pattern and the precipitation anomaly. This is the August which I presume is one of the periods treated in Mr. Semonin’s talk. You will note the anticyclonic cells are also pro- nounced, as in the 1936 case. What I am trying to emphasize is that drought is generally a very large-scale phenomenon, and its modification may require us to deal with events quite remote from the immediate drought area. One should be very careful not to draw conclusions about his efforts to modify drought on a large scale by rather localized seeding, par- ticularly in areas where there are few clouds, and these not of the proper type. As I indicated in my earlier talk, all of us as meteorologists must be aware of these large-scale problems. Mr. R. G. Semonin—The dry period was in August 1953, and was very similar to the mean pattern you have shown. You had asked how the amount of precipitable water is related to pre- cipitation. I have been trying to find out for two or three years now, and I have found no definite relationship. I just wanted to show what the con- ditions were during these periods rather than imply any relationship between them, but the water vapor is present, at least in these dry sum- mer periods, and in many cases the latent msta- bility is also there. However, there is no mecha- nism to release this. We can not burn cornfields, of course; they are quite expensive; so we have no way of initiating convection. Dr. Tor Bergeron—l want to point out the High over central Europe and southeastern Swe- den that co-existed with the American drought in 1955. In fact it was one of the driest summers on record in southwestern Sweden; and that was one of the first summers that we had our project Pluvius working. It almost ruined our project. Mr. Namias—Incidentally, I had an article published in the Monthly Weather Review (Some meteorological aspects of drought, with special reference to the summers of 1952-4 over the United States, September, 1955) describing the 1952 to 1954 drought in relation to the gen- eral drought problem. Maj. C. Downie—Experiments carried out by the Geophysics Research Directorate have yielded little encouragement that a drought 430 DISCUSSION OBSERVED MEAN 700-MILLIBAR CONTOURS __ , AUGUST 1955 ype U. S. DEPARTMENT OF COMMERCE WEATHER BUREAU HEAVY ZY OBSERVED PRECIPITATION 4 \: (APPROXIMATE) \| moperate [__] AUGUST 1955 we LIGHT Fig. 3—Mean 700-mb contours (above) and precipitation pattern (below) for August 1955 DISCUSSION 451 situation can be remedied artificially and, to the best of my knowledge, the artificial production of precipitation over a large area has never been conclusively demonstrated. However, the po- tentiality of particular techniques for producing focalized precipitation has been proven. Dr. Howell—In none of the experiments I re- ferred to, did we attempt to produce large-scale changes, or look for large-scale changes; and I believe that the points I was making were con- cerned entirely with small interruption of the drought in small-scale areas. Appendix List of Participants Bernice Ackerman Department of Meteorology University of Chicago Chicago 37, Illinois Luis Aldaz Mt. Washington Observatory Gorham, New Hampshire C. E. Anderson Aerosol Physics Laboratory Geophysics Research Directorate Air Force Cambridge Research Center Bedford, Massachusetts Pauline M. Austin Department of Meteorology Massachusetts Institute of Technology Cambridge 39, Massachusetts Louis J. Battan Institute of Atmospheric Physics University of Arizona Tueson, Arizona W. B. Beckwith United Air Lines, Inc. Stapleton Airfield Denver 7, Colorado Tor Bergeron Department of Meteorology Royal University of Uppsala Uppsala, Sweden Seymour J. Birstein Aerosol Physics Laboratory Geophysics Research Directorate Air Force Cambridge Research Center Bedford, Massachusetts Roy H. Blackmer, Jr. 110 Monalto Ave. Menlo Park, California Dunean C. Blanchard Department of Meteorology Massachusetts Institute of Technology Cambridge, Massachusetts Roscoe R. Braham Department of Meteorology University of Chicago Chicago 37, Illinois Andrew F. Bunker Woods Hole Oceanographic Institution Woods Hole, Massachusetts Gordon Burley Section 9.7 National Bureau of Standards Washington 25, D. C. Horace R. Byers Department of Meteorology University of Chicago Chicago 37, Ilinois Joseph Chase Woods Hole Oceanographic Institute Woods Hole, Massachusetts Albert C. Chmela Aerosol Physics Laboratory Air Force Cambridge Research Center Bedford, Massachusetts Robert M. Cunningham Aerosol Physics Laboratory Air Force Cambridge Research Center Bedford, Massachusetts Fred W. Decker Oregon State College Corvallis, Oregon Henri J. J. Dessens Observatoire du Puy de Déme Clermont-Ferrand, France J. E. Dinger Naval Research Laboratory Washington 25, D. C. Ralph J. Donaldson, Jr. Weather Radar Group Air Force Cambridge Research Center Bedford, Massachusetts 432 Currie 8. Downie 405 Rutledge Road Park Forest, Illinois Earl G. Droessler National Science Foundation Washington 25, D. C. Ralph G. Eldridge Office of Naval Research Lincoln Laboratory Lexington, Massachusetts Robert D. Elliott North American Weather Consultants Santa Barbara Municipal Airport Goleta, California Dr. Oskar Essenwanger U.S. Weather Bureau Asheville, North Carolina Alan J. Faller Woods Hole Oceanographic Institution Woods Hole, Massachusetts Robert W. Fenn Meteorological Division U.S. Signal R. & D. Laboratories Belmar, New Jersey Tetsuya Fujita Department of Meteorology University of Chicago Chicago 37, Illinois Hans W. Georgii Institut fiir Meteorologie und Geophysik University of Frankfurt Frankfurt, Germany J. L. Glover Headquarters Air Weather Service Scott Air Force Base, Illinois Alexander Goetz California Institute of Technology Norman Bridge Laboratory of Physics Pasadena, California Rosemary M. Griffith Meteorological Division U.S. Army Signal R. & D. Laboratories Belmar, New Jersey APPENDIX Johannes Grunow Deutscher Wetterdienst Meteorological Observatory Hohenpeissenberg, Germany Walter Hitschfeld Physics Department MeGill University Montreal 2, Canada Charles L. Hosler Department of Meteorology Pennsylvania State University University Park, Pennsylvania Henry G. Houghton Massachusetts Institute of Technology Cambridge 39, Massachusetts Wallace KE. Howell 35 Moon Hill Road Lexington 75, Massachusetts C. E. Junge Air Force Cambridge Research Center Bedford, Massachusetts Heinz W. Kasemir Meteorological Division U.S. Army Signal R. & D. Laboratories Belmar, New Jersey Delbar P. Keily Massachusetts Institute of Technology Cambridge 39, Massachusetts John J. Kelly Meteorological Division U.S. Army Signal R. & D. Laboratories Belmar, New Jersey Edwin Kessler Weather Radar Group Air Force Cambridge Research Center Bedford, Massachusetts Wilham V. Kielhorn Woods Hole Oceanographic Institution Woods Hole, Massachusetts G. D. Kinzer Physical Science Laboratory U.S. Weather Bureau Washington 25, D. C. 434 Dwight B. Kline U.S. Weather Bureau Washington 25, D. C. Joseph Levine Woods Hole Oceanographic Institute Woods Hole, Massachusetts Douglas K. Lilly U.S. Weather Bureau Suitland, Maryland Roland List Swiss Federal Snow and Avalanche Research Institute Weissfluhjoch-Davos, Switzerland James P. Lodge Robert E. Taft Sanitary Engineering Center 4676 Columbia Parkway Cincinnati 26, Ohio Choji Magono Department of Geophysics Faculty of Science Hokkaido University Sapporo, Japan Joanne 8. Malkus Woods Hole Oceanographic Institution Woods Hole, Massachusetts B. J. Mason Imperial College of Science & Technology Huxley Building London 8.W. 7, England Wendall A. Mordy 4 a Institute of Meteorology University of Stockholm Stockholm K, Sweden Ukichiro Nakaya Hokkaido University Sapporo, Japan Jerome Namias U.S. Weather Bureau Washington 25, D. C. Morris Neiburger Department of Meteorology University of California Los Angeles 24, California APPENDIX Chester W. Newton Department of Meteorology University of Chicago Chicago 37, Illinois Howard T. Orville Beckman and Whitley Company 985 San Carlos Avenue San Carlos, California Vernon G. Plank Geophysics Research Directorate Air Force Cambridge Research Center Bedford, Massachusetts Hans Pruppacher Department of Meteorology University of California Los Angeles 24, California Gerhard H. R. Reisig Army Ballistic Missile Agency Huntsville, Alabama Claude Ronne Woods Hole Oceanographic Institute Woods Hole, Massachusetts Claes Rooth Institute of Meteorology University of Stockholm Stockholm, Sweden Raymund Sanger Swiss Federal Institute of Technology Postfach Ziirich 23, Switzerland R. M. Schotland Department of Meteorology and Oceanography New York University New York 53, N. Y. Richard G. Semonin Illinois State Water Survey 605 E. Springfield Champaign, Ilinois Charles R. Shackford Allied Research Associates, Inc. 43 Leon Street Boston 15, Massachusetts J. Smagorinsky U.S. Weather Bureau Washington 25, D. C. APPENDIX 435 Waldo E. Smith American Geophysical Union 1515 Massachusetts Ave., N. W. Washington 5, D. C. P. Squires Division of Radiophysies University Grounds Sydney N.S.W., Australia Henry Stommel Woods Hole Oceanographic Institution Woods Hole, Massachusetts Donald M. Swingle U. 8. Army Signal R. and D. Laboratories Ft. Monmouth, New Jersey Clement J. Todd Meteorology Research, Inc. 2420 North Lake Avenue Altadena, California Florence W. van Straten Naval Weather Service Office, Chief of Naval Operations Washington 25, D. C. F. Volz Blue Hill Observatory Harvard University Cambridge 38, Massachusetts Bernard Vonnegut Arthur D. Little, Inc. Acorn Park Cambridge, Massachusetts Helmut Weickmann Meteorological Division U. 8. Army Signal R. and D. Laboratories Belmar, New Jersey Ray Wexler Allied Research Associates, Inc. 43 Leon St. Boston 15. Massachusetts Gunther A. Wolff U.S$. Army R. & D. Laboratories Ft. Monmouth, New Jersey ASH. Woodcock Woods Hole Oceanographic Institute Woods Hole, Massachusetts [NEFTUTIOM ARCHIVES W.H.O.L. DATA LIBRARY WOODS HOLE, MA. 02543