^OATMOSP ''Went of U.S. DEPARTMENT OF COMMERCE Maurice H. Stans, Secretary NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION Robert M. White, Administrator ENVIRONMENTAL RESEARCH LABORATORIES Wilmot N. Hess, Director Collected Reprints-1970 Volume II ATLANTIC OCEANOGRAPHIC AND METEOROLOGICAL LABORATORIES ISSUED SEPTEMBER 1971 8 v a «5 Atlantic Oceanographic and Meteorological Laboratories Miami. Florida 33130 For sale by the Superintendent of Documents, U. S. Government Printing Office, Washington, D. C. 20402 Price $4.50 Stock No. 0323-0002 FOREWORD An increased understanding of the ocean and its processes, of the underlying geological and geophysical structures, and of the overlying atmosphere and its interactions with the sea will result in man's increas- ed ability to deal intelligently with the problems of his environment. The scientific and technical accomplishments of the National Oceanic and Atmospheric Administration's Environmental Research Laboratories are contributing to this understanding. Because the published results of the Atlantic Oceanographic and Meteorological Laboratories are broadly scat- tered through the literature, they are being brought together in a series of annual publications. These provide a convenient summary of the results of the work of these laboratories for researchers and interested laymen alike. Because of the steadily increasing size of these annual volumes, this year we have limited the collection to those papers published only by the Atlantic Oceanographic and Meteorological Laboratories in Miami, Florida. Work of the Pacific Oceanographic Laboratories (Seattle and Honolulu) is not included. Although the Experimental Meteorology Laboratory was trans- ferred out of AOML in early 1971, their published papers for 1970 are included here. This volume, the fifth in the series, contains the published results of NOAA's Atlantic Oceanographic and Meteorological Laboratories for the Harris B. Stewart, Jr. Director Atlantic Oceanographic and Meteorological Laboratories TABLE OF CONTENTS Volume I GENERAL 1. Stewart, Harris B., Jr., ESSA becomes NOAA: Muse News I I , No. 8, Museum of Science, Miami, 25^-256, 280. 2. Stewart, Harris B., Jr., A great place to visit: Explorers Journal XLV III, No. 2, Explorers Club, 120-123- 3. Stewart, Harris B., Jr., The Ocean - A scientific and technical challenge, in Science and Technology in the World of the Future, ed . Arthur B. Bronwell, John Wiley and Sons, Inc., New York, 1 3 — 3 1 - k. Stewart, Harris B., Jr., Trouble in the bay: The Miamian, Donnelly Publishing Company, Miami, January, 10 and 70. MARINE GEOLOGY AND GEOPHYSICS 5. Bassinger, B. G., Hyman Orlin, and C. H. Gray, Continental shelf seabottom survey Cape Hatteras, North Carolina - Cape May, New Jersey: Operational Data Report NOS DR-11. 6. Bennett, R. H., G. H. Keller, and R. F. Busby, Mass prop- erty variability in three closely spaced deep-sea sediment cores: Journal of Sedimentary Petrology 4_0, No. 3, 1038-1043- 7- Brier, Chester, Robert Bennin, and Peter A. Rona, Prelim- inary evaluation of a core scintillation counter for bulk density measurement in marine sediment cores, A Reply: Journal of Sedimentary Petrology 40 , No. 3, 1370. 8. Butler, Louis W., Shallow structure of the continental margin, southern Brazil and Uruguay: Geological Society of America Bulletin 8j_, No. 4, 1079-1095- 9. Conolly, John R., Alan Flavelle, and Robert S. Dietz, Continental margin of the great Australian bight: Marine Geology 8_, 31 -58 . 10. Dietz, Robert S., Continents and ocean basins, in The Mega tec ton i c s of Continents and Oceans, ed . H. Johnson and B. Smith, Rutgers University Press, 24-46. 11. Dietz, Robert S., and John C. Holden, The breakup of Pangaea: © Scientific American 223, No. 4, 30-41. 12. Dietz, Robert S., and John C. Holden, Reconstruction of Pangaea: Breakup and dispersion of continents, Permian to present: Journal of Geophysical Research 75, No. 26, ^939-^956. 13- Dietz, Robert S., John C. Holden, and Walter P. Sproll, Geotectonic evolution and subsidence of Bahama Platform: Geological Society of America Bulletin 81, No. 7, 191 5-1927. 14. Dietz, Robert S., and Walter P. Sproll, East Canary Islands as a m i c r ocon t i ne n t within the Africa-North America Conti- nental drift fit: Nature 226 , No. 5250, June 13, 1 0 4 3 - 1 0 4 5 15- Dietz, Robert S., and Walter P. Sproll, Fit between Africa and Antarctica: A continental drift reconstruction: Science 1 67 , March 20, 1 6 1 2 - 1 6 1 4 . 16. Dietz, Robert S., and Walter P. Sproll, Overlaps and under- laps in North America to Africa continental drift fit: Proceedings SCOR W G 3 1 Symposium, March 2 3 - 2 7 , 1970, Cambridge, England, Geology of the East Atlantic Continen- tal Margin, Her Majesty's Stationery Office, London. 17- Epp, David, Paul J. Grim, and Marcus G. Langseth, Jr., Heat flow in the Caribbean and Gulf of Mexico: Journal of Geophysical Research 7_5_, No. 29, 5655~5669- 18. French, Bevan M., J. B. Hartung, Nicholas M. Short, and Robert S. Dietz, Tenoumer Crater, Mauritania: Age and petrologic evidence for origin by meteorite impact: Journal of Geophysical Research 7_5_, No. 23, k 3 96 - hk 06 . 19- Gassaway, John D., Mineral and chemical composition of sediments from the Straits of Florida: Journal of Sedimentary Petrology h_0_, No. h, 1136-1146. 20. Grim, Paul J., Bathymetric and magnetic anomaly profiles from a survey south of Panama and Costa Rica (USC&GSS 0CEAN0GRAPHER August 1969): ESSA Tech Memo ERLTM-A0ML 9- 21. Grim, Paul J., Computer program for automatic plotting of bathymetic and magnetic anomaly profiles: ESSA Tech Memo ERLTM-A0ML 8. 22. Grim, Paul J., Connection of the Panama fracture zone with the Galapagos rift zone, eastern tropical Pacific: Marine Geophysical Researches J_, 85~90. 23- Harbison, R. N., and B. G. Bassinger, Seismic reflection and magnetic study off Bombay, India: Geophysics 3 5 , No. k , 603-61 2 . 2k. Keller, George H., and Richard H. Bennett, Variations in the mass physical properties of selected submarine sedi- ments: Marine Geology 9, 2 1 5 - 2 2 3 - 25- Malloy, R. J., and R. J. Hurley, G eomo r p ho 1 og y and geologic structure: Straits of Florida: Geological Society of America Bulletin 8j_, No. 7, 1 9 ^ 7 ~ 1 9 7 2 . 26. Peter, George, Letters, Discussion of paper by B. P. Luyendyk, 'Origin of s h o r t - wa ve 1 e n g t h magnetic lineations observed near the ocean bottom1: Journal of Geophysical Research 75, No. 32, 6717-6720. 27. 28 Rona, Peter A., Comparison of continental margins of eastern North America at Cape Hatteras and northwestern Africa at Cap Blanc: American Association of Petroleum Geologists Bulletin 5k, No. 1, 129-157- D r . Howa r d A . margins of eastern Rona, Peter A., Reply to discussion by Meyerhoff of "Comparison of continenta North America at Cape Hatteras and northwestern Africa at Cap Blanc": American Association of Petroleum Geologists Bu 1 1 et i n 5k, No. 11, 2216-2218 . 29. Rona, Peter A., Submarine canyon origin on upper conti- nental slope off Cape Hatteras: Journal of Geology 7_8_, No . 2 , 141-152. 30. Rona, Peter A., J. Brakl., and J. R. Heirtzler, Magnetic anomalies in the northeast Atlantic between the Canary and Cape Verde Islands: Journal of Geophysical Research 7_5_, No. 23, 7^12-7^20. 31. Rona, Peter A., and A. J. Nalwalk, Post-early Pliocene unconformity on F u e r t e ve n t u r a , Canary Islands: Geological Society of America Bulletin 8j_, No. 7, 2117-2121. 32. Semtner, Albert J., and Paul J. Grim, A magnetic and bathymetric profile in the Pacific from the Cocos Ridge to central California: ESSA Tech Report ERL 179-AOML 3- 33- Von der Borch, C. C., J. R. Conolly, and R. S. Dietz, Sedimentation and structure of the continental margin in the vicinity of the Otway Basin, southern Australia: Marine Geology 8, 59"83- Rona, Peter A., Continental margin between Canary and Cape Verde Islands and symmetries with eastern North America: In Symposium, "Geology of the East Atlantic continental margin," Scientific Committee on Oceanic Research (SCOR), Cambridge, England, March 2 3 - 2 7 , 1970, Her Majesty's Stationery Office, London. Reprint not available. METEOROLOGY 34. Anthes, Richard A., Numerical experiments with a two- dimensional horizontal variable grid: Monthly Weather Rev i ew 9_8_, No. 11, 8l 0-822 . 35- Anthes, Richard A., The role of large-scale asymmetries and internal mixing in computing meridional circulations associated with the steady-state hurricane: Monthly Weather Review 9_8_, No. 7, 521-528. 36. Carlson, Toby N., and Joseph M. Prospero, Radon-222 in the North Atlantic Trade Winds: its relationship to dust transport from Africa: Science 167, February 13, 974-977- 37- Carlson, Toby N., Joseph M. Prospero, Enrico Bonatti, and Carl Schubert, Dust in the Caribbean atmosphere traced to an African dust storm: Earth and Planetary Science Letters S_, No . 3 , 287-293 . 38. Gentry, R. Cecil, Hurricane Debbie modification experi- ments, August 1969: Science 1 68 , April 24, 473-475- 39- Gentry, R. Cecil, The hurricane modification project: past results and future prospects: Proceedings Seventh Space Congress, Cocoa Beach, Florida, Canaveral Council of Technical Societies, 11-19 _ 11-27- 40 . Gentry, R. Cecil, Modifying the greatest storm on earth-- the hurricane: Underwater Science and Technology Journal 2 , No. 4 , 204-21 4. 41. Gentry, R. Cecil, Modification experiments on Hurricane Debbie, August 1969: Second National Conference on Weather Modification of the American Meteorological Society, April 6-9, 1970, Santa Barbara, California, 205-208 . TABLE OF CONTENTS Volume II METEOROLOGY (CON'T) 4 2. Gentry, R. Cecil, 1969, Staff of the Director, Project STORMFURY, 1969: Project STORMFURY Annual Report. 4 3- Gentry, R. Cecil, Tetsuya T. Fujita, and Robert C. Sheets, Aircraft, spacecraft, satellite and radar observations of Hurricane Gladys, 1968: Journal of Applied Meteorology 9_> No • 6> 837-850. 4 4 . Mallinger, William D . , Project Stormfury operations and plans: Mariner's Weather Log ]_4_, No. 5, 262-266. kS • Miller, Banner I., and Toby N. Carlson, Vertical motions and the kinetic energy balance of a cold low: Monthly Weather Review 98_, No. 5, 363*374. 46. Rosenthal, Stanley L., A circularly symmetric primitive equation model of tropical cyclone development containing an explicit water vapor cycle: Monthly Weather Review 98 , No. 9, 643-663. 47- Scott, William D . , An instrumented "hailstone" for cloud physics research: Proceedings of the National Cloud Physics Conference, Ft. Collins, Colorado, 109-110, American Meteorological Society. 48. Scott, W. D., and D. Lamb, Two solid compounds which decompose into a common vapor. Anhydrous reactions of ammonia and sulfur dioxide: Journal of the American Chemical Society 9_2_, No. 13, 3943-3946. 49- Scott, W. D., and Zev Levin, The effect of potential gradient on the charge separation during interactions of snow crystals with an ice sphere: Journal of Atmospheric Sciences 2_7_, No. 3, 463~473- " Gentry, R. Cecil, Hurricane modification-experiments and prospects: Presented at Hurricane Foresight Conference, New Orleans, Louisiana, and distributed by the New Orleans States- I terns . Reprint not available. EXPERIMENTAL METEOROLOGY 50. Simpson, Joanne, On the radar-measured increase in preci pitation within ten minutes following seeding: Journal of Applied Meteorology 9_, No. 2, 318-320. 51. Simpson, Joanne, Reply to Dr. Battan on "On the radar- measured increase in precipitation within ten minutes following seeding": Journal of Applied Meteorology 9, No. 6 , 951 -952 . 52. Simpson, Joanne, William L. Woodley, Howard A. Friedman, Thomas W. Slusher, R. S. Scheffee, and Roger L. Steele, An airborne pyrotechnic cloud seeding system and its use: Journal of Applied Meteorology 3, No. 1, 10 9-122. 53 54 55 56 Woodley, William L., Precipitation results from a pyro- technic cumulus seeding experiment: Journal of Applied Meteorology 9, No. 2, 2^2-257- Wood ley, William L cloud modification Rainfall enhancement by dynamic Science 170, October 9, 127-132. Woodley, William, and Alan Herndon, A raingage evalua- tion of the Miami reflectivity-rainfall rate relation: Journal of Applied Meteorology 9_, No. 2, 258-264. Woodley, William L., Joanne Simpson, Alan H. Miller, Steven MacKay, Richard Williamson, and Gerald F. Cotton, Some results of single cloud pyrotechnic seeding in Florida, 1970: N0AA Tech Memo ERLTM-A0ML 10. 57- Woodley, William L., and Richard Williamson, Design of a multiple cloud seeding experiment over a target area in south Florida ESSA Tech Memo ERLTM-A0ML 7 58. Woodley, William Lee, and Robert N. Powell, Documentation and implications of the behavior of seeded cloud 17, May 30, 1968: ESSA Tech Memo ERLTM-A0ML 6. PHYSICAL OCEANOGRAPHY 59- Chew, Frank, and George A. Berberian, Some measurements of current by shallow drogues in the Florida Current: Limnology and Oceanography 15, No. 1, 88-99- 60. Hansen, Donald V., Gulf stream meanders between Cape Hatteras and the Grand Banks: Deep-Sea Research 1 7 , Pergamon Press, June, 495"511- 61. Hansen, Donald V., Correlation of movements in the western North Atlantic: ESSA Tech Report ERL 164-AOML 1. 62. Hansen, Donald V., Review of K. 0. Emery's, "A Coastal Pond - -S t ud i ed by Ocea nog ra p h i c Methods": The Science Teacher 3_7 , No . 4 , 96 . 63- Hansen, Donald V., and George A. Maul, A note on the use of sea surface temperature for observing ocean currents: Remote Sensing of Environment 1 , No. 3 , Summer, 161-164. 64. Maul, George A., and James C. Bishop, Jr., Mean sounding velocity. A brief review: I.H.B. Review X LV I I , No. 2, 85-92. 65- Maul, George A., Precise echo sounding in deep water: I.H.B. Review XLV I I , No. 2, 93-106. 66. Starr, Robert B., An oceanographic investigation adjacent to Cay Sal Bank, Bahama Islands: ESSA Tech Report ERL 167-AOML 2. 67. Zetler, Bernard D., International Symposium on Earth Tides: E9>S 5J_, No. 1, 9~10, American Geophysical Union. 68. Zetler, Bernard D., and Wm. Mansfield Adams, International Tsunami Symposium: E$S 5_1_, No. 5, 479-480, American Geophy s i ca 1 Union. 69. Zetler, B. D., and D. V. Hansen, Tides in the Gulf of Mexico--A review and proposed program: Bulletin of Marine Science 20, No. 1, 5 7 - 6 9 . SEA-AIR INTERACTION 70. J e 1 es n i a n s k i , Chester P., "Bottom stress t i me - h i s t o r y " in linearized equations of motion for storm surges: Monthly Weather Review 9_8_, No. 6, 462-478. 71- McAlister, E. D., and W. McLeish, A radiometric system for airborne measurement of the total heat flow from the sea: Applied Optics 9_, No. 12, 2697-2705- 72. McLeish, William, Spatial spectra of ocean surface temperature: Journal of Geophysical Research 75, No. 33, 6872-6877. 73- Ostapoff, Feodor, Willard W. Shinners, Ernst Augstein, Some tests on the radiosonde humidity error: ESSA Tech Report ERL 194-A0ML 4. Ik. Ross, Duncan B., Vincent J. Cardone, and Jack W. Conaway, Jr., Laser and microwave observations of sea-surface condition for f e t c h - 1 i m i t e d 17_ to 25~m/s winds: IEEE Transactions on Geoscience Electronics GE-8, No. h, 326-336. 75. Shinners, W i 1 lard W., Status of instrument development for specialized marine observations: Meteorological Monographs 11, No. 33, 29/t"301. U.S. DEPARTMENT OF THE NAVY J.H. CHAFEE, Secretary Naval Weather Service Command E.T. HARDING, Captain, USN, Commander U.S. DEPARTMENT OF COMMERCE M.H. STANS, Secretary Environmental Science Services Administration R.M. WHITE, Administrator PROJECT STORMFURY ANNUAL REPORT 1969 MIAMI, FLORIDA MAY 1970 The cover is an enhanced photograph of the ATS III Satellite view taken of Hurricane Debbie, 201600Z August 1969 We extend our thanks to the staff members of the National Aeronautics and Space Administration for the cour- tesies given to Project Stormfury, and to Dr. T. Fujita of the University of Chicago for his invaluable technical assis- tance . Project STORMFURY was established by an interdepartmen- tal agreement between the Department of Commerce and the Department of the Navy, signed July 30, 1962. Additional support has been provided by the National Science Foundation under Grant NSF-G-1 799 3 . This report is the eighth of a series of annual reports to be prepared by the Office of the Director in accordance with the Project STORMFURY interdepartmental agreement. Additional copies of this report may be obtained from: U. S. Naval Weather Service Command Department of the Navy Washington Navy Yard Washington, D. C. 20390 or National Hurricane Research Laboratory P. 0. Box 8265, University of Miami Branch Coral Gables, Florida 33124 TABLE OF CONTENTS Page INTRODUCTION 1 HISTORY AND ORGANIZATION 3 PROJECT STORMFURY ADVISORY PANEL 5 PUBLIC AFFAIRS 5 PYROTECHNIC DEVI CES -S I LVE R IODIDE 6 AREAS OF OPERATIONS 6 PLANS FOR FIELD OPERATIONS - 1969 7 FIELD OPERATIONS - DRY RUNS 9 FIELD OPERATIONS - HURRICANE DEBBIE 10 FIELD OPERATIONS - CLOUDLINE EXPERIMENTS 16 RESEARCH ACTIVITIES 17 OPERATIONAL AND RESEARCH DATA COLLECTION 17 OUTLOOK FOR 1970 18 REFERENCES AND SPECIAL REPORTS 19 APPENDIX A. Recommendations of the Advisory Panel to Project STORMFURY A-l APPENDIX B. The Hurricane Modification Project: Past Results and Future Prospects B-l APPENDIX C. A Circularly Symmetric, Primitive Model of Tropical Cyclones and Its Response to Artificial Enhancement of the Convective Heating Functions C-l APPENDIX D. STORMFURY Seeding Pyrotechnics D-l APPENDIX E. Eye-Size Changes in Hurricane Debbie on 18 and 20 August 1969 E-l in APPENDIX F. Cloud Particle Samples and Water Contents From a 1969 STORMFURY Cloudline Cumulus F-l APPENDIX G. Project STORMFURY Hurricane and Typhoon Seeding Eligibility G-l APPENDIX H. Application of Bayesian Statistics for STORMFURY Results H-l IV PROJECT STORMFURY ANNUAL REPORT - 1969 INTRODUCTION The 1969 hurricane season was a highly productive one for Project STORMFURY, an interdepartmental program of the Department of Defense (Navy) and Department of Commerce, Environmental Science Services Administration (ESSA) , with U.S. Air Force participation. STORMFURY forces operated dur- ing the dry run held at NAS , Jacksonville, Florida, 28-31 July; during the seeding of Hurricane Debbie, 18-and 20 August and during cloudline experiments conducted 9-19 September from the Naval Station, Roosevelt Roads, Puerto Rico. Figure 1 shows the tropical cyclone tracks for 1969 near the STORMFURY areas. Of the storms, two were eligible for seeding under current criteria. Of these two, Debbie was seeded while Inga was not. Inga was technically eligible when near Bermuda, but was not seeded because she had poorly formed eyewall clouds, was weak, moved in an unusual manner, and in general was not desirable for experimentation. The multiple eyewall seeding experiments conducted in Hurricane Debbie were very impressive. The intensity of the storm decreased on both seeding days. On 18 August, the maxi- maximum wind velocity decreased 31%, and on the 20th it decreased 15%. Whether this can be attributed to the seeding remains unproven because natural variations of this magnitude do occur in hurricanes. Data collected, however, strongly suggest that the experiments were successful. (See app . B for amplification.) Figure 2 shows the track of Hurricane Debbie and the periods during which seeding was conducted. It also shows the operating area for the cloudline experiments. An extensive amount of data was collected. Work on re- ducing and analyzing these data is continuing into 1970 and may extend into future years. New methods and techniques for expediting their processing are evolving and results will be available more quickly after future experiments. Considerable progress has been achieved in the development of numerical- dynamical modelling of hurricanes. Aspects of this will be further discussed in the "Research Activities" section of this report and in appendix C. Figure 1. Tropioal oyalone tracks Figure 2. Track of Hurricane Debbie and the periods during which seeding was conducted. Because of the apparent success of the 1969 seeding ex- periments conducted in Hurricane Debbie, a great amount of national and international interest has been focused on Project STORMFURY. In later sections of the report these results and plans for the future will be discussed. HISTORY AND ORGANIZATION Project STORMFURY is a joint ESSA-Navy program of scienti- fic experiments designed to explore the structure and dynamics of tropical storms and hurricanes and their potential for modi- fication. It was established in 1962 with the principal objec- tive of testing a physical model of the hurricane's energy ex- change by strategic seeding with silver iodide crystals. These crystals have been dispensed by Navy aircraft using Navy- developed special pyrotechnic devices. The hypothesis calls for reducing the maximum intensity of a storm or hurricane by a measurable amount. Navy and ESSA scientists and aircraft, supplemented by those of the U.S. Air Force, have cooperated in STORMFURY experimental operations since 1962 when the Project began. Until 1969, one mature hurricane (Beulah, 1963) and two series of tropical cumulus clouds (August 1963 and July-August 1965) had been experimentally seeded in the western Atlantic and Caribbean Sea.* The initial 1962 Project STORMFURY agreement between the Department of Commerce and the Department of the Navy covered 3 years, and it has been renewed annually since then. The 1969 agreement was similar to the 1968 agreement, but was ex- tended to cover 3 years. Dr. Robert M. White, ESSA Administrator, and Captain E. T. Harding, U.S. Navy, Commander of the Naval Weather Service Command, had overall responsibility for this coop- eratively administered project. The Project Director in 1969 was Dr. R. Cecil Gentry, Director of the National Hurricane Research Laboratory (NHRL), Miami, Florida. The Alternate Director was Mr. Harry F. Hawkins, also of NHRL. The assistant Project Director and Navy Project Coordinator was Commander L. J. Underwood, U.S. Navy, Commanding Officer of the Fleet Weather Facility, Jacksonville, Florida (FLEAWEAFAC JAX). The alternate to the assistant Project Director was Commander J. 0. Heft, U.S. Navy, also of FLEWEAFAC JAX. Mr. Clement J. Todd of the Navy Weather Research Facility, Norfolk, Virginia ( WEARSCHFAC ) , was Technical Advisor to the Navy for STORMFURY; Mr. Jerome W. Nicker son, also of WEARSCHFAC, acted as Navy Liaison for Instrument Matters; Dr. S. D. Elliott, Jr., of the Naval Weapons Center, China Lake, was NWC Project Officer; Mr. Max W. Edelstein of the Naval Weather Service Command Headquarters, Washington, D. C., was assigned liaison duties representing the Navy,' and Mr. William D. Mallinger of the National Hurri- cane Research Laboratory was assigned liaison duties for the Project Director and ESSA and acted as Data Quality Control Coordinator . * See Project STORMFURY Annual Reports for 1963, 1964, 1965, 1966, 1967, and 1968. PROJECT STORMFURY ADVISORY PANEL The Advisory Panel of five members is representative of the scientific establishment and provides guidance through its consideration of various scientific and technical problems. Their recommendations have proved to be of great value to the Pro j ec t . The Panel reviews the proposed experiments and their priorities, as well as results from previous experiments. It makes recommendations concerning improving the effectiveness of data collection and evaluation, season length, eligibility criteria for storms to be seeded, and other items as applicable During 1969, the Advisory Panel consisted of the follow- ing prominent scientists: Dr. Noel E. LaSeur, Chairman (Florida State University) , Professor Jerome Spar (Department of Meteorology and Oceanography, New York University) , Dr. Edward Lorenz (Department of Meteorology, Massachusetts Institute of Technology) , Dr. Charles L. Holser (Dean, College of Earth and Mineral Sciences, Pennsylvania State University) , and Dr. James E. McDonald (Institute of Atmospheric Science, University of Arizona) . Meetings of the Advisory Panel and representatives of the cooperating agencies were held in Miami, 5 December 1969, and in Washington, D.C. on 9 and 10 February 1970. The panel was thoroughly briefed on the ex- periments in Hurricane Debbie and on the cloudline experiments conducted this season. They were also kept current on the re- sults obtained from research of the data collected during the seeding experiments. The latest recommendations from the Panel are included in this report as appendix A. PUBLIC AFFAIRS The public affairs team plan, implemented in 1967, was continued. The teams, composed of ESSA and Navy public affairs personnel at the staging bases, Miami and Washington, dispensed information to the public on Project STORMFURY. A coordinated press release and fact sheet on plans for STORMFURY were distributed in advance of the hurricane season. During the seeding of Hurricane Debbie, the requirements of the news media grew fantastically. STORMFURY personnel at the Naval Station, Roosevelt Roads, were kept busy, virtually around the clock, with press releases and answering telephone queries from all over the United States and from places as far away as Honolulu and London. In spite of the amount of interest and the activity required to satisfy the news media, the plan worked well. Much favorable publicity resulted from these experiments. During the seedings, two seats on project aircraft were made available on a pool basis to representatives of the media; one to a reporter and the other to a cameraman representing TV networks. This appeared to be sufficient for these opera- tions; however, it is likely that future experiments will evoke even more interest in STORMFURY operations. PYROTECHNIC DEVICES - SILVER IODIDE In the 1969 season, the pyrotechnic used was the STORM- FURY I unit developed under the leadership of Dr. Pierre St. Amand of the Naval Weapons Center, China Lake. Testing and evaluation of the nucleation effectiveness of the LW-83 com- pound that this unit contains is continuing. This and other STORMFURY pyrotechnics are discussed in appendix B of last year's STORMFURY Annual Report (1968) and in appendix D of this report. For the cloudline experiments the project used the STORMFURY III pyrotechnic unit. Its characteristics are more fully discussed in the Field Operations - Cloudline Experiments" section of this report and in appendix D. AREAS OF OPERATIONS Eligible areas for experimentation in 1969 were the Gulf of Mexico, the Caribbean Sea, and the southwestern North Atlantic region (see fig. 3) . Operations in these areas were limited by the following guidelines: a tropical cyclone was considered eligible for seeding as long as there was only a small probability (10 percent or less) of the hurricane center coming within 50 mi of a populated land area within 24 hours after seeding. There are two primary reasons for not seeding a storm near land. First, a storm seeded further at sea will have reverted to "nature's own" before affecting a land mass. Second, marked changes in the structure of a hurricane occur when it passes over land. These land-induced modifications would obscure the short-range effects produced by the seeding experiments and greatly complicate the scientific evaluation of the results . Figure 3. Project STORMFURY operational area PLANS FOR FIELD OPERATIONS - 1969 The period 4 August through 15 October was established for STORMFURY operations in 1969. The following aircraft were maintained in readiness: 1. Navy Weather Reconnaissance Squadron FOUR - four WC-121N' s . 2. Navy Attack Squadron ONE SEVENTY-SIX - five A-6 Intruders . 3. ESSA Research Flight Facility - two DC-6's, one B-57, one C-54. Air Force, 53rd Weather Reconnaissance Squadron - one WC-130 and one WB-47. The Operations Plan No. 1-69 was adapted from that of 1968, but was extensively revised to make it much simpler and more convenient to use. The plan specified details of the flight operations; communications; instrument calibration and use; data collection, distribution and archiving; logistic and ad- ministrative procedures; airspace reservations agreements; and public affairs. As recommended by the Advisory Panel, Project officials gave a higher priority to the seeding of hurricane rainbands and cloudlines this season than in previous years, but the eyewall multiple seeding experiment was to be accomplished whenever an opportunity arose. In accordance with these priorities, a cloudline experi- ment was scheduled for 9-19 September in the military opera- tional areas near Puerto Rico. Plans also provided for a series of fall-back research missions when no eligible hurricane or cloud system was available after deployment of Project forces. These would be primarily data-gathering and storm-monitoring operations in unseeded storms. The multiple seeding of the eyewall experiment calls for five seedings of the clouds around the eye at 2-hour intervals. Each seeding consists of dropping 208 pyrotechnic units along an outward radial flight path, starting just outside the region of maximum winds. The hypothesis states that the introduction of freezing nuclei (silver iodide crystals are produced by the pyrotechnics) into the clouds in and around the eyewall should cause a chain of events that includes the release of latent heat, warming of the air outside the central core, changes in temperature and pressure gradients, and a reduction in the maximum winds. Data from several cases may be needed, how- ever, before definite conclusions can be reached. Because the magnitude of natural variations in hurricanes is sometimes as large as the hypothesized artificially induced changes, it is difficult to distinguish between the two. The rainband is an important link in the hurricane's cir- culation system and may prove to be the best region in which to attempt hurricane modification. Research findings suggest that a redistribution of energy in the rainbands could lead to modification of the storm itself. The cloudline experiment may provide vital data to help understand the dynamics of clouds organized into systems, such as rainbands. It is important to know whether and to what extent modification of groups of clouds will affect other clouds in the same or nearby lines. These experiments can be conducted when there are no hurricanes and should provide opportunities for improving our understanding of seeding effects and for testing seeding procedures. FIELD OPERATIONS - DRY RUNS Dry runs were conducted at the Naval Air Station, Jacksonville, Florida, on 29, 30, and 31 July, with a general briefing held on 28 July. Participating in these dry runs were aircraft from the Navy Weather Reconnaissance Squadron FOUR (VW-4) , Jacksonville, Florida; five aircraft from Navy Attack Squadron ONE SEVENTY-SIX (VA-176), Oceana, Virginia; and the U.S. Air Force 53rd Weather Reconnaissance Squadron, Ramey AFB , Puerto Rico. The Environmental Science Services Administration's Research Flight Facility (RFF) was unable to participate in the dry run because its personnel had just returned from extensive operations in the BOMEX experiments . Also taking part were scientists from the Naval Weather Service Command Headquarters, Washington, D.C.; Naval Weapons Center, China Lake, California; Navy Weather Research Facility, Norfolk, Virginia; and ESSA's National Hurricane Research Laboratory . Although not all the STORMFURY participants were able to attend, the dry runs were considered successful. Coordination and flight patterns were practiced and data sensors and re- cording equipment tested. All groups performed in an outstand- ing manner. FIELD OPERATIONS - HURRICANE DEBBIE Project STORMFURY personnel went on alert for Hurricane Debbie at 10 A.M. (EDT) Saturday, 16 August, At this time, Debbie was well east of the Lesser Antilles, but was fore- cast to move in such a manner as to become eligible and within Project aircraft range for experimentation. Forces commenced deployment on Sunday, 17 August, Four Navy WC-121n's from VW-4 , five Navy A-6A jets from VA-176, and two DC-6's from ESSA's Research Flight Facility went to the Naval Station, Roosevelt Roads, Puerto Rico. An Air Force WC-130 and a WB-47 from the 53rd WRS stood by at Ramey AFB , Puerto Rico. Personnel gathered from China Lake, California; Washington, D.C.; Norfolk, Virginia; and Jacksonville and Miami, Florida. A general briefing for Monday's operation was held at 4:30 P.M. Sunday. Debbie was forecast to be about 650- 700 mi from the base at the planned time of the first seed- ing. This was an extreme range for the operation, but working on Monday, the 18th, insured at least one experiment even if Debbie took an unexpected (but not impossible) turn to the north and moved out of range. It also provided opportunity for a second experiment on Wednesday if the hurricane con- tinued on a northwestern track. Permission to seed on Monday was requested from and granted by Dr. Robert M. White (ESSA) and Captain E. T. Harding (U.S. Navy) . Flights departed for the hurricane starting at 0500 (GCT) on Monday. Figure 4 shows the on-station times and aircraft planned for the experiment. Considerable additional flight time was required to reach the hurricane and return. Figure 5 shows a seven-level projection of the tracks that were sche- duled for the multiple seeding experiment. Thirteen aircraft made 14 flights and completed all mis- sions close to scheduled time and without major incident. The five Navy A-6 seeder aircraft arrived on station at ap- proximately 2-hourly intervals and released their loads of silver iodide pyrotechnics in the proper regions of the eye- wall clouds . For the 1040 pyrotechnic canisters released by the five seeder aircraft, the firing failure rate was only about 6%. 10 o o o UJ Q 3 1 40 |"C" (RFF WB57l| (OUTFLOW MONITORS) 'J"(AFWB47) C2"(RFFWB57 33 "l","m" ,"n", "0","P", "o" (NAVY A-6'S) (SEEDING A/C ) 1 1 1 ! i i iii OR ) ONITORS ) LSEEDIN6SJ 29 '1" AF WC-130) (CLOUD PHYSICS MONIT (CLOUD PHYSICS AND VARIABILITY M 1 i i i -20 |"A" (RFF DC -61 "B" (RFF DC -6) "A2" (RFF DC -6) 1 ] 1 10 [ "H" (NAVY WC-121N) RADAR AND DROPSONDE 6 "E" (NAVY WC-121) COMMAND CONTROL ( INFLOW MONITORS) 1 "G" (NAVY WC 121 NO |"d" (RFF C-54) "F" (NAVY WC 121 N ) 1 0800Z 1000 Z 1200Z 1400Z T-4 T-2 TANGO T+2 1600Z 1800Z 2000Z 2200 Z 2400Z 0200 H T + 4 T +6 T+8 T + 10 T + 12 T+14 TIME (GMT) Figure 4. Time table for STORMFURY aircraft deployment eyewall experiment . One ESSA DC-6, scheduled to climb to 22,000 feet, lost an engine supercharger, and could not maintain this altitude. Its pattern was changed to 12,000 feet (the same as the re- lieving DC-6) and thus provided almost continuous monitoring of the hurricane at that altitude. One of ESSA's DC-6's completed two 11-hour flights during the experiment and re- turned at 0700 GCT Tuesday morning, signalling the end of this particular experiment. The Data Quality Control Coordinator collected the data logs, radar time lapse film, etc. , and thoroughly debriefed each flight immediately after landing. See tables 1 and 2 for types of data to be collected by the various flights for the eyewall and rainband experiments. A general operational and scientific debriefing was held on Tuesday, 19 August, followed by a briefing for the multiple 11 Figure 5. Various flight patterns flown at different altitudes during the eyewall experiment . 12 Table 1. STORMFURY Data Inventory - Eyewall Experiment FLIGHT A A2 B C C2 D E F G H I J L M N 0 P SF-1 MET. LOG X X X X X SF-2 WB-4 7 LOG X SF-3 SEEDER MET. X X X X X SF-4 RUN REPORT X X X X X SF-5 DAYS OPS X X X X X SF-6 WIND CALIB . X X X X X X X X X X SF-10 MDS LOGS X X X X SF-11 RADARSCOPE LOGS X X X X X X X X X SF-12 RADAR ADV. LOG X X X X X X X X AMQ 17 TAPE X X X X NAV LOG X X X X X X X X X X TRUE TRACK RECORD X DIGITAL TAPE X X X X X X X X PHOTO PANEL FILM X X X X X X RADAR FILM X X X X X X APS-20 FILM (230) X X X X X X X APS-20 FILM (81) X X X X APS-64 FILM x APS -45 FILM X X X X WP-101 FILM X X X RDR-1 FILM X X X X X CLOUD CAMERA FILM X X X X X DROPSONDES X X X X X COLD BOX LOG X X X MET. LOG (RFF) X X X X RADAR LOG (RFF-5) X X X X X X FLIGHT PROG. (RFF-l) X X X X X X FLIGHT INFO. (RFF-2) X X X X X X FLIGHT DATA (RFF -3) X X X X X X DIGITAL STA. (RFF-4) X X X X X X DRT. (RFF) X X X X ELECT. STATUS (RFF) X X X X MET. SYSTEMS (RFF) X X X X CLOUD PHOTOS (RANDOM) X X X X X X X X X X X X X X X X X PERSONAL NOTES X X X X X X X X X X Y Y X Y X x x WWV TIME CHECKS X X X X X X X X X X X X X X X X X FLIGHT DESIG. A A2 B c C2 D E F G H I J L M N 0 p TYPE AIRCRAFT DC 6 DC6 DC6 B57 B57 C54 121 121 121 121 130 B47 A6 A6 A6 A.6 A6 Voice Call is STORMFURY plus Flight Letter (STORMFURY Echo) (Each flight turns in the data collected to DQCC as soon as possible after landing.) 13 Table 2. STORMFURY Data Inventory - Rainband Experiment. FLIGHT A B c E F G H I J L M SF-1 MET. LOG X X X X X SF-2 WB-U7 LOG X SF-3 SEEDER MET . X X SF-a RUN REPORT X X SF-5 DAY'S OPS . X X SF-6 WIND CALIB. X X X X X X X X SF-10 MDS LOGS X X X X SF-11 RADARS GOPE LOGS X X X X X X SF-12 RADAR ADVISOR LOG X . X X . X AMQ 17 TAPE X X X X NAV LOG X X X X X. X X X TRUE TRACK RECORD X DIGITAL TAPE X_j X X X X X X PHOTO PANEL FILM I- x~ X X RADAR FILM X X X APS-20 FILM (230) X X X x X \ APS -2 0 FILM (81) X X J( X APS -6 U FILM X A.PS-U5 FLLM X X X X WP-10 1 FILM X X RDR-1 FILM X X X CLOUD CAMERA FI LM X X X DROP SONDES X X X COLD BOX LOG X X MET. LOG (RFF) X X RADAR LOG (RFF -5) X X X FLIGHT PROG. (RFF-1) X X X FLIGHT INFO . (RFF -2 ) X X X FLLGHT DATA (RFF -3) X X X DIG ITAL STA . ( RFF -U ) X X X DR.T . (RFF) X X ELECT . STATUS ( RFF ) x X MET. SYSTEMS (RFF) X X CLOUD PHOTOS (RANDOM) X X X X X X X X X X X PERSONAL NOTES X X X X X X X X X X X WWV TIME CHECKS X X X X X X X X X X X FLIGHT DESIG. A B c E F G H I J L M TYPE AIRCRAFT DC6 DC6 B57 121 12 1 12 i 12 1 130 B'4? A6 A6 Voice Call is STORMFURY plus Flight Letter (STORMFURY Echo) (Each flight turns in the data collected to DQCC as soon as possible after landing.) 14 eyewall seeding experiment planned for Wednesday, 20 August. Hurricane Debbie was forecast to be approximately 430 miles from base at first seeding time (1200 GCT) . This shorter distance simplified the operation and reduced transit time required to and from the storm. Once again all 14 flights were completed with 13 aircraft available and the second multiple seeding of the eyewall of a hurricane was successfully completed. A general debriefing was held the following morning, and the aircraft and personnel then returned to their home bases to go on standby for the next seeding opportunity. The spirit, teamwo cipants were outstandin technicians repairing i their data collection c facility even managed s DC-6, 40C, during the 2 it was sent back out wi to get a second C-130 f scheduled had to be use 12 hours before Tango ( pecially noteworthy sin such a heavy drain on r craft controllers on th control aircraft (Const directing the seeder ai previous practice opera equipment failed, comma aircraft, and in severa a remarkably short time rk and "can do" attitude of all parti- g. There were numerous incidents of nstruments in flight and restoring apabilities. The Research Flight ome fairly significant repairs on the -1/2 hours allotted for refueling before th a second crew. The Air Force managed light airborne after the flight originally d to obtain fixes on Debbie for 6 and seeding) time on Monday. This was es- ce Hurricane Camille had already made econnai s sane e resources. The Navy air- e command/control and back-up command/ ellations) did a far better job of rcraft (A-6A) than they had done in the tions. When radar or communications nd was shifted smoothly between the 1 cases the equipment was repaired in uch complicated instrumentation and -f the radars Naturally, with so much complicated with so many flights, there were outages were inoperative, or only partly operati Research reports on the data collected and evaluation of the seeding results are included in appendices B, E, and H. Some o: ve at times Additional research studies are continuing and will be published as soon as they are completed. 15 FIELD OPERATIONS - CLOUDLINE EXPERIMENTS STORMFURY forces again deployed to the Naval Station Roosevelt Roads, Puerto Rico, on 8 September 1969 for a series of cloudline experiments planned for the period 9-19 September 1969. Plans had been made to operate either north or south of Puerto Rico in the Atlantic Fleet Weapons Ranges Alpha or Bravo All were actually conducted in the southern, Bravo, region because most of the suitable cloudlines were found to the south during this period. After briefings were completed, flights commenced on 9 September 1969. The cloudline flights were as follows: Sept . WQ121N DC-6 CESSNA 401 WC130 9, 10 , 13 2 2 1 1 15 2 2 2 1 16,17 112 18 -22- Suitable cloudlines were not available on 11, 12, and 14 September, but on the other days forces were launched to con- duct experiments. Of the remaining seven operational days, four (9, 16, 17, 18) were considered good for cloudline experi- ments while three (10, 13, 15) were marginal for various reasons The STORMFURY III pyrotechnic unit used in these cloudline experiments is housed in a Mark 112 photo flash case in the same manner as the STORMFURY I units used in the eyewall seeding experiments. This unit contains , approximately 120 g of EW-20 mixture burning for 20 to 30 sec while falling through approxi- mately 2,000 feet. The Cessna seeder aircraft carried two racks, each with 26 units, located just below and aft of the engine nacelles. (See app . D for further information con- cerning the pyrotechnics.) The seeding aircraft dropped units into rising towers along the monitored cloudline. Following a period of drops, the seeder would depart the immediate area to permit the monitoring aircraft to penetrate the seeded clouds in the line. In addition to the normal aircraft data collection systems, photographic documentation was used extensively. 16 Analysis of these data has not been completed. On several occasions it appeared that individual clouds in a line were caused to fuse into a solid line and increase rapidly in size. Much remains to be learned in this area of research . RESEARCH ACTIVITIES Research on the data collected during the seeding of Hurricane Debbie and the cloudline experiments has continued throughout the year at the National Hurricane Research Labora- tory and at the Navy Weather Research Facility. Studies in- clude analyses of wind fields, temperatures, pressures and clouds (app. B) . Photographs made by time-lapse cameras on aircraft radar scopes are- also being studied. These studies are concerned with changes with time in eye size and shape (app. E) and wind vectors derived from following echoes on the radar photographs. Comparisons are also being made between the radar data and the satellite pictures available from the ATS-111 satellite during the seeding operations. Other studies are of ice and liquid water content, size and distribution of ice particles and water drops and other cloud physics data collected during some of the STORMFURY flights. (See app. F.) Dr. Rosenthal of the National Hurricane Research Labora- tory is continuing his work with the symmetrical hurricane model and in addition his group has begun the development of an asymmetrical model of the hurricane. The simulation of the seeding experiment conducted with the hurricane model is dis- cussed in appendix C. OPERATIONAL AND RESEARCH DATA COLLECTION During the dry run, the eyewall experiments, and the later cloudline experiments, the quality of data collection noticeably improved as experience was gained. Because several radars were partly or completely inoperative, difficulties were still encountered in obtaining all of the radar data needed. These outages were due largely to a shortage of parts with which to effect repairs. As stated earlier, an ESSA-RFF DC-6 aircraft was con- figured to collect cloud physics data during the eyewall ex- periments, but experienced an engine blower failure that pro- hibited a climb to the necessary altitudes. For this reason, 17 measurements of liquid and solid water content and particle size and distribution were made at temperatures below 0°C only during the cloudline experiments and in nonexper imental tropical cy- clones. (Hurricane Laurie, 19 and 21 October; Hurricane Inga, 30 September and 1 October; and Tropical Storm Kara, 11 October.) Data from these flights are still being processed. The system used for debriefing in the Hurricane Debbie seeding experiments worked quite well. Each flight was com- pletely debriefed with comments recorded by the DQCC as soon as possible after landing. This debriefing was in addition to a large general one held later (generally on the follow- ing day . ) Processing of all STORMFURY film was done by a single processor in Miami. This system worked well, except for delays encountered in obtaining duplicate copies of film. OUTLOOK FOR 1970 Project STORMFURY operations will be given increased em- phasis in 1970 . The season should start in late July and continue through October instead of 1 August to 15 October as in the past. Al- so under consideration is a change in the seeding eligibility rules to permit seeding if the hurricane will not be within 50 mi of a populated land mass within 18 hours instead of 24 hours after seeding. (Additional information is given in app . G . ) Priorities will be slightly modified in accordance with the Advisory Panel's recommendations (see app. A) . There will be a few changes in forces for 1970. The Air Force has been requested to provide two WC-130 aircraft be- cause the WB-47 provided last year is no longer available. The Air Force may also provide RB-57F aircraft for high altitude photographic coverage of seeding operations. The ESSA-RFF will be receiving a WC-130 type aircraft to replace the C-54 sometime in August or September 1970. The Navy is seeking a P-3 aircraft to be tested during 1970 for its capability as a seeder and cloud physics data collection platform. 18 Pyrotechnic generators for 1970 are expected to be slightly modified from those used last year. The new unit is called WMU-1 (XCL-D/B and as yet has no nickname. Its chemical contents . however , are similar to those used in 1969. REFERENCES AND SPECIAL REPORTS Edelstein, M.W. (1968): Project STORMFURY operations 1968. Presented at Tenth Interagency Conference on Weather Modification, Skyland, Virginia, October 17, 1968. Gentry, R.C. (1968) : Tropical cyclone modification. Pre- sented at Tenth Interagency Conference on Weather Modi- fication, Skyland, Virginia, October 17, 1968. Gentry, R.C. (1969): Project STORMFURY 1969, Presented at Sixth Technical Conference on Hurricanes, Miami Beach, Florida, December 2-4, 1969. Gentry, R.C. (1969) : Hurricane modification experiments and research in 1969. Presented at ICAS Interagency Confer- ence on Weather Modification, October 15-17, 1969, Skyline Drive, Virginia. Gentry, R.C. (1970) : Hurricane Debbie modification experi- ments, August 1969. Science , 168 , No. 3930. Gentry, R.C. (1970) : The hurricane modification project: Past results and future prospects. Presented at Seventh Space Congress, April 22-24, 1970, Cocoa Beach, Florida. Gentry, R. C. (1970) : Hurricane Modification — Experiments and Prospects. Presented at Hurricane Foresight Con- ference, April 30, 1970, New Orleans, Louisiana. Rosenthal, S.L. (1969) : Numerical experiments with a multi- level primitive equation model designed to simulate the development of tropical cyclones, Experiment 1. ESSA Tech Memo. ERLTM-NHRL 82, 36pp. Rosenthal, S.L. (1969) : Experiments with a numerical model of tropical cyclone development - Some effects of radial resolution. ESSA Tech. Memo. ERLTM-NHRL 87, 47pp. Rosenthal, S.L. (1970) : A survey of experimental results ob- tained from a numerical model designed to simulate tropical cyclone development. ESSA Tech. Memo. ERLTM-NHRL 88, 78 pp 19 Rosenthal, S.L. (1970) : Experiments with a numerical model of tropical cyclone development - Some effects of radial resolution. Monthly Weather Rev., 98 , No. 2. Rosenthal, S.L. (1970) : A circularly symmetric, primitive equation model of tropical cyclones and its response to artificial enhancement of the convective heating func- tions (submitted to Monthly Weather Rev.) . 20 APPENDIX A RECOMMENDATIONS OF THE ADVISORY PANEL TO PROJECT STORMFURY February 1970 INTRODUCTION Without doubt, the major new input for Panel consideration has resulted from the multiple seeding experiments in the eye- wall of Hurricane Debbie on 18 and 20 August 1969. Operation- ally, these experiments were an unqualified success; scientific- ally, the analyses of the results to date have established that a measurable and significant decrease in wind speed occurred subsequent to the seeding and persisted for several hours after seeding ceased, at least on 18 August. Encouraging as the re- sults may be, the analyses to date d_o not , and further analysis probably cannot, provide proof that the seeding caused the weak- ening. Examples of similar decreases in intensity followed by redevelopment can easily be found in past records of nonseeded hurricanes; thus what was observed in Debbie lies within the limits of natural variability, but departs significantly enough from typical behavior to be encouraging. Nor can solid support of cause-and-ef f ect relationship between the seeding and wind speed decrease be supplied from results of current computer simulation of natural and seeded hurricane behavior. Until these model simulations are improved, the results of the cal- culations cannot be considered definitive. Of course, the pre- sent sample of seeded cases is so small as to render statistical estimates of significance highly uncertain. The Panel would like to emphasize that the potentially enormous national benefits that may someday accrue from syste- matic mitigation of hurricane damage, even to a small degree, constitute a worthwhile target of the national weather modi- fication program. We believe the experimental results to date to be sufficiently encouraging to warrant further experimenta- tion, but we caution against such premature conclusions that these results constitute a scientific basis that would justify the implementation of an operational seeding program. The Panel makes the following recommendations at this time, with the objective of focusing attention, financial and material support, and Project effort on those aspects of the program we believe deserve emphasis. RECOMMENDATION ONE The Panel recommends that top priority at all required levels be given to the acquisition by the Project of aircraft and instrumentation necessary to obtain accurate and represen- tative observations of liquid and solid water content of the eyewall and vicinity in the layer from approximately 20,000 to 35,000 feet before, during, and after seeding. Reasons : The fundamental premise of the current eyewall seeding experiments is the existence of significant amounts of supercooled water in this layer and its conversion to ice as a result of the seeding. Measurements of changes in wind speed, pressure profiles, and other parameters cannot demonstrate the truth of this basic premise. Until the type of measurements recommended above has been realized, reasonable doubt as to the foundation of the seeding experiments will continue to exist Evaluations can thus be based upon the degree of the conversion of the eyewall to ice rather than upon the attempted conversion. RECOMMENDATION TWO The Panel recommends continued critical analysis of data collected in association with the experiments in Hurricane Debbie, 18 and 20 August 1969. Reasons : Every effort must be made to describe and under- stand as completely as possible the structure of Debbie before and after seeding and to establish association, if not cause- and-effect relationship, between the seeding and observed changes in storm structure. RECOMMENDATION THREE The Panel recommends continued monitoring of unseeded hurricanes in a manner similar to that carried out after seeding . Reasons : Further quantitative data on the natural var- iability of hurricanes are needed as a background against which to compare the observed behavior of seeded storms. Our know- ledge of natural variability remains quite inadequate to properly assess the reality of changes observed. This com- parison should not be primarily on a statistical basis, but rather on the basis of physical understanding and its com- puter simulation. A-2 RECOMMENDATION FOUR The Panel recommends further expansion of the encouraging efforts of Project personnel in the computer simulation of hurricane structure and behavior. Reasons : In the past few years interaction between those who have collected and analyzed improved data from hurricanes and those who have attempted computer simulation of these storms has certainly been an important factor in the increased degree of understanding we now have of the structure, formation, and behavior of hurricanes. However, hurricane models remain inadequate in providing realistic simulation of these aspects of the hurricane. Improved computer models combined with better data from both seeded and unseeded storms offer probably the most promising avenue of establishing the validity of modi- fication experiments and further improving our understanding of the hurricane. Increased participation by nongovernment groups in this field of research should be encouraged. RECOMMENDATION FIVE The Panel repeats its previous recommendation that pre- liminary investigation of other possible means of hurricane modification be continued. Reasons : There is no reasonable doubt that modification of air-sea energy exchange processes should significantly in- fluence the hurricane. Before undertaking field experiments, the magnitudes involved and the logistic feasibility should be asses sed . RECOMMENDATION SIX Again, the Panel recommends attempts to arrive at an eval- uation of the conflicting evidence as to the relative and ab- solute nucleating effects of the pyrotechnic devices under lab- oratory conditions, and dissemination of this information in appropriate publications. Reasons : Although the truly relevant observations must probably be made in the natural atmospheric environment rather than the laboratory, a resolution of current conflicting results should be attempted. If such a resolution is not possible, that result together with the reasons for it, should be disseminated. A-3 RECOMMENDATION SEVEN The Panel recommends the following priorities be adhered to in executing field experiments during the 1970 season: First Priority - repetition of the multiple eyewall seeding experiment. Second Priority - seeding of organized lines of convec- tive clouds, either in the form of a "rainband" associated with a hurricane or tropical cyclone, or a "cloudline" associated with tropical disturbances of lesser intensity. Reasons : It is imperative that final priority be given to attempts to duplicate the encouraging results obtained from the first multiple eyewall seeding experiments. Within the limits of available logistic capability, however, the Panel encourages cloudline and rainband seeding experiments. These should be attempted on any occasion when project personnel and equipment have been assembled for a potential eyewall experiment that had to be aborted, and in other circumstances, at the discretion of the Project directors. RECOMMENDATION EIGHT The Panel continues to recommend that preparation for field operations include a "dry-run" exercise in which all personnel and equipment are checked out. Actual cloudline seeding ex- periments could be executed as part of such a dry run. Reasons : It is obviously desirable that new personnel and equipment be checked out before an actual experiment. Past ex- perience with such dry runs clearly demonstrates their value. The addition of actual cloudline seeding experiments would fur- ther motivate participants and yield valuable data at little additional investment. RECOMMENDATION NINE The Panel recommends the following changes in eligibility criteria for seeding experiments, in order that the probability of such experiments be increased: (a) the period during which such experiments may be carried out to be extended to 1 July - 1 November, and A-4 (b) the time interval before which the hurricane is forecast to affect a populated land area with a probability greater than 10% be decreased from 24 to 18 hours . Reasons : Evaluation of experience with the current selec- tion criteria, and assessment of the proposed criteria for cli- matological data, suggest a small but useful increase in ex- periment probability would result without increased risk. RECOMMENDATION TEN The Panel renews its previous recommendation that planning for the Project consider longer-term (approx. 5 years) consi- derations with further increases in support. Reasons : This recommendation is perhaps implicit in the previous nine, but it is considered worthwhile to make it more explicit. The Panel believes the Project to be in a position to solidify present results and to extend these significantly if appropriate support and planning were available. Dr. Noel E. LaSeur, Chairman Dr. Charles L. Hosier Dr. Edward N. Lorenz Dr. James E. McDonald Dr. Jerome Spar A-5 APPENDIX B THE HURRICANE MODIFICATION PROJECT: PAST RESULTS AND FUTURE PROSPECTS Dr. R. Cecil Gentry Director, Project STORMFURY National Hurricane Research Laboratory Atlantic Oceanogr aph i c and Meteorological Laboratories ESSA Research Laboratories Miami , Florida INTRODUCTION Results from Hurricane Debbie modification experiments on 18 and 20 August 1969 are so encouraging as to offer hope that man may one day exert a degree of control over the intensity of these devastating storms that originate over the tropical oceans These were the first multiple hurricane seeding experiments ever conducted by STORMFURY or any other group. Earlier modification experiments have been reported by Simpson and Malkus (1964) . Two general considerations justify Project STORMFURY ex- periments: (1) recent improvements in our understanding of the physical processes fundamental to the maintenance of hurricanes suggest good avenues of experimentation, and (2) enormous re- wards can be derived from even a slight degree of beneficial modification. The first will be elaborated in later sections; the second may be illustrated by the following rough "cost- benefit" analysis. Hurricanes caused an average annual damage in the United States of 13 million dollars between 1915 and 1924. By the period 1960 to 1969, this figure had jumped to 432 million dollars. Even after adjusting these values for the inflated cost of construction in recent years, this represents a 650% increase in the average annual cost of hurricane damage in less than than 50 years (Gentry, 1966). Since Americans are constructing more and more valuable buildings in areas exposed to hurricanes, these damage costs should continue to increase. Hurricane Betsy of 1965 and Hurricane Camille of 1969 each caused more than 1.4 billion dollars in damage. If the United States continues supporting hurricane modification research at the present rate for the next 10 years and if by that time we modify just one severe hurricane, such as Betsy or Camille, sufficiently to reduce its damage by only 10 percent, the nation will have a 1000 percent return on its investment. The benefits in terms of prevention of human suffering are, calculable . of cour se , in- At least two fundamentals established in recent years by studies of hurricane structure and maintenance suggest avenues for beneficial modification: (1) an internal energy source is necessary if a hurricane is to reach or retain even moderate intensity; this source is the sensible and latent heat trans- ferred from the sea surface to the air inside the storm, and (2) the energy for the entire synoptic-scale hurricane is re- leased by moist convection in highly organized convective scale circulations located primarily in the eyewall and major rain- bands. In the first, we find an explanation of the observa- tions that hurricanes form only over warm tropical waters and begin dissipating soon after moving over either cool water or land, neither of which provides a flux of energy to the at- mosphere sufficient to keep the storm at full intensity. In the second, we find a more rational explanation of the low per- centage of tropical disturbances that become hurricanes. If a warm sea with its large reservoir of energy were the only requirements, we would have 5 to 10 times as many hurricanes as normally form. During the 1967 and 1968 hurricane seasons, 130 tropical waves were tracked in the Atlantic and adjacent areas where sea surface temperatures were warm enough for hurricane genesis, but only 13 of the areas developed storms of full hurricane intensity (Simpson et al . 1969) . If, how- ever, there are only a limited number of ways in which the convection and synoptic scales of motion can interact to achieve optimum utilization of the energy flowing upward from the ocean, then it is not surprising that few tropical dis- turbances intensify and become hurricanes. THEORY OF MODIFICATION Both of the above findings suggest possible field experi- ments that may beneficially modify a hurricane. On the basis of the first, we may attempt to reduce the flux of energy from the sea surface to the atmosphere, probably through attempts to inhibit evaporation. On the basis of the second, we may try to modify the release of latent heat in the small portion (2 to 5%) of the total storm occupied by the organized active convective-scale motions in a manner that redistributes heating to produce a weakening of the storm. We do not now know of any practical means of reducing the flux of energy from the sea surface to the atmosphere in the gale and hurricane force winds. B-2 We do have a means of modifying the rate of release of latent heat in the clouds of the hurricane. This we can do by introducing freezing nuclei into the clouds containing super- cooled water drops. By causing them to freeze, we could add heat to the air in the storm. The question to be answered is where in the storm could addition of heat result in a reduc- tion in the maximum winds. This is particularly pertinent be- cause the hurricane is a heat engine. It derives its enormous energy by converting latent and sensible heat extracted from the ocean and the warm moist tropical air into potential and then partially into kinetic energy. We have sought the answer to this question by theoretical investigation and numerical modelling work. The theor et i a number a number models a clone wi erize in interact They can interven hur rican lif cal of of re c th r a r ion not tion e qu e cycle mathema univers years ( apabl e ather 1 elative and the predict They ite wel of hurricane s tical models . i t ie s have bee Ooyama, 1969; of simulating imited vertica ly simple fash trans f er of e the effects o do , however , 1. can now be simulated by Researchers at ESSA and at n developing these models for Rosenthal, 1970). Current only an axially symmetric cy- 1 resolution and they paramet- ion the effect of air-sea nergy by cumulus convection, n storm motion of artificial simulate many features of a We also app by seedi iodide ) . have on first qu relative hur rican maximum the belt sugges ts in the h have use . C) to ng the s We hav the inte es t ion i ly warm e . Spec intens it of maxi that th urr icane d the mod get indie upercoole e also as nsity of s to rele air conce if ically , y of the mum winds is can re by about el deve at ions d cloud ked wha the hur ase the ntrated the be hurr ica outwar suit in 15 per lope of w s wi t ef r ica hea in s t c ne i d al a r cent d by here th f feet ne . t ju and hanc s to ong educ S .L to r eez the The st o arou e f o see a ra tion . Rosen release ing nuc seedin answer utside nd the r reduc d from dius . of max thai the lei g mi to the core ing the The imum (19 70; heat ( silver ght the mass of of the the core of model winds THE MODIFICATION EXPERIMENT The modification experiment, therefore, seeks to exploit energy sources within the hurricane. Hurricane clouds contain large quantities of water substance still in the liquid state at temperatures lower than -4°C (fig. B-l) . Introduction of sil ver iodide nuclei at these and lower temperatures should cause the water droplets to change to ice crystals and release the latent heat of fusion, thus providing a possible mechanism for adding heat to the hurricane. One objective of the STORMFURY B-3 Figure B-l. Schematic cross section of a hurricane . experiments is to verify indications from the numerical model that heat should be released at the outer edge of the mass of warm air occupying the central portion of the hurricane in or- der to cause a reduction in the storm's intensity. The experi- ments on Hurricane Debbie were designed to determine if addition of heat in this area would result in diminishing the maximum hor- izontal temperature gradients in the storm and, eventually, in weakening the maximum winds of the storm. HURRICANE DEBBIE EXPERIMENT Hurricane than 100 knots east-northeast operating base treme range for vorable and the course would br Thirteen aircra from ESSA, and the pyrotechnic and the others intensity begin continuing unti Debbie was a mature on 18 August. It wa of Roosevelt Roads, of Project STORMFURY the experiment, but storm was moving we ing it closer to the ft were available -- two from the Air For s for seeding the hu monitored the storm ning about 6 hours b 1 6 hours after the storm with winds stronger s about 650 nautical miles Puerto Rico, the primary (fig, B-2) . This was an ex- other conditions were fa- st-northwestward so that its base as the day progressed, nine from the Navy, two ce. Five aircraft carried rricane with silver iodide, for changes in structure and efore the first seeding and fifth and last seeding. B-4 Figure B-2. Track of Hurricane Debbie, August 1969. Seeding areas on 18 and 20 August are indicated on the track. south and e ly af per ie as we start s i 1 ve them (fig. each There 1014 (Elli The -sou nter ter nee 11 a ed d r io alon B-3 gram is nucl ot e Navy see thwest a ed the w entering sugges ts s the mo ropping dide . E g a line ) . Each should some evi ei activ t al . 19 der aircraft a t 33,000 feet, all cloud on t the wall clou one should cr st intense tern the pyrotechni ach aircraft c leading radia generator con produce in exc dence that eac e at temperatu 6 9 ; also app . pproached the s penetrated and he north-northe d and at a spot oss the radius perature gradie c generators th arr ied 208 of t lly away from t tained 190 g of ess of 1012 fre h gram might pr res found in th D) . torm from the crossed the eye, ast side. Short- where past ex- of maximum winds nt s , the crew at produced the hese and dropped he center silver iodide and ezing nucl ei . oduce more than e hurricane clouds B-5 >4— NAVY AIRCRAFT — 35,000 FT. STORM MOVEMENT <^ Figure B-3. Track of seeder aircraft Each seeding run lasted 2 to 3 min or between 14 and 20 n mi. The five seeding runs came at intervals of approxi- mately 2 hours on each of the 2 days. On the 20th, the first seeder aircraft flying at 30,000 feet commenced its dropping run after circling in the eye. Upon entering the eyewall clouds it experienced extremely strong downdrafts which forced the aircraft down to 27,000 feet. Release of the generators was made during the descent but close to the proper location. No other seeder flights on either experimental day en- countered turbulence that could be considered more than light or briefly moderate. B-6 DATA FOR EVALUATING THE EXPERIMENTS flig tail DC-6 simi brat Data ning to r stor hurr unti acco stor not the matu ment 95 p Many hts an ed inf aircr lar in ed and from and t elieve m , in icane 1 5 or mpl ish m was make t second re hur s at s er cent data wer d some b ormation aft of E s trument have cr the two esting c each ot order to by one o 6 hours ed , exce at such he round aircraf r icanes everal 1 as stro e coll y the was c SSA 's at ion ews tr aircra an mak her in provi f them after pt for great trip t coul such a evels , ng as ec te five olle Res e sy s t aine ft a e th mak de a fro the som rang to b d re s De the thos d by pe seeder cted at arch Fl ems whi d in us re as n em. Th ing rep lmost c m 3 hou fifth e time e that ase for main on bbie wh 12 ,000 e near r son air 12, ight ch h ing earl ese etit ont i r s b one . gaps the r ef s ta ere - f oo the nel in craft . 000 fee Facili ave bee the sam y compa aircraf ive pas nuous c e fore t This on 18 first a uel ing t ion . we have t winds surface the The t by ty. n cr e te r abl t we ses over he f was Augu ircr dur i In p mad hav (Ha monitor mos t d the tw They h oss- cal chnique e as pi re as s i aero ss age of irs t se e ssent i st when aft cou ng the r evious e measu e been wkins , ing e- o ave i- s . ali- gned the the eding ally the Id time re- about 1962) The flight patterns called for each aircraft to make a round trip across the storm from a point about 50 n mi east- southeast of it or to a point beyond the belt of strongest winds. Each aircraft then flew similar traverses from the south-southwest quadrant to the north-northeast quadrant until fuel shortage dictated departure from the storm. Since we have more data on the later passes, they are the ones presented in figures B-4 and B-5. In most cases with a storm moving west- northwest the strongest winds are found a short distance north- northeast of the center. RESULTS AND DISCUSSION Between successive passes on both the 18th and 20th, the winds sometimes increased and sometimes decreased. In the mean, however, the wind speeds decreased from shortly after the second seeding until at least 5 or 6 hours after the fifth seeding. This decrease was most marked on the 18th (fig. B-4) . Before the first seeding on 18 August, maximum winds at 12,000 feet were 98 knots. By 5 hours after the fifth seeding they had decreased to 68 knots, or by 31 percent. The storm re- intensified on 19 August, starting about 8 hours after the last seeding on the 18th. On 20 August the maximum wind speed before the first seeding was 99 knots. Within 6 hours after the final seeding the maximum had dropped to 84 knots, a decrease of 15 percent . B-7 100 90 - 80 w I- o z - 70 Q LU UJ CL CO 60 Q Z 50 40 ""PROJECT 1 r- STORMFURYk HURRICANE "DEBBIE" Modification Experiment AUGUST 18, 1969 WIND SPEEDS (12,000 feet) BEFORE FIRST SEEDING AFTER THIRD SEEDING 4 HOURS AFTER FIFTH SEEDING 40 30 20 10 0 10 20 30 40 ssw DISTANCE FROM HURRICANE CENTER (Nautical Miles) NNE Figure B-4 Changes with time of wind speeds at 12,000 feet in Hurricane Debbie on 18 August 1969. The winds were measured by aircraft flying across the storm from south-southwest to north-northeast or the reciprocal track. Profiles are given that show the wind speeds before the first seeding} after the third seeding, and after the fifth seeding. The response of the winds to the more impressive than this summary sug wall cloud structure on this day. Th centric walls with radii of approxima spectively. Each was associated with at corresponding radii. The hypothes for the nuclei to be introduced into distance than that of the maximum win so conducted relative to the inner ma seeding was performed beyond the oute of the inner maximum started decreasi seeding on ges t s . Debb at is , there tely 10 and a maximum o is for the e clouds at gr ds. All the ximum, but o r maximum, ng after the 20 August was ie had a double were two con- 2 0 n mi , re- f wind speed xperiment calls eater radial seedings were nly the fifth The wind speeds second seed- B-8 ^PROJECT STORMFURY" HURRICANE "DEBBIE" Modification Experiment AUGUST 20, 1969 WIND SPEEDS (12,000feet) 100 - 90 80 v> O z x 70 Q Id 2> eo 50 40 - BEFORE FIRST SEEDING 6 HOURS AFTER FIFTH SEEDING 40 ssw 30 20 10 0 10 20 30 DISTANCE FROM HURRICANE CENTER (Nautical Miles) 40 NNE Figure B-5. Same as fig. B-4, except that the wind speed profiles are for 20 August 1969 and are for the periods before and after the seedings . ing, but the outer maximum did not show after the last seeding. a net decline until Variations in the force of the wind are closely related to variations of the square of the wind speed or the kinatic energy of the air particles. These decreases in maximum winds repre- sent a reduction in kinetic energy in the belt of maximum winds of 52 and 28 percent, respectively, on 18 and 20 August. That Hurricane Debbie decreased in intensity following multiple seedings on 18 and 20 August is well established. What we do not know is whether the decrease was caused by the seeding, or whether it represents only natural changes in the hurricane . From analyses of past storms, we can, however, make some statements as to the probability that the changes observed might have occurred naturally. The rate of rise in central pressure in Debbie that accompanied the reduction in wind speed B-9 on 18 August has occurred in only 9 percent of 502 periods of similar length we have studied in other tropical cyclones. Our measurements of winds in previous hurricanes are less complete than are those of pressure changes, but it is believed that the rate of decrease in wind speeds on 18 August is a relatively rare event. Although the decrease in wind speeds on 20 August was smaller than on 18 August, this rate of decrease occurs in con- siderably less than one-half of the hurricane days. Further- more, on each of the days, the reduction in wind speed occurred at a time when it could reasonably have been caused by the seed- ing experiment. Rough agreement between resul experiment with the numerical mode Hurricane Debbie gives some suppor seeding caused a reduction in Debb experiment, M2 , suggests that the would begin about 4 hours after in seeding and would continue until a ceased. This is approximately wha August in the Debbie experiments, ment indicated that the reduction would be about 15 percent. The De tions of 31 and 15 percent at 12,0 many unknowns in both the model an this agreement should certainly be if not remarkable. It is clouded, the model experiment did not indie reduction in the maximum wind spee level in the model closest to 12,0 ts from th 1 (app. C) t to the h ie's maxim reduc tion itiation o bout 4 hou t happened The model of maximum bbie exper 00 feet, d the fiel cons ider e however , ate as muc ds at 700 00 feet (s e simulated seeding and those from ypothesis that the um winds. The model in sea-level winds f the simulated rs after seeding on 18 and 20 simulation experi- winds at sea level iments gave reduc- Considering the d experiments , d satisfactory by the fact that h as 15 percent mb , which is the ee app . C) . Analyses of other data collected on Debbie give some support to the hypothesis that the hurricane was modified by the seeding. In most hurricanes the diameter of the eye varies directly with the radius of the maximum winds. Since experi- ments with the theoretical model suggest that there would be an increase in the radius of maximum winds, we investigated changes in the structures of the hurricane eye and the clouds surrounding it . Airborne radar photographs of Hurricane Debbie, taken on 18 and 20 August 1969, were used to measure the echo-free area within the eye (see app. E) . Results for the 18th show sudden increases in echo-free area 1 1/4 hours after seeding time for several of the seedings. Results for the 20th were quite different. The most ob- vious evidence on that day suggesting seeding effects was the B-10 rotation rate of the major axis of the elliptical eye. A re- duced rate of rotation occurred within 10 min after each seed- ing. This was followed 1 1/2 hours later by a rapid increase in the rotation rate, which continued until the next seeding time. The period of the cycle (the time required for one com- plete revolution of the major axis) was about 2 hours, which was the approximate interval between seedings. Based on a limited number of cases for nonmodified storms, it seems likely that these changes observed in Debbie's radar images are relatively rare. We can conclude that changes in maximum wind speeds and other items related to structure of Hurricane Debbie were ap- preciable following modification attempts on 18 and 20 August. Study of past storms reveals that the changes come within the range of natural variability. The data are certainly very suggestive, however, that the experiment caused some modifica- tion in the storm. FUTURE PLANS The thing that seems obvious is that since results of the 1969 modification attempts suggest so strongly that modifica- tion was accomplished, the experiment must be repeated on one or more additional storms as soon as practical to seek further confirmation. We must also continue searching for clues from the data still to be analyzed, and from results of our theoret- ical investigations in order to better identify probable cause and effect relationships and to improve design of our seeding exper iments . The various groups supporting STORMFURY are proceeding with preparations that will make it practical to do the multiple seeding experiment on four different hurricane days during the 1970 season if nature provides the opportunities. In addition, other experiments are planned for use when a hurricane is not satisfactory for the big experiment. These involve seeding the bands of clouds spiraling around the hurricane, and seeding them at distances greater than 40 n mi from the center of the hurri- cane. At these radii the thermal structure and lapse rates in clouds are very different from those nearer the center of the hurricane. The objective of seeding these outer clouds would be to make them become more active and offer competition to those nearer the center. It is believed that in this manner the energy of the storm could be distributed over a larger area and not be as intense in the area of principal concentration. B-ll A dry run will be performed in July to check out new pro- cedures suggested by the Debbie experiments and to train the new crews that will be participating in the modification ex- periment for the first time. This will be followed by some experimental seedings of clouds arranged in lines but in cir- culations not related to a tropical cyclone. This will pro- vide opportunity to study not only the effect of seeding on individual clouds but also the interaction between adjacent clouds when both are seeded. Knowledge thus gained should be applicable to the design of modification experiments on the tropical storms and hurricanes to be seeded later in the summer. ACKNOWLEDGMENTS I wish to express deep appreciation and pay tribute to all those who have contributed to the success of STORMFURY. These include the Navy, Air Force, and ESSA crews who made the field experiments on Hurricane Debbie a success; members of the National Hurricane Research Laboratory and other agen- cies who have assisted in the research; and the STORMFURY Advisory Panel. The work herein reported has indeed been the result of a team effort. REFERENCES Elliott, S.D., Jr., R. Steele, and W.D. Mallinger (1969): STORMFURY pyrotechnics, Project STORMFURY Annual Report- 1968, U.S. Department of the Navy and U.S. Department of Commerce, App. B, 1. Gentry, R. Cecil (1966) : Nature and scope of hurricane damage, Hurricane Symp., October 10-11, American Society for Oceanography, Houston, Tex., 229. Hawkins, H.F. (1962) : Vertical wind profiles in hurricanes, National Hurricane Research Project Report No. 55, U.S. Weather Bureau, Washington, D. C. Ooyama, K. (1969) : Numerical simulation of the life cycle of tropical cyclones, J. Atmospheric Sci., 26 , No. 1, 3. Rosenthal, S.L. (1970): Experiments with a numerical model of tropical cyclone development: Some effects of radial resolution, ESSA Tech. Memo. ERLTM-NHRL 88.. Simpson, R.H. and J. S. Malkus (1964): Experiments in hurri- cane modification, Sci. American, 211 , 27. Simpson, R.H., Neil Frank, David Shideler, and H. M. Johnson (1969): Atlantic tropical disturbances, 1968, Monthly Weather Rev. , 97, No. 3, 240. ~~ B-12 APPENDIX C A CIRCULARLY SYMMETRIC, PRIMITIVE EQUATION MODEL OF TROPICAL CYCLONES AND ITS RESPONSE TO ARTIFICIAL ENHANCEMENT OF THE CONVE.CTIVE HEATING FUNCTIONS Stanley L. Rosenthal National Hurricane Research Laboratory Environmental Science Services Administration Miami , Florida INTRODUCTION Over the past few years, a primitive equation model that simulates the development and structure of tropical cyclones with a fair degree of reality has been developed at the National Hurricane Research Laboratory (Rosenthal, 1970a, 1970b) . While the primary motivation for this work has been to increase under- standing of hurricane dynamics, we have also realized that such a model would have some value for testing and evaluating var- ious experiments that have been suggested for trial in hurri- cane modification. The calculations discussed below were aimed at testing a variant of the hypothesis presented by Simpson and Malkus (1964) . The first few experiments carried out with the model dur- ing the early spring of 1968 suggested that a slight variant of Simpson's and Malkus' proposal might be worthy of con- sideration. These calculations showed that during (unmodified) intensification of the model storm, maximum heating (nominally associated with the "eyewall") was located at a significantly smaller radius than was the surface wind maximum. As develop- ment proceeded, the wind maxima moved inward more rapidly than did the heating maxima. Invariably, development ceased, and decay began when the heating maxima and the surface wind maxima became nearly coincident. The implication of this sequence of events, at least for the model storm, is that heating at radii less than that of the surface wind maximum is favorable for in- tensification and that the reverse is true for heating at radii greater than that of the surface wind maximum. Some seeding simulations performed in 1968 seemed to veri- fy this notion. However, at that time, the model was very crude and preliminary compared with its currant form. When the "-ssed- ing" was done at radii greater than that of the surface wind maximum, we found decreases in intensity of greater magnitude and of longer duration than those observed when the "seeding" crossed the maximum winds (Gentry, 1969) . In both cases, how- ever, the "seeding" was at radii greater than that of the strongest "natural" heating. The results of these calculations were used as guidance material for planning the 1969 field ex- periments (Gentry, 1969) . The calculations in 1968 were intended to simulate "single seeding" field experiments in which the seeder aircraft dis- charges its material once in a pass of 2 to 3 min covering a radial interval of about 30 km. Those involved in the field program (Gentry, 1969) were of the opinion that a single seed- ing experiment could release heat of fusion over the 500- to 300-mb layer equivalent to a heating rate of 2°C per 30 min and lasting for 30 min. At 300 mb , this amounts to freezing about 2.5 g of water per cubic meter per half hour. At 500 mb , the figure is approximately 4 g of water per cubic meter per half hour . To simulate this process, the heating function that repre- sents the cumulus feedback on the macroscale (Rosenthal, 1969) was simply increased by the amount and for the period cited above at selected radii. The author is well aware that substantial uncertainty exists concerning the "true" heat of fusion released in such ex- periments and recognizes the obvious need for further obser- vations and experiments aimed at establishing these freezing rates. Because of this uncertainty, because of the extremely crude manner in which the seeding is simulated, and for still other reasons to be cited later, results obtained from the model must not be taken too literally; at best they should be considered guidance material. Processed data from the 1969 field experiments on Hurricane Debbie became available in October 1969 and have been summar- ized elsewhere (Gentry, 1970; also app . B) . On both days sig- nificant decreases in wind speed at the 12,000-foot level were observed. On August 18, the wind maximum at the 12,000-foot level decreased by about 30 knots after the seeding was com- pleted . As part of the effort aimed at determining the extent to which the observed changes could be attributed to intervention by man, we attempted simulations of multiple seeding experi- ments of the Debbie type. Results are presented below. C-2 REVIEW OF THE MODEL As already noted, between the 1968 and the 1969 seeding simulations, the model had been substantially improved. A recent report (Rosenthal, 1970b) discusses these changes in detail; hence, only a brief summary is presented here. The vertical structure of the atmosphere is represented at seven levels with geometric height as the vertical coor- dinate. These levels correspond to pressures of 1015, 900, 700, 500, 300, 200, and 100 mb in the mean tropical atmosphere. All variables are defined at all levels. Circular symmetry is as- sumed, and the primitive equations are employed. External gravity waves are eliminated through a simplification of the continuity equation. The radial limit of the computational domain is 440 km, and the system is open at this lateral bound- ary. Boundary conditions here require the horizontal diver- gence, the vertical component of the relative velocity, and the specific humidity to be zero. The model simulates convective precipitation (and the macroscale heating due to this latent heat release) as well as the enrichment of the macroscale humidity due to the presence of the cumuli. Convection may originate in any layer, provided the layer has a water vapor supply from horizontal convergence and conditional instability exists for parcels lifted from the layer. Nonconvec tive precipitation is also simulated. With the exceptions cited here, the version of the model used for the 1969 seeding simulations is identical to the one described earlier (Rosenthal, 1970b). The original model simulated the air-sea exchanges of sensible and latent heat through the requirement that temperature and relative humidity at the lowest two levels (1015 and 900 mb ) be steady state and horizontally uniform. This pragmatic restraint is still pre- sent in the calculations discussed before (Rosenthal, 1970b) . However, by November 1969, when the new seeding simulations were performed, the program had been generalized to include explicit predictions of the air-sea exchanges of sensible and latent heat . In summary, changes in the model between the 1968 and 1969 seeding simulations consisted of (1) addition of the explicit water vapor cycle and the nonconvective precipitation, (2) sim- ulation of convection that originates above the boundary layer, (3) improvement of the surface drag formulation, (4) inclusion of the explicit predictions of air-sea exchanges of sensible and latent heat, and (5) refinement of the radial resolution from 20 to 10 km. C-3 Despite the fact that this model is one of the more so- phisticated of the circularly symmetric models in existence and that it has provided extremely realistic results (Rosenthal, 1970b) it does suffer from two major deficiencies. The first is the highly pragmatic parameterization of cumulus convection (Rosenthal, 1970b). Substantial improvements in this area must await increased understanding of both cumulus convection and its interaction with macroscale flows. The second major difficulty comes from the assumption of circular symmetry and precludes direct comparison between model calculations and specific real tropical cyclones. The latter are strongly influenced by interactions with neighboring synop- tic systems, and these vary markedly in character from storm to storm. The model results must, therefore, be considered representative of some sort of average cyclone. Despite this, some interesting comparisons between the seeding simulations described below and the field experiment are found elsewhere in this report and show a number of areas in which the model behaves in a fashion similar to the observed behavior of Hurricane Debbie. There are, of course, also areas in which the model calculation and the field experiments show significant differences. THE CONTROL EXPERIMENT The major characteristics of the control calculation se- lected for this purpose (Experiment S18) are summarized below. This experiment differs from one already published (Rosenthal, 1970b) only in the more general treatment of air-sea exchanges of sensible and latent heat as described in the previous sec- tion . Figure C~l summarizes the* sea-le ve 1 history of Experiment S18. Deepest central pressure and strongest winds occur at 168 hours. These peaks, however, appear to represent "over- shooting" of an equilibrium state and, as shown below, a closer approach to a steady state occurs between 192 and 216 hours. As we have noted in previous papers (Rosenthal, 1969, 1970a 1970b) the vertical motion at 900 mb is an excellent measure of the convective heating in the model. From the bottom sec- tion of figure C-l, therefore, it is clear that the relation- ship between the radius of maximum heating and that of the strongest surface winds is as described in the introduction, i.e., during the growth stage; strongest heating is at a radius smaller than that of the strongest surface winds. After maximum intensity is reached, the inverse appears to be the case . C-4 1015 975 J I I I I I I I I I I I L i i i i J I I I I I I 250 -.200 oc I- UJ 5 150 o 3 100 - Q < 48 96 144 192 240 288 336 TIME (HOURS) 48 96 144 192 240 288 336 TIME (HOURS) 50 *v 1 MAX. " LAYER 1 1 1 1 1 MAX SFC X. .WIND o \ 0 \ V BOUNDARY o\ VER MOTION^ o\ \°v 1 I I I I I i EXP Si8 . c GALE FORCE SFC WIND /HURRICANE FORCE SFC WIND o % °o 1 1 1 1 ^ nOOOOOOOOOO0OO" of 1 1 1 1 1 1 1 48 96 144 192 240 288 236 TIME (HOURS) Figure C-l Results from Experiment S18 . Top: Central pressure as a function of time. Center : max- imum surface wind as a function of time. Bottom, Radii of maximum surface wind; outer limit of hurricane and gale force winds at the surface . Radii of maximum 900-mb vertical motion. C-5 Figure C-2, which shows detailed histories of several var' iables during the 192- and 216-hour period, verifies the near- steady state of the model storm at this time. The net change in central pressure is less than 1 mb , while the surface wind maximum changes by less than lm-sec . An oscillation with a period of about 8 hours appears in the data, but the amplitude is quite small. In the 700-mb winds, where the amplitude ap- pears greatest, it is less than 0.5 m-sec Figures C-3, 4, 5, and 6 further verify the near-steady state of the model storm during the period of interest. The 8-hour oscillation is clearly also present in the 300-mb tem- peratures (fig. C-5) and the boundary layer vertical motion (fig. C-6) . Figures C-7 through 10 provide additional information concerning the structure of the model storm at hour 192 but may be considered representative of the entire period of 192 to 216 hours. PROCEDURES FOR THE SEEDING SIMULATIONS The heating rates for the seeding simulations were es- tablished after discussion with Dr. Gentry. These consulta- tions revealed that he continued in his belief that 2°C per 1/2 hour was the correct heating rate for a single seeding. However, he was now of the opinion that the effect would be felt for at least 1 hour (in contrast to the half hour cited at the time of the 1968 calculations) . It was also Dr. Gentry's belief that the enhanced heating might be more or less continuous over the 10-hour period spanned by a multiple seed- ing operation of the Debbie type. The seeding simulations may be distinguished from each other, therefore, on the basis of three characteristics: (1) Whether the enhanced heating function is applied continuously or intermittently. (2) The radii at which the enhanced heating is applied. (3) The magnitude of the enhanced heating. As for the 1968 calculations, the heating function is en- hanced only at the 300- and 500-mb levels, the levels in the model that are in the layer seeded in the field experiment. For enhanced heating of the intermittent type, the heating functions were increased during 192-193 hrs , 194-195 hrs , C-6 984 982 - i980 - 978 192 196 200 204 208 212 216 TIME HOURS) 192 196 200 204 208 212 216 TIME (HOURS) UJ Q < cc CD I- z u o 192 196 200 204 208 212 216 TIME (HOURS) cc < J.O _JL i i i 1 1 16 14 12 -♦ • — - i (P45-Bl5)V ^(P25-P5) 1 1 SPACE VARIATIONS SFC PRESSURE (Slfl)_ 1 1 192 196 200 204 208 212 216 TIME (HOURS) 10 9 8 7 6 £ 1 1 1 1 1 - aOOMB'^* ' """""" " — *~— -, — - - TEMPERATURE ANOMALIES (S18) RADIUS =5 km. ►— 300MB*5, 7**'** /500MB ,"""","<.ui.K«'>",,|l»»nutni.iu«"«" 1 ! 1 1 1 192 196 200 204 208 212 216 TIME (HOURS) Figure C-2 Results from Experiment S18. Time histories of: (A) Central pressure, (B) maximum sur- face wind, (C) maximum 700-mb winds, (D) sur- face pressure differences between 45 and 15 km Csolid) and between 25 and 5 km, and (E ) tem- perature anomalies at 5 km radius, 200 mb (solid), ZOO mb (dashed), and 500 mb (XXX). 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O 3 3 +5 is 3 CSS &4 (03S/W) Q336S QNIM OdS CO 03 O -u a co 00 0) is 3 E 3 O p v (o^: K Ss O s CU O OS * Cq ca ^ +s O if) if) E ■«» a ~1 is O ^ < <+--> is ca o fx, ca *• co a, ir +i r-o> co rO a o 3 -^ ^ ro CO T3 S ca « -^> O ^ oq 3 OJ o ex. -«HI ca )° is 3 tss C-10 (aw) aynssayd aavargvis +a £ <*-» -U> Q> o <3 S V s 3i Sh 0 TO CO **i « Cu-^ £ H « o tei 0) K to « S O CO Q> ?h CO Ss . «K O 3 to ?H 4i fc CO <0 « 3 +s Sh o Ki 0) ^ ,3 • Cl, CO °o s oo 0) T-H 0) Oi Oq to +i M Ci v-i ?H 3 C33 •^ k< 4^ s <+-> 0) o s V £ +^ Sh O <3 CD '^ G.-P *X3 H O 0) Pq c» co CO »j S co O CO h CO "C3 • *K O K co Ss V fc co O 3 3 ■P O ^ r^ rC 3 • « CO co +i . 1 1 1 1 1 1 204 HOURS _ - // s N V *l x. \ x. — fl fl fl 1 // - // // _// - Jl ' 1 ,t I I 1 1 1 1 10 20 30 40 50 60 70 80 90 RADIUS (KM) J I I L 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) Figure C-ll Results from Expervment Ml. Comparison of surface wind profiles with the control experiment (S18) as a function of time. Dashed arrows indicate grid points at which enhanced heating was applied. C-13 is about 5 m sec less than the maximum for the control. However, substantial portions of the "seeded" storm continue to show winds stronger than those of the control. Figures C-11D through F show the new wind maximum at 40 km to be a stable feature of the modified model storm. The de- crease in intensity noted between 204 and 208 hours does not continue indefinitely/ and the system appears to oscillate in an attempt to find a new equilibrium. At 216 hours, winds at the 20-km radius are about 14 m sec less than those of the control. However, the maxima for the two experiments differ by only about 3 1/2 m sec At 70 0 mb (fig. 12), intensification during the first 4 hours is significantly greater than at the surface, presum- ably because of the absence of the moderating effects of sur- face drag. By 200 hours, a new 700-mb wind maximum is estab- lished at 50 km, and, in contrast to conditions at sea level, the new maximum is stronger* (by about 3 1/2 m sec ) than that of the control. At the radius of the new maximum, 700-mb winds are about 10 m sec greater than those of the control. While the sense of the evolution of the 700-mb data is more or less similar to that found at the surface, only at 208 hours (6 hours after the termination of the enhanced heating) is the maximum in the modified storm less than that of the control. In summary, figures C-ll and 12 show the evolution of the wind field to be in some degree similar to that predicted by the slight variant of the Simpson hypothesis suggested in the introduction. The wind maxima do establish themselves in fairly stable configurations at larger radii and with less in- tensity. However, beyond 30 to 40 km, surface winds become more intense than those of the control. When the enhanced heating is terminated, winds tend to decrease. However, this decrease is not per s is tent, and the modified storm oscillates apparently in an attempt to find a new balanced state. The evolution at 700 mb is similar, but here the initial intensi- fication is greater, and during most of the calculation the 700-mb wind maximum is stronger than that of the control. However (see footnote) , the latter factor may be due to grid spac ing . The histories of these wind maxima as well as those of the central pressure are summarized in figure C-13. The central * The configuration of the control 700-mb profile indicates that with finer resolution the results at this level might change significantly. C-14 I — i — i — i — i — i — r 196 HOURS I I I l I I l L 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 40 1 _ D i i i i i i o , _ — *\ UJ _ / s ^-^ — CO ^30 / 1/ •^ ^k^ Q i ? 20 - fj - CO 5 fi O ji 208 HOURS r- 10 n ' i t t i i t iii i i i 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 40 i i i I I I I I o * — "v >^ ^^ LU CO ' /^, \ >* ' ^^ ^v £30 - o z if * ?0 J — CO 5 o o N 10 n f 212 HOURS _ f t t i i i i i i i i i i i 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) - c 1 — i — i — i — i — i — r 204 HOURS I l I I I i l 1 I L 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) i — i — i — i — r 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) Figure C-12. Results from Experiment Ml. Comparisons of 700-mb wind profiles with those for the control experiment CS18) as a function of time. Dashed arrows indicate grid points at which enhanced heating was applied. C-15 192 196 200 204 208 TIME (HOURS) 212 n — 216 192 196 200 204 208 TIME (HOURS) 212 216 200 204 208 TIME (HOURS) 216 Figure C-13. Comparisons of time histories of Experiment Ml with those of the control: (A) surface wind maxima, (B) 700-mb wind maxima* and (C) central pressure . c-16 pressure decreases during the period of the enhanced heating and begins to increase only after the "seeding" is terminated and even then is never more than about 1.5 mb greater than the control. The evolution of the 300-mb and 500-mb temperatures ( figs. C-14A and B) at the midpoint of the "seeded"region (35-km radius) shows rather small increases, which never exceed 2°C. However, the radial temperature gradients are reduced substantially ' (figs. C-14C and D) and the surface pressure gradient is correspondingly reduced (fig. C-14E). Figure C-15 (compare with fig. C-6) shows that the maximum low level vertical motion shifts outward to a radius of 35 km and increases slightly in strength until the enhanced heating is terminated. Thereafter, it remains fixed at the new loca- tion while oscillating in magnitude. CONTINUOUS, NORMAL HEATING AT LARGE RADII (EXPERIMENT M2 ) Experiment M2 was also conducted with normal and continu- ous heating, but the enhancement was at large radii. At this heating rate, the differences between heating enhancement at small and large radii were small, but in the sense predicted by the arguments in the introduction. EXPERIMENTS WITH EXTREME HEATING Two experiments are of prime interest in this section: (1) Experiment M5 (continuous, extreme heating at small radii ) . (2) Experiment M6 (continuous, extreme heating at large radii ) . Figure 16 compares surface wind maxima for these calcula- tions with those for Experiment M2 . A surprising aspect of the figure is the tendency for the three results to approach each other near the end of the calculations, despite the fact that enhanced heating in Experiments M5 and M6 is nine times that for M2 . The major differences are in the first few hours when the strength of the wind maximum for M6 (extreme heating, large radii) decreases dramatically and then increases in an equally dramatic fashion. The surface wind profiles for Experiment M5 behave very much like those for Ml and M2 (fig. C-17) . In M6 however, the original surface wind maximum is destroyed very rapidly. The sharp reduction in surface wind at 194 hours of M6 (fig. C-16) represents a transition period in which the orig' inal maximum has been weakened and the new maximum has not yet C-17 192 196 200 204 208 TIME (HOURS) 212 216 192 196 200 204 208 TIME (HOURS) 212 216 I 1 1 1 — I- 300 Mb ABS Temp Difference (45km-i5km) Radius *« -ENHANCED HEATING H I II I I 196 J L 200 204 208 TIME (HOURS) 212 216 192 196 200 204 208 TIME (HOURS) 212 216 16 — =is^ri- -,'--!«- -J--1— - — I ^CONTROL .1- — * * 1 1 E SFC Pressure Diff. (45Km-15km) Radius a? 14 < ^12 EXP Ml> -J * 10 ■ — ENHANCED HEATING H 1 1 1 1 1 1 1 1 1 1 1 192 196 200 204 208 TIME (HOURS) 212 216 Figure C-14 Comparisons of time histories of Experiment Ml with those of the control: (A) 300-mb temper- ature anomaly at a radius of 35 km3 (B) 500-mb temperature anomaly at a radius of 35 km3 (C) temperature differences at 300 mb between radii of 45 and 15 km> (D) temperature differences at 500 mb between radii of 45 and 15 kms and (E) surface pressure differences between radii of 45 and 15 km. C-18 3 • I 1 1 i VI 1 1 £ :/ ^k*^ o a to • -V ^ o h ""a ^ :§: X " »-«.. « v-^- -

to S -^ •v 'y ^ ^ o) Si g e &, O S^ ^ Cq x K"^ 0 " cl o: cl 0) s-, q> oo *.\ XXX LlI uj lu O h- £ !n fx, cu'ta "S. •^> 3 H H S a X / ? r " 1 ~ O CVJ E-i CO tq Eq « / ; 1 : i • ' > X • X i / to \ / CO v-i — • cr> --^ ^** «H 1 <0 ■V? 0) ■k — i- ■ r" 1 1 1 1 CVJ CD 3 ^ 1- ro CO >H o CD 00 1^- to in Cn> <; 1- 5^ ^ is O in 0) ^Q r«- fX, CO £ H S I tc] '^ Ci m ■Xj <^> to £ a Oi o $^ • ?H 1 <*-» £ <(-, 0) O O £ •^> CO *^ K -^> to 4^> &H O O in — ^5 ^ •^ £ s -^> < CO • O r-i m rO 03 r-H 0) « ^ ^ CO O m CVJ uo m 3WI1 i 0) C-19 40 o30 — 1 A t * /\ (i '7 ■I i i i i i 1 '""•^NT §20 5 - /• • • CONTROL '•-•^* • • EXP M6 J i « EXP M5 o w 10 n i t i I 194 HOURS T f_fEXf» M5 1 1 f j t^EXP M6 1 1 1 1 1 1 1 1 1 10 20 30 40 50 60 70 80 90 RADIUS (KM) 40 1 1 1 1 1 1 1 1 - /v/^^V. "30 en 2 ■ l' *"'• ^v*»-^ Q20 " / 5 - 1 o <"10 / 208 HOURS 7 t ♦ ♦ / 1 ' / til ' 1 1 1 1 1 1 1 1 1 1 1 10 20 30 40 50 60 70 80 90 RADIUS (KM) 40 1 B 1 1 i i i i / ^ ' "-.-4 ^ ^v i o30 " ' * \\ _ ID i / ■•■.. ^v co tl ^ •••. ^ 5 If: "■••.._ §20 - >h II - ? - J - 196 HOURS to 10 ' 1 t 1 1 t !,!, , .- 40- a30 §20 o Ul w10 1 _ E i . i i i 1 1 - ; // \ i. ». - / ■••..# h ■•. — j t i '•■•.. - // - - / 212 HOURS t \ ♦ ' i i i 1 ! ,1, 1 1 10 20 30 40 50 60 70 80 90 RADIUS (KM) ~0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 40- tf30 §20 to 10 1 1 1 ■I 1 ] 1 1 1 - • r / ' / ' ; / / :/ / - ■/ 1 •/ / // II - If Ii "* - / 202 HOURS 7 t ♦ t / 1 1 1 ! III 1 1 t — i — i — i — r 10 20 30 40 50 60 70 80 90 RADIUS (KM) 216 HOURS 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) Figure C-17 Comparisons of surface wind profiles for Experiment M5 (dashed), M6 (solid), and the control (dotted) , as a function of time. Arrows indicate grid points at which enhanced heating was applied. C-20 200 204 208 TIME (HOURS) 216 Figure C-18. Time history of the 700-mb wind maxima for Experiment M6. C-21 196 HOURS ENHANCED HEATING ~40 1 1 D 1 i i i i i o Ul s GO / s^^*+^^ — V / i\. >/ ^""V^ 5 "30 / ^*C^ Q 1 / ""- ■*. Z "■-^ 5 m?o .- - 5 o - - r- 208 HOURS 10 ■* n 1 1 ,! t t i 1 1 1 i i i 10 20 30 40 50 60 70 80 90 RADIUS (KM) 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 50 i 1 1 1 1 1 r 10 20 30 40 50 60 70 80 90 RADIUS (KM) 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 50 40- o to S 30 Q Z 5 o o 10- 1 _ c i i i i i i i .__, ^-^ N. 'r-W \ / "-^. J —■I — — 1^ ■*-«„ ft - ft /■ - :/ 204 HOURS _ ' i i i 1 i 1 i 1 i i i JU 1 1 - F 1 1 1 1 1 1 40 UJ oo •v —30 Q Z 5 ■— / / i i 1 f 1 / \ m20 1 / II - o o 10 - - 216 HOURS _ n 1 1 1 1 i i i i i 10 20 30 40 50 60 70 80 90 RADIUS (KM) 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) Figure C-19. Comparisons of 700-mb wind profiles for Experiment M6 (dashed) and the control experiment (solid) as a function of time, c-22 become well established. However, by 202 hours, when the enhanced heating is terminated, and thereafter, Experiments M5 and M6 provide results that are much the same (figs. C-17C through F). Beyond 208 hours, the differences between M5, M6, and Ml are all relatively minor (compare figs. C-ll and 17) The 700-mb winds obtained from Experiment M6 (figs. C-18 and 19) show the original maximum to be destroyed rapidly and to be replaced by a new maximum at a larger radius within the first 4 hours of the enhanced heating. The latter quickly intensifies and continues to intensify until the enhanced heating is terminated at 202 hours. Thereafter, it weakens rapidly. By 212 hours, a new and fairly stable configuration is reached (figs. C-19E and F). The behavior of the central pressure in Experiment M6 (fig. C-20) is no more dramatic than that found for the experi- ments discussed previously. CD 1 1 1 1 1 -984 EXR MS LU 3 982 co CO £980 Q_ — _j 978 |976 UJ 71 OT7A i i i i 1 — 192 196 200 204 208 TIME (HOURS) 212 216 Figure C-20 Time history of the oentral pressure for Experiment M6 . Figure C-21 compares experiments with normal, large, and extreme heating. In each case, enhanced heating is continu- ous and at large radii. Before 204 hours, the large heating calculation shows itself to be a transition between the normal and extreme cases. After this time, the solutions in all ex- periments tend to oscillate and no clear-cut relationship be- tween heating rate and response is apparent. By 216 hours (fig. C-21D) , differences between the three experiments have virtually disappeared. C-23 40 o &3( o 10- 1 _ A i i i i i i i A— ^x-"\-. j / N\\ if • • NORMAL HEATING ij « « LARGE HEATING • • EXTREME HEATING 196 HOURS ENHANCED HEATING ' i 1 1 1 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) "i — i — i — i — i — i — i — r 208 HOURS 111 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 40 1 1 _ B i i i i 1 1 /i "*" ■*■" \"s // . s •• o //.•' . \ ■. #30 V. 5 - / ^^ o / Z20 - / ■ 5 / o -/ - w10 [/ 200 HOURS. n ,t,t,t, i i 40- o $30 2 a 2 20 1 1 1 1 1 1 1 1 — • • * /■/ — r* ^%--7 /f 1/ 1/ ~ '/ - - // 212 H0URS_ /, , ,t.t t ill i i 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 10- 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 40 - 1 c 1 1 1 ■•• • 1 1 1 1 u ^^ *•. — o £30 2 - i li Vs ^^ ••■ - Q 2 20 5 - - P - <° 10 n 1 l ,t,l 204 H0URS_ ili i i 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 5 2: 30 t 2 l - ' Q li z 20 - /' — 3: /« // CO " // 2 , 10 — o o ,1, I 1 1 1 1 1 1 40 o UJ en 5 Q o o 30 20- 10- 1 1 _ D i i i i i i EXP. M7 ._ 206 Hours i i i i ji - li i% \i - i i - /,!,! 1 1 1 1 1 1 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) 0 10 20 30 40 50 60 70 80 90 RADIUS (KM) Figure C-23. Comparison of 700-mb wind profiles for Experiment M7 (solid) and the control experiment (dashed) as a function of time Arrows indicate grid points at which en- hanced heating was applied. C-27 2 42 Enhanced Heating- ' i I L i — i — i — i — r~ MAX SFC WIND EXP. M7 M/SEC 192 196 200 204 208 212 TIME (HOURS) MAX 700MB. WIND EXP. M7 M/SEC 36 •Enhanced Heating _l I I L I L 192 196 200 204 208 TIME (HOURS) 212 982 974 CENTRAL PRESSURE EXP. M7 — — Enhanced Heating I I I 192 196 200 204 208 TIME (HOURS) 212 Figure C-24. Results from Experiment M7. Time histories of: (A) maximum surface winds (B) maximum 700-mb wind, and (C) central pressure . C-28 APPENDIX D STORMFURY SEEDING PYROTECHNICS 1969 Shelden D. Elliott, Jr. Naval Weapons Center China Lake, California As described in the STORMFURY Annual Report-1968, the primary seeding unit for the STORMFURY 1969 season was the STORMFURY I, whose characteristics are summarized in table D- 1(a). After check firing at NWC, 2,340 STORMFURY I units from 1968 production were available for the 1969 season. To make up the stipulated quantity of 4,000 rounds, an additional 1,000 rounds of STORMFURY I were manufactured in early July 1969, and 660 of the hybrid STORMFURY II units (table D-l(b)) manufactured for the 1968 season were drawn from stock as a reserve. These 4,000 units were received at NAS , Jacksonville, on 23 July 1969, well in advance of the dry-run exercises that opened the 1969 season. The dry runs provided an opportunity both to familiarize the VA 176 crews with firing and to test the STORMFURY I (1969) rounds (which had been shipped directly from the manufacturer without verification firing at NWC) . Satisfactory performance was indicated; only two misfires occurred among 60 rounds flown on two days (29 and 31 July) . The remaining 3,940 rounds were subsequently shipped to NAVSTA Roosevelt Roads in two lots, one before and one during the Hurricane Debbie operations. Five seeding missions were flown on each of the two Hur- ricane Debbie eyewall operations (18 and 20 August); each A6 was loaded with 208 STORMFURY I units, for a total of 2,080 rounds. Of these, 1,697 were produced in 1968 and 383 in 1969. An additional 17 units (all 1968) were rejected during pre- loading inspection for loose wads, dented cases, etc. On the first day, 64 rounds were returned as misfires; on the second day, 62, giving a misfire rate of 6.1% of the total rounds flown. These data are presented in somewhat greater detail in table D-2. From the distribution of misfires in the firing racks, it was evident that most were due to "skips" in the firing sequence system. This was borne out by subsequent inspection 1 The Project STORMFURY Annual Report-1968, NHRL, ESSA, May 1969, pp. B-l to B-4. OS Co ?o OS t-H CO g o o ?H S?S ft, s Oj (H ft; ft, ft; o o CO CO s^ +1 « r-n I « Eh H H H P a o Eh CD Cm 2 s o En CO £ H CD Cn 2 o En CO ,-C 05 id H u * -P '4-1 •H 0 IH 0 M rd -p 4J U3 in O u 0 O 1 O +J dJ ,c 1 ■n S rH in CO - UO S +J 2 en rH I O o ,fl CO CO rH u A^ P P l+H •H U 4-1 m U 0 M 03 CU 4-> -P 10 P O 0 CO 0 u 1 O 0 £ cu < u O 0 0 ft H 0 » >■ CN (1) L3 p ro cn tn in 0 H CN (1) u CO ro CM 1 rH ft O rt! CD 1 0 0 1 1 O H >! IT) 1 •n & cn C7\ n co O 2 p S cn cu J CN H ro rH H 0 • CD P 4-1 0) CO 3 -P s CO 0) C CO ■P £ »-» cd 0 *— 0 O X Cn CD G H •H e ■H •H 4-1 rH CO H p CD 0 e CD 3 CD -P CO cd Cn P •5 P4 U CO IH u T) M-l Cn 4J •H d ■H u c CD 3 C O Cn CD +J g CD T3 P •rH c u C (h -H P CD rd H cn u 4-1 Sh rcJ P. •H CD A Cn CD 0 ■— ' 0 U ft Cn CO U «C a m CQ D-2 of the misfired rounds at NWC, virtually all of which proved to have functional, unfired primers. Nighttime firings of STORMFURY I-type units over the NWC ranges indicate that less than 2 percent of those rounds that are ejected fail to ignite and burn properly over the full length of fall. Since this is comparable with the variation in AgIC>3 content of the individual pyrotechnic grains, the nucleant delivery totals indicated in table D-2 may be taken for all practical purposes, as correct. In preparation for the STORMFURY "cloudline" exercises 9-18 September, a new type of seeding round designated STORM- FURY III was fabricated (table D-l(c)). Since the NWC Cessna 401 seeder aircraft were to be operated at only 18,000 - 19,000 feet, instead of the 33,000 feet specified for the A6's in the eyewall experiment, a high- ef f iciency short-burning pyrotechnic grain was required. This was provided by loading a 2.6-inch long EW-20 grain, perforated with a 1/8-inch hole to induce simultaneous burning from the center and both ends, into the same photoflash cartridge used for STORMFURY I, the remaining interior length of the cartridge being occupied by a light wooden spacer. This arrangement insured that virtually all of the Agl produced by each unit would be released above the zero-degree isotherm in the seeded clouds. Each aircraft carried two 26-station ejector racks, firing downward from beneath each engine nacelle. Of 299 STORMFURY III units provided, 137 were fired dur- ing 10 aircraft missions on 6 operational days; an additional seven rounds were fired on a "down" day for test and photo- graphic purposes. Two misfires occurred, but each was success- fully refired on a subsequent flight. Otherwise, all the rounds whose trajectories could be observed appeared to func- tion properly. The quantities of the various STORMFURY seeding units currently on hand are indicated in table D-3. Of these the short-burning STORMFURY III is completely unsuited for hur- ricane seeding under current operational procedures; the hy- brid STORMFURY II was manufactured as a stopgap effort and is substantially less reliable in its performance than the STORM- FURY I and differs in its seeding properties. There remains a sufficient number of the latter for one eyewall or several rainband seeding experiments, but not enough to repeat the two days' seeding performed on Hurricane Debbie. The STORM- FURY I -pyrotechnic device is, moreover, classed as strictly experimental; it must be loaded under the supervision of a NWC ordnance technician, and the lack of specific safety devices D-3 £ s 3 ft CM I C5 &H. -a a> W ITS a> rH a; < ■H W 10 C O T3 U •H (0 G o T3 CO O O en CO IT) o r» 00 10 "5J" CO ro n m (*1 ro 00 CM CO m in "* CM o en o rj» 00 o rH CM rH H CN CO CO CO CO CO o o O o o CM CN CM CM CM A g 3 O PL. tn < CO >* ^ LD CO <3< U0 o o rH LD P O En CT> T3 0) (/] 0! rH cu IX T3 J c O P Cn -rH rH P «J Q en on ro CO on CO ro CM CO CO CO in CM rH r» o r> CO O Ol (Tv m CM H rH rH rH CO CTi CO CO CO CO CO o o o o o CM CM CM CM CM o o Cm m CP < O CM rd P O B P H 0) a, en 0.5 0.0 300° 330° 360° 030° 060° 090° 120° 2500 g2000 :1500 1000 500 30 5 25 W20 o <15 LARGE EYE 10- H00Z FYF RADII K MAJ0R AXIS LYL RADIUS M|N0R AX|S 30 25 : 20 ; 1200Z 1300Z 1400Z 1500Z 1600Z 1700Z 1B00Z 1900Z 2000Z 2100Z HURRICANE DEBBIE AUGUST 20,1969 Figure E-4. Eye- configuration changes in Hurricane Debbie from 1300Z to 2300Z on 20 August 1969. E-7 The area and radius of the large and small eyes showed only minor changes, with the following noteworthy features. The area of the large eye showed a general trend to decrease in size dur- ing the day. The area of the small eye remained nearly constant until 1900Z, when it began a slight increase, resulting in a much reduced separation between the two eyes by the end of the seeding operation. There was a significant increase in the area of the smaller seeded eye when it increased by 50% about 1 hour and 15 min after the fourth seeding. EYE-SIZE CHANGES IN UNSEEDED STORMS The question may be asked whether or not the eye-size changes described above would have occurred if the storm had not been seeded. W. Hoecker and G. Brier (1970, private com- munication) have conducted a study of the eye-size changes of Hurricanes Carla (1961), Betsy (1965), and Beulah (1967), cover- ing a continuous time period of about 24 hours for each storm. Ground-based radar was used for all three storms, and airborne radar was also used for the Carla study. During the period of study, both Carla and Beulah had a double eye structure, while Betsy had a single eye. The data sample for Carla was the longest (40 hours) . The eye size of this storm showed a trend to decrease from 30 mi in diameter to 23 mi in diameter during the first 24 hours and to remain relatively constant thereafter. Superimposed upon this trend were shorter fluctuations of the order of + 4 mi in 4 hours. The Betsy and Beulah eye sizes behaved some- what similarly. The data gave no evidence of a cyclic change in eye size or even any sudden individual changes occurring in less than 1 hour. From this limited sample, therefore, it appears that eye-size changes of the type observed in Debbie may be unique. However, further study of unseeded storms is necessary to be more certain of this. SUMMARY Airborne radar photographs of Hurricane Debbie, taken on 18 and 20 August, 1969, were used to measure the echo-free area within the eye at 5-min intervals beginning 1 hour before the first seeding and ending 1 hour after the last seeding on both days. Results for the 18th show a sudden increase in echo-free area 1 hour and 15 min after seeding time. Increases ranged from 50% to threefold. E-8 Results for the 20th were quite different. A double eye structure was present on this day, as opposed to the single eye on the 18th. The echo-free area within the smaller eye remained constant throughout the day, and the larger eye slowly decreased in area. The only evidence of seeding effects on the 20th was ob- served in the rotation rate of the major axis of the elliptical eye. A slowing of the rate was observed within 10 min of each seeding followed 1-1/2 hours later by a rapid increase in the rotation rate, which continued until the next seeding time. The period of this cycle (the time required for one revolution of the major axis) was about 2 hours. From these results we arrive at the c storm responded in two entirely different each day. As noted earlier, the storm had structures on the two days. The more conv type storm as encountered on the 18th has Rosenthal (1970) , and according to his wor carried out from the maximum wind region o have the biggest effect on the storm struc double eyewall type structure, where there has not yet been modelled to try to determ place to seed would be. The fact that on seeded outside the inner wind maximum, but maximum, would intuitively lead one to exp suits, which indeed was the case. onclusion that the ways to seeding on quite different entional single eyewall been modelled by k, seeding must be utward in order to ture. However, the are two wind maxima ine where the best the 20th the storm was inside the outer wind ect different re- Therefore, until more sophisticated model experiments are carried out, it is suggested that if other storms of the double eyewall type are encountered, seeding be carried out on the outer eyewall. REFERENCES Gentry , R. C . Soc . , 50 , (1969), Project STORMFURY , Bull. Amer pp. 404-409. Meterol Jordan, C.L., and F.J. Schatzle (1961), The "Double Eye" of Hurricane Donna, Monthly Weather Rev., 8_9, 354-356. Rosenthal, S.L. (1970), A circularly symmetric, primitive equation model of tropical cyclones and its response to artificial enhancement of the convective heating functions (in preparation) . E-9 Simpson, R.H., M.R. Ahrens , and R.D. Decker (1963), A cloud seeding experiment in Hurricane Esther, 1961, Report No. 60, National Hurricane Research Laboratory, 30 pp. Simpson, R.H., and J.S. Malkus (1964), Hurricane modification: Progress and prospects 1964, U.S. Weather Bureau, 54 pp. STORMFURY Operations Plan (1969), U.S. Fleet Weather Facility, NAS , Jacksonville, Fla. E-10 APPENDIX F CLOUD PARTICLE SAMPLES AND WATER CONTENTS FROM A 1969 STORMFURY CLOUDLINE CUMULUS Edward E. Hindman II Navy Weather Research Facility INTRODUCTION Navy Weather Research Facility (WEARSCHFAC) personnel operated cloud particle samplers onboard the ESSA-RFF aircraft in 1969 Project STORMFURY operations. The primary objective was to measure the liquid and ice water contents in seeded por- tions of STORMFURY hurricanes and cloudline cumuli. Technical difficulties prevented useful samples from being obtained on the 18 and 20 August 1969 Hurricane Debbie flights. These difficulties were corrected during the 9 to 19 September 1969 operations, and useful particle samples were obtained in both seeded and nonseeded cloudline cumuli. This report concerns the WEARSCHFAC cloud particle analy- sis system and preliminary analyses of water content measure- ments from particle samples taken during the 15 September 1969 flight south of NAS Roosevelt Roads, Puerto Rico. CLOUD PARTICLE SAMPLERS The ESSA-RFF aircraft are equipped with Formvar and foil particle impactors. The Formvar sampler has been described by Sheets (1969) and MacCready and Todd (1964). Cloud particles blast through a small slit and embed in liquid Formvar on rapidly moving 16-mm film. The Formvar hardens shortly after exposure and permanent replicas of the particles are produced. The par- ticle-impregnated film is viewed with a 16-mm stop motion pro- jector equipped with a magnifying lens. The smallest size par- ticle that can be viewed is approximately 2 U ill diameter. The largest water and ice particles viewed are roughly 100 U in diameter. Most larger particles shatter on impact, leaving spurious replicas. The foil sampler is similar to the one described by Brown (1961). A strip of aluminum foil moves slowly past a large sampling orifice equipped with a shutter. The shutter exposes the foil for only an instant and prevents particles from landing on one another. The particles leave distinct indentations in the foil, because it is pressed against a drum with regularly spaced 250-y striations. Unlike the Formvar samples, fragments from shattered particles do not leave impressions on the foil. The crater-pocked foil strips are photographed and viewed with a 35-mm filmstrip projector (see fig. F-l) . Particles larger than 200 U in diameter can be viewed. Ice and water particles can be differentiated with some uncertainty. CLOUD PARTICLE ANALYSIS SYSTEM The 16-mm Formvar and 35-mm foil film strips are projected on the WEARSCHFAC CALMA 302 digitizer. The magnified particle images are digitized onto magnetic tapes, which are processed by the WEARSCHFAC UNIVAC 1107 computer. Particle size and num- bers are calculated from the digitized information. Particle number-densities are computed from: N(i) = n(i)/ (U E A) , O 4- "U where N(i) is the particle number-density (cm ) for the i th size interval, n(i) is the particle number for the i size interval, U is the true air speed (cm sec ) , E is the exposure time of the foil to the air stream (sec) , and A is the exposed foil area from which n(i) was counted (cm ) . The total water content is given by wm = WT + w + w T L I U where W is the total water content, W is the liquid water m r -a, content, W is the ice water content, and W is the unknown water content (particles that cannot be recognized as either ice or water) . The liquid, ice, and unknown water contents are determined from n W = I - TT r (i) 3 N(i) p , i = l where_W is the particle water content for all size intervals (g cm 3) , r(i) is the particle radius for the i size interval (cm) , and p is the particle mass-density (g cm- ) . At present, the foil data-processing program is operational, and the more complicated Formvar program is being developed. Cloud particle images from the foil sampler are counted and sized by the digitizer operator according to a modified scheme F-2 ry r^ CO C35 a 3 fei-^ ^ s 3 to co B Cj s • 3 Cj &4 V CD CD * t--j K +i fi, •^ to S r-^ « r-i t-~i CO 3 v> 0 o CD r-j ^-.rc CD &H « K . ^ O s &, CD S: s £ ft; s '^ O o <3}E- r« CQ to 0) h G Oi 0) a CO fa> S C3J a •*i l~H E •^ a Ss CD CD cd £ 4-i &H •rJ» « t-H 1 &4 CD Sh s c^ I •^ Pt, F-3 originally developed by Takeuchi (1969). Briefly, the foil strip is subdivided into 5-sec segments (see fig. 1) . Within each segment, all particles greater than three striations (d >_ 500 y) in size are traced with the digitizer. Only these particles can be recognized as either ice or water. The one- and two-str iation particles are lumped into the unknown water content category. These particles are assumed to be approxi- mately 200 and 300 \i in diameter, respectively. At least 105 of the one- and two-str iation particles should be counted in a segment to produce a statistically significant sample. CLOUD PARTICLE SAMPLES AND WATER CONTENT RESULTS Preliminary results of the total water-content analysis from one pre-seed penetration of 15 September 1969 STORMFURY "cloudline" cumulus are presented in figures 2 and 3. The re- maining pre- and post-seed analysis is underway. The aircraft LEVINE -1.0 19000 ft I850Z *••.. -5C 1851 APPROXIMATE CLOUD PROFILE ;ea level 1852 TOTAL WATER CONTENT (grrf3) V4 18532 Figure F-2. Comparison of total water contents measured by the Levine instrument and foil aloud particle sampler . The data are from STORMFURY "cloudline" flight B3 cloud 1, pass 1, on 15 September 1969. F-4 - «■ ■■■■ 1 V 19000 ft 1850 Z '•-. -5C SEA LEVEL WATER CONTENT ( gm"3) -.01 ICE WATER LIQUID WATER UNKNOWN WATER •- .001- 1651 1652 v-t ••..J853Z Figure F-3. Components of the total water contents from the foil instrument . flight data used to construct these figures were provided by ESSA-NHRL. from the f peaks are p sampl to me these sampl with agree ins tr water amoun produ (1970 from Flags es tab throu Figure F-2 the Levine oil sampler and trough robably a r es particle asur e . The smaller pa es is compl the foil va more close shows the periodic trace instrument and the water A tenuous agreement is s of the two traces. The esult of the fact that th s smaller than the foil s Formvar instrument was d rticles. When the analys ete and the results have lues, the resulting water ly with the Levine values of the water content content measured by apparent between the larger Levine values e Levine instrument ampler was designed esigned to measure is of the Formvar been incorporated contents should The components of the total water content from the foil ument are illustrated in figure F-3. Partitioning the total content in this manner may aid in identifying the large ts of ice hypothesised by St. Amand et al . (1970) to be ced by seeding. Takeuchi (1970) and Weinstein and Takeuchi ) have tentatively identified artificially produced ice similar foil and Formvar particle samples taken in seeded taff cumuli. WEARSCHFAC will make a determined effort to lish the effects of seeding hurricanes and tropical cumuli gh its STORMFURY cloud particle sampling program. F-5 ACKNOWLEDGEMENTS The bulk of the tedious particle digitizing was done by AG2 N. SHEARY. ENS D. B. JOHNSON took the excellent photographs of the foil strips. REFERENCES Brown, E.N. (1961) - A continuous -record ing precipitation particle sampler. J . Meteorol . , 18 , 815-818. MacCready, P.B., Jr., and C.J. Todd (1964) '. Continuous particle sampler. J. Appl . Meteorol., 3_, 450-460. Sheets, R.C. (1965)' Preliminary analysis of cloud physics data collected in hurricane Gladys (1968) • Project STORMFURY Annual Report-1968, U.S. Department of the Navy and and U.S. Department of Commerce, 17 pp. St. Amand, P., W.G. Finnegan, and L.A. Burkardt (1970); The relevance of cloud chamber tests to ice nuclei activity. Preprints of papers presented at the Second Natl. Conf . on Weather Modification, April 6-9, 1970, SantaBarbara , California, 361-365. Takeuchi, D.M. (1969)', Analysis of hydrometeor sampler data for ESSA cumulus experiments . Miami, Florida, May 1968, MR169 FR-849, Meteorology Research, Inc., 464 W. Woodbury Road, Altadena, California 91001, 44 pp. Takeuchi, D.M. (1970) : Precipitation development in seeded and natural cumulus clouds . Preprint of paper presented at the Second Natl. Conf. on Weather Modification , April 6-9, 1970, Santa Barbara, California, 198-204. Weinstein, A.I., and D.M. Takeuchi (1970) ; Observations of ice crystals in a cumulus cloud seeded by vertical fall pyro- technics , J. Appl. Meteorol., 9, 265-268. F-6 APPENDIX G PROJECT STORMFURY HURRICANE AND TYPHOON SEEDING ELIGIBILITY William D. Mallinger National Hurricane Research Laboratory- Atlantic Oceanogr aph ic and Meteorological Laboratories ESSA Research Laboratories Miami , Florida During the past 2 years, studies were completed to deter- mine opportunities for seeding hurricanes in the Atlantic and Pacific. These studies were published in the Project STORMFURY annual reports of 1967 and 1968, and cover the rules for seed- ing eligibility adopted in 1967. One of these rules said, "A storm or hurricane is eligible for seeding as long as the fore- cast states that there is a small probability (10% or less) of the hurricane coming within 50 miles of a populated land area within 24 hours after seeding." This study of new hurricane areas concerns probable increases in number of storms for experimentation that would result from changing the rules for eligibility for seeding and from length- ening the STORMFURY season. Tracks of hurricanes in the years 1954-69 were checked to determine if the storms would have been eligible for seeding under either of the 1967 rules stated above or possible revisions of that rule that would change the 24-hour limitation to either 18 hours or 12 hours. The study was also expanded to add the months of June, July, and November. As in previous studies, this one includes both hurricanes (Atlantic) and typhoons (Pacific) . Table G-l lists the hurri- canes by month and year, area where seeding could have occurred, most likely base of operations, and the type of redefined eli- gibility for seeding. The small probability (10% or less) stipulated was also examined to determine if an increase to 25% or 50% would sig- nificantly change the number of storms eligible. It appeared that this increase would not be significant, but that a change of the "time after seeding" requirement with its attendant re- duction in probability ellipse size would be more effective. In addition, retention of the "10% or less" portion of the rule appears advantageous politically until we really understand the effects of the modification attempts. Table G-l shows several interesting things. First, only three, or 8%, of the hurricanes (during the 16 years for which we have forecast data) would have been eligible for seeding, during June, July, and November. Two of these hurricanes oc- curred in July, one in November, and none in June. One addi- tional hurricane would have been eligible in July if the "time after seeding" portion of the rule had been relaxed. This sug- gests that benefits of extending the STORMFURY season to the other months may be less than the probable costs and inconven- ience of having all of the forces of other programs committed to STORMFURY for a longer period. Having a dry run and cloud- line mission in July, however, would be very desirable to help prepare all forces for the earlier August storms. During the same 16 years, eight additional hurricanes would have become eligible based on the "18 hours after seed- ing" rule. Of these eight, three were in the Atlantic, three in the Caribbean, and two in the Gulf of Mexico. Three addi- tional opportunities would be added if the rules were further relaxed to the "12 hours after seeding" rule. All of these occurred in the Gulf of Mexico. One of these hurricanes was also eligible while it was in the Caribbean Sea. Even though the increase in opportunities achieved by lowering the time after seeding to 18 hours is rather small, it is worth- while if it affords an opportunity that would otherwise be lost by rules that are-overly restrictive. Table G-2 lists the hurricanes eligible for seeding under current eligibility rules. This list contains only hurricanes that occurred between 1 August and 30 October. Table G-3 lists the tropical storms that would have been eligible during the 16 years for which we have data. Fourteen of these storms could be considered as candidates for rainband- type experiments. Of these 14, three were also eligible when they were of hurricane intensity. From this, one might expect that an average of nearly one opportunity for experimenting on tropical storms per year should occur . The study of typhoons passing within range of Pacific bases was governed, as during the earlier studies, by the following guidelines: 1. The typhoon must be within 600 miles of the operation bases, Guam or Okinawa. 2. Maximum winds must be at least 65 knots. G-2 Table G-l. Hurricanes Eligible for STORMFURY Experiment Year/M onth Name Ocean Operating Bases Ellipse 1954 8 Carol Atlantic Jack sonvil le 2 4 hr 1954 9 Edna Atlantic Jack sonvi lie 18 hr 1954 10 Hazel Caribbean Guantanamo Bay 24 hr 1955 8 Connie Atlantic Jacksonville/Roosevelt Rds 24 hr 1955 8 Dianne Atlantic Jacksonville/Roosevelt Rds 2 4 hr 1955 8 Edith Atlantic Roosevelt Rds 24 hr 1955 9 Flora Atlantic Bermuda 2 4 hr 1955 9 lone Atlantic Roosevelt Rds/Jacksonville 24 hr 1955 9 Janet Caribbean Guantanamo Bay 24 hr 1956 8 Betsy Atlantic Jacksonville 24 hr 1956 11 Greta Atlantic Roosevelt Rds 24 i.i 1957 9 Carrie Atlantic Roosevelt Rds 24 hr 1958 8 Cleo Atlantic B ermuda 2 4 hr 1958 8 Dai sy Atlantic Jacksonville 24 hr 1958 9 Fif i Atlantic Roosevelt Rds 2 4 hi 1958 9 Helene Atlantic Jacksonville 24 hr 1958 9 Ilsa Atlantic Roosevelt Rds 24 hr 1958 10 Janice Atlantic Jacksonvi lie 24 hr 1959 7 Cindy Atlantic Jacksonvi lie 2 4 hr 1959 9 Gracie Atlantic Jacksonville 24 hr 1959 9 Hannah Atlantic Roosevelt Rds 24 hr 1960 7 Abby Caribbean Roosevelt Rds 24 hr 1960 8 Cleo Atlantic Jacksonvill e 2 4 hr 1960 9 Donna Atlantic Barbados/Roosevelt Rds 18 hi 1961 7 Anna Caribbean Guantanamo Bay 18 hr 1961 9 Betsy Atlantic Bermuda 24 hr 1961 9 Carla Gulf of Mexico New Orleans 24 hi 1961 9 Esther Atlantic Roosevelt Rds 2 4 hr 1961 10 Frances At lant ic Jacksonvil le 2 4 hr 1962 9 Dais.y Atlantic Roos e vel t Rds 2 4 hr 1962 10 Ella Atlantic Jacksonville 2 4 hr 1963 6 Beulah Atl an t i c Roosevelt Rds 2 4 h r 1963 9 Flora Atlantic Roosevelt Rds 2 4 hi Caribbean Roosevelt Rds IS hi 1963 9 Edith Caribbean Roosevelt Rds 18 hr 1963 10 Gi nny Atlantic Jacksonville 24 hr 1964 8 Dora Atlantic Roosevelt Rds 24 hr 1964 9 Ethel Atlantic Roosevelt Rds 2 4 hi 1964 9 Gladys Atlantic Roosevelt Rds 24 hr 1964 9 Hilda Gulf of Mexico Pensacola lb hr 1964 10 Isbell At lanti c Jacksonville 18 hr 1965 8 Betsy Atlantic Roosevelt Rds 24 hr 1965 10 Elena Atlantic Roosevelt Rds 2 4 hr 1966 8 Faith Atlanti c Jacksonville/Roosevelt Rds 24 hr 1967 9 Beulah Caribbean Guantanamo Bay 12 hr Gulf of Mexico New Orleans 12 hr 1969 8 Debbie Atlantic Roosevelt Rds 24 hr 1969 8 Camille Gulf of Mexico Jacksonville 12 hr 1969 10 Laurie Gulf o f Mexico Jacksonville 18 hr 1969 10 Inga Atlantic Bermuda 24 hr G-3 Table G-2. Annual Frequency of Hurricanes Eligible for Seeding Between 1 August and 31 October Under Forecasting Techniques Criteria approv- ed for STORMFURY Operations Subsequent to 1967, G ulf of Caribbean Year Atlantic M exico Sea Total 1954 1 0 1 2 1955 4 0 1 5 1956 1 0 0 1 1957 1 0 0 1 1958 5 0 0 5 1959 2 0 0 2 1960 1 0 1 2 1961 2 1 0 3 1962 2 0 0 2 1963 3 0 0 3 1964 3 0 0 3 1965 2 0 0 2 1966 1 0 0 1 1967 0 0 0 0 1968 0 0 0 0 1969 2 0 0 2 Total 30 34 3. The typhoon must be within range for a minimum of 12 daylight hours. 4. The predicted movement of the typhoon must indicate that it will not be within 50 miles of a land mass within 24 hours after seeding. From 1961 through 1969, during the months of August, September, and October only, 27 typhoons would have been eli- gible for experiments conducted from Guam and 28 from Okinawa (see table G-4) . This gives an average number of 3.0 oppor- tunities per year for operations based from Guam and 3.1 op- portunities per year from Okinawa. Because the 55 eligible typhoons contain 7 that were counted eligible from both Guam and Okinawa, the average number of individually eligible typhoons per 3-month period is 5.3. G-4 Table G-Z. Tropical Storms Eligible for Rainband Seeding 1954-1969. (Seeding Time: 0700-1300. ) Year/Month Name Ocean Operating Base 1955 8* Dianne Atlantic 9* lone Atlantic 8 (Unname d) Gulf of Mexico 1956 9 Flossy Gulf of Mexico 1957 9 Frieda Atlantic 10 (Unname d) Atlantic 1958 8 Becky Atlantic 9 Ella Gulf of Mexico g * Helene Atlantic 1959 6 (Unname d) Atlantic 1961 10 Gerda Atlantic 1966 7 Celia Atl antic 9 Greta Atl antic 1967 10 Heidi Atlantic Roosevelt Roads Roosevelt Roads Roosevelt Roads Roosevelt Roads Roosevelt Roads Roosevelt Roads Roosevelt Roads Jacksonville Roosevelt Roads Roosevelt Roads Roosevelt Roads *Also seedable as hurricane Table G-4. Number of Typhoons Meeting Criteria for Seeding Eligibility . Staging Operations From Guam/ Okinawa . G uam/Okinawa Year June July Aug . Sept. Oct. Nov . Dec . Total 1961 0/0 0/0 0/3 2/2 2/2 1/0 0/0 5/2 1962 0/0 0/0 1/2 1/1 1/2 i/0 0/0 4/5 1963 0/2 1/1 o/i 0/2 2/2 0/0 1/0 4/8 1964 0/0 2/1 0/0 2/0 o/i 0/0 1/0 5/2 1965 1/0 2/1 1/2 1/2 I/O 1/0 0/0 7/5 1966 0/1 0/0 0/0 3/2 0/0 0/0 0/0 3/3 1967 0/0 0/2 0/0 0/0 2/0 3/1 0/0 5/3 1968 1/2 1/1 1/0 1/2 3/1 2/0 0/0 10/6 1969 0/0 1/0 0/0 1/1 2/0 1/2 0/0 5/3 G-5 Since some would be eligible more than once and others could be seeded both from Guam and Okinawa, it is realistic to assume more than six opportunities per 3-month period. Frequency of eligible typhoons during the months of June and July, although much lower than September and October, are worth noting. On the average, two typhoons per year could be seeded during this 2-month period. This study yields the following conclusions: The seeding opportunities for hurricanes are increased by only 8% (three hurricanes during 16 years) if June, July, and November are added to the seeding season. The month of July produced two of the three opportunities. One additional hurricane would have been eligible in July with the slightly relaxed (18 hour) seeding eligibility rules. The "18 hour after seeding" rule and attendant probability ellipse with requirement for 90% probability of forecast accu- racy, adds eight seeding opportunities. The "12 hour after seeding" rule would add only three additional opportunities. Conducting seeding experiments on typhoons in the Pacific during June and July could be expected to provide an average of two opportunities per year. G-6 APPENDIX H APPLICATION OF BAYESIAN STATISTICS FOR STORMFURY RESULTS Robert C. Sheets National Hurricane Research Laboratory Atlantic Oceanographic and Meteorological Laboratories ESSA Research Laboratories Miami , Florida INTRODUCTION The number of hurricane seeding experiments performed to date is quite small and probably will remain so in the near future. This then limits what can be done through classical statistical techniques to calculate the significance of the results. For this reason, various knowledgeable statisticians have suggested that Bayes ' equation be used to test the signi- ficance of the seeding experiments and to update the proba- bility distributions based on the experimental and model re- sults. An attempt to accomplish this task is described here. CLIMATOLOGY The first step was to obtain background information on the fluctuations that occur naturally in a mature hurricane. Various detailed and complicated studies have been made to determine these fluctuations, but for the specific require- ments of this study, a rather simple and limited study was made . Graphs of minimum sea-level pressure versus time were constructed for all tropical cyclones of hurricane strength in the Atlantic, Gulf of Mexico, and Caribbean areas for which data were available at 6-hourly intervals for at least 24 hours for the years of 1961 through 1968. The maximum wind speeds (defined as the strongest winds present in the storm at the given time) were then computed from the minimum sea-level pressure at 6-hour intervals based on a relationship presented by Holliday (1969) . The data presented by Holliday in deriving this relationship showed an average error of less than 5 knots. This results in some uncertainties in the relationship used but probably less than the other uncertainties which result from assumptions made in later computations. The percentage of maximum wind speed changes were then computed for intervals of 6, 12, 18 and 24 hours. The number of cases ranged from 510 for the 6-hour changes to 429 for the 24-hour changes. The results are shown in figure H-l, where the mean changes ranged from +1.91 to +7.32 percent, reflecting a bias toward deepening storms, and the standard deviations ranged from 7.8 to 18.95 percent for the 6- and 24-hour changes respectively. The data are slightly biased because more storms were moni- tored during the deepening and mature stages than during the weakening stages. Also, some of the storms struck land and dis- sipated rapidly, and in these cases a dissipating stage compar- able to the deepening stage was not recorded. The 12-hour changes were used as a starting point in this study and for reasons of simplicity the speed changes in the ISO 170 160 150 140 130 120 110 100 90 80 70 60 50 40- 30 20 10 -i 1 1 1 1 r V a CASES 1 6HR CHANGES 1.91 78 510 2 12HR CHANGES 3 75 12 05 483 3 18HR CHANGES 561 15.86 456 4 24HR CHANGES 7 32 1895 429 0^ -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 MAXIMUM WIND SPEED CHANGES (%) Figure H-l. Maximum wind speed changes for Atlantic hurricanes from 1961 through 1968 for periods of 6, 12, 18, and 24 hours. (Computed from time changes of minimum sea-level pressures . ) H-2 calculated maximum winds during the hurricane stage were as- sumed to follow a normal distribution with a mean of zero and a standard deviation of 12%. This distribution, despite the slight bias in the data, closely approximates that computed for the 12-hour changes and will hereafter be referred to as the climatological distribution. RESULTS OF EXPERIMENTS A total of six hurricane eyewall seeding experiments had been attempted by the end of the 1969 hurricane season. The experiments performed on Hurricane Debbie on 18 August and 20 August 1969 were quite different from the other four, which were performed in Hurricanes Esther (1961) and Beulah (1963) . The s eeding Esther a period . release August 1 About Be s i 1 ver i and prob 2 1/2 ho S impson iodide w addition exper ime by Rosen the Debb model ex ments ar lat ions Debb ie e summar i z Hurr i period nd B eu There of the 964 an ulah , odide ably c ur mon e t al . as re 1 to th nt was thai ( i e see per ime e main that f xperim ed in cane D s a t 2 lah ex are a s il ve d the Simpso was dr ould n i tor in (1963 eased e f iel run w 1970) . ding e n t in ly use ollow ents . table ebbi -hou peri lso r io Esth n an oppe ot h g pe ) st d ex ith Th xper this d as sine The H-l. e expe r in te ments some q dide i er exp d Malk d in a ave en r iod a ate th in th per ime a nume i s exp iments paper backg e they r esul r iments rval s ( cons is t ues t ion n the B er iment us (196 n open ter ed t fter se at "App e clear nts men rical h er iment and wi The round i were q ts of a cons l Gentry ed of s abou eulah on 17 4) sta almost he tal eding . ar ent 1 air o t ioned urr ica was d 11 be Es the r nf orma ui te d 11 the s ted of , 1970) , only one t the lo exper ime S ept emb te that cloud- f 1 towers About y all th f the ey above , ne model es igned referred and Beu t ion in if f erent s e exper five wh i see ca t i n t o er 1 it r e e dur Est e si e . " a si de v to s to lah the fro imen s epara te le the ding on of the n 23 961 . the port ion ing the her , 1 ver In mulated eloped imul ate as the exper i- calcu- m the t s are Each seeding experiment is assumed to be independent for the purpose of the computations made here. This assumption seems quite reasonable since in each case at least 24 hours elapsed between experiments, and in the Hurricane Debbie experi- ments 38 hours elapsed between seeding operations. A rough calculation based on a mean radial wind component of 10 knots in a layer 1 n mi thick shows that the air located within 60 n mi of the storm center from the surface to 100 mb would be replaced within 18 hours. For a radius of 100 n mi the time required for the complete ventilation would be approxi- mately 30 hours. The assumption of a mean radial wind component H-3 Table R-l . Results of Rurrioane Seeding and Model Experiments . Approx Max . Wind Speed No . of Change No. Name Date Seedings (percen t) 1 Hurr . Beulah 23 Aug •63 1 0* 2 Hurr . Beulah 24 Aug •63 1 -14 3 Hurr . Esther 16 Sep •61 1 -10 4 Hurr . Esther 17 Sep '61 1 0* 5 Hurr . Debbie 18 Aug ■69 5 -30 6 Hurr . Debbie 20 Aug ' 69 5 -15 7 Rosenthal Model 1969 Continuous -15 for ■ 10 hours *Silver iodide was apparently released in cloud-free regions . of 10 knots in the lowest 1 n mi layer seems quite reasonable based on previous studies (Malkus and Riehl, 1959; Sheets, 1965). In addition to the long-term ventilation effects, much of the seeding material is expected to be carried upward into the strong outflow region in a very short time and other por- tions of the agent will be "rained out." In the Debbie ex- periments, the storm on 20 August seemed to have recovered from the seeding effects that occurred on 18 August,as the maximum wind speeds had again increased to over 100 knots by the time of the second day of seeding. HYPOTHESIS TESTING The basic question regarding the success or failure of the seeding experiments is: Did the seeding cause the changes observed in the seeded storms? An attempt is made to answer this question below through hypothesis testing and the use of the evidence form of Bayes ' equation. If we assume that the hurricane seeding experiment repre- sents a problem in sequential testing, we can use Bayes1 equa- tion in the evidence form given by (Tribus, 1969, p. 84) : H-4 ev(Hl|EnC) = ev(Hl|C) + 10 log10 p(£ P(E |h. C) n 1 H, C) n ' 2 (H-l) where and H is a given hypothesis, H is all other possible hypotheses, C is background climatological information, E is the sequence of outcomes on the nth test, n ev(H |E C) is the evidence in favor of H given the truth of E and C, n ev(H I C) is prior evidence in favor of H given the truth of C, P (E |h C) is the probability that the sequence E would be observed if H and C were true, P (E |H C) is the probability that the sequence E would occur if H and C were true. 2 In the computations that follow, we will assume that there are only two possible hypotheses. This is obviously erroneous, as there are an infinite number of hypotheses that could be advanced, but it does give us an opportunity to compare the two proposed here. Also, these two hypotheses are being proposed after the fact, that is after the experimental results have been documented, and a hypotheses could be chosen that would predict the sequence of outcome exactly. However, we shall restrict ourselves to probability distributions resulting from the seeding experiments that are similar in form to the clima- tological distribution. We have indicated earlier that assuming a normal distri- bution to represent climatology is quite reasonable. If we also assume that the seeding experiment superimposes a con- stant factor on the climatological distribution, i.e., simply shifts the location of the distribution, an assumption of a normal distribution for representing the seeding effect would be justified. The major argument then arises as to just how much the shift should be. Complete agreement on this will probably never be reached, and even majority agreement may be H-5 difficult to obt tions representi ranging from con expected from a paper . We are c speed changes ob suit of the seed distribution, an occurred by chan tion represented ain. Therefore, a variety of normal distribu- ng the probability densities were investigated, servative to liberal estimates of the change seeding experiment; two are presented in this hoosing the hypothesis H to be that the wind served after a seeding experiment were a re- ing that generates some given probability d H is the hypothesis that the observed changes ce and can be considered coming from a popula- by the c 1 ima tologi cal distribution. For the first two cases, we assume that there is no evi- dence in favor of either hypothesis and that both are equally probable before application of the experimental results. Since no evidence is assumed in favor of either hypothesis before the experimental results, the term ev(H |C) is zero in the first step of each computation. For the first case, we are choosing the following hypo- the ses : H = The observed wind speed change after seeding has a probability distribution described by curve A, figure H-2. H = The observed wind speed change after seeding occurred by chance and has a probability des- cribed by curve C, figure H-2, which represents the c limatological distribution. That is, H is the hypothesis that the wind speed changes observed after each seeding experiment came from a population represented by a normal distribution with a mean and standard deviation of -3 and 12% respectively. This distribution indi- cates a 60% chance of getting a wind speed reduction and a 40% chance of observing a wind speed increase after each seeding experiment . The senting H) This distribution would indicate mean value of the cl imatological distribution (repre- is 0 and the standard deviation is 12 percent. a 50-percent chance that the wind speeds of a given storm would decrease during the 12-hour period after seeding and a similar probability for showing an inc r eas e . The value of the observed maximum wind speed change was used to determine the probability that such a change would occur, given the distribution associated with Hn as compared with the one associated with H The results of t he comparison H-6 3- >- I- 55 2 r i i i -III (O) PROBABILITY DISTRIBUTION \ " " ' ASSOCIATED WITH HYPOTHESIS (A) PROBABILITY DISTRIBUTION f X / / ' ASSOCIATED WITH HYPOTHESIS / V / ^ \ HiN CASE 2 AND 3.TABLE 2 H, IN CASE 1, TABLE 2 / A • ^ \ )i=-iao 0=120 _ |L=-3.0 *^ n,n- ■ • .. i i - -50 -40 -30 -20 -10 0 10 20 MAXIMUM WIND SPEED CHANGES (PERCENT) V' 40 Figure H-2. The probability distribution used in the hypothes-is testing listed in table H-2. of these two hypotheses are listed as case 1 in table H-2. This computation indicates that after the two Debbie seeding ex- periments, the probability that H is correct compared with H has increased from 50 to 70%. For the situation listed as case thesis chosen for 2 in table H-2, the hypo- H is the same as above, but that chosen for H is as follows: H = The observed wind speed change after seeding has a probability distribution described by curve B, figure H-2. Curve B is a normal distribution with a mean and standard de- viation of -10 and 12 percent respectively. This particular distribution was chosen because before the Hurricane Debbie experiments meteorologists participating in Project ST0RMFURY were of the opinion that if the seeding operation were prop- erly performed, a reduction in maximum wind speeds of the order of 10% could be realistically expected. This value was H-7 Table H-2. Results of Hypothesis Testing. Case 1 H = N(-.03, .12), Curve A, Fig. H-2; H = N(0, .12), Curve C, Fig. H-2. Experiment (E ) n Evidence Probabil ity Assumed before Debbie experiments Debb ie 18 Aug . 69 (-30%) * Debbie 20 Aug. 69 (-15%) * (EV (H E C) 1 n 0 2 .57863 3. 80005 Hl .5 .644 .706 H2 .5 366 294 Case 2 H = N(-.10, .12), Curve B, Fig H-2; H = N(0, .12), Curve C, Fig. H-2. Experiment (E ) n Evidence Probabi lity Assumed before Debbie experiments Debb ie 18 Aug. 69 (-30%) * Debbie 20 Aug. 69 (-15%) * (EV(H, E C) 1 ' n 7 . 5398 10 .5557 1 2 5 .5 850 .150 919 .081 Case 3 H = N(-.10, .12) Curve B, Fig. H-2; H = N(0, .12), Curve C, Fig. H-2 Experiment (E ) n Evidence (EV(H1 |E C) 1 n -9 .5425 -2 .0027 1 .0132 Probabil ity Assumed before Debbie experiments Debbie 18 Aug. 69 (-30%) * Debbie 20 Aug. 69 (-15%) * 1 .1 . 387 . 558 H2 .9 .613 .442 * Observed maximum wind speed change H-8 based partly on the results obtained from the Esther and Beulah experiments and on rough calculations of the location and amount of heat that would be released by the seeding experiments and the resulting wind speed changes. This distribution indicates a probability of 80% that a wind-speed reduction would be observed after each seeding and a 50% chance that the reduction would be more than 10%. The computed results from equation (H-l) indicate that the proba- bility of the truth of hypothesis Hi compared with H2 reaches 92% based on the results of the two Debbie experiments. Many meteorologists have been quite skeptical about the possibility that the eyewall seeding experiment would reduce the maximum wind speeds. If we take this view and say that before Hurricane Debbie experiments we believed that there was only one chance in 10 that the seeding experiment would result in a 10% reduction in the maximum wind speeds, then our re- sults would follow those illustrated for case 3 in table H-2. That is, the hypotheses H and H would be the same as those used for obtaining the results listed in case 2, but instead of assuming that they were equally probable before the experi- ments, we assume that H is nine times more likely than H . As a result of the two Debbie experiments, the accumulated dence indicates that the probability of the truth of H com- pared with H has increased from 10% to approximately 56% and that, similarly, the probability of the truth of H compared with H has decreased from 90% to approximately 44%. evx- UPDATING THE PROBABILITY DISTRIBUTIONS In the preceding section one approach was used in an attempt to answer the basic question as to whether the seeding operation actually caused the changes observed in the seeded storms. In this section a slightly different approach is used in an attempt to answer that same question. We would like to determine what we can say about the mean change of maximum wind speeds as a result of our sequence of experiments and, given a similar experiment, what changes can we expect. To accomplish this task, we assume the outcome of seeding events to consist of a continuous set. We can then write Bayes ' equation in the following form, using probability den- sities (Tribus, 1969, p. 79): H-9 p (a I x) p (E . |ax) P (alEiX) = P (a|x) P(B.|ax) ^ (H-2) where E. is the percentage of change in the maximum wind speeds measured after the i seeding experiment , a is a continuous variable representing the average percentage of change in the maxi- mum wind speeds, X is all background information, P(a|X) is the probability distribution prior to the seeding experiment, P (E . ax) i p (a e . x) 1 i is the probability of observing a reduction E. , given a mean reduction of a, and is the updated probability destribution ob- tained from the application of- (H-2) and is interpreted as the probability that an average change in maximum wind speeds of size ot has occurred, given a seeding ex- periment result. We assume the distributions P(a|x) and P (E . |ax) are nor' mally distributed as was proposed earlier, i.e. , we have probability densities of the form p (a| x) = n(u , ax) (H-3) and p (e . | ax) = n (a, a ) (H-4) From (H-2), (H-3), and (H-4) we obtain P (a E X) = N (\1,0) ' n (H-5) with ]i = V2 + ai ? , Ei 1 = 1 rr2 2 a2 + „a H-10 and a = VI + _n for the sequence of n experimental data symbolized by E . We are introducing a family of probability distributions for the maximum wind speed change after seeding of the form H = normal (mean = a, standard deviation 0 ) and use equation (H-2) to obtain equation (H-5) after a sequence of seeding experiments. The problem then becomes one of selecting appropriate normal distributions to represent P(ajX) and P(E. |ax) . For P(a|x), i.e., the prior distribution, we should use all background information, such as theoretical calculations, re- sults of previous experiments, climatology, etc. Before the Debbie experiments, such information indicated that a wind speed reduction should occur, i.e., Esther and Beulah experi- mental results and theoretical calculations. However, to avoid any bias in favor of the seeding reduction, we chose the distribution P(a|x) = N(0, .12) . In a sense, we are saying that we expect the seeding to have no effect and that the natural fluctuations will continue to play their role. For 3 2 UI K 10 U15 A/C TRACK L. 90 80 SOUTH RADIAL DISTANCE (N.M. ) A TO 80 NORTH HURRICANE "GLADYS" OCTOBER 17,1968 NORTH -SOUTH CROSS SECTION FLIGHT 681017A ALTITUDE 6400FT - 100 - 90 - 80 RADIAL DISTANCE (N.M.) B Fig. 11. Cross section of composited radar echoes (from vertically oriented 3.2-cm radar) and profiles of temperature, wind speeds relative to the moving storm center, and the relative humidities for north-south oriented passes through the storm at 1770 ft for 1230-1313 GMT, a., and 6400 ft for 1813-1848 GMT, b. Both sections show echoes from the CEC. 5. A model of the Circular Exhaust Cloud (CEC) a. The CEC in hurricane Gladys It is rather unfortunate that no televised satellite pictures of Gladys were available concurrently with Apollo 7 pictures exposed between 1530 and 1531 GMT. ATS-III spin-scan pictures were taken later at 1713, 1927, 1952, 2017 and 2107, as well as ESSA 7 pictures exposed at 1935. Combined analyses of these pictures revealed that the diameter of the CEC increased signifi- cantly during the period of the exposures. These di- ameters as tabulated in Table 2 permit us to estimate the mean divergence inside the CEC at the height of its expanding leading edge if we assume that the cloud edge expanded with the speed of the normal component of the wind. Data are insufficient to fully support this assumption, but results obtained are reasonable. The mean divergence is expressed by U rec VJS, (4.1) December 1970 GENTRY, FUJITA AND SHEETS 847 40 20 Okl IN-TOWER HORIZONTAL VELOCITY t'=-25min i5xid"5sec' — CEC-SCALE CONVERGENCE Fig. 12. A model of the circular exhaust cloud based on data for the CEC inside hurricane Gladys of 17 October 1968. where Acec denotes the horizontal area of the CEC, and V e the component of expanding velocity normal to the edge segment dS of the CEC. Under the assumption of a circular cloud with constant rate of expansion, we may- reduce (4.1) to 5, 2 dR 2 AR R dt R At (4.2) where R is the radius of the CEC and the tilde denotes the mean value averaged during the period At. The mean divergence thus computed for a 1.7-hr period (1530-1713 GMT) turned out to be 17X10"5 sec-1, while that for a 3.1-hr period (1731-2017) was only 5X 10~5 sec-1. These values indicate that the diver- gence at the CEC level decreased considerably. But the total expansion rate as defined by VedS = Ace<:Dcec^TvR2Dcec decreased from 2.8 to 2.0 km2 sec-1. This would mean that the total convective mass transport beneath the CEC remained almost unchanged for ~5 hr after Apollo 7 pictures were taken at 1530. The displacement of the CEC as a whole is of ex- treme interest. The CEC center, located some 35 km north-northeast of the hurricane center, rotated in 4 hr by about 100° around the hurricane center which was closely tracked by the land-based radars. The rotation speed of the CEC relative to the storm center was there- fore only ~6 kt which is no more than 10% that of the Table 2. Diameter of the CEC measured from various satellite pictures taken on 1 7 October 1968. 1530 1713 Time (GMT) 1927 1934 1952 2017 Diameter (km) 55 Determined by Apollo 7 93 ATS-III 110 110 ATS-III ESSA 7 115 ATS-III 120 ATS-III 848 JOURNAL OF APPLIED METEOROLOGY Volume 9 Fig. 13. Time changes in the CEC's seen inside hurricane Debbie of 16 August 1969. Picture sequence was selected from digitized ATS-III pictures produced by NASA for the Hurricane Watch Experiment, 1969. low-level flow directly beneath the CEC. It is likely that the motion of the CEC corresponds to that of the field of low-level convergence shown in Fig. 10. The main- tenance and the motion of such a CEC-scale conver- gence area is closely related to the asymmetric nature of a hurricane. While the CEC rotated very slowly around the hurri- cane center, the WSR-57 Tampa radar indicated that cellular echoes inside the CEC area were moving at the rate of ~30 kt, just about 50% of the low-level wind speed. Evidently, echoes either formed or intensified near the upwind edge of the CEC ; meanwhile, contin- uous dissipation was taking place along the downwind edge. A schematical cross section of the CEC including a convective tower was constructed in Fig. 12 in which the vertical and the horizontal velocities of the air inside the tower are given to the left and the right, respectively. Step-by-step computations revealed that it would take ~25 min for the inflow air at the cloud base to reach near the cloud top. According to Fujita and Grandoso's (1968) concept of a sliced cloud disc, December 1970 GENTRY, FUJITA AND SHEETS 849 the axis of a convective tower and trajectories of parcels occupying various parts of the tower are quite different. For instance, a parcel A near the cloud top must have entered the cloud base 25 min earlier. Its trajectory is shown by a tilted curve connecting a with A. The end points of successive trajectories departing from a through e at the cloud base determine the present shape of the tower axis, A, B, . . . , F. It should be noted that the displacement rate of a, b, . . . , e is controlled by the propagation of the field of an impulse giving rise to the vertical acceleration of uprising air. In order to account for a gain of some 5 m sec-1 vertical velocity within about a 1-km layer above the surface, the impulse should be identified as a convergence field of subcloud convergence of 5 m sec-1 (1 km)-1 = 500 X 10-5 sec-1. Despite the significant tilt of the trajectory of ascending air, the tower axis is maintained more or less in an up- right position. The figure clearly indicates the major difference between trajectories and the tower axis. While the maximum convergence beneath each tower is estimated to be ~500X10-5 sec-1, the overall con- vergence beneath the CEC shows a maximum of ~15X10-5 sec-1. These values imply that the area of tower-scale convergence is only a few percent of that of CEC-scale convergence. b. The CEC in other hurricanes The foregoing study suggests that a CEC could be formed where a CEC-scale convergence area is topped by a weak flow at the hurricane outflow level. Most weak hurricanes are characterized by such a structure. In order to find similar CEC's in premature hurricanes, a number of ATS-III pictures were examined. One of the best examples in hurricane Debbie of 16 August 1969 will be discussed. As shown in Fig. 13, the first indication of a CEC was seen at 0952 GMT on the eyewall southwest of the hurricane center. The cloud identified by A increased its diameter from 50 to 110 km in ~2 hr. The second CEC identified as D appeared at 1005 in a pair. Then they grew and merged. A total of five CEC's were spot- ted during early morning hours when the low angle of the sun permitted their easy identification. In most cases the CEC started in the form of isolated point sources such as D at 1005 and C at 1018. These points grew into circular clouds with about a 20-km diameter in less than 15 min. All CEC's rotated around the hurricane center cy- clonically at the rate of 23 kt for A, 20 kt for B, 16 kt for C, and 25 kt for D. The maximum wind speed of Debbie was ~50 kt, indicating that the storm had not reached hurricane intensity yet. It is seen, from these data, that the CEC's rotated at about one-half the tangential wind speed of the parent storm. In the case of Gladys, however, the motion of the CEC was only about 10% of the maximum wind speed around the storm center. Further research on the wind and cloud motion in other storms is required in order to establish their dynamical relationship. Nevertheless, the finding of a number of CEC's in the development stage of Debbie is rather encouraging since we now feel that the CEC could be found in many other hurricanes. 6. Conclusions Data collected for hurricane Gladys of 17 October 1968, by Apollo 7 manned spacecraft, aircraft of ESSA's Research Flight Facility, ATS-III and ESSA 7 satel- lites, WSR-57 search radars and conventional weather networks have been integrated in this study of the storm. Description of the various types of data are provided and techniques for utilizing .them are explained. By using data from all the sources, it was'practical to deduce features of the three-dimensional mass circu- lation through the hurricane and to gain new insight concerning the mechanisms by which a hurricane de- velops. The circular exhaust cloud which dominates the Apollo 7 pictures of the hurricane is a prominent fink in this three-dimensional circulation and may be typical of a type of cloud developed in hurricane genesis situations. REFERENCES Fett, R. W., 1968: Some unusual aspects concerning the develop- ment and structure of Typhoon Billie — July 1967. Mon Wea Rev., 96, 637-648. Fujita, T., 1963 : A technique for precise analysis for satellite data, Vol. 1. Photogrammetry Meteorological Satellite Lab., Rept. 14, ESSA, 106 pp. , 1969: A method of computing cloud height from an Apollo picture using cloud shadows. Satellite Mesometeorological Research Project, University of Chicago, Rept. 82 (in press) . , and H. Grandoso, 1968 : Split of a thunderstorm into anti- cyclonic and cyclonic storms and their motion as determined from numerical model experiments. /. Atmos. Set., 25, 416- 439. Gentry, R. C, 1964: A study of hurricane rainbands. National Hurricane Research Project, Rept. 69, Weather Bureau, 85 pp. , 1967 : Structure of the upper troposphere and lower strato- sphere in the vicinity of Hurricane Isbell, 1964. Papers Meteor. Geophys., Tokyo, 18, No. 4, 293-310. Hawkins, H. K., and D. T. Rubsam, 1968a: Hurricane Hilda, 1964, 1. Genesis, as revealed by satellite photographs, conven- tional and aircraft data. Mon. Wea. Rev., 96, 428-452. , and , 1968b: Hurricane Hilda, 1964, II. Structure and budgets of the hurricane on October 1, 1964, Mon. Wea. Rev. 96, 617-636. Kessler, E., and D. Atlas, 1956: Radar-synoptic analysis of Hurri- cane Edna, 1954. Geophys. Res. Paper No. 50, AFCRL, Bedford, Mass., 113 pp. La Seur, N. E., and H. F. Hawkins, 1963 : An analysis of Hurricane Cleo (1958) based on data from research reconnaissance air- craft. Mon. Wea. Rev., 91, 694-709. McFadden, J. D., 1970: Airborne investigation of the effects of hurricanes on the thermal structure of the surface layer of the ocean. Proc. Symp. Investigations and Resources of the Carib- bean Sea and Adjacent Regions, Willemstad, Curacao, 18-23 November 1968 (in press). 850 JOURNAL OF APPLIED METEOROLOGY Volume 9 Neuman, S., and J. G. Boyd, 1962 : Hurricane movement and vari- Soules, S. D., and K. M. Nagler, 1969: Two tropical storms viewed able location of high intensity spot in wall cloud radar echo. by Apollo 7. Bull. Amer. Meleor. Snc, 50, 58-65. Mon. Wea. Rev., 90, 371-374. Sugg, A., and P. J. Hehert, 1969: The Atlantic hurricane season Sheets, R. C, 1969: Preliminary analysis of cloud physics data of 1968. Mon. Wea. Rev., 97, 225-239. collected in hurricane Gladys (1968). Project Stormfury, Wexler, H., 1947 : Structure of hurricanes as determined by radar. Ann. Rept. 1968, Appendix D, 1-11. Ann. New York Acad. Sci., 48, Article 8, 821-844. Reprinted from Mariners Weather Log 1 k , No. 5, 262-266 ii PROJECT STORMFURY OPERATIONS AND PLANS William D. Mallinger National Hurricane Research Laboratory and Atlantic Oceanographic and Meteorological Laboratories, ESSA Miami, Fla. After several frustrating years, Project Stormfury 1969, no hurricane had been seeded since the Beulah finally had a good year for experimentation in 1969. experiment in August 1963. The results from the Until hurricane Debbie was seeded twice in August Debbie seeding are highly encouraging: on the first NAVY CESSNA A.F. WC-130 NAVY A-6 A.F WB-47 ESSA B-57 r - i 1 m i* -^P^ l';^m^T ESSA DC-6 ESSA C-54 NAVY WC-121N Figure 8. The fury of the hurricane will be probed again this year by many of the above types of aircraft. 262 day of seeding there was a decrease of 31 percent in the maximum wind speeds and on the second day a de- crease of 15 percent. Although it still cannot be con- clusively stated that the seeding alone was responsible for the change in intensity, radar pictures of the clouds near the eye also suggest that a modification of the hurricane was caused by the seeding. For the Debbie experiment, the Project Director, Dr. R. Cecil Gentry and the Navy Project Coordinator, Commander L. J. Underwood, U.S. Navy, assembled all the participating units in Puerto Rico on August 17. Aircraft and crews from the Navy's "Hurricane Hunter" Weather Reconnaissance Squadron 4 and Attack Squad- ron 176; the Environmental Science Services Admin- istration's Research Flight Facility; and the U.S. Air Force 53d Weather Reconnaissance Squadron were deployed to await the signal to begin the multiple seeding of the clouds around the eye of Debbie. Fig- ure 8 shows the types of aircraft used in the 1969 Stormfury operations. On August 18, the first flight took off at 0600 GMT, and the last flight returned near 0600 the following morning. Figure 9 shows the on- station time table for theeyewall seeding experiment. Of the 14 flights made, five jet aircraft were used as seeders. They seeded the hurricane in the clouds a- round the eye every 2 hr for 8 hr. Each seeder air- craft released 208 generators that produced silver iodide smoke as they fell. The other aircraft moni- tored the operation and the storm with radar and other data collection instruments in order to detect any changes or effects that could be measured. Figure 10 is a multilevel projection showing the various flight patterns during the experiment. On the 19th, the forces rested and were debriefed from the previous day's operations. A general briefing was also held for another attack on hurricane Debbie to be attempted on the 20th. Once again the 24-hr operation began and again Debbie was subjected to the bombardment of her clouds near the eye. All flights were completed on schedule, and no major problems or mishaps occurred. For the first time, not only one, but two multiple seeding experiments in a hur- ricane had been completed. Figure 11 is an enhanced NASA ATS 3 photograph of hurricane Debbie. During the flights by the seeder aircraft into the hurricane on the 2 seeding days, only one incident of severe turbulence was reported. This occurred on the 20th after the first jet seeder crossed the eye and approached the surrounding clouds to begin its drop- ping run. Extremely strong downdrafts were encoun- tered, which forced it to lose 6, 000 ft of altitude. Undaunted, the crew still made their pyrotechnic 40 33 |'C"(RFFWB57J| UJ Id b. it O 0) b o o UJ Q 29 2 12-20 < 10 n i (OUTFLOW MONITORS) !j"(AFWB47) b2"(RFFWB57T| "l","m","N , "0","P", Q" (NAVY A-6'S) j (SEEDING A/C ) I I I I -SEEDINGSJ 1" AF WC-130) 1 (CLOUD PHYSICS MONITOR) | "A" (RFF DC-6) (CLOUD PHYSICS AND VARIABILITY MONITORS "B' (RFF DC-6! "A2" (RFF DC-6) | 1 "H" (NAVY WC-121N) RADAR "AND DROPSONDE | | "s" (NAVY WC-121) COMMAND CONTROL ( INFLOW MONITORS) - "G" (NAVY WC 121 NO |"P" (RFF C-54) "F" (NAVY WC 121 N ) 0800Z 1000 Z 1200Z 1400Z 1600Z 18002 2000Z 2200 Z 2400Z 0200 Z T-4 T-2 TANGO T+2 T + 4 T +6 T+8 T + 10 T + 12 T+14 TIME (GMT) Figure 9. Time table for Stormfury aircraft employment for the eyewall experiment. 263 V^KVV VkV^WNWft Figure 10. Seven-layer flight level diagram depicting aircraft flight patterns during the eyewall experiment. canister drops close to the proper location in the clouds. The forces, elated at the accomplishment, were now faced with the tedious and demanding work of assessing the effects. All the data had to be collected, processed, and evaluated. Scientists at the National Hurricane Research Laboratory, Miami, Fla., and at the Navy Weather Research Facility, Norfolk, Va. , are still working on these data. Many very interesting facts have already emerged. Although it cannot be conclusively proven that the seeding decreased the hurricane's intensity, there was a decrease of maximum wind velocities on both days the seeding was done. On the 19th, between the seedings, the storm increased in intensity. Other data are also being examined to determine if 264 Figure 11. Enhanced NASA ATS 3 satellite photo of hurricane Debbie taken at 1504 Aug. Florida is at upper left. 20, 1969. Peninsula the seeding caused a modification of Debbie. If a storm were moving over colder water, it would decrease in intensity without human intervention,, A quick review of sea surface temperatures in Debbie's path does not indicate that she was moving over colder water at the seeding times. Further research is being carried out on the sea surface temperature fields during the experimental period. These temperatures taken by ships traversing the area before and after the seeding are vital in the analysis work„ If the seeding caused a modification in the storm, one might expect to find some periodicity in the changes of eye shape and size. Preliminary radar data analyses indicate that there was a periodicity about the same as that of the seedings. Figure 12 shows a radar (U.S. Navy APS-45) photograph taken of Debbie on August 20. Studies concerning the probability that the changes observed in Debbie could have occurred in an unseeded hurricane suggest strongly that some degree of bene- ficial modification was achieved. Because of the apparent success of the Debbie seeding, Project Stormfury has been given increased support to conduct additional experiments as soon as possible,, The 1970 Stormfury season started in July instead of August as in the past and will extend through October. There may be a slight relaxation of the ground rules under which seeding may be conducted to permit seeding of a tropical cyclone when there is only a small probability (10 percent or less) of its center coming within 50 mi of a populated land area within 18 instead of 24 hr after seeding. Other types of silver iodide generators and methods of delivery by aircraft are also being investigated,, The Project hopes to obtain funding for research into additional areas of possible modification of tro- pical cyclones. One area is that of sea to air evapor- ation inhibitions If a film or chemical of proper 265 Figure 12. This radar picture, taken about 15 min after the satellite photo appearing in figure 11, was snapped while a Navy plane infiltrated the northeastern portion of Debbie's eyewall. qualities could be spread across the sea surface where the evaporation and heat energy is being released to feed the storm, a significant decrease in intensity could be expected. Unfortunately, there is no chem- ical that meets the criteria for this purpose,, The compositions that have been used for inland reservoir evaporation suppression experiments tend to break up or blow away when the wind speeds reach 15-20 kt, which obviously makes them unacceptable for use in a tropical storm or hurricane environments A new type of chemical with special properties needs to be developed for use under high wind and sea state con- ditions. The combined use of ships releasing chemi- cals on the sea surface while aircraft disseminate cloud seeding agents in the clouds may prove to be a better way to achieve hurricane modification . All Stormfury operations to date have been conducted in the Atlantic. Considerable thought is now being given to moving to new areas to increase experimental opportunities. In the Atlantic, Caribbean, and Gulf of Mexico areas, one can expect an average of two eligible storms per year. A group operating from Guam and Okinawa in the Pacific might expect to have about six typhoons per year that could be seeded under current, eligibility rules. If the Project gets the necessary resources to operate in the Pacific, the desired experiments can be carried out in a much shorter time„ Even with an average of two storms per year in the Atlantic areas, periods of up to 2 yr have occurred during which no storms were eligible for seeding. Project Stormfury is hoping for a good experimental season in 1970 and is looking ahead to better experi- ments that may eventually lead to the modification of some of the most intense and damaging effects of hurricanes. If this can be done, huge savings to man- kind can be achieved. 266 45 Reprinted from Monthly Weather Review SQ_, No. 5, 3 6 3 ~ 3 7 ^ May 1970 363 UDC 551.658.29:651.516.11:551.511.2(263.6) "1965.10' VERTICAL MOTIONS AND THE KINETIC ENERGY BALANCE OF A COLD LOW BANNER I. MILLER and TOBY N. CARLSON National Hurricane Research Laboratory, ESSA, Miami, Fla. ABSTRACT Vertical motions have been computed for a 6-day period during which an upper tropospheric cold Low moved through the eastern Caribbean, and a kinetic energy budget for the region has been constructed. During the first 3 days, the kinetic energy inside the volume increased. The computations indicate that the increase was caused by lateral advection of kinetic energy into the volume plus a small internal conversion pf potential to kinetic energy. The kinetic energy decreased during the last 3 days, as the circulation became indirect. Visual agreement between the vertical motions and the observed weather was good. 1. INTRODUCTION Analyses of the data from Project ECCRO (Carlson 1967a, 19676) have provided one of the most complete descriptions in existence of an upper tropospheric cold Low. Data were collected by research aircraft at five levels, ranging from 976 to 238 mb, and extended over a 6-day period in October 1965. While the analyses cover only a limited geographical area (fig. 1), the data offer a unique opportunity for studying the structure and ener- getic processes of a cold Low, a common feature of the lower latitudes in summer (Ricks 1959, Frank 1966). The data also appear to be of sufficient accuracy to permit meaningful testing of some of the features of dynamical models. This paper will present selected vertical motion patterns along with some of the energy transformations associated with the passage of a cold Low over the network of stations, and make an attempt to assess the realism of a numerical model that has been designed for analysis and prediction of tropical weather systems (Miller 1969). 2. MODIFICATION OF THE INITIAL ANALYSES Carlson (1967a, 19676) analyzed the aircraft data, supplemented by conventional upper air soundings from the Caribbean stations, at 976, 841, 692, 501, and 238 mb. The first paper (Carlson 1967a) contains a detailed description of Project ECCRO, including a summary of data and selected analyses of the data fields. In the second paper (Carlson 19676), the cold Low was the subject of investigation in which the winds, temperatures, geopoten- tial heights of constant pressure surfaces, and mixing ratios were composited from the individual analyses by means of a sliding average made according to the mean (westward) speed of the cold Low. In this way, an artificial- ly enlarged area was formed that encompassed more of the cold Low than any of the individual analyses. Thus, the original 10X13 grid was expanded in the composite to a 10X19 grid, the spacing being 1° of longitude for both grids (108 km). Calculations of vertical motion were performed for a seven-level model (Miller 1969), the levels ranging from 1000 to 100 mb, with a pressure increment of 150 mb. The u and v components of the wind field at 100 mb were obtained from the stream function, which was obtained from the analyzed height field by solving the balance equation. At both 250 and 100 mb, the mixing ratio was obtained by assuming a constant value of 50 percent relative humidity, since mixing ratios were not measured above 500 mb. This is not critical since the variation of moisture at these levels (and low temperatures) is not of great significance in the model. Values of u, v, and q were obtained at 550 and 400 mb by linear interpolation from the levels used on Carlson's analyses. Geopotential heights for these levels were obtained by logarithmic variation between existing analyses. Carlson's analyses for the 976-, 841-, 69 1-, and 238-mb levels were accepted for the 1000-, 850-, 700-, and 250-mb levels. It was felt that the small grid area and relatively large number of boundary grid points (approximately one-third of the total grid points) would have a deleterious effect on the results calculated within the boundaries. By quad- ratic interpolation between the original grid points, a num- ber of additional points were generated to somewhat reduce the boundary effects. The individual 10X13 array was thus expanded to a 19X23 array (51-km spacing at 22.5° N.), and the composite grid expanded to 15X19 points (grid length 66 km at 22.5° N.). Carlson's examination of the original fields, from a purely kinematic standpoint, revealed that the basic wind fields contained small-scale spurious fluctuations which were the result of inconsistencies in the basic raw data. For minimizing this, the u and v components of the wind were smoothed once in the horizontal, using a nine- point operator and a smoothing coefficient of 0.50. The . fields were also smoothed in the vertical, using a three- point centered smoothing in which one-quarter of the values on the adjacent levels above and below were 364 MONTHLY WEATHER REVIEW Vol. 98, No. 5 71° 70° 69° 68° 67° 66° 65° 64° 63° 62° 61' 60r Figure 1. — Map showing area of Project ECCRO. The flight path is shown by the connected line segments (shown dashed for track of Navy aircraft). added to half the central value. Vertical smoothing was not done at 400 and 250 mb to avoid smoothing the actual vertical wind shears which varied rapidly with height at these levels. Smoothing these fields was found to reduce the implicit temperature gradients in the upper troposphere in an unacceptable manner. Carlson attempted a rough hydrostatic balance between his temperature and height analyses. However, some degree of independency remained in the height, tempera- ture, and wind fields. To obtain a set of data as internally consistent as possible, we used the following procedure, referred to as method A: 1) The smoothed winds were accepted as the most reliable data for the daily calculations. On the 13th and 17th, the time-dependent terms in the divergence and omega equations were evaluated by taking the averages of the observed changes over 2-day periods (12-14 and 16-18). 2) The height of the northwestern grid point was accepted as analyzed. Other boundary heights were gene- rated from the normal wind component, assuming geo- strophic balance, and applying a small correction to insure that the height returned to its initial value at the starting point following the taking of the line integral. 3) A first estimate of the height field was oblained by solving the divergence equation dD dt~ VvD+w d~+D2-2J («., v) -Jt+fiu dp 3oj du do) 6V> „ . d~xd~p+dy¥p~K,N' ydp\dx^dy )+V2=0. (1) (See the list of symbols at the end of this section.) At this point, both the divergence and the vertical motion were set equal to zero ; this procedure is approximately equivalent to solving the balance equation with friction. 4) The temperatures were computed from the geo- potential field obtained from equation (1); the lapse rate for the lower layer was specified. 5) The vertical motion was obtained by solving the omega equation (5) in section 3. Time-dependent terms were evaluated. 6) A new wind field was constructed by adding the divergent and rotational components obtained after solving dv du ,_, ^=d-x-d-y (2) May 1970 Banner I. Miller and Toby N. Carlson 365 and VX=— ^r- dp (3) Boundary values for ^ were determined from the tangential component of the wind (Sanders and Burpee 1968) ; x was set equal to zero on the boundary. 7) The divergence was computed from the omega field, and a second estimate of the heights was obtained by solving equation (1) again. The time-dependent term in equation (1) was a 48-hr average of dD/dt, the divergences at t— 24 and 2+24 hr being obtained from preliminary estimates of omega obtained in a manner to be described later. Temperatures were recomputed. For the composited data, the wind field obtained from the analyzed heights via the balance equation resulted in vertical motions that appeared to fit the weather patterns better than those generated by the pro- cedure described above. The difference in results may be attributable to the difference in the way the scalar height and vector wind fields were composited, or to a greater amount of noise in the composited wind field. In the composite case, all time-dependent terms were set equal to zero, since they could not be realistically evaluated, and since it was reasoned that the compositing procedure resulted in a relatively steady state, although a somewhat fictitious description of the cold Low. Symbols in this report have the following meanings: cd drag coefficient, <■„ specific heat of air at constant pressure, 1) divergence, J Coriolis parameter, ./"„ mean value of Coriolis parameter, 1\ flux of water vapor, Fs flux of sensible heat, 9 acceleration of gravity, II total heating function, 11, sensible heat (cal gur1 sec-1), II, latent heat (cal gm~' sec-1), I net moisture convergence, J Jacobian operator, K kinetic energy per unit mass, K„ a coefficient for lateral mixing, Km a coefficient for vertical mixing, L latent heat of condensation, in map scale factor, V pressure, 8 mixing ratio, geopotential, X velocity potential, stream function, w dp/dt, vertical p velocity, and V2 horizontal Laplacian operator. 3. SOLUTION OF THE OMEGA EQUATION The vertical motions were obtained by solving a diabatic and viscous omega equation , . , U ill , V )- This technique is consistent with the maintenance of a quasi-moist adiabatic lapse in the lowest layers and permits the upward transport of sensible heat against a potential temperature gradient. Over water, the drag coefficient was made an empirical function of the wind speed, and over land a constant value of 0.005 was assumed. Sensible heat and evaporation were set equal to zero over land. The latent heat added to the system was composed of two parts, first being a parameterization of the heat released by cumulus convection, HLU originally proposed by Kuo (1965). Kuo defined a quantity, Q, as the moisture required to saturate the atmosphere and (following condensation of a portion of the water vapor) to raise its temperature to that of the moist adiabat passing through the base of the cloud. Q is defined as Table 1. — Correlation coefficients and standard deviations of vertical motions computed by methods A and B Q=p«i.-£. JPb 9 JPb J-> 9 (7) The net moisture convergence within a column may be obtained by /aas_pag«2_-s£. (8) Jpt dt g g where q0 and «0 are the mixing ratio and the vertical motion at 1000 mb, pb and p, are the pressures at the base and the top of the clouds, qs and T, refer to the saturation mixing ratio and temperature along the moist adiabat determined by the lifting condensation level of the sub- cloud air, while T and q refer to the environmental conditions. Forty-eight-hour averages computed from known values were used for bq/dt. The heating function may now be expressed by HU=±cp{T-T). (9) HLi is set equal to zero at 1000 and 100 mb, if I is zero or negative, or if T is equal to or greater than Ts. It will be noted that the Kuo heating function is self-limiting, since it tends to approach zero as the lapse rate within the cloud becomes moist adiabatic and the cloud becomes saturated. The second part of the latent heat release is due to the ascent of moist air with the broad-scale vertical motion. It was defined as HL - 1000 0. 9996 0.4527X10-3 0.4533X10-3 850 .9651 . 8788X10-* .8942X10-1 700 .9899 .1249X10-3 . 1298X10-3 550 .9909 .7853X10-1 .8179X10-* 400 .9890 . 1389X10-3 .1308X10-3 250 .9947 .3755X10-" .3491X10-* r(») „B (17) 1000 0. 9980 0.3445X10-3 0. 3758X10-1 850 .9826 .1255X10-3 .1371X10-3 TIKI .9733 . 5647X10-< .6516X10-' 550 .9919 .1034X10-3 .1213X10-3 400 .9926 . 1428X10-3 .1571X10-3 250 .9866 .3458X10-' .3882X10-" 700 to 200 mb. Accordingly, the quantity in the brackets was set equal to a constant and has the value of 0.06; this was done to speed up the calculations. (The total heating function H is the sum of HLi-\-HL2JrHs.) The omega equation (5) was then solved, subject to the boundary conditions that omega was zero at 100 mb, and that omega at 1000 mb was as proposed by Cressman- (1963), o} (ID U«7EC^^ 4. ALTERNATE METHOD FOR COMPUTING VERTICAL MOTIONS Since time-dependent terms could be evaluated from known values on only 2 of the 6 days for which data were available, another and somewhat less satisfactory method was used to compute geopotentials, temperatures, and vertical motions. This scheme (referred to as method B) consisted of the following steps: 1) The heights were computed from equation (1) with divergence, omega, and the local time-derivative set equal to zero. The temperatures were computed from the heights and the mixing ratios. These temperatures and heights were accepted as the best obtainable esti- mates and were used in subsequent calculations. 2) The stream function was obtained from equation (2), and the observed wind was replaced by the rotational wind, which was used in the omega equation. 3) The omega equation was solved with the time- dependent terms assumed to be zero. The sum of these terms is identically zero for a quasi-geostrophic omega equation. The convergence of water vapor, needed to determine the heating function in equation (8) was obtained from the forecast equation, dq dq dq dq . dFq v . (12) Initially, these tendencies were large and seemed to re- May 1970 Banner I. Miller and Toby N. Carlson 367 suit in an overestimate of the upward motion in regions of intense convection, as will be seen later. Recalculation of the omegas with dq/dt=0 appeared to give more real- istic results. 4) The divergence was computed from the vertical motions, the divergent part of the wind was obtained from the velocity potential derived from equation (3), and the divergent wind was added back to the rotational wind. Comparisons between vertical motions computed on 2 days by methods A and B are shown in table 1 . Differences appear to be small, and the correlation coefficients high. We will, therefore, use the complete set of vertical motions for discussion and energy computations. 5. CORRELATION BETWEEN VERTICAL MOTION AND OBSERVED WEATHER Selected analyses of the observed wind fields, in the form of analyzed streamlines and isotachs, the vertical motion patterns, the observed distribution of cloud and weather, and the generated (from equation (1)) height and temperature fields are shown in figures 2 through 7, respectively, for the 700- and 250-mb levels on the 13th and 17th of October 1965, and (below) for the composite case. The cold Low was moving westward at a speed of about 6 kt from a position centered just east of the Antilles on the 13th to the vicinity of the Virgin Islands on the 17th. Accompanying the disturbance was an extensive cloud cover situated along its eastern side. Within this cloud shield was a small region of deep cumulonimbus convec- tion southeast of the low center (see fig. 6). The numerous categories of cloud and weather patterns in figure 6 are presented in an attempt to represent exist- ing conditions in the form of a detailed whole sky code. Basically, the symbols B and C refer to normal or sup- pressed trade-wind cloudiness; D and E to active to weakly disturbed trade-wind regimes; and I, G, and H to dis- turbed conditions. The latter three (contained by the scalloped border on the 13th and composite maps) con- sist of a convective regime I and a nonconvective regime with dense middle and high cloud cover (areas G and H). The symbols X and Y refer to the existence of cirrus layers without a middle cloud cover. Agreement between cloud cover and vertical motion (figs. 4 and 5) appeared to be the most satisfactory at upper levels in the composite case and least satisfactory at low levels and on the 13th. Strong upward motion (1 to 2 cm sec-1) was occurring over most of the cloud shield on the 17th and in the composite while descending motion or very weak ascent was coinciding with the suppressed areas to the west. On the 13th, the vertical motions show some correspondence between regions of descent and sup- Figuhe 2. — Observed streamline and isotach analyses for the 700-mb level on October 13 (upper left), October 17 (upper right), and for the composited data (below). 380-965 0—70^—5 368 MONTHLY WEATHER REVIEW Vol. 98, No. 5 Figure 3. — Same as figure 2, but for the 250-mb level. 76 152 228 304 380 456 532 608 684 760 836 912 988 1064 DISTANCE (NAUTICAL MILES! Figure 4. — Vertical motions (mm sec-1) and isotherms (°C, obtained from the divergence equation) for the 700-mb level on October 13 (upper left), October 17 (upper right), and for the composited data (below) : method B. May 1970 Banner I. Miller and Toby N. Carlson 369 Figure 5. — Same as figure 4, but for the 400-mb level. Figure 6. — Cloud and weather analysis in the form of whole sky code (see legend) for October 13 (upper left), October 17 (upper right) and composite case (below) . The main cloud shield is outlined by a scalloped border. Shading signifies areas in extract deep convection as occurring. Standard meteorological symbols are used. 370 MONTHLY WEATHER REVIEW Vol. 98, No. 5 LONGITUDE 68* 67° 66° 65° 64° 63° 62 76 152 226 304 380 456 532 608 684 760 836 912 988 1064 DISTANCE (NAUTICAL MILES) Figure 7. — Geopotential contours (meters) and isotherms at 400-mb as derived from the divergence equation for October 13 (upper left), October 17 (upper right), and the composite case (below). pressed cloudiness, but the ascent is clearly too wide- spread and intense for the rather inactive conditions which existed on that day (except over South America where cumulus convection was always very active). The results for the composite case offer the best agree- ment of all between weather and vertical motion. This outcome may reflect the computational hazards involved in the use of a very small area and a fine grid in synoptic scale work. The pattern of composite vertical motions does not appear to differ very drastically from that pre- sented by Carlson (19676) which was based on a much cruder (kinematic and adiabatic) model. In figures 4 and 5, the composite vertical motions show an essentially cellular pattern at lower levels, with some descending motion in the disturbed region and an area of weak ascent to the west (except in the most suppressed area B where descent predominated). At higher (and strongly baro- clinic) levels, the vertical motion pattern supports Carlson's conclusion that the cold Low possesses a dipole pattern of ascent and descent with rising motion (and cloudiness) to the east of the low center and descent dominating on the west. Centers of rising and sinking motion are thus located some distance from the low center, with little significant vertical motion in the center itself. Additional vertical motion computations (fig. 8) were carried out for the 13th and 17th where in one instance the moisture tendency was not evaluated in the formula- tion of H(dq/dt)=0 in equation (8) and in the other total heating function was neglected. Neglect of dq/dt resulted in a visible improvement in the vertical motion calcula- tions. On both the 13th and 17th, most of the ascending motion found in the largely undisturbed areas (B, C, and D) was replaced by weak descent. Within the main cloud shield on the 17th, strength of the ascending motion was reduced by about one-half. Elimination of the heating function itself led to a further reduction in the strength of the updrafts in the disturbed area and over South America, but with little change in the overall pattern. While it may be useful to evaluate the moisture tendency in the heating term in a forecast model such as that described by Miller (1969), the initial tendency appears to affect the computed vertical motions adversely in a nonforecast problem. Some additional vertical motions, computed by method A, are shown in figure 9. It should also be noted that these resemble more closely those of figure 8 than those of figure 5. 6. THE KINETIC ENERGY BUDGET The kinetic energy equation may be formed by taking the scalar product of V and the vector equation of motion. When integrated over a volume bounded by a lateral boundary L, and having an area A on fixed pressure sur- faces in the atmosphere, one obtains (Palmen 1959, Palmen and Holopainen 1962) May 1970 Banner I. Miller and Toby N. Carlson 371 76 152 228 304 380 456 532 60S 684 760 836 912 988 1064 DISTANCE (NAUTICAL MILES) Figure 8. — Vertical motions (mm sec-1) computed by evaluation of 3.4 with /= —woQo/9- 9 dt fPo l rp<> a a rp° Kdp=-±\ KVJp+^[Ku)p-^\ \.v III IV +-[0^7! --("atfdp-A&Vl 9 L J pa 9 Jph -4>IW+(D> <* where the first term on the right (term I in table 1) is the lateral transport of kinetic energy, the fourth term on the right (term II in table 2) is the work done on the boundary by asymmetries in the wind and geopotential fields, the sixth term on the right (term III in table 2) is the internal conversion of potential to kinetic energy, and the seventh term on the right (term IV in table 2) is the dissipation caused by surface friction. Other terms on the right include the vertical transport of kinetic energy through the top of the volume (second term), the work done by the mean pressure forces acting on the boundary (third term), the transport of potential energy through the top of the volume (fifth term), and the dissipation resulting from internal friction (last term). Following the convention of Palmen and Holopainen (1962), a bar operator denotes areal mean, a primed quantity denotes the deviation from the areal mean, a circumflex denotes a mean along the boundary, and the double prime denotes the deviations from the mean along the boundary. The two terms evaluated at ph vanish because omega was assumed to be zero at the top of the volume (100 mb). The mean boundary work term was also vanishingly small due to the geostrophic assumption in evaluating the geopotential along the boundary. No attempt was made to evaluate the internal friction in equation ( 14) . This will certainly be negative and possibly about the same order of magnitude as the surface friction term. •372 MONTHLY WEATHER REVIEW Vol. 98, No. 5 63° 62" 61" Figure 9. — Vertical motions at 400-mb (13th and 17th) computed by method A. Table 2.- -Kinetic energy budget for the eastern Caribbean during Oct. 12-14 and 16-18, 1965 12 13 14 16 17 18 Com- posite III IV Advection of K.E +3.35 +3.62 +3.22 +0.92 Eddy boundary work -0.76 -0.41 +0.56 -0.69 Mean boundary work. . . -^W +0.03 +0.09 +0.14 -0.11 Surface friction.. -0.26 -0.45 -0.35 -.47 Total' (I+II+III+IV).. +2.36 +2.84 +3.54 -.35 -V-V0 -0.99 -1.19 +1.05 -1.23 Total" (I+IV+V) +2.10 +1.99 +3.92 -0.78 +0.68 -0.06 +0.40 -0.04 - .60 -2.59 -0.13 - .35 +0.16 -0.24 +0.08 -0.03 - .27 -1.09 -1.42 -0.48 -1.05 -3.70 -3.61 -4.26 Total K.E. in volumet-- +3.98 +4.89 +5.20 +3.40 +3.08 +1.95 •In units of 1016 ergs sec" tin units of lO" ergs Since it was not possible to calculate omega on the boundary and since the procedure used in calculating the boundary heights (that is setting the normal component equal to zero) greatly reduces the amount of work done on the boundary, the outer rows were eliminated from the boundary calculations, leaving an array of 17X21 points for the daily analyses and a 13X27 grid array for the composite. The results of these calculations are shown in table 2. The total kinetic energy tendency was computed in two ways. The first total is the sum of advection, boundary work, internal conversion, and surface friction (terms I +11+111+ IV), while the second total combines the boundary work and the internal conversion (terms 11+ III) into the production term —\»V (term V), and is therefore the sum of terms (I+IV+V). The agreement is quite good; better agreement could probably be expected if the boundary work term had not been underestimated. During the first 3 days, the kinetic energy inside the volume increased. The calculations show that this in- crease was caused largely by the lateral advection of energy into the volume from the environment. The eddy boundary was negative on the first 2 days, the volume doing work on the environment, but became positive on the third day. The internal conversion of potential to kinetic energy was positive but not large. During the last 3 days, the total kinetic energy within the volume decreased. The tendency calculations show a decrease on the 16th and 18th, while on the 17th the tendency indicates a nearly steady state. The lateral transport of kinetic energy was much smaller during the last 3 days than it was during the first half of the period. Negative transport on the 18th signifies an export of kinetic energy from the volume. The internal conversion term was still small on the last 3 days but was negative, signifying an indirect circulation within the volume. When the kinetic energy tendency totals were averaged over the first 3 days, the mean tendency was found to be in the right sense, but was a little larger than the observed 48-hr increase in kinetic energy within the vol- ume. Similarly, the tendency averaged over the last 3 days was in the right sense, but a slight underestimate of the observed decrease in kinetic energy. Even closer agreement between observed and calculated energy ten- dencies would be expected had not internal friction been neglected. In the composite case, the computed tendency shows that the cold Low was decreasing in intensity, all terms being negative except the lateral advection term which was slightly positive. The internal conversion term was much larger, and the advection term generally May 1970 Banner I. Miller and Toby N. Carlson 373 Table 3. — Energy conversion term (a'u') evaluated over 150-mb levels for Oct. 12-14 and 16-18, 1965 {units, ergs gm~l sec'1 X 10~l) Table 4. — Kinetic energy budget for the eastern Caribbean during Oct. 12-14 and 16-18, 1965 Pressure (mil) Composite case 925 0.022 0.148 0.272 0.175 0.044 0.010 0.696 776 .067 .119 .130 —0.034 -0.124 .035 .. 625 ---- .047 .147 249 - .353 - .256 -0.041 -0. 829 475 .105 . 339 .558 - .740 - .707 - .207 -2. 879 325 .111 .272 .364 - .324 - .501 - .100 -2.083 175 -. .. -0.045 -0. 135 -0.176 +0. 136 +0.203 +0.030 +0. 339 Summary 0. 307 0.890 1.397 -1.140 -1.341 -0.273 -4.75 Figure 10. — Kinetic energy conversion term ( — a'u') at 475mb (that is the 400- to 550-mb layer) for the composite case, showing widespread conversion of kinetic to potential energy; limits are in ergs gm-1 sec-1. smaller that those of the individual days as the result of the larger volume considered. While the area for the composite case does not contain the entire circulation of the cold Low, the calculations reflect a real decrease in intensity which occurred after the 13th or 14th of October. On these 2 days, winds in excess of 60 kt were observed at 250 mb (fig. 3), and the lowest level of closed circulation was near 850 mb. By the 17th, maximum wind speed observed at this level was little more than half that of the 13th, and the lowest level of closed circulation had risen to near 550 mb. A slow but progressive weakening of the temperature and geopoten- tial gradients was also noted during this interval. On the 18th, the convective closed pattern appeared to be break- ing up and becoming disorganized. In table 3, the integrated values of a'w' (by 150-mb layers) show that this term was uniformly positive in all but the top layer on the first 3 days and negative on the last 3 days at all levels but the top and bottom. Largest values are found in the upper troposphere. Also, figure 10 reveals the uniformly indirect nature of the composite circulation at a level (475 mb) where the greatest trans- formation from kinetic to potential energy was taking place. The dipolar pattern reflects cold air rising on the east and warm air descending on the west. Although the cold Low may have been operating in the direct sense on the first 2 or 3 days of the period, the composite results I Advection of K.E • +3.81 +0.70 II Eddy boundary work —0.55 + .14 Mean boundary work III -177 - +0.03 -0.04 IV Surface friction _ -0.48 - .31 Total' (I+II+III+IV) +2.81 +0.50 V -V.V* -1.20 -0.12 Total- (I+IV+V) +2.13 +0.27 Total K.E. in volumet +3.98 +4.98 +5.20 +3.40 +3.08 +1.95 •In units of 10" ergs sec-1 t In units of 102' ergs show the net behavior of the system to be indirect over the 6-day period. Moreover, had the analyses encompassed the entire circulation of the cold Low, the results would likely have shown a still larger energy transformation and possibly a smaller boundary effect. Finally, it should be stated that the energy calculations based upon the vertical motions obtained from the omega equation with either bg/dt or the total heating H set to zero differed only slightly from those presented in table 1 . In regard to the energy conversion term, «'&/, its magni- tude decreased by about one-half, with neglect of dq/bt and slightly more than that with H=0, its sign remaining unchanged. The kinetic energy for the 13th and 17th, based on the vertical motions computed by method A, is listed in table 4. The results are almost identical to those in table 2 for the 13th, and the differences are not large on the 17th. 7. SUMMARY AND CONCLUSIONS An upper tropospheric cold Low passed through the eastern Caribbean during a 6-day period in October 1965, when the area was the subject of intensive aircraft reconnaissance at several levels. Analyses based on the data collected by coordinated aircraft missions and special radiosonde ascents at island stations have been used to compute vertical motions and an energy budget for the region. In general, the agreement between com- puted vertical motions and weather was quite good for the 6-day composite case, but was slightly less satisfactory for the individual days. The computed kinetic energy tendencies were found to agree with the changes observed to take place within the volume. Conversion between potential and kinetic energy was small; most of the changes in kinetic energy in the domain were caused by boundary work plus lateral advection. During the 6-day period, the circulation within the volume changed from weakly direct to weakly indirect, although the results for the composite data show that the mean circulation was definitely indirect. The overall satisfactory agreement between the com- puted results and observation would seem to indicate that the dynamical model employed is reasonably adequate 374 MONTHLY WEATHER REVIEW Vol. 98, No. 5 in its simulation of the tropical atmosphere. Conversely, this would suggest that the data themselves are suitable for numerical work. REFERENCES Carlson, Toby N., "Project ECCRO: A Synoptic Experiment in the Tropics," ESSA Technical Memorandum IERTM-NHRL 80, U.S. Department of Commerce, National Hurricane Research Laboratory, Miami, Fla., Aug. 1967a, 31 pp. Carlson, Toby N., "Structure of a Steady-State Cold Low," Monthly Weather Review, Vol. 95, No. 11, Nov. 19676, pp. 763-777. Cressman, George P., "A Three-Level Model Suitable for Daily Numerical Forecasting," Technical Memorandum No. 22, U.S. Weather Bureau, Washington, D.C., 1963, 22 pp. Frank, Neil L., "The Weather Distribution With Upper Tropo- spheric Cold Lows in the Tropics," Technical Memorandum No. 28, U.S. Department of Commerce, Weather Bureau Southern Region, Ft. Worth, Tex., Oct. 1966, 22 pp. Kuo, H. L., "On Formation and Intensification of Tropical Cyclones Through Latent Heat Release by Cumulus Convection," Journal of the Atmospheric Sciences, Vol. 22, No. 1, Jan. 1965, pp. 40-63. Miller, Banner I., "Experiment in Forecasting Hurricane Develop- ment With Real Data," ESSA Technical Memorandum IERTM- NHRL 85, U.S. Department of Commerce, National Hurricane Research Laboratory, Miami, Fla., Apr. 1969, 28 pp. Palmen, Erik, "On the Maintenance of Kinetic Energy in the Atmosphere," The Atmosphere and the Sea in Motion, The Rocke- feller Institute Press, New York, 1959, pp. 212-224. Palmen, Erik, "On the Generation and Frictional Dissipation of Kinetic Energy in the Atmosphere," Commenlaliones Physico- Matkematicae, Vol. 24, No. 11, Finska Vetenskaps-Societeten, Helsinki, 1960, 15 pp. Palmen, Erik, and Holopainen, E. 0., "Divergence, Vertical Velocity and Conversion Between Potential and Kinetic Energy in an Extratropical Disturbance," Geophysica, Vol. 8, No. 2, 1962, pp. 89-112. Ricks, R. L., "On the Structure and Maintenance of High Tropo- spheric Cold-Core Cyclones of the Tropics," unpublished M.S. thesis, Department of Meteorology, University of Chicago, 1959, 32 pp. Sanders, Frederick, and Burpee, Robert W., "Experiments in Barotropic Hurricane Track Forecasting," Journal of Applied Meteorology, Vol. 7, No. 3, June 1968 pp. 313-323. [Received October 18, 1969; revised January 9, 1970] m Reprinted from Monthly Weather Review 98, No. 9, 6 ^ 3 _ 6 6 3 September 1970 643 UDC 551.515.21:641.57:551.509.313 A CIRCULARLY SYMMETRIC PRIMITIVE EQUATION MODEL OF TROPICAL CYCLONE DEVELOPMENT CONTAINING AN EXPLICIT WATER VAPOR CYCLE STANLEY L. ROSENTHAL National Hurricane Research Laboratory, ESSA, Miami, Fla. ABSTRACT The tropical cyclone model described in previous reports is extended to include an explicit water vapor cycle. Results of experiments that examine effects due to initial humidity conditions, radial resolution, and the finite- difference scheme are discussed. Growth to the mature stage is more rapid in the moist environment, but peak intensity is not strongly affected by the initial moisture content. Rainfall rates are quite reasonable, and nonconvec- tive precipitation is found to be a significant proportion of the total rainfall, in agreement with recent empirical results. Experiments with upstream differencing yield more realistic solutions than do experiments with centered differences. This surprising result is discussed in detail. 1. Introduction 643 2. Convective adjustments of macroscale temperature and humidity 644 3. Water vapor budget 645 4. Vertical diffusion of horizontal momentum 646 5. Review of the model 647 6. Experiment Wl 648 7. Experiment W2 650 8. Effects of the initial humidity distribition 651 9. Further consequences of upstream differencing 652 10. Conclusions 660 Appendix 661 Initialization 661 Computational cycle 661 Generation of available potential energy 662 Kinetic energy budget 662 Kinetic energy dissipation by upstream differencing 663 Acknowledgments 663 References 663 1. INTRODUCTION Our circularly symmetric tropical cyclone model (Rosen- thal 1969a, 19696) has been extended to include an explicit calculation of the humidity content of the free atmosphere. The old version1 of the model could only simulate cumulus convection that originated in the Ekman layer. The new model is able to simulate convection originating at higher levels. Nonconvective precipitation is also simulated and, in agreement with recent empirical results obtained by Hawkins and Rubsam (1968), makes a substantial con- tribution to the total precipitation. Examination of the effect of the initial humidity dis- tribution on tropical cyclone development indicates that the mature stage is reached more rapidly in a moist en- vironment. However, the ultimate intensity of the storm does not appear to be strongly influenced. The adjustments of macroscale humidity and tempera- ture that are intended to simulate the effects of cumulus convection are described in section 2. Section 3 gives the equations for the macroscale water vapor budget. In sec- tion 4, we derive a parametric representation of the vertical 1 The old version is called the "old model"; hereafter, the new version is referred to as the "new model." transport of horizontal momentum by cumulus scale eddies. Section 5 gives a fairly complete review of the dynamic aspects of the model. In section 6, the results of a benchmark experiment (experiment Wl) are presented. This experiment is conducted with 10-km radial resolution, upstream differencing, and a selection of friction and viscosity coefficients that provide a "good" solution based on the author's intuitive concepts of hurricane structure and dynamics. For computational economy, the remaining experiments are conducted with 20-km radial resolution. For isolating effects due solely to resolution, section 7 describes an experiment (experiment W2) identical to Wl in all respects except radial resolution, which is 20 km. Section 8 describes the experiment designed to study the effects of the initial mositure distribution, the results of which have already been summarized above. In section 9, we discuss the results of a number of trial and error experiments that were useful in the design of experiments Wl and W2. Section 10 reviews the main conclusions of the paper. In comparison to the models devised by Ooyama (1969) and Yamasaki (19686), our model seems to provide substantial improvement in certain areas while, perhaps, making sacrifices elsewhere. Ooyama's model uses the gradient wind assumption and carries horizontal velocity at three levels in the vertical. Temperature is represented only at an upper level and in the Ekman layer. No allow- ance for the vertical variation of static stability is pro- vided; water vapor content is predicted only in the boundary layer. Neither nonconvective precipitation nor convective precipitation from convective elements origi- nating above the surface boundary layer is included. In contrast, our model represents all variables at seven levels, uses the primitive equations, and, as already noted, explicitly predicts water vapor content, nonconvec- tive precipitation, and multilevel convection. Ooyama, however, uses superior finite-difference techniques, finer radial resolution, a computational domain more than twice as large as ours, and makes an explicit prediction of air-sea exchanges of sensible and latent heat. The latter are treated rather pragmatically in the calculations re- ported on here. 644 MONTHLY WEATHER REVIEW Vol. 98, No. 9 Yamasaki (19686) provides for 13 levels in the vertical and uses the primitive equations. His model, however, contains neither an explicit water vapor cycle, the effects of multilevel convection, nor an explicit treatment of nonconvective precipitation. Yamasaki uses the upstream method for advection terms and variable radial resolution; his smallest grid increment is 20 km. His calculations, therefore, should be expected to have substantially more truncation error than our experiments with a fixed resolution of 10 km and somewhat more truncation error than our calculations with a fixed resolution of 20 km. On the other hand, the radial extent of Yamasaki's compu- tational domain is about five times greater than ours. Yamasaki demands the "cloud" equivalent potential temperatures to be constant in the horizontal and with time. In our model, these are allowed to vary as they will according to the scheme developed in sections 2 and 3. Yamasaki's paper (19686) provides no information con- cerning the rainfall rates yielded by his model. The storm structure developed by Yamasaki's model is generally quite realistic. However, horizontal temper- ature gradients in the lower troposphere appear to be unrealistically large, and the elevation of the greatest temperature anomaly is too low. Our model yields better results in this area. On the other hand, Yamasaki obtains a better vertical profile of radial motion in the upper tropospheric outflow layer. The following symbols are used : CD drag coefficient, cv specific heat of air at constant pressure, / Coriolis parameter, g acceleration of gravity, KZM kinematic coefficient of eddy viscosity for vertical mixing, KM kinematic coefficient of eddy viscosity for lateral mixing, K*T kinematic coefficient of eddy diffusivity for vertical mixing of heat, KT kinematic coefficient of eddy diffusivity for lateral mixing of heat, ICW kinematic coefficient of eddy diffusivity for vertical mixing of water vapor, K%, kinematic coefficient of eddy diffusivity for lateral mixing of water vapor, L latent heat of evaporation, M relative angular momentum, p pressure, p0 1000 mb, g specific humidity, R specific gas constant for air, r radius, T absolute temperature, t time, u radial velocity, V horizontal vector wind, v tangential velocity, w vertical velocity, z geometric height above mean sea level, Ar radial increment, At P P 01 time increment, potential temperature, equivalent potential temperature, air density, standard air density, cMp0)R/cp, and (j> at level one. 2. CONVECTIVE ADJUSTMENTS OF MACROSCALE TEMPERATURE AND HUMIDITY This discussion assumes that the reader will make re- peated reference to figure 1. We consider a layer of the conditionally unstable lower tropical troposphere centered at a reference level zp. We assume the roots of an organized system of cumulonimbi to be within the layer. We further assume that the cumulonimbi transport upward and con- dense 8pE mass units of water vapor per unit area in some period of time. Part of the condensate reevaporates and enriches the macroscale humidity as the clouds mix with their environment. The remaining condensate falls from the atmosphere as rain. The latent heat released during the formation of this portion of the condensate is assumed available for increasing the macroscale temperature. The convection therefore produces adjustments in the macroscale humidity and temperature at levels above zp and below the cloud tops (z\ov). These adjustments are assumed to obey the energy budget p P{cpApT(z)+LApq_(z)}dz=L8pE (1) where ApT(z) and Apqiz) are the macroscale changes of temperature and specific humidity at level z produced by convection originating at level zp. We assume (see Rosenthal 1969a for justification) that the convective adjustments are such that the macroscale temperature and equivalent potential temperature tend toward vertical profiles appropriate to parcel ascent from Zp (dry adiabatic lifting to the lifting condensational level followed by pseudoadiabatic ascent to z'/"). Following Kuo (1965), z't,0" is taken as the height at which the appropriate pseudoadiabat intersects the macroscale sounding after an intervening layer in which the pseu- doadiabat is warmer than the macroscale. Denote this level by z*9, z'fi°p=z*. Now let p8ce = 0e(zp) (2; be the equivalent potential temperature of a parcel rising from zp and let T%=T'{fi, zp) (3) be the temperature of the parcel when it reaches level z {zpelationships (4) are zero or negative, the convective adjustments were taken as zero. Following Kuo (1965), 8pv is assumed independent of height and is obtained from the energy budget (1) in a manner to be described later. We consider short time periods so that the convective adjustments are small and make use of the relationship We may then write AB8E A3T . L (5) (6) By use of (3), (4), (5), and (6), we obtain for any reasonable conditions of temperature and humidity <&-i (7) As in the case of (4) , if the right-hand side of (7) is nega- tive or zero, the adjustment is taken as zero. The adjust- ment relationships (4) and (7) are similar to those given by Kuo (1965). From (1), (4), and (7), 8aE £P{C> 2fl ^S > Zg (Tl-T)+L(q2|. (8) 8 a E Now let the conditionally unstable portion of the lower tropical troposphere be divided into n thin layers all of which contain cumulonimbi roots and behave as the layer described above. For the sake of brevity, it is assumed that conditional instability is found from 2=0 to z=zmax with- out intervening stable layers. It is also assumed that each of these layers has a water vapor supply sufficient to support moist convection. These assumptions (not made in the numerical model) avoid tedious repetition in the mathematical manipulations. The net temperature change at a level z due to the convection from the n layers is then m m AT(2)=2 A,r(2)=2 {Tt(z)-T(z)}8pv> z<~zmax (9) 13=1 (3=1 where m is the number of convective layers below z and m < n. Also, AT(z)=j: {Ti(z)-T(z)] r<2<4« (10) where z*mttX is the highest cloud top. Equations (9) and (10) are somewhat similar to those recently suggested by Estoque (1968) for convection originating from multiple layers. From (9) and (10), AT(z)- = gm{71(2)-T(2)}^|^2 (ID where 8pz is the thickness of the /3th convective layer. The analogous equation for humidity is A2(«)= S {2«(s)-2(2)} spy; ' o=i opn, osz (12) The macroscale heating per unit time and area may be written Q{z)=\ lm ~l ', y .(-*> \ At J (13) and the convective precipitation rate for a column of unit area (mass of water per unit time) is h: pQ X1 (14) The calculation of 83v and 8$E is described in the next section. 3. WATER VAPOR BUDGET In the absence of phase changes, we take the macroscale specific humidity to be governed by - dg_ 1 dpuq_r pdi~~r~dT dpviq - K"v d '^z~+p~d, K'IH(^8> (15) Consider a vertical column extending from the sea surface to the top of the atmosphere. Except for transfers across the upper and lower boundaries of the column, the second and fourth terms on the right-hand side of equation (15) represent vertical redistributions of vapor that do not affect the vapor content of the column as a whole. The contribution to the vertically integrated time rate of change of humidity by processes in the reference layer 8pz (fig. 1) may then be written as S(z„> HK&d /dq\ ldjuqr} \ r dr\ dry r dr f (16) 646 MONTHLY WEATHER REVIEW Vol. 98, No. 9 If S(zp) is positive and if parcel ascent from z$ becomes w are the means. From equation (22) and. by use of the warmer than its environment over some layer, we will continuity equation in the form assume that the vertical redistribution of the vapor im- ported into the column in the layer 8pz is entirely by cumulus convections and that dz +V.psV*=0, we obtain 8eE=AtS(Zf,). (17) The left side of (17) is the 5PE of equation (1). The humidity change at any level z ,- in such a column is then Ps dM* ■V°PsV*M*- dPsw*M* n dz Averaging in the usual way, one obtains pt where "(S&.-M^5('2H^}.+'A* _/0ifi=/S\ (18) (19) at dz ps dz (24) (25) (26) Assume the eddy motion to be produced solely by cumulus activity. Denote values in cloud by ( ) and values in clear air by ( ) ; assume the clouds to cover a fraction When convection originates from n contiguous layers, «2 of a 8'rid module. Mean values, M and w, may then be written as and A^i is given b}^ equation (7) When convection originates : the humidity change at any level is given by dq\ 1 dp'uqr "GDr^-C^K' drj r dr where An (20) (21) V)—ahoJr{\ — a2)w. The eddy correlation then takes the form M'w'=a\M-M){w-w) + {l-a2){M-M){w-w); (28) The method used to compute nonconvective condensation and by use of (27) to eliminate values in the clear air, is described in the appendix. 4. VERTICAL DIFFUSION OF HORIZONTAL MOMENTUM M'w'=c?{M—M){w—w){l+c?). (29) Under realistic conditions, a2 > w, so (30) M'w' =c?w{M-M)=w(M-M). M=Mn Vertical transports of horizontal momentum produced by cumulus scale motions play a significant role in the macroscale dynamics of hurricanes (Gray 1967). While Ooyama (1969) provided an explicit parameterization of If the air rising in the cumuli tends to conserve M, this effect, Yamasaki (1968a, 19686) and Rosenthal A (1969a, 19696) have obtained realistic results from their models without explicit representation of the cumulus transports of momentum. However, as will be shown below, their upstream differencing introduces a compu- tational diffusion that behaves somewhat like momentum diffusion by cumuli. To see this, consider the advective contribution to the momentum tendency in the presence of cumulus activity: (31) The last term on the right-hand side of equation (26) may then be written as 1 dpsw'M' 1 6 r , . dW\ — ~Jsd7z\^z-z*)w-dz)- Ps dz dM* dM* dt dz (22) = fsfziPsGddf} Asterisks denote the total motion (sum of the mean and eddy components; means are calculated horizontally over a grid interval). Then, and M*=M+M', V*=V+V, w*=w-{-w' Psdz\ where the exchange coefficient 6? is given by G=(z—z0)w. When the advection equation dA dA -dt=-Wte (32) (33) (34) (23) is differenced with an upstream space difference and a forward time difference, the solution of the resulting where the primes denote eddy components and M, V, and difference equation (Molenkamp 1968) is a second-order September 1970 Stanley L. Rosenthal approximation to the solution of the differential equation 647 dA dt'~ dA . w d2A dz dz2 (35) where the computational viscosity coefficient (Fz) is given by F2=$\w\Az{l-\-^\=k*\w\Az. (36) While the general similarity of expressions (33) and (35) is clear, there are some important differences. The most significant of these is that the former appears in (32) as a conservation form and, therefore, makes no contribution to the vertically integrated value of M. The computational diffusion will, however, effect the vertically integrated value of the quantity^, (equation 35). Despite this, section 9 will show that velocity distributions ob- tained from numerical experiments with upstream differ- encing of vertical advection terms are far more realistic than those obtained with centered differencing. These results clearly indicate that the computational diffusion, in some sense, tends to simulate the momentum transports by cumulus. 5. REVIEW OF THE MODEL The model uses the primitive equations, assumes circular symmetry, and has seven levels (table 1). The system is open at the lateral boundary. The basic equations are dM dt ~~ dM , .13 /-„, -fru+= xz (pill/ dM dr dz p dz d_M\ dz) m-my <*> du_ _ du ~di~ U dr' du , M ( dz' , M( ., M\ dr I- llhm,^\4-K dz dz) ?£{-£©}■ <*> dt wdr de , cBK$ d / de\ , Q . c„K? d ( de\, -w n — — ~ a- ( r 3- )+ dz r dr \ dr/ dz' dpw_ dY= 1 dpru r dr --cP(p/po)R/c*, S=cvT, and M=rv. (39) (40) (41) (42) (43) (44) Equations (37) and (38) are forms of the tangential and radial equations of motion, respectively. Equation (39) is the thermodynamic equation. Equation (40) is the hydrostatic equation and (41) is a form of the continuity equation that is easily justified by an order of magnitude analysis and has been used by others (Charney and Eliassen 1964) for the hurricane problem. Boundary conditions on the vertical motion at the top and bottom levels are W:=W7 = 0 (45) where the subscript denotes level. Equations (41) and (45) filter the external gravity wave and thus allow larger time steps. However, as shown below, they place a restriction on the pressure field that must be retained in the numerical model for physical consistency. From (41) and (45), ! pudz = 0. (46) From (38) and (46), r'i_aty>, Ch_CM{, ,M\ du du\ , Jz; ped-rdz=)ll p\VV+^))-u^-wdrfdz +*t(i;K'W}',s-B- <47) By use of the hydrostatic equation (40), h-peb£dzJ-p C" dr dr t'MZ't pdw dz (48) in which H=f'jdz' (49) where z' is a dummy variable. From (47), (48), and (49), 6> dr , »+J>"* x: (50) :edz The manner in which the restriction (50) is employed in the computational cycle is shown in the appendix. Discarding viscous and diabatic effects, the system of equations with the boundary condition (45) gives the energy integral a fz* rr'-fu- dtjo JoP\" + V' }■ +cpT-\-gz Yrdrdz provided that the domain is mechanically closed at r=r*. If the complete form of the continuity equation dp dpw 1 dpru dt dz r dr is used in place of (41), the energy integral analogous to 648 MONTHLY WEATHER REVIEW Vol. 98, No. 9 Table 1. — Heights and mean pressures of the information levels. The mean pressures are approximate and are based on a mean hurricane season sounding (Hebert and Jordan 1959). Height Mean pressure (meters) (millibars) 0 1015 1054 900 3187 700 5898 500 9697 100 12423 200 16621 100 (51) is irr-c^'M'**- j:x'#* that can be written in the more familiar form £CT'(*?V*0 rdrdz=0. (52) (53) By comparison of (51) and (52), we see that the model is only approximate in its conservation of total energy. Time derivatives are estimated by forward differences except in the case of specific humidity where a Matsuno (1966) type integration is employed. Advective derivatives are calculated by the upstream method except for the special experiments described in section 9 and for the case of humidity where a conservation form of the equations is used. All nonadvective space derivatives are calculated as centered differences. All variables are defined at all levels. Vertical integrals are evaluated by trapezoidal integration. Grid points in the radial direction are staggered. Horizontal velocity is defined at the radii ■■(j-l)Ar, j=l,2, ... (54) Temperature, pressure, vertical motion, and humidity are carried at the radii rj = ij-\)&r, j=l, 2, . (55) Air-sea exchanges of sensible and latent heat are simu- lated by the pragmatic constraint that relative humidity and temperature are invariant in both space and time at levels 1 and 2. On the other hand, the surface stresses in the equations of motion are treated explicitly by use of a drag coefficient and the usual quadratic stress law. That is, to evaluate vertical mixing terms at levels 1 and 2, we invoke the boundary conditions and (p#i,^)ii=0>?1|V|1Ml (56) (57) where CD is the (constant) drag coefficient and |V1|=fe2+^)1«. Equations (37) and (38) are applied at the radial grid given by (54) and at vertical grid points i=l,2, . . ., 7. At j = 1 (where r= 0) , M=0 and u=0. Atj=Jmai (where r== 440 km), and (ru)j =(ru)j -i v 'Jmax s /Jmax 1 Mj =Mj _i (58) (59) (60) which are the conditions, respectively, that the horizontal divergence and relative vorticity vanish. The potential temperature tendencies are evaluated on the radial grid defined by equation (55) and at the verti- cal grid points i=3, . . ., 7. At i=l, 2, the potential temperatures are computed from (43) so that the tem- perature is maintained at its initial value. The boundary condition at Jmax for potential temperature is Jmax Jmaz 1 ' (61) An outline of the complete computational cycle is found in the appendix. 6. EXPERIMENT W1 The results of experiment Wl are fairly typical of what can be expected of the model. A number of parameters utilized in experiment Wl are listed in table 2. For com- putational economy, the first 72 hr of the calculation were conducted with 20-km radial resolution and a time step of 120 sec. The data were then linearly interpolated to a 10-km grid, and the calculation was continued on the finer mesh with a time -step of 60 sec. Friction and viscosity coefficients were established largely by trial and error. The initial conditions of wind, pressure, and temperature are identical to those used in our previous experiments and consist of a weak vortex in gradient balance with zero meridional circulation. The central pressure is 1013 mb; the maximum wind is 7 m sec-1 and is located at a radius of approximately 250 km. The mathematical derivation of this balanced state is also given in the appendix. The initial field of specific humidity varies only with height and corresponds approximately to relative humidities (table 3) that are very nearly equal to those of the mean tropical atmosphere (Hebert and Jordan 1959). As before, the mathematical details of the initialization are given in the appendix. Figure 2 summarizes the storm's evolution at sea level. The "organizational" period consisting of the first three or so days is characteristic of tropical cyclone models that are initialized with nondivergent winds (Ooyama 1969, Rosenthal 1969a and 19696) and seems to have a coun- terpart in nature (see section 8). The intensification that occurs between 72 and 96 hr is not related to the change in radial resolution introduced at hour 72 since, as will be shown in the next section, nearly the same intensification takes place if the mesh is not refined. September 1970 Stanley L. Rosenthal 649 The storm reaches peak intensity at about hour 144. The central pressure and strongest surface wind at this time are 976 mb and 45 m sec-1, respectively. Hurricane- force winds are present from about 108 hr to the end of the calculation. The radius of maximum surface wind decreases rapidly during the deepening period and is more or less constant theraf ter. Figures 3, 4, 5, 6, and 7 illustrate various aspects of the storm structure and confirm that the model yields results that are quite reasonable. While it is not shown on figure 7, the vertical motion pattern contains a narrow zone of upper tropospheric subsidence at the storm center. The old model showed a more distinct "eye" (Rosenthal 19696). Average rainfall rates for the inner 100 km of the storm circulation are shown by figure 8. From 96 to 216 hr, the total rainfall averages about 25 cm day-1 or, roughly, 10 in. per day, a quite reasonable rate. The nonconvective rainfall is about two-thirds of the convective precipitation. According to Hawkins and Rubsam (1968), radar data gathered in hurricane Hilda (1964) indicate substantial rain from stratiform clouds. Their observations also indicate that, while a large portion of Hilda's circulation contained appreciable rain, active cumulonimbi were present only in the eye wall region. In view of these observations, the partitioning of rain between convective and noncon- vective components (fig. 8) is acceptable. Figure 8 also illustrates the efficiency of the inner 200 km of the storm. This quantity is defined in the usual manner (Palmen and Riehl 1957) as the ratio of the rate of kinetic energy production to the rate of latent heat release. The values during the mature stage are quite close to the empirical value of 2.7 percent found by Palmen and Riehl (1957). The generation of available potential energy2 (fig. 9) during the mature stage is fairly close to the empirical estimate made by Anthes and Johnson (1968) for hurricane Hilda (1964). Figure 9 also shows that nonconvective condensation provides a substantial part of the generation and that virtually all of the generation occurs in the inner 100 km. The kinetic energy content of various rings of the model storm are shown by figure 10. In comparison to the old model (Rosenthal 1969a, 19696), there is a dramatic improvement in the behavior of the outer rings of the storm. In the 300-400-km ring, the old model showed a monotonic increase of kinetic energy with time. Figure 10, on the other hand, shows that this is not the case with the new model where a definite maximum of kinetic energy is reached before the calculation is terminated. Figure 11 shows the kinetic energy budget as a function of time (the details of the computation are described in the appendix) . The contributing terms, in a relative sense, behave in a fashion similar to that found for the old model (Rosenthal 1969a, 19696). However for the storm as a whole (0-400-km radial interval), the magnitudes of the Table 2. — Parameters for experiment Wl Parameter Symbol Time increment _ ._ ai 60sec Radial increment _ at 10 km Radial limit of computational domain 440 km Kinematic coefficient of eddy viscosity for lateral mix- ing of momentum Km Vfi m* sec -' Kinematic coefficient of eddy conductivity for lateral mixing of heat k" 10« m' sec-1 Kinematic coefficient of eddy conductivity for lateral mixing of water vapor K& W m2 sec-' Drag coefficient Cd 3X10-3 Kinematic coefficient of eddy viscosity for vertical mix- 10 m2 sec-' at level 1. ing of momentum K'M 5 m2 sec-' at level 2, 0 elsewhere Table 3.- -Initial values of relative humidity at the information levels Height Relative humidity (meters) (.percent) 0 90 1054 90 3187 ■c4 5898 -.: 9697 30 12423 30 16621 30 ! The computational equations are given in the appendix. various terms are about half that found with the old model. The difference is largely due to the fact that the outer rings of the new model are far more inert energetically than is the case for the old model. Loss of energy through truncation errors (computed as a residual in the budget equation, see appendix) is com- parable in magnitude to the surface dissipation by drag friction. The major portion of this truncation error can be accounted for by computational diffusion in the sense of Molenkamp (1968). Figures 12 and 13 illustrate the computational (or, in Molenkamp's terminology, the "pseudo") viscosity coef- ficients calculated for experiment Wl. In the mature stage, the coefficient for lateral mixing averaged over the entire storm is about 5 X 103 m2 sec-1. This is five times greater than the explicit coefficient for momentum (table 2). In the inner 100 km, the computational coefficient for lateral mixing averages over 104 m2 sec-1, while for vertical mixing this coefficient is about an order of magnitude greater than its average value for the storm as a whole. Figures 14 compares the explicit dissipation of kinetic energy with the total (explicit plus computational). Detads of the calculation are presented in the appendix. The figure shows the unexplained truncation error to be . fairly small. Despite the extremely large coefficients for vertical computational diffusion, the kinetic energy dis- sipation due to this effect is quite small compared to dissipation by drag friction at the lower boundary. The bulk of the truncation error is produced by upstream differencing of horizontal advection terms. This will be discussed in greater detail in section 9. 650 MONTHLY WEATHER REVIEW Vol. 98, No. 9 _l 985 - TIME (HOURS 1 1 1 — 1 EXP Wl 1 - - - 1 i i i 96 144 192 TIME (HOURS) jflljjjjlfr 48 96 144 192 240 TIME (HOURS) Figure 2. — Results from experiment Wl. Top, central pressure as a function of time; center, maximum surface wind as a function of time; bottom, radii of maximum surface wind and inner and outer limits of hurricane-force and gale-force winds at the surface. 7. EXPERIMENT W2 As noted in section 1, the experiments discussed in later sections of this report were conducted with 20-km radial resolution. Because of this, we present a brief summary of experiment W2 that is identical to Wl in all respects except for the values of Ar and At; these are 20 km and 120 sec, respectively. The first 72 hr are, of course, identical to those of Wl. Central pressures 3 and maximum surface winds for the two experiments are compared in the upper two graphs 3 Pressure Is not denned at zero radius because of the grid staggering (equations 54 and 55). Central pressure values presented in this paper are, therefore, pressure values at z=0, r=Ar/2. EXP wl 72 HOURS 100 2O0 500 RADIUS ( Km) 100 200 300 400 RADIUS (Km) 100 200 100 RADIUS (Km) ' 1 I 1 ' 1 ' 1 EXP Wl - _A 144 HOURS - 1 i 1 i 1 i 1 10O 200 300 RADIUS (Km) Figure 3. — Results from experiment Wl, radial profiles of surface wind speed. in figure 15. After hour 72, Wl deepens somewhat more rapidly at first; but in both experiments, greatest intensity is reached by about hour 144. At this time, Wl is 8 mb deeper in central pressure, and maximum surface winds differ by about 4 m sec-1. After hour 144, experiment Wl decays more rapidly; and when the two calculations are terminated at hour 216, central pressures and maximum surface winds are very nearly the same. By comparison of the bottom sections of figures 2 and 15, we find that W2 develops a somewhat larger storm, as was to be expected Differences are, however, much less than was the case when the resolution was varied in the old model. The surface pressure and wind profiles for experiment W2 (not shown) are similar to those obtained from Wl September 1970 Stanley L. Rosenthal 651 a: loos - a. 1 1 ' 1 ' 1 ' 1 EXP Wl 96 HOURS 1 1 I 1 I 1 > 1 100 200 3O0 400 RADIUS (KILOMETERS) 1 1 1 1 I 1 I 1 EXP Wl - / 1?0 HOURS 1 1 1 i 1 i 1 I 1 - 100 200 300 4O0 RADIUS (KILOMETERS) 1015 m ioio X 1005 111 ft 1000 to W 995 tc °- 990 Ul 985 O C 980 ac 1 I 1 100 200 300 400 RADIUS (KILOMETERS) Figure 4. — Results from experiment Wl, radial profiles of surface pressure. (figs. 3 and 4). The profiles of vertical motion at level 2 (not shown) indicate boundary layer convergence to be 30 to 50 percent weaker than that for Wl, but to cover a broader horizontal area. Experiment W2, therefore, gives a broader but weaker convection zone. Vertical cross sections of the dependent variables at hour 144 of experiment W2 (not shown) are similar to those for Wl (figs. 6 and 7). Rainfall rates and efficiencies for W2 (fig. 16) except for the sharp peaks near hour 108 are just slightly larger than those of Wl (fig. 8). The kinetic energy content of the inner 100 km of W2 (not shown) is very nearly the same as for Wl (fig. 10). In the outer rings of the storm, however, W2 contains somewhat more kinetic energy. Overall, it seems fair to conclude that results with 20-km radial resolution are fairly representative of those obtained with 10-km resolution. The larger radial incre- ment leads to a larger storm with greater kinetic energy in the outer portions of the circulation. The differences are, however, relatively minor and far less than those found with the old model. RADIUS (Km) , 100 EXP Wl 120 HOURS RADIUS (Km I "I 1 1 T" EXP Wl 144 HOURS Figure 5. — Results from experiment Wl, radial profiles of vertical velocity at the 1054-m level. 8. EFFECTS OF THE INITIAL HUMIDITY DISTRIBUTION Riehl (1954) emphasizes that tropical storms form only in preexisting disturbances and that deepening is usually a slow process which requires several days. This "organi- zational" period is evident in the experiments described above. As also noted by Riehl (1954), large moisture content to great heights seems to be necessary before substantial deepening will occur. In the early stages of development when low-level convergence is still relatively weak, a deep moist layer would seem essential if entraining cumulus with small horizontal cross sections are to grow in the vertical and reach the cumulonimbus stage. On the other hand, the depth of the moist layer is tuned to the macroscale motion (Riehl 1954) and increases with low-level convergence. The role of the preexisting dis- 400-552 O - 70 652 MONTHLY WEATHER REVIEW Vol. 98, No. 9 100 %gZZZZZZ7g. MM ISO 200 250 300 350 400 RADIUS ( Km ) Figure 6. — Results from experiment Wl at hour 144. Top, cross section of tangential wind; center, radial wind; bottom, total wind. turbance or "organizational period" may well be the development of the required deep moist layer from a humidity distribution that initially approximates that of the mean tropical atmosphere. Once the moist layer had been developed, cumulus cells entrain relatively moist air, making their growth to the cumulonimbus stage more likely. With the onset of increased cumu- lonimbus activity, the chances of rapid development of the macroscale disturbance would seem to be better than before. While the convective adjustment described in section 2 does not contain an explicit representation of entrainment (and, indeed, assumes the cumulus to rise with undilute ascent), the sense of the sequence described above is simulated. The partitioning of condensate between pre- cipitation and reevaporation depends directly on the 50 100 150 200 250 300 RADIUS (Km) 150 200 250 RADIUS ( Km) Figure 7. — Results from experiment Wl at hour 144. Top, cross section of vertical motion; bottom, temperature anomaly. difference between cloud and environmental humidities (equations 4, 7, and 8). Hence, a model atmosphere that is drier will have substantially less precipitation and, hence, less macroscale heating. On this basis, it seems reasonable to argue that a shorter organizational period would be present if the initial humidity were greater. Experiment W6, which differs from W2 only in that the initial relative humidity is 90 percent everywhere, tests this hypothesis. Central pressures and maximum surface winds obtained from the two experiments (fig. 17) seem to verify the arguments of the previous paragraph. While the peak surface winds and deepest central pressures are about the same for the two calculations, those for W6 occur about 48 hr earlier than those for W2. An organi- zational period of 72 hr is required for development in W2, but only 24 hr is needed in W6. From figures 16 and 18, we find the average rainfall for W6 to be about 10 cm per day greater than that for W2. Maximum efficiencies for the two experiments are very nearly the same. 9. FURTHER CONSEQUENCES OF UPSTREAM DIFFERENCING In section 6, it was shown that the truncation errors due to upstream differencing play an important role in the kinetic energy budget of the model storm. Further- September 1970 Stanley L. Rosenthal 653 _ 30 I I I L 72. 120 168 TIME (HOURS) 120 168 216 TIME (HOURS) Figure 8. — Results from experiment Wl. Top, efficiency of the radial interval 0 to 200 km; bottom, average rainfall over the radial interval 0 to 100 km. 126 174 222 TIME (HOURS) 126 174 222 TIME (HOURS) more, we found that the bulk of the total internal dissipa- tion of kinetic energy (explicit lateral mixing plus computational lateral and vertical mixing) is produced by upstream differencing of the horizontal advection terms. It has been our stated intention (Rosenthal 1969a) to reformulate the model in a more accurate difference scheme at a time when this became economically feasible. In this section, we will show the results of a number of experi- ments (table 4) in which various advection terms in the equations of motion and in the thermodynamic equation were estimated by a centered finite-difference analog. (The water vapor equation, however, was not altered and, hence, is treated as described earlier.) The numerical technique adopted for this purpose is the second-order advection form given by Crowley (1968). This method employs forward time steps and, therefore, required mini- mal modification of the original program. To calculate vertical advection, Crowley's equations were modified to take into account the variable vertical resolution (table 1) employed in our model. This modifica- tion was made in such a way that the second-order accuracy of the technique was preserved. For linear advection with a constant advecting velocity, Crowley's scheme reduces to the Lax-Wendroff method. It is, there- fore, a damping system but far less so than the upstream method (Crowley 1968). Parameters not listed in table 4 are identical to those used for experiment W2. Initial conditions are again hour 72 of experiment W2. In experiment WCl, the explicit parameters are identi- cal to those of experiment W2. The two experiments differ 78 126 174 222 TIME (HOURS) Figure 9. — Results from experiment Wl. Top, generation of avail- able potential energy by convective condensation heating; solid line is for radial interval 0 to 400 km; dashed line is for radial interval 0 to 100 km; center, generation of available potential energy by large-scale condensation heating; bottom, generation of available potential energy by total condensation heating. only in the finite-difference analogs to the advection terms in the equations of motion and in the- thermodynamic equation. In view of the crucial role played by computa- tional diffusion in experiment W2, it was anticipated that this experiment would give unrealistic results; it was necessary to terminate the calculation after 17 hr because limits on the table used to compute temperatures along the pseudoadiabats had been exceeded. Tangential winds in excess of 100 m sec-1 and radial winds over 50 m sec-1 had already been generated. The structure was completely unrealistic, showing large amplitude waves in the radial 654 MONTHLY WEATHER REVIEW Vol 98, No. 9 i — i — i — i — i — r 72 96 120 144 168 192 216 TIME (HOURS) FrGURE 10. — Results from experiment Wl, variation with time of the kinetic energy content of various rings of the storm. uj 80 o 40 in 1- z Ijj Z 20 o Q- 5 o o 0 _ 1 1 1 1 1 y^. EXP Wl / \p < r < +00 Km - /GEN-'' ^.^ - / \" / SFC OISt / F/*\l *^^^~ - 1 I/ TRUNC^V ~ _ / ^OUTFLOW _LAT M|X 96 120 144 168 192 216 TIME (HOURS) Figure 11. — Results from experiment Wl, components of the ki- netic energy budget as a function of time. "GEN" is generation; TRUNC" is dissipation by truncation error computed as a residual in the budget equation; "SFC DIS" is dissipation by drag friction at the surface; "LAT MIX" is dissipation by explicit lateral mixing. Top, radial interval 0 to 100 km; bottom, radial interval 0 to 400 km. -r ^ 20 - EXP Wl _ 0-400 Km 1 . r EXP Wl - 100-200 Km ^y i I.I. - 120 168 EXP Wl 200- 300 Km - 1 I I L 72 120 168 216 4U - I'll A EXP W 1 - / \ 300 - 400 Km 20 - / \ ^ i 1 1 1 1 — 72 120 168 216 TIME (HOURS) Figure 12. — Results from experiment Wl, variation with time of the mass-averaged computational, or pseudo, coefficient of vertical viscosity for various radial intervals. The scale of the top graph differs from that of the others. direction. It was clear that the explicit lateral mixing coefficients (table 4) were too small. The computational viscosity coefficients for experiment W2 (figure not shown) were used as a basis for selecting a value of 2X104 m2 sec-1 for the diffusion coefficients for heat, momentum, and water vapor to be used in experi- ment WC2. All other aspects of WC2 are identical to those for WCl. Experiment WC2 was terminated after hour 24. Surface winds over 58 m sec-1 had already been generated. While the radial profiles of wind and pressure in the boundary September 1970 Stanley L Rosenthal 655 O UJ CO LlJ o CO o o CO o a UJ CO a. 1 | 1 | 1 EXP Wl - 1 5«104 - 1 OxlO4 _ / 0 -100 Km O.SxlO4 ... ' 0-400 Km i 1 I 1 i - 72 120 168 216 1 0x10 OSxlO" 0 0 ' '/Y ' ' - J EXP Wl - / 100-200 Km _ (III; 72 120 168 216 0.5x10 0 0 1 1 1 1 1 EXP Wl 200-300 Km _L I I I L 72 120 168 216 1.0x10 0 0 120 168 TIME (HOURS) 216 Figure 13. — Results from experiment Wl, same as figure 12 but for lateral viscosity. layer were fairly realistic, there were serious deficiencies in the vertical structure. These are illustrated by a cross section of tangential wind (fig. 19). The outward slope of the wind maximum and the strong vertical gradients of wind in the inner 50 km are entirely unrealistic and far different from the pattern obtained in experiment W2 (similar to fig. 6). This deficiency of WC2 is clearly related to the lack of a parametric representation of vertical transport of horizontal momentum by cumulus and other subgrid eddies. In experiments Wl and W2, the upstream dif- ferencing of the vertical advection terms (section 4) tends EXP Wl 0x li i > i i 1 i 1 i 1 48 96 144 192 240 TIME (HOURS) ?50 I 1 1 1 I 1 I 1 ' 1 EXP W2 200 \max sfc WIND 150 - GALE FORCE SFC WIND 100 \, HURRICANE FORCE - 50 _ X SFC WIND? 1 • ni'i.. i j v£r , i i i ,— T i i 0 48 96 144 192 240 TIME (HOURS) Figure 15. — Top, comparison of central pressure as a function of time for experiments Wl and W2; center, comparison of maximum surface winds for experiments Wl and W2; bottom, results from experiment W2. Radii of maximum surface wind and inner and outer limits of hurricane-force and gale-force winds at the surface. verified from figure 21; this figure shows that the storm expends at an unreasonable rate during its decay. Clues to the explanation of this rapid expansion are found in the sequence of temperature patterns shown by figure 22. In all previous experiments, largest temperature anomalies at the storm center have always been at the 200-mb level, in agreement with observations. In contrast, figure 22 shows experiment WC3 to produce its largest temperature anomaly at 300 nib. A second point of im- portance lies in the rapid destruction of the horizontal temperature gradient. We will see below that both of these difficulties appear to be produced by truncation errors in the calculation of w(dd/dz) and, surprisingly enough, the upstream method provides a more accurate result. The full curve on figure 23 shows the base state potential temperature plotted from the data given by table 2. This is the thermal structure that the model "sees." The dashed curve shows the thermal structure obtained when all data points given by Hebert and Jordan (1959) are plotted. The slope of the solid curve between 200 and 100 mb is 120 168 216 TIME (HOURS) i I'll EXP W2~ - 1 \ TOTAL \ CONVECTIVE L 1 LARGE SCALE 1 i 1 > 72 120 168 216 TIME (HOURS) Figure 16. — Results from experiment W2. Top, efficiency of the radial interval 0 to 200 km; bottom, average rainfall over the radial interval 0 to 100 km. substantially greater than the actual slope at 200 mb (if the dashed curve is taken as the standard). On this basis, we might anticipate that a noncentered difference using 200- and 300-mb data might provide a better estimate of w(dd/dz) at 200 mb than would a centered technique using 300-, 200-, and 100-mb data. If we assume an upward vertical velocity of 1 m sec"1 and take a time step of 120 sec, the contribution to the potential temperature change at 200 mb due to vertical advection based on the dashed curve and using Crowley's second-order advection form is — 0.439°K. If we take this as a "true" value and apply the same technique to the solid curve using the 100-, 200-, and 300-mb data, we obtain —0.682°, a 55 percent overestimate of the adiabatic cooling. The upstream method gives —0.310° which is a 29 percent underestimate of the cooling. Therefore, with the resolution of the seven-level model and with the thermal structure of the mean tropical atmosphere, the second-order advection form over- estimates adiabatic cooling at the 200-mb level. The upstream method underestimates this effect but comes closer to that which would be obtained if the model had greater vertical resolution. This type of truncation error in WC3 accounts for both the displacement of the maximum temperature anomaly to 300 mb and for the rapid destruction of the temperature gradient since the convective heat supply is simply unable to sufficiently compensate for the excessive adiabatic cooling at 200 mb. September 1970 Stanley L. Rosenthal 657 _> — I — K I I I \ \ EXP W2 \ \ \ \ \ \ „..— " " X. EXP W6 i i i i TIME (HOURS) V 40 " EXP Wf v^~ r- i /i E * o 50 / • EXP W2 " z * / 2X10> 2X101 Crowley Do. Do. Upstream Crowley Do. Do. Do. Crowley Do. Upstream Do. Crowley Do. Do. Do. 100 150 RADIUS (Km) Figure 19. — Results from experiment WC2, cross section tangential velocity at hour 96. of ternal and surface dissipation. While these "beneficial" aspects of upstream differencing are clearly fortuitous, their consistency in dozens of experiments demands rationalization. The material presented in section 4 is part of this rationalization and is really all that we have been able to obtain by analytical means. While the remainder of this discussion is clearly heuris- tic, the implications of some of the material are interesting. They seem to lead to the conclusion that, with our pres- ent lack of knowledge concerning the interactions between the cumulus scale and the macroscale, the diffusive effects provided by upstream differencing are probably as good a representation of the statistical effect of the cumulus motions on the macroscale velocity fields as anything currently available. Such a conclusion, of course, only points to a high degree of ignorance with regard to an extremely important meteorological problem. It is by no means a solution to the problem. We first point out that Riehl and Malkus (1961) estimated a vertical mixing coefficient for hurricane Daisy of the order of 100 m2 sec-1, which is also the order of the vertical coefficient of computational diffusion in the core of the storm (fig. 12). They also estimated a lateral mixing coefficient of the order of 105 m2 sec-1 for the mature stage of hurricane Daisy and a value of less than 104 m2 sec-1 for the immature stage. In comparison (fig. 13), the computational lateral mixing coefficient has the same temporal variation and, if anything, a somewhat smaller magnitude. If the Riehl-Malkus estimates are to be given any credence and if further we realize that the 100 130 RADIUS ( Kn Figure 20. — Results from experiment WC3, cross section of tangential velocity at hour 96. mixing coefficients must vary markedly in the horizontal because of the highly concentrated nature of the hurricane cumulonimbus pattern, realistic mixing coefficients (both for vertical and horizontal diffusion) must vary by orders of magnitude in both space and time. The computational coefficients have the proper spatial and temporal variations and, as we have seen, more or less the correct magnitude. At this time, it is difficult to see how these coefficients could be improved upon through explicit representations. While equation (32) might be adequate for vertical mixing, a valid formulation for lateral mixing is not at all clear. Here, one is quickly led to think in terms of Smagor- insky's (1963) nonlinear eddy viscosity. However, Lilly (1961) in a discussion of the upstream method noted "Motions are damped, but rather selectively, and the general results appear to be very similar to those obtained using Smagorinsky's eddy friction form, although the physical significance is not clear." If the results are, indeed, to be similar, the computing economics strongly favor the upstream method. In addi- tion, the classical "hourglass" shape of the cumulonimbi strongly suggests that significant lateral mixing between the clouds and their environment is concentrated in the surface boundary layer and in the upper troposphere. For lateral mixing, the computational viscosity coefficient is given by \u\Ar f \u\At \ _ \u\Ar T~ I Ar~ f 2~" FB=>- (62) With the vertical variation of radial velocity typically found in real hurricanes and in models (fig. 16), the sense of the vertical variation of FH will be similar to that sug- September 1970 Stanley L. Rosenthal 659 i UJ 100S J-J — » — \ I ' I l EXP WC3 \ \ / , I , I i I ' TEMP ANOMALY (DEG K) I 96 144 TIME (HOURS) S 'I'll 1 ' £ to l\ EXP WC3 / \ z * JO 1 \ o < \ zo *\ - to 1 - 3 X < 10 I ' > , 1 i 1 i 1 i 16 96 UJ TIME (HOURS) n — I — I — r GALE FORCE SFC WIND - TIME (HOURS) Figure 21. — Results from experiment WC3. Top, central pressure as a function of time; center, maximum surface wind as a function of time; bottom, radii of maximum surface wind and inner and outer limits of hurricane-force and gale-force winds at the surface. gested by the cloud shapes. Finally, it is noted that F„ is of the form of the product of an advecting velocity and a characteristic scale that is, in some sense, analogous to the type of relationship usually obtained from mixing length theory. On the basis of these considerations, we have decided to retain the upstream method for the immediate future. It is interesting that a recent paper by Orville and Sloan (1970) makes similar comparisons between the upstream method and Crowley's scheme. Their calculations indicate I , J 5 -** 2 ' EXP WC3 144 HRS RADIUS (Kin) RADIUS (Km) Figure 22. — Results from experiment WC3, cross sections of temperature anomaly. i — i — i — i — i — i — r HEBERT-JORDAN - 320 340 360 380 400 POTENTIAL TEMPERATURE (*K) Figure 23. — Potential temperature as a function of height in the mean tropical atmosphere after Hebert and Jordan (1959). The dashed curve shows the structure when all data points are plotted. The solid curve shows the profile obtained when only the points that coincide with information levels of the seven-level model are plotted. that the two numerical schemes yield similar solutions for a cloud model, provided that the explicit diffusion coeffi- cients used with the upstream method are increased when Crowley's method is applied. However, grid spacing (both in the horizontal and in the vertical) for this model is of the order of tens of meters. Hence, subgrid motions are "small" scale turbulence elements and not clouds as in the 400-552 O - 70 660 MONTHLY WEATHER REVIEW Vol. 98, No. 9 EXP WC4 120 HRS TEMP ANOMALY I I I 1 L RADIUS (Km) 900 O ■«- EXP WC4 144 HRS TEMP ANOMALY 50 100 190 200 RADIUS (Km) 100 200 300 1 1 1 1 ■*- — 1_ "-- — ^^ ~ l^ _____-/ ^0.2- * __ o 1 EXP WC4 168 HRS TEMP ANOMALY 1 1 1 1 50 100 150 200 RADIUS (Km ) Figure 24. — Results from experiment WC4, cross sections of temperature anomaly. hurricane model. This consideration probably explains the differences between the conclusions reached in this paper and those reached by Orville and Sloan (1970). 10. CONCLUSIONS The new version of the model, which contains an ex- plicit prediction of specific humidity and which simulates the evaporation of cloud material and subsequent enrich- ment of the macroscale humidity, yields more realistic rainfall rates and efficiencies than were obtained from older versions of the model (Rosenthal 1969a, 19696). Recent empirical results (Hawkins and Rubsam 1968) that indi- 96 144 TIME (HOURS) Figure 25. — Results from experiment WC4. Top, central pressure as a function of time; center, maximum surface wind as a function of time; bottom, radii of maximum surface wind and inner and outer limits of hurricane-force and gale-force winds at the surface. cate nonconvective precipitation to be a significant pro- portion of total precipitation are reproduced by the model. An experiment with extremely moist initial conditions (90 percent relative humidity at all grid points) shows that growth to the mature stage is more rapid in the moist environment but that the ultimate intensity of the storm is not greatly affected by the initial humidity distribution. A sequence of experiments in which various advection terms were evaluated using Crowley's second-order ad- vection form yielded results clearly inferior to those obtained with the upstream method. In an attempt to rationalize this surprising result, we found that the magni- tude as well as the sense of the temporal and radial variations of the computational diffusion coefficients associated with the upstream method were much the same as deduced by Riehl and Malkus (1961) for the eddy viscosity coefficients of hurricane Daisy (1958). September 1970 Stanley L. Rosenthal 661 50 100 150 RADIUS (Km) 50 100 150 RADIUS (Km) Figure 26. — Results from experiment WC4, cross sections of tangential wind. APPENDIX INITIALIZATION A field of standard temperature, ~0=~6(z), is specified. These values are very nearly those of the mean hurricane season sounding (Hebert and Jordan 1959) and are listed in table 5. The lower boundary condition, 4>1=cp(1015/1000)R«=>, is adopted, and a set of standard 0=0(2) are calculated from the hydrostatic equation (40). A set of standard temperatures, T=T(z), are calculated from (43). Equation (42) is then used to calculate standard pressures, p=p(z). Figure 27. — Results from experiment WC4, centra! pressure plotted against maximum surface wind for hours 96, 120, 144, and 168. Parallel sloping lines are drawn to enclose most of Col6n's (1963) empirical data points from a large number of tropical cyclones in various stages of life cycle. 1 I 1 ■ i 1 i i i T \ 96 o . >v EXP W2 \s ,§N jfe. - \ 1& - 1 . " ■ i i i ' ' ' 1 , X ?o so <0 MAXIMUM SFC WIND (tr Figure 28. — Same as figure 27, but for experiment W2. Finally, the standard densities, p=p(z), are obtained from ~p=~PIRT. The initial temperature field is given by Tii}=Tt+T, |cos^r,+ l| sin — z. where T'+=0.16oK and r=(Jmax— l)Ar. With the bound- ary condition 07,;=07, the hydrostatic equation, in the form d/dz=—gd/c„T is integrated by the trapezoidal rule to obtain <£,,_, for i = 6, 5, . . ., 1. With T and 0 initialized, initial values of 6 are calculated from equation (43), the gradient wind equation is solved for the initial distribution of v, and M is then calculated from (44). Initial conditions for specific humidity were established as follows. A base state relative humidity, very nearly equal to that of the mean hurricane season (Hebert and Jordan 1959), was specified as a function of height (see table 3 of the text). By use of the base state temperature and pressure, the relative humidity was converted to a specific humidity. The specific humidity at the initial instant was then assumed horizontally homogeneous and equal to the base state value. COMPUTATIONAL CYCLE For beginning a time step, Mr, uT, wT, 8T, and qT are 662 MONTHLY WEATHER REVIEW Vol. 98, No. 9 required. The superscript is the time index. Dependent variables are replaced with their new values as soon as they become available. The scheme is, therefore, semi- implicit, and the results depend on the order in which the calculations are carried out. Indeed, computational sta- bility is dependent on the order of the calculations. The sequence given below has proved to be highly stable. 1. Calculate dM/dt from equation (37). Use a forward time step to obtain MT+l. Replace MT with MT+l for subsequent calculations. 2. Calculate B from equation (47) and H from (49). 3. Integrate equation (50) to obtain T at level 1. 4. Calculate 4>T at the remaining levels by trapezoidal integration of the hydrostatic equation (40). 5. Calculate du/dt from equation (38). Use a forward time step to obtain uT+1. Replace W with ur+l for sub- sequent calculations. 6. Calculate wT+l by trapezoidal integration of the continuity equation (41) and by use of the boundary condition (47). Replace W with wr+l for subsequent calculations. 7. Use the method described in sections 2 and 3 to es- tablish the convective adjustments of humidity and temperature. 8. Obtain a first estimate qT+1 from the method de- scribed in section 3. Include the convective adjustment. 9. Obtain a first estimate of 0T+1 from the thermody- namic equation (39). Include the convective adjustment. 10. Check for supersaturation. If supersaturation exists and if parcel ascent from the grid point is condi- tionally unstable, use the excess water vapor for a second convective adjustment. If supersaturation exists but parcel ascent is stable, condense water vapor at constant pressure until the temperature (humidity) has been raised (lowered) sufficiently to reach 100 percent relative hu- midity. The condensate is removed from the system as nonconvective precipitation. 11. Return to step (1) above for the forecast through the next time step. GENERATION OF AVAILABLE POTENTIAL ENERGY The generation of available potential energy was cal- culated from the approximate relationship Table 5. — Standard values of thermodynamic variables where G=~ \ \Zl=2—2prdrd 2tt f ( ) rdr v ' *2 irr* r-*=400 km, ( )'=( )-(~~~ ), gft N2= edz (63) (64) (65) (66) (67) Level Height e T P p (m) (°K) (°K) (mb) (ton m-3) 1 0 300 301.3 1015. 0 1. 174X10-3 2 1054 ;« a 294.1 900.4 1.067X10-3 3 3187 313 282.6 699.4 0. 862X10-5 4 5898 325 266.5 499.2 0.653X10-1 5 9697 340 240.8 299.2 0.433X10-2 6 12423 347 218.9 199.5 0.318X10-3 7 16621 391 203.1 101.1 0.173X10-3 and H is the total (convective plus large-scale) conden- sation heating per unit time and mass. KINETIC ENERGY BUDGET From the equations presented in section 5, we may derive the following expression for the kinetic energy tendency of the model storm: dK dt = where Dy = and -TB+I-DV-DH Te=—2t\ " I "jrud -£ dzdr, /=-27rJ2|2,pr^(^±^)^, 2T^l?{ul ^k"Tz)+v¥z O^)}**' (68) (69) (70) (71) (72) +1 By use of the boundary conditions given in the text (equations 56 and 57) and the distribution of K"M used for our experiments (table 2), the dissipation of kinetic energy by vertical mixing may be approximated by Dv~2wfT r-piCD\Vtfdr. (74) For the sake of brevity, the dissipation due to lateral eddy viscosity is written in the form (73) rather than in a form that separates internal dissipation from dissi- pation at the lateral boundary. A If we average equation (68) over a time interval t, we obtain dK g"+"-g( dt~ -TB+I-Dy-DB, t where 1 Ct+t (-)^j; ( )*. (75) (76) September 1970 Stanley L. Rosenthal 663 The kinetic energy budgets discussed in the text are based on 12-hr averages with computations performed at 12-hr intervals. Ah terms in equation (75) may be evaluated directly from the output of the model. In general, there will be a significant residual due to trun- cation error. It is this residual that is plotted on figure 11. KINETIC ENERGY DISSIPATION BY UPSTREAM DIFFERENCING The dissipation due to differencing w(dM/dz) and w(du/dz) by the upstream method may be written as <■-, d2u , d2v~\ , , ,__, u 5~2+y ^2 rdzar (77) where the pseudo viscosity coefficient is given by F,=iWA2{l-^}. (78) The dissipation due to upstream differencing ofu(dM/dr) and u(du/dr) is where CH=-2, j;j; JF.{v Zg+ru g}^ (79) ^ = |[,|A,{l-M^}- (80) ACKNOWLEDGMENTS The author is indebted to Mrs. Bonnie True who typed the manuscript. Mr. Robert Carrodus drafted the illustrations, and Mr. Charles True was responsible for the photography. 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Palmen, E., and Riehl, Herbert, "Budget of Angular Momentum and Energy in Tropical Cyclones," Journal of Meteorology, Vol. 14, No. 2, Apr. 1957, pp. 150-159. Riehl, Herbert, Tropical Meteorology, McGraw-Hill Book Co., Inc., New York, 1954, 392 pp. Riehl, Herbert, and Malkus, Joanne S., "Some Aspects of Hurricane Daisy, 1958," Tellus, Vol. 13, No. 2, May 1961, pp. 181-213. Rosenthal, Stanley L., "Numerical Experiments With a Multilevel Primitive Equation Model Designed to Simulate the Develop- ment of Tropical Cyclones, Experiment I," ESSA Technical Memorandum ERLTM-NHRL 82, U.S. Department of Com- merce, National Hurricane Research Laboratory, Miami, Fla., Jan. 1969a, 36 pp. Rosenthal, Stanley L., "Experiments With a Numerical Model of Tropical Cyclone Development. Some Effects of Radial Reso- lution," ESSA Technical Memorandum ERLTM-NHRL 87, U.S. Department of Commerce, National Hurricane Research Laboratory, Miami, Fla., Aug. 19696, 47 pp. Smagorinsky, J., "General Circulation Experiments With the Primitive Equations: I. The Basic Experiment," Monthly Weather Review, Vol. 91, No. 3, Mar. 1963, pp. 99-164. Yamasaki, Masanori, "A Tropical Cyclone Model With Param- eterized Vertical Partition of Released Latent Heat," Journal of the Meteorological Society of Japan, Vol. 46, No. 3, June 1968a, pp. 202-214. Yamasaki, Masanori, "Detailed Analysis of a Tropical Cyclone Simulated With a 13-Layer Model," Papers in Meteorology and Geophysics, Vol. 19, No. 4, Dec. 19686, pp. 559-585. [Received December 12, 1970; revised February 16, 1970] Reprinted from Proceedings A~l National Cloud Physics Conference, Ft. Collins, Colorado AN INSTRUMENTED "HAILSTONE" FOR CLOUD PHYSICS RESEARCH William D. Scott Cloud Physicist, National Hurricane Research Laboratory, ESSA Adjunct Professor, University of Miami, Florida Probes of the atmosphere for meteorological data have taken many forms including the ordinary radio- sonde and the dropsonde. (1,3) These devices are satisfactory only for measuring variables such as tem- perature, wind speed, and particle concentration, quantities that vary slowly and are, in a sense, 'pas- sive'. With these instruments it is not possible to measure the rapidly varying quantities or 'active' quantities of importance in the formation of precipitation or in the electrification of clouds. These quantities include the number of particle collisions per unit time, the trajectory of a precipitation particle, and the electrical charge transferred when particles collide; they are ultered beyond recogni- tion by present measuring techniques. These particular variables require a simulation of actual happen- ings in the cloud and measurements during particle interactions. This paper describes perhaps the first attempt at such a measurement. The instrument used is a dropsonde the size of a hailstone, called herein a 'dropstone.' INSTRUMENT DESIGN The general instrument design is shown in Figs. 1 and 2. Fig. ywvi 1. Dropstone Transmitting to a Remote Receiver. - RECEIVER "Active" Date ANTENNA POWER TRANSMITTER VCO DATA CHOPPER OR MULTIPLEXER CATTERY POWER CONVERTER DETECTOR ACTIVE DATA The dropstone transmits a vertically polar- ized FM signal to a remote receiver. The upper surface of the dropstone acts as the ground plane. A single wire trailing the dropstone in fall acts as the antenna. This design makes possible the inclu- sion of ancillary data in the telemetered signal. These data might include the in- stantaneous acceleration of the dropstone or even its mass. The use of microcir- cuits and micropower signal conditioners (MOSFET) leaves sufficient room for a bat- tery pack that should allow transmissions during most of the fall to ground. Fig. 2. Block Diagram of the Electronics Inside the Dropstone. 109 A picture of a prototype wor'.ing dropstone is shown in Fig. 3 with a pictorial description. The prototype was built to detect the electrical charge exchange that occurs when a hailstone collides with ice crystals in a real cloud. The detector was a protected, insulated gate transistor; its gate was di- rectly connected to the lower hemispherical portion of the dropstone. The transmitter was built from a single transistor and the upper, hemispherical portion of the dropstone served as the ground plane. The voltage difference between the two hemispheres was output at a transmitting frequency of 100 MHZ. A sin- gle, vertically inclined, elevated wire served as the receiving antenna for an ordinary FM receiver. ANTENNA GROUND PLANE SENSITIVE SURFACE Fig. 3- The Internal Construction of the Prototype Dropstone, a, with Description, b. TESTING THE DROPSTONE The transmitting efficiency of the instrument was low and the signal could only be detected up to 500 m. and a usable output could only be obtained to about 50m. This was a consequence of the necessity to transmit at low frequencies for long time periods to produce an operational instrument. After final development, of course, data would only be obtained for a minute or so at higher, more useful power levels. A major problem to the testing was the outside noise and local radio stations which made it es- sential to do the testing in remote locations. The Arctic proveu to be the best testing ground; an actual trace during a short drop from a balloon is shown in Fig. h. Fig. k. Output during a Fall in Arctic Diamond Dust. In this case diamond dust was present in the air and it appears that two collisions of the hailstone with the small ice particles were observed. This result agrees with the expected nomber of collisions; the sizes of the pulses indicate that the charges produced are of the same order as have been observed during simulated experiments on the ground in similar conditions. FUTURE APPLICATIONS The device is operational and, with a powerful, efficient transmitter and a high gain, directional antenna-receiver system, it should be able to transmit useful information several miles. (2) It is pre- sently one inch in diameter and, with present state-of-the-art electronics, it probably could be made one centimeter or smaller. This should make it possible to make measurements of hydrometeor interactions in a realistic simulation. Also, the transmission itself will locate the trajectory of the hailstone in the real cloud. This ultimately should give an insight into active cloud processes, and hence become an in- valuable tool in assessing cloud models. REFERENCES 1. C. Magono and S. Tazawa, Design of Snow Crystal Sondes, J.A.S. 23; 6l8-625, 1966. 2. O.Z. Ray and J.S. Hart, A Multi-Channel Transmitter for the Physiological Study of Birds in Flight, Med. & Biol. Eng. h. 1+57, 1966. 3. P. Squires, The NCAR Dropstone Development, NCAR Quarterly, Spring, 1966. 110 Reprinted from Journal of the American Chemical Society 92, No. 13, 3 9 ^ 3 " 3 9 ^ 6 Two Solid Compounds Which Decompose into a Common Vapor. Anhydrous Reactions of Ammonia and Sulfur Dioxide1 W. D. Scott and D. Lamb Contribution No. 219 from the Department of Atmospheric Sciences, University of Washington, Seattle, Washington 98105. Received October 20, 1969 Abstract: Measurements of vapor pressure over products of direct gaseous reactions between NH3 and S02 are in agreement with a thermodynamic model which assumes the products to be two mutually soluble solids with NH3 : S02 stoichiometric ratios of 1 : 1 and 2:1. A family of curves results on a semilogarithmic plot of pressure vs. re- ciprocal temperature which forms a sloping trough when composition is added as a third dimension. The fitting procedure yields a value for the composition of each experimental solid as well as the standard enthalpies and en- tropies of decomposition. 3943 Anhydrous reactions between NH3 and S02 produce a . complex system containing compounds in the solid state in equilibrium with a vapor phase consisting of the two gases, NH3 and S02. In our laboratory2 equilib- rium vapor pressures above the solids have been mea- sured and it appears that the system is analogous to the NH3-CO2 reacting system that produces ammonium carbamate.3 Simplicity is lost, however, because more than one chemical compound is formed in the NH3-S02 system. Indeed, NH3 and S02 appear to have a great affinity for each other and react in nearly all stoichio- metric ratios, producing red, orange, yellow, pink, and white reaction products. Reactions between these two gases have been known for over a century and a half but they are not mentioned in most textbooks. The chemist is led to believe that NH3 and S02 do not react unless they are dissolved in water and undergo a normal, weak base-weak acid neutralization reaction. Exactly which products are formed is not agreed upon. Ogawa and Aoyama4 and Badar-ud-Din and Aslam5 have carried out thorough analyses of the gaseous reactions. Both these investi- gations, as well as the experimental evidence of others,6 support the hypothesis that a yellowish compound with an NH3-S02 stoichiometric ratio of 1 : 1 and a white compound with a 2:1 ratio are the two primary re- actions products, provided the temperature of reaction is maintained below about 10° and water is excluded from the system. In addition, infrared absorption spectra of the vapor made in our laboratory2 indicate that the solids de- compose reversibly into NH3 and S02 in the vapor, suggesting that the system is, indeed, one in which one solid phase containing two chemical compounds is m equilibrium with a common vapor of two gases, NH3 and S02. This paper presents a theoretical treat- (•) Research supported by the Atmospheric Sciences Section of the National Science Foundation (Grant No. NSF GA-780). <2) W. D. Scott, D. Lamb, and D. Durly, J. Atmos. Set., 26, 727 0969). O) M. J. Joncich, B. H. Solka, and J. E. Bower, J. Chem. Educ. 44, 598(1967). (4) M. Ogawa and S. Aoyama, Scl. Rent. Tohoku Unit:. First Ser., ("1121(1913). (5) Badar-ud-Din and M. Aslam, Pakistan J. Sci. Res.. 5, 6 (1953). (o) A summary of previous work is presented in another paper (see rcf 2). ment of this unusual system and compares the results with experimental data. Equilibrium Expressions. Assuming that only the 1:1 and 2:1 compounds are formed, the chemical equations for their decomposition are7 NH,SO,= (NH3)sS02: NHj + SO, : 2NH3 + S02 (I) If, furthermore, it is assumed that the two compounds form an ideal solid solution which has a mole fraction X of the 1 : 1 compound, the following ideal equilibrium expressions are obtained K, PJ\ X y{\ - y)P> (3) (4) where the subscripts a and s refer to the gases, ammonia and sulfur dioxide, and y is the mole fraction of am- monia in the vapor. These equations can be combined to give an expression for the equilibrium total pressure P P = X^KS (1 - X)K2 + (1 - X)K2 XKX (?) Further, the equilibrium constants can be written in terms of the standard Gibbs free energies of decomposi- tion, AG° AG,0 = -RT]n Kx AG2° = -Win Kt Or, in terms of the standard entropy and enthalpy of reaction, the equilibrium constants are / AG,°\ /AS^X / A//,°\ * = eXP{--RT ) = CXF\ R-)nP\--RT ) I AG2°\ /AS2°\ / A//2°\ K, - exp^- — j = exp(^— j exp^- _j (7) These products have been unsystematically called amidosulfurous acid and ammonium amidosulfltc or monosulfinic acid and ammonium amine monosullmate, respectively. Since the true structure of the com- pounds is not well known, it is appropriate at present to use the simple stoichiometric formulas. Scott, Lamb / Anhydrous Reactions of Ammonia and Sulfur Dioxide Cold TjoP Ood Vocujm Pump Figure 1 . Vapor pressure apparatus and reaction vessel. The temperature dependence of the equilibrium total pressure is, therefore r,„eIp(«)+^B»p(?) ,6, 1 - X where A = exp /2A5,° - AS,0 - AS2°\ R ) _ /AS,0 - A^°\ 5 - £XP(, * ) A//2° - 2A//!° 0 A//!° - Atf2° — = — 0 = — - — (7) R R As a result of the relative importance of the two terms on the right side of eq 6, a plot of log P vs. IjT at con- stant X produces curves with two distinct slopes at the extremes of temperature. Measurements of the two slopes directly establish values of a and /3 (or AHX° and A//,0). Best values of A and B (or AS,° and AS2°) are obtained by trial and error. Later, it will be shown that with a family of curves of constant X values, it is possi- ble to obtain best X values as well as the standard enthalpies and entropies. Experimental Section Experimental details are presented in our previous paper.2 A diagram of the glass experimental apparatus is shown in Figure 1. Both gases were frozen onto the inner walls of a reaction vessel with a liquid nitrogen bath. The vessel was then allowed to warm and the gases reacted violently at about —10°. The steady-state pres- sures at temperatures between —10 and —70° were then measured using a McLeod gauge; the data are presented as points in Figure 2. The apparatus had two potentially limiting features. First, the McLeod gauge is limited in use to substances which do not condense out in the compression section of the gauge. No effects of conden- sation in the gauge were noted, however. Second, the system ex- posed the sample to relatively large surfaces of glass, stopcock grease, and mercury, and thus to probable sorption. Consequently, large equilibration times were required and hysteresis effects were observed. As a result a pressure measurement over a given product generally was reproducible to only about 30%. Further- more, data in the lowest decade shown are limited by the read- ability of the McLeod gauge, the precision of which was 0.002 Torr. Fitting the Data The products of the reaction coated the walls of the reaction vessel and contained at least ten times the material in the vapor. Therefore, it is a good approxi- mation to consider that the m;i'.s of the solid was not appreciably altered by sublimation into the vapor during the pressure measurements at selected temperatures. The mole fraction of 1 : 1 compound, X, can therefore 3.8 4.0 4.2 4.4 1000 T 46 4.8 5.0 52 CK"1) Figure 2. Experimental vapor pressure measurements (symbols) with theoretical curves superimposed. be assumed constant during the measurements of pres- sure over a given sample. The theoretical expression (eq 6) can be used to in- terpret the data in Figure 2. The final theoretical curves are drawn upon the graph. Two straight lines do, indeed, naturally occur in the data. The require- ment that all parameters of the model be physically meaningful necessitates that the absolute value of a be less than that of (3. This requires that the 1:1 com- pound predominates where the slope is smallest. The values of a and 8 that give a best fit are —1080 and - 15, !00°K, respectively. Using these values, the exponential terms in eq 6 are determined for all temperatures. Corresponding to each set /' of data at constant X there is a pair of pre- exponential factors Ml and N, that form a best fit to the data Mt = X,' 1 - AY N, = X~-^B (8) By eliminating the X, in eq 8 an expression relating to A to B can be obtained A = MtNlNt + B) IV - (9) This expression is valid for al two sets (/ and j) of data curves, so that for any B = MI^lMI (io) M,N, - M,N, Back-substitution into eq 9 then gives a corresponding value of A. The constants A and B were calculated Journal oj the American. Chemical Society / 92:13 / July I, 1970 39-45 4.0 4.5 !opo ,.,-,, Figure 3. Calculated total vapor pressures above solid mixtures containing a constant mole fraction X of the 1 : 1 compound. for all possible sets of curves; the best value was selected for a best fit of the data. The values obtained were A = 56 Torr and B = 3.7 X 10" Torr. Substituting the values for A, B, a, and /} into eq 7, standard en- tropies and enthalpies of decomposition of the pure compounds can be calculated. The values refer to the decomposition of the pure solids into the gases, NH3 and S02, at atmospheric pressure and are listed in Table I. Values of X, the mole fraction of 1 : 1 corn- Table I. Standard Enthalpies and Entropies of Decomposition of the Compounds Compound A//°, kcal/mol AS0, cal/(mol °K) NH, SO, (NH.fc-SO, 32.2 62.2 84.8 174.8 pound in the solid, are then calculated using eq 8. These X values are shown in Figure 2 along with the theoretical curves for the above values of A, B, a, and /3. The theoretical curves fit the data within the experi- mental accuracy. The significant point, of course, is that the data are well described by the interaction of two straight lines. Discussion To show their behavior in the extremes of pressure and composition, the theoretical curves for constant X are replotted on a larger scale in Figure 3. The curves show several interesting features. Visualizing the curves in space, with composition as a third dimension, Ihey form a trough that slopes toward lower tempera- tures (higher values of 1000/7") and smaller values of X. When there is a large excess of NH3 in the vapor (large >') the steep, constant X curves in the "background" (lines of small A") apply and the 2:1 compound pre- dominates in the solid mixture. Increasing the amount of S02 in the vapor then results in a general lowering of •he vapor pressure curves due to the formation of the 1:1 compound in solid solution. Eventually, however, 'he contribution of the 1:1 compound to the total Figure 4. Calculated total vapor pressures above solid mixtures in equilibrium with a vapor containing a constant mole fraction >■ of NH,. vapor pressure becomes comparable to that of the 2:1 compound. At this point the X lines become curved (develop "knees") and fold into the "foreground"' (lines with X ~ 1) surface of lines with a lesser slope. As the amount of S02 is further increased (y decreases), the X lines move upward and the amount of 2:1 com- pound in the solid becomes negligibly small. How- ever, even at this point, this small amount of 2 : 1 com- pound has a marked effect on the total vapor pressure. It is also significant that neither compound can exist in a pure form. The pure state of either solid is most nearly approached when there is an extremely large excess of one of the gases in the vapor. The "knees" of the curves are noteworthy in their relationship to the standard techniques for the measure- ment of equilibrium partial pressures. They define a minimum critical vapor pressure, Pc, exerted by any of the solid mixtures at a given temperature. Corre- sponding to this Pc there exists a critical mole fraction of 1 : 1 compound, Xc. This Xc is found by differenti- ating the equation for the total pressure (eq 6) with respect to X and setting the derivative equal to zero. The resulting expression is (1 ~ *c)2 Xc\2 - Xc) A (a - Bexp-T (3) AV (11) This equation and eq 6 determine the line PQ = PC{T) which is the locus of the "knees" of the curves. The rather complex form of eq 11 does not show the simple stoichiometric ratios that exist in the vapors over these solid solutions. Consider curves of con- stant v, the mole fraction of ammonia in the vapor. The equations of these curves are found by solving eq 3 for X and substituting into eq 4. An implicit equation containing y and P results 1 y(\ - y) p2 ypZ Ki K? (12) These curves of constant y arc plotted on Figure 4. They are nearly straight lines, with a small negative Scot t. Lamb / Anhydrous Reactions of Ammonia and Sulfur Dioxide curvature at higher temperatures. In the surface of y lines it appears that the y lines are nearly parallel and the "knee" curve is one of constant y. This is true only at the extremes of temperature. If the equilibrium constant expressions (eq 3 and 4) are substituted into the right side of eq 11, a simpler expression for the critical mole fraction of NH3 in the vapor, yc, is ob- tained y* = 3 - Xc (13) This equation can also be obtained by differentiating eq 12 with respect to y, setting dP/d>» = 0, and using eq 4. The extremes of this equation are interesting in light of the normal techniques for measuring the equilib- rium constant in systems containing but a single com- pound in the solid phase. If Xc ~ 1, then yc = 1/2. This line is indicated by the upper arrow in Figure 4. It is exactly the line for a hypothetical, pure 1 : 1 solid that is not affected by another compound being present. It represents the hypothetical experiment in which the 1 : 1 compound exists in a pure form and its vapor pres- sure is simply measured. Then the sublimed vapor above the solid must be the NH3:S02 ratio of the solid and y = 1/2. If Xc « 1, then yc = 2/3. This is the corresponding vapor pressure curve for a hypothetical, pure 2:1 solid. The line is indicated by the lower arrow; it is nearly identical with the y = 0.9 curve. Of course, real substances are not generally pure and if there is a tendency for the formation of other com- pounds, the stoichiometry of the solid will not be main- tained in the vapor. The authors suggest that there is a slight tendency toward the formation of the 1 : 1 compound in the NH3-C02 system, forming carbamic acid. This may explain the differences between the values of the thermodynamic properties of ammonium carbamate that have been obtained by different work- ers.3 It is important not to be misled into believing that enthalpies of formation are directly associated with the slopes of the X curves since this system is complex and must be considered rigorously as a whole. Gener- ally, however, the pressure of the vapor above a solid phase that contains large amounts of the 2 : 1 compound exhibits the largest dependence on temperature, whereas mixtures containing mostly the 1 : 1 compound exhibit a relatively small dependence of pressure on tempera- ture, so that the curves of Figure 3 cross. This means that the 2:1 compound is the more volatile at higher temperatures and the 1 : 1 compound is the more volatile at lower temperatures. The compounds themselves do not vaporize but decompose reversibly into NH3 and S02. The en- thalpies of decomposition of the solids, in Table I, reflect heats released both in sublimation and the break- ing of chemical bonds between the two gases. It is unlikely that the heat of sublimation of the 1:1 com- pound is greater than about 15 kcal/mol, so the addi- tional intramolecular bonding of the 1:1 compound must account for more than about 17 kcal/mol. This energy indicates strong chemical bonding in the solid compounds which may be represented by the covalent acid structure H O \ II NSOH / H 1 The 2: 1 compound would then have the ionic structure NH,+ H O \ J! NSO- / H 2 which would have high bonding energy. However, it was observed that when two of the products were dissolved in water,2 the solution pH was very close to 7.0. This may be explained by assuming that some portion of the product contained the acid 1 and formed acidic constituents in solution where- as another portion of the product contained the salt 2 and formed basic constituents in solution. The pH of ammonium bisulfite solutions is approxi- mately 4.0; the pH of ammonium sulfite solutions is approximately 8.O.8 The acidic and basic elements then merely neutralize each other. But it is not generally expected that the portions of acid and base will exactly form a neutral solution. It is more likely that the structure 1 transforms into the tautomer, a zwitterion H O I II HN— SO- which tends to be a neutral buffer. The 2:1 salt would be expected to contribute very little basic strength to the solution, in any case, since the pH of ammonium sulfite solutions is approximately 8. (8) W. (1967). D. Scott and J. L. McCarthy, Ind. Eng. Chem. Fund., 6, 40 Journal of the American Chemical Society / 92:13 / July /, 1970 Reprinted from Journal of Atmospheric Sciences 27, No. 3, **63-473 49 May 1970 W. D. SCOTT AND ZEV LEVIN 463 The Effect of Potential Gradient on the Charge Separation During Interactions of Snow Crystals with an Ice Sphere1 W. D. Scott and Zev Levin Dept. of Atmospheric Sciences, University of Washington, Seattle (Manuscript received 14 November 1970, in revised form 9 February 1970) ABSTRACT Charge separation which occurs when polarized ice particles collide in a potential gradient has been found to be an extremely important charge generating mechanism. The fair weather potential gradient is sufficient to initiate considerable charge separation (3X 10-5 esu per collision). Then positive feedback effects inherent in this polarization charging mechanism can readily explain the strong charging found in glaciated clouds or thunderclouds in general. This theoretical prediction is well corroborated by the present experimental results obtained during simulated experiments in the field with potential gradients <5000 V irr1. However, higher potential gradients produced even more charge than predicted by theory. Also shown are distributions of the original charges carried by the ice particles, the charges transferred to the ice sphere, and the charges carried off after separation. The distributions also support the theory of polarization charging which predicts charging in proportion to the square of the ice particle radius. 1. Introduction Many theories of charge generation involving ice particles within a thundercloud can be found in the scientific literature. Some deal with the effect of collisions between ice particles and water droplets; some deal with collisions between ice particles. The underlying physical principle in many of the theories is the thermoelectric effect (see Mason, 1953). Recent evidence indicates that the thermoelectric effect is either ineffective (Scott and Hobbs, 1968) or acts in the wrong direction to explain thundercloud electrification at temperatures > — IOC (Shio and Magono, 1968). In any case, charging has been observed in natural clouds and in the laboratory that is not easily explained by what is generally known as the thermoelectric effect. Other theories involve rubbing or breaking of the interacting elements. For instance, Magono and Takahashi (1963) suggested a mechanism in which the surface of one of the ice particles is rubbed off onto the other one. Depending on the temperature and the surface state, separation can occur to give charges of either sign on the particles. Apart from these theories are those requiring the presence of a potential gradient. The primary way charge generation can be effected in a potential gradient is by polarization of the larger particles. In a positive potential gradient these particles acquire a positive charge on their lower side and a negative charge on their upper side. As such a hailstone falls through a cloud momentary contacts with smaller ice crystals result in 1 Contribution No. 217, Department of Atmospheric Sciences, University of Washington, Seattle. Research supported by the Atmospheric Sciences Section, National Science Foundation, under Grant NSFGA-780. the hailstone acquiring a net negative charge. This effect (called "the polarization charging effect") was first considered in relation to interacting water drops by Elster and Geitel (1913). However, Sartor (1954) was the first to treat the problem of interacting water drops or ice particles in a potential gradient in detail. He found that sufficient charge is separated during a single interaction of precipitation-sized particles to explain the charge build-up in thunderclouds. Muller-Hillebrand (1954, 1955) applied the theory specifically to inter- actions of ice crystals with polarized graupel pellets and found the same result. Later, Sartor (1961a, b) calculated the field build-up to be expected by this general charge separation mechanism. He showed that this charge generating mechanism can build electric fields of thundercloud magnitude even with relatively few particle interactions. Latham and Mason (1962) repeated Sartor's original calculations and found that, indeed, the mechansm is a powerful one. However, a laboratory experiment in which small ice particles collided with a cylindrical ice specimen did not show a significant increase in the charging as a result of an imposed potential gradient. Latham and Mason attempted to explain this discrep- ancy between theory and experiment by considering the relaxation time tr for charge transfer in ice and the contact time tc between the two ice pieces. The ice acts as an insulator to events which occur with characteristic times 2). (5) This is an analytic solution for two spheres which make contact. The series solution derived by Davis (1964) for the electric field between two spheres with a small but finite separation distance (O.OOlr) gives the same result when contact is simulated by setting this electric field equal to zero. Note that in the present experiment r«i? so Q is almost completely transferred to the large sphere. Eq. (5) is derived for conducting spheres. Ice spheres may be considered conducting provided the time of charge transfer or the time for equilibration of charge carriers (relaxation time, tr) is short compared with the time scale of the experiment (in this case the time of contact, tc). Insertion of appropriate values for the physical properties of ice into Eq. (1) should establish the validity of this assumption. Low-frequency values of e and K are rel event. The static dielectric constant 6 of ice at — 5C is approxi- mately 90 (see Cole and Worz, 1969). The dc con- ductivity of pure ice is 10-8-T0-9 mho cm-1 at — 5C (Bullemer et al., 1969; Camp et al., 1969; Ruepp and Kass, 1969). As a result of natural pollution, the conductivity of natural ice particles will be at least 10 times greater than this value or 10_7-10-8 mho cm-1 (see Muller-Hillebrand, 1954, and Camp et al, 1969). This is in agreement with the value of K for freshly fallen, partly compacted snow measured by Kopp (1962). This means the relaxation time is 0.1-1 msec. In fact, the surface conductivity of the ice pieces is all important and has been shown to be approximately 10 times greater than the bulk conductivity (Bullemer etal.; Camp et al.; Ruepp and Kass). Also, impurities will be concentrated in the ice surface and tend to make K larger and tr even smaller (Camp et al.). Hence, this is an upper limit value for tr. Signals generated during charge transfer from the ice pellets to the ice sphere had rise times in the milli- second range which suggests that the contact time is longer than the relaxation time. Therefore, to a first approximation the ice pieces can be considered as conducting spheres. May 1970 W. D. SCOTT AND ZEV LEVIN 465 Induction ring hieldinq cones To recorder High voltage plates Metal shielding boi Fig. 1. Schematic diagram of apparatus. 3. The experiments The apparatus is shown schematically in Fig. 1. It consists of a cylindrical tube 8| inches in diameter with axially centered, conical-shaped electrical shields. In the lower section an ice sphere was placed on the axis of the cylinder half-way between two parallel plates to which various potentials could be impressed by a battery. The ice sphere was connected directly to a sensitive electrometer (henceforth called sphere electrometer) which was developed in our laboratory. The electrometer was similar to the one described by Scott (1968); Fig. 2a shows the circuit diagram. Above, axially centered and shielded from the lower section, was an induction ring 2 inches in diameter by f inch high, connected to another electrometer (henceforth called ring electro- meter). The electronics of this electrometer were modified so that the device had a voltage gain of approximately 10 (see Fig. 2b). The electrometers were shielded with two layers of Conetic and Netic foil and were rigidly mounted in a solid sheath of fused quartz. This, together with the external galvanized iron electronic shields and the use of batteries throughout resulted in a high signal-to-noise ratio. Both electrometers could detect charges as low as 10~6 esu. A natural ice particle falling vertically entered the apparatus through a hole in the conical shield on top and passed through the induction ring. Passage of the particle through the ring caused a deflection on the oscillograph (Brush Mark 280) proportional to the charge on the particle. The crystal then fell through another conical shield which isolated the ring from the high electric potential on the parallel plates. In further fall the crystal entered the region of potential gradient and collided with the ice sphere. The charge transferred to the sphere was measured on the second pen of the recorder. IN _» Fig. 2. Circuit of sphere electrometer, a., and ring electrometer, b. 466 JOURNAL OF THE ATMOSPHERIC SCIENCES Volume 27 04,- 0.3 -|z 02 0.1 0.5 I 1.5 2 25 3 3.5 Characteristic size (mm) Fig. 3. Sample size distribution of natural ice crystals. The entire apparatus was placed ~1 m above the ground outside in a clear area relatively free from electronic noise. The environmental temperature was recorded every few minutes and did not vary by more than 1C during an experiment. The falling crystals were generally stellar with a filled-in hexagonal pattern, but many broken crystals and some rimed crystals were noted. An approximate size distribution of the falling ice crystals was made by measurements from photo- graphs taken during Experiment 6 (see Fig. 3). Only crystals with very small horizontal velocities were chosen by the three conical shields. As a result, only a fraction of the crystals entering the apparatus passed through the ring and subsequently collided with the ice sphere; it took several minutes to obtain enough collisions for a charge distribution. The crystals generally collided with the ice sphere and passed on, but occasionally a crystal would stick on the top surface of the ice sphere. These crystals were removed by wiping the surface with a clean tissue. 4. The electrical pulses The electrical pulses were recorded on the strip chart of the oscillograph, but an exact interpretation of their meaning is not possible without some knowledge of the physics of the interaction and how the pulses were modified by the electronics. The pulses recorded on the sphere electrometer are most easily understood; they appear to be the result of an abrupt transfer of charge accompanied by a slow bleed off of this charge through the large 10n A resistor. The time constants observed are, indeed, those that would be predicted if this were the case. Also, when known charges on water drops were transferred to the sphere electrometer, the peaks of the output signals were proportional to the charges. Final calibration of the sphere electrometer was done by measuring the effective capacity C and calculating the charge Q from the relation Q = CV, where V is the peak value of the measured output voltage. The capaci- tance of the sphere electrometer was measured by noting the attenuation of a 1000-Hz signal when a precision 3-pF capacitor was placed in series with the input. The effective capacity of the sphere electrometer was 4.7 pF. The signal output from the ring electrometer was calibrated relative to the sphere electrometer so that relative differences could be measured. For this purpose, the ice sphere was replaced by a wooden cup filled with steel wool and the capacitance of the sphere electro- meter remeasured. Then simultaneous deflections from the ring and sphere electrometers were recorded when water drops with various charges passed through the ring and were caught in the wooden cup. Measurements of the initial height of the pulses from the ring electro- meter gave a value of 6.0 pF for the effective capacitance of the electrometer. As the equi-potential lines between the two plates are distorted due to the hole in the upper plate, it was necessary to determine the uniformity of the field near the ice sphere. To this end an equi-potential experiment was performed which simulated the apparatus in two dimensions. A two-dimensional view of the apparatus was drawn on graphite conducting paper with highly conductive silver paint. Voltages were connected to the simulated plates and the equi-potential surfaces were traced with a galvanometer. Fig. 4 shows the result of the simulated experiment. The figure clearly shows that near the sphere the equi-potential lines are parallel and uniform. Due to the high sensitivity of the ring electrometer, all the charges on the crystals that collided with the sphere were recorded. However, occasionally no corresponding Fig. 4. Equi-potential surfaces around the ice sphere. May 1970 W. D. SCOTT AND ZEV LEVIN Table la. Summary of results. 467 Ambi- Total num- ent ber of tem- Applied events re- Exper- pera- potential Average charges ( msc)* Med ian charges (msc)* corded iment ture gradient On snow Transferred Carried On snow Transfered Carried On On no. (°C) (V cm"1) crystals to sphere off crystals to sphere off ring sphere 1 -3 0 -0.0056 +0.0176 -0.0238 -0.020 -0.005 -0.0075 232 172 2 -3 59 -0.0118 +0.556 -0.569 -0.015 +0.075 -0.085 90 78 3 -3 -59 +0.0103 -0.602 +0.610 -0.013 -0.097 +0.085 50 42 4 -3 59 -0.0083 +0.574 -0.58 -0.015 +0.122 -0.125 51 41 5 -2 0 -0.0039 +0.0194 -0.0235 -0.012 +0.015 -0.020 134 120 6 -2 102 -0.0203 + 1.58 -1.00 -0.020 +0.36 -0.45 62 4,1 7 -2 -102 -0.0177 -1.16 + 1.14 -0.015 -0.12 +0.10 122 78 8 2 51 -0.0158 -0.30 +0.285 -0.021 -0.12 +0.090 122 LOS 9 -2 -51 -0.0158 +0.378 0.394 -0.022 +0.077 -0.11 158 106 10 -2 is -0.0208 +0.15 -0.174 -0.022 +0.040 -0.075 213 183 11 -2 -18 -0.0215 -0.212 +0.189 -0.023 -0.080 +0.040 316 276 12 -3 0 -0.0330 -0.0230 -0.0093 -0.027 -0.017 -0.006 L23 107 13 -4 59 -0.0231 +0.22 -0.241 -0.025 +0.078 -0.119 IIS 91 14 - 3 -59 -0.0325 -0.325 +0.291 (1.027 -0.058 +0.026 95 66 * Millistatcoulomb (msc). Table lb. Correlation coefficients between charges. Correlation coefficients between charges Originally on Originally on Transferred to Applied snow crystals snow crystals sphere and Exper- potential and transferred and carried off carried off iment gradient to sphere after separation after separation no. (V cm"1) (CRS) (CRD) (CSD) 1 0 +0.428 +0.127 -0.842 2 SO -0.184 +0.246 -0.998 3 -59 -0.084 +0.143 o.ws 4 59 -0.096 +0.160 -0.998 5 0 +0.572 +0.284 -0.625 6 102 -0.162 +0.195 -0.999 7 102 +0.192 -0.147 -0.999 8 51 +0.218 -0.102 -0.993 9 -51 -0.085 +0.180 -0.995 10 18 -0.122 +0.296 -0.984 11 -18 +0.286 -0.156 -0.991 12 0 +0.803 -0.177 -0.729 13 59 -0.120 +0.204 -0.996 14 -59 +0.231 0.147 -0.996 signal from the sphere electrometer was observed because, perhaps, the trajectory of the crystal did not intercept the ice sphere. This explains the difference between the number of events recorded by the ring and the sphere in Table la. Many events were recorded in each experiment, and the distributions of the original charges on the snow crystals, the charges transferred to the ice sphere, and the charges carried off by the small crystals after separation (initial charge on a crystal minus the charge transferred to the sphere by that crystal) were plotted on histograms. In all cases, individual charges were between —10 and +10 milli-statcoulombs2. When small potentials were applied, the charges concentrated around 0.1 msc, but when large potentials were applied, the charges were close to 10 msc. Positive and negative fields were applied and the charges observed carried 2 A milli-statcoulomb (msc) is defined as 10~3 esu. both positive and negative values. The tallies, calcula- tions and plots of the data were all made by IBM 7094 digital computer. Table 1 summarizes some of the experimental results. It was impossible to plot this large range of data on an ordinary histogram with either a linear or logarithmic plot and still be able to compare data from different experiments. The linear scale tends to separate the data into a large group in one location with many individual events scattered throughout the scale, and a logarithmic scale does not allow both negative and positive values to be plotted. Thus, in order to plot all the experimental data on a single scale for comparison, the abscissa of the histogram plot was distorted as follows: The abscissa was divided into 56 equal divisions to cover the range — 10 to +10 msc. Divisions on the positive side were labeled using the numeric pattern, 0, 1, 2, 3, . . . , 10, 20, 30 . . . 100, where the number 1 was given the unit 0.01 msc. The same pattern was used for the negative 468 JOURNAL OF THE ATMOSPHERIC SCIENCES Volume 27 side. Figs. 5, 6, 7 and 8 are shown with this abscissa. This scale is neither logarithmic nor linear but is logarithmic in decades and linear between decades. 5. Analysis In experiments with a potential gradient present it is easy to see the high negative correlation between the charge transferred to the ice sphere and the charge carried off by the ice crystals after separation (CSD, see Table lb). Similarity, the correlation between the charge given up to the ice sphere and the original charge (CRS) is relatively high with no potential, but it was very small otherwise. This means that when no field was applied most of the charge on the ice sphere was due to direct transfer with a small contribution from actual generation of charge on collision by fracture of the crystal surfaces, thermoelectric effects, etc. However, O.30 ^.20 Ml LtLrx 0 0.1 CHARGE (msc.) .50 .40 O.30 .20 .10 "10 n irrTrfl 1 1 1 [TLr^ o CHARGE (msc) 0.1 O.30 ..'0 . in rfirimn u -10 -1 -0.1 0 0.1 1 CHARGE (msc) b. .MM O.30 .10 Ml IdJLrJb CHARGE (msc.) .40 O.30 ..20 M cMJ m. CHARGE (msc.) Fig. 5. Charges on the incoming snow crystals (Experiment 1), a., and those communicated to the ice sphere with no potential gradient (Experiment 1), b. Fig. 6. Charges on incoming ice particles (Experiment 2), a., those communicated to the ice sphere when 58.7 V cm-1 were applied (Experiment 2), b., and net charges remaining on the rebounding ice crystals (Experiment 2), c. May 1970 W D. SCOTT AND ZEV LEVIN 469 when relatively high electric fields were applied, the portion of the original charge transferred appeared small compared to the charge separated due to polariza- tion charging. The correlation coefficient between the original charge and the charge carried off by the small ice crystals after separation (CRD) is relatively low for all experiments. This indicates again that when a potential gradient was applied, the charge carried off by the small ice crystals came mainly from the charge separation due to polariza- tion. The fact that CRD was relatively small when no potential was present implies that under these conditions the charge carried off on the particles is mainly the charge actually generated by collision. Direct charge transfer is evident in the similar appearance of Figs. 5a and b. The shape of the distribution in Fig. 5a is nearly as Gaussian as one would expect from random charging effects which occurred .50r O-30; .JO iimm 0.1 CHARGE (msc.) Fig. 8. Charges communicated to the ice sphere when —102 V cm-1 is present (Experiment 7). O.30 .20 . 50 ,U0 O.30 .10 y10 0 CHARGE (msc) -0.1 IL 0. 1 QH CHARGE b. (msc.) Fig. 7. Charges on the incoming ice particles (Experiment 6), a., and those communicated to the ice sphere when 102 V cm-1 were applied (Experiment 6), b. before the crystals entered the apparatus. The differ- ences between Figs. 5a and b may be accounted for by charge generated (not separated by polarization) during the interactions. In this case, with no applied potential, the average charge communicated to the sphere was 0.018 msc. Later, in the following experiment, a potential gradient of 58 V cm-1 was imposed and the average charge communicated increased to 0.38 msc (see Figs. 6a and b). The charge carried off by the rebounding ice crystals was almost exactly the negative of the charge left on the sphere (see Fig. 6c). As even higher voltages were applied, the distribution moved to even larger charges (see Figs. 7a and b) so that when 102 V cm-1 was applied, the average charge communicated to the sphere was 1.6 msc. When opposite electric fields were applied, exactly opposite charging occurred. Fig. 8 shows the distribution when —102 V cm"1 was applied; the average charge was —1.2 msc. The forms of the distributions are noteworthy. The distributions show both normal and log-normal trends. To show this the data were plotted as cumulative dis- tributions on linear-probability plots. Fig. 9 shows cumulative distributions for Experiment 9. The cumula- tive distribution of the original charges is represented by a nearly straight line in the center of the graph, indicating a normal distribution. However, the charges transferred to the sphere and the charges carried off after separation show exponential features as would be expected from log-normal distributions. In all histograms many charges can be found near 0.01 msc. This is possibly due to collisions of the stellar crystals with their basal face. When the crystals are oriented so as to collide with their basal face, the proba- bility of separation directly after the collision is reduced. This means that most of the charge recorded in such collisions is the result of direct transfer of the initial charge on the falling ice crystals. 470 JOURNAL OF THE ATMOSPHERIC SCIENCES Volume 27 The effect of potential gradient is summarized in Fig. 10, where the abscissa represents the applied potential gradient and the ordinate the average charge transferred to the ice sphere for all experiments listed in Table 1. The straight line represents Eq. (5) for particles of characteristic size (diameter) of 1 mm. Since the particles were stellar, \ of a millimeter was used as the effective radius for polarization charging. The data are very well described by the theoretical curve below potential gradients of 50 V cm-1. At higher 2.251- 20 75 1.9 1.25 10 0.73 0.5 S 0.25 E O -0.25 <-> -0.5 - • Charge transferred to ice sphere a Original chorge on ice crystals 0.75 do o Charge carried off after separation by ice crystals -1.0 -1.25 I -1.5 -1.75 ■2.0 9 23 ill ii i ill" i 05 12 5 10 20304050607080 90 95 98 99 Percent charge less than Q Fig. 9. Linear probability plot of charging events in Experiment 9. 99 8 May 1970 W. D. SCOTT AND ZEV LEVIN 471 16 X S '5 J 1.4 3 8 |.3 o * 1.2 I '"' £ 1.0 1 °9 S 0.8 ° 0.7 w 0.6 I 05 X / 2 0.4 S- 0.3 5 °2 X x 0.1 1 i | 1 1 . j / i * 1 1 1 1 1 1 1 MOO -80 -60 X X -40 -20 S / x "0.2 -0.3 20 Poter 40 tiol 60 80 100 gradient (Volts/cm) -0.4 -0.5 X Theoreticol curve (Eq.2) Experimental average values X -0.6 -0.7 -0.8 -0.9 -1.0 X -1 .1 -1.2 Fig. 10. Electric field vs average charge transferred to ice sphere. gradients, however, more charge is separated than the theory predicts. This may be a result of several effects, including point discharge and an asymmetric charge distribution in the real snow crystals, as well as the omission of second-order terms in the mathematical solution. 6. Discussion It is most significant that the potential gradient is such an effective charging agent. Polarization charging explains this effect satisfactorily. With no consideration for the physics of ice (thermoelectric effect, Workman- Reynolds effect, etc.) the electrification of thunderclouds can be explained. Of course, Sartor (Sartor, 1967; Sartor and Abbot, 1968) has shown theoretically and experimentally that polarization charging during collisions of water drops is an effective mechanism for charge generation in clouds. Also, Sartor (1954), Miiller- Hillebrand (1954), and Latham and Mason (1962) have shown theoretically that the mechanism is effective during ice particle collisions. The present results demon- strate experimentally that polarization charging is indeed effective in the case of ice-ice interactions. Polarization charging easily explains the charging that occurs in glaciated clouds without supercooled droplets (Hobbs and Burrows, 1966 ; Stow, 1969). It also explains the high correlation between particle charges and the potential gradient observed in real clouds in Arizona (Latham and Stow, 1969). Muller-Hillebrand (1954, 1955) predicted that such polarization charging in ice could be important in cloud electrification. His predic- tion was based on a theoretical analysis similar to the one leading to Eq. (5). However, our experimental 472 JOURNAL OF THE ATMOSPHERIC SCIENCES Volume 27 results show that this equation underestimates the charging at high electric fields. In other words, this mechanism is much more efficient than predicted. Montgomery and Dawson (1969) have observed an analogous increase in charging on collisions of water drops. According to the results shown in Fig. 10, in the early stages of the development of a thundercloud the fair weather positive potential gradient is sufficient to cause a substantial charge separation. A positive charge of 0.03 msc is transferred to a 1-mm particle when it collides with a larger particle. Separation of the larger particles from the smaller ones by gravity further en- hances the positive potential gradient, resulting in a positive feedback, and more charge is separated. The only necessary condition for polarization charging is that there be particles or droplets which have sufficient size relative to their neighbors so that they have a large relative velocity. Water droplets, of course, undergo the same charging but the faster relative growth of ice in clouds (Wegener-Bergeron mechansim), and the higher separation efficiency may explain the causal relationship between the occurrence of ice and the concurrent charge build-up in thunderclouds in mid-latitudes. It remains to explain the differences between the present experimental results and those of Latham and Mason (1962). There appear to be at least three ways in which our results differ from those of Latham and Mason. First, we experimented with natural snowflakes which, as a result of contamination in the atmosphere, should have an electrical conductivity at least one or two orders of magnitude greater than the pure ice used by Latham and Mason. The use of pure ice results in a greatly increased relaxation time and therefore less charge transfer. Second, in the laboratory experiments of Latham and Mason very small crystals were blown at relatively high velocities past a cylindrical probe. Sartor (1965) has shown that only a relatively small amount of charge build-up in clouds can result from the small hydrometers of the size used by Latham and Mason. The velocities were higher than the terminal velocities of the snow crystals used in our experiments and probably resulted in smaller contact times and, perhaps, less charge transfer. Finally, the natural ice particles in our experiments undoubtedly had rough surfaces so that there was more sticking and a larger contact time. The fact that the distribution of the charge trans- ferred to the sphere under a potential gradient is log- normal while the distribution of the original charge on the crystals is normal can be explained by assuming that the size of the crystals is log-normally distributed. In a potential gradient, then, the charge transferred should follow Eq. (5). If the initial charge on the ice crystal is small, the charge transferred will vary as the square of the particle radius. The particle size appears to be log-normally distributed (see Fig. 3). Any power function of a parameter which is log-normally dis- tributed is also log-normal (see Herden, 1960). There- fore, the charge transferred should be log-normally distributed. The original charge on the particle is insignificant when potential gradients are applied so that the original charge distribution does not signifi- cantly affect the final distribution of the transferred charge. 7. Concluding remarks This experiment demonstrates the effectiveness of charging by collisions of polarized ice particles. Follow- ing the ideas of Sartor (1961a, b), it appears that this mechanism could account for the large charging found in glaciated clouds and thunderclouds in general. Further experiments are required to see the effect of temperature, ice crystal shape and size, and impact velocity on the charge transferred in the presence of a potential gradient. Also, higher potentials should be used to follow the dramatic increase in charging at higher potentials observed in these field measurements. Acknowledgments. The authors would like to thank Drs. J. D. Sartor and J. Latham for their helpful dis- cussions, Mrs. W. D. Scott for tending the experiment, taking photographs and making drawings, and Dr. P. V. Hobbs for his critical reading of the manuscript. REFERENCES Bullemer, B., H. Engelhardt and N. Riehl, 1969: Protonic con- duction of ice : High temperature region. Physics of Ice, New York, Plenum Press, 416-429. Burrows, D. A., 1969 : The role of ice in cloud electrification. Ph. D. thesis, Dept. of Atmospheric Sciences, University of Washington. Camp, P. R., W. Kiszenick and D. Arnold, 1969: Electrical con- duction in ice. Physics of Ice, New York, Plenum Press, 450-470. Cole, R. H., and O. Worz, 1969: Dielectric properties of ice I. Physics of Ice, New York, Plenum Press, 546-554. Davis, M. H., 1964: Two charged spherical conductors in a uniform electric field: Forces and field strength. Quart. J. Mech. Appl. Math., 17,499-511. , 1969 : Electrostatic field and force on a dielectric sphere near a conducting plane-A note on the application of electrostatic theory to water droplets. Amer. J . Phys., 37, 26-29. Elster, J., and H. Geitel, 1913: Zur Influenztheorie der Nieder- schlagselektrizitat. Phys. Z., 14, 1287-1292. Herden, 1960: Small Particle Statistics. London, Butterworth's, 84-86. Hobbs, P. V., and D. A. Burrows, 1966: The electrification of an ice sphere moving through natural clouds. /. Aimos. Set., 23, 757-763. Kopp, M., 1962: Conductivete electrique de la neige, en courant continu. Z. Angew. Math. Phys., 13, 431-441. Latham, J., and B. J. Mason, 1962: Electrical charging of hail pellets in a polarizing electric field. Proc. Roy. Soc. London, A266, 387-401. , and C. D. Stow, 1969: Airborne studies of electrical pro- perties of large convective clouds. Quart. J. Roy. Meteor. Soc, 95, 486-500. Magono, C, and T. Takahashi, 1963 : Experimental studies on the mechanism of electrification of ice pellets. /. Meteor. Soc. Japan, 41, 197-209. May 1970 W. D. SCOTT AND ZEV LEVIN 473 Mason, B. J., 1953: A critical examination of theories of charge generation in thunderstorms. Tellus, 5, 446-460. Montgomery, D. N., and G. A. Dawson, 1969: Collisional charging of water drops. /. Geophys. Res., 74, 962-972. Miiller-Hillebrand, D., 1954: Charge generation in thunderstorms by collision of ice crystals with graupel falling through a vertical electric field. Tellus, 6, 367-381. , 1955: Zur Frage des Ursprunges der Gewitterelektrizitat. Arkiv Geofysik, 2, 395-416. Ruepp, R., and M. Kass, 1969: Dielectric relaxation, bulk and surface conductivity of ice single crystals. Physics of Ice, New York, Plenum Press, 555-561. Sartor, J. D. 1954: A laboratory investigation of collision effi- ciencies, coalescence and electrical charging of simulated cloud droplets. /. Meteor., 11, 91-103. , 1961a : Calculations of cloud electrification based on a general charge-separation mechanism. J. Geophys. Res., 66, 831-838. , 1961b: Recalculations of cloud electrification based on a general charge-separation mechanism. /. Geophys. Res., 66, 3070-3071. , 1965: Induction charging thunderstorm mechanism. Problems of Atmospheric and Space Electricity, Amsterdam, Elsevier, 307-310. , 1967: The role of particle interactions in the distribution of electricity in thunderstorms. J . Atmos. Sci., 24, 601-615. — , and C. E. Abbott, 1968: Charge transfer between uncharged water drops in free fall in an electric field. /. Geophv. Res., 73, 6415-6423. Scott, W. D., 1968: Single charging events due to collisions in natural snowfall. Planetary Electrodynamics, New York, Gordon and Breach, 85-99. , and P. V. Hobbs, 1968 : The charging of ice surfaces exposed to natural ice particles. Proc. Intern. Conf. Cloud Physics, Toronto, 609-613. Shio, H., and C. Mogono, 1968: Frictional electrification of ice above and below —IOC. Planetary Electrodynamics, New York, Gordon and Breach, 309-323. Stow, C. D., 1969: On the prevention of lightning. Bull. Amer. Meteor. Soc, 50, 514-520. 50 Reprinted from Journal of Applied Meteorology 9, No. 2, 318-320 318 JOURNAL OF APPLIED METEOROLOGY Volume 9 On the Radar-Measured Increase in Precipitation Within Ten Minutes Following Seeding Joanne Simpson Experimental Meteorology Lab., ESSA, Coral Gables, Fla. 14 November 1969 and 8 January 1970 It will be shown using measurements, a numerical cumulus model, and physical reasoning that the radar- measured precipitation from a seeded cloud will increase markedly (relative to an unseeded cloud) within 10 min following seeding. First it is important to bring out that the University of Miami 10-cm radar sees a layer ranging in height from 2000-9500 ft when the subject cloud is 55 n mi from the radar (Fig. 1, after Senn and Courtright, 1968) which was the mean distance of the seeded clouds in the experiment. The beam is thus centered at an elevation of ~5750 ft above ground at the cloud's range. The reasoning in this note is illustrated schematically in Fig. 2. The case of cloud 6 on 16 May 1968 will be used in this illustration since it is completely docu- mented by measurements, calculations and numerical modeling (Simpson and Woodley, 1969). The control cloud does not grow above the seeding level of 6 km (above cloud base). The top of the seeded cloud has reached 10.3 km after 10 min following seeding. The calculation to be presented will show that precipitation n - 10 - 9 e 7 6 5 4 3 2 I 0 — 5°C level freezing level B beam center Fig. 2. Schematic illustration of the calculations for seeded (right) and control (left) clouds for a period 10 min after seeding. particles from level L in the seeded cloud will reach the radar beam center B in 10 min. The level L is 1 km above level /, the top of the unseeded cloud. Thus, in 10 min following seeding the radar will observe precipi- 35 ELEVATION ANGLES SET TO STUDY CLOUD AT 40 n. mi. 1 T— —r— — r— — i BEAM PATTERNS i 4.5- i I- I ~ 0.5* ±\* tj REGION OFOVERLA 25 15 40 50 RANGE (n mi ) Fig. 1. 10-cm half -power beam widths at various tilts for a typical echo at 40 n mi (after Senn and Courtright, 1968). April 1970 NOTES AND CORRESPONDENCE 319 Table 1. Velocity and fall time of precipitation. Height interval above Drop base < diameter Vt 0.7 VTi r+4 At (km) (mm) (m sec l) (m sec-1) (m sec 1 ) (sec) 7-6 1.2 6.59 1.61 8.61 116 6-5 1.5 6.94 4.86 8.86 113 5-4 1.9 7.42 5.19 9.19 109 4-3 2.3 7.78 7.78 11.78 85 3-2 2.7 8.07 8.07 12.07 83 2-B 3.1 8.22 8.22 12.22 82 588 sec < 10 min tation from the layer l-L in the seeded cloud, which is above cloud top in the unseeded cloud and hence con- tributing no precipitation. The cloud tower rises from / to L in 2-3 min following seeding, simultaneously dropping out an amount of precipitation calculated by our numerical model (Simp- son and Wiggert, 1969). We will first show that precipi- tation originating at L can easily penetrate down to level B within 10 min. We have measurements of the volume median drop size of the precipitation at two levels1, 5 km and cloud base. We assume a cloud water content of 0.8 gm m~3 in the cloud body, a conservative value. With this and a simple continuous collection equation we derive column 1 of Table 1, the volume median precipitation diameter as a function of height, as the particles fall through the cloud growing by coales- cence. To calculate the terminal velocity of water drops we use a; after Kessler (1965), where p0 is taken as 1.2X10_3gm cm-3. The droplet diameter D is in meters and Vt in meters per second. This equation gives smaller values than Mason (1957) and hence is conservative. For ice particles we use the observation of Braham (1964) that the terminal velocity is 0.7 times that of water drops of equal mass. We neglect the small density difference he found between ice and water and we use the simi- larity of our ice formvar replicas to Braham 's to apply the same ratio for our ice terminal velocity. Finally, to complete Table 1 we assume a downdraft of 4 m sec-1 bringing the precipitation particles down. Aircraft measurements2 in this cloud at about the 6-km level showed a downdraft of 4-5 m sec-1. Generally, these downdrafts may be expected to increase down- ward (Malkus, 1955). Therefore, this is a conservative value. Byers and Braham (1949) found considerably 1 Values for higher levels have been taken from the numerical model. Its drop size predictions have checked very well with ob- servations whenever direct checks have been possible. 2 The downdrafts were calculated by Mr. R. Sheets (personal communication), using the radar altimeter and the aircraft atti- tude, power setting, etc., to calculate its sinking speed. larger downdrafts prevailing through a sizable portion of a typical mature thunderstorm. The total time re- quired for a precipitation particle starting at 7 km to reach level B is just under 10 min. We will next show that the amount of precipitation contributed to the radar measurement from the layer L-l in 10 min is large enough to account for the average measured rainfall difference between seeded and control clouds in the interval 0-10 min (Woodley, 1970). The latter amount is about 25 acre-ft or about 18% of the total average difference between seeded and control clouds of 140 acre-ft. The EMB 68 numerical model gives a total fallout from the rising tower as 4.92 gm of water per kg of total mass for the unseeded tower and 8.72 gm kg-1 for the seeded tower for the case of this 16 May cloud. The layer L-l contributes 1.47 gm kg-1 or 39% of the difference between the seeded and unseeded fallouts. A simple cloud physics calculation in progress considers the growth of the fallout from the tower as it descends through the cloud body and the droplets grow by coales- cence. This calculation shows that the final difference between radar-measured seeded and control rainfall is readily accounted for. Here we will only consider the 1.47 gm kg-1 contributed by layer L-l. Taking the mea- sured volume of the tower and multiplying by the appropriate density, we get 7.2X 109 gm of precipitation starting its descent between level L and level /. The drops have the sequence of diameters shown in Table 1 so that the mass increment in each layer is propor- tional to the ratio of diameters cubed. With this, we find that if half the precipitation in the layer L-l is caught in the downdraft we produce 109 acre-ft of rainfall at cloud base. If only 15% of the fallout in layer L-l is caught in the downdraft and carried to cloud base, we get the 25 acre-ft measured difference between average seeded and average control cloud in the interval 0-10 minutes following seeding.3 In conclusion, we note that none of this reasoning depends on an invigorated downdraft in the seeded rela- tive to the control cloud. If the downdraft in the seeded cloud is enhanced relative to the control cloud, we would expect a faster response and a bigger response in seeded vs control rainfall soon after seeding. There is reason to expect the downdraft would be enhanced in the seeded cloud concomitantly with its updraft. Seed- ing has been shown to increase the updraft throughout the cloud body in a very few minutes. In laboratory plumes an accelerated updraft at the core is accompanied by accelerated downdrafts at the outer edges. Finally, the important point to emphasize is that pyrotechnic seeding fills the whole supercooled depth of the cloud with silver iodide and hence rapidly freezes 3 This 16 May cloud produced a total of 850 acre-ft in the first 40 min after seeding, compared to only 26 acre-ft in a comparable period by a control cloud. Hence, the first 10 min after seeding can readily contribute 13% of the difference according to this calculation. 320 JOURNAL OF APPLIED METEOROLOGY Volume 9 all the cloud existing above — 5C. We have shown that the precipitation contained in a layer 2 km deep above — 5C reaches the center of the radar beam within 10 min after seeding. REFERENCES Braham, R. R., 1964: What is the role of ice in summer rain- showers? /. Atmos. Set., 21, 640-645. Byers, H. R., and R. R. Braham, 1949: The Thunderstorm. U. S. Dept. of Commerce, Govt. Printing Office, Washington, D. C, 282 pp. Kessler, E., 1965 : Microphysical parameters in relation to tropical cloud and precipitation distributions and their modification. Geofis. Intern., 5, 79-88. Malkus, J. S., 1955 : On the formation and structure of downdrafts in cumulus clouds. /. Meteor., 12, 350-354. Mason, B. J., 1957: The Physics oj Clouds. London, Oxford Univ. Press, 421 pp. Senn, H. V., and C. L. Courtright, 1968 : Radar hurricane research. Final Rept. to U. S. Weather Bureau, Institute of Marine Sciences, Univ. of Miami, 31 pp. Simpson, J., and V. Wiggert, 1969: Models of precipitating cumulus towers. Mon. Wea. Rev., 97, 471-489. , and W. Woodley, 1969: Intensive study of three seeded clouds on May 16, 1968. Tech. Memo ERLTM-8, Dept. of Commerce, ESSA Res. Labs., 42 pp. Woodley, W. L., 1970: Precipitation results from a pyrotechnic cumulus seeding experiment. /. Appl. Meteor., 9, 242-257. Reprinted from Journal of Applied Meteorology CI 9, No. 6, 951-952 Reprinted from Journal of Applied Meteorology, Vol. 9, No. 6, December, 1970, pp. 951-952 American Meteorological Society Printed in U. S. A. Reply Joanne Simpson Experimental Meteorology Laboratory, NOAA, Coral Gables, Fla. 10 August 1970 The pleasures of working in cloud physics have been considerably enhanced by the constant challenges at every step of Dr. Battan. We aie happy to substantiate further our previous reasoning regarding seeded cloud 6 on 16 May 1968. Extensive studies of this cloud by photogrammetry, radar and aircraft penetrations have been reported elsewhere (Simpson and Woodley, 1969; Simpson and Wiggert, 1970) ; these observations all fit together in supporting the picture presented in my note (Simpson, 1970). The use of a 4 m sec-1 downdraft in my calculation was based on measurements; it should not have been presented as an assumption. Fig. 1 shows measured vertical velocity profiles on two DC-6 aircraft penetra- tions through the cloud at 5.8 km elevation, the first at 4 min before (above) and the second 10 min following VERTICAL MOTION CLOUD 6 PASS 1 MAY 16,1968 19,100 FT _i I i I L 4 3 2 £ 0 S -l -2 -3 VERTICAL VELOCITY CLOUD 6 PASS 2 ~ 18.900 FT MAY 16,1968 1835 TIME (GMT) Fig. 1. Draft profiles in seeded cloud 6 of 16 May 1968 showing vertical motion (m sec"1) as a function of time. Seeding occurred at about 1826. 952 JOURNAL OF APPLIED METEOROLOGY Volume 9 seeding (below). These profiles were constructed by Sheets and Carlson1 using the radar altimeter and the aircraft attitude, power setting, etc., to calculate its sinking speed. Since publication of my previous note, the Sheets- Carlson method of draft determination has been placed on a fairly firm footing in a study by Turbulence Con- sultants, Inc.2 Their tests consisted of a comparison, on six different cloud penetrations, of drafts as measured by the gust probe system and those measured by the Sheets-Carlson method. Good agreement was obtained in draft locations and magnitudes, particularly in the more vigorous clouds. In the figure, the before-seeding (upper) penetration was made 700 m below the top of an actively rising tower (Simpson and Woodley, 1969). By the time of the next (lower) penetration, ~10 min after seeding, the cloud top had grown above 11 km, so that there was 5.2 km of cloud above the aircraft. These profiles show that there was a strong persistent downdraft, of the size used in my calculation, during the most actively rising phase of the cloud. The following data show the photogrammetrically measured rise rates of the tower during this period: Height interval (km) Measured tower rise rate (m sec-1) 7-8 8-9 9-10 10-11 6.1 12.0 9.7 6.0 Average 8.5 Our observations show that it is the rule, not the excep- tion, to find downdrafts, comparable in magnitude to the updrafts, on the downshear side of tropical cumuli in the active and vigorously growing portion of their life cycle. Similar results are reported by Telford and Warner (1962). The next question is whether the downdraft shown in the figure extended down to cloud base. The tempera- ture and accelerometer records of the cloud base air- craft (an S2D of the Naval Research Laboratory) pro- vide nearly definite proof that it did. Of particular interest are base passes made 7 and 13 min after seeding. 1 Personal communication. 2 Communication on file at the National Hurricane Research Laboratory, Coral Gables, Fla. It will appear in a forthcoming report by Sheets and Carlson. On the first of these a 250 m wide region of strong nega- tive acceleration was found in the central portion of the cloud, which was 3.5C colder than the surroundings. On the next pass, the negative accelerations were stronger and the temperature deficit (over a somewhat wider region) was 5C. The aircraft observer, Mr. R. Shecter, estimated a sustained downdraft in this region of not less thin 800 ft min-1, or ~4 m sec-1. This in- dication of a penetrative downdraft in an active cloud is supported by previous data. Years of cloud observa- tions at Woods Hole, only a small fraction of which have been published (Malkus, 1954, 1955; Levine, 1965) show that when a tropical cloud begins to precipitate, the downdraft commonly extends to cloud base and is found there in association with the precipitation shaft. Cloud 6 on 16 May 1968 began to precipitate at 1810 GCT or ~16 min before seeding. Our model of the precipitation growth in a cumulus has been explained quantitatively, using this cloud as an example, in another publication (Simpson and Wiggert, 1970). Briefly, precipitation grows to some extent by autoconversion and collection in the updraft. Updraft air is continually "detrained" (Malkus, 1949, 1954) into the adjacent downshear downdraft where the precipitation particles continue to grow by collection. About 90% of the growth in mass of the precipitation is accreted in the descending portion of its travel. Thus, we expect, and commonly find, that the strongest 10-cm radar echo is found in the downshear, downdraft portion of the cloud. REFERENCES Levine, J., 1965: The dynamics of cumulus convection in the trades — a combined theoretical and observational study. Ph.D. dissertation, Dept. of Meteorology, M.I.T., Cam- bridge, Mass. Malkus, J. S., 1949: Effects of wind shear on some aspects of con- vection. Trans. Amer. Geophys. Union., 30, 19-25. , 1954: Some results of a trade cumulus cloud investigation. /. Meteor., 11, 220-237. , 1955: On the formation and structure of downdrafts in cumulus clouds. J. Meleor., 12, 350-354. Simpson, J., 1970: On the radar-measured increase in precipitation within ten minutes following seeding. /. Appl. Meteor., 9, 318-320. , and V. Wiggert, 1970: 1968 Florida cumulus seeding experi- ment: Numerical model results. Mon. Wea. Rev. (in press). , and W. L. Woodlev, 1969: Intensive studv of three seeded clouds on May 16, 'l968. Tech. Memo. ERLTM-APCL 8, ESSA Research Laboratories, Boulder, Colo., 41 pp. Telford, J. W., and J. Warner, 1962: On the measurement from an aircraft of buoyancy and vertical air velocity in cloud. J. Atmos. Sri., 19, 415-423. Reprinted from Journal of Applied Meteorology M 9, No. 1 , 1 09" 1 22 Reprinted from Journal of Applied Meteorology, Vol. 9, No. 1, February 1970, pp. 109-122 American Meteorological Society Printed in U. S. A. An Airborne Pyrotechnic Cloud Seeding System and Its Use Joanne Simpson and William L. Woodley Experimental Meteorology Lab., ESS A, Coral Gables, Fla. Howard A. Friedman Research Flight Facility, ESS A , Miami, Fla. Thomas W. Slusher Olin Mathieson Corp. Marion, III., R. S. SCHEEFEE Atlantic Research Corp., Alexandria, Va. and Roger L. Steele Mech. Eng. Dept., Colorado State University, Fort Collins (Manuscript received 29 July 1969) ABSTRACT The development, testing and use of an airborne pyrotechnic cloud seeding system is described. Pyro- technic flares producing 50 gm of silver iodide smoke each were developed by two industrial corporations and laboratory tested for nucleation effectiveness in the Colorado State University cloud chamber. A delivery rack and firing system were developed, under ESSA supervision, and installed on its B-57 jet aircfaft. Night flight tests were made of reliability, burn time and flare trajectory. The flare system was used in a Florida cumulus seeding experiment in May 1968 conducted jointly by ESSA and the Naval Research Laboratory, with the participation of the U. S. Air Force, the University of Miami Radar Laboratory, and Meteorology Research, Inc. A randomized seeding scheme was used on 19 supercooled cumuli, of which 14 were seeded and 5 were studied identically as controls. Of the 14 seeded clouds, 13 grew explosively. Seeded clouds grew 1 1 ,400 ft higher than the controls, with the difference signifi- cant at better than the 0.5% level. Rainfall from seeded and control clouds was compared by means of cal- ibrated ground radars. Large increases in rainfall were found from seeded clouds, but at a significance level ranging from 5-20% depending on the statistical test used. A single successful repeat of the experiment could result in rainfall differences significant at the 3% level with the most stringent test. 1. Introduction and physical changes in the seeded clouds and to com- A-, -j-iij j- j-jr pare these with unseeded control clouds, both chosen on A silver iodide cloud seeding system was desired for a ^ . . . !•/-.• • , -J--J1 i ij a statistically randomized basis, modification experiment on individual cumulus clouds J i ,r T7i -j • i • ■,, Some previous randomized seeding experiments are growing over and near the Honda peninsula in May / . . ° ^ iriAo to.- • * j j • • ^i u t-cca summarized in Table 1, including the first results of the 1968. This experiment, conducted jointly by ESSA . ' . 6 . j , , tvt i x> u t u -,,., ,. . May 1968 Florida experimentation. The amount of and the JN aval Research Laboratory with the participa- J r .• r ,i TT o a- i? ,, tt • v r if • silver iodide introduced per cloud is seen to varv widelv, tion ot the U. S. Air rorce, the University of Miami r . Radar Laboratory and Meteorology Research, Inc., the only very hl§h concentrations being achieved with was the sequel to the Stormfury cumulus seeding experi- Pyrotechnics. Since complete and rapid latent heat ment conducted in the Caribbean in 1965 (Simpson release was desired, the aim was to introduce not less el al., 1966, 1967; Simpson, 1967; Ruskin, 1967). than about 100 nuclei per liter into the supercooled The seeding was intended to release as rapidly as portion of the clouds. This figure is based on a calcula- possible all the latent heat of fusion in selected super- tion by MacCready (1959). To achieve this concentra- cooled cumuli. The size of the subject, clouds was about tion in clouds of the size mentioned requires that about 1.5-3.0 km in tower diameter and 6-8 km in height, the 1015 nuclei be introduced and distributed through the cloud bases were at ~ 500- 1000 m, and the freezing cloud in a few minutes. This could be done with 1000 level was at ~4 km at this location and season. gm of silver iodide smoke if the nucleation efficiency The purpose of the experiment was to study with air- is 1012 active particles per gram, which is within the craft and calibrated ground radars the induced dynamic capacity of pyrotechnics (Davis and Steele, 1968). 110 JOURNAL OF APPLIED METEOROLOGY Table 1. Supercooled cumulus seeding experiments using aircraft. t Volume 9 NO. CLOUDS AMT. PER CLO NUCLEI RANDO- IN (ESTIMATEO) PER LITER HOW AVERAGE CHANGE SIGNIFICANT NAME METHOD MIZED SAMPLE KGM AT-IO°C(EST) RESULT MEASURED MAGNIT. % TO 5% LEVEL COONS AND DRY ICE NO 44 2 3-3 6 Kgm p«r mile CLOUD DISSIPATION VISUALLY NO GUNN ( 19511* SINGLE (ALABAMA) 9 0-l8Kgm occosionally OHIO AND CLOUD >60 put into individual eld ALABAMA (OHIO) WARNER AND AGI GENERATOR NO 29 -2 10 1- 10 INCREASED PRECIP VISUAL OBS NO TWOMEY (SINGLE CLOUD) AUSTRALIA (1956) BRAHAM ETAL DRY ICE YES 53 8 -14 I04 INCONCLUSIVE RADAR — _ NO CENTRAL UNITED STATES (1957) MALKUS AND AGI PYRO- NO 12 10 - 20 2XI03- 2XI04 INCR CLD 6R0WTH PHOTOGRAM- 4-6 km — NO SIMPSON TECHNICS ETRY AND CARIBBEAN (SINGLE CLOUD ) AIRCRAFT (1964) 2 3 INCR CLD GROWTH VISUALLY 1.6 km _ NO DAVIS AND DRY ICE NO 9 50 lbs (EQUIV TO 10 - 10 HOSLER (SINGLE CLOUD) I.5X l6'-2.0 X I0"' PENNSYL. Kgm AGI PER CLD. (1967) -2 BETHWAITE AGI GENERATOR YES 26 2X10 1- 5 INCREASED PRECIP AIRBORNE 2I0ACRE 650 YES ET AL (SINGLE CLOUD) (CLD T0PS<-I0C ) HYDROMETEOR FEET AUSTRALIA SAMPLER (1966) BETHWAITE AGI GENERATOR YES 25 -4 2 X 10 01 - 05 INCONCLUSIVE AIRBORNE — — NO ET AL (SINGLE CLOUD) (CLO TOPS<-IOC) HYDROMETEOR AUSTRALIA SAMPLER ( 1966) BATTAN AGI GENERATOR YES - -2 2 X 10 1-5 INCR RADAR RADAR AND - - NO ET AL (AREA) ECHOES, NO CHANGE RAINGACES ARIZONA IN PRECIPITATION (1966, 67) 3 4 SIMPSON AGI PYRO- YES 2 J 10-20 2X10 -2X 10 INCR CLO GROWTH PHOTOGRAM- 16 km. — YES ET AL TECHNICS ETRY AND CARIBBEAN (SINGLE CLOUD ) AIRCRAFT (1967) -3 -2 NEUMANN AGI GENERATOR YES 2XIO-2XIO 0.1 - 5 INCREASED PRECIP RAIN — 18 - 19 YES ET AL (AREA) GAGE3 ISRAEL (1967) -1 -1 2 INCR CLD GROWTH RADAR AND 1 8 km 23 YES DAVIS AGI GENERATOR YES 18 1 6X 10-3X10 5X10 VISUALLY ET AL ll«66 1 ( SINGLE CLOUD) INCR PRECIP. INCR CLOUD DURATION RADAR RADAR 3 mm. (-5ACRE- FT PER CLD.) II MIN 186 YES YE S FLUECK, AGI PYRO- YES _ _ _ INCONCLUSI VE RAI N _ _ NO (I96B I TECHNICS GAGES MISSOURI (AREA) KORIENKO DRY ICE YES 162 _ _ INCR. PRECIP. AIRBORNE 5X10 TONS 240 YES ET AL ( SINGLE CLOUD) WATER (»3 5ACRE .RUSSIA COLLECTOR FT PER (1966) CLD ) SIMPSON AGI PYRO- YES 19 -1 5X10 - 1 5XI02-5XI03 INCR CLD GROWTH AIRCRAFT 3 km 346 YES ET AL TECHNICS FLORIDA (SINGLE CLOUD INCREASED PRECIP RADAR 100-150 1 4 0 ? (1968) ACRE FT (BY 4 0 MINUTES AFTER SEEDING) * DATES IN PARENTHESES REFER TO PUBLICATIONS AS LISTED UNDER REFERENCES f The magnitude change given for Korienko el al. should be 5X103 tons. Most airborne generators would require ~ 1 hr to pro- 2. The pyrotechnics duce the necessary quantity of silver iodide particles Pyrotechnic flares were desired that could be dropped at temperatures near — IOC. This and the distribution from the ESS A Research Flight Facility B-57 jet air- problem precluded their use in our experiments. craft. For optimum distribution, it was planned to drop February 1970 SIMPSON ET AL, 111 twenty 50-gm flares into each cloud top at ~100 m horizontal intervals. The flares were to be ejected on two successive seeding passes, made at right angles to each other ~3 min apart. The flares were to burn at ambient pressure for ~60 sec and to fall ~3 km vertically be- fore burning out. Complete burnout was required for safety in use over land areas. Design goals were es- tablished in terms of laboratory tests of the efficiency and flight tests of the ignition reliability. The efficiency goal was 1010 active nuclei gm_1 at — 5C and 1012 at — IOC, with equal or better efficiency at lower tem- peratures. The tests of efficiency and related matters were to be undertaken in the isothermal cloud chamber at the Colorado State University according to prescribed procedures (Steele, 1968). The flight goal was that 80% of the flares should ignite and remain ignited until burnout when dropped from 20,000 ft. The Olin Mathieson Corporation and the Atlantic Research Corporation undertook the development of suitable pyrotechnic mixes producing the silver iodide. The former company worked on its own initiative, the latter under contract with ESSA. Altogether more than 50 mixes were developed and tested. Preliminary tests were run at the company laboratories for such vital properties as safety, shelf life and burn characteristics, and the most promising mixes were then sent to Colo- rado State University (CSU) for efficiency tests in the cloud chamber. The work by the Atlantic Research Corporation is described in detail in a report by Schef- fee et al. (1967). In a systematic program of research carried out to develop, test and evaluate pyrotechnics for dissemination of Agl in a form suitable for cloud seeding, a large number of pyrotechnic compositions containing either powdered Agl or AgI03 as the source of Agl particles in the smoke were developed and found to be safe and reliable in terms of ballistic and physical properties and shelf life. Results of the program indicated that the most promising mixes containing Agl were composed of KCT04 and thiourea as the oxidizer and fuel, respectively, while those containing AgI03 were composed of KCIO4, magnesium, and nitrocellulose plastecized with triacetin. These com- positions were found to be safe to manufacture and use and to have acceptable physical properties and shelf life. Better combustion characteristics were found for compositions containing AgI03 and magnesium than for Agl-KCIO-i-thiourea in terms of ease and uniformity of combustion at simulated altitudes up to 40,000 ft. Of the several dozen mixes tested at CSU, those most efficient in the —8 to — 15C temperature range had two properties in common. The first was high percentages of metallic condensed species in the output, and the second a high flame temperature (>2000K). With the high flame temperature, the silver iodate is reduced, and the products are vaporized/dissociated and react to form solid silver iodide during the quenching proc- Table 2. Composition of Atlantic Research Corporation formulation 1-20M-45A. Material Per cent by weight Silver iodate 45.0 Potassium perchlorate 27.0 Magnesium 20.0 Nitrocellulose 4.0 Triacetin 4.0 ess. The high burn temperatures should favor nuclea- tion efficiency by shifting the particle size distribution in the smoke toward smaller particles. The metallic species consisted of high percentages of aluminum and magnesium oxides (roughly 20-30%) and smaller percentages of alkali chlorides and iodides. Aluminum and magnesium oxides are active freezing nuclei, starting at — 6.5C and — 9.3C, respectively (Fukuta, 1958). In the case of the alkali chlorides and iodides, a possible explanation has been given by St. Amand et al. (1969). They suggest, in the warm range of supercooled cloud temperatures, that nucleation may take place predominantly by droplet freezing (con- tact nucleation), rather than by sublimation and dif- fusion as at lower temperatures. With only pure Agl, they assert that it is unlikely that condensation will occur at all in the regimes of saturation pressures found in nature, and particles > 1 n are required. With super- saturations of ~3%, particles as small as 0.01 n be- come effective as condensation nuclei. St. Amand et al. state that the process of condensation can be made vastly more effective by treating the Agl with alkali iodides and chlorides, which should reduce the vapor pressure of water over the surface of the material by much more than 3% locally. Experimental evidence supporting this hypothesis is presented by Mossop (1968) and jiusto and Kochmond (1968). The chemical compositions of Atlantic Research formulation 1-20M-45A and Olin Mathieson formula- tion X1055 chosen for the field experiment are given in Tables 2 and 3. The reaction of Agl with likely combustion products is an important consideration in the design of pyro- technic compositions. Since the computation of equi- librium mixtures is arithmetically complex and la- borious, equilibrium calculations of mixtures of com- pounds at an assigned temperature and pressure were carried out at both the Atlantic Research Corporation and the Olin Mathieson Corporation by means of digital Table 3. Composition of Olin Mathieson Corporation formulation X1055. Material Per cent by weight Silver iodate Potassium iodate Magnesium Aluminum Strontium nitrate Polyester binder 53.0 8.0 5.6 12.9 10.5 10.0 112 JOURNAL OF APPLIED METEOROLOGY Volume 9 computer programs. These programs are used on a routine basis primarily for the computation of rocket propellant specific impulse and associated interior ballistics parameters in which it is assumed that com- bustion at an assigned pressure is adiabatic, thai expansion of the combustion products to an assigned exhaust pressure is isentropic, and that thermodynamic equilibrium exists between the combustion products at both combustion and exhaust pressures. Based on available variations of this program, equilibrium values of the flame temperature and combustion product composition of ARC formulation 1-20M-45A and Olin formulation X1055 were computed and are given in Tables 4 and 5. These results may or may not be repre- sentative of the actual species in the products but plume sampling by ARC does verify some of the predicted outputs. Tables 4 and 5 show a considerable degree of dissocia- tion of silver iodide gas into atomic species. The degree of dissociation increases with the flame temperature. Recombination will occur as the combustion products cool. The calculations also show that in the case of the composition containing potassium perchlorate, potas- sium chloride and silver iodide are the major stable products rather than potassium iodide and silver chloride. This was confirmed by x-ray analysis of Table 4. Equilibrium composition of the combustion products of composition 1-20M-45A for adiabatic combustion at 1 atm.abc Combustion product composition [gm mol (100 gm)-1] Specie Amount Specie Amount Ag(g) Ag(l) AgCl(g) AgH(g) Agl(g) Agl(l) AgOfe) Ag2(g) C(g) C(s) CO(g) C02(g) CKg) Cl,(g) ClO(g) 1(g) life) ICl(g) NOfe) NOI(g) N2(g) H(g) HCl(g) HI(g) H2(g) 0.1466 0 0.0020 0.0002 0.0100 0 0 0.0002 0 0 0.1548 0.0983 0.0266 0 0.0001 0.1207 0 (i 0.0054 0 0.0153 0.0337 0.0230 0.0014 0.0199 K(g) KClfe) KC1(1) KCl(s) Klfe) Kl(l) K2I2(g) KO(g) KOH(g) KOH(l) Mg(g) MgCKg) MgCl2(g) Mgcua) Mgl(g) Mgl2(g) MgO(g) MgO(l) MgO(s) MgOH(g) Mg(OH)2(g) O(g) 02(g) OHfe) H20(g) 0.0359 0.1315 0 0 0.0216 0 0 0.0011 0.0048 0 0.0865 0.0071 0.0024 0 0.0054 0 0.1278 0 0.5721 00201 0.0011 0.0584 0.1098 0.0564 0.0930 Table 5. Equilibrium composition of the combustion products of composition X1055 for adiabatic combustion at 1 atm.a'b>c Combustion product composition [gm mol (100 gm)-1] Specie Amount Specie Amount Ag(g) 0.1011 Kg) 0.0311 AgH(g) 0.0007 Agl(g) 0.0841 Kfe) 0.0030 Agl(l) 0 KCN(g) 0.0001 Ag2(g) 0.0008 KCN(l) 0 Klfe) 0.0343 Alfe) 0.0350 KI(1) 0 Al(l) 0 KHfe) 0 AlH(g) 0.0021 K2(g) 0 AlOH(g) 0.0002 K2I2(g) 0 Al20(g) 0.0429 AlN(g) 0 Mgfe) 0.1584 AlN(s) 0.0357 MgH(g) 0.0013 Ab03(s) 0.1597 Mgl(g) 0.0700 A1203(1) 0 Mgl2(g) 0.0005 MgO(g) 0 Cfe) 0 MgO(s) 0 C(s) 0 MgN(g) 0 CO(g) 0.5905 C02(g) 0 N*(g) 0.03122 CH2(g) 0 NHfe) 0 CEUfe) 0 NH2(g) 0 C2H(g) 0 NH3(g) 0 C,H2(g) 0.0001 CNfe) 0 Srfe) 0.0495 SrHfe) 0.0001 Hfe) 0.0066 SrO(g) 0 HCN(g) 0.0010 SrO(s) 0 HI(g) 0.0044 SrOH(g) o H2(g) 0.3101 H20(g) o1 "■ Flame temperature = 2296K. b Total moles of gas= 1.5589 gm mol (100 gm)™1. c The letters g, 1, s, in parentheses represent gas, liquid and solid, respectively. samples collected in the smoke plume, where the latter products could not be detected at the 5% level. Tables 6 and 7 give the expected combustion products when the smoke is cooled to ambient temperature, if one assumes recombination of dissociated species and, in the case of formulation X1055, oxidization of excess fuel with atmospheric oxygen. The flame temperatures (estimated by calculation) were 3082K for the 1-20M-45A mix and 2296K for the X1055 mix. Attempts are currently underway to measure the flame temperatures. 3. Laboratory tests A facility has been constructed at CSU for testing and comparing silver iodide generators and other de- Table 6. Expected exhaust products at ambient temperature of formulation 1-20M-45A. Compound Amount gm (100 gm of mix) a Flame temperature = 3082K. b Total moles of gas =1.4208 gm mol (100 gm)-1. 0 The letters g, 1, s, in parentheses represent gas, liquid and solid, respectively. Silver iodide Potassium chloride Magnesium oxide Carbon dioxide Water Nitrogen 37.4 14.5 33.2 11.1 3.3 0.5 February 1970 SIMPSON ET A L 113 Table 7. Expected exhaust products at ambient temperature of formulation X1055. Amount* Compound gm (100 gra of mix)-1 Silver iodide 44.0 Potassium iodide 6.1 Magnesium oxide 9.5 Aluminum oxide 24.1 Strontium oxide 7.2 Nitrogen 1.4 Carbon dioxide, water etc. 31.7 * Total adds up to more than 100, since some oxygen to burn the metal fuels is incorporated from the surrounding atmosphere. vices for weather modification experiments. The test facility has been described in detail by Steele (1968). One of the main objectives of the laboratory tests is to determine how many active freezing nuclei are produced per gram of silver iodide in the smoke. This is done by burning the flares in a wind tunnel, collecting a smoke sample in a syringe, diluting it a known amount, and finally introducing the dilute smoke into a temperature-controlled chamber in which a super- cooled cloud is maintained. The number of ice crystals in a fixed portion of the chamber are counted and re- lated to the mass of silver iodide burned. The intention in the tests is to burn the flares and nucleate the cloud under as realistic conditions as possible. Free fall is currently being simulated in a ver- tical wind tunnel in which actual free fall velocities can be simulated by LaGrangian techniques. Wall effects are minimized, as the tunnel has a test section of 1.15 m. Flows of 3100 m3 min-1 are possible at velocities up to 62 m sec-1, which is a little faster than the ter- minal fallspeed of our pyrotechnics. Recent results show that the measured nucleation efficiency depends strongly on ventilation past the pyrotechnic. Fig. 1 shows the test results for Atlantic Research formulation 1-20M-45A and Olin Mathieson formula- tion X1055 under conditions as close to field conditions as possible. In the cloud chamber, the cloud liquid water content was controlled at 2.0 gm m~3. Both mixes comfortably exceed the program goal of 1012 nuclei gm-1 at-lOC, but it is unlikely that either has much effectiveness at -5C. The X1055 mix produced 1012 nuclei gm"-1 at — 8C but no count was detectable at — 7.5C which means an effectiveness of less than 1010 nuclei gm-1. For the 1-20M-45A mix no data are yet available at temperatures warmer than — 9.5C where the effectiveness was 5X1011 nuclei gm-1 and falling off rapidly. In dealing with steady-state silver iodide generators Steele and Davis (1969) found a sensitive dependence of efficiency upon liquid water content. In the range just above 1 gm m~3, for example, increasing the cloud water content by only 50% increased measured nuclea- tion efficiency of the generator by a factor of 100 at temperatures in the range of — 12C. For this reason, our pyrotechnics were also tested at controlled cloud water contents of 1 gm m~~3. No detectable differences from Fig. 1 were measured. Therefore, in normal tropical cumuli with liquid water contents of 1-3 gm m~3 it would not be reasonable to use these p)Totechnics at temperatures > — 8C. With this reservation, the mixes performed satisfac- torily, with efficiencies close to 1013 nuclei gm-1 at — IOC and better than 1015 at -20C. As shown by Davis and Steele (1968) and by Scheffee and Steele,1 coagulation of smoke particles is a major problem with either fast burn rates or slow ventilation speeds. For this reason, Atlantic Research Corporation scientists are currently working on a mix similar to 1-20M-45A with a slower burner rate, with the hope of increased efficiencies at the warmer temperatures. Work is also underway to test the hypothesis that with these pyrotechnics the coagulation effect masked the dependence of efficiency upon cloud water content. For this purpose experiments are underway in which the concentration of particles in the pyrotechnic flame is varied over a range of two decades of lower concentration. 4. Flare configurations and delivery system The standard aircraft signal flare case was found to be sufficient size to meet the 50-gm Agl output require- 10" 69- 25 gm/min. ni-L ■ OLIN X 1055 Agl BURN RATE • ARC I-20M-45A Agl BURN RATE 177-125 gm/min. LIQUID WATER CONTENT = 2 0 gm/m5 AIR VELOCITY PAST PYROTECHNIC SAMPLE = 62 m/soc. _J I I I l_ -8 ) -10 -12 -14 -16 TEMP. °C -18 -20 -22 _ Fig. 1. Nucleation effectiveness of the two pyrotechnic composi- tions used in the 1968 Florida experiment shown as function of temperature. Wind tunnel ventilation was 62 m sec-1 and cloud chamber liquid water content 2 gm m-3. 1 Production of silver iodide smokes by pryotechnics. Paper listed by title only in Proc. First Natl. Conf. on Weather Modifi- cation, Albany, 1968. 114 JOURNAL OF APPLIED METEOROLOGY Volume 9 SEALANT CLOSURE DISC SPACER DISC CANDLE CASE FLARE COMPOUND FIRST FIRE WASHER EXPULSION CHARGE WAD ELECTRIC SQUIB POTTING COMPOUND FLARE CASE Fig. 2. Diagram of flare cartridge used with mix X1055 in 1968 Florida program ; 1-20M-45A cartridges had the same case and were similar in construction. merit. The unique feature of the signal flare cartridge as adapted to this application was an electric squib for ignition. A sketch of this 40 mm outside diameter by 96 mm long device is shown in Fig. 2 and a photograph in Fig. 3. The flare cartridge was designed to use the exhaust gas pressure to expel the candle to assure positive ignition while providing mild fail-safe expul- sion. The flares weigh a total of 120 gm and cost about $14.00 each. The firing control for the dispensing system is pro- vided by an AN/ALE-20 flare ejector set. The ESSA Research Flight Facility (RFF) installation is a slightly modified version of the set originally manufactured by the Dynalectron Corporation for military applications. The AN/ALE-20 flare ejector consists of the following components: 1) control panel (Fig. 4), 2) junction box, 3) stepping switch assembly, and 4) in the present RFF configuration, flare mounting racks. Fig. 5 is a func- tional diagram of the overall flare-dispensing system. The RFF B-57 aircraft carries two flare-mounting racks, each housing 56 flares. The mounting location of the rack was suggested by the RFF, the Olin Mathieson Corporation designed and manufactured the rack, and the RFF designed the mating hardware and electronics. Currently, the system is limited to the B-57 aircraft, but it could readily be installed on almost any other type of aircraft. The racks themselves are 18 inches long (parallel to the longitudinal axis of the aircraft), 16 inches wide, 4^ inches deep, and weigh ~50 lb each unloaded. Each rack contains 56 steel cylinders, which house the flare canisters arranged in an 8X7 matrix, which are fired in a fixed sequence. The racks are installed on the left and right undersides of the aircraft wing, with the output end of the tubes mounted flush with the ex- terior surface. The flares are ejected downward into the slipstream during flight. To eject and ignite the flare, a 28 Vdc, 1 A (approxi- mately) pulse of 35-msec duration is supplied by the AN/ALE-20 flare ejector system to the selected flare (or flares). The pulse ignites the firing of the electric squib that is bonded to the back of the pyrotechnic Fig. 3. Photograph of two flares used in Florida 1968 experiment (centimeter scale). February 1970 SI M PSON ET AL. 115 material within each canister (Fig. 2), causing the Agl flare to be ejected and the first fire or match mixture to be ignited. The control panel (Fig. 4) is located within the B-57 aircraft at the flight meteorologist's position. The setting of the controls on this component of the AN/ ALE-20 system determines the number of flares ejected and the interval between flare ejections. Flare ejection can be initiated manually with the "release" button or automatically by establishing a firing program with other control panel settings (i.e., "interval selector" and "burst selector"), the selection of the number of flares per burst, and then initiating the firing program through the "release" button. The "release" button thus serves to initiate the firing program established by the other control panel settings. Available options permit the selection of from one to three flares per burst. Under our operating condi- tions in 1968, this switch was set in the "1" position, which would indicate that only one flare per burst was fired. Automatic firing interval selection from 2-20 sec is provided. In our 1968 program the flares were ejected manually to insure an even distribution through- out the active portion of the cloud. On bombing runs, the B-57 was flown at a true airspeed of ~150 m sec-1, and the flight meteorologist therefore pressed the "release" button approximately three times every 2 sec in order to deliver roughly one flare per 100 m of active cloud. CONTROL PANEL AN/ALE-20 JUNCTION BOX -STEPPING SWITCHES V : rack ; — — : rack : — Fig. 5. Functional diagram of overall flare- dispensing system. There are several safety items in the AN/ALE-20 flare ejector system. Radio noise filters are incorporated to prevent ac voltages in the 240 to 1000 MHz fre- quency range from causing erratic operation of the unit and/or accidental initiation of flare firing. There are also means of rapidly ejecting all flares in flight by a "fast train switch," which serves to salvo (simul- taneously discharge) all flares from both racks in suc- cession at a rate of one flare every 65 msec. While the flares do have to be carefully handled and stored, they do not require specially trained pyro- technic experts for loading. Normal loading is approxi- mately 1| man hours per rack. Figs. 6 and 7 show side and front views of the rack in the "down" or loading position. The delivery system costs about $20,000, including installation. Details of its operation and use are described in a manual by Conrad el al. (1969). 5. Flight tests The major consideration in the development of this system was performance under actual flight conditions. Several configurations of units with various amounts Fig. 4. Control panel of AN/ALE-20 flare- ejector delivery system. Fig. 6. Side view of loading flare rack on ESSA B-57 aircraft, showing connecting circuitry from stepping switch (inside air- craft) to individual flares via the rack terminal strips. Nose of aircraft is on left. 116 JOURNAL OF APPLIED METEOROLOGY Volume 9 Fig. 7. Front view of flare rack (in "down" position on ESSA B-57 aircraft) looking toward tail of aircraft. Numbers on flares indicate firing sequence. and types of expulsion and first fire materials were evaluated in flight. The first series of tests was con- ducted in daylight, with observers on the ESSA DC-6 following the B-57 seeder aircraft. These tests were adequate for tailoring the types of ignition materials, but the full fall of the flares was hard to observe for measurement of burn characteristics and trajectory. A subsequent series of nighttime flight tests was undertaken at Cape Florida State Park, located at the southern end of Key Biscayne or about 7 mi south- southeast of downtown Miami. The B-57 flights were made parallel to the beach. The flare drops were monitored by observers on the beach who were in radio communication with the aircraft. Time exposures were taken of all drops, providing information on flare Fig. 8. Time exposure photograph of nighttime release of two ARC 1-20M-45A flares ejected at 20,000 ft. Fig. 9. Time exposure photograph of nighttime release of five Olin X1055 flares ejected at 20,000 ft. Streak on top is aircraft's landing light, on for exactly 10 sec. Aircraft's true airspeed is 400 ft sec-1. reliability, burn time and trajectory. Representative photographs of an ARC and Olin flare test are shown in Figs. 8 and 9, respectively. The aircraft was flown at 400 ft sec-1, and the landing light was turned on for 10 sec simultaneously with the first release. The light streak is thus 4000 ft long and provides a distance scale. Both groups of flares followed similar trajectories, moving forward only about 1500 ft from the ejection point. This feature insures accurate bombing when the flares are released within the desired portion of the cloud tower; little chance exists of missing the cloud or of dropping flares into the wrong tower or into clear air. When dropped from 20,000 ft, the Atlantic Research flares had a burn time of 30 sec and burned out in 4500 ft of fall. The Olin flares had a burn time of 80 sec and burned through about 12,000 ft. Both sets of flares thus had a terminal fallspeed of ~150 ft sec-1. The Olin flares were tested with units having both 10 gm and 20 gm of first fire material. Twenty-five of 25 units with 20 gm first fire burned completely, while only 9 of 25 units with 10 gm of first fire burned com- pletely. The other units went out after the first fire was consumed because of the high velocity and tum- bling rate during the first few seconds after ejection. Twenty grams of first fire sustained burning during deceleration to a velocity where the X1055 would remain ignited. February 1970 S I M PSON E T A L 117 A breakdown of the tests with 20 gm of first fire is as follows : Successful tests 15 of 15 2 of 2 2 of 2 3 of 3 3 of 3 Altitude (ft) 20,000 15,000 12,000 11,000 10,000 The low altitude tests were conducted (over water) to check the calculated vertical fall distance during burning. This was 10,000 ft when the drops were made at 10,000 ft. When drops are made from 20,000 ft, the lower ambient air density permits the 20% greater fall distance. Unfortunately, the 1-20M-45A flares had both ejection and ignition problems due to poor squibs at this stage of development. Only 50% of the 30 flares tested ejected, and of these only 76% burned com- pletely. A slightly better ejection record was obtained in the field. On the first two days of the program, 1-20M-45A flares were used with a correspondingly larger number ejected to compensate for unreliability. Then the switch was made to the more reliable X1055 flares. Unfor- tunately, some with the 10 gm first-fire mix were inadvertently used on the last five days of the program. Careful post-operational checks of the flare loading showed that only one seeded cloud (the first one) could have received as little as 400 gm of silver iodide, while the remaining ones almost surely received 650 gm or more. 6. Design of the 1968 Florida experiment The field phase of the 1968 Florida cumulus seeding program encompassed the period 15 May-1 June, during which time there were 13 days of successful flight operation. Participating in the program were the Experimental Meteorology Laboratory (EML) and the Research Flight Facility (RFF) of the Environ- mental Science Services Administration (ESSA), the Naval Research Laboratory (NRL), the Radar Mete- orology Laboratory of the University of Miami, the U. S. Air Force, and Meteorologv Research, Inc. (MRI) of Altadena, Calif. Aircraft altitudes and tracks flown are shown in Fig. 10. The RFF supplied two aircraft, a DC-6 for com- mand control, cloud physics measurements, and pho- togrammetry at 19,000 ft (~— 9C), and a B-57 for seeding and monitoring cloud top. The NRL supplied two aircraft, a WC-121 Super Constellation for cloud physics measurements at 17,000 ft (~— 5C) and a S-2D for measurement of rainfall and other parameters at cloud base. The Air Force provided a C-130 for drop- sondes at 90-min intervals on experimental days. The Radar Laboratory contributed its calibrated 5- and 10- cm ground radars, which were used to infer rainfall from cloud base. These radars and their use will be discussed fully in a subsequent paper. MRI installed and operated a condensation nucleus counter, a con- tinuous cloud replicator and a hydrometeor foil sampler on the ESSA DC-6 and installed a foil sampler on the Navy S-2D. The numerical cumulus model developed by Simpson FLIGHT TRACKS OF EXPERIMENTAL AIRCRAFT B- 5T MONITORING FLIGHT ALTITUOES (FEET) AIRCRAF i DC-6 ; WC-121 , S-20 B-57 (SEEDER) POSITIONS OF FLARE DROPS PLAN VIEW 2000-3000 PROFILE Fig. 10. Plan view (left) and profile view (right) of aircraft tracks in Florida 1968 cumulus experiment. 118 JOURNAL OF APPLIED METEOROLOGY Volume 9 -i H h h ■*s HI — a u u x » 3- is & i i ^ -t «- >- >- >- < < < 2 2 2 O O O CO IO to IO 5 CD m Isl M o CM CM m 1- t S i^- ao en S CP h- 00 H' — — — O UI o or >- >- >- < < < 2 2 2 U)DN CO o CM tO ZQn M IM LU Ul i- O 0> . » CD ■£ «o" o}t!2 It m 2 z o o > V < < < - >- or ao < < < < S 2 o z o 2 2 O - z CM CM CM o or N N M ui p a> CO ^ ui ^ ■» o to RY S MES 7. 17 Cn o — CM co oS < H •5 PRII AND MAY >- > < < 2 2 w CO * en cr> < UI — — UJhN IM IM or < k IO (£ < <=> to to o f- o z — — CM UI UI - > > Q < < < z 2 2 2 < io co co o — — — UI N N IM or O IO CM IO tO CM o> h- co - CM to ' February 1970 SI M PSON ET AL 119 and Wiggert (1969) was run on the Miami 1200 GMT radiosonde each possible operational day. If the model predicted that all horizontal tower sizes would either grow naturally or would fail to grow even if seeded, no operation was scheduled. If it predicted good seed- ability or potential growth from seeding (see Simpson et al., 1967), the command DC-6, the WC-121 and Air Force C-130 were launched for a day's operation. After rendezvous at a predesignated point, these aircraft surveyed the experimental area for clouds that might meet the selection criteria. These were supercooled clouds that must be relatively isolated, with tops in the 19-26,000 foot range. If suitable clouds were found, or expected within an hour, the shorter range seeder and cloud base air- craft were launched. When all project aircraft were joined together (by radar and/or visually), a cloud was selected for experimentation by one of the first two authors. The monitoring aircraft (DC-6, WC-121 and S-2D) made an initial penetration of the cloud while the seeder aircraft broke from a position slightly above and to the right of the command aircraft to set up for a seeding run (Fig. 10). If the cloud chosen neither died nor grew above about 26,000 ft, the final go-ahead was radioed to the seeder pilot ; he opened one envelope from his random- ized set of instructions for a decision whether or not to seed. Regardless of which decision was made, the flight pattern was exactly the same: one pass through cloud top, followed by a pass at right angles to the first ap- proximately 2-3 min later. If he had received a seed instruction, 10 silver iodide flares2 were dropped at about 100 m intervals on each pass. Following the seeding run, the B-57 aircraft monitored the cloud top, following it up as it grew. In addition to frequent top height reports, the pilot obtained valuable nose camera motion pictures and a sounding of the air near the cloud. The Air Force C-130 remained over water but as close as possible to experimental clouds, ejecting dropsondes from 30,000 ft and recording winds and temperatures at that level. At the time of cloud selec- tion, the scientists at the University of Miami Radar Laboratory were informed of cloud location. They immediately began monitoring the cloud in a set sequence to be described elsewhere. All aircraft monitored the experimental cloud for as long as practicable (sometimes 1 hr) after the seeding pass. The NRL aircraft made repeated penetrations of the cloud, while the DC-6- flew a compromise pat- tern, a rectangle with the cloud centered on one of the long sides of the rectangle (Fig. 10). Three of the legs provided cloud photogrammetry (see Simpson, 1967), while the last leg served as a cloud penetration run. The randomization scheme adopted for the May 1968 program was similar to that used in the 1965 2 When 1-20M-45A flares were used, 15 per pass were dropped to compensate for unreliable ignition. Stormfury experiments (Simpson et al., 1967). Two hundred envelopes in sets of 10 were prepared by Mr. J. Cotton of the Meteorological Statistics Group of ESSA. The instructions were weighted 0.65 vs 0.35 in favor of the seed instruction. There were not more than two consecutive "no seed" and not more than three consecutive "seed" instructions. The details of the series were not known to anyone involved in the project, nor did the experimenters know of the actual decision in each case until the aircraft landed on completion of a day's work. A new set of 10 envelopes was begun on each day. 7. First results of the Florida 1968 seeding program A total of 19 experimental clouds was selected from the command control aircraft. Fourteen were seeded and five were used as controls. The dates and locations of all experimental clouds are shown in Fig. 11. A cloud summary for each cloud is given in Table 8. The cloud top heights were first measured by the B-57 and then checked by photogrammetry. Heights are given in pressure altitude. The average growth following the seeding run was 12,500 ft for the 14 seeded clouds and 1100 ft for the five control clouds. The difference is 11,400 ft, which is significant to better than 0.5% based on a two-sided "t" test. The average maximum top of the seeded clouds was 35,800 ft, and the corresponding figure for the controls was 25,800 ft. Thirteen of the 14 seeded clouds underwent explosive growth; one died without growth. Of the 13 explosive growths, 10 oc- curred soon after seeding and involved the actual tower seeded, while three were delayed or "hesitation" growths, where a newer tower than the one originally selected for seeding appeared and grew. Verification that the silver iodide p}TOtechnics burned was made by in-cloud measurements of ice nuclei. The measurements were made in a Bigg-Warner expansion chamber on the DC-6 (Kline and Brier, 1961). From a chamber base temperature of — 12C the cloudy air was cooled by expansion to — 20C and the activated ice nuclei were counted as they fell into a sugar solution at the bottom of the chamber. The cold box was "calibrated" in clear air prior to each series of cloud runs so that clear air counts were in the range 0-0.4 per liter. The remaining counts are therefore relative values to the calibration for clear air. The nuclei measurements are summarized in Fig. 12. All of the experimental clouds are not represented because the cold chamber was inoperative on several days. The ice nuclei measurements indicate that the pyrotechnics burned in the experimental clouds. In only one of the 10 seeded clouds in which there were measurements was the maximum post-seeding nuclei count less than the pre-seeding count. Two of the 10 seeded cases were indeterminate because of no pre- seeding nuclei count. In five instances the nuclei count 120 JOURNAL OF APPLIED METEOROLOGY Table 8. Summary of results of May-June 1968 cloud seeding program. Volume 9 DATE UJ Z> CD or -J 3 o O uj <->S u.o£ t- "1 TIME OF DURATION ACTION SEEDING ALTITUDE ESTIMATED TOP TOP AT MAX TOP TOP GROWTH 0- 5z la"' SEEDING RUN MIN SEC (WITHIN 100 FT.) TEMP. AT SEEDING SEEDING AFTER SEEDING AFTER a I- iZ (GMT) * (TO NEAREST °C ) (FEET)K ( FEET) * SEEDING RUN MAY/15/68 1 5 1930 193859-194324 4 25 S 19,100 -35.0 30,000 4?, 500 12,500 MAY/16/68 2 5 1753 180050- 180450 4 20 S 20,200 -1 0.0 19,000 19 ,000 0 MAY/16/68 3 6 1822 182409- 182901 4 52 s 20,200 - 16.0 22,000 40,500 18,500 MAY/16/68 4 8 1937 194855- 195222 3 27 s 20,200 -18.0 23,000 45,000 22,000 MAY/19/68 5 1 1755 175520- 175853 3 33 s 20,300 -15.0 22,000 34,000 12,000 MAY/19/68 6 4 2006 201035- 201232 1 57 NS 20,000 -13.0 21,500 2 1 ,500 0 MAY /2 0/68 7 1 1748 175757- 180051 2 54 NS 20,300 -17.0 23,000 23,000 0 MAY/20/68 8 5 1908 190945- 191230 2 45 S 18,500 -12.0 20,000 36,000 16,000 M AY /2 1/68 9 2 2034 203555-203825 2 30 S 19,200 -16.0 23,000 40,000 17,000 MAY/26/68 10 9 1738 174138- 174440 3 02 NS 20,000 -13.0 21 ,000 21,000 0 MAY/26/68 II II 1823 182455-182800 3 05 S 19,300 -24.0 26,000 36,000 10,000 MAY/27/68 12 1 1529 153230- 153504 2 34 NS 20,200 -34.0 29,300 31 , 500 2,000 MAY/27/68 13 2 1618 162600- 162855 2 55 S 20,250 -27.0 26,000 37,000 1 1,000 MAY/28/68 14 5 1635 163850- 1641 37 2 47 S 18,700 - 12.0 19,300 32,500 13,000 MAY/30/68 15 6 1659 170137- 170440 3 03 NS 20,300 -310 28,500 32,000 3,500 MAY/30/68 16 7 1750 175147- 175437 2 50 S 21,000 -22 0 25,000 33,000 8,000 MAY/30/68 17 8 1842 184845- 185141 2 56 S 20,400 -31.0 28,500 37,000 8,500 MAY/30/68 18 10 1942 193630- 193836 2 06 S 20,000 - 16 .0 2 1 , 000 38,000 17,000 J'JNE/I /68 19 8 1824 182817- 183059 2 42 s 20,200 -13.0 21,000 31 ,000 10,000 * HEIGHTS IN PRESSURE ALTITUDE in the seeded clouds jumped an order of magnitude or more following seeding. In view of the difficulty of directing the DC-6 back to the seeded portion of the cloud, this verification is regarded as very good. There were ice nuclei measurements in two control clouds; one showed a decrease in nuclei following the seeding pass and the other showed a slight increase. 8. Conclusions and future work In terms of cloud growth, the 1968 Florida program was much more successful than the 1965 Stormfury Caribbean program. In 1968, both a larger fraction of the seeded clouds grew (93% vs 66%) following seed- ing, and the average difference between seeded and control cloud growth was more than twice as great (11,400 ft vs 5,200 ft). An important reason was the use of the comptiter program in real time so that all but one case of predicted poor seedability were excluded. In 1965 it was found only a posteriori that the one- third of the seeded clouds that failed to grow were seeded under conditions of poor seedability. Other reasons for the better results in 1968 are probably a more effective seeding technique and the more continental character of the clouds. More and smaller pyrotechnics ejected on two successive passes at right angles not only give better distribution within a cloud but enable fresh towers to receive seeding material. Continental clouds quite likely have a greater tendency than maritime clouds for repeated tower gen- eration in or near the same spot. Additional effects of continentality, such as higher water contents dis- tributed in more smaller drops, are also being inves- tigated. Further work with the data from this program falls into five main categories : 1) Quantitative analysis of the rainfall data on all "go" clouds and numerous others. The primary analysis tool is the calibrated ground radars, supplemented by the S-2D .aircraft foil sampler records and raingage measurements. 2) Numerical model studies of all "go" clouds based on the actual sounding nearest the cloud in space and time. 3) Analysis of each cloud with the penetration data obtained on the monitoring aircraft to study the dynamics and physics of each cloud and the changes following seeding. 4) Photogrammetric study of each cloud based on the aircraft time-lapse cameras and on the flight tracks determined by Doppler navigation. February 1970 SI M PSON ET AL. 121 LEGEND DATE CLOUD ACTION 1 MAY 15, 1968 5 S 2 MAY 16, 1968 6 S 3 MAY 16, 1968 8 s 4 MAY 19, 1968 1 3 5 MAY 20, 1968 1 NS 6 MAY 20, 1968 5 S 7 MAY 21, 1968 2 S 8 MAY 30, 1968 6 NS 9 MAY 30, 1968 7 S 10 MAY 30,1968 8 s II MAY 30, 1968 10 s 12 JUNE 1 , 1968 8 s * PRE -SEEDING PASS NUCLEI COUNT NOT AVAILABLE + POST-SEEDING PASS NUCLEI COUNT < PRE-SEEDING PASS COUNT MAX NO OF ICE v NUCLEI/ LITER / AFTER SEE0IN8 PASS MAX NO. OF ICE \ NUCLEI / LITER BEFORE SEEDING PASS S S SSNSS SNSS S S S Fig. 12. Ice nuclei counts in selected experimental clouds. Measurements were made with the Bigg- Warner cold box with expansion to — 20C. Counts presented are relative to clear air. 5) Satellite, synoptic and aircraft study of the weather and cloud conditions over and near the Florida peninsula on each operational day to determine the context of the experiment and to delineate conditions favorable for seeding both individual cumuli and groups of cumuli. An attempt will be made to determine whether seeding individual clouds had mesoscale or larger scale effects on cloud patterns. Preliminary results of the radar-rainfall study indi- cate that the precipitation from seeded clouds averaged about double that from control clouds. These results also suggest that the rain increases were on the order of 100-150 acre-feet per cloud,' which could be im- portant. Unfortunately, the small sample and large cloud-to-cloud variability in precipitation reduces the statistical significance of the rainfall results to the marginal level, namely between 5 and 20% depending on the test used. Calculations show that if the experi- ment was repeated one more time with identical out- come, and the results of both experiments combined, the rainfall increases would be significant to better than 3% with the most stringent test. Hence it is imperative to repeat this experiment at least once. Acknowledgments. The writers are deeply indebted to many persons and organizations who helped with the planning and execution of this experiment and in the design and fabrication of the necessary technology. We dedicate this effort to Dr. Robert M. White, Administrator of ESSA, who first suggested this pro- gram and supported it through many vicissitudes. We are deeply grateful to the ESSA Research Flight Facility and its director, Mr. Howard J. Mason, Jr. The whole of RFF went far beyond the call of duty in the implementation of this program. Particularly noteworthy contributions were made by RFF's Mar- shall Hatch and Harlan Davis, flight meteorologists' on the B-57 and DC-6, respectively; Jack Lubin, Chief Controller ; and Paul Connor for operation, installation and information on the flare deliverv svstem. Richard 122 JOURNAL OF APPLIED METEOROLOGY Volume 9 Decker and Frank Norimoto capably carried out the photography. We also thank the Federal Aviation Administration for handling this difficult operation in an area with heavy air traffic and for the fine cooperation of their Miami staff at both the planning and execution stages of the work; the senior staff of the Naval Weapons Center, China Lake, Calif., for many useful discussions on the physics, design and use of pyrotechnics in rela- tion to cloud seeding ; and the Naval Air Systems Com- mand, who, through Mr. Robert Ruskin of the Naval Research Laboratory, purchased and provided the X1055 flares used in the experiment. REFERENCES3 *Battan, L. J., 1966: Silver-iodide seeding and rainfall from con- vective clouds. /. Appl. Meteor., 5, 669-683. * , 1967 : Silver-iodide seeding and precipitation initiation in convective clouds. /. Appl. Meteor., 6, 317-322. *Bethwaite, F. D., E. J. Smith, J. A. Warburton and K. J. Heffer- nan, 1966: Effects of seeding isolated cumulus clouds with silver iodide. J. Appl. Meteor., 5, 513-520. *Braham, R. R., Jr., L. J. Battan and H. R. Byers, 1957 : Artificial nucleation of cumulus clouds. Meteor. Monogr., 2, No. 11, 47-85. *Coons, R. D., and R. Gunn, 1951: Relation of artificial cloud modification to the production of precipitation. Compendium of Meteorology, Boston, Amer. Meteor. Soc, 235-241. Conrad, G, P. Connor and H. A. Friedman, 1969: The ESSA Research Flight Facility: Instrumentation systems. ERL- ESSA Tech. Rept. (in press). Davis, C. I., and R. L. Steele, 1968: Performance characteristics of various artificial ice nuclei sources. /. Appl. Meteor., 7, 667-673. Davis, L. G, and C. L. Hosier, 1965: The design, execution and evaluation of a weather modification experiment. Fifth Berkeley Symposium on Mathematical Statistics and Probabil- ity, Univ. of California Press, 253-270. * , J. I. Kelley, A. Weinstein and H. Nicholson, 1968 : Weather modification experiments in Arizona. Dept. of Meteor., Pennsylvania State Univ., 128 pp. *Flueck, J. A., 1968: A statistical analyses of Project VVhitetop's precipitation data. Proc. First Natl. Conf. Weather Modifica- tion, Albany, N. Y., 26-35. ' References with asterisks have been given in Table 1. Fukuta. N., 1958: Experimental investigations on the ice-forming ability of various chemical substances. J. Meteor., 15, 17-26. Jiusto, J., and W. C. Kochmond, 1968: Condensation on non- hygroscopic particles. /. Rech. Atmos., 3, 19-24. *Korienko. E. E., B. N. Leskow and I. P. Polvina, 1968: Results of seeding clouds with solid C02 aimed at the stimulation of precipitation over the Ukraine. Proc. Intern. Conf. on Cloud Physics, Toronto, 724-729. Kline, D. B., and G. W. Brier, 1961 : Some experiments on the measurement of natural ice nuclei. Mon. Wea. Rev., 89, 263-273. MacCready, P. B., 1959: The lightning mechanism and its relation to natural and artificial freezing nuclei. Recent Advances in Atmospheric Electricity, London, Pergamon Press, 369-381. *Malkus, J. S., and R. H. Simpson, 1964: Modification experi- ments on tropical cumulus clouds. Science, 145, 541-548. Mossop, S. C, 1968: Silver iodide as nucleus for water condensa- tion and crystallization. J. Rech. Atmos., 3, 185-190. *Neumann, J. K., R. Gabriel and A. Gagin, 1967: Cloud seeding and cloud physics in Israel. Results and Problems, Intern. Conf. on Water for Peace, 53 pp. Ruskin, R. E., 1967: Measurement of water-ice budget changes at — 5°C in Agl-seeded tropical cumulus. /. Appl. Met- eor., 6, 72-81. St. Amand, P., W. Finnegan and F. K. Odencrantz, 1969: Effects of the type of nucleant on modification of clouds for the stimu- lation of rainfall. Naval Weapons Center, China Lake, Calif., Weather Modification Assoc, Fresno, Calif, (in press). Scheffee, R. S., R. W. Evans and C. Huggett, 1967: Development of a pyrotechnic cloud seeding system. Part 1 : Development of pyrotechnic compositions. Rept. by Atlantic Research Corp. to ESSA under Contract CWB-11346, 42 pp. Simpson, J., 1967 : Photographic and radar study of the Stormfury 5 August 1965 seeded cloud, /. Appl. Meteor., 6, 82-87. , R. H. Simpson, J. R. Stinson and J. W. Kidd, 1966: Storm- fury cumulus experiments: Preliminary results 1965. J. Appl. Meteor., 5, 521-525. , G. W. Brier and R. H, Simpson, 1967: Stormfury cumulus seeding experiment 1965: Statistical and main results. /. Atmos. Sci., 24, 508-521. ■ , and V. Wiggert, 1969: Models of precipitating cumulus towers. Mon. Wea. Rev., 97, 471-489. Steele, R. L., 1968: Evaluation of ice nuclei sources and their de- velopment : Production and delivery of cloud nucleating materials. Proc, Skywater Conference III, Office of Atmo- spheric Resources, Bureau of Reclamation, U. S. Dept. of Interior, Denver, Colo., 51-92. , and C. I. Davis, 1969: Variation of ice nuclei effectiveness with liquid water. /. Atmos. Sci., 26, 329-330. Warner, J., and S. Twomey, 1956: The use of silver iodide for seeding individual clouds. Tellus, 8, 453-457. Reprinted from Journal of Applied Meteorology 9, No. 2, 2^2-257 53 Reprinted from Journal of Applied Meteorology, Vol. 9, American Meteorological Society Printed in U. S. A. No. 2, April, 1970, pp. 242-257 Precipitation Results from a Pyrotechnic Cumulus Seeding Experiment William L. Woodley Experimental Meteorology Laboratory, ESSA, Coral Gables, b'la. (Manuscript received 23 September 1969, in revised form 10 November 1969) ABSTRACT In an attempt to specify the changes in precipitation produced by alteration of cloud dynamics, airborne seeding with silver iodide pyrotechnics was carried out in South P'lorida during May 1968. Emphasis was placed on altering cloud dynamics and on increasing precipitation as a by-product of the dynamic alteration. Nineteen clouds were studied; 14 were seeded and 5 unseeded (controls) as dictated by the randomized seeding instructions. Each of the 14 clouds received approximately 1 kg of Agl smoke. Seeding was found to be effective in promoting increased cloud growth; the average growth difference between the seeded and con- trol clouds was 11,400 ft, significant at the 0.5% level. The induced growths took many forms and in many cases were produced in clouds containing significant amounts of natural ice. A 10-cm radar with iso-echo contouring was used to infer changes in precipitation. Analysis indicates that seeding increased rainfall an average of 100-150 acre-ft 40 min after the seeding pass, an increase of over 100%. The result is changed little by using an alternate analysis scheme or by including five additional control clouds selected after the program. The rainfall increases would probably have been greater if calcu- lations had been possible for entire cloud lifetimes. The significance of the rainfall results ranged between 5 and 20% based on two-sided statistical tests. Comparison between radar and raingage rainfall demonstrates that the rainfall calculations are probably underestimates by no more than 30%,. The Z-R relation used in the rainfall calculations was equally valid for the seeded and control clouds. The amount of rain from the seeded clouds was positively correlated with the maximum top growth following seeding. The seeded rainfall increases were apparently the result of larger and more lasting clouds that were the by-product of the dynamic invigoration. The natural glaciating behavior of the experimental clouds would appear to preclude the "colloidal instability" approach to rainfall augmenta- tion from Florida cumuli. 1. Introduction Since laboratory discoveries of the ice nucleating properties of dry ice (Schaefer, 1946) and silver iodide (Vonnegut, 1947), there have been numerous attempts to increase precipitation by seeding supercooled cumulus clouds with these materials. Most efforts have been pre- dicated on disturbing cloud stability by inducing ice particle formation in the supercooled cloud. The induced ice particles grow by diffusion at the expense of the water drops because the equilibrium vapor pressure of water with respect to ice is less than that with respect to liquid water at the same subfreezing temperature (the Bergeron-Findeisen theory). When the ice parti- cles are large enough to fall relative to the cloud updraf t, they grow further by accretion of other cloud hydro- meteors. If conditions are right, the falling particles grow large enough to reach the ground before evaporat- ing. Between 1 (McDonald, 1958) and 10 (Fletcher, 1962 ; Mason, 1962) artificial ice nuclei per 10 liters of cloud air are considered optimum for promoting pre- cipitation growth. Massive seeding of cumulus clouds, producing man)' ice crystals, is avoided because the competition for cloud vapor reduces their chances of reaching precipitation size. Seeding to produce "colloidal instability" is a passive approach to rainfall enhancement because its aim is to precipitate some fraction of the water in the cloud dur- ing seeding. The active approach would be the modifi- cation of the buoyancy forces and circulations that sustain the clouds, referred to here as dynamic modifica- tion. If it were possible to artificially increase cloud buoyancy and invigorate cloud circulations, a larger and more lasting cloud would result. Water, in addition to that contained in the cloud at seeding, would be processed, and precipitation increases would be the natural consequence. It has long been recognized that seeding to transform a supercooled cumulus cloud to ice might increase cloud buoyancy. From the first law of thermodynamics, one can show that the fusion heat release and the conversion of the vapor excess over ice saturation following seeding might produce a warming of 0.5-1.0C, even if only a fraction of the liquid water is artificially glaciated. Because most clouds, exclusive of intense thunder- storms, are rarely more than 1C warmer than their environments, seeding might, under ideal circumstances, effectively double cloud buoyancy and lead to increased growth. One hundred ice nuclei per liter of cloud air is thought to be the minimum number for sudden and complete glaciation (MacCready, 1959) — a number, interestingly enough, that in the "colloidal instability" approach to rainfall enhancement is thought to repre- sent overseeding. 243 JOURNAL OF APPLIED METEOROLOGY Volume 9 Although there is a theoretical basis for dynamic modification, serious doubts existed as late as 1960 that man could significantly affect cloud dynamics (Mc- Donald, 1958). Except for isolated cases (Kraus and Squires, 1947; Orr et al., 1949; Vonnegut and Maynard, 1952), dynamic modification was not observed during seeding experiments before 1960. There are several rea- sons for this circumstance. The objective of most of the early experiments was to alter cloud precipitation pro- cesses directly, not cloud dynamics. In many instances the seeding may have been done under statically stable conditions which precluded visible dynamical effects. Also, the quantities of seeding material required for dynamic alteration were rarely used, either because of a desire to avoid overseeding or because the technology for massive seeding was lacking. Since 1960, more attention has been given to the possibility of modifying cloud buoyancy forces and circulations. Individual cumulus clouds have been seeded with silver iodide from an aircraft penetrating a cloud. (In such experiments there is greater certainty that the silver iodide reaches the right portions of the clouds in the intended concentrations at the right moment to be effective.) Notable examples are the Stormfury cumulus experiments over the Caribbean south of Puerto Rico in 1963 (Malkus and Simpson, 1964) and in 1965 (Simpson et al., 1967), and over Arizona in 1967 (Davis el al., 1968). In these experi- ments, impressive and statistically significant cloud growth was noted subsequent to seeding. Further cumulus model predictions of seeded cloud behavior, incorporating the postulated effects of seeding, agreed very well with observed behavior, demonstrating that the physical hypothesis behind dynamic modification has basis in fact and that man can alter cloud dynamics under specifiable conditions. There has been little study of the effect of dynamic changes on precipitation. Where attempts were made (Davis el al., 1968), no evidence was found of real pre- cipitation increases on the ground. 2. Background of the Florida program Individual cumulus clouds growing over and near the Florida peninsula were seeded with silver iodide in May 1968. The experiment was conducted jointly by ESSA and the Naval Research Laboratory (NRL) with the participation of the Radar Meteorological Laboratory of the University of Miami, the U. S. Air Force, and Meteorology Research, Inc. (MRI) to study with air- craft and calibrated ground radars the induced dynamic and precipitation changes in the seeded clouds and to compare these with the unseeded control clouds, both chosen on a statistically randomized basis. Simpson et al. (1969) discussed the experimental design, the pyro- technic seeding system and the first results. The seeding was designed to glaciate the supercooled portions of the clouds suddenly and completely in order to provide the impulsive fusion heat release necessary for dynamic invigoration and increased cloud growth. Precipitation changes were expected as the by-product of the dynamical alteration. The selection criteria for the experimental clouds were: 1) hard, cauliflower appearance with tops between 19,000 and 26,000 ft, indicating a vigorous cloud with its top cooled below the activation threshold of silver iodide (— 4C) but not cold enough for complete natural glaciation; 2) minimum supercooled water content of 1 gm m~3 as measured by Johnson-Williams instrumentation during cloud pene- tration, indicating the fusion heat potential necessary for dynamic changes; 3) cloud still vigorous after first penetration by the three monitoring aircraft; and 4) isolation from other convective activity, especially cumulonimbus, where the risk of natural seeding is especially great. Twenty 50-gm silver iodide pyrotechnics were dropped into the seeded clouds at about 100 m intervals, ten on each of two mutually prependicular passes of the seeded aircraft through the experimental cloud. The seeding altitude averaged 20,000 ft MSL. Each flare seeded ~3 km of cloud depth in 80-90 sec. The multiple pass technique was used to insure better distribution of the silver iodide in the seeded cloud. The flight patterns were exactly the same for the seeded and non-seeded clouds. There were 19 experimental clouds during the Florida program ; 14 were seeded and 5 were controls as dictated by the randomized seeding instructions. The seeded clouds grew an average of 11,400 ft more than the con- trols, a difference significant at the 0.5% level. Woodley (1969) and Simpson and Woodley (1969) treated in- stances of dynamic alteration in some detail. Because cloud dynamics and precipitation physics are intimately connected in cumulus clouds, alteration of one must affect the other. This effect is treated exten- sively in this paper. 3. Radar systems and procedures The modified UM/10-cm radar of the Radar Meteor- ological Laboratory, Institute of Marine Science, Uni- versity of Miami, was the main tool for measuring precipitation from the experimental clouds. The characteristics and operation of this radar are treated in detail by Senn and Courtright (1968). The radar has a 2° conical beam, a transmitter power of 5.5 X105 W, a minimum detectable signal of 10~14 W, a pulse length of 2 /usee, and a pulse repetition rate of 300 pulses sec-1. Important features include special logarithmic and linear radar receiver systems and an rf range attenuation corrector (Hiser and Andrews, 1966). The UM/10-cm radar has a four level iso-echo contour (IEC) unit de- veloped by Senn and Andrews (1968). The effective antenna gain of the 12-ft reflector and radome of the radar was calibrated by Andrews' (1966) solar method. A semiautomatic system was devised by April 1970 WILLIAM L . 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OF CLOUD FROM RADAR (N.MI.) f> O CM CM CM * io m • K z o F- u < (O CO CO CO CO Z z z z z TIME OF SIMULATED SEEDING (GMT) (O CO CO CD r- — neon 0> N CO «» «o UI F- a MAY/ 15/6 8 MAY/ 16/6 0 MAY/ 20/6 8 MAY/26/68 MAY/28/68 April 1 z CO £ oo 00 00 « W CA £ 00 « 00 £ 00 00 £ g £ t/> 00 00 -J o uj z CM CM CM CM CM CM CM CM CM CM CO K) lO k> Z QC EXPER RELATI BEFOR UJ o < >- < 5 = = = ■ = = = = « = , o <-> CE < < - » ■ UJ < < • T WATER PERI0C o Z> in o or >r> g * 00 — V — m £ CM CO = - N «1 l I » r- co Q — rj PO V If) oo r- go oo o — CM rO [_ * 1 ♦ ^'Bft '■ j2 R 3 1_ D U — - L) — - * ra 3 fc£ _ — a -. o o 0 t^ i/) OJ -t-j u. 7 C- O be _2 J= 133d 3U0V) U31VM April 1970 W I L L I A M L. WOO D LE Y 250 Table 3. Correlation between maximum growth and total watet in 10-min intervals after first seeding pass (seeded clouds). Time interval 0-10 10-20 (min) 20-30 30-40 40-50 No. of clouds Correlation coefficient Significance 13 0.20 >50% 12 0.18 >50% 11 0.54 10% 8 0.91 <1% 6 0.79 <5% The bar graph of rainfall (Fig. 5) reveals that the sample is dominated by the few wet clouds, especially cloud 6 on 16 May. Seeded cloud 8 on 16 May probably produced more rain than any in the sample, but because of its azimuth from the radar the rainfall estimates are grossly too low. Cloud 8 was at the azimuth of the partially blind cone, 262°-273°, of the UM/10-cm radar which is due to interference by the University of Miami Library and the WSR-57 radome on its roof. The energy loss is worst when the 10-cm radar antenna is at a small elevation angle while scanning near cloud base. The contention that the radar rainfall for cloud 8 is an underestimate is supported by Simpson and Woodley (1969) who compared measured reflectivities with those computed theoretically. Woodley (1969) calculated the the actual rainfall from this cloud is probably twice that computed. Seeded cloud 1 on 19 May, 10 on 30 May, and control cloud 4 on 19 May were also within the partially blind region at some time during their life histories. The esti- mates of rainfall from these clouds are probably also too low, Cloud 10 on 30 May almost certainly produced more rainfall than cloud 8 on this day, implying that the rainfall calculation for cloud 10 is an underestimate by at least a factor of 4. The amount of rain from the seeded clouds was posi- tively correlated with the maximum top growth follow- ing seeding. Table 3 shows the correlations between maximum cloud top growth following seeding and the total water produced by the clouds in 10-min intervals after the first seeding pass. The correlation is positive in all intervals, increasing to a maximum with high statistical significance in the 30-40 min following seed- ing. This finding implies that the more a cloud grows following seeding the more rain it is likely to produce. The high correlation between cloud growth and water production suggests that a dynamic cumulus model such as the one developed by Simpson and Wiggert (1969) that can predict cloud growth following seeding can also be used to infer the effect of seeding on precipitation. The positive correlation between cloud growth and water production in Florida cumuli after seeding differs from the finding in Australia (Bethwaite et al., 1966) of large cloud-base increases in rainfall from seeded clouds without detectable changes in cloud top height. The rainfall calculations indicated that precipitation decreases accompanv the collapse or the cutoff tower growth of seeded clouds consisting of one primary tower. This is consistent with the conclusions reached above and is supported by the analysis of cloud 5 on 16 May and cloud 8 on 30 May. The seeded tower of cloud 5 collapsed completely following the seeding, and no new towers appeared. In successive 10-min intervals after seeding, this cloud produced increasingly less rainfall than it had in the 10-min period before seeding (Fig. 5). In seeded cloud 8 on 30 May, discussed by Woodley (1969), a cutoff tower growth was followed by collapse of and then regeneration of the cloud body, and explo- sive growth. The rainfall calculations are consistent with this behavior. During the cutoff tower regime, 0-10 and 10-20 min periods after seeding, this cloud produced 22.8 and 8.0 acre-ft less water, respectively, than it had in the 10 min before seeding. During the period 20-30 min after seeding, regeneration and intense growth began, with the cloud producing 26.7 acre-ft more water than it had in the 10 min before seeding. Subsequently, this cloud merged with its neighbors and was dropped from the sample. The average rainfall statistics are of interest, pro- vided one is aware of the small sample and of the effect of the few wet clouds on the averages. The average total water from the experimental clouds is presented in Fig. 6a. The number in parentheses near each data point refers to the number of clouds contributing to the aver- age. P- ainfall values are presented only to 40 min after the seeding pass, because the sample is very small after this. Inclusion of the radar control clouds in the sample does not change the curves significantly. The average total water from the seeded clouds after the seeding pass exceeds that from the controls by at least a factor of 2 for each time interval. The results of the analysis change little when the post-seeding pass rainfall is compared with that in the 10-min period before the seeding pass (Fig. 6b). The average rainfall difference (seeded cloud rainfall minus control cloud rainfall) increases with time and is greater than the average rainfall from the controls. An interesting, if not perplexing, feature of the average rainfall statistics is the increased seeded rainfall relative to control rainfall within 10 min after seeding. At first thought it is difficult to imagine how increased rainfall could propagate from the seeded, supercooled region of the cloud (freezing level 14,000-15,000 MSL) to near cloud base in only 10 min. The increased seeded rainfall in this time period cannot be ascribed to chance selection of wetter clouds, because the average seeded rainfall 10 min after seeding referred to that 10 min before seeding also exceeds that from the controls. The effect of the initial intensity of the echo is removed, suggesting that the seeded clouds developed more pre- cipitation 10 min after the seeding pass than did the controls. Simpson has treated this problem in some detail. I 'sing droplet measurements, a numerical model and 251 JOURNAL OF APPLIED METEOROLOGY Yolume 9 ro I 1 1 T 1 1 (12) I ! (12) / / 1 1 T" >s>»>(in 60 / N.I8) (13)/ 60 / (13)/ / / / / / s s X(8) so / / / 50 / ill 40 " / _ / / ^^ - / (5) / Ul -/ r~r [13) I/T ^."^ ^0 a: o 5 30 (13)/ X -^ \ V /i \ CE UJ 1- \.(9) 20 V ' \ (5) / \<4) < S 20 \(9) - 10 / _ / / / 1 10 (io>r '/ 7 - 0 0 _ 10 1 1 1 1 1 -10 INCLUDING RADAR CONTROLS 1 1 1 -10-0 0-10 10-20 20-30 30-40 40-50 50-60 TIME INTERVAL RELATIVE TO SEEDING PASS -10-0 0-10 10-20 20-30 30-40 40-50 50- TIME INTERVAL RELATIVE TO SEEDING PASS ■10-0 0-10 10-20 20-30 30-40 40-50 50-60 TIME INTERVAL RELATIVE TO SEEDING PASS INCLUDING RADAR CONTROLS J_ 10-0 0-10 10-20 20-30 30-40 40-50 50-60 TIME INTERVAL RELATIVE TO SEEDING PASS CONTROL CLOUDS SEEDED CLOUDS DIFFERENCE (SEEDED -CONTROL) ( ) INDICATES NUMBER OF CLOUDS IN SAMPLE b. Fig. 6. Average rainfall from the experime ital clou Is inferred from Z = 300/c1-4. The number in parenthesis near each data point refers to the number of clouds contributing to the average: a., average total water in 10-min intervals relative to the time of the first seeding pass; b., average water relative to the water produced in the 10-min period before the seeding pass. Time intervals are relative to the time of the first seeding pass. physical reasoning, it is shown that the radar-derived precipitation from a seeded cloud will increase markedly (relative to an unseeded cloud) within 10 min after seeding. Calculations for cloud 6 on 16 May, a typical seeded cloud, 40 n mi from the radar, show that pre- cipitation particles from a supercooled (T< — 5C) layer, 2 km deep, will reach the center of the radar beam in the 10 min following seeding.1 The computation is based on calculations of the terminal fallspeeds of the precipita- 1 For clouds at greater ranges the elapsed time for precipitation particles in the seeded region to reach the center of the more ele- vated radar beam will be less than 10 min. April 1970 WILLIAM L. WOO D L E Y 252 Table 4. Comparison of average seeded and control cloud rainfalls 40 min after seeding pass. TOTAL WATER CALCULATION: WITHOUT RADAR CONTROLS SEEDED CLOUDS 237 ACRE FEET CONTROL CLOUDS 1 10 ACRE FEET DIFFERENCE - 1 27 ACRE FEET % DIFFERENCE— - "],S"~ " 100 ■ 115 % WITH RADAR CONTROLS FEET SEEDED CLOUDS — 237 ACRE CONTROL CLOUDS 97 ACRE FEET DIFFERENCE 140 ACRE FEET % DIFFERENCE 237 ~ 97 x 100 ■= 144 % WATER CALCULATION RELATIVE TO 10 MINUTE PERIOD BEFORE SEEDING PASS WITHOUT RADAR CONTROLS SEEDED CLOUDS 167 ACRE FEET CONTROL CLOUDS 40 ACRE FEET DIFFERENCE 127 ACRE FEET % DIFFERENCE l67/^4° » 40 100 = 316 % WITH RADAR CONTROLS FEET SEEDED CLOUDS-- 167 ACRE CONTROL CLOUDS 49 ACRE FEET DIFFERENCE 118 ACRE FEET % DIFFERENCE '677„49» 49 100 = 2 4 1 % tion particles and an assumption of a 5 m sec-1 down- draft. A final portion of the calculation shows that the amount of precipitation contributed to the radar mea- surement from the supercooled layer is large enough to account for the average measured rainfall difference between seeded and control clouds in the 10 min follow- ing seeding, even if only a small fraction of the available water enters the downdraft. None of the above reasoning depends on invigoration of seeded cloud downdrafts. Seeding greatly enhanced cloud updrafts as manifested by increased cloud growth, and there is reason to believe that invigorated cloud downdrafts also attended the intensified updrafts. If so, the precipitation in the seeded supercooled layer would reach the center of the radar beam more quickly than was calculated. A summary of the comparison of the average seeded cloud rainfall with that from the control clouds is pre- sented in Table 4. Forty minutes after the seeding pass, the average seeded cloud had produced 100-150 acre-ft more water than the average control cloud, an increase > 100%. This result is independent of the analysis scheme. The average total water difference between the seeded and control clouds might be increased bv a fac- tor of 2 if there were calculations for entire cloud life- times, and if a true rainfall representation were available for the clouds in the blind radar cone. 6. Statistical test of rainfall results The difference in average total water for the seeded and control clouds 40 min after the seeding pass was tested for significance by 1) a pooled Student t statistic with the variances assumed equal (a good assumption), 2) the Normal Scores test, and 3) the Wilcoxon-Mann- Whitney test. The Student t test is probably the most powerful if the data are normally distributed. However, the assumption of normality is not satisfactory for the rainfall data. The Normal Scores test is also based on the normal distribution, but it has been shown to be a powerful test when the distributions are non-normal (highly skewed and bimodal) (Neave and Granger, 1968). The Wilcoxon-Mann-Whitney non-parametric test makes no assumption about the shape of the popu- lation distribution from which the samples are drawn ; the disadvantage is that it is not as powerful as the former two tests when the data are drawn from a popu- lation having a normal distribution. Table 5 shows the results of the statistical tests on rainfall. In the last category (radar controls plus the mergers), the clouds dropped from the May data sample because of mergers with surrounding echoes were assumed to persist in a steady state until 40 min after the seeding pass. The rainfalls produced by these clouds in the 10 min before being dropped were assumed to fall in 10-min intervals until the 40-min cutoff. This artifice permitted all clouds to be retained in the sample, which resulted in total population of 23 clouds (13 seeded and 10 controls). The test results indicate that their signifi- cance ranges between 20 and 5%, depending on the category and test chosen. Note that all the tests are two-sided. The results give strong statistical support for the hypothesis that dynamic cloud modification pro- duces precipitation increases. A rather different approach to the statistical analysis of the precipitation results strengthened the conclu- sions reached above. A fourth-root transformation was Table 5. Significance levels (per cent) of various statistical tests of rainfall results.3 Wilcoxon- Normal Mann- Type of Student scores Whitney test / test test test Without RCb Nsc = 8 Nnsd = 4 20% !/„_,, 0.975 Otherwise, we do not reject Hi. For the problem at hand, /* = 2.35 and tvi, 0.975 = 2. 179, so we reject Hi. This implies that the difference between the actual seeded rainfalls and those predicted, using the control cloud prediction equation, is significantly different at the 5% level. This says, in effect, that the seeded and control cloud rainfalls constitute distinctly different popula- tions, which is the same conclusion suggested by the more conventional statistical analysis. 7. Accuracy of the rainfall calculations Because of the uncertainties in the radar observations and in the analysis, there is little likelihood that the calculations made from the radar data represent exact rainfall. Fortunately, many of the uncertainties are compensating. Even if the radar return is a poor repre- sentation of rainfall, the comparison of seeded and con- trol cloud rainfalls should still be valid. The radar errors associated with the quantitative measurement of precipitation are rather difficult to define quantitatively. In this study major sources of error are probably uncertainties associated with the radar beam width and the loss of an indeterminate amount of beam energy while the antenna scanned at 0.5° elevation. In addition there are many minor sources of error. The net importance of the errors associated with the radar measurement of precipitation during May 1968 was evaluated by a direct comparison of radar and raingage rainfall. Woodley and Herndon (1970) treat this in detail in the companion article in this issue. Only total shower rainfalls were compared because the re- cording raingage measurements were too coarse to permit rainfall rate comparisons. A radar-raingage com- parison was not possible for the seeded clouds because none passed over raingages during the operation of the radar. Based on the raingage as the standard, the average error is an 8% underestimate by the radar when the differences are summed algebraically and about 30% if their absolute values are summed. The average percent- age difference is defined here as the average difference between the gage and radar rainfalls divided by the average gage rainfall, rather than the mean of the indi- vidual percentage differences, in order to avoid giving undue weight to the few comparisons showing small absolute differences but with large percentage differ- ences. The correlation coefficient between the radar and gage rainfalls was 0.93, significant at the 1% level. The radar-raingage comparison suggests that the radar approximated point and area unmodified shower Table 6. Fourth root of seeded cloud rainfalls (observed vs predicted). Units are in acre-ft. 1 '0 (observed) Yp (predicted) Ya-YP=d 3.31 3.71 -0.40 2.37 3.23 -0.86 5.40 3.34 2.06 3.88 1.19 2.69 4.20 2.90 1.30 4.48 3.07 1.41 3.93 2.27 1.66 2.01 2.46 -0.45 3.06 2.75 0.31 2.05 1.19 0.86 3.76 3.61 0.15 4.37 4.38 -0.01 3.14 2.81 0.33 H180p) were observed in the experimental clouds at cloud base and at 20,000 ft with MRI continuous hydrometeor samplers (Mee and Takeuchi, 1968) that had been Installed on the RFF DC-6 and NRL S-2D aircraft. A sampler of this type is described in detail by Duncan (1966). A moving strip of soft aluminum foil approximately 3 inches wide was exposed to the ambient airflow through a 1.5X1.5 inch slot. Cloud particles with diameters > 180 fi striking the foil leave distinct impressions that can be measured and counted. With this information, the speed of the foil moving by the slot, the true air- speed of the aircraft, and the ratios of imprint to particle size, one can compute representative size distributions of the sampled particles, water contents in ice and water, radar reflectivity, and rainfall intensity. The foil calibration and data reduction and analysis procedures are discussed bv Takeuchi (1969). The individual sample calculations (sample volume ~1 m3) of reflectivity Z and rainfall rate R from the foil observations in the experimental clouds at 20,000 ft and at cloud base (1500-3000 ft) were used to derive Z-R relationships in the seeded and control clouds. Empirical relationships of the form Z=ARb (7) were determined by the method of least squares. Reflec- tivity was calculated from (6), and rainfall rate was derived from the water mass by size interval and the terminal fall velocities calculated by Gunn and Kinzer (1949) for water and by Weickmann (1953) for ice. The Z-R relationships derived are found in Table 7 with 95% confidence intervals placed on the A's and b's. Rainfall rate R was the independent variable in the regression analysis. Analysis of covariance (Li, 1961) showed no signifi- cant differences in the exponents b and coefficients A at the 5% level between the relationships for the seeded and control clouds. The sample calculations of Z and R in the seeded and control clouds were then pooled to obtain the combined relationships. The Z-R analysis indicated no detectable difference in droplet spectra and the derived Z-R relationships in the seeded and control clouds. This means that (2) was equally valid for showers from seeded clouds and also implies that the rainfall increases from the seeded clouds calculated with (2) were real and not spurious because of an alteration of seeded cloud droplet spectra. 8. Natural glaciating behavior of Florida cumuli A striking feature of the hydrometeor observations at 20,000 ft (temperature ~— 9C) was the concentra- tions of natural ice (diameters >180yu) in the experi- mental clouds before the seeding pass. Virtually all clouds in which measurements were made had at least one ice particle per liter of cloud air before seeding. It is unlikely that contamination from seeding on other days can explain this ice. 255 JOURNAL OF APPLIED METEOROLOGY Volume 9 A preliminary analysis of the MRI continuous parti cle sampler (MacCready and Todd, 1964) observations (particle diameter < 180 n) made from the same air- craft in the same clouds (Takeuchi, 1969) indicates substantial amounts of liquid water in cloud droplets before the seeding pass concurrent with the predomi- nance of ice in precipitation size particles. There was still enough fusion heat potential in the smaller super- cooled drops to provide the impetus for dynamic changes induced by seeding. This agrees with Sax (1969) who found that portions of the cumuli studied during the 1965 Stormfury cumulus experiments were partially glaciated at — 5C. However, he could explain the dy- namical behavior of the clouds following seeding only if their updraft cores remained largely supercooled to — IOC or colder. The presence of one ice particle per liter of cloud air in the experimental clouds before the seeding pass has an important implication. The "colloidal instability" approach to rainfall enhancement requires that seeding produce about one ice particle per liter of cloud air in clouds that are almost completely supercooled. Because Florida cumuli have this ice concentration naturally, this approach to increased rainfall does not seem to be applicable here. Braham (1964) has found natural con- centrations of ice as high as 10 liter-1 in Missouri cumuli with top temperatures of ^ — IOC. A partial explanation for the failure of the "colloidal instability" approach to produce rainfall increases from seeded Missouri cumuli (Flueck, 1968; Neyman et al., 1969) may be related to the natural ice concentrations in these clouds. 9. Discussion The increases in precipitation noted during May 1968 Florida program were the result of dynamical invigora- tion of the cloud and not the direct result of important alteration of cloud microphysics. This agrees quite well with the prediction by Simpson and Wiggert (1969) based on model calculations of seeded cloud behavior. Except for momentary increases in ice in the clouds after seeding, no important differences in cloud particle habit or spectra were noted between the seeded and control clouds. The seeded clouds were larger and more lasting and processed more moisture than their unseeded counterparts, which accounted for the increases in pre- cipitation. Because dynamics and not microphysical processes is the controlling factor for rain from cumuli in Florida, Missouri (Braham, 1964), and Arizona (Battan, 1963), the dynamic approach to rainfall en- hancement from these clouds would seem to be the most promising. 10. Summary and conclusions In analyzing the observations made during May 1968, Woodley (1969) and Simpson et al. (1969) showed clearly that silver iodide pyrotechnic seeding of super- cooled Florida cumuli induced cloud growth. This phase of the research strongly suggests that seeding increased rainfall and that these increases were positively corre- lated with increased cloud growth. Precipitation in- creases were the result of dynamic alteration, not of direct alteration of cloud microphysics. Pyrotechnic silver iodide seeding apparently provides the impetus for increased cloud growth, following which prolonged and enhanced natural precipitation processes (espe- cially in secondary unseeded towers) account for the increased rainfall. The average rainfall difference between the seeded and control clouds was subjected to three different, two-tailed statistical tests and was found to be signifi- cant between the 5 and 20% levels, strongly supporting the hypothesis that invigoration of cloud dynamics increases rainfall. Silver iodide pyrotechnic seeding had an important effect on cloud dynamics even when certain portions of the clouds contained significant amounts of natural ice. The remaining supercooled water was still adequate to provide the fusion heat necessary for dynamic altera- tion. This is an important finding, considering the natural glaciating behavior of cumulus clouds in Mis- souri, Florida, and elsewhere. The presence of pockets of ice at relatively warm temperatures ( — 5 to —IOC) need not preclude Agl seeding to alter cloud dynamics and increase rainfall. However, the "colloidal insta- bility" approach to rainfall enhancement is apparently not applicable to Florida cumuli ; whether it is to clouds of other seasons and locations must still be determined. The calibrated 10-cm radar of the Radar Meteoro- logical Laboratory was particularly effective in evaluat- ing precipitation changes following seeding, not only relative precipitation differences between seeded and control clouds but, as indicated by the radar rainfall- raingage rainfall comparison, the magnitude of the volume rainfall was within 30% of the actual. This is probably the first time dynamic modification has been demonstrated to result in precipitation increases on the ground. The efficacy of other silver iodide seeding systems in promoting dynamic changes in cumulus clouds has not been evaluated here, However, their effectiveness will probably depend on where and at what rate the Agl is released in the cloud. (A critical amount of Agl is un- doubtedly necessary to affect cloud dynamics, but its distribution is probably of greater importance.) As this research indicates, as little as 500 gm of Agl can induce growth if it is strategically placed in the active super- cooled portion of a cloud. To recommend routine use of pyrotechnic seeding of individual clouds for augmenting rainfall would be pre- mature. Cloud and environmental conditions favoring large increases in rainfall must be better specified. Model predictions, which indicate that large precipita- tion increases can be expected from clouds with large April 1970 \Y I I. L I A M VV OODLEY 256 seedability, are a first step, but the optimum amount of silver iodide for the desired effect is still to be specified. The large-scale effect of pyrotechnic seeding is unknown. Invigoration of one cloud with subsequent increase of rainfall might represent only a reorganization of the rainfall over an area, not a net increase, The effect of seeding all suitable clouds over a large area, such as the South Florida peninsula, must still be investigated. Should it be possible to dynamically invigorate whole groups or areas of clouds with subsequent precipitation increases, this would be an important finding indeed. Acknoidedgments. I am greatly indebted to Dr. Joanne Simpson, Director of the Experimental Meteor- ology Laboratory, for her help throughout all phases of this research. Without her efforts, the seeding experi- ment would never have been possible, and her advice and suggestions were invaluable in planning and in seeing this research to its completion. I am very grateful to the following groups and indi- viduals for their outstanding assistance: the Research Flight Facility (RFF) which under its Director, Mr. Howard Mason, did its customary superb job in carry- ing out the May 1968 experiment; Dr. Gerry Conrad of RFF, who was particularly helpful in discussions and in helping reduce the liquid water data ; the Radar Meteor- ological Laboratory, University of Miami, which pro- vided radar observations of high quality; Prof. Harry Senn whose discussion of the radar systems was most helpful; the Naval Research Laboratory and particu- larly Mr. Robert Ruskin of NRL, who made his obser- vations available to me; the personnel of the Federal Aviation Agency in Miami for their spirit of cooperation during all phases of the seeding operation; Mr. Alan Herndon of the Experimental Meteorology Laboratory who suffered with me through the many tedious calcula- tions; Mr. Don Takeuchi of Meteorology Research, Inc., for helpful discussions and for his work with the hydrometeor observations; Mr. Glenn Brier, Director of the Meteorological Statistics Group, Washington, D. C., and his associate Mr. Gerald Cotton, for guidance on the statistical analysis and compilation of the randomized seeding instructions; and Mr. John Brown for selecting the radar controls. REFERENCES Andrews, G. I'., 1966: Solar radiation-A useful tool for radar antenna orientation. Tech. Rept., Southern Region, Federal Aviation Agency (unpublished). , and H. V. Senn, 1968: Semi-automatic calibration of receiver and video system characteristics for weather radars. Proc. 13th Meteor. Con)'., Montreal, 20-23. Battan, L. J., 1963: Relationship between cloud base and initial radar echo. J . Appl. Meteor., 2, 333-336. Bethwaite, F. D., E. J. Smith, J. A. VVarburton and K. J. Heffer- nan, 1966: Effects of seeding isolated cumulus clouds with silver iodide. J. Appl. Meteor., 5, 513-520. Braham, R. R., Jr., 1964: What is the role of ice in summer rainshowers? /. Atmos. Sci., 21, 640-645. Davis, L. G., J. I. Kelley, A. VVeinstein and H. Nicholson, 1968: Weather modification experiments in Arizona. Rept., Dept. of Meteor., Pennsylvania State University, University Park, 128 pp. Duncan, A. D., 1966: The measurement of shower rainfall using an airborne foil impactor. /. Appl. Meteor., 5, 198-204. Fletcher, N. H., 1962: The Physics of Raindouds. Cambridge University Press, 386 pp. Flueck, J. A., 1968: A statistical analysis of Project Whitetop's precipitation data. Proc. First Natl. Conf. Weather Modifica- tion, Albany, N. Y., 26-35. Gerrish, R., and H. W. Hiser, 1965: Meso-scale studies of in- stability patterns and winds in the tropics. Rept. No. 7, U. S. Army Electronics Labs., Fort Monmouth, N. J., 63 pp. Gunn, R., and G. D. Kinzer, 1949: The terminal velocity of fall for water droplets in stagnant air. /. Meteor., 6, 243-248. Hiser, F£. W., and G. F. Andrews, 1966: A new approach to range normalization and stepped attentuation for weather radars. Proc. 12th Conf. Radar Meteor., Norman, Okla., 62-66. Howell, W. E., 1960: A comparison between two transformations used in normalizing meteorological data. /. Meteor., 17, 684. Jones, D. M. A., G. E. Stout and E. Mueller, 1968: Raindrop spectra for seeded and unseeded showers. Proc. First Natl. Conf. Weather Modification, Albany, N. Y., 99-106. Kraus, W. E. B., and P. Squires, 1947: Experiments on the stimu- lation of clouds to produce rain. Nature, 159, 489-491. Li, J. C. R., 1961 : Introduction to Statistical Inference. Ann Arbor, Mich., Edward Brothers, 586 pp. MacCready, P. B., 1959 : The lightning mechanism and its relation to natural and artificial freezing nuclei. Recent Advances in Atmospheric Electricity, London, Pergamon Press, 369-381. , and C. J. Todd, 1964: Continuous particle sampler. /. Appl. Meteor., 3, 450-460. McDonald, J. E., 1958: The physics of cloud modification. Advances in Geophysics, Vol. 5, New York, Academic Press 223-303. Malkus, J. S., and R. H. Simpson, 1964: Modification experiments on tropical clouds. Science, 145, 541-548. Mason, B. J., 1962: Clouds, Rain and Rainmaking. Cambridge University Press, 145 pp. Mee, T. R., and D. M. Takeuchi, 1968: Natural glaciation and particle sLre distribution in marine tropical cumuli. Final Rept., Meteorology Research, Inc., Contract No. E22-30-68 (N), 71 pp. Neave, H. R., and C. W. J. Granger, 1968: A Monte Carlo study comparing various two sample tests for differences in mean Technometrics, 10, 509-522. Neyman, J., E. Scott and J. A. Smith, 1969: Areal spread of the effect of cloud seeding at the Whitetop experiment. Science, 163, 1445-1449. Orr, J. L., D. F'raser and K. G. Pettit, 1949: Canadian experiments on artificially inducing precipitation. Water Resources, Vol. 4, U. N. Conf. Conservation and Utilitzation of Resources, p 27. Sax, R. I., 1969: The importance of natural glaciation on the modification of tropical maritime cumuli by silver iodide seeding. /. Appl. Meteor., 8, 92-104. Schaefer, V. J., 1946: The production of ice crystals in a cloud of supercooled water droplets. Science, 104, 457-459. Senn, H. V., ana J. F. Andrews, 1968: A new, low-cost multi-level iso-echo contour for weather-radar use. J . Geophys. Res., 73, 1201-1207. , and C. L. Courtright, 1968: Radar hurricane research. Final Rept., Institute of Marine Sciences, Univ. of Miami, Radar Meteorology Section, Contract No. E22-62-68 (N), 31 pp. Simpson, J., 1970: On the radar measured increase in precipitation within ten minutes following seeding. /. Appl. Meteor., 9, 318-320. 257 J () I k N A L <) I- A P I' I. ]) M K I E UROLOGY Volume 9 — , G. W. Brier and R. H. Simpson, 1967: Stormfury cumulus seeding experiment 1965: Statistical analysis and main results. /. A twos. Sri., 24, 508-521. , and V. Wiggert, 1969: Models of precipitating cumulus towers. Mon. Wea. Rev., 97, 471-489. — , and W. L. VVoodley, 1969: Intensive study of three seeded clouds on Mav 16, 1968. ESSA Tech. Memo ERLTM-APCL 8, 42 pp. — , , H. A. Friedman, G. W. Slusher, R. S. Scheffee and R. L. Steele, 1969: A pyrotechnic cloud seeding system and its use. ESSA Tech. Memo. ERLTM-APCL 5, 44 pp. Sims, A. L., E. A. Mueller and G. E. Stout, 1963: Investigation of quantitative determination of point and areal precipitation by radar echo measurements. Quart. Tech. Rept., 1 July 1963- 30 September 1963, Meteorological Lab., Illinois State Water Survey, Urbana, 27 pp. Takeuchi, D. M., 1969: Anaylsis of hydrometeor sampler data for ESSA cumulus experiments, Miami, Florida, May 1968. Final Rept., Meteorology Research, Inc., Contract No. E22-28 -69 (N), 44 pp. Vonnegut, B., 1947: The nucleation of ice formation by silver iodide. /. Appl. Phys., 18, 593-595. , and K. Maynard, 1952: Spray-nozzle type silver iodide smoke generator for airplane use. Bull. Amer. Meteor. Soc, 33, 420-428. Weickmann, H., 1953 : Observational data on the formation of precipitation in cumulonimbus clouds. Thunderstorm Elec- tricity, University of Chicago Press, 66-138. Woodley, W. L., 1969: The effect of airborne silver iodide pyro- technic seeding on the dynamics and precipitation of super- cooled tropical cumulus clouds. Ph.D. dissertation, Flordia State University, 187 pp. , and A. Herndon, 1970: A rain gage evaluation of the Miami reflectivity-rainfall rate relation. /. Appl. Meteor., 9, 258-264. Reprinted from Science 1 70 > October 9, 127-132 54 Rainfall Enhancement by Dynamic Cloud Modification Massive silver iodide seeding causes rainfall increases from single clouds over southern Florida. William L. Woodley There has recently been discussion on whether the relevant seeding technol- ogy is reliable for practical use (/). This question has proved a difficult one to resolve. Some of the confusion can be attributed to failure to recognize two major points: (i) there are essentially two approaches to seeding for precipi- tation increases, static and, more re- cently, dynamic, with each approach involving different seeding techniques and amounts of seeding material; and (ii) the seeding result depends on the initial conditions of the cloud-environ- ment system. This article elaborates on these points in presenting the results of a new and exciting approach to cloud seeding for rain enhancement. Background Most cloud seeding efforts are predi- cated on producing instability in a su- percooled cloud by introducing one artificial ice nucleus active at — 10°C per liter of cloud air. The artificially induced ice crystals then grow at the expense of the cloud water and, under ideal conditions, reach the ground as precipitation. This approach is referred to here as the static approach to cloud The author is a research meteorologist in the Experimental Meteorology Laboratory, Atlantic Oceanographic and Meteorological Laboratories of the Environmental Science Services Admin- istration (ESSA), at the University of Miami, Coral Gables, Florida 33124. seeding (1, 2). Project Whitetop, ana- lyzed rather extensively by Neyman et al. and by Flueck (3), is an example of static cloud seeding for rainfall en- hancement. The results of such experi- mentation have been rather variable. Although some efforts have produced statistically significant precipitation in- creases, the results from some of the major experiments have been incon- clusive and highly controversial. An alternate approach to cloud seed- ing for precipitation enhancement is directed at the buoyancy forces and circulations that sustain the clouds; it is here referred to as dynamic cloud modification. This approach involves massive silver iodide seeding (100 to 1000 nuclei active at — 10°C per liter of cloud air) of individual supercooled cumulus clouds, which results in in- vigorated cloud dynamics through in- duced release of fusion heat. Dynamic cloud modification is not a new con- cept; it originated in the early days of weather modification (4). Dynamic seeding effects were observed so rarely prior to 1960, however, that serious doubt existed (5) as to the applica- bility of this seeding approach to rain enhancement. The dynamic seeding hypothesis was not tested statistically until randomized cloud seeding experiments were con- ducted over the Caribbean in 1965 (6). Two main results emerged from the experimentation. First, massive seeding can, under predictable conditions, cause cumulus growth, and the cumulus model of the Experimental Meteorology Laboratory (EML) has considerable success in predicting this growth. Sec- ond, the seeding outcome depends on the initial conditions of the cloud- environment system. It was suspected, but not proved, that a cloud under- going explosive growth would precipi- tate more than its unseeded counter- part. Verification had to await the sequels to this experiment. Although not new by concept, the use of dynamic cloud modification in producing documented changes in pre- cipitation is a new feature of recent experimentation in Florida and Arizona (7). As such, it represents a new ap- proach to seeding for rain enhance- ment. The Florida study is the subject of this article. Florida Program Individual supercooled cumulus clouds growing over and near the Florida peninsula were seeded with sil- ver iodide pyrotechnics in May 1968. The cooperative ESSA-Navy effort was conducted to study with aircraft and calibrated ground radars the induced dynamic and precipitation changes in the seeded clouds and to compare them with unseeded clouds, with both seeded and unseeded clouds chosen on a sta- tistically randomized basis. Enumera- tion of project participants and a dis- cussion of the experimental design and pyrotechnic seeding system can be found elsewhere (5). There were 19 experimental clouds during the Florida program: 14 seeded clouds and 5 control clouds, as dictated by the randomized seeding instructions. Twenty 50-gram silver iodide pyro- technics were dropped into each cloud — ten on each of two mutually perpen- dicular passes of the seeder aircraft near cloud top. The seeded clouds grew an average of 3500 meters more than the controls (P<.01) (9). A typical instance of explosive cloud growth subsequent to seeding is shown in Fig. 1 for experimental cloud 5 on Table 1. Comparison of average rainfalls from seeded and control clouds 40 minutes after seed- ing pass. The last group of calculations is relative to the radar-measured rainfall in the 10-minute period before the seeding pass (taken as a standard in our measurement). RCC, radar control clouds. Rainfall from Difference (acre-feet) Difference (%) Seeded clouds Control clouds (acre-feet) (acre-feet) Water calculation (total) Without RCC 237 110 127 115 With RCC 237 97 140 144 Water calculation (relative to standard) Without RCC 167 40 127 $18 With RCC 167 49 118 241 19 May 1968. The rise rate of cloud top was computed photogrammetrically. Photographs of cloud development are shown as insets. Numbers along the rise rate curves correspond to the num- bers of the photographs. Picture 1 was taken from 5500 meters above mean sea level, and all others were taken from 6100 meters. Tower A of experimental cloud 5 was penetrated by a vertical stack of three aircraft at 1755 G.M.T. (Fig. 1, picture 1). After penetration, a fourth aircraft seeded towers A and B with a total of 1 kilogram of silver iodide smoke. In the 5 minutes after seeding, both towers became fuzzy and ap- peared to decay (Fig. 1, pictures 2 and 3). Subsequently, the upshear (south- west) portion of tower B hardened in appearance and grew to over 1 1 ,000 meters above mean sea level at a rate of 12 meters per second (Fig. 1, pic- tures 4 to 8). Predictions based on the EML dynamic cumulus model (70) indicate that experimental cloud 5 would not have behaved as it did had it not been seeded. This cloud pro- duced 312 acre-feet of water in the 40 minutes after seeding compared with 87 acre-feet produced by the control cloud in the same time interval (11, 12). Calculating Cloud Rainfall The main tool for measuring precipi- tation from the experimental clouds was the modified UM/10-cm radar of the Radar Meteorology Laboratory, Rosenstiel School of Marine and At- mospheric Sciences, University of Miami. Its characteristics and opera- tion are treated in detail by Senn and Courtright (13). This radar has a four- level iso-echo contour (IEC) unit that permits contouring of the signal strength of the experimental cloud echoes. An example is shown for part of the life cycle of experimental cloud 5 on 19 May 1968 (Fig. 2). Each contour cor- responds to a discrete radar reflectivity Z(mmi;m-:1), which was converted to the rainfall rate /?(mmhr-1) by using the Miami Z-R relation, Z = 300 /?' 4. The technique of obtaining rainfall 1 l ' I ' I ' T-"1 l ' I i i i i i i i i i i 1 1 1 r 1802 1804 TIME (MINUTES) Fig. 1. Explosive growth of experimental cloud 5 (19 May 1968). Rise rates were computed photogrammetrically. Photographs shown as insets: picture 1 from 5500 meters above mean sea level; all other photographs from 6100 meters above mean sea level. Numbers along rise rate curves correspond to the numbers of the photographs. has been discussed extensively (//). Es- sentially, it involves planimeter inte- gration of the contoured target echoes to provide the total area contained be- tween the contours, with each contour corresponding to a discrete rainfall rate. The contour areas are plotted versus time and are time-integrated. Multiplication of each time-integrated contour area by the appropriate mean rainfall rate and a constant, followed by summation, provides total rainfall during the period of integration. Radar calibration was provided by the scheme of Andrews and Senn (14). The rain- fall analysis for an individual experi- mental cloud was discontinued when its echo merged with a neighbor. As a consequence, the analysis represents a bias in favor of the smaller, drier, nonmerging clouds. A representative cloud sample was possible to 40 min- utes after the seeding pass. Five addi- tional control clouds, conforming to the selection criteria for the experi- mental clouds, were included in the rainfall analysis (//). These clouds will be referred to as radar controls to dis- tinguish them from the controls that were selected randomly. Two comparisons were made be- tween seeded and control rainfalls. First, total radar-measured rainfall from the seeded clouds in 10-minute intervals (after the time of the first seeding pass) was compared with rain- fall from the control clouds. Second, the seeded and control clouds were compared among themselves and then with one another. The radar-measured rainfail from a given cloud in the 10- minute period before the seeding pass was taken as a standard, which was then subtracted from the radar-mea- sured rainfall produced by the cloud in 10-minute intervals after the seed- ing pass. Precipitation varied widely from cloud to cloud and from day to day, but, on the average, the seeded clouds precipitated twice as much as the con- trol clouds, with the difference aver- aging between 100 and 150 acre-feet by 40 minutes after seeding (see Fig. 3a). The number in parentheses near each data point refers to the number of clouds contributing to the average. Inclusion of the five additional radar control clouds does not change the curves significantly. The average post- seeding total water from the seeded clouds exceeds that from the controls by at least a factor of 2 for each 10- minute interval. Table 2. Statistical test of rainfall results. All tests were two-sided. RCC, radar control clouds. Type of test Significance (%) With- out RCC* With RCCt With RCC and mergers}: Student's / 20 <10 <10 Normal scores <10 <5 <5 Wilcoxon- Mann- Whitney . 20 <10 <10 * JV, (size of seeded sample) = 8; /Vn* (size of nonseeded sample) —4. t NB — 8; Nns = 9. JN., = 13; N„» = 10. The results of the analysis change little when the rainfall after the seed- ing pass is referenced to the rainfall in the 10-minute period before the seed- ing pass (Fig. 3b). The mean of refer- enced seeded rainfall is greater than control referenced rainfall in all time intervals. Average rainfall from seeded clouds is compared with rainfall from the con- trol clouds in Table 1. The differences would have been greater if calculations had been possible for entire cloud life- times. The difference in mean total water between the seeded and control clouds 40 minutes after the seeding pass was tested for significance by (i) a pooled Student's,/ statistic with the variances as- sumed equal (a good assumption), (ii) the normal scores test, and (iii) the Wilcoxon-Mann-Whitney test. The re- Seeding time suits are shown in Table 2. In the last category (radar control clouds plus the mergers), the clouds that were dropped from the data sample because of merg- ers with surrounding echoes were as- sumed to persist in a steady state until 40 minutes after the seeding pass. The rainfalls produced by these clouds in the 10 minutes before they were dropped from the sample were assumed to fall in 10-minute intervals until the 40-minute cutoff. This artifice per- mitted all clouds to be retained in the sample, which resulted in a total popu- lation of 23 clouds. The significance of results from two-tailed tests increases with sample size. The results give strong support for the hypothesis that dynamic cloud modification increases precipita- tion. An alternate statistical approach to the problem (11) supports the con- clusions reached above. Accuracy of Rainfall Calculations When radar is used in the evaluation of a cloud seeding experiment, it is necessary to determine how accurately the radar-derived precipitation changes represent real effects at the ground. The errors associated with the radar measurement of precipitation during May 1968 were evaluated by 50 direct comparisons of rainfall measured by radar and by rain gage (15). A direct comparison was not possible for the seeded clouds because none passed over 1821 GMT 1830 GMT 1838 GMT Greater than .05 mm/hr 1850 GMT Greater than 89.0 mm/hr Fig. 2. Example of cloud base iso-echo contouring for cloud 5 (19 May 1968). rain gages during the operation of the radar. Based on the rain gage as the standard, the average error is an 8 per- cent underestimate by the radar when the differences are summed algebraically and about 30 percent when their abso- lute values are summed. The average percentage difference is defined here as the average difference between the rainfalls measured by gage and radar divided by the average gage rainfall, rather than the mean of the individual percentage differences, in order to avoid giving undue weight to the few com- parisons with small absolute differences but with large percentage differences. The correlation coefficient between the radar and gage rainfalls was 0.93 (P < .01). The radar-rain gage comparison in- dicates that the radar in conjunction with the Miami Z-R relation gave a rather good approximation of unmodi- fied shower rainfall. Because the Miami -10 (12) A-, (id IIS)/ X(8) Including radar controls -10-0 sor 0-10 10-20 20-30 30-40 -10-0 0-10 10-20 20-30 30-40 Time interval relative to seeding pass -10 -10-0 0-10 10-20 20-30 30-40 -10-0 0-10 10-20 20-30 30-40 Time interval relative to seeding pass Fig. 3. Average rainfall from the experimental clouds inferred from Z = 300 R1-*. Solid lines, control clouds; dashed lines, seeded clouds; dot-dashed lines, difference between seeded and control clouds. Numbers in parentheses indicate the number of clouds in the sample. Time intervals are in minutes, (a) Average total water in 10-minute inter- vals relative to the time of the first seeding pass, (b) Average water relative to the water produced in the 10-minute period before the seeding pass. Z-R relation is just as valid for showers from seeded clouds (11), the radar represented seeded shower rainfall equally well; thus, the radar-derived precipitation increases probably repre- sent real increases at the ground. Interpretation of Seeding Results The amount of rain from the seeded clouds was positively correlated (cor- relation coefficient 0.90, P < .01) with the maximum top growth that followed seeding (7/). The more a cloud grew after being seeded, the more rain it produced, which suggests that the precipitation increases were the result of the dynamic invigoration of the seeded clouds. The seeded clouds were larger and longer lasting; they processed more moisture than their unseeded counterparts and thus accounted for the increases in precipitation. Cloud physics research revealed that the static approach to cloud seeding is apparently not applicable to supercooled Florida cumuli. All cumuli in which measurements were made had one ice particle per liter of cloud air at — 10°C before the seeding pass. Because the static approach to cloud seeding re- quires that this ice concentration be produced artificially for optimum re- sults, this approach is not germane for cloud seeding over southern Florida. The dynamic approach worked despite the natural ice concentrations because there was still enough fusion heat potential in the smaller unfrozen drops to provide the impetus for dynamic changes induced by seeding. This discussion is particularly perti- nent to Project Whitetop, in which the static cloud seeding aproach was used in an attempt to increase rainfall. While researching basic cloud physics during the program, Braham (761 found natu- ral ice concentrations as high as 10 particles per liter in Missouri cumuli with top temperatures of — — 10CC. In commenting on these findings, Bra- ham noted, "The presence of numerous small particles in these clouds at tem- peratures warmer than — 10°C casts doubt upon the value of seeding with ice nuclei for rain inducement." Bra- ham's finding may be a partial explana- tion for the failure of the static ap- proach to produce rainfall increases from seeded Missouri cumuli. With re- spect to Whitetop, the relevant question is not whether seeding is reliable enough for practical use but whether seeding was done under conditions favoring precipitation increases. The an- swer to the latter, more pertinent ques- tion is apparently in the negative. The failure of one cloud seeding ap- proach in a region need not preclude the other. Dynamic cloud modification may be relevant for rain inducement from Missouri cumuli despite the fail- ure of the static approach. McCarthy (17) has made a first step in resolving this uncertainty. The discussion above is not an in- dictment of the static approach to cloud seeding for all areas and all seasons. This approach has been eminently suc- cessful in some areas — in Australia (18), for example — and there may be situations in which it is the only rele- vant approach to cloud seeding. The point for emphasis is that basic research must precede any seeding effort, whether it be static or dynamic, to de- termine which seeding approach, if any, is germane to producing the desired effect. Stratification of the rainfall results of a seeding operation frequently pro- vides information not obvious in ini- tial examination of the data — as, for instance, in the analysis of the May 1968 Florida experiment. Large in- creases in precipitation were noted dur- ing the first half of the seeding pro- gram, which was characterized by fair conditions with only isolated natural showers. Little effect of seeding was noted during the second, naturally rainy half of the program (19). Dennis and Koscielski (20) had essentially the same result from a cloud seeding experiment in South Dakota, as did Davis et al. (21) in stratification of data obtained by Battan (22) during southern Arizona seeding operations. Preliminary analysis of Project Whitetop indicates a similar finding for Missouri (23). The high positive correlation between cloud growth and water production sug- gests that a dynamic cumulus model that can predict cloud growth after seeding can also be used to infer the effect of seeding on precipitation. This effect has been quantified in terms of EML numerical model predictions by establishment of a relation between seedability (5) and the measured rain- fall increase from seeding (AR) (see Fig. 4). Seedability is the predicted dif- ference between the seeded and un- seeded maximum top height of the same cloud. Rainfall decreases are found for seedabilities less than about 0.8 kilom- eter, but increases of several hundred acre-feet per cloud are associated with seedabilities above 3 kilometers. This i i i S (km) Fig. 4. Rainfall change (SR) as function of seedability (S). finding is in agreement with the strati- fication of seeding results by weather regime because large seedabilities are characteristic of fair weather conditions with only isolated showers, whereas small seedabilities are characteristic of disturbed, naturally rainy conditions. The relationship between S and AR indicates that the dynamic approach to cloud modification can produce both increases and decreases in rainfall un- der specified conditions. Further, it argues against blindly seeding all avail- able clouds before some attempt has been been made to delineate favorable versus unfavorable seeding conditions. Our results have shown that massive seeding of an individual cumulus cloud may increase rainfall by several hun- dred acre-feet per cloud, but it is im- portant to know whether this increase represents a net increase, a decrease, or merely a redistribution of the rainfall over an area encompassing the seeded cloud. This uncertainty was investigated with two different approaches (24). The results showed that the large-scale ef- fects of single cloud seeding were small precipitation increases, but severe data limitations and the low significance level of the increases (P ~ .20) do not allow much confidence in this result. The success of massively seeding in- dividual cumuli for precipitation in- creases does not necessarily imply its success on a larger scale. It must still be demonstrated that individual seed- ings of many supercooled cumuli are effective in altering cloud developments and precipitation over hundreds of square kilometers. To investigate this uncertainty, EML designed a multiple cloud seeding experiment for a target area of 5000 square kilometers in southern Florida (25), which was exe- cuted during July 1970. Acceptable experimental days satisfied a predeter- mined set of suitability criteria. Ran- domization was in time rather than in space. Radar was the main tool for precipitation evaluation. Summary and Conclusions In summary, the following points are made: 1) There are essentially two ap- proaches to seeding for rain induce- ment, static and dynamic. 2) The dynamic approach is effective in inducing growth and increasing pre- cipitation from individually seeded con- vective clouds under specifiable condi- tions. 3) The static approach to seeding for precipitation increases is apparently not relevant to the summer cumuli of Florida and Missouri. 4) Regional seeding climatologies, in- cluding studies of natural freezing processes in convective clouds, should be completed before commencement of a seeding operation. 5) The results of a seeding operation are frequently better understood by stratification of the data, especially with respect to weather conditions. Precipi- tation increases from seeding are usu- ally found under fair weather regimes with isolated showers, whereas de- creases are often noted under naturally rainy conditions. It is premature to recommend rou- tine use of dynamic modification as a practical means of increasing precipita- tion over large areas. Cloud and en- vironmental conditions favoring large increases in precipitation must be bet- ter specified. Predictions by the EML numerical model, which indicate that large precipitation increases can be ex- pected from clouds with large seed- abilities, are a first step. The optimum amount of silver iodide for the desired effect is still to be specified. The effect of dynamic seeding on cloud develop- ments and precipitation in the near and distant environments of the individually seeded clouds, and the precipitation effects of massively seeding many con- vective clouds over hundreds of square kilometers remain unknown. Although it is still too early for a proper evaluation of dynamic cloud seeding as a routine tool for altering rainfall, first results are very encourag- ing. If dynamic seeding proves success- ful on a large scale over many regions of the globe, man will have taken a major step toward water management and the mitigation of severe storms. References and Notes 1. J. Simpson, Med. Opin. Rev. 5, 39 (1969). 2. M. Tribus, Science 168, 201 (1970). 3. J. Neyman, E. Scott, J. A. Smith, ibid. 163, 1445 (1969); J. A. Flueck, Proc. First Nat. Cont. Weather Modification (Albany, New York, 1968), pp. 26-35. 4. V. J. Schaefer, Compendium of Meteorology (Waverly, Baltimore, 1951), pp. 221-234; E. B. Kraus and P. Squires, Nature 159, 489 (1947). 5. J. E. McDonald. Advances in Geophysics (Academic Press, New York, 1958), pp. 223- 303. 6. J. S. Malkus and R. H. Simpson, Science 145, 541 (1964). 7. A. J. Weinstein and P. B. MacCready, Jr., J. Appl. Meteorol. 8, 936 (1969). 8. J. Simpson, W. L. Woodley, H. A. Friedman, T. W. Slusher, R. S. Scheffee, R. L. Steele, ibid. 9, 109 (1970). 9. Symbol P represents the two-tailed signifi- cance probability. 10. J. Simpson and V. Wiggert, Mon. Weather Rev., in press. 11. W. L. Woodley, J. Appl. Meteorol. 9, 242 (1970). 12. 1 acre-foot = 1.23 X 103 m3 = 1.23 X 10» grams of water. 13. H. V. Senn and C. L. Courtright, Final Rep. [Institute of Marine Sciences, University of Miami, Radar Meteorology Section, contract E22-62-68(N), 1968], 31 pp. 14. G. F. Andrews and H. V. Senn, Proc. 13th Radar Meteorol. Conf. (Montreal, Canada, 1968), pp. 20-23. 15. W. L. Woodley and A. Herndon, J. Appl. Meteorol. 9, 258 (1970). 16. R R. Braham, Jr., /. Atmos. Sci. 21, 640 (1964). 17. J. McCarthy, Proc. First Nat. Conf. Weather Modification (Albany, New York, 1968), pp. 270-279. 18. F. D. Bethwaite, E. J. Smith, J. A. Warbur- ton, K. J. HefTernan, /. Appl. Meteorol. 5, 513 (1966). 19. J. Simpson, paper presented at the symposium on tropical meteorology (American Meteorol- ogical Society-World Meteorological Organiza- tion, Honolulu, Hawaii, 2-11 June 1970). 20. A. S. Dennis and A. Koscielski, J. Appl. Meteorol. 8, 556 (1969). 21. L. G. Davis, J. I. Kelley, A. Weinstein, H. Nicholson, "Weather Modification Experi- ments in Arizona" [Report No. 12A of the Department of Meteorology, Pennsylvania State University, University Park (1968), 128 pp.]. 22. L. J. Battan, J. Appl. Meteorol. 5, 669 (1966); ibid. 6, 317 (1967). 23. R. R. Braham, Jr., personal communication. 24. W. L. Woodley, A. Herndon, R. Schwartz, ESSA Tech. Mem. ERLTM-AOML 5 (1969), 26 pp. 25. W. L. Woodley and R. Williamson, ESSA Tech. Mem. ERLTM-AOML 7 (1970), 24 pp. 26. I thank Dr. Joanne Simpson, director of EML, and Alan Miller, Robert Powell, and Mrs. Suzanne Johnson for advice and assistance in writing this article. COVER Cloud on 19 May 1968 that is grow- ing explosively 13 minutes after hav- ing been seeded with silver iodide pyrotechnics. Height of the cloud top is 11.5 kilometers enroute to a maxi- mum height of approximately 12.5 kilometers. Picture was taken from a DC-6 aircraft flying at 6.1 kilometers over southern Florida. See page 127. [Environmental Science Services Ad- ministration Research Laboratories, Coral Gables, Florida] Reprinted from Journal of Applied Meteorology 3, No. 2, 258-264 55 258 JOURNAL OF APPLIED METEOROLOGY Volume 9 A Raingage Evaluation of the Miami Reflectivity-Rainfall Rate Relation William Woodley and Alan Herndon Atlantic Oceanographic and Meteorological Labs., ESS A, Coral Gables, Fla. (Manuscript received 23 September 1969, in revised form 10 November 1969) ABSTRACT To provide a foundation for other radar studies in the Miami areas, 50 comparisons were made between shower rainfall recorded by raingages and observed with radar to evaluate the reflectivity Z, rainfall rate R relation, Z = 300i?M, referred to here as the Miami Z-R relation. Total shower rainfalls measured by recording raingages were compared with estimates derived from the Miami Z-R relation in conjunction with radar reflectivity measurements with iso-echo contouring and the analysis scheme described. Rainfall rate com- parisons were not possible because of the poor time resolution of the raingage observations. The radar and raingage estimates of shower rainfall were highly correlated (+0.93, significant at the 1% level) ; they had an average difference of 8% and a mean absolute difference of 30%. Stratification by shower amount revealed that the radar estimate of gage-recorded rainfall was too high for small shower amounts (<0.25 inch) and too low for large shower amounts. In terms of percentage the comparison was best for the heavy showers. Stepwise regression analysis showed that consideration of the square of the range from gage to ra- dar, in addition to range normalization already provided in the radar receiving system, made a small (3%) but statistically significant (<1% level) reduction in the variance and improved the correlation (0.93 to 0.944) between the gage and radar estimates of precipitation. It is concluded that the Miami Z-R relation, when used with the radar system described, is an effective tool in representing point and area rainfall from South Flordia convective showers. 1. Introduction Over the last two decades radar has been tised for quantitative measurements of rainfall, based on investi- gations relating rainfall rate R to reflectivity Z. The Z-R relations, computed directly by measuring radar reflectivity and rainfall amount or indirectly by mea- suring raindrop size spectra, have been derived for various locations, seasons and storm types. Stout and Mueller (1968) give an excellent survey of these rela- tions and a discussion of their accuracv when used for quantitative rainfall measurements. The accuracy of Z-R relations is assuming greater importance because these relations are now being used in evaluating the results of seeding experiments designed to increase rainfall. Cloud seeding experiments in Arizona (Davis et al, 1968) and in Florida (Woodley, 1970) are but two recent examples. The Florida study showed that seeding increased rainfall an average of 100-150 acre-ft per cloud by 40 min after the seeding pass, representing an increase of over 100%. If these radar-derived precipitation results are to have credi- bility, it is important to demonstrate that the Z-R rela- tion and the radar system used in the analysis accurately represented rain reaching the ground during the period of experimentation. The Miami Z-R relation is based on the work by Sims et al. (1963) who obtained the Z-R relation Z = 286fl1-« (1) by independently calculating reflectivity (Z inmm6m-3) and rainfall rate (R in mm hr_1) from raindrop photo- graphs taken during showers in Miami. Eq. (1) has been modified slightly to lZ=S00R1A, (2) by Gerrish and Hiser (1965), who averaged the coeffi- cients and exponents of the Z-R relations derived by Sims et al. (1963) for air mass (wet season), easterly wave, cold trough and overrunning situations, and for showers and thunderstorms for Miami. Eq. (2), referred to here as the Miami Z-R relation, is evaluated in this paper by comparing recording raingage measurements with shower rainfall estimated from the same filmed radar observations used in studying the experimental clouds during May 1968. Only total shower rainfalls were compared because the time scale on the recording raingage trace was too compressed to permit rainfall rate comparisons. Gage measured rainfall was the stan- dard of comparison, although the accuracy might be questionable since no attempt was made to evaluate the condition and exposure of the raingages used. 2. Radar systems The modified UM/10-cm radar of the Radar Meteor- ological Laboratory, Institute of Marine Sciences, Uni- versity of Miami, was used in the comparison. It has a 2° conical beam, a transmitter power of 5.5 X105 W, a April 1970 WILLIAM WOODLEY AND ALAN HERDNON 259 81*30' 81 15 81*00' 80*45' 80*30' 80*15' 27*00' — 26*45' 26 30 26*15' — i 26*00' — 25*45 25*30' 25*15' 26*15' -*r 27*00 26*45' 26*30' 26*00' — 25*45- — 25*3C 25* IS 81*30' 81*15' ei'oo1 80*45' 80*30' aCis4 Fig. 1. Example of contoured echoes superimposed on the South Florida raingage network. The first (boundary) contour corresponds to 0.006 inch hr""1, the second to 0.09 inch hr-1. Inside the white area the rainfall rate >0.40 inch hr-1. 260 JOURNAL OF APPLIED METEOROLOGY Volume 9 Table 1. Comparison of radar (Ra) and raingage ((/') rainfall using recording raingages and the UM/10-cm radar. DATE STN. NO. RAIN GAGE MEASUREMENTS RADAR MEASUREMENTS (IN.) G-Gp Gp=-0. 1468 + 1 I426R DIST. OF GAGE (MAY) MAX RAINFALL SHOWER RAINFALL (RQ) , FROM RADAR RAINFALL (G) RATE (IN HR-1) DURATION (IN.) + OOOISSd* (N. Ml.) (IN.) (MIN.) 1 6 433 00 2 0 1 1 01 -.0 1 -.03 33.3 16 423 .07 45 37 10 -.03 -.0 9 35.8 1 6 4 1 5 05 1 0 35 03 0 2 .0 5 27.5 19 422 1.22 3.40 52 .71 51 22 47.0 1 9 423 22 2.00 44 .29 -.07 -.1 6 35.8 1 9 425 .1 5 .80 70 22 -.07 -.0 7 2 7.4 1 9 430 .1 8 1.50 56 37 -.19 -.18 2 3.0 1 3 4 1 5 .OS 1.50 62 1 8 -.1 3 -.1 2 27.5 1 9 425 08 60 30 .10 -.02 00 2 7.4 1 9 424 03 20 29 .02 .0 1 0 8 2 1.6 1 9 424 .20 1.00 34 .1 3 .0 7 .1 3 2 1.6 20 8 1 2 .78 1.50 62 .4 1 .37 .35 2 7.0 20 426 1.4 1 3.60 56 1.19 22 .08 28.1 2 0 428 10 40 1 5 03 07 -.0 1 38.2 20 604 2 1 4.00 35 46 - 25 -.2 3 20.4 20 605 ! 9 2.00 22 .2 1 -.02 -.0 1 2 6.5 20 423 .1 1 50 2 09 .0 2 -.04 35.8 20 435 39 3.50 28 40 -.0 1 .0 0 2 3.5 20 807 99 3.50 65 92 .07 .0 1 22.5 20 6 1 3 1 8 60 48 .1 1 07 .1 2 2 3.5 2 1 435 .10 1.00 35 .1 3 -.03 .02 23.5 2 1 605 0 1 50 1 6 02 -.0 1 .03 26.5 2 5 807 .4 8 65 3 8 39 09 1 1 22.5 26 702 .20 1.50 32 1 3 07 -.03 38.7 26 433 1.06 3 00 35 77 29 1 6 33.3 27 426 1 1 1.50 1 8 1 4 -.03 -.02 28 1 28 428 30 55 35 1 8 1 2 .0 2 382 2 8 8 1 2 .1 7 50 50 1 6 .01 .0 2 2 7.0 2 8 8 1 2 .47 90 55 33 14 .1 3 2 7.0 2 8 6 1 1 .1 5 50 48 .16 -.01 . 14 22.1 28 432 02 40 22 0 5 -0 3 -.2 1 45.6 2 8 422 .43 .45 1 7 06 37 .1 7 47.0 2 8 807 .13 45 50 1 1 02 .0 8 22.5 2 8 807 03 60 20 06 -.0 3 .0 3 22 5 2 8 804 1 5 60 22 07 08 .02 36.1 30 6 1 3 00 40 1 4 04 -.04 .02 23.5 30 423 06 .60 28 10 - 04 -.10 35.8 30 605 68 4.00 64 .81 -.13 -.2 1 26.5 30 423 90 4 00 60 77 13 -.03 35.8 30 423 .98 4.00 73 1.04 -.06 -.26 35.8 30 605 .22 5.00 17 .62 -.40 -.45 26.5 30 424 .38 5.00 32 55 -.17 -. 17 2 1.6 30 426 .1 8 1.00 2 1 .17 .0 1 .0 1 28.1 30 807 22 2 45 2 1 30 -.08 -.05 22.5 30 807 .60 2 00 38 46 .1 4 -.15 22.5 30 8 1 1 04 55 26 07 -.03 .0 3 22.1 30 8 1 2 .05 .60 20 09 - 04 -.02 2 7.0 30 6 1 1 48 3.55 30 38 .10 1 2 22 1 30 702 1.40 4.00 1 1 3 1.05 35 .12 38.7 3 0 435 1 59 5.00 75 1.30 .29 .17 23 5 minimum detectable signal of 10~H W, a pulse length of 2 jusec, and a pulse repetition rate of 300 pulses sec-1. Included are special logarithmic and linear radar re- ceivers, an rf range attenuation corrector, and an iso- echo contour (IEC) unit. The UM/10-cm radar was calibrated twice daily during the experiment. For more details on this radar unit, including a discussion of its calibration, the reader is referred to Senn and Court- right (1968) and Woodley (1970). The comparisons between radar and raingage rainfall observations were made in the annulus 20-50 n mi from the radar. The antenna tilt was 0.5°, which means that the center of the radar beam was within 1500 ft of cloud base (~2500 ft) for clouds within this annulus. All April 1970 W AM WOODLEY AND A I. A N HERNDON 261 Table 2. Statistical summary of comparison between rainfall recorded by rain gages (G) and observed by radar (/?„). Columns 1-5 are in inches, columns 6 and 8 percentages, the others dimensionless. 1. 2. G 3. ZRa 4. Ha 5. 6. G-Ra — XlOO G 7. 8. 9." 10> b 11 \g-r«\ — XlOO G ZG G-Ra \G-Ra\ *.. 17.51 0.36 16.58 0.33 0.03 8 0.11 30 0.93 0.80 0.06 a Correlation of G and Ra. b Slope of least-squares best fit line. c Intercept on Ra axis of least-squares best fit line. cloud echoes were contoured with the IEC unit built at the radar laboratory (Senn and Andrews, 1968). 3. Method The photographs of the radarscope were projected frame by frame onto the raingage map as shown in Fig. 1. The map projection represents true distances to within 50 ft. The ground targets on the map were aligned with the corresponding ground targets on the radar film. Several areas of contoured echoes are shown schematically on the raingage map. Each contour corre- sponds to a reflectivity threshold and rainfall rate; the former was obtained with the calibration systems de- scribed by Andrews and Senn (1968), the latter from the Miami Z-R relation (2). Readings were made from the radar photographs taken at 1-2 min intervals at the location of a recording raingage, plotted vs time, integrated with a planimeter to provide total shower rainfall, and then compared with the shower rainfall recorded by the raingage. Evaporation of the raindrops in falling from the level of scan to the ground was neglected. The person reading rainfall rate from the film did not know the gage amount until after the reading. A linear interpolation scheme was used to determine the radar rainfall rate at a gage location between two known contours. The rainfall rate for a point bounded by only one contour, A for example, was obtained by linearly interpolating between A and the next higher contour permitted by the system, which was assumed to exist as a point value at the center of the area con- tained by A. The rainfall rate for a point within the highest contour permitted by the system was linearly interpolated between the boundary value and a rainfall rate of 6.00 inches hr_1, which was assumed to exist as a point value at the center of the contoured area. 4. Analysis problems Comparing a radar estimate of shower rainfall with a raingage estimate is difficult. The vertical separation (1000-4000 ft) between the gage and the level of the radar scan, and the drift of the precipitation while fall- ing this distance, are decided problems. Also degrading the comparison are the tremendous differences between the size of the radar and raingage samples and the likelihood that the radar beam at 0.5° elevation is never uniformly filled with precipitation. The most serious obstacles are the convective rains in Florida; the ob- servation that it often rains heavily on one side of the street and not on the other, is certainly true here. Un- fortunately, the 10-cm radar does not have resolution to this distance scale, and even if it did, the 0.5 n mi diameter of the dot representing the raingage precludes accurate rainfall rate interpolation on a scale less than one-half the dot's diameter. Because a gage might easily be placed too close or too far by 0.25 n mi with respect to an echo, there will be errors in representing rainfall with a radar at the location of a gage even if the Z-R relation, the map projection, and the raingage locations on the map are perfect. However, the resulting error in estimating point rainfall should not be systematic. 5. Results The raingage (G) and radar observations (Ra) per- mitted 50 comparisons, none of which involved seeded clouds. These comparisons are tabulated in Table 1 and summarized in Table 2. Using the raingage results as the standard, the mean absolute difference is about 30% while the mean difference is an 8% underestimate by the radar. The mean difference is defined here as the average difference divided by the average gage-recorded rainfall, rather than the mean of the individual percent- age differences, in order not to give undue weight to the few comparisons with the small absolute differences but Table 3. Stratification by shower amount of G and Ra comparison. n* Rainfall G — Ra o category (inches) G G-Ra (inches) G (inches) G—Ra 00.50 15 17 7 11 0.046 0.175 0.418 1.055 -0.023 -0.49 0.04 -0.046 -0.27 0.13 0.091 0.22 0.18 0.200 0.20 0.20 -1.74 -2.83 1.98 1.00 T.L{G~Ra^-{G-Ra)J n-2 * Number of observations. 262 JOURNAL OF APPLIED METEOROLOGY Volume 9 1.70 1.60 1.50 1.40 1.30 1.20 v> 1.10 uj I o 5 1.00 'o IE ~ .90 _1 _i 10,000 ft) growth with a subsequent increase in horizontal size and cloud duration All growth modes were noted in the Caribbean experimentation while the explosive growth mode predominated in Florida in 1968. In all studies silver iodide rockets called Alectos (Malkus and Simpson, 1964) or flares (Simpson et al.,1970) were dropped into the cloud near its top. The growth mode a cloud exhibits is a function of the meteorological environment in which it grows. None of the modes are peculiar to seeded clouds; all have been observed at one time or another in non-seeded con- vective clouds. Only through proper physical modelling and statistics can one be certain that the behavior of a seeded cloud is truly the result of seeding and not due to natural causes. Physical modelling has been accomplished in the cited experiments through the use of a one-dimensional model of a rising cumulus tower as both a prognostic and diagnostic tool. This model has undergone continuing development over the past ten years (Simpson et al., 1965; Simpson and Wiggert, 1969; Simpson and Wiggert, 1971). The 1965 Caribbean experiment, an effort both suggested and guided by the numerical model which predicted its outcome, showed conclusively that the model had considerable success in predicting both seeded and unseeded cloud tops to an accuracy within several hundred meters, and in delineating the growth mode as a function of environmental conditions. Although qualitative inferences of the effect of single cloud seed- ing on rainfall were made during the Caribbean studies, no quantitative information was available until analysis of results obtained during the 1968 Florida experimentation (Woodley; 1970). Fourteen seeded clouds, five controls and five radar controls were obtained during this experiment. The seeded clouds grew an average of 11,400 ft more than the five controls, a difference significant at the 0.5 percent level. The 10-cm radar derived precipitation results indicated that the seeded clouds precipitated an average of 100 - 1 50 acre-feet more than the controls by kO min after the seeding pass, a difference significant at the 5-20 percent level using three d ifferent, two-tailed statistical tests. The average percentage precipitation increase produced by seeding exceeded 100 percent using two different analysis schemes. An important result was the statistically significant, positive correlation between precipitation and cloud growth following seeding, demonstrating that dynamic cloud invigoration produces precipitation increases. It was found from a radar-rain gage comparison (Woodley and Herndon, 1970) that the absolute magnitudes of the radar-derived precipitation are accurate to within 30 percent and the similarity of the drop spectra measure- ments in the seeded and non-seeded clouds suggested that the reflectivity- rainfall rate relation (Miami Z-R relation) used in the precipitation cal- culations was equally valid for the seeded clouds. An investigation of the large-scale precipitation effects of single cloud seeding (Woodley et al«, 1969) indicated that if present these were not detectable in the re- stricted data sample. The cumulus model results are especially interesting (Simpson and Wiggert, 1971). With measured cloud base and radius, and an environmental sounding as input, the model predicted cloud growth and provided an esti- mate of tower rainfall. The average absolute error for the top predictions was 291 m for the seeded clouds and 528 m for the controls. The correlation 1 O between seedability and seeding effect was 0.96 (significance 0.5 percent), while the correlation between seedability and seeded minus control rainfall was 0.87 (significance 0.5 percent). While the model grossly underestimated 1 Seedability is the predicted difference between the seeded and unseeded maximum top height of the same cloud. 2 Seeding effect is the difference between observed cloud top height and predicted cloud top height if the cloud is not seeded. rainfall from all clouds, the 1 968 data suggested that an empirical regression between seedability and measured increases might be useful in estimating the potential amount of rain augmentation. The effect of seeding depends on the synoptic conditions in which the cloud grows (Simpson and Wiggert, 1971). !n 1 968 the first half of the Florida program (May 15-21) was fair with only scattered showers and weak wind shear while the latter half (May 26-June 1) was highly disturbed with strong vertical wind shear (Fernandez-Partagas , 1969). Seedab i 1 i t ies were about twice as large in the fair period and cloud explosion following seeding was more common and more pronounced. As a consequence, the average rain- fall change due to seeding was large and positive in the fair period and small or negative during the disturbed period (Simpson and Wiggert, 1971), perhaps due in part to the inhibiting effects of strong vertical wind shear upon cloud explosion. 2. APPROACH TO CURRENT STUDY Because of the inadequate cloud sample, particularly of control clouds, obtained in 1968, the Experimental Meteorology Laboratory (EML) and Research Flight Facility (RFF) of NOAA in conjunction with the Naval Research Laboratory (NRL) , the Radar Laboratory of the University of Miami, the U.S. Air Force and the National Weather Service, has conducted an im- proved repeat of the single cloud experiment and advanced the next logical step in cumulus modification, namely a multiple cloud experiment to see if the effects of single cloud seeding can be enhanced in many clouds over a target area. Only the single cloud studies are treated here. The 1970 repeat of the single cloud experiment was planned to in- clude the following improvements, some of which will be discussed in detail later: (a) a longer experimental period, (b) randomization in pairs, (c) seeding by the RFF DC-6 and (d) improved instrumentation including a trans- ponder receiver in the Radar Laboratory. The goals were a cloud sample large enough (-"30) to put the rainfall results on stronger statistical grounds, better specification of the conditions for precipitation changes, improved numerical modelling and understanding of the cloud physical and dynamic processes and their interaction. With the 1968 data a limited attempt was made (Woodley et al., 1969) to determine the large-scale effects of single cloud seeding; it is hoped with the current data that this rather inconclusive study can be extended and improved. This paper reports on the design, execution and rainfall results of the 1970 single-cloud experiment. Further reports will follow later on the aircraft penetration data and the numerical modelling studies. 3. DESIGN OF THE EXPERIMENT The design of the 1970 single cloud seeding program was essentially that used in 1 968 with several improvements described below. The seeding was designed to glaciate the supercooled portions of the clouds rapidly and completely to provide the impulsive fusion heat release necessary for dynamic invigoration and increased cloud growth. Precipitation changes were expected as the by-product of the dynamic alterations. 3.1 EML Cumulus Model Predictions of the EML cumulus model in real time assumed more im- portance than ever before in the 1970 program. Morning model predictions of seedability were invaluable in anticipating the results of a day's seeding operation. Model predictions of no seedability during the spring drought were often the basis for early cancellation of flight operations. During the program no seedable cases were missed, and no major errors were made in timing or launching a flight, showing the value of the model predictions . The version of the model used was EMB 68P (as found by Simpson and Wiggert, 1971, to be the most realistic so far). It was run each day with the 1200 GMT sounding, using a hierarchy of five radii, ranging from 750 to 2000 m,the range measured in 1968. Four different cloud bases were also used, namely 396, 610, 915 and 1220 m. It was generally possible to estimate from the condensation level and the previous day's conditions which cloud base was most applicable. Frequently the model predictions by themselves were a clear indication for cancellation of the day's flight program. On suppressed days, no cloud radii reached the -k C level, while on highly disturbed days natural cloud growth was so large that seedabi 1 i t ies did not much exceed 1 km. Flights were usually attempted on days where seedabi 1 i t ies exceeded 1 km for one or more radii. That this procedure with the model worked rather well is attested to by the fact that only six flights were made without seeding, out of a possible total of fifty-nine. Clouds were actually seeded on nine operational days, as will be described later. 3.2 Randomization Randomization in pairs to insure a control cloud for every seeded cloud was planned for the 1970 program instead of the weighted randomization in favor of the "seed" instruction used in May 1968 . The possibility of bias is the price one must pay for this improvement because there are times when the experienced scientist may recognize a seeded cloud from its growth behavior. With randomization in pairs the seeding decision for the second "GO1 cloud is the opposite of the first. Therefore, sealed seeding instructions are opened for every other cloud selected. 3.3 Seeding System and Procedures A marked improvement in the design of the 1970 program was the in- stallation of a seeding capability on the NOAA DC-6. This change in no way reflects dissatisfaction with the performance of the B-57 seeder during May 1968. The reasons for this change are many, including: (a) DC-6 seeding permits a faster, more coordinated operation, allows the scientist select- ing the clouds to do the seeding in the active portion of the cloud while remaining unaware of his seeding action, and eliminates a pre-seeding pass thereby reducing destruction of the cloud by the aircraft, (b) DC-6 seeding permits liquid water, temperature and particle measurements, vital for EML model predictions, to be made in the cloud seconds before seeding and (c) DC-6 seeding frees the B-57 to follow cloud top and make particle measure- ments in the rising tower top. (Prior to 1970 we had had no in-cloud measure- ments of seeded clouds above about 22,000 ft), (d) the DC-6 seeding capa- bility gives the RFF a multiple seeding capability that is important for massive or prolonged seeding operations, and (e) the change is an economy 3 The randomized seeding instructions were prepared by Mr. G. Cotton of the Meteorological Statistics Group of NOAA. move in that the seeding operations could be conducted with one aircraft instead of the two that were necessary in May 1968. The silver iodide pyrotechnics used in the 1970 program were 01 in Mathieson X 1 055 flares. Flares from the Lee Wilson Engineering Company (LW-83 flares) were used experimentally in one cloud on July 16, 1970 and for area seedings in conjunction with 01 in X 1 055 flares on July 18, 1970. The 01 in X 1 055 flare is the same flare used in May I968. Simpson et al- (1970) described tests of the 01 in flares in the laboratory, flight tests and results of their use in the field, and these details will not be repeated here. However, flare configuration and the delivery system were changed to facilitate seeding by the N0AA DC-6. These changes are described below. The DC-6 seeding system consisted of four standard A-6 flare ejector racks (52 cartridge capacity for each rack) mounted in aerodynamic pods on the wing tips (fig. 1). Each pod contained two A-6 racks, giving the DC-6 a total flare capacity of 208 flares. The pods were attached to the wing tips with standard, electrically operated shackles. In the event of a flare emergency, the entire pod could be jettisoned from the aircraft. The pods were also used as platforms for other instrumentation that was needed in the experiment. Figure la shows the right pod; the boom protruding from the pod contains both the Levine(1965) cloud and precipitation liquid water probes. The vertically striped boom extending from the leading edge of the wing is a Rosemount Pitot-Static source for the instrument package pressure altimeter and airspeed indicator. The left pod (fig. lb) contains a con- tinuous foil hydrometeor sampler in addition to the flare racks. The odd- Fig. la. Right wing tip pod showing the Levine probe protruding forward below the Pitot-Static pressure probe and the seeding flares in position. Fig. lb. Left wing tip pod showing Lyman-Alpha probe extending through the leading edge of the wing, the continuous hydrometeor sampler (foil sampler) and seeding flares in the pod. shaped probe extending forward of the leading edge of the left wing is the Cambridge Systems Hydrogen Lyman Alpha Total Water Content sensor. The use of standard A-6 photo-flash flare racks reduced the time required to load the flares to less than one man-hour instead of the four- to six man-hours that were necessary to load one half the DC-6 flare com- plement on the B-57 during May 1968. (Subsequently, the B-57 flare rack was modified to facilitate rapid loading.) The new racks permitted the use of machine-crimped electric squib flares and eliminated the require- ment of physically attaching a pair of electric squib leads per flare to terminal strips on the flare rack. The command to fire a flare may be initiated at either of two posi- tions in the aircraft. During the experiment, the first author occupied the "jump seat" immediately behind the flight engineer and controlled the firing of the flares with a simple pushbutton switch. Ultimate control was vested in the "randomizer" who sat in the rear of the aircraft and armed or disarmed the flare racks as dictated by the randomized seeding instruc- tions. Figure 2 shows the master control box with the necessary switches to arm either pod or to jettison either pod if a hazard develops, and a counter to monitor the number of flares ejected from either pod. Because of the minor changes in flare configuration and the new delivery system, several flare tests were conducted prior to the 1970 experimentation. The test results are tabulated in table 1. All but the first flare test were conducted from the DC-6 aircraft in Miami, Florida. In the first test, conducted in Denver, Colorado, the flares were dropped from the B-57. 10 Fig. 2. Flare pod master control panel operated by the project randomizer. The actual seeding was via a switch plugged into the "remote" receptacle. 11 The ejection failures experienced in the first two tests were not the fault of the flares. In the first test, the failures were due to poor electrical continuity at seven positions in the B-57 flare rack while in the second test ejection failures were due to human error. Table 1. Flare Test Results # # # Burn Test Date Flares Flares Completely Time Alt. (1970) Tested Ejected Burned (sec) (ft) 1) 2/27 50 2) VI 20 3) k/6 10 10 k) 4/13 20 5) 5/22 20 k 10 10 20 20 hi k 8 10 18 19 70-80 20,000 70-80 20,000 70-80 20,000 3,000 70-80 20,000 70-80 20,000 Temp _£cj_ -26 -13 IAS (KTS) 160-220 155 165 165 TOTALS 130 07 102 70-80 (avg. value) The flares tested in tests 2 through k had defective sealers around their bottom caps. This defect permitted premature ejection of the burning flare, resulting in flare extinction in four cases. This defect was corrected before the fifth flare test. The one extinction in this test occurred 12 sec after flare ejection. Based on the test results the following conclusions seem justified: 1. The flare ejection reliability is probably about 95%. 2. The flare burn reliability (number that burn after ejection) is 12 nearly 100%, now that we have a better sealer on the end of each flare. 3- When dropped from 20,000 ft, flare burn times are 70 to 80 sec. h. Time-exposure photography reveals that flare trajectories are the same as those published by Simpson et al. (1970). Twenty 50-gm silver iodide pyrotechnics were programmed, but not necessarily expended, at 100 m intervals during multiple seeding passes through the cloud selected for seeding. The selection criteria for the experimental clouds were: (a) hard, cauliflower appearance with tops prefer- ably between 19,000 and 26,000 ft, indicating a vigorous cloud with its top cooled below the activation threshold of silver iodide but not cold enough for complete natural glaciation, (b) minimum supercooled water content of 0.5 gm m as measured by DC-6 Johnson-Williams hot wire instrumentation during the seeding run, indicating the fusion heat potential necessary for dynamic changes and (c) isolation from other convective activity, especially cumulonimbus, where the risk of natural seeding is especially great. Upon selection of a "GO" cloud by the first author, the randomizer in the rear of the aircraft opened a sealed envelope for the seeding in- struction and armed or disarmed the seeding racks accordingly. During penetration the first author sequenced the flares into the cloud at ^100 m intervals when his Johnson-Williams liquid water readout indicated a value -3 >0.5 gm m . The seeding was accomplished with a remote flare release cable running from the randomizer control panel in the rear of the aircraft to the seeding position just behind the flight engineer in the front. At no time was the seeder aware of his seeding action. All subsequent seeding 13 passes were made on the upshear side of the cloud into the new actively growing towers where there is the greatest likelihood of having important quantities of supercooled liquid water. If the upshear towers did not meet the liquid water criterion no additional flares were expended, account- ing for the variable amount of silver iodide introduced into the seeded clouds Following the seeding passes all aircraft flew patterns to monitor the clouds, while the University of Miami 10-cm radar (UM/10-cm) maintained surveillance from the ground. Idealized aircraft flight altitudes and patterns are shown in figure 3. Although not shown, the WC- 121, S-2D and B-57 typically made a penetration of the cloud before the seeding run of the DC-6. The NRL aircraft were available until May 27, flying on k days of seeding operations, and the Air Force C-130 was available for dropsondes until problems with the system forced termination on May 22, 1970. 3.4 Radar Systems The unique modified UM/10-cm radar of the Radar Meteorology Laboratory, Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, was the main tool for measuring precipitation from the experimental clouds. The characteristics and operation of this radar are treated in detail by Senn and Courtright (1968). The UM/10-cm radar has a 2 conical beam, a 5 -\k transmitter power of 5.5 x 10 W, a minimum detectable signal of 10 W, a pulse length of 2(^s, and a pulse repetition rate of 300 pulses/sec. Important features include special logarithmic and linear radar receiver systems and an RF range attentuation corrector (Hiser and Andrews, 1966). The UM/10-cm radar has an iso-echo con-tour (IEC) unit developed by Senn and Andrews (1968) . \h PLAN VIEW DC-6 POSITIONS OF FLARE DROPS LWC > 0.5 gnrfm5. PROFILE VIEW SHEAR - DURING SEEDING \ r DC-6 AND WC-I2I ) SHEAR- c ( \ \ — ^t- -f — s • \ s \ J x ^ J \ -X V) V AFTER SEEDING 30,000'- C-130 £ 26,000' B-57 CLOUD BASE S-20 Figure 3. Field design of single cloud experiment. Flight patterns of all aircraft are shown on the left while their altitudes are indicated at the right. 15 The effective antenna gain of the 12-ft reflector and radome of the UM/10-cm radar was calibrated by Andrews' (1966) solar method. A semi-automatic system was devised by Andrews and Senn (1968) to calibrate many features of the UM/10-cm radar system simultaneously. This was done twice daily during the experiment. Table 2 presents the signal levels used and the radar reflectivities and approximate precipitation rates, all normalized to 100-n mi range. The Miami Z-R relationship 1 k Z = 300 R * (1) was used to obtain the values in table 2. This relation (Woodley, 1970) and its accuracy in representing shower rainfall in Miami, Florida (Woodley and Herndon, 1970) are discussed elsewhere. The UM/10-cm radar was used to collect precipitation rate data on film. During individual cloud experiments the operator raised the antenna to provide PPI scans of both the lowest levels (0.5° tilt) and the 14,000 and 20,000 ft levels through the experimental clouds. The radar scope was photographed once with each scan. The scan levels were chosen to get ob- servations at, or close to the flight levels of the experimental aircraft and to obtain precipitation rate data at low,br i ght-band middle and slightly higher levels. The upper scans were used only for clouds within kO n mi of the UM/10-cm radar. The Navy Model AN/MPS-4 5-cm radar of the Radar Meteorology Labora- tory was used in the RH I mode to obtain height data for some of the experi- mental clouds. The characteristics of this radar are discussed in detail by Senn and Courtright (1968). Whenever an experimental cloud was being 16 Table 2. 1970 Florida Seed values and equiva ing Program, lent precipi UM/10-cm signal levels (Pr) , Z tation rates (R) Date Pr (dbm) 1 (mm6m"3) R (in hr"1) Pr (dbm) Z (mm°m~3) R (in hr-1) Contour 5/25 MDS -106 10 .004 Contour -81 3.5xl03 .21 5/26 -103 22 .006 -81 3.5xl03 .21 5/27 -104 17 ..005 -81 3.5xl03 .21 5/28 -109 5 .002 -86 1 .lxlO3 .09 6/29 -103 22 .006 -85 1 .6x10 .11 6/30 -103 22 .006 -85 1 .6xl03 .11 7/1 -103 22 .006 -85 1 .6x10 3 1 .1x10 .11 7/2 -105 14 .004 -86 .09 7/3 - 98 80 .014 -86 1 .lxlO3 .09 7/7 -100 4o .009 -84 2.0xl03 .15 7/8 -100 ko .009 -82 3.0xl03 .19 7/16 - 98 80 .014 -78 7.5xl03 .35 7/17 -100 4o .009 -85 1 .6x10 .11 7/18 - 96 110 .019 -80 5.0xl03 .27 Contour 5/25 2 - 74 2.0x10^ .68 Contour 3 -64 1.9x10$ 3.50 5/26 .. 75 1 .7x10^ .70 -65 1 .6xl05 3.00 5/27 - 74 2.0x10^ .68 -63 2.0xl05 4.00 5/28 - 11 9.0xl03 .40 -64 1 .9xl05 3.50 6/29 - 78 7.5xl03 .35 -63 2.0xl05 4.00 6/30 - 78 7.5xl03 3 6.0x10 .35 -63 2.0xl05 4.00 7/1 - 79 .30 -67 9.0x10 2.30 7/2 - 80 5.0xl03 .27 -67 9.0x10^ 2.30 7/3 - 81 3.5xl03 .21 -65 1 .6x10 3.00 7/7 - 78 7.5xl03 .35 -64 1 .9xl05 3.50 7/8 - 77 9.0x1 03 .40 -64 1 .9xl05 3.50 7/16 - 74 2.0x10^ .68 -63 2.0x1 05 4.00 7/17 - 78 7.5xl03 .35 -63 2.0xl05 4.00 7/18 - 74 2.0x10^ .68 -64 1 .9xl05 3.50 17 worked, it was found on the RH I scope and pictures were taken every few seconds scanning slowly back and forth through about 10 to 20° centered on the echo in azimuth while the antenna rocked rapidly in the vertical. A great improvement in the design of the 1970 seeding program was the installation of L (1090MHz) and S (3GHz) band transponder receivers in the Radar Laboratory that permitted accurate location of the DC-6 aircraft over South Florida. The transponder system required the addition of a standard "L" band, FAA approved interrogator/receiver and antenna at the ground radar site which was mounted remotely from the research UM/10-cm radar antenna but synchronously slaved to it. With the "L" band interroga- tion of the airborne transponder a typical encoded reply would be retrans- mitted at "L" band and the same pulse train used as a trigger for the "S" band transponder. The S band transponder incorporated in the RFF DC-6 for our experiment is a slightly modified MRT-2 (Meteorological Raingage Trans- ponder-2) which was originally used in conjunction with a WSR-57 or CPS-6 10-cm radar such that rainfall measured by raingage could be displayed on a standard PPI radarscope as a series of coded hash and slash marks. For our experiments the 10-cm transponder reply appeared on a PPI scope as one enhanced "skin paint" or simply an elongated slash which could be displaced in time and thereby space so that the research cloud echoes were not en- hanced by the transponder reply. During normal operation the research aircraft could be acquired and identified by displaying the L band transponder reply on the PPI indicator then eliminating the L band video leaving only the meteorological echoes at S band (10 cm), the "skin paint" echoes of nearby aircraft and the 18 reply of the MRT-2. The versatility of the University of Miami Radar Laboratory's video mixing and switching system allows elimination of the myriad of L band replies due to the locally heavy commercial and business traffic while enabling the staff to keep close track of the research aircraft k. EXPERIMENT SUMMARY The field phase of the program was scheduled for the period April 15 to May 31? 1970, during which both the single and multiple cloud experiments would be conducted, but because of highly unfavorable weather and public relations problems, the experimental period was extended from June 29 to to July 19, 1970. Heavy rains in March (fig. k) were followed by a severe drought from April 1 to May 20 in which no seedable clouds presented them- selves. From May 20 to 31 conditions were highly disturbed. Layers of cirrus and altostratus commonly made seeding impossible while high natural growth made seedabi 1 i t ies small even when operationally possible. There were four operational days in this period, three of which provided a seeded sample under disturbed weather conditions. The July phase of the experiment was far more successful than the May phase. There were no public relations problems and the weather was only slightly more unfavorable than usual. Table 3 presents a summary of weather conditions and the reason for flight action on all days scheduled for experimentation. There were nine days of single cloud seeding operations during the two experimental periods. The locations of the experimental clouds with respect to the radar are shown in figure 5 and summary information is given in table k. Twenty-nine single clouds were obtained, 13 seeded clouds, six random controls and 10 radar controls. The random control number is 19 80* 10' 1 1 » ' 1 30* 1 1 \ 1 1 MARCH 1970 RAINFALL 5 \ \ 1 YvL \ ill 7T " / J / 1 1 ^k / ' A 5 f 6 -TO8 -HH0 8 \^ ( ^~ J-12 io^s: — z?^ — Vl4 C3e I2-Vr C w.4 ___ it^v^a ^^~ ^^ 18 i ) / /_^^~ N / 16 \ ///C^L V.0 10^ 4^z j , V3 /*2 2-'* 1 | |^-j^2 1 1 0 o° 1 ^ 0 1 < 80* Figure k. March 1970 rainfall in South Florida. Isohyets labelled in inches. Target area for multiple seeding experiment outlined 20 Table 3. Summary of weather DATE ACTION 5/17 5/25 5/26 5/27 5/28 5/29-5/31 and research activities REMARKS 4/15-V22 No f 1 ights South Florida experienced subsidence. Climate too dry for cloud qrowth. V22 Test f 1 ight Tested new flares for reliability 4/23-5/12 No f 1 ights Area still affected by synoptic scale situation- Still subs ident . 5/12 Data f 1 ight No seeding - clouds did not grow beyond 13,000 ft 5/13-5/15 No f 1 ights South Florida still in subsidence 5/15 Cal ibrat ion £■ comparison flight Flew only for calibration purposes and CCN comparison. Also took samples of warm clouds. 5/16-5/17 No f 1 ights South Florida still too dry for cloud development Data flight No seeding. Tropical depression in southern Gulf of Mexico created a dense cirrus overcast. Only suitable clouds formed over tomato fields. 5/20 Data flight No seeding. The day had poor seedability. Multiple stratus decks, all possible clouds over tomatoes. 5/21-5/25 No flights Poor seedability and multiple stratus decks still pers ist . Data flight One cloud seeded. Still somewhat disturbed. Seedability poor; natural growth very good. Data flight One cloud seeded, results good despite fairly strong shear. Data flight One cloud seeded. The day was very disturbed with Cb's in all quadrants. Control and seeded cloud grew about equally. Data flight One cloud seeded. Semi -d i sturbed day with some shear. Seeded cloud and radar controls grew, random control cloud died. No f 1 ights Still too disturbed. Seedabi 1 i t i es low. 5/31 Data flight No seeding. Cold low traversed the South Florida peninsula causing subsidence and strong shear. Only good clouds developed over tomato fields. 21 Table 3. continued. Summary of weather and research activities PART I I OF EML EXPERIMENT DATE ACTION REMARKS 6/29 Data flight No single cloud seeding. Area experimental day. Random decision was to seed. Clouds grew somewhat even though the sounding was dry. 6/30 Data flight No single cloud seeding. Area control day; very wet sounding and large natural growth. 7/1 Data flight One cloud seeded. No area seeding. Cloud exploded upon seeding, whereas controls did not. 7/2 Data flight Area seeding day as well as two seeded single clouds, one random control and one radar control. All seeded clouds exploded. 7/3 Data flight Area day which became a single cloud day due to lack of targets in the area. Three seeded clouds. Towers cut off at maturity. One radar control. 7/4-7/7 No flights Synoptic scale disturbance over S.Fla. precluded flying 7/7 Data flight No single clouds seeded. Area control case-no cloud growth 7/8 Data flight No single clouds seeded. Area seed day resulting in good tower growth & consequent rainfall increases. 7/9-7/11 No flights Weather too disturbed; low seedab i 1 i t ies 7/11 Data flight No seeding. S. Fla. still socked in; natural growth too much; seedab i 1 i t ies low. 7/12 No flights Quite disturbed, high natural growth. 7/13 Data flight No seeding. Change in regime created a severe drying Evening out. Navy flares tested from B-57 in evening. Flare test 7/14-7/16 No flights Still too dry. 7/16 Data flights No area experiment ;one single seeded cloud, two con- trols, one random, one radar, all clouds grew well. 7/17 Aborted data Became area control day due to aborted flight caused flight by aircraft electrical malfunction. 7/18 Data flight Area seed day a success as well as two single seeded clouds, as compared to a radar control cloud. 7/19 No flights Another tropical depression approached the region. 22 24* Q SEEDED CLOUDS (7) CONTROL CLOUDS (£) RADAR CONTROLS • LOCATION OF RADAR D LOCATION OF RADIOSONDE CAUSE AZIMUTH ELEVATION ANGLE TO TOP OF OBSTRUCTION U.M. LIBRARY (MAIN BLD6.) 262.3° — 272.3° (ROOF STRUCTURES) 265.2° — 268.2° (RADOME) 266.7° U.M. DORMS 225.0°— 228.4° 229.0° — 232.6° 0.5° 0.8° 2.0° 0.3° 0.3° 24° 82* 8I( 80° Figure 5. 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CM l 1 >H in ce M-/ ^g CM r- OC o o cr en CI cr. m iC in ^-i in CM sC ^ MO' r~ m m ~H 1 o p> > > > ^ > > SX ^ >, iV >, >t > i>. > ^ ^ > > > ^H l-l CO m 1 u m 03 01 10 HI 3 3 3 3 3 3 3 -I a o 3 3 3 0 0 3 3 ■z. r X r X T. r S i: >-> ■— 1 "0 ^0 •I -0 -i —1 >-} -o -0 >-l — 1 —1 ^0 -o "1 01 j-j 40 kw p OJ 01 CC '■ ci •H J-l j-i u in c. j-i B ■rg m -o c > OJ oi x; c kg N CJ 4J •H UJ -rg HI j-j kg ct Uh C ra CO c ^H E TO -CI m CI OJ og M-j c o kj Of i- c c kg ■H UJ 01 -oj nj 01 f= 01 k- J-J *g CO CO CO T1 en g-g ig-g o 3 3 to C C -rg 0 j-i T) -n co m m C u < H OS C£ (V SF * CO jo o TJ 29 reader is urged to evaluate each case carefully so that he might be better able to judge the validity of the conclusions that are based on these cal- cul at ions . 6. EXPERIMENT SUMMARY BY DAY We now summarize the observations for each day of single cloud seed- ing operations. The details on each cloud can be found in table k. May 25, 1970 The weather on May 25, 1970 continued in the disturbed mode of the previous day, when there were heavy rains (2.17 in at Coral Gables) in the late afternoon and evening associated with the remnants of what was once hurricane "Alma". The real time EML model predictions indicated a maxi- mum seedability of 0.95 km for cloud radii in the interval 1000 m < R < 2500 m with the 1200 GMT Miami rawinsonde and a 2000 ft cloud base as input, suggesting that unseeded clouds would behave little differently than seeded clouds on this day. Results of flight operations showed that this was an accurate prediction. It was very difficult to obtain experimental clouds on this day because of the organized nature of the convection. New convective towers grew on the upshear (SW) flank of large mature cloud complexes and rapidly merged with them. In spite of these difficulties, two experimental clouds were obtained, the first seeded and the second unseeded as dictated by the randomization in pairs. Both clouds were active during the seeding passes, with the control cloud being the larger of the two. Both clouds grew following seeding with the control cloud behaving the more spectacularly of the two. 30 A photograph of the seeded cloud is shown in figure 6a, three minutes before seeding when its top was barely at the 22,000 ft flight level of the DC-6. The number below the lower right portion of each photograph is the time (in minutes) relative to the time of seeding repre- sented by the letter T. The lettering in the upper left is the direction of the photograph. By nine min after seeding (figure 6b) its top had descended to 29,000 ft after attaining a maximum height of 31,000 ft. The control cloud is seen in figure 6d , three minutes before seed- ing when the tower in the right background (marked by arrow) was rapidly growing through the DC-6 flight level. Subsequent cloud development was most impressive, culminating in the large cumulonimbus shown in 6e . The view here is at a much greater range from the cloud than was the case in panel d. The central portion of the cloud mass is the experimental cloud (arrow) while that to the left is cloud matter that has merged with it. The control cloud had attained its maximum top height of 39»000 ft 15 min earl ier . The rainfall calculations were not without difficulty. Both clouds moved into a radar blind cone within one half hour after the seeding passes and analysis was discontinued at these times. The seeded cloud had all but dissipated while the control cloud merged with neighboring convection upon traversal of the blind cone. Neither cloud produced much rainfall in the 40-min after the seeding pass and the control was by far the wetter of the two. Details of the rainfall calculations are presented in fig 6c. The entire portion of each bar is total water in the 10-min period in question. The solid or hatched portion of each bar is water differenced with that in the 10-min period before the seeding pass. The number above each 31 MAY 25, 1970 CLOUD i — SEEDED 1721 GMT T-3 1733 GMT T + 9 MAY 25, 1970 2.0 • I NORMALIZED TOTAL | RAINFALL Aw SEEDED CONTROL 1 ACRE -FOOT ■ l.23X10'gm 0-10 10-20 20-30 TIME INTERVAL (mini CLOUD 2 — CONTROL 1827 GMT 1903 GMT T + 33 Figure 6. a. Cloud 1 at 3 min before seeding. b. Cloud 1 at 9 nnin after seeding. c. Rainfall results for clouds 1 & 2. d. Cloud 2 at 3 min before"seeding" e. Cloud 2 at 33 min after "seeding" 32 bar is rainfall normalized to that in the 10 min before the seeding pass. Solid coloring of a bar indicates a seeded cloud and hatching indicates a control. This explanation is valid for all subsequent bar graphs of cloud rainfal 1 . May 26, 1970 The weather changed significantly on the 26th before returning to the disturbed rainy mode on the 27th. A trough at middle levels that had been just west of Florida on the 25th passed eastward into the western Bahamas on the 26th with the trough line passing Miami shortly after 1200 GMT. Heavy convection continued in the Bahamas all day with echo develop- ment commencing over South Florida at about 1530 GMT. The real time model predictions were helpful in understanding cloud developments. The maximum seedability from the morning model run was 1 .80 km corresponding to a 915 m (3000 ft) cloud base and a cloud radius of 2000 m. However, the afternoon prediction (using the 1800 GMT Miami sound- ing) indicated a maximum seedability of 3.^ km with the same cloud base and a cloud radius of 1250 m. The seeding potential on May 26 improved as conditions suppressed west of the trough line. For the four days of seed- ing operations during May 1970, the model indicated that the effects of seeding on cloud growth and rainfall relative to unseeded clouds should have been greatest and positive on May 26. This is borne out by observations Four clouds were studied on May 26, one seeded and three radar con- trols. The seeded cloud grew impressively in the "hesitation growth" mode while all controls grew very little (< 5000 ft) in rather good agreement with model predictions. The ^0,000 ft seeded cloud was the first cumulo- 33 nimbus over peninsular Florida south of 27°N until another formed on the east coast near Palm Beach at 1930 GMT. The latter eventually moved into the Atlantic and grew to 50,000 ft. The radar controls of 1970 are slightly different from those select- ed in May 1968 in that the former were selected in real time during the experiment. Their method of selection on May 26 is treated in detail below. In the period 1650 to 1710 GMT the scientists in the DC-6 monitored two potential experimental clouds, one near Homestead, Florida and the other 20 n mi to the WNW of the first. Both clouds produced successive towers with maximum tops of 20,000 to 23,000 ft, and visually, at least, they were an identical pair. Because of their similarity and the impossibility of working both clouds at once, the westernmost cloud was designated a radar control and the other an experimental cloud. With this decision we ran the risk of having paired control clouds, but fortunately the randomization dictated that the experimental cloud be seeded. Everything seemed perfect until it was learned that the experimental cloud was very close to the ground clutter of the UM/10-cm radar at selection and that it moved into the ground clutter shortly after the seeding. If this had been known at the time, the eastern cloud would have been discarded and the western one would have been the experimental cloud. Because of the movement of the seeded cloud into the ground clutter, quantitative radar measurements were possible only before the seeding pass. Fortunately, the cloud moved over a fairly dense network of raingages in the Miami-Homestead area. These gages were used in the analysis of seeded cloud rainfall. 34 The seeded cloud is seen in figure 7a. Cloud top height was 23,000 ft. A much later view shows the cloud, its top near 35,000 ft, streaming off to the east (7b). The view at 1822 GMT downshear shows two cumulonimbus towers with tops 38,000 to 40,000 ft. The radar control cloud is seen in 7d , 8 min before a simulated seeding. Although this cloud persisted on radar 50 min after its simu- lated seeding, no other photographs were made because of its increased range from the aircraft. The other two clouds designated radar controls on May 26 were actually clouds that had been designated "GO" clouds. In both cases the Federal Aviation Administration (FAA) would not permit penetration of these clouds after the "GO" designation because of heavy commercial air traffic in the area. As a consequence, these clouds were designated radar controls. They are more valid control clouds than the first radar control on this day, but the first was the wetter of the three. The second radar control is shown in figures 7e and f. The cloud had passed its peak by eight min after its simulated seeding. The third radar control is seen at close range in figure 8a. It had a rather vigorous appearance at this time. Subsequently the cloud began to dissipate (fig. 8b). The rainfall analysis of the seeded cloud on May 26, 1970 was the most difficult we have ever attempted. There was also more subjectivity in the analysis. The rainfall calculation for the seeded cloud presented a threefold problem: 1. Obtaining a plot of the raingage observations after verifying that they 35 MAY 26, 1970 CLOUD 3 — SEEDED CLOUD 4 — (RC) 1712 GMT T-2 1652 GMT T-8 CLOUD 5— (RC) 1756 GMT T + 42 1836 GMT T-3 1822 GMT T + 68 1847 GMT Figure 7 a. Cloud 3 at 2 mi n before seeding. b. Cloud 3 at k2 min after seeding, c. Cloud 3 at 68 min after seeding d. Cloud k at 8 min before "seeding" e. Cloud 5 at 3 min before "seeding" f. Cloud 5 at 8 min after "seeding" 36 CLOUD 6 — (RC) MAY 26, 1970 1904 GMT T-3 1908 GMT T + l MAY 26, 1970 ISO 42 ■i4 4-2 129 p UIOO lr5 -J < S 90 25 0 10 10 0 6J 1.2 •is, ■ SSMJKJB M Ui 3 3 4 5 6 4 5 6 3 4 RMS S 3 4 sssT6 -25 5 5 J -KJ-0 0-K) 10*20 TIME INTERVAL (**-> 20- JO MAY 26, 1970 Figure 8. a. Cloud 6 at 3 min before "seeding" b. Cloud 6 at 1 min after "seeding" c. Isohyets of 2k hr rainfall (inches) in South Miami area from midnight May 25 to midnight May 26, 1970. Dashed lines are tangents to the seeded cloud echo as it traversed the area. d. Rainfall results for clouds "i , h , 5 & 6 up to 30 min after seeding. e. Rainfall results for clouds 3, ^, and 5 from 30 min after seeding to 70 min after seeding. 37 were made on the day in question and then obtaining an isohyetal analysis for the area. 2. Delineating the area for rainfall calculations. 3. Obtaining the time distribution of the rainfall and separating out the rainfall of two other clouds that also traversed the area for rainfall cal cul at ions , The plot of the raingage observations was accomplished in a straight- forward manner. The isohyetal analysis was made by Mr. Jose Fernandez- Partagas, an experienced synoptic meteorologist, who had no idea why he was asked to do the analysis. The area for rainfall calculation was that area traversed by the seeded cloud. Because the edges of the seeded echo could be seen in the ground clutter, this area was defined by tangents to the echo along its direction of movement at several times in its life history. The area for rainfall calculations (defined by dashed lines) and the isohyetal analysis is shown in figure 8c. The two other smaller echoes, traversing the area of rainfall calculation after seeding, were added complications. There was no objective scheme of calculating their rainfall contributions to the analysis area. The few recording raingages in the area were of little help. For objectivity the total rainfall calculated for the land portion of the analysis area was evenly distributed in 10-min intervals for the three-hour period that en- compassed the two-hour lifetime of the seeded cloud and the one-hour life- times of the secondary unseeded clouds. In effect this represents a double bias against the seeded cloud because (1) it gives equal weight to all showers even though the seeded cloud was by far the larger and more lasting 38 of the three and (2) some of the seeded rainfall fell over water areas to the east (fig. 8c) . Total rainfall over the analysis area defined by the dashed lines (8c) was obtained by planimeter integration of the a.eas between the iso- hyets, multiplication of each isohyetal area by the appropriate mean rain- fall, summation and then conversion of the result to acre-feet. The results of the rainfall calculations are shown in panels d and e of figure 8. The rainfall in 10-min intervals in the three hours after the seeding pass was obtained by subtracting the before seeding radar-measured rainfall from the total rainfall and then dividing this difference by 18. Considering the difficulties encountered in this analysis, the accuracy of the calculation does not approach that which is possible for clouds with good radar histories. Seeded cloud rainfall is certainly an underestimate because we have not included in the analysis the water that fell over Biscayne Bay, nor is the time distribution of rainfall a constant. However, the calculation was worthwhile in that we have a minimum value of seeded rainfall for comparison with the controls on this day. May 27, 1970 The weather on May 27 was highly disturbed over most of South Florida There were echoes over the peninsula during the early morning, cumulonimbus development near Lake Okeechobee by 1300 GMT and heavy convective rains over most of South Florida by 1900 GMT. Model predictions of maximum seedability for cloud radii in the interval 1000< R< 2500 m, and a cloud base of 396 m (1200 ft) for the Miami 1200 GMT and 1800 GMT soundings were 0.85 and 2,0 km 39 respectively suggesting a weak dynamic effect of seeding relative to un- seeded clouds on this day. The seeded and control cloud on this day were an excellent pair. They were separated by only 20 n mi in space and by only one hour in time. Both clouds were nearing 30,000 ft (fig. 9) during the initial seeding passes and both grew explosively subsequently to over 40,000 ft. The ex- perimental clouds eventually merged with neighboring convection and became part of the convective mass over South Florida. The first view of the control cloud is seen in figure 9a at a range of approximately 5 miles. Cloud top was approximately 23,000 ft. The view 10 min after seeding shows it as a large cumulonimbus with its top nearing 38,000 ft (9b) . The seeded cloud is seen one minute before seeding when its top was nearing 27,000 ft (9d) . A later view (9e) shows it as a large cumulonimbus, its top at 37,000 ft, draped in the anvil of the control cloud. Subsequently, a vigorous tower penetrated the cirrus anvil and grew to about 46,000 ft. Once again the rain analysis was not without difficulty. The seeded cloud moved into the southwestern radar blind cone (fig. 5) for the 0.5 scan near the time of the initial seeding pass. The low level radar scans were unusable while the cloud traversed the the blind cone but the middle and upper scans were little affected. Seeded cloud rainfall during its traversal of the blind cone was obtained by using the middle level (14,000 ft) radar observations. This was done by computing the ratio of low level to middle level radar-measured water content when the cloud was clear of the blind cone and then applying this ratio (0.64) to the middle level 40 MAY 27, 1970 CLOUD 7 — CONTROL 1614 GMT T-IO 1634 GMT T+IO MAY 27, 1970 4.1 - - 2« 2.4 35 2J 23 r 1 k ECHOES MERGE 1.0 |«8 1.4 || g is - 1 Pi E88 HI 1 1 1 ■. 1 - 7 8 7 6 -10-0 0-10 10-20 20-10 30 -<0 TIME INTERVAL {mini c CLOUD 8 — SEEDED 1758 GMT T+29 Figure 9 a. Cloud 7 at 10 min before "seeding" d. Cloud 8 at 1 min before seeding b. Cloud 7 at 10 min after "seeding" e. Cloud 8 at 29 min after seeding c. Rainfall results for Clouds 7 & 8. Ifl observations when the lower scans were unusable. This was done for the 10-min before to ^+0 min after the initial seeding pass. These cal culat ions -are accurate to the extent that this ratio re- mained constant during the cloud's traversal of the blind cone. Such a ratio is.A certainly not constant from cloud to cloud, and it is doubtful that it remains constant for one cloud over an extended period of time. Both the seeded and control clouds produced substantial amounts of water in the kO min after the initial seeding passes (fig, 9c). The control cloud produced the greater amount of rain in the first 20 min after the seeding pass while the seeded cloud was wetter in the 20 to kO min period after seeding. The normalized rainfalls suggest that post-seeding pass rainfall development was greatest for the seeded cloud. The control cloud produced about kk acre-feet more rainfall in the hO min after the seeding pass than did the seeded cloud. This difference is only 5% of the mean rainfall produced by these clouds in this 40-min period. The control cloud produced more precipitation in this time period than any other control cloud that we have studied in Florida. May 28, 1970 The weather on May 28 continued in the rainy disturbed mode of the previous day with 1.86 in falling in Coral Gables during the daylight hours. It was showering over much of Miami when the DC-6 became airborne for seed- ing operations. Real time model predictions using the Miami 1200 and 1 800 GMT soundings revealed maximum seedab i 1 i t ies in the range 2.00 to 2.50 km for cloud radii in the interval 1 000 < R<2500 m for 610 and 915 m cloud bases . k2 Three nearly identical clouds were studied early in the flight. The northern and western clouds were radar controls and the southern cloud was seeded as dictated by the randomized seeding instructions. The northern radar control was selected in real time and the western cloud was selected from the nose camera film of the DC-6. All clouds formed within 20 n mi of one another and they behaved nearly identically after actual or simulated seeding times. The northern control and the seeded cloud eventually merged with one another in the 30 to kO min after the first seeding pass. The third cloud on this day was a control as determined by the randomized seeding instructions. There were three "seeding passes" through this cloud, two through the first tower and one through the second. The first tower would have received 11 flares and the second would have received nine. All towers failed to grow following the "seeding passes" and, in fact, their demise appeared to be hastened by the aircraft. Representative pictures of the experimental clouds on this day are shown in figure 10. In 10a we see the cloud to be seeded barely at the flight level of the DC-6. Pictured in 10b are the seeded cloud (center) and its nearly identical unseeded neighbor (left). The unseeded cloud, the fourth radar control during the experiment, is the higher of the two at this time. A representative picture of the radar control that was selected from the films is shown in 10c looking to the west. It had attained cumulonimbus stature and was producing heavy precipitation at this time. The last two pictures (lOd and lOe) show the dissipation of the first tower of the randomly determined control; in the first the view is at close range and the second view is at a greater range. A subsequent even larger tower suffered the same fate as the first. h2> MAY 28, 1970 CLOUD 9 — SEEDED CLOUD 12 — CONTROL 1541 GMT T-2 1559 GMT T+16 CLOUD (RC) 1739 GMT MAY 28, 1970 n 1623 GMT T+23 Figure 10. a. Cloud 9 at 2 min before seeding b. Cloud 9 at 16 min after seeding. Note Cloud 10 at the left. Simu- lated seeding time for Cloud 10 is same as actual seeding time for Cloud 9. c. Cloud 11 at 23 min after "seeding". d. Cloud 12 at 1 min before "seeding". e. Cloud 12 at 5 min after "seeding." f. Rainfall results for Clouds 9, 10, 11 and 12. kk The rainfall analysis was straightforward on May 28. The radar control clouds were wetter than either the seeded cloud or the randomly determined control, which was the driest of the four (fig. lOf). Without the radar control clouds in the sample we might have reached the erroneous conclusion that seeding greatly enhanced precipitation on this day. Iron- ically, the radar control cloud selected from the DC-6 nose camera films - probably the least valid in terms of method of selection - was the wettest 1970 control cloud for which we have a complete life history. July 1 , 1970 July 1 was a relatively dry day with little wind shear. During the early morning hours there were numerous but isolated echoes in the Straits of Florida, the Florida Keys and the western Bahamas. Echoes first appear- ed over the southern tip of the peninsula at 1^+30 GMT and developed progres- sively northward during the day. Echo motion was negligible. The area seeding experiment had priority on this day, but no suitable echoes had formed in the target by 1830 GMT, so rather than waste time waiting for target developments, we decided to conduct single cloud exper iments . The first experimental cloud on this day was seeded at 1852 GMT when its top was at 22,000 ft: there were two subsequent seeding runs. This cloud exploded following seeding, doubling its height in kO min. Later it showed a tendency to pinch off in the middle levels, a characteristic ex- hibited by other clouds in the vicinity. h5 There were two controls, a radar control and a randomly determined control. The random control grew as impressively as the seeded cloud. The appearance of the seeded cloud between seeding runs is shown at close range in figure 11a. Cloud top is about 2000 ft above the aircraft. A later' view (fig. lib) shows the cloud on the right during its explosive growth phase. The cloud in the left background is the calibration cloud that is discussed below. The seeded cloud is slightly taller and covers about the same area as the calibration cloud at this time. The randomly determined control is shown at a range of about 3 miles :igure lie. The tower pictured was hard and vigorous as it passed through the flight level of the DC-6. A later view shows the cloud after it had attained small cumulonimbus stature, its top near 30,000 ft. (fig. lid) The cloud was dry and produced relatively little precipitation. The radar control cloud on July 1 is not shown because no satisfactory photographs were obtained. The rainfall calculations were routine for the control clouds but difficult for the seeded cloud which was on the exact azimuth of the western blind cone of the UM/10-cm radar (fig. 5). As a consequence, its cloud base radar presentation was almost non-existent throughout its life history. A rough estimate of the precipitation from the seeded cloud was obtained by comparing it to a nearly identical neighbor, called the calibration cloud, 15 n mi south-southeast (fig. lib). Both clouds were similar in size and they both attained approximately the same maximum top height (note the area and height comparisons in fig. lie). 46 JULY I, 1970 CLOUD 13 — SEEDED 1856 GMT T + 3 CLOUD 14 — CONTROL d. 2103 GMT T+22 1 SEEDED CLOUD JULY I, 1970 1 so " • • HEIGHT OF CALIBRATION CLOUO J • SEEDED CLOUO 50 "" - . A,/Ae • "b "0 x . t 30 I (0 $20 . t 50 100 • ./At 10 50 0 50 1650 1900 1910 1920 1930 1940 1950 2000 2010 2020 20 TIME F i gure 11 Cloud 13 at 3 min after seeding Cloud 13 at 29 min after seeding (right). The calibration cloud ap- pears on the left denoted by C. Cloud 14 at 1 min before "seeding". Cloud 14 at 22 min after "seeding". Height of seeded cloud 13 (solid line) and calibration cloud(stars) as function of time determined by RH I radar. Dashed line is ratio of area of seeded cloud to that of calibration cloud as determined by WSR-57 radar. 47 The procedure for obtaining seeded cloud rainfall involved several steps. First, total rainfall in 10-min intervals after the time of the first seeding pass through the seeded cloud was computed for the neighbor- ing cloud using UM/10-cm radar observations. Second, Weather Service WSR-57 radar observations were used to obtain the ratio of area coverage for the seeded cloud to the area coverage of its neighbor in the same time intervals, (fig. lie). (The Miami WSR-57 radar has no blind cones and, in fact, its radome constitutes part of the obstruction to the UM/10-cm radar). Third, this time-area ratio was applied to the rainfall of the calibration cloud to provide an estimate of seeded cloud rainfall. The. assumption that is critical to the discussion above is that a seeded cumulonimbus cloud is no different on 10-cm radar than a natural cumulonimbus of the same size in its environment. The work of Woodley (1970) and Takeuchi ( 1 969) supports this assumption. In studying the echo structures and particle spectra of seeded and unseeded clouds they found no differences between them. Apparently seeding can induce cumulo- nimbus development in a convective cloud that was not so disposed naturally, but once formed, it behaves similarly to the unmodified clouds in its env i ronment . The rainfall calculations are presented in figure 12a. Because of the analysis problems, normalized rainfall and Aw water values have not been computed. In the 10-min period before the initial seeding pass all clouds produced less than five acre-feet of water. The difference shows up dramatically after seeding. Both controls dissipated in the 20 to 30 min after the seeding pass after producing nearly identical amounts of 48 JULY 1, 1970 JULY 1, 1970 JULY 1, 1970 300 - 250 - C • CALIBRATION CLOUO - C • CALIBHATION CLOUC - w 200 . , — | X 5 ISO ^ | 100 3 50 1 1 1 <3<5 <5 <3 n~l<5<5 1 <5<5 0 0 0 0 0 0 0 0-1 0 0 13 C 14 15 13 C (4 15 13 C 14 15 11 C 14 15 13 C 14 15 13 C 14 IS 13 C 14 13 13 C 14 15 -10-0 0-10 10-20 20-30 30-40 40-30 30-60 60-70 TIM£ INTERVAL Imir. 1 TIME INTERVAL (mini 0 JULY 2, 1970 CLOUD 17 — (RC) 1902 GMT T + 2 c. 1911 GMT T + CLOUD 16 — CONTROL 1929 GMT T-6 e. 1946 GMT T+ll Figure 12, a. Rainfall results for calibration cloud and Clouds 13, 14 and 15. b. Cloud 17 at 2 min after "seeding". c. Cloud 17 at 11 min after "seeding1 d. Cloud 16 at 6 min before "seeding1 e. Cloud 16 at 11 min after "seeding' 49 precipitation while estimated precipitation production from the seeded cloud was still increasing. The seeded cloud produced much more precipi- tation than the unseeded clouds on this day. July 2, 1970 This was the first day during the experiment that we conducted both single and multiple cloud seeding experiments. In many respects the day was similar to July 1, 1970- There were numerous small echoes in the Straits of Florida and the western Bahamas during the early morning hours with echo development over land by 1500 GMT. Echo development over land was slow and isolated. Cell movement was to the southwest at about 10 kts. The predictions of the EML cumulus model were of considerable interest on this day. The model predicted that a seeded cloud with a 1000 m radius and either a 6 1 0 or 915 m base would grow 4.25 or 5.00 km more .respect ively , than an unseeded cloud with the same radius and base. The predicted seeda- bilities were less for clouds with radii greater than 1000 m. The first cloud on this day, a radar control near Naples, Florida, is shown in figure 12b at fairly close range. Its top was near 29,000 ft at this time; it produced several towers in the 30,000 ft height range before and after its simulated seeding. A later view of the radar control is seen in figure 12c. This cloud was just west of the multiple cloud seeding target area. If it had been in the area, its penetration by the DC-6 would have signalled the beginning of the area experiment. The second cloud on this day was a control as dictated by the ran- domized single cloud instructions. It is seen on the right in figure 1 2d ; its top is below the DC-6 flight level. A later view (fig. 12e) shows the 50 cloud after it had reached its maximum height with its middle portions evaporat i ng due to entrainment of dry air. The third and fourth clouds on this day were seeded clouds that were obtained during multiple cloud seeding operations. These clouds were desig- nated eligible for single cloud analysis (they were also included in the multiple cloud analysis) before the seeding decision was known. It was fortunate that the area decision was to seed. Otherwise, we would have had four control clouds and no seeded clouds for comparison on this day. The first seeded cloud is shown in figure 13a, four minutes after seeding. The tower, marked by an arrow, was above 30,000 ft and growing strongly at this time. A later view shows the seeded cloud at great range after it had attained cumulonimbus stature (13b). The second seeded cloud is shown in the right foreground of figure 1 3c when its top was at the OC-6 flight level. Subsequently, this cloud grew into the anvil overhang that was produced by seeded clouds to the east, (fig. 13d). Because of the disappearance of its top into layer cloudiness it was impossible to obtain an accurate estimate of its maximum top height. The seeded clouds on July 2 produced almost an order of magnitude more precipitation than the controls in the kO min following the seeding pass (figure 13e). Cloud 18 continued long into the afternoon while the other three clouds dissipated within one hour after real or simulated seedings July 3, 1970 July 3, 1970 was an interesting but frustrating day for cloud seeding operations over South Florida. Although there were large precipitating clouds 51 JULY 2, 1970 CLOUD 18 — SEEDED 2108 GMT T+4 b. 2127 GMT T+23 CLOUD 19 — SEEDED 2137 GMT T+2 2212 GMT T + 37 JULY 2, 1970 P. 00 w 7S 5 IS I T IS 19 16 17 IS 19 JULY 2, 1970 0-10 10- JO TlUC INTERVAL (mini <0 -50 50 - 60 TIME INTERVAL (mm I 6. F igure 13 • a. Cloud 18 at k min after seeding, d. Cloud 19 at 37 min after seeding, b. Cloud 18 at 23 min after seeding. e. Rainfall results for Clouds 16, 17, 18 and 19. c. Cloud 19 at 2 min after seeding. 52 in the Miami area associated with the sea breeze (the authors had to sprint to the aircraft through a heavy downpour), very few clouds developed over the areas designated for cloud seeding operations. Echo development commenced over the extreme southern part of the Florida peninsula at 1500 GMT. Subsequent development was confined primarily to the west coast of Florida. By late afternoon there were several cumulo- nimbus clusters over this region. Because the criteria for the area experi- ment (Woodley and Williamson, 1970) had been satisfied, the authors took off in the DC-6 with the intention of conducting multiple cloud seeding operations over the fixed target. A radar control was obtained north of the multiple cloud seeding target area at 183^ GMT and multiple cloud seed- ing operations commenced in the target at 190^ GMT. There were several other seedings after which no other suitable clouds developed in the fixed target. Because of the lack of suitable seedable clouds, July 3 was not used as an area day; it did not pass the ultimate test that there be at least six seeded clouds or a total expenditure of 60 flares for a day to qualify for an area day. The seeded clouds in the fixed target were then designated as single clouds for comparison with the radar control. This accounts for the clustering of clouds in the fixed target that is shown in figure 5. The three seeded clouds did not behave very differently than the radar control on this day. All clouds grew to between 30,000 and 36,000 ft in the cut-off tower regime and produced similar amounts of precipitation. The first and only view of the radar control is seen in figure ]ka, six minutes after a simulated seeding. The tower on the right was dying 53 JULY 3, 1970 CLOUD 20-(RC) CLOUD 23 — SEEDED " 9 K2 Pi- I836 GMT T + 6 I925 GMT T+I6 CLOUD 21 — SEEDED I907 GMT CLOUDS 2I,22&23 SEEDED c. I9I6GMT (20T + I2 (22)T + 4 (23)T+7 CLOUD 22— SEEDED I932 GMT T+20 JULY 3, 1970 Figure ]h. a. Cloud 20 at 6 min after "seeding", b. Cloud 21 at 3 min after seeding. f. d. Cloud 23 at 16 min after seeding. e. Cloud 22 at 20 min after seeding. c. Clouds 21, 22 and 23 at 12, k and 7 f. Rainfall results for Clouds 20, 21 min after seeding respectively. 22 and 23- 5^ while the one on the left was entering its vigorous growth stage. No other photographs were made because the aircraft left the cloud after this time. The seeded clouds are seen in successive panels of figure ]k. In panel b, cloud 21 is shown three minutes after seeding. Old cloud matter is shearing to the west. In panel c all three seeded clouds are seen. The clouds are marked by their appropriate numbers for identification. Cloud 21 was near its maximum height at this time. In panel d Cloud 23 is shown. Cloud 22 is shown at its maximum development in panel e looking south. The B-57 jet aircraft traversed the top of the cloud at this time measuring a height of 35,000 ft. The cloud debris in front of Cloud 22 is the remains of Cloud 21 . The rainfall calculations (fig. l4f) produced nothing startling. It does not appear that seeding was effective in producing important alter- ations of precipitation on this day. July 16, 1970. July 16, 1970 was one of the more interesting days during the program, During the morning hours a large convective cluster with its associated cirrus shield moved southward off the central Florida east coast, impinging on land and then dissipating in the Palm Beach - Fort Lauderdale coastal region. Strong northeast winds at 200 mb carried the cirrus over much of south Florida with the heaviest concentration over the multiple cloud seed- ing target area. The cirrus overcast decreased the insolation here, delay- ing cumulus development to very late in the day. As a consequence, no mul- tiple cloud seeding operations were possible. Single cloud seeding 55 operations were conducted south of this area in a region where there was only scattered to broken cirrus cloudiness. Echo development commenced over the peninsula at 1530 GMT. Develop- ment was slow and never extensive at any time during the day. However, the clouds that did form were exceptionally vigorous. The first experimental cloud was seeded with LW-83 flares - the first time this flare had been used in cloud seeding operations in Florida. Subsequent behavior is puzzling in view of the 2.0 to 3.0 gm m ; liquid water that was available in each seeded tower. The cloud did not begin to grow until 25 min after the first seeding. Precipitation development lagged accordingly. The subsequent control clouds behaved more like seeded clouds than did the actual seeded cloud and the authors were deceived that this was the case throughout the day. Analysis of the seeded cloud by the EML cumulus model may clarify the situation. Once the seeded cloud commenced its growth a separate cloud formed and grew vigorously 3 to 5 n mi to the east-northeast. (While a remote possibility, it does not appear that the second cloud ingested any silver iodide from the seedings). Both clouds paced one another to great heights with the seeded cloud reaching 40,000 ft before merger. After merger, the consolidated cloud system reached 53,000 ft. It became one of the more impressive cloud systems that was studied during the program. Both control clouds, the first randomly determined and the second a radar control, were slightly above the DC-6 flight level during the initia' "seeding pass". Both grew vigorously to over 40,000 ft after the initial 56 pass. The updrafts in both control clouds were very strong. Best early estimates indicate drafts in the 15 to 20 m sec" range in both clouds. These estimates help explain the observation of no precipitation clatter upon penetration of updraft cores - only the occasional thud of large ice particles hitting the aircraft. The strong updrafts also help explain their interesting reflectivity profiles during their growth stages. These profiles showed a reflectivity maximum aloft corresponding to the region of suspended precipitation water with little if any echo on the cloud base scan of the clouds. A representative reflectivity profile for the randomly determined control cloud is shown in figure 1 6a . The reflectivity maximum may have been at a greater altitude than is shown. With the reflectivity maximum at 19,500 ft (or about 6 km) the work of Hamilton (1966) suggests that the mean updraft in the cloud is about 8 m sec . It will be interesting to compare this radar-deduced value with those directly measured by the aircraft and computed by the model. The first view of the seeded cloud when it was nearing the flight level of the DC-6 is seen in figure 15a. The cloud directly behind the ex- perimental cloud is a cumulonimbus over the Atlantic more than 50 miles southeast. A later view (fig. 15b) shows the cloud when it had started to grow; cloud top was still below 30,000 ft. The companion cloud (marked with a C) east of the seeded cloud is seen in the foreground of figure 15c. The edge of the seeded cloud can be seen in the right background. Visually the companion cloud appears to be the more vigorous of the two. The last view in this cloud sequence shows both clouds after they had merged into a massive cumulonimbus complex (fig. 15d). 57 JULY 16, 1970 CLOUD 24— SEEDED I9I4GMT b 1944 GMT T+26 c. 2001 GMT T+43 2033 GMT T + 75 CLOUD 25— CONTROL 2049 GMT T-4 Figure 15. a. Cloud 24 at 4 min before seeding. b. Cloud 24 at 26 min after seeding. c. Cloud 24 (arrow) at 43 min after seeding, with companion cloud (C) in foreground. 2123 GMT T+31 d. Merged complex of Cloud 24 and (unseeded) companion cloud C at 75 min after seeding Cloud 24. e. Cloud 25 at 4 min before "seed i ng". f. Cloud 25 at 31 min after "seedi ng". 58 JULY 16, 1970 REFLECTIVITY PROFILE FOR CONTROL CLOUD JULY 16, 1970 -2104 GMT 35 .- — EXTRAPOLATION \\\ \ X \ 30 -3 X X \ X N 1 x N 25 \ \ X \ \ MJlxl \ \ x 20 ■53 dbl i , * *43 Db il? dt> Vl9 dt> £ ►- 1 / s^ 13 15 — I / / UJ X 1 / / 10 - ; / / ' i / i ' / a / 5 -U / ' / i i i i i 5 10 15 20 25 AREA Inmi'l CLOUD 26 -(RC) JULY 16, 1970 0-10 10-20 20-30 TIME INTERVAL (min.) SEEDED CLOUD MEHGES CONTROLS DISSIPATE 24 25 26 24 25 26 40-50 50-60 TIME INTERVAL (mini -I 1 1 1- JULY 16, 1970 — i 1 1 1 — 0-10 30-40 60-70 90-100 120-130 150-160 TIME INTERVAL (mini 2226 GMT T+20 e. Figure 16. a. Vertical radar reflectivity profile for Cloud 25 (control) on July 16, 1970 at 11 min after "seeding". The area covered by radar echoes of a given intensity are plotted as a function of height. b. Cloud 26 at 2 min before "seeding". c. Cloud 26 at 20 min after "seeding". d. Rainfall results for Clouds 24, 25 and 26. e. Rainfall (in acre-ft) for Cloud 2k (dashed) and companion cloud (dashed-dotted) in 10-minute intervals and their sum (solid line). Note enormous increase of total rainfall following merger. 59 Two views of the randomly determined control cloud are seen in figures 15e and 15f; the first at a range of about 3 miles when the cloud was near the flight level of the DC-6 and the second at greater range when cloud top was near 40,000- ft. This cloud grew very vigorously after its simulated seeding. The radar control cloud is shown in panels b and c of figure 16; the first at a range of about 6 miles when the cloud was growing vigorously through the flight level of the DC-6 and the second after the cloud attain- ed cumulonimbus stature with a top height near 40,000 ft. This control was also exceptionally vigorous. In fact, during the second pass through this cloud large ice particles shattered the heated window for the 16 mm time- lapse movie camera (the pictures shown were taken with a hand-held 35 mm camera) and dented several of the flare cannisters that protruded from the seeding pods. The radar-derived precipitation for these clouds is surprisingly small considering their vigor. The controls produced only 150 to 250 acre- feet of water in their entire lifetimes which is small considering some of the experimental clouds produced more in only 10 minutes of lifetime. The controls produced more precipitation than the seeded cloud in the first 30 min after real or simulated seedings but the seeded cloud surpassed the controls after this. The control clouds had radar lifetimes less than one hour while the seeded cloud lasted much longer by virtue of its merger with its eastern neighbor. The merger of the seeded cloud with its neighbor resulted in greater than an order of magnitude more precipitation when compared with the produc- tion of isolated clouds on this day (fig. l6e) . Compare the precipitation 60 production from the two clouds before merger to the production after merger. Almost 9000 acre-feet of water was produced by this system during its life history. Once again we have verification of the observation of Woodley and Powell (1970) that merged clouds produce more precipitation than they could have as separate entities with a corresponding increase in cloud life- times. The implications for weather modification for rain enhancement are obvious. If dynamic seeding is to be a useful tool for increasing rainfall, it must be effective in reproducing the type of cloud merger that is described here. The area seeding experiment (Woodley and Williamson, 1970) is directed toward this end. July 18, 1970 Both single and multiple cloud seeding experiments were carried out on this day. There was one radar control cloud and two seeded clouds that were isolated enough for comparison with the radar control. The radar control cloud was probably the largest of the three single clouds at the t:me of the initial seeding pass, but it grew slightly less subsequently than did the two seeded clouds. All clouds showed the cutoff tower growth regime. The first view of the radar control cloud is seen in figure 17a from the vantage point of the co-pilot. The picture was taken six minutes after this cloud was designated as a radar control. The main tower (marked by an arrow) had almost dissipated and the cloud was at the DC-6 flight level. Later a second tower, similar to the first, grew out of the cloud body (fig. 17b) and dissipated 10 min later (f i g. 1 7c) showi ng all the symptoms of the cutoff tower regime. 61 JULY 18, 1970 CLOUD 27 — (RC) CLOUD 28— SEEDED 831 GMT T+6 1850 GMT 1858 GMT 1842 GMT T+17 1852 GMT T + 27 JULY 18, 1970 JO " 14 - 20 10 ■ - £ ■ ■ 5 '° < -L o < z "-10 0 0 M _ H ... ' m 27 28 29 27 26 29 M| ^B 1 - -20 " 10 - 0 0-10 10-20 20 • JO . TIME INURV4I Hi f. F igure 17. a. Cloud 27 at 6 min after "seeding". d. Cloud 28 at 1 min before seeding. b. Cloud 27 at 17 min after "seeding", e. Cloud 28 at 7 min after seeding. c. Cloud 27 at 27 min after "seeding", f. Rainfall results for Clouds 27, 28 and 29. 62 The first seeded cloud behaved in a similar manner. The first view shows the cloud at a range of about 3 miles when it was growing through the DC-6 flight level (fig. 17d). A later picture shows the cloud nearing its maximum height with pileus (marked by an arrow) draped over its top (fig. 17e). This picture shows a truly classic example of what is meant by cutoff tower growth. The cloud top was continuing to rise almost com- pletely cut off from the cloud body below. A dry layer in the middle levels (700 to 500 mb) in the environment of a cloud is apparently one of the prerequisites for this growth regime. Entrainment of this dry environmental air by the cloud weakens its mid-section and natural or artificially in- duced buoyancy near cloud top serves to sever the connection of the top of the cloud with its body below. The rainfall calculations (fig. 17f) produced nothing particularly noteworthy. Total precipitation production was small from all clouds but the seeded clouds produced slightly more precipitation than the radar control in spite of our subjective, real-time impressions to the contrary. 7. MEAN RESULTS AND THEIR SIGNIFICANCE In this section the mean rainfall results are presented in conjunc- tion with the results of statistical tests of their significance. A detail- ed discussion of the statistical testing is presented in the Appendix. After the evaluation of the growth and precipitation histories of individual experimental clouds, mean seeded and unseeded comparisons were made using several analysis schemes. In the first scheme, mean total seeded and unseeded rainfalls were computed and compared for the first kO min after seeding and for entire post-seeding cloud lifetimes until 63 merger or dissipation. Seeding time is defined as that of the initial actual or simulated pass of the seeder aircraft. The former measure was chosen because few mergers occurred prior to kO min after seeding. For those periods when mergers occurred in the 0-^0 min time interval the mean value of the preceding periods was accepted for the missing periods in the analysis. There is an unknown bias in the former measure in the case of mergers because equating rainfall production until merger to total water production represents a great underestimate of total rainfall in some instances. For 1 968 and 1970 there were nine seeded mergers and five control mergers indicating a greater bias against seeded cloud rainfall. The results of this analysis are presented in figure 18 and table 6. In the figure, the number near each data point refers to the number of clouds contributing to the average. Note that the sample size decreases with time after seeding. The results for both 1970 alone and 1968 and 1970 combined indicate that for all 10-min intervals the seeded clouds averaged more precipitation than the controls, with the mean difference increasing with time after seeding. It should be noted that the seeded clouds averaged six to nine acre-feet more water than the controls in the 10-min before seeding - a small difference compared to the difference after seeding. In table 6, the top part gives the results for the first forty minutes following the seeding run, while the lower part of the table gives the figures for the entire duration of the cloud echoes. For the first forty minutes, the seeded minus co*ntrol difference is about 100 acre-ft, an increase of about 55-75 percent. For the whole cloud lifetime, the difference exceeds 250 acre-ft or considerably more than 100 percent. 64 TABLE 6 EML SINGLE CLOUD SEEDING - SUMMARY OF RAINFALL RESULTS Average Rainfall (R) after Seeding (acre-ft) Avg. Differ- Seeded_ Unseeded _ence_ Significance* Year n Rc n R Rc - R 1 2 3 4 s ns s ns 0-40 Minutes 1970 13 258.4 16 164.0 94.4 .10 .10 1968 & 1970 26 249.3 26 140.8 108.5 .005 .005 .05 .005 Total 1970 13 490.8 16 204.8 286.0 .05 .05 1968 26 433.8 26 163.3 270.5 .005 .01 .05 .005 1970 *A11 tests one-tai led. Si gnif icance equal to or better than listed . Footnotes : 1. Wi lcoxon-Mann-Whi tney 3- Analysis of covariance 2. Covariate regression 4. Analysis of daily means Can these differences be attributed, beyond reasonable doubt, to the seeding? The results of the statistical significance tests show that the answer is affirmative. The statistical analyses in table 6 were performed by Mr. Gerald Cotton of the N0AA Meteorological Statistics Group and are discussed in detail in the Appendix; they will only be briefly summarized here. In all the tests shown in this table, the fourth roots of the rainfall amounts 65 1 o 1 1 1 1 1 III' en 05 K)« \ N 2^- / / / - 00 2\ 7 22 / / / / - "'K ■\ 1 UJ \ 1 •J o X -1 z flO" s. QOU • / / lu Q \ • \ / CNJ / 7 1 ! / 1 1 \ / 1 i If t*/ C4 A. / \ - 1 1 1 1 1 \ \ »\ 1 \ \ \ \ • — ^^. i^.'h. 2 o o o o O O o o o en CD N •£> iTi c 2 T5 o to UJ 2 c 4-J 0J ID L. o oj • — 4- X M- C X 1/1 c s_ 03 CU CU -Q • E E CU D E "O Z • — c 4-J to • JZ , — . 0) 4-1 x> E .— 1) — 3 J= 4-J in in 03 cn CU X) C (J *■ — • — c • X CU X 1/1 CU L. 0) X) cu CU c D in 14- • — O 4- _Q — O .— E u 4-J X O o 1 — o o l_ • — r^ 4-J 4-J CU CT\ c vO 1 — i_ CU o 1 — 1 . — 1— (0 CU o to <4- l_ > C o c o • — fD ■ — r» (D CT\ i_ c in i — ' — X c D i_ fD ^ — V O O cu X i — 14- s: CU CO X i — 1 — 1 L. fD -C (0 > oj in -Q i_ fD E D X 3 CD - — ' C fD o o o (J) o CO o o o If) o o -OS o CM — OH (i33d-3aov) mvjNiva nvsw 66 were taken in order to minimize the effects of non-normality and to make the statistical models more appropriate in view of the known day-to-day variations in seeding effect. The first test used is the W i 1 coxon-Mann-Wh i tney , which does not require a normal distribution of the data. The second test is a covariate regression. The total control cloud transformed rainfall after seeding is plotted as a function of that for the 10 minutes before seeding and a linear regression is fitted. The resulting equation is used to predict the total (transformed) seeded rainfall, the predicted and observed quantities are subtracted and the significance of the difference is tested. The low values demonstrate that seeded and control populations differ significantly, particularly when the 1 968 and 1970 cases are combined. The third test, analysis of covariance, is performed by plotting the total (transformed) rainfall after seeding versus that for the 10 minutes before seeding separ- ately for seeded and control clouds. A linear regression is fitted to each set of points and the difference between the two lines is tested for significance. The results of this test are less satisfactory than the others due to the i nhomogene i ty of the 1968 and 1970 control cloud popula- tions that will be discussed further in Section 10. The fourth test, en- titled "Analysis of Daily Means" tests the difference between seeded and control mean (transformed) rainfalls on each day averaged over all days. This test allows for the fact that there were unequal numbers of seeded and control clouds on many days. They turn ont to be parallel 67 8. STRATIFICATION OF DATA INTO FAIR VERSUS RAINY DAYS From our 1 968 results it appeared that the effects of seeding on both cloud dynamics and rainfall were very much larger on fair than on rainy disturbed days (Simpson and Wiggert, 1971) • We now undertake to define objectively a rainy day in terms of area covered by radar echoes at 1800 GMT. All echoes within a radius of 100 n mi of Miami are planimetered on the WSR-57 radar scope tracing. The results for the three Julys 1968- 1970 as well as for the experimental period are shown in figure 19. 2 A clear break in the data in figure 19 is seen at about 4000 n mi , or about 12.7 percent of the area covered. Setting the boundary between fair and rainy days at this point is consistent with studies of tropical rainfall (Riehl, 1954) which show that about 50 percent of the total rain falls on 10 percent of the days with rain; in the study of the three Julys (1968-1970) the rainiest one-tenth of the days (nine days) had a coverage 2 of 4000 n mi or more, while the remaining nine-tenths (84 days) had a 2 coverage of less than 4000 n mi . With this definition, three of the nine experimental days in 1970 are classified as rainy (table 4) and one of the eight experimental days in 1 968 . Table 7 shows the effect of this stratification on the amounts of seeded and control rainfalls and their differences. 5 This radar, operated by the N0AA National Weather Service, is calibrated once weekly so that the minimum detectable signal is kept constant at -103 aom. 6 Although there were actually ten days in 1 968 on which clouds were seeded one had no control cloud and on one other the GO clouds were out of radar range. 68 I I I I I I I I I I I TT | I I I I | I I I LU 2 {2 O LU o cr o LU Q < -; x O C/) LU - Z LU I cr LU CL X LU QC O I I I I I I I I I I 1 I I I I I I I I I If) CM O IT) O »D sxva jo u3awnN o o o o o o GO CM . T3 4-J •— c — 0) o o in L. 1) C Q. O O r-.- — ' - OO TO cn — a) — c -j -cm in •— l- i- E O TO Li- - O •

i- x: •— U ■!-> TO C D .- 1_ O" o O TO DN 111 okti l to — cn u x> QJ > c cn 0 TO TO o l_ OD OJ O vD > _c cn C) u ■ — L) u TJ o 14- 0 sz 0 •— u L. u B 1) TO Q-X) i_ TO cn i — -C 0 TO ■M 4-i - — .. l/l C 1/1 .— a> >■ X H TO •— T> . 4) O a) 4-> 69 TABLE 7 STRATIFICATION OF TOTAL RAINFALL RESULTS Mean Ra i nf al 1 (acre-ft) 1968 Fai r & Rai ny 1970 All 1970 Fai r 1970 Rainy 1970 All 1968 Fai r & Ra iny 1970 All One-Tai led Stratifi- S ign i f icance* Year cation n Rs n Rns Rs~Rns W i 1 coxon-Mann-Wh i tney 22 458.7 20 89.1 369.6 .005 4 297.1 6 411.4 -114.3 — I 26 433.8 26 163.3 270.5 .005 1 RAI NY DAY DEFINED I AS >4000 (N Ml) 10 519.6 11 74.0 445.6 .005 ( ECH0 C0VERAGE 3 395.0 5 492.7 -97.7 13 490.8 16 204.8 286.0 .05 ' In-, -1 ,D 0^0 I nn r nnr I RAINY DAY DEFINED 6 276' 8 ^' 1 AS>2000 (NHI)2 5 2/b.5 o 312.1 -35.0 -- _ n rnWrRArP 26 433.8 26 163.3 270.5 .OO5) )$°0 SaLUES UNCHANGED The lower part of the table presents a test showing that the results are not sensitive to the exact point of demarcation between "fair" and "rainy" days. When the boundary is set at 2000 n mi or about 6.3 percent of the area, there is no change in the 1970 results, while in 1968 one day moves from the "fair" to the "rainy" category. The important result of table 7 is that on fair days the rainfall increases due to seeding are in the range of 350-400 acre-ft, or on the order of 400 percent of the unseeded clouds' precipitation. The differences are significant at the 0.5 percent level. On rainy days, it appears from the table that seeding may actually decrease rainfall, although the sample is not large enough to determine whether the negative difference is signifi- cant. In going from a fair day to a rainy day, it should be noted that the control cloud precipitation increases by 3-6 times. This is due in 70 considerable part to the fact that many clouds, even those of rather small radius, reach cumulonimbus stature naturally on disturbed days, that is, the seedability is small. This effect is probably compounded by the fact that of two clouds with the same top height, the one in the disturbed environment probably rains more. Also in going from a fair to a rainy day, the table suggests that seeded clouds rain less. Using the 1968 data, Simpson and Wiggert (1970 showed that in South Florida rainy days are commonly associated with strong vertical wind shear. They presented evidence that strong shear inhibits the explosive growth of seeded clouds and re- stricts the length of their lifetime. From table k we find in 1970 also that the mean shear (850-200 mb) was nearly 50 percent stronger on rainy than on fai r days . 9. INTRADAY COMPARISONS It was pointed out earlier that the 1970 experiment was originally planned as a paired experiment; that is, a pair of clouds was to be chosen with the seeding to be conducted on one of the pair as determined by the appropriate randomization scheme. In view of the earlier day-by-day discussion it is obvious that this was not operationally possible in all instances, yet it is still believed that comparisons between seeded and unseeded clouds on a given day have more meaning than comparisons of clouds on different days. In keeping with this belief, intraday rainfall differences were computed by permuting all seeded clouds with all controls, resulting (for example) in four pairs on a day with two seeded and two control clouds. In case of merger, the paired comparison is truncated at the time of merger. 71 The results of this analysis are presented in the left-hand half of table 8. Unfortunately the results of this scheme cannot be subjected to statistical tests because the pairs generated in this way are not independent TABLE 8 STRATIFICATION OF TOTAL RAINFALL RESULTS Intraday Rainfall Comparisons (acre-ft) Mean Mean of Difference Intraday Mean D if ference All Permu- Stratifi- tations Signifi- Year cation n ^S-Rns n ^s"^ns cance- 1968 Fair 29 432.6 13 369.6 .025 .004, & Rainy 6 -22.2 4 -54.6 1970 All 35 35^.6 17 269.8 .025 .01 1970 Fair 16 557.2 6 561.2 .05 .02 1970 Rainy 5 -27.5 3 -74.1 1970 All 21 418.0 9 349.4 .10 .08 RAINY DAY DEFINED AS >4000 (N Ml)2 ECHO COVERAGE 1968 Fair 27 464.6 12 400.4 .025 .0051 RAINY DAY DEFINED AS & Rainy 8 -16.5 5 -43.5 - - J >2000 025 .01 f ^CHO COVERAGE^^^^ "All tests one-tailed. Significance levels equal to or better than listed. Footnotes : 1. "t" test for paired comparisons. Rs = seeded rainfall 2. Wilcoxon signed rank test. Rns= control rainfall On the right-hand side of table 8 intraday mean seeded versus control differences were calculated by calculating mean seeded and control rainfall on a given day and then differencing. In this analysis only one difference is obtained per day of experimentation resulting in a drastic decrease in 72 sample size. However, it does have the advantage that the mean of the intraday mean differences can be tested statistically. For 1970 alone the statistical significance is marginal, but it is satisfactory when 1968 and 1970 are combined. The magnitudes of seeded-cont rol differences do not differ significantly between these two methods of determination. On fair days the differences range from 370 acre-ft to above 550 acre-ft, while they are small and negative for rainy days. For fair and rainy days together, the mean differences range from 270 acre-ft to above 400 acre-ft which is equal to or higher than the difference between the overall mean seeded and mean control cloud presented earlier in table 6. Figure 20 shows the mean intraday rainfall difference in 10-min intervals relative to seeding time computed by permuting all seeded clouds with all controls on the same day. The number near each data point refers to the number of clouds contributing to the average. Note that the sample size decreases with time after seeding. A reference line corresponding to the before-seeding mean rainfall difference has been drawn (see fig. 18) so that the reader may relate subsequent precipitation differences to the before-seeding mean. The results for 1970 alone (left) and 1 968 plus 1970 combined (right) indicate that for all 10-min intervals the seeded clouds average more precipitation than the controls with the mean difference in- creasing with time after seeding. In figure 21 all seeded minus control pairs (for all permutations each day for the whole cloud lifetime or until merger) are plotted against echo area at 1800 GMT, or degree of disturbance or "raininess". Note that with one exception, all di sturbed AR ' s are either negative or zero, regard- less of whether the demarcation dividing fair from disturbed is at 4000 n mi 73 - 1 1 1 1 1 1 1 1 1 - 00 / 0*> mS UJ z Id <-> z UJ or ^*^s_0O UJ u. UJ cc o z w^\ Q UJ UJ " UJ cc o u. UJ CD - 1 1 I 1 mi 1 1 1 1 - O o O O O o o o O o CD 00 r- u3 in f ro CM (133J-3HDV) 3DN3H3Jdia TIVdNIVU NV3W 4-J QJ QJ 4-J u 4-J u_ 1 o 4-J O ro QJ QJ QJ 1_ l/l _Q i_ o O !_ ra a) QJ >- * u_ _C ro o «-» c QJ 4-J E m c J ■— s_ O i_ * — .. 4-J 4-J QJ _l i/l c XI < C ■ — Ol ro > O O c QJ F, x> .— a .— 1_ • o UJ "" 4-> X) QJ * 1— z ro ro c QJ o ♦ 4-J 4-J o JZ C o 3 ro Q- 4-J QJ IO UJ 2 E "a i/) 1_ L. QJ 4-> QJ (- QJ _c v_ ro 4- Cl o L _C M- ro O 4-J .— i — QJ O X3 X) »— o QJ o ra i_ QJ in C C CM — •* ro C ro — ♦ QJ • — ^-^ QJ XI o 1/1 C — OO E E QJ ' — O u !_ QJ cn o c QJ U c UJ X) C OJ — o 1_ E QJ •— x> r^ 0) D L. 4- qj cr> 4- C QJ QJ ~- o * M- u. QJ i/i • — QJ QJ QJ 1 X X) _C i_ i/i QJ C '? ro 1— < c 2 1_ (TJ O 4- OO QJ >X) u_ QJ ro xi cn c E QJ i_ . — • — • — cn x QJ ro 4-J ro x: i- L. L. C 4-1 o CD QJ QJ u- o i — c > QJ O 00 O • — ro _Q 4-J 1/1 ♦ l_ "O QJ o 4-J QJ QJ l/l l/l 3 r- c QJ JZ ro QJ — O in 4-J -C U TJ o C > O 0 QJ QJ en 4-J 4J U L. 3 c QJ • C QJ cn QJ 4- JD o .— > c L. 4- O O QJ s_ 1_ .— ,— _l QJ 4-J i — 4-i ro 01 i — c i — CD ro o ro 4-> O So >- > u 4- — r-^. O CO i_ C o. cn 1/1 E l 4- o E C QJ QJ 3 O o cn D — CM , — u c cr ro O CM ♦ QJ .— QJ > -C XI x> Ul l_ u E QJ XI 9 n ro D QJ D C71 QJ c m i/i ro Oii (133d-3aDV) 30N3>J3ddia "llVdNIVM NV3W 2800 2600 2400 2200 2000 - 1800 Ld Lj 1600 Ll_ or o < 1400 cc — 4- 03 nj m O -o *~> en D 03 «u o E '1) r-. i_ "D 1_ en OJ a) en i — a. *j OJ 4-J TD « ■ — o i/i . — 1 — L. 0) 03 Cl O u 1_ »• ~ l_ O 1_ •— ■ — 4- OJ E o en 03 - s_ .— a- OJ 2T 1 E 03 4- 4-J - i — o 03 i/i •— ■a L. 4-J 1/1 •— . C 3 GO ID 3 .— -JD a TD 1 — h- c i/i o Z ■— a C3 c i — 3 - — . — O 03 < 0 O 1_ _c CO I . 4J 1 L. i — S_ 4-J O CM O 03 4- CD Hi 03 u L. >- 0) c D 1) L. 03 en "a 03 _Q -200, i I i I i i I i I i J I I I 1000 2000 3000 4000 5000 6000 7000 8000 ECHO AREA AT 1800 GMT in. mi 2\ 75 or 2000 n mi . In the case of fair days, the/AR's consist of nine very large values (>400 acre-f t) , five moderately large values (100 4000 (n mi) 2 echo coverage within 100 n mi of Miami No change if > 2000 (n mi)2 Footnotes : 1. "t" test for pai red compari sons 2. Wilcoxon signed rank test Now that the randomized dynamic seeding experiment on single clouds has been conducted three times, on a total of 28 operating days and 71 GO clouds (k] seeded and 30 controls) have been studied in detail, it is 78 possible to construct mean soundings that typify the atmospheric conditions prevailing with each growth regime. These mean soundings are shown in figure 22. In the upper left, we see the typical condition where cumulus growth is suppressed. On days like this, cloud tops do not reach the seed- ing level. When the inversion and concomitant drying are somewhat higher, cumuli may reach the seeding level but seedability is small or zero (cf . Simpson, Brier and Simpson, 1967, fig. 11 and discussions; also Simpson, 1967, fig. 7 and discussion). On the upper right appears the typical sounding for the cutoff tower regime. The extremely dry, stable layer in mid-levels causes the seeded tower to separate from the cloud body; it is not necessary to have wind shear for this growth mode to prevail (Simpson, 1967, p. 113 and Simpson and Wiggert, 1969, fig. 10 and discussion' In the lower left, we see the most favorable sounding for dynamic seeding. Here there is a weak stable dry layer in mid-levels, restricting natural growth, and an unstable upper troposphere (Simpson, 1967, tables 1 and 2). Seeded clouds with this environment commonly explode in two phases: The first is a vertical growth to 35,000 - 45,000 ft altitude, requiring about 10-15 minutes and the second is a horizontal expansion requiring another 15-20 minutes (Simpson, 1967, fig. ^ and discussion). The resulting giant cumulonimbus may persist for two hours or more. The sounding on the lower right is typical of rainy, disturbed conditions where seedab i 1 i t ies are again small, here due to large natural cloud growth. In South Florida, these conditions are often, perhaps usually, accompanied by strong vertical wind shear which inhibits explosive growth. 79 Figure 22. Mean soundings for four different cumulus growth regimes in the tropics. Upper left: Suppressed growth. 7 soundings. Upper right: Cut-off tower growth, k soundings. Lower left: Explosive growth. 6 soundings. Lower right: Large natural cloud growth. 8 soundings. 80 11. CONCLUDING REMARKS AND RECOMMENDATIONS We believe that with the 1970 experiment the growth and rainfall aspects of seeding individual Florida cumulus clouds have been fairly con- clusively established. Conditions have been specified quantitatively under which it is possible to greatly enhance vertical growth, consequently pro- ducing precipitation increases of more than 100 percent or several hundred acre- ft. A next logical step, in both the science and the application of cumulus seeding entails advancing to multiple seeding experiments. Such an experi- ment has been designed by EML (Woodley and Williamson, 1970) and a small start on its execution was made in July, 1970. The seven cases obtained will be discussed in a forthcoming EML report. One important aspect of single cumulus seeding that has not been resolved is the amount of seeding material required to release rapidly all the available fusion heat latent in the cloud's supercooled water. To resolve this question in a field experiment would be a costly and quite possibly unfeasible undertaking, in view of the high natural variability in cloud properties. A theoretical study by Cotton (1970) suggests that the optimum amount may be highly sensitive to supercooled precipitation liquid water content, for example. A serious obstacle facing such a determination is that there presently exists no really adequate method of determining the nucleation efficiency of silver iodide generators. More- over, the various processes by which silver iodide particles nucleate clouds are not fully documented or understood; they are probably sensitive to in- cloud temperature and water content. The size spectrum and chemical composition and structure of the nucleating particles are surely important 81 but the exact way that nucleation depends on these variables is not present- ly known. Accelerated basic research on these topics is strongly urged as essential both to further progress in cloud physics and to the science and application of modification experiments. Much further work remains to be done and reported involving the EML 1970 single cloud data. In the course of the rainfall analyses for this report much was learned about the precipitation structure and echo characteristics of the natural Florida thunderstorm. A summary of this material is being prepared by Dr. W. L. Woodley and will appear in a separ- ate article. In future analysis high priority is being allotted to the aircraft cloud penetration data. For the first time we have available fairly accurate vertical velocity measurements (at 20,000 ft) with which to relate the other physical and dynamical variables and to test models. In addition, there are several types of water content measurements, im- proved in-cloud temperatures, continuous formvar particle replicas and foil hydrometeor samples at several levels (some up to 40,000 ft). Detailed photogrammetry will be done on some of the clouds with the aircraft side and nose cameras for the purpose of documenting the growth of individual clouds (and later cloud groups). A basic goal of all these data analyses is to improve numerical cumulus models. EML has perfected, possibly to the point of diminishing returns, a one-dimensional tower model (Simpson and Wiggert, 1970 which will be used with the 1970 data. In addition, we are working on a hierarchy of more sophisticated models, including a one-dimensional time dependent model of the type pioneered by Weinstein (1970) and a grid model (two- 82. dimensional and axi symmet r ic)of the type pioneered by Murray (1970). Although it will be a formidable long-range undertaking to incorporate the ice phase in the latter, it is hoped to have it in the former and ready for use with the seeding data within a year. It is also hoped to use these data to examine the two most important unsolved problems in cumulus dynamics, namely entrainment and horizontal cloud size. The postulate that entrainment is inversely dependent on tower radius, which is fundamental to one-dimensional models, is hotly contested and possibly only roughly correct to first order. The fact is that nearly 25 years after its introduction to cumulus studies (Stommel, 19^7) the turbulent mechanisms of entrainment are still not adequately understood or formulated. Concerning the factors determining horizontal dimension, it has been hypothesized qualitatively to depend among other things, upon syn- optic scale convergence (Malkus and Riehl, 1964) but no adequate theories or models today exist to predict the scales of either individual clouds or cloud groups. This lack is a major obstacle facing the cloud group modelling studies which must be done in connection with multiple cloud modification experiments. To further this end and to provide the necessary context for relating cumulus structure to the large-scale flow, synoptic- satellite studies are underway of the three-dimensional atmosphere over and near the Florida peninsula during the 1970 experimental periods. 12. ACKNOWLEDGMENTS This effort is dedicated to Dr. Myron Tribus whose enthusiastic interest and support were important in carrying out this experiment in the face of what appeared to be almost insuperable obstacles. The authors are 83 also grateful to Dr. Robert M. White, Dr. Wilmot N. Hess and Dr. Harris B. Stewart, Jr. who also helped greatly in clearing the way for the work to go forward. Numerous persons and organizations participated in and supported this program and we thank them all. Particular credit is due to the Federal Aviation Administration without whose cooperation successful flights would have been impossible and to the Radar Laboratory of the University of Miami whose skill and efficiency provided the basic data of this report. The NOAA Research Flight Facility performed with their usual dedica- tion' and excellence. Mr. Brad Patten's contribution in the design and con- struction of the DC-6 seeding pods was superb and invaluable. Mr. Richard D. Decker capably carried out near-perfect photography and Mr. Thomas Nunn aided greatly in voice recording and communications. Mr. Howard Friedman acted as a capable and secretive "randomizer". We appreciate the statistical advice of Mr. Glenn Brier and his - staff of the NOAA Meteorological Statistics Group. On the EML staff, Mr. Robert Powell contributed excellent ice nucleus measurements on the flights and also prepared all the illustrations herein. Mrs. Peggy Lewis and Mrs. Suzanne Johnson capably typed the several versions of the manuscript and Mr. Richard Schwartz aided in the rainfall analyses. Last but by no means least, deep gratitude is due to Mr. Nolan Durre and Mr. Seymour Goldweber of the Dade County Agricultural Board who worked in the Radar Laboratory on all operational days monitoring the aircraft tracks and seeded cloud positions as representatives of the South Florida agriculturists. Their participation greatly improved our relationships with local interests and prevented any credibility gap from developing. 8k The research in this report was supported in part by the Office of Atmospheric Water Resources, Bureau of Reclamation, U.S. Department of the Interior, under Contract 14-06-W-176. 13. REFERENCES Andrews, G.F. (1966), Solar radiation - a useful tool for radar antenna orientation. Tech. Rept. Southern Region, Federal Aviation Agency. Unpublished report on file at Univ. of Miami Radar Laboratory. Andrews, G.F. and H. V. Senn (I968), Semi-automatic calibration of receiver and video system characteristics for weather radars, Proc. 13th Radar Meteor. Conf . , Montreal, 20-23. Atlas, D. (1964), Advances in radar meteorology, Advances in Geophysics 10, 337-387. Austin, P.M. and C. Richardson (1952), A method of measuring rainfall over an area by radar, Proc. Third Radar Weather Conf., McGill Univ., Montreal , D13-D20. Cotton, W.R. (1970), A numerical simulation of precipitation development in supercooled cumuli, Ph.D. dissertation, Dept. of Meteor., Penn . State Univ., 179 pp. To be published. Fernandez-Partagas , J.J. (1969), The mean circulation, synoptic disturbances and rainfall patterns over South Florida and adjacent areas in May 1968, Report, Grant No. E-22-29-69-G, Division of Atmospheric Science, Inst, of Marine and Atmospheric Sciences, Univ. of Miami, Coral Gables, Fla., 60 pp. Hamilton, P.M. (1966), Vertical profiles of total precipitation in shower situations, Quart. Jour. Roy. Meteor. Soc, 92, 3^6-362. Hiser, H. W. and G. F. Andrews (1966), A new approach to range normalization and stepped attenuation for weather radars, Proc. 12th Conf. Radar Meteor., Norman, Oklahoma, 62-66. Levine, J. (1965), The dynamics of cumulus convection in the trades: A combined observational and theoretical study, Ph. D. Dissertation, Dept. of Meteor, Mass. Inst, of Tech., 131 pp. 85 Malkus, J. and H. Riehl (1964), Cloud structure and distributions over the tropical Pacific Ocean, Univ. of California Press, Berkeley and Los Angeles, 229 pp. Malkus, J. and R. H. Simpson (1964), Modification experiments on tropical cumulus clouds, Science 145, 541-548. Murray, F.W. (1970), Numerical models of a tropical cumulus cloud with bilateral and axial symmetry, Monthly Wea. Rev.. 98, 14-28. Riehl, H. (1954), Tropical Meteorology. McGraw-Hill Book Co., New York, Toronto and London, 392 pp. Senn, H. V. and G. F. Andrews (1968), A new low-cost multi-level iso-echo contour for weather radar use, J. Geophys. Res. 73, 1201-1207- Senn, H. V. and C. L. Courtright (1968), Radar hurricane research, Final report by Inst, of Marine Sciences, Univ. of Miami to ESSA, Contract No. E22-62-68 (N) , 31 pp. Simpson, J. (1967), An experimental approach to cumulus clouds and hurri- canes, Weather 22, 95-114. Simpson, J. (1969), Cloud building and breaking, Medical Opinion and Review 5, 38-58. Simpson, J., R. H. Simpson, D. A. Andrews and M. A. Eaton (1965), Experi- mental cumulus dynamics, Reviews of Geophysics 3, 387-431. Simpson, J., G. W. Brier and R. H. Simpson (1967), Stormfury cumulus seeding experiment 1965: Statistical analysis and main results, Jour. Atmos . Sci . 24, 508-521 . Simpson, J. and V. Wiggert (1969), Models of precipitating cumulus towers, Monthly Wea. Rev. 97, 471-489. Simpson, J., W. L. Woodley, H. A. Friedman, T. W. Slusher, R. S. Scheffee and R. L. Steele (1970), An airborne pyrotechnic cloud seeding system and its use, Jour. Appl . Meteor. 9, 109-122. Simpson, J. and V. Wiggert (1970, 1968 Florida cumulus seeding experiment: Numerical model results, Monthly Wea. Rev. 98, in press. Stommel , H..(1947), Entrainment of air into a cumulus cloud, J. Meteor. 4, 91-94. Takeuchi, D.M. (1969), Analyses of hydrometeor sampler data for ESSA cumu- lus experiments, Miami, Florida, May 1968, Final report, Contract No. E22-28-69(N) , Meteorology Research, Inc. Altadena, California, 44 pp. 86 Weinstein, A. I. (1970), A numerical model of cumulus dynamics and micro- physics, Jour. Atmos . Sci. 27, 246-255. Wilson, J. W. (1968), Accuracy of radar measurements of heavy rainfall, Proc. 13th Radar Meteor. Conf., McG i 1 1 Univ., Montreal, 37^-377. Wilson, J. W. (1970), Integration of radar and rain gage data for improved rainfall measurement, Jour. Appl. Meteor. 9, 489-^97. Woodley, W. L. (1970), Precipitation results from a pyrotechnic cumulus seeding experiment, Jour. Appl. Meteor. 9, 242-257. Woodley, W. L. and A. Herndon (1970), A raingage evaluation of the Miami reflectivity-rainfall rate relation, Jour. Appl. Meteor. 9,258-264. Woodley, W. L., A. Herndon and R. Schwartz (1969), Large-scale precipita- tion effects of single cloud pyrotechnic seeding, ESSA Tech. Memo. ERLTM-AOML 5, 26 pp. Woodley, W. L. and R. Powell (1970), Documentation and implications of the behavior of seeded cloud 17, May 30, 1 968 , ESSA Tech Memo. ERLTM- AOML 6 29 pp. Woodley, W. L. and R. Williamson (1970), Design of a multiple cloud seeding experiment over a target area in South Florida, ESSA Tech Memo, ERLTM-AOML 7, 24 pp. 87 APPENDIX - STATISTICAL ANALYSIS BY Gerald F. Cotton The statistical analysis of the single cloud experiment includes several standard techniques for testing seeding effect on precipitation amount. The conclusion that seeding has significantly increased precipi- tation amount in individual clouds is supported by the analyses presented b e 1 ow . Two precipitation amounts are defined for purposes of analysis. One is the rainfall (acre-feet) which was measured in the first 40 minutes after seeding time, R (0 , 40). Seeding time is defined as that of initial actual or simulated seeding pass of aircraft. The second is the total rainfall (acre-feet), R(total), from the experimental cloud from seeding time until merger or dissipation. The former measure was chosen so that clouds could be compared at the same stage of their lifetime. Since only three clouds merged prior to 30 minutes after seeding, the (0, 40) minute amount was adopted as the best compromise for this purpose. For those clouds for which mergers occurred in the (0, 40) time interval the mean value of the preceding time period was accepted for the missing time period in the R(0,40) data. There is an unknown bias in R(total) values because ten of the seeded clouds merged while only six of the control clouds did so. The fourth root transformation was applied to both R(0, 40) and R(total) values in order to reduce the influence of the extremes. This transformation was generally successful for the requirements of the tests used in the analyses presented below. Al The analysis is devoted to both the 1970 data alone and to the combination of the 1968-1970 data. Physical reasoning considered along with the increased precipitation by seeding in the 1968 experiment permits use of one-sided tests of positive seeding effect in this analysis. The experiment was originally planned as a paired experiment; that is, a pair of clouds was to be chosen for testing with the seeding to be conducted on one of the pair by an appropriate randomization scheme. Al- though it became obvious in the initial stages of the experiment that the pairing scheme was not operationally possible it was believed that compari- sons between clouds on a given day would have greater precision than those on different days. In addition, several concommitant variables were meas- ured for each cloud; however only two were used for the present analysis. The first is the initial wetness of the cloud defined as the amount of precipitation in the ten-minute period prior to seeding, R (- 1 0 , 0). The fourth root of this variable was used in the analysis. The other, C, is a measure of atmospheric disturbance on the experimental day, defined as the percent of the area within 100 n mi of the radar that is covered by rain echoes at 1 800 GMT. The statistical tests are described in the following order below: Wi 1 coxon-Mann-Whi tney , covariate regression, covariance analysis, and analysis of daily means. A summary of the results is exhibited in table 6 in the main text. 1A WILC0X0N-MANN-WHITNEY This is a distribution free rank test. That is, the test does not require assumptions about the distribution of the individual rainfall A2 amounts but only the relative ranks of these values. The statistic for the test is defined U = n,n2 + nl'n,l + ') - R, (la) where n, is the sample size of control clouds n2 is the sample size of seeded clouds Rj is the sum of ranks assigned to the group whose sample size is rii and rank of 1 is assigned to lowest amount. The critical levels of test were abstracted from appropriate tables (W i 1 - coxon, 1 9^+5) , (Mann and Whitney, 1 9^+7) or when the sample sizes were large enough to assume normality of the statistic U, were determined from the relat ion . N = U - (n|n2)/2 (n1n2(n1 + n2 + 1)/12)? (2a) where n, and n are sample sizes of seeded and control clouds. These critical values are given in table Al which, in addition, illustrates the stability of the test results to modifications of the data sample (1) for the effect of using mean values for merged clouds in the (0, 40) minute period and (2) for inclusion of radar control clouds in the data sample. Since the experiment deals with a natural process over which one has little control of the various factors affecting cloud behavior, the experimenter must -select a population of clouds that so far as he can determine has nearly the same physical properties. Hence validity of this test rests heavily on the concept of randomization. That is, one might A3 LA O X (0 C 1- O O * -O O O o a: O — MD LA OA CM LT\ vD CnI CM LA CsJ — 00 r-^ o CM — CM CA LA — CM CA — CM LA (0 O en t*b (0 a o CO — en en < — — — 00 CNl oa Cn cn Csl O CM 00 rA vo — CM O CM -a CD 4-> ID — c O — 1- E +j — c — O a> o in i- X> ub "O 3 o 00 O r^ \D — cn cn o — — LA CA CM LA vO CSJ LT\ vD en -cr r^. r^- CM 0 CM 1 — vO Cn — CM 0A LA — CM CA — CM LA O r-- cn (0 4-1 05 ^ O — — r-«. ro — CA +j < — O a: — 00 cn vO -j- — 00 CNl OA cn rA — CM 0O sO CM r~» — 0 h> CM 0A X> CU 4-J 03 1 — C 0 • — !_ E O 4-J • — r*> C — en O 03 3 O 00 "O 0 r^ M3 ro . — cn en 0£ 0 1 — 1 — CD CD CD -Q 03 3" CT CD C cn CO A4 argue that radar control clouds which resulted from operational difficulties may not always fulfill this requirement. As shown in table Al there is little evidence of bias in selecting trial clouds. There is another possible source of bias in this test resulting from the imbalance of the number of seeded and control clouds on each experimental day. For example, it is possible that the seeding effectJs not the same on such day and if those days with the larger seeding effects did in fact have more seeded than control clouds and conversely for the remaining days, the ranking of the seeded clouds would be enhanced relative to the control clouds. Similarly, the same statements could be made about initial wetness of the clouds or amount of disturbance in the atmosphere. However as shown in the sections below there is no evidence that this situation obtained. 2A COVARIATE REGRESSION Effective use of the initial wetness of the cloud, R(-10, 0), as the covariate in regression analysis was demonstrated in the report of the 1968 experiment (Woodley , 1970 ). This technique which utilizes the t-distr ibut ion is applied here to the 1970 data and the combined data for both R(0, kO) and R(total). The results are contained in table A2. The control cloud equation of the 1970 experiment differed appreciably from that of the 1 968 experiment causing some doubt about the significance levels obtained in the tests. To overcome this objection the analysis of covariance is introduced in the following section to account for the variability in the estimate of the control line. In addition the second variate, C, is included in the analysis. A5 Table A2a. Covariate Regression - R(0, 40) 1968 & 1 970 1968 Data 1970 Data Data "Regress ion a. 1 .188 2. 501 1.985 Coef f ic ients b. 1 .028 0. 418 0.659 R R4 1 R* 1 R4 i R^ 1 R^ Obs. Obs. Pred d Obs Pred d Pred d 120.6 3.31 3.72 -0.40 3.60 -0.29 31.^ 2.37 3.23 -0.86 3.29 -0.92 850.2 5.40 3.34 2.06 3.36 2.04 227.1 3.88 1.19 2.69 1.99 1 .90 311.5 4.20 2.90 1.30 3.08 1 .12 403.7 4.48 3.07 1.41 3.19 1 .29 238.0 3.93 2.27 1.66 2.68 1.25 16.4 2.01 2.47 -0.46 2.81 -0.79 87.8 3.06 2.76 0.30 2.99 0.07 17.5 2.05 1.19 0.86 1.99 0.06 200.7 3.76 3.61 0.15 3.54 0.23 366.5 4.38 4.38 -0.01 4.03 0.34 250.9 3.15 2.81 0.33 3.03 0.12 7.7 1.67 3.00 -1.34 2.78 -1 .11 552.0 4.85 3.50 1.34 3.57 1.28 792.9 5.31 3.71 1.60 3.89 1 .42 264.8 4.03 3.52 0.52 3.59 0.45 475.8 4.67 3.62 1.05 3.75 0.92 318.6 4.23 3.21 1 .02 3.10 1 .12 118.3 3.30 3.30 0.00 3.25 0.05 255.0 4.00 3.48 0.52 3.52 0.44 114.5 3.27 2.74 0.54 2.36 0.92 55.2 2.73 2.50 0.23 1.99 0.74 32.7 2.39 3-35 -0.96 3.32 -0.93 40.6 2.52 2.50 0.02 1.99 0.54 d 0.696 0.378 0.490 s cT 0.241 0.252 0.173 t 2.35 1.50 2.83 tdf,a 2.18 1 .36 2.80 S ign i f icance level a 0.05 0.10 0.005 *R4 control = a + b R(-10,0)^ A6 Table A2b. Covariate Regression - R(Total) 1968 & 1970 1968 Data 1970 Data Data -Regress ion a. 1. 209 2.400 1.932 Coef f i cients b. 1 . 036 0.532 0.734 R 1 R" 1 R^ 1 R4 1 1 R<* Obs. Qbs. Pred. d Obs. Pred. d Pred. d 129.6 3.37 3.75 -0.38 3.73 -0.36 31.4 2.37 3.26 -0.89 3.38 -1 .02 2698.5 7.21 3.37 3.83 3.47 3-74 490.0 3.88 1 .21 2.67 1.93 1.95 430.0 4.55 2.93 1.63 3.15 1 .40 302.8 4.17 3.10 1.07 3.28 0.90 119.0 3.30 2.29 1 .01 2.70 0.60 4.1 1 .42 2.50 -1.08 2.85 -1.42 92.4 3.10 2.79 0.31 3.05 0.05 17.5 2.05 1 .21 0.84 1.93 0.11 200.7 3.76 3.65 0.12 3.66 0.10 274.7 4.07 4.42 -0.35 4.21 -0.14 250.9 3.98 2.84 1.14 3.09 0.89 7.7 1.67 3.04 -1.38 2.82 -1.15 1656.0 6.38 3.67 2.71 3.69 2.69 978.0 5.59 3.93 1.66 4.05 1.55 198.6 3.75 3.69 0.06 3.71 0.04 697.8 6.42 3.83 2.59 3.90 2.52 334.1 4.28 2.88 1 .40 3.17 1 .10 118.3 3.30 3.42 -0.12 3.34 -0.04 255.0 4.00 3.65 0.36 3.64 0.35 115.3 3.28 2.70 0.58 2.34 0.93 242.5 3.95 2.40 1.55 1.93 2.01 32.7 2.39 3.48 -1.09 3.42 -1.03 40.6 2.52 2.40 0.12 1.93 0.59 d 0.763 0.703 0.655 s 0.387 0.377 0.256 Z t 1.97 1.86 2.56 tdf ,ct 1.78 1 .80 2.49 S ign if i cance level a 0.10 0.05 0.01 *R4 control = a + b R(-10,0)^ A7 3A ANALYSIS OF COVARIANCE The analysis of covariance is applied to the combined data only using the two concomitant variables, initial wetness of the cloud and atmospheric disturbance on the experimental day. The correlation between R (- 1 0 , 0) and C is low in this data set (0.12 for control clouds and 0.05 for seeded clouds) permitting nearly independent estimates of the effective- ness of the two covariates. As expected R(-10, 0) still contributes significantly to the regressions which are shown for R (- 1 0 , 0) alone in table A3. Only for R(total) was non-zero regression suggested for variable C. The significance level was low (approximately 0.20) , however the fitted equations are of some interest. l i R(total)4 control = 2.00 + 0.7^ R(-10,0)i+ - 1 .21 C (3) R(total)7* seeded = 2.92 + 0.7^ R(-10,0)^ - 6.82C (4) 1 1 Taking the difference R(total)4 seeded - R(total)i+ control and solving the resulting equation for C yields the result that the seeding effect is zero for C = 0.16. This implies that the seeding effect for days with C near this value is small or zero. Examination of the data suggests that this would include those four days with C > 0.13- This is in agreement with the stratification, fair and rainy, shown in table 7 of the main text which was based on meteorological considerations. Caution should be exercised about this conclusion however since the number of clouds in this disturbed cate- gory is small (10 out of 51). Further, the true seeding effect may have been masked by mergers that occurred before the effect could be detected (note that of the four seeded clouds in the "rainy" classification, three A8 Table A3a. Analysis of Covariance R(0,40) 1968 and 1970 Combined 2 2 2 A. Regression Data Sx Sxy Sy df S req, 1. Common regression of 46.0827 31.6031 66.3159 49 21.6731 seeded & control clouds 2. Regression of control clouds 3. Regression of seeded clouds 4. Regression of seeded & control clouds with common slope &• separate means 5. Separate regressions of seeded & control clouds B. Test of Significance of Difference Between Regressions of Control and Seeded Clouds on Initial Wetness Source ss df ms F__ 1. Residual after fit of common regress ion 2. Residual after f i t of common slope & separate means 21.6734 44.6428 1 48 23.8365 15.7177 34.0805 24 10.3642 20.8131 12.8617 25.8558 24 7.8480 18.2122 44.6496 28.5794 59.9363 18.2932 41 .6431 59.9363 48 1 47 48 18.2932 >uds 18.2122 41 .6241 2 46 44.6428 48 41.6431 47 0.8860 2.996 1 41.6431 47 41 .6241 46 0.9069 3. Difference between adjusted means 2.996 3.36* 4. Residual after fit of common slope & separate means 5. Residual after separate regress ions 6. Difference between slopes .0190 1 0.02 C. Regression Equations R(0,40)^ control = 2.010 + 0.640 R(-10,0)* Fl ,47, .025 = Af,°5 R(0,40)ir seeded = 2.508 + 0.640 R(-10,0)^ *Fl'47'.05 = 2-82 A9 Table A3b. Analysis of Covariance R(total) 1968 and 1970 Combined 2 2 ,- 2 A. Regression Data Sx Sxy Sy df S reg, 1. Common regression of 46.0827 36.2106 99.9504 49 28.4534 seeded & control clouds 28.4534 1 71.4970 48 23.8365 17.5026 39.9074 24 12.8518 20.8131 14.8822 49.8295 24 10.6413 23.4931 44.6496 32.3848 89.7370 23.4890 66.2480 89.7370 48 1 47 48 23.4890 ds 23.4931 66.2439 2 46 2. Regression of control clouds 3. Regression of seeded clouds 4. Regression of seeded & control clouds with common slope & separate means 5. Separate regressions of seeded & control clouds B. Test of Significance of Difference Between Regressions of Control and Seeded Clouds on Initial Wetness Source ss df ms F 1. Residual after fit of common regress ion 2. Residual after fit of common slope & separate means 3. Difference between adjusted means 4. Residual after fit of common slope & separate means 5. Residual after separate regress ions 6. Difference between slopes 71.4970 48 66.2480 47 1 1 .4095 5.2490 3.72* 66.2480 47 66.2439 46 1 .4397 .0041 1 0.00 C. Regression Equations R(Total)£ control = 1.943 + 0.725 R(-10,0)? ¥]t 47,-025 = 4.05 RtTotal)4 seeded = 2.602 + 0.725 R (-1 0 ,0)^ v.p ^ ^ _ 2>g2 A10 merged). Examination of these control and seeded clouds before mergers however does not suggest a positive seeding effect. Additional evidence is presented in the next section as well. Unfortunately one cannot give a probability statement about seeding effects, on these days alone because of these ambiguities. kf\ ANALYSIS OF DAILY MEANS The present experiment may be analyzed by the analysis of variance technique called a two-way classification analysis with unequal numbers of observations in subclasses (Kempthorne, 1962). This procedure permits various comparisons of the daily mean difference of the seeded and control clouds. In this section the term mean will stand for what is normally called the "adjusted mean", that is, each mean is corrected in the least squares sense for the imbalance in the number of observations in the various groupings. The analysis is shown in table f\k . It is worth noting that in the context of the two previous sections the daily control mean may be viewed as a co- variate for the seeded mean of the same day. Since there are 17 experimental days with both seeded and control clouds, 17 independent comparisons can be made between these mean differences. At least two of these are of interest in the present experiment. The first is the overall seeding effect which is assumed to be the same on every day. This mean effect is found to be highly significant when compared to the error variance. The error variance is computed in the standard manner from data on those days with multiple seeded or control clouds. The remaining possible comparisons can provide a test of the assumption of uniform seeding All Table A4. Analysis of Variance 1. R(0,40) ANOVA 1968 and 1970 Data Combined Source ss df ms_ Fit day means 39.1 12 17 Seed vs control 5.5328 1 Fai r vs rainy 1 .3232 1 Interaction 12.2524 15 Error 8.0837 16 Total 67.1023 50 Fit day means 45.81 18 17 Seed vs control 12.1678 1 Fai r vs rainy 3.4722 Interaction 20.4157 15 Error 21.3006 16 Total 103.1681 50 *F , 16, .100 - 3 . 04 **FM6, .0,0 =8-53 ***F 1,16, .005 = l0-6 2.35 4.65 5.53 10.9- 1 .32 2.62 0.77 1.52 0.51 2. R(total) ANOVA 1968 and 1970 Data Combined Source ss df ms 2.69 1.95 12.17 9.15 3.47 2.61 1.36 1 .02 1.33 A12 effect. The variability associated with these comparisons is usually lumped together as "interaction" in the analysis of variance table and tested for significance against the error variance. In this instance however there is a second important comparison which is suggested by the physics of cloud behavior, i.e. the difference in seeding effects after stratification by fair and rainy days. The difference of seeded and control means on fair days is compared with the difference of seeded and control means on rainy days after both have been adjusted for overall seeding effect. Using the definition of rainy days as those days with greater than 4000 (n mi) (0 0.13) covered by rain echoes, the dif- ference in seeding effect resulting from this stratification has about the same level of significance (table A4) as for the inclusion of the covariate C in the regression equation in the previous section. This again may suggest that this differential seeding effect does exist however, in view of the modest significance level and the complicating factor of mergers in R(total), the evidence based on the data alone is not overwhelming. There is no hint that any other comparisons of these means could lead to a statement of significant effects (see the F statistic for interaction in table Ah) . Analysis of the residuals from the fitted equations indicates that even with the fourth root transformation the error variance still gives evidence of some non-normal i ty , i .e . comparing sample third and fourth moment calculations. Fortunately F-tests in this type of analysis are robust to departures from normality (Scheffe , 1959). It should be noted that of the tests applied in this report only the Wi lcoxon-Mann-Whi tney test completely circumvents the distributional problem. A13 Finally an estimate of seeding effect in terms of the nont ransformed data can be obtained in the following manner. The original R(total) seeded amounts are multiplied by a suitable constant ( < 1 .0) such that the estimated seeding effect is identically zero when these reduced values are trans- formed by the fourth root and reanalyzed in the analysis of daily means. For the combined 1 968 and 1970 data this constant is approximately 0.3, that is, seeding increased the amount of precipitation by a factor greater than three. 5A SUMMARY A series of standard statistical tests was applied to the data of two single cloud seeding experiments, one in 1 968 and the other in 1970. Significant results were obtained with tests which involve rather different assumptions about the distributions and models relating to the data set. This is very encouraging since the test of hypothesis of positive seeding effect appears to be robust to different initial assumptions. 6A REFERENCES Kempthorne, 0. (1962), The design and analysis of experiments, chapter 6, 68-119. John Wiley and Sons, N.Y. Mann, H. B. and D. R. Whitney (19^7), On a test of whether one or two random variables is stochastically larger than the other, Ann. Math. Stat. 18, 50-60. Scheffe, H. (1959), The analysis of variance, chapter 1, 10, 331-369 John Wiley and Sons, N.Y. Wilcoxon, F (19^+5), Individual comparisons by ranking methods, Biometrics Bull . 1 , 80-93. Woodley, W. L. (1 970) , Precipi tat ion results from a pyrotechnic cumulus seeding experiment, Jour. Appl. Meteor. 9, 242-257- A14 57 U.S. DEPARTMENT OF COMMERCE Environmental Science Services Administration Research Laboratories ESSA Technical Memorandum ERLTM-AOML 7 DESIGN OF A MULTIPLE CLOUD SEEDING EXPERIMENT OVER A TARGET AREA IN SOUTH FLORIDA William L. Woodley Richard Williamson Experimental Meteorology Laboratory Atlantic Oceanographic and Meteorological Laboratories Miami, Florida February 1970 TABLE OF CONTENTS Page ABSTRACT iv 1. INTRODUCTION 1 2. APPROACH TO THE PROBLEM 2 3. THE TARGET AREA 3 k. CRITERIA FOR AN EXPERIMENTAL DAY k 5. EXECUTION OF THE EXPERIMENT 7 6. EVALUATION OF THE RESULTS 11 7. EXPECTED RESULTS 13 8. FREQUENCY OF SUITABLE SEEDING CONDITIONS 13 9. TARGET CONTROL RAINFALL ANALYSES 16 10. CONCLUSIONS 22 1 1 . ACKNOWLEDGEMENTS 23 12. REFERENCES 23 in ABSTRACT The design of a multiple cloud seeding experiment over a target in South Florida is presented. Because of its success during May 1968, the dynamic cloud seeding approach has been adopted for the experiment planned for April 15 to May 31, 1970, when supercooled cumuli over the target area will be individually seeded with silver iodide pyrotechnics to produce changes in cloud dynamics, increase areal precipitation, and manipulate mesocloud systems. The proposed target area, criteria for days suitable for experimentation, seeding techniques, and methods of evaluation are discussed. The meteorological suitability factor for an experimental day during April and May 1970 was evaluated by applying it to comparable periods during 1968 and 1969. Of the 62 days studied, ^3 percent satisfied the suitability factor. This factor was also effective in eliminating days with suppressed or overdeveloped shower development. Target rainfall analyses are presented for \k of the 27 days satisfying the suitability factor. Total target rainfall and rainfall normalized to that in the 10 min before a simulated seeding are presented. These analyses will be valuable as controls for comparison with similar analyses for April and May 1970. Seeding is expected to increase target rainfall a factor of two over rainfall without seeding. IV DESIGN OF A MULTIPLE CLOUD SEEDING EXPERIMENT OVER A TARGET AREA IN SOUTH FLORIDA William L. Woodley and Richard Williamson 1. INTRODUCTION Experimentation over South Florida during May 1 968 revealed that silver iodide pyrotechnic seeding of supercooled cumuli was effective in promoting cloud growth and, as a consequence, increased precipitation from these clouds (Woodley, 1969). The seeding apparently had little effect on other cloud and precipitation developments in the vicinity of the individually seeded clouds (Woodley et al»,1969). We do not know whether it is possible to alter mesoscale cloud developments and precipitation by individual seeding of many supercooled cumuli, but if it is, man will have taken a major step toward water management and the mitigation of severe storms. The Experimental Meteorology Laboratory (EML) is now in a position to investigate this possibility in a multiple cloud seeding experiment over a target in South Florida planned for April and May 1970. The overall design of the proposed experiment is outlined here in order that the scientific community be given the opportunity to evaluate it before its execution. 1 On a space scale of tens of miles. 2. APPROACH TO THE PROBLEM Numerous options are open to a scientist in designing a multiple cloud seeding experiment. Randomization and massive silver iodide pyro- technic seeding of individual cumulus clouds to produce dynamic changes have been chosen for the proposed experiment. Randomization is desirable if one intends to eliminate unconscious bias and to subject the data to statistical scrutiny. The seeding technique is chosen because of its success in May 1968. Other scientists (e.g., Battan 1966, 1967; Dennis and Koscielski, 1969; Flueck, 1968; Neumann et al., 1 967) have approached multiple cloud seeding over a target from a microphys ical standpoint, seeding upwind of the target clouds or at cloud base to provide one ice nucleus per liter active at -10 C. The rainfall results of such experimentation have been rather variable; dynamic changes have neither been expected nor observed in these experiments. During the proposed experiment we will introduce 100 to 1000 nuclei per liter active at -10°C into each seeded cloud in an attempt to reproduce in cloud groups the dynamic changes that were observed during single cloud seedings in May 1968. Cloud growth, precipitation increases, and altera- tion of mesocloud systems are possible by-products of the seedings. There are two basic approaches to randomization (in space or in time): (1) two target areas, randomization of "seed" and "no seed" areas, and seeding whenever conditions are favorable (crossover design); or (2) randomly determined "seed" and "no seed" days over one target area. The first approach is appealing because rainfall in the two areas can be compared on any operat ional day when, presumably, both areas are subject to the same weather conditions. For the proposed experiment, however, this approach has been rejected in favor of the second for the following reasons : (a) The Florida peninsula is too small to obtain two areas within UM/10-cm radar range (100 n mi) that are large enough to provide the cloud population potential necessary for successful seeding. (b) Nonrandom bunching of seedable clouds may occur in one area and not the other. (c) Developments in the seeded area might have an adverse effect (compensating subsidence near seeded cumulonimbus clouds, anvil cirrus shield, etc.) on convective developments in the neighboring control area. (d) The control area may be contaminated by silver iodide from the seeded area. (e) Area selection is complicated by the blind cones on certain azimuths produced by obstructions to the UM/10-cm radar beam. On all operational days - for which criteria are discussed later - the "seed" or "no seed" decision will be determined from a set of random- ized seeding instructions, weighted 2 to 1 in favor of the "seed" instruction 3. THE TARGET AREA The target area for the multiple cloud seeding experiment, shown o in figure 1, is a quadrilateral covering approximately 2700 n mi . The azimuths and ranges of its four corners from the UM/10-cm radar are, with azimuths and ranges from the Miami VORTAC given in parentheses: 326 , 19 n mi (0° 0 n mi); 359°, 56 n mi (012°, k] n mi); 308°, 93 n mi (303°, 76 n mi); and 283°, 76 n mi (270°, 64 n mi). The target area has very low population density but very high air traffic density. Because only one or at most two project aircraft near a fixed level will be used, the Federal Aviation Administration (FAA) may be able to vector other aircraft around them. FAA cooperation was vital to the success of the May 1968 seeding experiment and will be no less important during the projected program k. CRITERIA FOR AN EXPERIMENTAL DAY The criteria for days suitable for the multiple cloud seeding experiment over the target include: (a) The meteorological suitability factor (MSF) of S - Ne > 1 .00 , where S is the maximum predicted seedability (in km) of the EML 2 cumulus model (Simpson and Wiggert, 1969) based on the Miami 1200 GMT sounding and for assumed cloud radii in the range 1000 m 0) 0> -C >/> u X) 03 3 X o o O o> en . — ■ — Q. • — ' i_ ■4-J ■ — HJ 1 ro T> 3 03 b >- 03 1_ 03 T. F ■u o .— 0 1 L. i-j o O 1 — . — LTV *v Ll. 1 2: 0) ■ — . r • — 0) t-> L. -C D. ■tj i_ < 0 M- M- O O oj <-)- 1/1 0) OJ i_ XI c fO 0> 0 1 — 0 4-J D 0> X> X) en 0) c L. _c •— ro o ■ — h- i/i -Q en The MSF is an important part of the design of the planned experiment. In determining this factor, we consider atmospheric moisture and stability for calculating S,and shower development in the target area for calculating N . By definition, the most suitable days are those with large S and small N . This is compatible with Woodley's (1969) suggestion that clouds with large seedabi 1 i t ies are best suited for seeded precipitation in- creases. Small Ne means that target shower development is not too ad- vanced before the 1600 GMT decision time. The MSF will be valuable in stratifying the experimental days before "seed" versus "no seed" compari- sons are made. One of the unfortunate features of the May 1968 tests was meteoro- logically premature cancellation of the flights because of light require- ments for photography and other contingencies. During the 1970 area experiments, the main requirement will be adequate lighting to visually judge a cloud's acceptability for seeding. Airborne time-lapse photography, while highly desirable, is not as important in multiple as in single cloud experiments. Thus, during the planned experiment, flight operations will be possible as late as sunset. This is important because it has been noted that on the drier, more suppressed days suitable clouds are often not present until a few hours before sunset. This may be due to a combi- nation of several factors including: (1) cumulative effect of heating over the Florida peninsula, (2) lunar-solar tides that enhance convection around 0600 and 1800 local time (Malkus, 1964), and (3) net radiational cooling from cloud tops after sunset. 5. EXECUTION OF THE EXPERIMENT After a day has been chosen as suitable for seeding, the decision to seed will be made from a set of randomized seeding instructions. In the case of a "seed" decision, the final decision to fly will depend on convective development in the target area. If the decision is "no seed", there are two options: (1) not to fly, or (2) to fly and penetrate all suitable clouds without seeding. In either case the target will be sub- jected to continuous UM/10-cm radar surveillance. Where time and money are major considerations, the first option is favored. However, flights on "no seed" days are desirable to obtain an aerial photographic survey of the target cloud populations for post-analysis. The mere designation of a day as suitable for experimentation does not make it so; the atmosphere must cooperate in providing the cloud popu- lations for successful seeding. On suitable days with favorable target cloud populations the DC-6 will take off for flight operations. When in the target area at 20,000 ft, the scientists aboard will look for clouds acceptable for seeding (for selection criteria, see Woodley, 1969). Mean- while, the UM/10-cm radar will have the target area under surveillance while operating on 360° scan at 0.5° elevation with four-level iso-echo contouring. The MPS-4 5-cm radar will be operated continuously in the 3 CAPPI (constant altitude PPI) mode. The scientists in the radar laboratory will be in VHF radio contact with the project aircraft, directing it to 3 A method of using annular rings from PPI photographs taken at various programmed antenna tilt angles in an attempt to show the precipitation patterns at several constant altitudes. favorable cloud groups and making certain no clouds are seeded outside the target area. Radar identification of the project aircraft will be facilitated by a transponder receiver in the radar laboratory. Preliminary plans call for ten 50-g silver iodide pyrotechnics to be introduced per cloud or cloud tower, five on each of two right-angle passes of the DC-6 seeder flying at 20,000 ft. More flares may be necessary if the clouds prove unresponsive to 500-g silver iodide. With the 208 flare capacity of the DC-6, 10 flares per cloud will permit 20 clouds to be seeded. If the DC-6 exhausts its supply of flares, the RFF B-57» with a 112 flare capacity, will be deployed to continue the seeding. The scientists in the command DC-6 will continue to select the clouds, but the B-57 will do the seeding from 21,000 ft MSL based on flight patterns de- veloped during the May 1968 seeding experiment (Woodley, 1969). With both aircraft operating, approximately 31 clouds can be seeded per day. Neither aircraft is expected to have sufficient time to return to base for a second load of flares. When the DC-6 acts as the seeder aircraft, its first pass through the experimental cloud will be the seeding pass. The project scientist in the DC-6 will sequence the flares into the cloud when the aircraft en- counters updrafts coincident with Johnson-Williams liquid water contents exceeding 0.5 g m . If the cloud is inactive during the aircraft pene- tration, no seeding will be attempted. Since all cloud physics instrumen- tation on the DC-6 is forward of the pyrotechnic racks, all measurements made only seconds before release of the silver iodide will be much more representative of the seeded portion of a cloud than were the before-seeding measurements made in May 1968. 8 The primary task of the scientists in the seeder aircraft will be to promote increased cloud growth and, as a consequence, increased rainfall from the seeded clouds in the target area. Multiple seedings of individual clouds will be carried out to promote cloud mergers and mesocloud systems. This may be difficult to accomplish because little is known of the natural forces that organize convective clouds into groups and lines. The approach of Davis et al . ( 1 968) to mesoscale seeding experiments in Flagstaff, Arizona, may prove helpful in this regard. Woodley and Powell (1970) suggest that merger of individual precipitating convective clouds is an important mechan- ism for rain enhancement. In one instance studied, two clouds produced greatly increased precipitation immediately after merger compared with the sum of their precipitation contributions in the same time period immediately before merger. An example of the proposed seeding plan for the experiment during the spring of 1970 is presented in figure 2, where the unseeded target convective developments on May 20, 1968, are used for illustration purposes. Each contour represents a threshold hourly rainfall rate having the value shown in the figure. It is hypothesized that seeding will be effective in promoting the type of development shown, but more rapidly and, in some in- stances, when it could not have occurred naturally. If the seeder aircraft had been in the target area at 1751Z(fig. 2A) , the echoes in line AB would have been prime candidates for seeding because (1) echoes in lines show more development than those without linear organi- zation, (2)the echoes reached 20,000 ft but not above 30,000 ft, as verified by aircraft flying near the cloud line, and (3)the echoes were moving 0 I75IZ 0 I8I3Z 0 00 * $ I H I836Z <£> p o * * K) O • r- i ■ (A W ! ■ o rA o m c c (0t> 01 0£) M 18 8 s w 3 & n c\i AS oj & fc M »o a I 96«:))Am <° Ol ^ N 1 zS* 8 ?-§ "SS o »- »~X 2 ■o?8 m -a! ^T. -^s:'-' : (A *! O K te*;'--. 2-i PcSk?'**- K ^ 1 I | pv*^»^ i 5 / i (OOIOI-)M (02 I 01 0M)M c JZ •~ ul o 4-J X) 1- -l-J f— 01 QJ ro 4-> _Q 4- > 4-1 F= 4- i_ o zs O c 0 CD • — CD 4-1 ■a c c 0) • — l/l 3 h "O X o •— CI) c J_ 4-i 0) o ul CL. 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The precipitous decrease in both rainfall measures after 1 hour 50 min is not significant and is the result of no data being available for two of the more productive rainfall days. In 1 hour 50 min after the simulated seeding, the mean target rainfall is 440 acre-feet, representing nine times more rainfall than was produced in the 10 min before the simulated seeding. The 440 acre-feet mean target rainfall is small compared with the rainfall produced by single seeded clouds during May 1968. As an example, experimental cloud 3 on May 16, 1968, produced 850 acre-feet in the 40 min after seeding. It will be interesting to compare these precipi- tation curves with those obtained in the analysis of seeded days during the multiple cloud seeding experiment this spring. The mean normalized target rainfall in the 40-min interval after simulated seeding (14 cases) was compared with the average normalized rainfall for 9 of the 14 clouds seeded during May 1968 in the 40-min 5 period after actual seeding. The mean 40-min normalized rainfalls for the seeded and nonseeded cases were 4.60 and 2.70 respectively. Mean normalized rainfall for seeded clouds was 1.7 times that for the control cases. Despite the small sample on which it is based, this comparison is important; it implies that if we are able to reproduce the results of May 1968 over the target during May 1970, normalized target rainfall after seeding will be a factor of two greater than that noted in the control cases presented in figure 3. Such a difference would almost certainly have rather high statistical significance . 5 Not all of the seeded clouds produced rain in the 10 min before seeding, and these clouds could not be used in the calculations of normalized rainfal 1 . 20 10 8 - 7 - .< 6- < Q 5 LU N 2 4 O NORMALIZED RAINFALL (10) — ■ — = TOTAL RAINFALL — <14! 03), (13) AIO) — / "^ \ / — 1 / V 11)/ ' 1 / )( / 11 / V / / / / / (13)/ (II) / 031/ yu4) / / / / / 1 \\ — / / w — 1 1 1 u U(8) ^^ 1 1 ! __ (14)/ (14) - / «i, (14^/ 1(8) — / / (14)/ (lW (14) (I4K — *fl4) — 1 1 1 1 1 1 1 1 1 1 1 1 2 - 10- 20 30- 40 50- i:oo i:io- 1:20 130- 1:40 1:50- 2:00 TIME INTERVAL (min) 500 -450 -400 -350 O H > -300 23 > 2 H250EI > o JQ 200 m Tl m m H 1I50~ - 100 - 50 Figure h. Mean normalized and mean total target rainfalls versus time interval after a simulated seeding. The number in parentheses near each point is the number of days contributing to the mean. 21 The EML numerical model predictions of precipitation development do not contradict the conclusions reached above. The total precipitation production calculations for seeded and unseeded clouds were compared for the 17 acceptable days during April and May 1969. The input radii were those tabulated in table 1. The mean ratio of total precipitation produc- tion after seeding to total precipitation production without seeding was 1.25. If we assume that all invigorated seeded clouds will produce at least one more cloud tower than the unseeded clouds - a reasonable assump- tion - the mean ratio of seeded to unseeded precipitation production is 2.50. Again, we see that a factor of two increase in target precipitation 6 with seeding is not an unreasonable expectation, and this increase will be greater if seeding is effective in altering mesoscale precipitation development . 10. CONCLUSIONS The groundwork has been laid for a multiple cloud seeding experi- ment over a target in South Florida. We believe that the approach out- lined is probably the best for accomplishing our goals of increased areal rainfall and manipulation of mesocloud systems. The objectives to be reached are within our grasp, and analysis suggests that the criteria for an experimental day and the 1600 GMT seeding decision time are not un- reasonable. The 14 target rainfall analyses from May 1968 and May 1969 5" Simpson (1969) and Woodley and Powell (1970) show that the ratio of seeded to unseeded precipitation production would be much larger if coalescence in the deeper seeded clouds were considered. 22 will be very valuable controls for comparison with the experiment planned. By including these controls we will probably have a sample large enough for meaningful statistical testing. It is our opinion that, with some luck during the projected experiment, we will be able to reach definitive conclusions about man's ability to manipulate mesocloud systems and in- crease areal rainfall through silver iodide pyrotechnic seeding. 11. ACKNOWLEDGEMENTS During the course of this study,we appreciate the free rein given us in the design of the experiment by Dr. Joanne Simpson, Director of EML; the model predictions of seedability run for us by Mr. Victor Wiggert; and the advice and assistance afforded us by Messrs. Ron Holle, Alan Miller, and Robert Powell, and Mrs. Suzanne Johnson. The Radar Meteorological Laboratory, Rosenstiel School of Marine and Atmospheric Sciences, graciously provided us with the radar observations used in this study. 12. REFERENCES Andrews, G.F., and H. V. Senn(1968), Semi-automatic calibration of receiver and video system characteristics for weather radars, Proc. 13th Radar Meteorol . Conf., Montreal, Canada, 20-23. Battan, L. J. (1966), Silver iodide seeding and rainfall from convective clouds, J. Appl . Meteorol. 5., 669-683. Battan, L. J. (1967), Silver-iodide seeding and precipitation initiation in convective clouds, J. Appl. Meteorol. 6, 317-322. Davis, L. G., J. I. Kelley, A. Weinstein, and H. Nicholson (1968), Weather modification experiments in Arizona, Dept. Meteorol., Pennsylvania State University, State College, Penn. 128 pp. 23 Dennis, A. S. and A. Koscielski (1969), Results of a randomized cloud seeding experiment in South Dakota, J. Appl . Meteorol . 8, 556-565. Flueck, J. A. (1968), A statistical analysis of Project Whitetop's precipitation data, Proc. First Natl. Conf. Weather Modification, Albany, New York, 26-35. Malkus, J. S. (1964), Tropical convection: Progress and outlook, Proc. Symp. Tropical Meteorol., 5-13 November 1963, Wellington, N.Z., 247-277. Neumann, J. K. , R. Gabriel , and A. Gagin (1967), Cloud seeding and cloud physics in Israel, Results and Problems, International Conference on Water for Peace, 53 PP« Simpson, J. and V. Wiggert (1969), Models of precipitating cumulus towers, Monthly Weather Review 97(7) , 471-489. Simpson, J., (1969) Modification experiments on tropical cumulus clouds, Report presented at Sixth Tech. Conf. on Hurricanes, Miami, Florida, Dec. 2-4, 1969. Woodley, W. L. (1969), Precipitation results from a pyrotechnic cumulus seeding experiment, ESSA Tech. Memo. ERLTM-AOML 2. Woodley, W. L., A. Herndon, and R. Schwartz (1969), Large-scale precipi- tation effects of single cloud pyrotechnic seeding, ESSA Tech. Memo. ERLTM-AOML 5. Woodley, W.L., and R. Powell (1970), Documentation and implications of the behavior of seeded cloud 17, May 30, 1968, ESSA Tech. Memo. ERLTM-AOML 6 (to be published). 24 58 U.S. DEPARTMENT OF COMMERCE Environmental Science Services Administration Research Laboratories ESSA Technical Memorandum ERLTM-AOML 6 DOCUMENTATION AND IMPLICATIONS OF THE BEHAVIOR OF SEEDED CLOUD 17 MAY 30, 1968 William Lee Woodley Robert N. Powell Experimental Meteorology Laboratory Atlantic Oceanographic and Meteorological Laboratories Miami, Florida January 1970 TABLE OF CONTENTS Page ABSTRACT , 1. INTRODUCTION , 2. TOOLS 2 3. SYNOPTIC SITUATION 2 4. DOCUMENTATION OF CLOUD BEHAVIOR 4 5. RAINFALL CALCULATIONS ,, 6. NUMERICAL MODEL STUDY OF CLOUD 17 14 7. ENVIRONMENTAL CONDITIONS AND SEEDED CLOUD GROWTH 25 8. SUMMARY AND CONCLUSIONS 26 9. ACKNOWLEDGMENTS 27 10. REFERENCES 28 iii ABSTRACT Convective clouds over South Florida were seeded with silver iodide pyrotechnics from 15 May to 1 June 1968. The seeded clouds reacted dramat- ically to seeding during the fi/st half of this period but less impressively, compared to unseeded clouds, during the latter half of this period. One of the more interesting experimental clouds during the latter half of the seeding program was seeded cloud 17 on May 30, 1968, a day on which there were three seeded clouds and one control. The sequence of events follow- ing its seeding was: minor growth (<300m), collapse and separation from the main cloud body, regeneration of the cloud body and explosive growth to 12 km, followed by merger with a flanking cloud and rapid intensifica- tion of the consolidated cloud system. Cloud 17 receives a detailed analysis using aircraft cloud physics and photogrammetr ic measurements, ground-based 10-cm radar observations, and a parameterized numerical model, which predicts the rise rate, cloud and precipitation water contents, and radar echo intensity of a rising cloud tower. Model predictions are tested against observations whenever possible. Calculations of the rainfall production of cloud 17 are made using the contoured 10-cm radar observations. The behavior of cloud 17 is compared with that of the seeded clouds on May 16, 1968, a day which favored a dramatic cloud response to seeding. Model predictions indicate that all towers of cloud 17 had small seedabi 1 i t ies , suggesting that cloud performance subsequent to seeding was not appreciably different from what would have occurred naturally. The model estimate of precipitation fallout from the rising cloud tower was a factor of fourteen underestimate of the total tower fallout. Accretion and coalescence of other hydrometeors by the precipitation from the rising cloud tower must be invoked as the major mechanism for augmenting the precipitation mass. This contention is supported by an alternate approach to the problem. This finding provides a partial explanation for the seeded precipitation increases that were observed in South Florida during May 1968. i v DOCUMENTATION AND IMPLICATIONS OF THE BEHAVIOR OF SEEDED CLOUD 17 MAY 30, 1968 William Lee Wood ley and Robert N. Powell 1. INTRODUCTION During the May 1 968 Florida seeding program seeded clouds grew more and, as a consequence, produced more precipitation than their un- seeded counterparts (Woodley, 1969). The response of the clouds to seed- ing was not uniform. Simpson and Woodley (1969) have studied three clouds seeded on May 16, 1968, a day on which environmental conditions favored a dramatic cloud response to seeding. There were other days during the seeding program not as favorable for seeding; May 30 was such a day. It is instructive to study one of the experimental clouds of May 30 for comparison and contrast with those of May 16. Better specification of cloud behavior as a function of environ- mental conditions is one expected by-product. Seeded cloud 17 was one of the more interesting of the four experi- mental clouds of May 30, 1968. It is of interest from several standpoints; the primary seeded tower, which was also the highest, grew very little and then separated from the main cloud body. It was followed by a new tower that grew explosively, presumably in response to a shower of ice crystals and silver iodide falling into it from the decaying seeded tower. The behavior of this cloud is documented using aerial time-lapse photography and photogrammetry , detailed cloud pass observations at two levels, iso- echo radar data, and EML numerical model predictions. 2. TOOLS Photographic documentation of cloud behavior was provided by 16- and 35-mm aerial time-lapse photography. The 35-mm cameras were mounted on the left and right sides of the Research Flight Facility (RFF) DC-6, while the 16-mm cameras were mounted on the noses of the RFF DC-6 and B-57 aircraft. The photogrammetr ic calculations of rise rate were made from the time-lapse photography based on a system described in a report by Herrera-Canti lo (1969). The radar measurements were obtained from the ground-based UM/10-cm radar of the Radar Meteorological Laboratory, Rosenstiel School of Marine and Atmospheric Sciences of the University of Miami operated with the i so- echo contour system described by Senn and Andrews (1968). This system provided four contours of echo return corresponding to -100, -86, -75, and -63 dbm on May 30, as verified by the calibration scheme of Senn and Courtright (1968). The DC-6 internal pass measurements Include absolute pressure, radar and pressure altitude, relative humidity measured by an infrared hygrometer, temperature measured by a vortex thermometer, and liquid water measured by Johnson-Williams hot-wire instrumentation. 3. SYNOPTIC SITUATION There were deep westerlies over Florida and the adjacent Atlantic waters on May 30, 1968 (table 1). A trough that had previously been over the eastern Gulf of Mexico moved eastward over Florida as the frontal remnants associated with this trough moved into South Florida. Table 1. Wind Estimates for the Location of Seeded Cloud 17 May 30, 1968 Altitude (ft x 103) Wind (ddff) deqrees/kts Shear deqrees/kts k 8 12 16 20 25 30 35 300/08 180/10 230/10 270/15 280/17 250/22 250A5 230/55 155/16 295/08 310/10 330/04 200/11 250/23 180/20 Satellite pictures showed extensive cloudiness over the northwestern Caribbean, western Cuba, the Florida Straits, and the Bahamas. This cloudiness was aligned ahead of the frontal remnants. An inverted trough with its associated cloud mass, in which Hurricane "Abby" formed 2 days later, was located over the western Caribbean. The northern edge of the cirrus shield associated with the extensive cloudiness oscillated over extreme South Florida most of the day; its presence was an undesirable feature of the weather for experimentation on May 30 for two reasons: (1) the cirrus provided a poor background for cloud photography, and (2) there was the risk that ice crystals falling from the cirrus may have seeded supercooled cumulus clouds growing below. k. DOCUMENTATION OF CLOUD BEHAVIOR Cloud 17 first appeared on the 0.5° scan of the UM/10-cm radar at I825Z at an azimuth and range of 292°, 46 n mi , 25 min before seeding at 1850Z. It was first visible on the nose cameras of the B-57 and DC-6 aircraft at about 1 83 72 . It consisted of one large tower (A) on which a succession of smaller towers (Aj , A2, and A3) with lifetimes of 10 to 15 min would be superimposed. The first view of cloud 17 from the nose camera of the DC-6 flying at 20,000 ft MSL is shown in plate 1 of figure 1 at 1840Z. The remnants of tower Aj can be seen to the right of the growing tower A2 • The position where the DC-6 penetrated the cloud at 1842Z is marked by an X on the photograph. The internal measurements made by the DC-6 in tower A2 of cloud 17 at 1842Z are shown in the graph in figure I. A temperature rise of 0.9°C, a peak Johnson-Williams liquid water content of 0.6 gm m"-*, and updrafts as suggested by the 200 ft increase in aircraft radar altitude (despite constant aircraft attitude) indicate that tower A2 was fairly active during the first penetration. The 18*+2Z radar scan at 0.5° elevation (center of beam at 3500 ft) shows a core with boundary value of -75 dbm, corresponding to a rainfall rate of 0.55 in. hr" (obtained from Z=300R ). Aircraft position and heading at the time of each photograph are indicated on the 10-cm radar depict ions ; numbers correspond to numbers of plates. At 1847Z tower A] had evaporated, A2 was beginning to decay, and An was approaching maturity on the upshear side of tower A (plate 2, fig. 1). Heavy precipitation was falling from tower A, especially on the downshear CLOUD 17 — MAY 30, 1968 1. I840Z T-9 \ CAMERA HEADING - ACFT. HEADING- -75dbm 7 ./ -86 dbm -100 dbm I 10 n.mi- I842Z 2. I847Z T - 2 850Z DC-6 F i gure 5 PASS 1 HT. 20,000 ft. 3. I850Z T + 1 4. I85IZ T + 2 side beneath A2. The photogrammetric estimate of maximum cloud top at this time is 27,500 ft MSL (see fig. 2). The numbers along the rise rate curve in figure 2 correspond to the numbers of the plates. The towers flanking tower An and An at this time had top heights below 16,500 ft MSL. The views of cloud 17 during seeding (184855 - 185141Z) are shown in plates 3 and k of figure 1. During this period tower A~ dissipated, and tower Ao reached maturity and began to decay, reaching a maximum height of 29,500 ft MSL (fig. 2). Ice nuclei measurements in cloud 17 made with a Bigg-Warner cold box (activation temperature -20 C) were 7 active nuclei per liter before seeding and 56 nuclei per liter after seeding. By 185^Z cloud 17 had weakened considerably as shown by the DC-6 pass measurements at 20,000 ft. Tower A was subsaturated (with respect to water) with a negligible environmental virtual temperature excess and no measureable liquid water. The 1855Z radar scan at 0.5° elevation (center of beam at approximately 3500 ft MSL) was little changed from that 5 min earlier as much of the precipitation once contained in tower A at 20,000 ft continued to fall through cloud base. The towers flanking weakened tower A had tops below 18,000 ft at this time. The view of cloud 17 at 1859Z (plate 5, fig. 3) shows that the remnants of tower A^ had completely separated from the convective towers below, shrouding much of the cloud body in a veil of precipitation (presumably ice crystals). The situation had changed little by 1902Z; tower A3 continued to settle on the towers growing below. Viewing this cloud three-dimensional ly with the method of Fraser (1968) verified that 3 O QJ 4-J XI -C c en O •— a QJ IT) _c a 1- o o 4-J U E l/l -f 3 QJ E > "O » — s_ c X 3 1 — 4-J cn tS) M- c QJ O O 1_ . — 3 l/l ro cn c •— O LO u- • — L. 4-J QJ c ID -O *_ i — E a 3 iyi o C QJ i — 4-J fU QJ fD o -C *-• h- Q. u • — QJ s_ • JZ 4-J DO 4-J QJ vD E CT, u_ E i — 0 fU L. - if) (DO 1_ o PO QJ 4-1 n 0 >- E .C fD 3 a. 21 C K- * !!" E " - Q. ,oo .0 - ■ ** .0 Ci a- is i to — > o §5 o - - Id ; -4 0 ' -.0 - " o .0 _ UJ 3 - '0 < 1 or - j _-0 3 $* *~ -.00 ■ E -.. o ■ - - ■ : ■ -1 §. -II 0 h ■ •a * . • NfkDlM JO»- . _1 v J ■'.'..' r * jj 1 F i gure 3. PASS 3 HT 20,000 ft 8 5. IR59Z T+ 10 6 I902Z T + 13 I906Z the debris of tower A^ was settling directly into tower B. Subsequently, tower B penetrated and enveloped the remains of Ao , a process taking about 10 min, during which distinct cloud photography became very difficult. The 1904Z DC-6 pass through cloud 17 showed a negligible tempera- -3 ture rise, a Johnson-Williams liquid water peak of 0.7 gm m that coincides in time with a peak in the relative humidity, and a radar altitude increase of 80 ft. The sharp peak in these parameters coincides with the first pass of the DC-6 through the very top of tower B, which had just reached the DC-6 f 1 ight level . The 1906Z radar scan of cloud 17 showed less organization than on earlier scans. The third contour was still present but only in isolated cores. Much of the precipitation from Ao had apparently fallen through the cloud base, while no organized precipitation cores had developed from the new growing towers. By 1912Z an organized core at the third contour reappeared in cloud 17 while a separate echo began to develop on its north- east flank. It is possible that this new development, while physically separate by 3 n mi , was in some way induced by cloud 17. Cloud 17 became quite photogenic after tower B enveloped the re- mains of tower A. The view from a distance at 191^Z (plate 7, fig. *0 shows tower B, its top at 26,000 ft (fig. 2) and growing rapidly. A closer view at 1917Z, 1 min before the DC-6 penetration (marked with an X) , shows the top of tower B, nearing 33,000 ft (fig. 2) as tufts of pileus appeared above its top (plate 8, fig. k) . The 1917Z radar return of cloud 17 had changed little from that at 1 91 2Z , while the echo on its northeast flank had intensified considerably. CLOUD 17 MAY 30, 1968 7 1914 Z T - 25 9I2Z 10 n.mi. 1 CLOUD 17 I9I7Z 63 dbm I- 10 n.mi I920Z Figure k. 8. I9I7Z T - 28 i- 1 — t — i — i — i — i — i — r _L i ' i ] TIME PASS 4 DC-6 HT. 20,000 ft 10 The DC-6 penetration of cloud 17 at 1 9 1 8Z corroborates the rather impressive regeneration of cloud 17. The internal measurements show that this cloud had the following characteristics: a 2.5°C virtual temperature excess over the environment, a Johnson-Williams liquid water content of 1.5 gm m~*, a broad relative humidity peak exceeding 100% (due to evapora- tion of liquid water), and strong updrafts as evidenced by the 600 ft gain in altitude of the DC-6 while flown at a constant attitude. The sharp drop in temperature after exiting the cloud Is an error caused by evapora- tional cooling of the thermometer. The monitoring of cloud 17 was discontinued after the 1 91 8Z DC-6 penetration, and experimental cloud 18 was selected approximately 20 n mi to the west-southwest. Cloud 17 continued to grow and intensify during this period, eventually merging with its neighbor on its northeast flank, as depicted in the 1 920Z radar scan (fig. k) . At this time there was a core value of -63 dbm at the center of cloud 17 corresponding to a rain- fal 1 rate of 4.00 in. hr . 5. RAINFALL CALCULATIONS The total rainfall from cloud 17 has been calculated by Woodley (1969) in a separate report devoted to the precipitation results of the seeding during May 1968. The pertinent results appear in figure 5. Time periods are relative to the time of the first seeding pass; the volumetric water unit is acre-feet. The water values presented are probably accurate to within 30% (Woodley and Herndon, 1969). The rainfall calculations for cloud 17 are consistent with its visual behavior, characterized by minor tower growth, collapse of the 11 F igure 5 650 600 550 500 UJ UJ u. UJ 450 ,6.:. O < -J 400 _J < '[•L. :h «J 350 300 250 200 150 100 50 CLOUD 17 SATELLITE CLOUD MERGED ECHOES 3 3 C ACRE -FOOT • I 23 X 10 m -123X10 hgm ,\ / / / I i /rainfall from / merged clouds RAINFALL FROM SATELLITE CLOUD 10 MIN. BEFORE MERGER J. i ± J_ -10-0 0-10 10-20 20-30 30-40 40-50 50-60 TIME INTERVAL AFTER SEEDING PASS (MIN.) Rainfall calculation in 10-min intervals relative to time of first seeding pass. Cloud 17, May 30, 1968 12 primary seeded tower, regeneration of the cloud body and explosive growth. During the minor growth and collapse regimes in the 0 to 10 and 10 to 20 min periods after seeding, this cloud produced 23.0 and 8.0 acre-feet less water, respect ively, than it had in the 10-min period before seeding. During the 20 to 30 min after seeding, characterized by regeneration and intense growth, cloud 17 produced 27 acre-feet more water than it had in the 10-min before seeding. In the 30 min following seeding cloud 17 produced about 275 acre-feet of water, which amounts to about 0.25 in. of precipitation, 2 when evenly distributed over the 15.2 (n mi) average echo area during this time period. By 30 min after seeding, cloud 17 had merged with the small cloud echo on its northeast flank. Subsequently, the amalgamated cloud produced three times more precipitation (367 acre-feet) in the 10 min after merger than cloud 17 had in the 10 min before merger (119 acre-feet) (fig. 5). In the 30 min after consolidation approximately 1500 acre-feet of water was produced by the amalgamated cloud compared to the 275 acre-feet produced by cloud 17 in the 30 min following seeding. The former water contribu- tion represents about 0.15 in. of precipitation when evenly distributed 2 over the k6.k (n mi) average echo area during the 30 min following merger. No attempt was made to determine the exact distribution of water on the ground. The impressive precipitation production of the amalgamated cloud cannot be explained by the mere addition of the rainfall contributions from cloud 17 and its flanking neighbor, which had produced only 8 acre feet in the 10 min prior to merger. Rather, it is due to development 13 of the consolidated echo that commenced immediately after merger, apparently because of the mutual reinforcement of the merging clouds. The details of this interaction are not understood. The behavior of the consolidated echo and others like it during the May 1968 seeding program suggests that multiple cloud seeding aimed at meso-scale cumulus organization may have tremendous potential for increasing the precipitation over large areas. If it were possible through selective seeding to invigorate single convective clouds and then organize them into groups and lines, as described here, more precipitation might be expected than the simple summation of the rainfall from widely separate seeded clouds. This possibility will be investigated during the Florida seeding program scheduled for April and May 1970. 6. NUMERICAL MODEL STUDY OF CLOUD 17 The numerical cumulus model of the Experimental Meteorology Labora- tory (EML) was used to predict the behavior of cloud 17, and its predicted behavior was compared with that observed. Measured cloud base and tower radius and the most representative sounding nearest the cloud in space and time are input information. Maximum cloud top, rise rate, liquid water (both cloud water and precipitation water), radar echo intensity, and an estimate of precipitation fallout constitute some of the model output. The version of the model used in this study is called EML 68Pg. In this model, Berry's (1968) autoconvers ion equation is used, 60% of the liquid water present in the cloud at -k C is frozen, the collection efficiency of ice for ice is 100%, the ice terminal velocity is 0.70 that of water drops having equal mass to be consistent with measurements made by Braham (1964) in convective clouds similar to those studied in Florida, and the Marshal 1 -Palmer parameter nQ is changed from 10 m in the liquid 8 i water portion of the cloud to 10 m in the ice region, with a linear transition in the "slush" region (region between -k°C and -8°C) . A hier- archy of EML models with precipitation growth and different seeding sub- routines has been discussed by Simpson and Wiggert (1969). The current model results in the most realistic comparisons of predicted cloud para- meters with those observed. Berry's (1968) autoconvers ion equation generally gives slightly better results than the autoconvers ion equation suggested by Kessler (1965), and it permits the introduction of the droplet number and relative spectral dispersion at cloud base. In this study the cloud 3 base particle concentration was 500 per cm , which is the nuclei count measured by the Naval Research Laboratory (NRL) cloud physics aircraft (Ruskin, un- published manuscript, 1969) at cloud base on May 30, 1968. The relative spectral dispersion was assumed to be 0.1^6, an average figure for conti- nental clouds. Input for the model calculations for cloud 17 was obtained by measurement. The input sounding was provided by Miami 1800Z radiosonde. Although there were three dropsondes from 300 mb as near cloud 17 in space and time as the input sounding, these were not used because: (1) all drop- sondes passed through a cloud layer between 680 and 720 mb, a layer not present near cloud 17; (2) aircraft measurements of temperature and humidity near cloud 17 compared very well with the Miami 1800Z radiosonde, as shown in figure 6. In most instances the temperatures from the different aircraft are within 1°C of the radiosonde temperatures. The cloud base 15 rvi O rvi i £\ ... — * z o n ^ ^ 0 5^ o W OTN |V- o > X 8 > CVJO^ Q, £ < GO ^ cnooQ x 4 • O ^ °

r* h L J I /« /« / /" ~. < °^ 5 0°, \ 0 % / • — A c> % 7 / / • 1 o o. ! O % .a t i • \ o O \ \ \ 1 / ° \ o v \ o V \ CVJ i nf Y \ 0 o ro i % \ e/ Y • / • / / — 0 c 1 \ \/ \ O i "1 o / \ * / / / \/ • 0 t O if) / ° / / • 0 O CO i 0 ^> O \c 0/ \^ i 1 \ 1 1 1 1 1 1 X i 1 1 0 O C 0 •+- S O in o ro U in • - 0) < ^- 0) 0 o • 10 (\J E ~o 03 3 1- o CD — •- U 0 CL *— O 0) 03 4-1 4-> C 03 (D E c — O i- 0) o X> D. o p lot te the ex o o o 1 0 " o 00 *-> 1 LU (T\ 0) • — i/i o o b o u o CM I < en >- c 03 — Q_ 2: >- s o o UJ i- M O 4-> O <4- i OO 03 . !_ O 1_ 1_ o — 0 U- 03 O CU 0) i iosond r thre r i son . o T3 O 03 o 03 M- Q. IT) 1 i ami r al ues or com 0 s: > m- o i vO L. 0 D O cn h- i_i_ S10 0 o o 00 ro O CD ro O ro O C\J ro O O rO heights were measured by the NRL S2D and all tower radii were measured by photogrammet ry . The results of the model calculation for cloud 17 are shown in figure 7- In comparing the heights in figure 2 with those in figure 7, one should note that the latter gives the height of the tower center above cloud base. To find absolute height of cloud top, cloud radius and base height must be added. The model overpredicted the maximum top of seeded tower A (corresponding to tower Ao in the photographs) by about 1 km, while its prediction for tower B was very close to that observed. Both towers had seedabi 1 i t ies of 1.5 km, suggesting only a weak cloud response to seeding. There is good correspondence between the predicted and observed top of tower B, only if tower B was glaciated between -h C and -8 C. This is independent verification that tower B must have been seeded by the silver iodide and ice crystals from decaying tower A. Comparisons of predicted and observed tower rise rates were made whenever possible. The observed rise rate of tower A between 7 and 8 km above cloud base was 6 m/sec, while model predictions are an average of 9 m/sec in this height interval. Model overprediction of rise rate is consistent with its overprediction of maximum top. Observed rise rate of tower B in the 6.1 to 8.9 km interval above cloud base was approxi- mately 15 m/sec compared to a modelled rise rate of 17 m/sec in the same interval. The observed rise rate of tower B from 6.1 km to its maximum height is 10 m/sec (fig. 2) but the slope of the upper portion of the rise 1 Seedabi lity is the predicted difference between the seeded and unseeded maximum top height of the same cloud. 17 1 — O Z •- E < (DO> U O _l O O O CD < Ul UJ O O o 00 o CO o o C\J 1— I i i < l l 1 T 1 1 1 csj 4-1 Q . ru^ ED- l- _ _ COCO ' / ^y' ~"\ \ - cvj >- g • — i/i v. v» C E E 2< / /■•■•■" 1 > ro fO O 1— 1) v£) i- — 2 4-J — tP / V 4-1 L. 03 • T3 l 3 £C t^ to i « 2 >- <3J O t- 3 / \ ui O ■ — / lL 1 1 (D 4-i i/i C O h3gL. 1 ./ / 1 / , i . i . i . o 2 xi o) X) O U O X 4J z o o UJ Q 1- ■ / f "■■■■! \ i 7i #i-ii i i i i \ o .« 1968. Dud ba radar ties o the b t^ I /' y i y I i I • I • / / ' - — 1- Ul o o xi O -C 2t o o S 7 >- X O i- Ul O O CO CC 30 m A 775 m 1100 nn ro 4J — Q. O _l o O Q < O _l u. V 0T or CM X XI 4-J CNJ - CD ul X A - CSI l_ 0) QJ r^ cl ui c j- •z. CC CD " " O ^ i — • Ul OJ < uj L_ K O- (C m Old) 3 1) *J 1 m f- or < Q 3 Q H XI — X OX OJ — —— • -^-* — • — ^~^ — ^^ 3 l+- 4-J Ul 4-J E S LU Q LU < \ a. CD CO u Q 3 to -* o < O _J CD O Q o o E ^j- uj E S|c/ O — 13 5 --■' " ^Ss. — X QJ X) CD — O 4J 1_ — XI 4- 2 CL OJ X LU CO m UJ 3 O <-> H— i i i -» i— i --I- i i i N -3 o ° O E X) 2 2: CD O O 0Q l. 0 E - !- r^- CO -i i i i > i • i • i • f0 4-J OJ XI Cl O OJ C 4-J o <£> UJ C E H- X OJ m cn o r# H3 O 4-14-12 Z) 2 O C o , < • OJ 0 c _l o O ul O U O o >- v-""'"' ^^^^^^^v lO Ul 4-J QJ C — I- 3 •— L. 4-J 0) ul ■ — ul 0) 13 < 5 CM 2 4-J r0 4J 4-i O X > - ro — a UJ ~ 1- z UJ 4-j cn xi 2 cl ._ _ Oj ._ i- OJ CD XI — u O X X) X> ro QJ E O Q O M_ 0 ro 4-j i_ Ul UJ 111 /-» 1 CL E O Cl CO UJ ' -*f 1 r | fr 1 | 1 1 1 | — ^T— 1/1 O Ul 4-J o z uj o >. 4-1 4-1 QJ .— XI _ O CO °& — X ul C R 1 m or E 3 4-j 4-j qj 3 m or 1 UJ * Ul L. Ul O 1 K'" QJ QJ O ro X ^-, 1 < 1- > 4-1 x Ul 1 ^""/^ ^N. + * c i — O X) XI — 0 a CD U 0) 3 CD O E Ul o o UJ Ul UJ o Ki X3 X) O C CNJ O O X) — ro 2: 1— ro O CL V m CO Ul Z UJ N r> co fsl . a 1 i r-^ or 1 i ! o ' S ' \ - t- o \ - ■ 1- \ D ' 1 1 1 1 1 \ o Cn o CO o o I UJ — 13 II- < CO O > 18 O J03Q CD < CO Id rate curve is not reliable. The top of tower B was not visible on the air- craft nose cameras for several minutes while the aircraft penetrated a deck of cirrus. The time tower B reached its maximum height of 12 km corresponds to the time the aircraft topped it at that level; it is not necessarily the time tower B first attained this height. Because of this uncertainty, no comparisons were made with model predictions. Few comparisons were possible between observed and model predicted cloud temperatures. The first pass of the DC-6 through the rising bubble of tower A2 , a tower not studied by the model, showed a temperature rise of 0.9 C. Tower A? had a radius of 620 m, slightly less than the 775 m radius of modelled tower A?. The modelled before seeding temperature ex- cess of the cloud over its environment at the level of the DC-6 is 0.6°C, slightly less than that observed in the smaller tower. Model temperature rises (over ambient) for tower B at the level of the DC-6 range between 2.2 and 3-5 C depending on the extent of glaciation. Temperature values obtained by the DC-6 at 1 9 1 8Z , just below the rising bubble, show a temper- ature rise of 2.5°C, which agrees fairly well with model pred i ct ions, s i nee the extent of glaciation was probably bracketed by the modelled extremes (no glaciation until -kO C and glaciation between -k C and -8 C) . Comparisons were made between the 20,000 ft echo intensities of towers An and B, as observed by the UM/10-cm radar and echo intensities predicted by the model. The 20,000 ft radar scan of cloud 17 at 18U5Z, the time at which the bubble portions of towers A~ and At were near the center of the radar beam, showed a core 1 n mi wide and 2.5 n mi long having a boundary value of 50 db (fig. 8). Modelled echo intensity for the unseeded tower when passing through 20,000 ft is k2 db. A similar 19 OBSERVED ECHO INTENSITY * CLOUD 17- — MAY 30, 1968 I845Z 10 N.MI. t N I9I3Z * CENTER OF BEAM AT 20,000 FT. Figure 8. Observed echo intensity of cloud 17, May 30, 1968 Center of 10-cm radar beam at 20,000 ft. comparison for tower B at 1913Z again shows an observed core with a 50 db boundary compared to a modelled value of 4-5 db. One reason for the model's underestimate of echo intensity might be accretion and coalescence of hydro- meteors in the depth of the cloud illuminated by the radar beam. The collection of cloud hydrometeors would lead to larger particles and, because of the sixth power dependence on droplet diameter, a larger ob- served reflectivity than was modelled. The numerical model provides an estimate of the precipitation fall- out from the rising cloud tower, although it makes no provision for collection of other hydrometeors as the fallout passes through the cloud body below. The model prediction of precipitation fallout from seeded tower 20 A^ is 5.*+ acre-feet essentially unchanged from the fallout from the same tower if unseeded (table 2). Model results for seeded tower B indicate a precipitation fallout of 13.0 acre-feet of water, representing a slight decrease in precipitation over that from the same tower, if unseeded. However, if seeding was in some way responsible for the behavior of tower B, then all precipitation fallout from tower B can be ascribed to seeding. A clue to the decreased precipitation fallout predicted for the seeded towers despite their greater predicted growth relative to the same towers if unseeded is found in column 2 of table 2. Total precipitation production, fallout plus the precipitation water remaining in the tower when it reaches its maximum height, is tabulated here. Total precipitation production is greatest for the seeded towers even though the precipitation fallout for the seeded and unseeded towers is little different. Model predictions indicate that the slightly larger seeded towers are producing more precipitation water but that much of it is suspended in the upper portions of the towers. In the study of the May 16 clouds Simpson and Woodley (1969) found that the much larger seeded clouds were predicted to have a larger precipi- tation fallout than that from the controls. In light of the current study, the model suggests that seeding must produce a significantly larger tower for precipitation increases. The observed precipitation fallout for cloud 17, derived from UM/10- cm radar measurements, was compared to that predicted for towers An and At. This should be a valid comparison because towers A2 and A, of cloud 21 1/1 c o *-> 11 CO 3 vD u CT\ 1 — i — 4- — -Q IT) — 0) u — Q) 0j L. 1 L. "13 c QJ UJ ~ — 1_ l/l (D ro O O cc o: < -); N T3 ,. — s X) 3 4-1 O cu 1 u N (_) 1 F l_ 0) + 03 0) L- ^ — ^ 4-J *-> u N 0 O 0) (— 4-1 0) — l_ 1- m u £L IL < CM LT\ LA o -cl- o cn J; LA O LA LU Q LU Q LU CM rA LA CO rA cn CM o l— O 3 lu ac < cn c • XI c a> •- a) E t/i rsi to < O l. LU + J-J 3 C u_ O OA — ID I- < w O CM O oa CO a LU Q LU Q LU LU LO O 3 lu cc vO CL.1 CU CO O a L. E cr> 0) cn 0 ft) 2 m vj CM • X3 1 — CU E 11 3 1/1 j_i 1/1 0 ro 0 14- c 1 O cu s_ XI u QJ ro t/1 ro 1 — CD 22 17 were probably contributing the major portion of the observed precipita- tion during the period of comparison. The following assumptions are integral to the comparison: (1) all modelled fallout water eventually reaches the level of the radar scan, (2) the predicted precipitation fall- out from A2 equals the predicted unseeded fallout from A? (this assumption overestimates the precipitation from tower A2 because A was smaller than Ao) , (3) the predicted fallout leaves the towers in the 10-min period after they reach their maximum height, and (k) 5 min elapse before the precipi- tation reaches the level of the radar scan (3,500 ft for cloud 17). With these assumptions the predicted precipitation from towers Ao and Ao in the 20 min following seeding is about 11 acre-feet compared to the 155 acre-feet that was observed by radar in this period. If model predictions are correct, the discrepancy suggests that accretion and coalescence of other hydro- meteors by the precipitation from towers An and At augmented the precipita- tion mass by a factor of 14 in transit through the cloud. A similar com- parison was not possible for tower B because there were other towers con- tributing to the rainfall from cloud 17, making an objective radar determina- tion of the precipitation from tower B impossible. Model predictions of droplet size in the rising tower and measurements of droplet size at cloud base were used to test whether accretion and coalescence could have accounted for the augmentation of tower fallout indicated for cloud 17. The predicted average volume median diameter in the 1 km height interval where the predicted fallout is greatest was 2 compared to the measured volume median diameter at cloud base. The ratio 2 Droplet measurements made by a continuous hydrometeor sampler flown at cloud base on the NRL S2D aircraft. 23 of base measurements to in-cloud pred ict ions ( ZjlLS— 221 j w^s 2.39, indicating \ 1 . Ik mm/ that the water mass was increased by a factor of \k (mass a function of the diameter cubed) between the region of maximum fallout and cloud base, in perfect agreement with the earlier analysis. The perfect agreement of the two analysis schemes is merely fortuitous; exact agreement is not important. The important point is that both methods of analysis indicate that collection of cloud hydrometeors by fallout from a rising tower can easily increase the precipitation mass at cloud base by an order of magnitude. The foregoing demonstrates that collection of other hydrometeors by the precipitation from the rising towers must be invoked as the major mechanism for augmenting the precipitation mass in a cloud. This finding provides an insight into one of the mechanisms (besides repeated tower generation) that produced greatly increased precipitation from the dynamically invigorated, deeper seeded clouds during May 1968. A portion of the increased seeded precipitation was the result of droplet collection by the precipita- tion mass from the initially seeded towers through a greater cloud depth than would have been available in the same clouds had they not been seeded. This accounts for the positive correlation between seeded cloud growth and precipitation production found by Woodley (1969) and suggests further that clouds with large predicted seedabi 1 i t ies are most suitable for seeded precipitation increases. Precipitation decreases might be expected from seeded clouds with small seedab i 1 i t ies because of decreased fallout and the insignificant increase in collection depth of the seeded cloud. It is an interesting exercise to assume that the vertical liquid ater profiles for ascending tower A? represent the water profiles through 2k w the entire tower depth at any one instant . This assumption should max- imize total tower water content. When this is done the integrated total water for seeded tower A at its maximum height is 31.0 acre-feet. Making the assumption that tower A? contained an integrated total water equal to that of unseeded tower A- , we find that 57.0 acre-feet, less than half that observed, could have been produced in the 20 min following seeding if both towers were entirely precipitated to the ground. This suggests that con- densation processes were active in these towers during this period to replenish the cloud water continually depleted by precipitation formation and collection, thereby accounting for the increased water production over that contained in the tower at any one instant. 7. ENVIRONMENTAL CONDITIONS AND SEEDED CLOUD GROWTH The major difference between seeded clouds on May 16 and May 30 was their predicted seedab i 1 i t ies . The larger seedabi 1 i t ies on May 16 suggest that seeding had the greatest effect on this day. The Miami 1800Z soundings on May 16 and 30 were compared in an attempt to specify the environmental conditions that favored the different seedab i 1 i t i es . The May 30 sounding was more moist between the surface and 700 mb and drier above than was the sounding on May 16. More important, the sounding on May 30 was as much as 2 colder and much less stable between 400 and 500 mb than that on May 16. Above *+00 mb the May 16 sounding was the less stable of the two. With, the greater moisture and lesser stability (to A-OO mb) the clouds on 3 One should remember that the plots in figure 7 represent the character- istics of the tower as it ascended through successive height intervals. The plots are not cloud profiles unless the cloud is steady state. 25 :Aay 30 would be expected to grow higher naturally than clouds of comparable size on May 16. Further, most natural clouds on May 16, except those with rather large radii ( > 1 2 50 m) , would be stopped by the stable region between 400 and 500 mb. However, high cloud growth might be expected on May 16 if by massive seeding a cloud could be induced to penetrate the stable region between 400 and 500 mb . Similar characteristics of good growth (large seedability) soundings were found by Simpson et al . (1965) and Simpson et al. (1966). 8. SUMMARY AND CONCLUSIONS The conjunctive use of photogrammet ry , aircraft penetration, cali- brated radar, and a numerical model has provided a rather complete docu- mentation of the behavior of seeded cloud 17. The collapse, regeneration, and explosive growth of this cloud is best understood using the numerical model. The initially seeded tower had a small seedability; it was near its maximum predicted height and unloading much of its water at seeding. This probably induced a downdraft that effectively destroyed the seeded tower. There were no new secondary fresh towers immediately available that could have been seeded at the time of the initial seeding. The regenerative phase of cloud 17 is not well understood. After the decay of the primary seeded tower, several growing towers, including especially prominent tower B, enveloped the remains of the decaying tower. Subsequently, tower B grew to 12 km. Model predictions indicate that tower B could not have behaved as it did unless it was seeded indirectly by ice crystals and nuclei from the decaying seeded tower. It is not known 26 whether tower B with its larger radius relative to those of towers A| , A2»and A3 was in some way induced by the seeding. If so, seeding had a greater effect on cloud 17 than is suggested in this paper. Model estimates of seeded precipitation fallout indicate negligible precipitation changes relative to precipitation from the unseeded towers. Model estimate of fallout from two rising towers was a factor of ]k under- estimate of the total, radar observed, cloud rainout. Accretion and coalescence of other hydrometeors must be invoked as the major mechanisms for augmenting the precipitation mass. The explosive growth phase of tower B of cloud 17 was not unlike those on May 16, 1968, studied in detail by Simpson and Woodley (1969), with the major exception that the model predicts that cloud 17 would have grown all but 1.5 km of its maximum height naturally. An examination of the cloud proximity soundings on May 16 and May 30 helps explain why May 16 was the more favored of the 2 days for seeded cloud growth. An interesting feature of the study was the merging of cloud 17 with its flanking neighbor and the tremendous increase in precipitation after consolidation. The behavior of the merged clouds has important implications for attempts to modify meso-scale cumulus developments planned for Apri 1 and May 1970. 9. ACKNOWLEDGMENTS We are greatly indebted to Dr. Joanne Simpson, Director of the Experimental Meteorology Laboratory, and to Mr. Victor Wiggert for help- ful discussions throughout all phases of this research. We also appreciate the efforts of Mr. Jose Fernandez-Partagas in delineating the synoptic 27 weather situation on May 30, 1968. Other groups and individuals deserv- ing special mention include: University of Miami Radar Laboratory for the radar observations; Southern Region, U. S. Weather Bureau; the Director and Staff of the National Hurricane Center, Miami, Florida for making the extra radiosonde observation at 1800Z that was an integral part of the cloud modelling; Mr. Robert L. Daniels of RFF and his staff for their valuable roles in instrument performance, and Mr. Merle Ahrens of RFF for the computer reduction and plotting of the DC-6 records. 10. REFERENCES Berry, E. X. (1968), Modification of the warm rain process, Proc. First Natl. Conf. Weather Modification, Albany, N.Y., April 28-May 1, 1968, 81-85. Braham, R.R. (1964), What is the role of ice in summer rainshowers? J.Atmos Sci. 21 , 640-645. Fraser, A. B. (1968), Stereoscopic cloud photography, Weather 23., No. 12, 505-514. Herrera-Cant i lo, L. M. (1969), Aerial Cloud Photogrammetry Based on Doppler Navigation, Report on work performed under Contract No. 22-2-68(N) between ESSA and the Univ. of Miami. Kessler, E. (1965), Microphys ical parameters in relation to tropical clouds and precipitation distribution and their modification, Geofisica Intern. 5, No. 3, 79-86. Senn, H. V. and G. F. Andrews (1968), A new low-cost multi-level iso-echo contour for weather-radar use, J. Geophys. Res. _73.> 1201-1207. Senn, H. V. and C. L. Courtright (I968), Radar hurricane research, Final report by Institute of Marine Science, Univ. of Miami, Radar Meteorology Section to U. S. Weather Bureau, Contract No. E22- 62-68(N) , 31 pp. Simpson, J., Simpson, R. H., Andrews, D. A. and Eaton, M. A. (1965), Experimental cumulus dynamics. Reviews of Geophysics, 3, No. 3, 387-431. 28 Simpson, J., Simpson, R. H., Stinson J. R. and Kidd J. W., (1966), Stormfury cumulus experiment: Preliminary results 1965, J- Appl. Meteor., 5_ No. k, 521-525. Simpson, J. and V. Wiggert (1969); Models of precipitating cumulus towers, Monthly Weather Rev. 97 No. 7, ^71-489. Simpson, J. and W. L. Woodley (1969) Intensive study of three seeded clouds on May 16, 1 968 , ESSA Tech. Memo. ERLTM-APCL 8. (unpublished rept.) Woodley, W. L. (1969), Precipitation results from a pyrotechnic cumulus seeding experiment. ESSA Tech. Memo ERLTM-AOML 2 (unpublished rept.) Woodley, W. L. and A. Herndon (1969), A rain gage evaluation of the Miami reflectivity-rainfall rate relation. ESSA Tech Memo ERLTM-AOML 3 (unpublished rept.). 29 Reprinted from Limnology and Oceanography 15, No. ] SOME MEASUREMENTS OF CURRENT BY SHALLOW DROGUES IN THE FLORIDA CURRENT Frank Chew and George A. Berberian Physical Oceanography Laboratory, Atlantic Oceanographic Laboratories, Environmental Science Services Administration, Miami, Florida 33130 ABSTRACT Several shallow parachute drogues were cast adrift in the region of the speed axis of the Florida Current and tracked for 27 hr by a Decca Hi-Fix navigation system in a test run to explore the advantages of combining Lagrangian- and Eulerian-type data. Their initial separations were of the order of 50-100 m, 200-500 m, and 2—4 km, but all turned cyclonically and then anticyclonically to trace out a meander with amplitude of some 3 km and a wavelength of some 150 km. Bathythermograph casts along the path revealed a thermal field marked by a cool column at the cyclonic bend. In the absence of friction and downstream acceleration, the geostrophic departure is computed at -27 cm/sec at the cyclonic and 16 cm/sec at the anticyclonic turn. The implied difference in the cross-stream slope of the sea surface is consistent with the presence of the cool column. For stationary, homogeneous conditions, the turbulence level is estimated to be 1%, with a corresponding coefficient of lateral kinematic eddy viscosity of 8.5 X 101 cmVsec. The drogue data were combined with Richardson dropsonde data collected by Nova University personnel a day before, for a synoptic view. The presence of the cool column, detected along the drogue path, may then be interpreted as a consequence of upstream horizontal divergence, detected by the dropsondes. The magnitude of the horizontal diver- gence is of the order of 10~D/sec. AH these features are consistent with a proposed meander- ing model based on the theorem of conservation of potential vorticity. Some alternative interpretations are reviewed. 59 88-99 INTRODUCTION Most applications of the theorem of con- servation of potential vorticity have been to processes where the latitudinal variation of the Coriolis parameter / is an important factor. This /3-effect plays an essential role, for example, in theories of the Gulf Stream as an inertial boundary layer, as well as in the theory of Gulf Stream meandering as proposed by Warren ( 1963 ) . In these processes, the expected magnitude of hori- zontal divergence is, at most, of the order of pv/f, or 5 x 10"7/sec for /? = 2 x 10 13 /cm, sec / = 10"4/sec, and a meridional ve- locity component v of 250 cm/sec. Where upwelling is induced by local winds, the order of magnitude of the horizontal diver- gence is even smaller at 5 x 10 8/sec, since v is then only some 25 cm/sec (Yoshida and Mao 1957). Recent direct measurement by Schmitz and Richardson (1966) sug- gests that the magnitude of horizontal di- vergence in the Florida Current is of yet another order. Figure 1 shows the cross- stream profiles of the mean northward ( v ) and eastward (u) components of the sur- face current at two sections off Miami. The northern profile, based on 12 transects, is 25 km downstream of the southern profile, based on 11 transects. In the open stream, the profiles of u are relatively flat between 30 and 55 km east of Virginia Key. In Cartesian coordinates with the x, y axes pointing respectively to the east and north, the magnitude of horizontal divergence in the open stream in this section of the cur- rent is thus given approximately by dv/dy = 15 cm sec-1 25 km"1 or 6 x 10"6/sec. This implies that the /^-effect is secondary, and consequently, in the conservation theorem we can take / as constant. This version of the theorem, first suggested by Stommel (1953) to explain the wide anticyclonic flank in the current, is the basis of the suggestion by Chew (1967) that horizon- tal divergence is a relevant, measurable parameter in the dynamics of the Florida Current. As potential vorticity is conserved MEASUREMENTS OF CURRENT IN THE FLORIDA CURRENT 89 only for a parcel, Chew considered the feasibility of determining horizontal diver- gence directly by following a water par- cel tagged by parachute drogues. If the drogues are released in a region where the turbulence level is low and the kinematic field is linear, both the horizontal diver- gence and the vertical component of rela- tive vorticity can be determined, and hence, from the same set of measurements, all variables in the conservation theorem. If the conservation theorem holds also for the individual parcels forming the speed axis of the current, then a meandering mechanism is implicit in the theorem. In the speed axis, the relative vorticity is re- duced to KV, where K is the horizontal curvature of the streamline and V the hori- zontal speed of the parcel. For these par- cels the theorem may be written ( KV + f0 ) x A — constant, where f0 is the mean value of / in the region, and A is the variable horizontal area of the parcel. If the parcel enters a region of convergence, the area A will decrease while KV increases. It follows that when a parcel with constant speed passes through alternate regions of con- vergence and divergence, it will tend to turn alternatively toward first the cyclonic and then the anticyclonic flank. Although the advantages of data sampled from a combined viewpoint of Lagrangian, Eulerian-time, and Eulerian-space are well known, most studies of the ocean have tended to emphasize the collection from only one point of view. The oceanographic group at Nova University has been accumu- lating direct measurements of Eulerian type data on the Florida Current; when the opportunity to work with them material- ized, we decided to add some Lagrangian- type data to see what the combined data might reveal in light of the new meander- ing model. This report represents our first attempt at this approach. We are indebted to Dr. W. S. Richard- son of Nova University for his dropsonde data and for the use of his computer pro- gram and facilities in reducing position fixes, to Dr. C. Rooth for his invaluable comments, and to Comdr. C. K. Townsend KILOMETERS EAST OF VIRGINIA KEY, MIAMI, FLA. Fig. 1. A cross-stream plot of the horizontal components of the mean surface velocity in the Florida Current at two sections off Miami. The northern section, denoted by N, is 25 km down- stream of the other, denoted by S. Mean north- ward and eastward components are labeled by v and u, respectively. Original data from Schmitz and Richardson (1966). and his officers and crew for unstinted help aboard the USC&GSS Peirce. THE MEASUREMENT The drogue system was of conventional design, each consisting of a small surface float suspending an 8.53-m-diam parachute lowered to a nominal depth of 47 m below the sea surface. Each float was numbered and identified with a different arrange- ment of lights. The drogues were set adrift from an area upstream of a section ( marked section 1 in Fig. 2) of the current across which, on the day before, both Nova Uni- versity and ESSA personnel had made cur- rent measurements. The initial, relative, horizontal positions of the several drogues are given in Fig. 3 for the time of launch- ing as listed in Table 1. During daylight all drogues were tracked in turn by placing the ship adjacent to them and determining the position of the ship by a Decca Hi-Fix system. During darkness drogues 7 and 8 were launched close to drogue 2 and the ship drifted with this trio; in this interlude the position of the ship was fixed every 15 min while bearings and distances of the three drogues relative to the ship were determined by visual fixes. During the 90 FRANK CHEW AND GEORGE A. BERRERIAN Fig. 2. Drogue track, general hydrography of the region, and mensuration triangle. Depth in fathoms. tracking period of 27.5 hr, 37 temperature soundings by the same bathythermograph (BT) were made at irregular intervals, depending generally on when the ship reached a drogue for a position fix. For the 7-hr span when the ship was drifting with drogues 2, 7, and 8, however, BT casts were made half-hourly. The procedure used for reducing Hi-Fix readings to x, y distances is that given by Schmitz and Richardson ( 1966 ) whose error formulas also give the error estimates in Table 2 for the listed uncertainty (AR) in Hi-Fix readings. Because the baseline R3 (Fig. 2) was short relative to the final Table 1. Hours when drogues mere set adrift and their subsequent average speed Drogue Hour first set adrift (GMT) Avg speed throughout expt (cm /sec) 15 Jun 1967 1 1641 154 2 1654 152 3 1705 151 4 1715 155 5 1718 156 6 1721 16 Jun 1967 153 7 0331 149 8 0335 146 Fig. 3. Initial relative position of drogues. length of the track, these errors amounted to 170 m in the last 3 hr. The distance between ship and drogue also introduces an error which we estimate to be of the order of the length of the ship, or ±50 m. In view of the uncertainty in geographical location for the last 3 hr of tracking, we have omitted from the following considera- tion the east-west positions of all drogues for this interval. However, relative posi- tions, especially when the drogues are less than 1 km or so apart, are better deter- mined since the errors involved generally have the same sign. Table 2. Probable errors in Hi-Fix position de- terminations for different portions of the experi- ment (add ±50 m for total error, see text) Portion of track AR (m) Ax (m) Ay (m) First Middle Last ± 2 ± 3 ± 5 ± 15 ± 30 ±170 ± 15 ± 20 ± 55 MEASUREMENTS OF CURRENT IN THE FLORIDA CURRENT 91 600 - 550 - 500 - 450 - 400 - 350 - 300 - 250 - 200 - 150 - 100 50 - 0.6 0.8 39 0 0 4 0 6 0.8 40 0 0.2 0 4 0 6 KILOMETERS EAST OF SLAVE STATION 2 Fic. 4. Cumulative east-west displacements versus time elapsed for drogues 4, 5, and 6. RESULTS For drogues 4, 5, and 6, with Slave Station S2 (Fig. 2) as origin, the east- west cumulative displacements versus time lapsed are plotted in Fig. 4; these displace- ments are also plotted in Fig. 5 for all drogues at a reduced scale for an assumed common starting point. For drogues 1, 2, 7, and 8 the cumulative total displacements versus time lapsed are plotted in Fig. 6; the slope of the line connecting two successive points gives the speed of the drogue over the corresponding interval. Because of un- certainties due to the short baseline, we have drawn a line with a slope correspond- ing to the average speed throughout the tracking period as given in Table 1. Table 1 also lists the average speed for drogues 3 through 6, which are omitted from Fig. 6 to avoid clutter. In Figs. 5 and 6, only the data for drogue 2 are continuous throughout as darkness interrupted the tracking of the others. The temperature data collected along the drogue track are plotted in Fig. 7 where, for clarity, every other BT cast is shown, although all casts were used in the analy- sis. During the tracking period there was considerable atmospheric convective activ- ity; rain squalls and even a waterspout were seen. In the vicinity of the ship, easterly winds remained gentle except when an occasional rain squall approached. On a background of low, medium-period swells, the local sea was 1 m or less. DISCUSSION These data are not sufficiently refined for an evaluation of the applicability of the new meandering model. In particular, the technique of position fix for each drogue was too crude; some transponder system permitting simultaneous location of all drogues seems necessary. However, the three features that emerge from the obser- vation will serve as a basis for a preliminary examination of this and some alternative models. Geostrophic departure The first feature is the sign and magni- tude of the geostrophic departure in the meander shown in Fig. 2 obtained by com- bining the east-west cumulative displace- ments in Fig. 5 with their corresponding northward displacements. On the basis of zero phase speed, the meander had an amplitude of some 3 km, a wavelength of some 150 km, and a radius of curvature of 92 FRANK CHEW AND GEORGE A. BERBERIAN S 750 - 0 10 20 E - W CUMULATIVE DISTANCE IN KILOMETERS Fig. 5. Cumulative east-west displacements versus time for all 8 drogues plotted from a common origin. 120 km at the cyclonic turn and of 200 kin at the anticyclonic turn. In terms of natural coordinates the geo- strophic departure for a parcel in friction- less, horizontal motion is dependent on both the tangential and transverse accelera- tions. Although our data do not permit a reliable evaluation of the tangential accel- eration, Fig. 6 shows it to be relatively small. When the tangential acceleration is neglected the geostrophic departure ( V - V0) reduces to V-Vg = -KV*/f, where V = horizontal speed, Vg — geo- strophic speed, K = horizontal curvature of the path, and / = 7 X 10"5/sec, the Coriolis parameter for this latitude. For drogue 2 at the cyclonic and anticyclonic bends, Table 3 tabulates the geostrophic depar- ture, the Rossby number defined as the ratio of the centripetal to the Coriolis accel- erations, and the normal pressure gradient force as a sum of the two accelerations. In his discussion of geostrophy, Broida ( 1966 ) stressed the need for simultaneous data coverage to minimize errors. Our re- sults in Table 3 show that neglect of path curvature can lead to equally large errors, as much as 10 to 18% of the observed speed as the values of the Rossby number show. Of the pressure gradients given in the last Table 3. Geostrophic departure, Rossby number, and pressure gradient force for fluid parcel tracked by drogue 2 Location v v-v9 (cm/sec)(cm/sec) KV2/fV KV2 + fV (cm /sec2) Cyclonic Anticyclonic 150 150 -27 16 0.18 0.10 1,239 X 10"5 945 X 10"6 MEASUREMENTS OF CURRENT IN THE FLORIDA CURRENT 93 DROGUE 8 146 CM/S FOR DROGUES #7 AND #8 THE ORDINATE IS ARBITRARY 16 20 24 28 32 i i J I i i i 1 i i i i L_J i i — i — Li — i i i — u_i 250 MINUTES 500 1000 CUMULATIVE TIME 1250 1500 1750 Fig. 6. Cumulative total displacements versus time elapsed for drogues 1, 2, 7, and 8. For drogues 7 and 8 the initial ordinate is arbitrary. column, that for the cyclonic bend is the larger, implying a greater slope in the sea surface. If temperature was the dominant factor in the mass distribution, as is the usual case in the surface layer, then if the water along but immediately to the east of the meander was of uniform temperature, one would expect cooler surface water at the cyclonic bend. This is consistent with the temperature data along the drogue track (Fig. 7), where for depths to 90 m the water temperature was lower at the cyclonic than at the anticy clonic bend. Estimate of turbulent dispersion The second result of our experiment is a lack of any clear evidence for significant horizontal turbulent activity. In the ocean, horizontal dispersion of a cluster of drogues may be caused by deformation or turbulent activity or both. Horizontal deformation is a change in the horizontal shape of a fluid mass by space variations in the ve- locity field. For a given varying velocity field, location of individual drogues in a cluster can be predicted for any instant — at least in principle. On the other hand, in turbulent dispersion there can be no prediction of the location, speed, or direc- tion of the individual fluid masses and hence of the individual drogues. Throughout the tracking period the rela- tive positions of the individual drogues in the cluster remained substantially as in 94 FRANK CHEW AND GEORGE A. BERBERIAN LAI 27°00' N 10 20 30 40 50 60 70 I 1 r~ 90 100 110 120 130 140 ISO — 1 1 1 1 1 1 1 — 160 170 ~1 -i 1 r TEMPERA1URES IN DFGREFS CELSIUS I I I I 24 26 2B 30 32 34 36 38 40 42 44 46 48 50 52 54 55 57 58 59 BATHYTHERMOGRAPH CAST NUMBER Fig. 7. Temperature section along drogue track. Fig. 3; in particular, there was no exchange in east-west positions, except for drogue 1 relative to the tight cluster of drogues 4, 5, and 6. For every drogue, the drift was quite regular and its position was predict- able from the last observed velocity, a fact used routinely when the ship was run- ning between drogues. This situation im- plies that the root-mean-square (r.m.s.) value of the turbulent intensity, is at most Vw of the magnitude of the mean current, V0- But a realistic value is much smaller. Let Arms, denote the r.m.s. displacement of a drogue from its initial position as a result of random motion in a horizontally iso- trophic turbulent regime. When displace- ments in excess of this are excluded, all possible positions of the drogue at a sub- sequent instant are contained within a circle of radius Ar.ms. for that instant. A drogue pair may exchange positions when their respective circles overlap to the extent that the radii are equal to the initial sepa- ration. Provided that our experimental in- terval was long enough for a complete realization of the random process, the ob- servation that there was no exchange in the east-west positions of any drogue pair with initial separation in excess of 1 km allows approximation of the turbulent intensity encountered. For the situation where the Lagrangian correlation coefficient for tur- bulent velocity is unity, or nearly so, Taylor (1921) gives Hence orm s. km2, and t - = 1.1 cm/sec for Ar 1 day. MEASUREMENTS OF CURRENT IN THE FLORIDA CURRENT 95 If the field of turbulence was both sta- tionary and homogeneous, then successive drogue releases over a region can be taken as simultaneous releases at a single point. The lateral dispersion depicted in Fig. 5 then offers another estimate of the turbu- lent intensity. With 8 drogues, taken 2 at a time, we have 28 pairs with final separa- tion that has a range of 0.1 to 2.7 km, a mean of 1.1 km, a mean-square value of 1.61 km2, and a 95% confidence interval given by 0.44 < (cr2/Ar.m.s.2) < 4.1 for a chi- square distribution with 7 df. Thus the true value cr2, of which Arm.s.2 is a sample estimate, may be as large as (4.1) (1.61) or 6.6 km2. Again for t = 1 day, the cor- responding turbulent intensity ur ms. is 1.5 cm/sec, but may be as large as 3.0 cm/sec. In considering errors due to effects of tur- bulent diffusion on current measurements, Okubo (1968) found them to be generally of the order of 1 cm/sec, though in some extreme cases, they may be as large as 10 cm/sec. These independent estimates are quite consistent. Of particular interest is the turbulence level fr.m.s./Vo. This is only of the order of 1% in our case. For the region of the speed axis in the current off Miami, the data reported by Schmitz and Richardson (1966), as well as those by Webster (1961), all imply a turbulence level of 10%. How- ever, this difference may be compatible. First of all, our estimate represents a Lagrangian measure, while the larger esti- mates are Eulerian statistics. Secondly, the larger estimates were based on instruments that respond only to water motion in the top 1-2-m layer of the sea surface, while our estimate is based on the motion of cir- cular parcels 8 m in diameter at a depth of 47 m. Differences in the scales of motion must be expected in these circumstances; for example, the present Lagrangian sta- tistics describe only the interior of the cur- rent, while the Eulerian statistics probably include perturbations of the stream as a whole. The magnitude of the friction force rela- tive to the other terms in the normal equa- tion of horizontal motion can be evaluated if the Reynolds stress is assumed propor- tional to the turbulent intensity. Of the three friction terms in the equation, we shall consider only the term correspond- ing to the cross-stream derivative of the Reynolds stress -puu which we shall take to be zero at the rigid western boundary where all normal components of motion must vanish, and to be numerically equal to the turbulent intensity at distance S0 about midway across the stream. The magnitudes of the two other friction terms will be of no greater order. Then with the magnitude of the centripetal force at K0V02, the ratio of the two forces has the value given by duu/dn KV2 -(iW,7Vo2)(l/K0So) For S0 = 35 km, the value of 1/K0S0 is as large as 6 for the observed meander. Hence the ratio of forces is some 6 X 10-4 for tfr.m.s./V = 1/100. From the values of the Rossby number in Table 3, the ratio of the friction to the Coriolis terms is, in any case, no more than about 10 4. If this ratio holds for all components of friction in the equations of horizontal motion, we can esti- mate the coefficient of lateral kinematic eddy viscosity ( E ) , again for S0 = 35 km, as follows: E = (fV/m/(d-V/dn-) ~ /S02/104 = 8.5 x 104 cm2/sec. This is a probable lower limit. On the other hand, for a turbulent level of 10%, £ would be 8.5 X 106 cm2/sec, a likely up- per limit. The estimate by Stommel ( 1955 ) for the cyclonic flank of the current falls between these limits. In models of the Gulf Stream as inertial boundary layer, lateral friction force is postulated to be of signifi- cance only in the sublayer adjacent to the solid boundary. Moreover, this sublayer is generally identified with the cyclonic flank of the Gulf Stream. In this framework, using Stommel's estimate of E as a refer- ence, we see that only the lower turbulence level of 1% and its corresponding E are consistent with the inertial model. 96 FRANK CHEW AND GEORGE A. BERHERIAN 80"00' 79°30' 1 RICHARDSON'S DROPSONDE 14 JUNE 1967 z 5 180 u S 160 < DC => 140 O 120 z o | 80 O 60 $ 40 O 20 z 20 CM/S DROGUE 2 60 70 KILOMETERS 800 o. z 700 a 600 O z o 400 5 O < 200 5 100 O z 120 20 DROGUE #2 KILOMETERS 50 60 1 70 80 90 130 140 I 100 200 E 300 LU 400 . 500 600 700 . 800 . \" 6.6 t? H 14 JUNE 1967 900 MEASUREMENTS OF CURRENT IN THE FLORIDA CURRENT 97 Horizontal divergence The third feature emerges when the drogue data are combined with the current measurement at section 1 to form a synop- tic view and simultaneity in observation is assumed (Table 4, Figs. 8 and 9). The relevant kinematic feature in the section is the pattern of east-west transport. In gen- eral, the data show the cross-stream trans- port was westward at stations west of, and eastward at stations east of, the location where the paths of the drogues intersected section 1. In particular, in the vicinity of the intersection there was definite evidence for diffluence of streamlines above the 150-m depth. As the component owing to change in horizontal speed along the path is negligible (see Fig. 6), diffluence, in this case, is horizontal divergence and is seen to have a magnitude of the order of 26.0 - (-1.1)/15 x 105 sec"1 or 1.8 x 10"5 sec1. This feature is supported by the pres- ence of the cool column observed 20-30 km downstream at the cyclonic bend. The top layers in the region between section 1 and the cool column thus appear to be under- going upwelling. The thermal structure shown in Fig. 7 for this region bears little resemblance to the situation where upwell- ing is induced by local winds. This differ- ence cannot be entirely accounted for at present, but a probable cause is the much greater baroclinity found in the Florida Current where advection from different sources at different levels may be consider- able. Another is the regional difference in such surface effects as heating, cooling, convection, and wind mixing. Some alternative interpretations The outstanding features of the meander are the small radius of curvature, short wavelength, and large magnitude of hori- Table 4. Transport measurements of the Florida Current on 14 June 1967 at section 1. Data source: Nova University Time Depth uT vT Sta.* (EST) (m)t (m2/sec)i: (m2/sec)§ 101 1035 40 1| 18 -3 102 1111 64|| -6 5 103 1313 106|| 7 68 104 1347 169 j| -28 108 105 1413 98 -9 194 105 1415 221 1| -9 201 106 1446 92 -1 186 106 1445 141 _2 245 106 1447 328 1| -1 313 107 1515 423 -20 428 108 1602 96 25 171 108 1604 151 21 248 108 1605 364 -39 574 108 1610 596 1| 1 660 109 1652 409 22 519 109 1653 717|| 57 753 110 1733 55 9 59 110 1734 429 17 471 110 1736 672 1| 86 627 111 1816 92 30 58 111 1817 151 20 125 111 1818 589|| 18 366 112 1904 98 -16 56 112 1906 141 6 83 112 1907 273 4 163 112 1906 423|| 18 213 113 1944 156|| -7 21 * Station locations are indicated in Fig. 8 beginning with 101 on the left. t Depth to which a dropsonde reached. t East— west transport component, positive eastward. § North— south transport component, positive northward. || Dropsonde reached sea bottom. zontal divergence along with the cool col- umn downstream. These features, in addi- tion to the low turbulence level, are all consistent with the new meandering model. Some possible alternatives are the superim- position on a steady current of rotary tides, inertia currents, and internal waves, as well as the possibility that the cool column was the result of nocturnal cooling. The last Fig. 8. Cross-stream profiles of the northward component of the volume transport and sea surface current. Data supplied by W. S. Richardson. Fig. 9. East-west components of current (cm/sec) averaged over the interval from the sea surface to depths indicated by stars. Hours of observation (in local EST) are given along the abscissa. Data supplied by W. S. Richardson. 98 FRANK CHEW AND GEORGE A. BERBERIAN may be disposed of readily, but the remain- ing can only be shown as implausible. The cool water was observed over a 2-hr period on a calm night when long-wave radiation was probably the only significant cooling process. For this period, we com- pute, according to Laevastu ( 1960 ) , a loss of 17 g cal/cm2, for a relative humidity of 50% and a sea surface temperature of 28.4C. Distributed over a 100-m depth of water, this loss would amount to a tempera- ture reduction of 0.002C — clearly too small to be significant. We take the amplitude of the current speed in rotary tides and inertia currents as constant in a cycle; but if their super- positions on a uniform flow are to give a lateral meandering of 2.5 km in 6 hr, the amplitude must be ( tt/2 ) ( 2.5 km/6 hr ) or 17.5 cm/sec. The superpositions will, how- ever, also give rise to speed extrema along the path of a parcel whose speed will change by 35 cm/sec in 12 hr. It is un- likely that such large, systematic change eluded our observation. Furthermore, there is no apparent mechanism whereby rotary tides and inertia currents could account for the presence of the cool column and the pattern of diffluent streamlines. Another alternative is the superposition on a north-flowing, uniform current of an internal wave of tidal period generated by tidal movement past the continental slope. The wave, having a period of 1 day, will have a phase speed of 116 cm/sec if the wavelength is 100 km. In addition, if the wave has an amplitude of 15 m, the cor- responding maximum parcel speed in the upper 100 m layer will be 116 (15/100) or 17.5 cm/sec, which compares favorably with the speed of most of the transverse components plotted in Fig. 9. Moreover, if the wave is moving landward while the observer is moving seaward, Doppler effect may account for the diffluence feature in Fig. 9. The feature was 25 km wide and was observed in 2.25 hr, or an observer speed of 309 cm/sec. If the observation at stations 40 and 65 km correspond to a change of 180° in the phase of the wave, an apparent period of 4.5 hr is required to Fig. 10. Sea surface temperature for 22 June 1967 with drogue track superimposed. The obser- vation was made by R. Stone who covered the region in 1 hr. An airborne Barnes infrared radia- tion thermometer was used on board a Coast Guard plane flying at elevations 90-150 m above the sea surface at a speed of 70 m/sec. account for it. The apparent period result- ing from Doppler shift is 24/ [1 + (309/ 116)] or 6.5 hr, perhaps not too large. There remain two difficulties to this al- ternative. The first is suggested by the observation in Fig. 10 where, in contrast to the adjacent 27C isotherm, the 28C iso- therm had a meander pattern with a wave- length comparable to that of the drogue track. The temperature observation was obtained in 1 hr, so there is no apparent way by which the internal wave, with a period of 24 hr, can account for it. On the other hand, if the phase difference be- tween the drogue track and the 28C iso- therm is taken to indicate wave progression, the temperature pattern suggests a mass field not inconsistent with the interpreta- tion where potential vorticity is conserved. The second difficulty arises from the kine- matics of internal waves. Where they are MEASUREMENTS OF CURRENT IN THE FLORIDA CURRENT 99 predominant, as required in this alterna- tive, one expects little net transport in a column extending from sea surface to sea bottom. For most of the columns sampled, the observation, as can be seen in Table 4, does not support this expectation. CONCLUDING REMARKS The combined drogue and dropsonde data have permitted a discussion of some aspects of an instance of meandering in the Florida Current, in terms relevant to an application of the theorem of conserva- tion of potential vorticity. They are the sizable geostrophic departure, low turbu- lence intensity, and large magnitude of horizontal divergence. For future observa- tion, the relative magnitude of the last two features are particularly important. For ex- ample, for the magnitudes reported here, the turbulent effect on the measurement of the area A in the conservation theorem can be kept below a level of 10% if one begins the measurement with a deployment of drogues inclosing an area of some 50 km2 for observation lasting a day. The advan- tages of the combined data are especially evident in delineating the feature of hori- zontal divergence. REFERENCES Broida, S. 1966. Interpretation of geostrophy in the Straits of Florida. Ph.D. thesis, Univ. Miami, Miami, Fla. 108 p. Chew, F. 1967. On the feasibility of measuring horizontal divergence in inertial ocean cur- rents by a Lagrangian method. Abstr., Trans. Am. Geophys. Union 48: 125. Laevastu, T. 1960. Factors affecting the tem- perature of the surface layer of the sea. Commentat. Phys.-Math. 25: 136. Okubo, A. 1968. A note on the effect of dis- persion on mean current measurements. Ab- str., Trans. Am. Geophys. Union 49: 698. SCHMITZ, W. J., AND W. S. RlCHARDSON. 1966. A preliminary report on operation Strait Jacket. Inst. Mar. Sci. Lab., Univ. Miami, ML 66202. (Mimeographed.) 222 p. Stommel, H. 1953. Example of the possible role of inertia and stratification in the dynam- ics of the Gulf Stream system. J. Marine Res. 12: 184-195. . 1955. Lateral eddy viscosity in the Gulf Stream system. Deep-Sea Res. 3: 90—93. Taylor, G. I. 1921. Diffusion by continuous movements. Proc. London Math. Soc. 20: 196-212. Warren, B. A. 1963. Topographic influence on the path of the Gulf Stream. Tellus 15: 167-183. Webster, F. 1961. The effect of meanders on the kinetic energy balance of the Gulf Stream. Tellus 13: 392-401. Yoshtda, K., and H. L. Mao. 1957. A theory of upwelling of large horizontal extent. J. Marine Res., 16: 40-54. 60 Reprinted from Deep-Sea Research, June, H95_511 Gulf stream meanders between Cape Hatteras and the Grand Banks Donald V. Hansen* (Received 13 November 1969) Abstract — The position of the Gulf Stream between Cape Hatteras and approximately 60°W was delineated at intervals of a few days to a month using the 15°C isotherm at 200 m depth as an indicator for the thermal front associated with the stream. The dominant pattern inferred from the sequence of observations is a quasi-geostrophic wave pattern of 200-400 km wave length moving to the east with phase speeds of 5-10 cm/sec, and amplitudes generally increasing steadily to the east, except for a breakdown in summer when very large amplitude meandering between 69°W and 64°W led to extremely complicated thermal conditions in this region. Evaluation of topographic and Coriolis effect variations along the paths indicates that for plausible current structure the mean path of the stream is consistent with the topographic control hypothesis advanced by Warren (1963). Although the meanders too must be strongly influenced by topographic variations, these variations are in general insufficient to account for the curvature of meanders in the observed paths. Comparison of unstable wave properties inferred from the observations with results from several investigations of dynamic instability as a possible cause of the meanders shows that baroclinic instability theories yield good estimates of wave length of the fastest growing wave component, and a baroclinic theory with some topographic influences yields a good approximation to the phase speed as well. An equivalent spatial growth rate computed from the disturbance group velocity and the temporal growth predicted by all the theories is generally larger than that of the observed meanders. INTRODUCTION East of Cape Hatteras the Gulf Stream develops large amplitude lateral meanders and detached eddies, leading to the ultimate loss of continuity as a coherent flow. Data from Operation Cabot, a multiple-ship study of the stream east of Cape Hatteras conducted for two and one-half weeks in 1950 were interpreted by Fuglister and Worthington (1951) as a wave-like current pattern in the western part of the study area, and as an extreme meander in the process of detaching to form a cyclonic eddy in the eastern part. Following a second such study in 1960, Fuglister (1963) reported shifts in position of parts of the stream at rates of 5 cm/sec or less, the overall impression being one of an almost stationary stream pattern during the entire period of two and one-half months. A deep meander to the south was considered to be indicative of eddy formation, but complete separation was not observed. Attempts to explain these and other less intensive observations of Gulf Stream paths have usually followed one of two distinct lines of reasoning; one hypothesizing disturbance of the basic flow by unstable wavelike pertubations that interact with and extract energy from the basic flow, the other hypothesizing an inertial jet in which ♦Physical Oceanography Laboratory, Atlantic Oceanographic and Meteorological Laboratories, Environmental Science Services Administration, Miami, Florida, U.S.A. 495 496 Donald V. Hansen gradients of depth and Coriolis parameter determine the configuration of a stationary quasi-geostrophic wave which changes but slowly in response to a varying initial condition near Cape Hatteras. Information about the meanders and their evolution in time has been too sparse to discriminate between these interpretations. In 1965, the U.S.C. & G.S.S. Explorer undertook systematic delineation of the thermal front associated with the Gulf Stream to provide a better observational basis for understanding Gulf Stream dynamics. This paper presents some results from the project. METHODS AND PRECISION The equipment and procedure adopted for the project were essentially as described by Fuguster and Voorhis (1965). The 15° isotherm was selected as an index to the center of the main thermal front at 200 m, and therefore as an indicator for the position of the Gulf Stream. After locating the main thermal front by means of bathythermograph observations off Cape Hatteras, the front was tracked to the east using a V-FIN NAVITHERM system supplied by the Braincon Corp., Marion, Massachusetts. This system permitted continuous shipboard monitoring of temperature at a pre- scribed depth, and could be towed at 200 m depth in the stream at a speed of 8 knots.* Under favour- able conditions, the sensors could be maintained within 10 m of the nominal depth and the indicator isotherm could be crossed every few minutes, and was in fact usually crossed no less frequently than every five to ten kilometers. During periods of operational difficulty with the V-FIN, segments of the front, occasionally an entire path, were delineated by means of conventional bathythermo- graph observations. In this mode of operation it was possible to cross the indicator isotherm at approximately 30 km intervals. It generally was not possible to make both types of observations simultaneously. On the return leg of each cruise, bathythermograph observations were made on passages north or south of the stream, or recrossing the path at selected points to obtain further data on the coherence and variability of the front. Delineation of Gulf Stream path lengths limited by endurance of Explorer at monthly intervals was selected as scientifically valuable and within the capability of a single ship. In retrospect, the criterion for tracking the stream appears to have been well chosen. Contact with the indicator isotherm could be maintained over long distances, and as far east as 60°W the isotherm was encountered only in association with the strong temperature gradient typical of the stream, and set and drift computations on Loran A navigation when possible nearly always revealed the expected current. The mean temperature in the center of the strongest temperature gradient at 200 m depth from bathythermograph data obtained on 100 crossings of the stream was 14-7 ± 1-5°C (1 s. d.). For most of the project the observations are judged adequate to define the momentary configuration of thermal front features greater than 50 km downstream extent and 10 km cross-stream extent, or roughly 0-5 and 0-1 stream width respectively. Some exceptions to these statements will be discussed later. THE OBSERVATIONS The stream path observations and the project modifications made in response to them fall naturally into two phases. The observational procedure as initially planned was begun in September 1965 and sustained through twelve consecutive months (Fig. 1). The first nine of these paths exhibit strong similarities; all are characterized by wave-like features with wavelength of 200-400 km and with amplitude increasing to the east. The large amplitude meandering encountered in the eastern part of the region made it impossible to develop paths east of 55°W, but it appears unlikely that longer paths would be of much synoptic signifiance because east of 60CW the front became sufficiently weaker and variable that identification of the Gulf Stream position with a particular isotherm became increasingly tenuous. The path for December shows an extreme example of the conditions encountered. Horizontal gradients were relatively weak *1 knot =■= 1-853 km per hour. Gulf Stream meanders between Cape Hatteras and the Grand Banks 497 * o to /' t — \ 1 1 CO C'-) CN '. cncn^: 1 1 e ,_,-»(/) °o ~) _ X- ''-) ) — >■ — 1 ^. % '"/*' ■ I ! I %\ . ,--r\ ■4>-N c v ■7 'z^^^ L ~" \ .• 1 -''-> ^ ....... \-i\ i-J^-'' ] y> ■ '■: \j >v V /"'/ 1 w r '• c::-'': -J, / SOS 1 J '••■ N. i UJq^'-IJ coOZ \ - / i \ ; ; - y) .'.' (Ya .• ■■■■:■ ' ' :;■■'■■ ' ' \ . / h v: - .. ssgffcs l2__ i_i 5--: '"^Jf - '■. *;'.',*>. ■ 1 ~ S , , ^ _ 00 J_^i-; r— 1 ""^ "" ) \ '.' ~/^ ' ■— r-CN \ > i A ry«d' '' ' 1 ' S '^ joJL XKi i % D ^W-;s U_i * ^A o^^>- & /J ^ '■ U "?- \y ; f |; A >\ fe. -.. "'•-,, ■ -O ■'■i V'-'Si^- i _/\3 <"> J 'l* / '»; -J ; ' i c - r I O U o Oh Uh 498 Donald V. Hansen X Gulf Stream meanders between Cape Hatteras and the Grand Banks 499 in the region between 60°W and 63°W, and the tongue of cold water advanced 35 miles* to the south- east in approximately 50 hours. The relatively simple view of structure of the Gulf Stream implicit in application of this means of determining the stream path becomes inappropriate in the event of such narrow loops in the indicator isotherm. A more plausible interpretation is that a warm eddy was separating on the north side of the stream. The same general kinematic situation of a warm eddy becoming separated by the intrusion of cold water being advected along the edge of the stream was observed on other occasions (cf. March 1966, March 1967), and warm regions suggestive of separated eddies were occasionally found north of the main front. Following discovery of two separated eddies south of the stream in September (Fuglister, 1967), no others were found, but no thorough search was made for them and only recently formed eddies would be detected by bathythermo- graph in any case. In general, data obtained during the return passages supported the primary path delineation very well, showing few features not expected from the outgoing line. That for March 1966 (Fig. 2d) is a somewhat atypical example in that the path was recrossed more times than usual. With the excep- tion of a small region of warm water at 63°W which may have been a detached eddy, or perhaps an elongate and tenuously connected meander missed on the outbound track, strong thermal fronts at 200 m were encountered only in strict association with the outgoing track, and except on obviously oblique crossings the front was sharp (on the order of 5°C temperature change in 20 km or less) and spanned the 15°C isotherm at 200 m depth. Between the cruises of May and, June, 1966, an abrupt change in the nature of the meandering of the stream occurred. A large loop in the thermal front pushed up into very shallow water on Georges Bank (Fig. Id). The 15°C isothermal surface in fact intersected the continental slope. Gulf Stream water has been reported on the continental shelf previously (cf. Hachey, 1939), but I have found no previous documentation of continuity with the Gulf Stream proper. There is of course some question of interpretation in this situation because, although the indicator isotherm generally corre- lates well with the temperature and velocity maximums of the stream at the sea surface (confirmed by computation of set and drift along the return track for June), the volume transport of the stream extends 50-100 km to the warm side of the surface current maximum, which is clearly not consistent with the geometry of such a loop. Evidently in this situation the stream becomes even more baroclinic than usual in that the vertical shear involves directional as well as speed gradients. The rate of this development is remarkable; there was no evidence of it on the return track, made entirely north of the stream, in May. A full month had elapsed betweeh return from the May cruise and departure on the June cruise due to required ship repairs,! and a major marine-meteorological event, passage of hurricane Alma, the eye of which passed northward through this region along 73°W (DeAngelis, 1967), had occurred. It is also of interest but of uncertain significance that the northerly loop in the June pathline almost exactly encompasses the northwestern end of the New England Seamount Arc. In July the front had become even more complicated. The wavelike pattern of earlier months evolved to a folded pattern having considerably greater meridional extent than previously between 65°W and 70°W, Hurricane Celia interrupted operations sufficiently that this path was developed in several short pieces. Several recrossings of the front at short intervals indicated that parts of the front were shifting position rapidly and erratically. In August the short-period variability of the front became so pronounced that contact was lost repeatedly and a large warm lobe (perhaps a detached eddy) between 63 °W and 64°30'W and north of the indicated path was missed entirely on the path delineation. Its presence is inferred from a large body of warm water bounded by strong currents crossed on the return track. It appears that the northerly lobes of warm water were becoming separated from the Sargasso Sea by a complicated ridge of cold water along approximately 38°N. The top of such a ridge should be nearly level in the mean; higher frequency vertical movement of isothermal surfaces as by internal waves then lead to greater translation of isotherms on depth surfaces than is normally expected in the Gulf Stream. The difficulty of maintaining contact with the stream in August appeared to be associated with vertical motion of the thermocline on a time scale of the order of one day. The passage of hurricanes Alma and Celia through the area in June and July may have contributed to the complicated thermal conditions en- countered during the summer, but direct effects of these storms seems an unlikely explanation for * 1 nautical mile = 1-853 km. tThe June path was in fact observed by the U.S.C. & G.S.S. Whiting using BT and assisted by experienced personnel from Explorer. 500 Donald V. Hansen the observed meandering.* In any case, the method employed begins to have questionable value for delineating the stream path through such conditions. Even under favourable conditions, it is clear that monthly sampling alone is insufficient for unambiguous definition of the evolution of even the major meanders. To help resolve the difficulties of delineation and interpretation of the 12-month sequence of paths, it was decided to delineate a shorter section of the front more frequently. A shorter length of path was traced three times at short intervals in September (Fig. 2a) and twice in October, 1966 (Fig. 2b). This more frequent sampling yielded a satisfying degree of persistence and propagation to the east with phase speeds of the order of 5-10 kilometers per day for the major wave-like feature of the path. A warm water mass with anticyclonic circulation crossed while returning north of the stream path in October 1966 appears to be a remnant of the northerly lobes of warm water observed during the summer. Finally, a semi-monthly series of path observations was conducted in March and April, 1967 (Fig. 2c) by Explorer alternating with U.S.C. & G.S.S. Peirce for development of paths, the Peirce using BT only. This series is characterized by small meander amplitudes as far east as 65°W, and well-documented separation of an •anticyclonic eddy north of the stream in March. No evidence of the eddy was found in this region in April but other observations precluded making a thorough search for it. West of 66°W there was remarkably little difference between the two path delineations made in March. Observations made while returning from the second cruise in March 1967 indicated that the wavelike features in the vicinity of 80°W had begun to move rapidly eastward, and the first path delineated in April was so changed and so featureless that no continuity could be established with earlier paths. KINEMATIC SYNTHESIS Although the monthly sampling interval used for development of most of this sequence of paths is inadequate to define the evolution of paths unambiguously, the weight of evidence indicates persistent eastward propagation as the dominant factor in evolution of the major meanders. Wavelike meanders in the western part of the study area moved eastward at a net speed of approximately 7 cm/sec during the two week duration of Operation Cabot, and subsequently, Fuglister and Voorhis (1965) observed eastward movement of meanders at speeds on the order of 5 cm/sec over intervals of a week and a month during their exploratory work with the V-FIN equipment. This characteristic is also sufficiently evident in the paths observed in September and October, 1966, somewhat less so in March, 1967, and in the return trip data from several of the monthly cruises. Of more than 40 potentially informative recrossings of the paths developed during the first nine months of this study, 16 gave a more or less clear indication of eastward propagation of meanders (four instances are shown in Fig. 2d), one indicated west- ward movement, and the others permitted no unambiguous conclusion. Speed of ♦Inclination of the isothermal surfaces across the stream is on the order of one per cent. Theoretical studies by Ichiye (1955) and O'Brien and Reid (1967) suggest that vertical motion associated with cyclonic storms should not exceed 100 m, and internal wave and tide ranges are also expected to be within this limit. Horizontal translations of the path indicator due to these short period vertical disturbances should therefore be of the order of 1 0 km, about the same as the precision with which the front can be defined. It seems clear therefore that the meanders observed during this project are a manifestation of fundamental Gulf Stream dynamics rather than of extraneous influences. Gulf Stream meanders between Cape Hatteras and the Grand Banks 501 movement estimates over time intervals of less than a week vary widely due to the effects of higher frequency vertical movement of the thermal field as well as sampling and position uncertainties. The first nine monthly paths displayed (Fig. 3) chronologically and relative to the rhumb line through 70°W; 37°30'N, 60°W; 40°N illustrate an interpretation of phase propagation consistent with the observations, generally the minimum eastward phase speed consistent with persistence of the major meanders in the paths. The time and distance scales are such that a slope of minus 45° of the diagonal lines corresponds to eastward phase propagation velocity of 10 km/day. The inferred pattern is therefore a system of waves of mean wave length about 320 km; propagating to the east with mean phase speed of approximately 8 cm/sec. More than 4000 bathythermograph soundings from other vessels operating in the area during this period were obtained from the National Oceancfgraphic Data Center and examined for further support of the progressive wave interpretation of the sequence of paths. These data were separated into 10-day periods selected before, during, and after each cruise of Explorer. An immediate con- clusion was that even in this intensively studied part of the ocean, the ambient sampling density alone is inadequate to document the position and evolution of Gulf Stream meanders. The BT data taken concurrently with Explorer cruises however, were consistent with the paths, and those taken between Explorer cruises provided support of varying degree for the 1 1 of 3 1 postulated phase progressions shown as solid lines in Fig. 3. This supporting evidence is distributed through six of the eight transition intervals, and since the weight of evidence suggests that the meanders are relatively persistent, support for progression of even a short interval of phase points implies similar movement of adjacent phases during the interval. It is still possible however that some phase points may have been lost by coalescence of waves or undetected separation of eddies. The phase acceleration between April and May, 1966 inferred for the eastern portion of the region may be due to some such event although that in the western portion is well documented. As has been shown, even greater com- plications followed immediately. Details of the abrupt transition in the nature of the path between May and June, 1966 remain obscure. To the west of 65° W the path is very similar in these months, and a short piece of path between 71°W and 67°W developed by Crawford (Warren and Volkmann, 1968) during this interval is also in essentially the same position, suggesting that following the very rapid movement during April and May this portion of the path became almost stationary from mid-May till mid-June, or else continued to move approximately three times as rapidly as in earlier months. Although satisfying documentation of events in the complicated thermal regime observed during the summer has not been possible, it appears in retrospect that the northerly lobes of warm water may have persisted through the summer, still propa- gating to the east but at a much slower speed than the smaller amplitude waves of previous months. It is not difficult to visualize the compound vortex street configur- ation proposed by Barkley (1968) for the Kuroshio-Oyashio front, also in these data, particularly that for July, but in the absence of more complete synoptic data and a relevant dynamical theory, it has not seemed useful to develop the analogy for the Gulf Stream. Also shown in Fig. 3 is the unambiguous evolution and eastward propagation of the well-defined meander observed in September-October, 1966. During this time the mean phase velocity was on the order of 6 cm/sec. The paths shown for September 30 and November 15 are actually from surface data obtained by airborne radiation thermometer (ART) aboard aircraft of the U.S. Naval Oceanographic Office. Further 502 Donald V. Hansen c rt bl) r3 -j o pi .c D. 1) u -C 0 0 c >, — x en Ti U V a i- 0 C. c a c u 0 ■d l- a 0 n a u E ■d E -i 0 C3 3 3 0 n c Q. c u 0 ed .2 c -a 0 a t Tl .2 c U "" n T) ro U u. Gulf Stream meanders between Cape Hatteras and the Grand Banks 503 work to evaluate the potential of surface temperature data for delineation of Gulf Stream meanders is in progress. DISCUSSION Evaluation of free inertia! jet hypothesis The wealth of position and bathymetric data obtained during this operation permits evaluation of bathymetric influences on the path of the Gulf Stream. The parameter f/D, where / is the Coriolis parameter and D is the depth, which frequently occurs in barotropic models of ocean circul- ation, was evaluated at selected points along several paths. The ratio is not constant on the path, either in detail or in the mean. Rather it is dominated by the increasing depth, decreasing irregularly by 30-50% over the length of a path, but no useful purpose can be served by reiterating detailed results of this evaluation. Clearly a more sophisticated model taking account of the structure of the flow is required. Of the many published works directed to the general question of topographic effects on oceanic and atmospheric flow, the most explicit development relevant to the Gulf Stream is that given by Warren (1963), and subsequently elaborated by Robin- son and Niiler (1967), and Niiler and Robinson (1967) for extensive numerical experimentation. The essential result derived in these papers is expressed by M*=fT(AD)- V(Af), (1) where the parameters M, V, and T denote the momentum transport, volume transport, and volume transport per unit depth near the bottom, A/is variation of the Coriolis parameter from an initial point placed for convenience at an inflection point on the path, A D is the corresponding variation of mean depth weighted by bottom current speed, and k is the curvature of the streamline. Warren computed stream paths for comparison with individual observed stream paths using best estimates of stream parameters. Comparisons of this sort were terminated when the computed positions departed sufficiently from the observations that the computed path encounters forcing conditions unlike those experienced by the actual stream. Niiler and Robinson (1967) experimented with a range of fixed and variable stream parameters in an attempt to reproduce certain path statistics rather than details of individual paths. The approach taken here is simply that of evaluating observed path parameters for consistency with equation (1). Such comparison was first made using Warren's (1963) values for transport para- meters and observed values of A/and A D to evaluate the curvature forced by variations of Coriolis effect and bathymetry encountered along the paths. Observed parameters were evaluated at 1/2° latitude (55 km) intervals along individual paths, relative to the first inflection point in greater than 3500 m depth. Depths were computed as the average of uncorrected soundings over 1° (110 km) squares centered approximately 30 km to the Sargasso Sea side of the path in recognition of the fact that although the chosen indicator appears to correlate reasonably well with the position of the maxi- mum surface current, it is somewhat to the left of the center of the main body of the stream or the stream near bottom. The results are relatively insensitive to details of evaluation of/; it was simply evaluated at the central latitude of each path segment. The curvatures forced by variations of depth and latitude encountered along the path were then computed from equation (1) for comparison with the observed curvatures of the paths. Observed curvature, the rate of change of the direction of the tangent to the path, was estimated from the change in direction between successive 55 km chords of the path and smoothed by a two-point running mean. In an exemplary month (March 504 Donald V. Hansen 1966, Fig. 4) the correspondence is good out to about 66°W, or nearly out to the New England Seamounts. Effects of individual seamounts appear as local features of considerably smaller horizontal scale than that of the major meanders in the stream path, suggesting a lack of strong coupling between seamounts and the major meanders. Farther east, the amplitude of curvature variation computed from variation of depth 1 5 1.0 / \ /N C\ / \ 1 ' ^ / V*^^*"' \ / \ / \ / *"» \ / \J \ / \ 1 S \ / xx \\ ' N 0.5 / * \ / 0 i i i I E J EFFECT OF 100m CHANCE OF DEPTH 02 < > A. -/''in ec 3 '/V A ''/ .01 / / \ \ /\, ' / /A ' / \ \ /\ i ' \ ' — / \ ' v // \ / \ ^ / V v \ ^S \ l\ / // \\ // \ / — \ J \ / // v I Vy V/ \ / V- — 7 ^"^ \ / -.01 1 SEAMOUNT PROVINCE , 1 ll 1 1 500 1000 DISTANCE ON PATHUNE (km) Fig. 4. Distribution of parameters on pathline for March, 1966. Upper portion: solid line denotes 10/(A D) in m/sec, dashed line denotes 105(A/) in sec-1. Lower portion: solid line denotes curvature of observed pathline, dashed line denotes curvature calculated from equation (1). and Coriolis parameter is significantly less than the observed path curvature, primarily because the forcing effect of bathymetric variation experienced along the stream path is too weak. The path here lies over what is largely abyssal plain, and thus encounters little topographic forcing in spite of large amplitude meandering. Furthermore, the computed curvature remains positive in this entire region, and in some months the computed curvature has no downstream zeros at all. Paths computed from the forced curvature should therefore diverge to the north, tending to fall down off the continental slope more slowly than is observed. Gulf Stream meanders between Cape Hatteras and the Grand Banks 505 o 2 t-^l A/1 506 Donald V. Hansen The possibility remains, however, that the hypothesis is correct and that the differences result from use of incorrect transports for the stream. Volume and momentum transports of the stream are reasonably well known, but the current speed near the bottom is very uncertain. Point to point agreement is not to be expected in any case, but the validity of the theory can be judged by its ability to reproduce the major features: extremes and zeros of the observed curvature distribution. The locus of points of inflection of the paths characterize in a general way the mean position of the stream. At these points, the first term of equation (1) is zero, so the required ratio of bottom transport to volume transport may be evaluated in terms of observed variations of latitude and topography. Figure 5a shows values of this ratio calculated on inflection points downstream from the first inflection point in depths greater than 3500 m, summarized by longitude.* The scatter in values of T/Vis considerable, as can be expected for this type of estimation, but the distributions are plausible and the mean value is consistently between 0-05 and 0-06 km-1 over nearly twenty degrees of longitude. Warren's (1963) value for this ratio was 0T km-1, and subsequent investigation by Warren and Volkman (1968) yielded a value of 0-02 km-1 between 65°W and 70°W. The obvious conclusion is that the observed mean paths of the Gulf Stream are consistent with the topographic control hypothesis, but with a somewhat smaller, still entirely plausible, ratio of bottom transport to volume transport than that initially used by Warren. Equation (1) was next used to evaluate the ratio of momentum transport to volume transport from parameters evaluated along the stream paths. Because there is no significant trend in the ratio T/V on inflection points (cf. Fig. 5a), and virtually nothing is known about meander-scale variation of this ratio, the approximate mean value on inflection points, 0-06 km-1, was used to evaluate M/V at curvature maxi- mums and minimums. Again there is considerable scatter but still a decided clumping of values around 20 cm/sec (Fig. 5b). Bathymetry smoothing incurred through the use of soundings uncorrected for sounding velocity variations, and the spatial dis- tribution of soundings used for this evaluation will tend to bias the computed ratio downward, by perhaps 10-20%. The recent determination by Warren and Volk- mann (1967) of 6 x 1015cm4/sec2 and 1014cm3/sec for the momentum and mass transports per unit mass is good confirmation of Warren's original choice of 50 cm/sec for their ratio. Although the mean position of the stream is consistent with the topographic control idea, it appears that the forcing applied by bathymetry is in general too weak to explain Gulf Stream meanders quantitatively in terms of the steady state theory. In and west of the seamount arc, occasional strong coupling between topography and meanders doubtless occurs, however. Fig. 4 shows one of the best examples of agreement, but the weight of evidence summarized in Fig. 5b is to the contrary. These conclusions are consistent with the result of numerical modelling experiments by Niiler and Robinson ( 1 967) in which use of probable Gulf Stream transports yielded realistic mean position and meander amplitudes, but longer than observed meander wavelengths, which implies insufficient curvature. Their model incorporated real bathymetry, but effective bathymetry along the path was evaluated somewhat differently from both the method used here and that used by Warren. It is clear This ratio was also evaluated at all adjacent pairs of inflection points as a more sensitive test for downstream variation, but the values so obtained were scattered over so wide a range of positive and negative values that the interpretation appeared completely inappropriate, and attempts to achieve this type of resolution were abandoned. Gulf Stream meanders between Cape Hatteras and the Grand Banks 507 from equation (1) that use of a stronger bottom current would enhance bathymetric variation so as to increase curvature in computed paths, but would also tend to hold the mean path higher on the con- tinental slope than is observed, thus degrading this aspect of path computation. It is perhaps possible to improve agreement between theory and observations somewhat by experimenting with other smoothing and weighting functions for the depth along the path, but this is nearly as specula- tive as postulation of meander-scale variation of transports. Proper modelling of the time-dependent aspects of the meanders appears to be the more promising and urgent task. No adequate model exists of time-dependent inertial jets with topography, and present data are insufficient for complete observational analysis. Effects of local changes within the stream, but not those of possible coupling with the surrounding ocean can be estimated by the simple device of retaining the local change of vorticity in derivation of a time-dependent counterpart to equation (1). For this estimation the local change of vorticity is derived from the local turning of the direction of the path, no &e w Ad — = c — = — — ck cos 0, (2) it At a* At where 0 is the direction of the tangent relative to the mean axis of the path, c is the propagation speed of the meanders in the downstream (x) direction, and A0/At denotes the change of direction at a phase-point fixed in the meanders. The approximate time-dependent counterpart to (1) becomes (M - cVco&0) k =fTAD - V A/ + — . (3) Change of direction following the meanders is generally negligible relative to the change of Coriolis parameter, and k — 0 on the inflection points, so the evaluation of the ratio of bottom transport to volume transport (Fig. 5a) is not significantly altered. At points of extreme curvature, 0 is near zero, hence the greatest effect of this aspect of time dependence is to increase the computed ratio of momentum to volume transport by an amount equal to the phase speed of the meander pattern. Inasmuch as the probable mean speed over several months was less than 10 cm /sec eastward, this effect has the correct tendency, but is of insufficient magnitude (cf. Fig. 5b) to bring agreement with expected Gulf Stream transports. However, only a partial accounting has been made of the effect of the very evident time dependence of the meanders. Effects of their interaction with the flow in which they are imbedded are required for a more complete appraisal. Evaluation of unstable wave hypothesis The properties of disturbances in the form of unstable quasi-geostrophic waves which may increase their amplitude through interaction with velocity shear in the basic flow have been studied by several investigators. Greatly simplified basic velocity distributions are used for isolation of mechanisms, and for mathematical tractability. Barotropic instability, in which kinetic energy is extracted from the basic flow through interaction of the disturbance with horizontal shear in the basic flow was considered as a possible cause of Gulf Stream meanders by Haurwitz and Panofsky (1950), and further refined by Lipps (1963) who included some effects of finite depth, stratification, and divergence. Duxbury (1963) studied the behavior of stable waves by means of a model otherwise sharing many features of Lipps' model of the stream, and obtained phase speeds in accord with Lipps' result for the wave number range of interest. Because they afford no basis for selection of a preferred mode, his results do not bear upon the origin of Gulf Stream meanders except as disturbances that may arise from extraneous influence and be propagated along the stream. Purely baroclinic instability in which the disturbance interacts with vertical shear in the basic flow to draw upon the potential energy content of the implied baroclinicity was investigated by Tareev (1965), and a simplified form of the general problem of stability of a basic flow containing both horizontal and vertical shear has been 508 Donald V. Hansen examined by Orlanski (1969). For application of these several studies to the Gulf Stream, only that of Tareev includes friction and beta effect, and only that by Orlanksi includes topographic effects. Properties of the fastest-growing wave, which is expected to be manifested most strongly in observations, computed from the results of each of these studies are summarized in Table 1 . It is apparent that the baroclinic models yield closer approach to the observed range of wavelengths, and that only Orlanski's model yields a good approximation to the phase velocity observed. Several of these investigators have considered the growth rates obtained too large. An unstable wave having growth rate Table 1. Summary of parameters for fastest growing wave mode. 2 rr/k, (km) Of/kr (cm/sec) (lO^secr1) 5ar (cm/sec) fa* (lO-3 km"1) Duxbury (1963)t Haurvvitz and Panofsky (1950) 190-500 220 45-95 60 15 75 20 Lipps (1963) 180 50 3 100 3 Tareev (1965)$ 250 (325) 49 (48) 4-3 (2-8) 51 (52) 8-4 (5-4) Orlanski(1969) 365 7 1-6 11 15 Observed Sept. 1965-May 1966 320 8 — — 2± 1 *Computed as ki fStable waves, phase velocity evaluated for first three transverse quasigeostrophic modes in wave number band of interest. JOpen values for frictionless case; bracketed values obtained for Ku = 5 x 107cm2/sec. o-j = 2 x 10-6 sec-1 will double its amplitude in about 4 days, for example, which is considerably too rapid to be consistent with these or earlier observations. All of these theories for unstable waves proceed by postulation of an infinitesimal amplitude disturbance having time and space dependence of the form e'(kx-°o. The reai anc| imaginary parts of the complex frequency yield the phase velocity and temporal growth rate of the disturbance in terms of the (assumed) real wave number k and parameters describing the basic flow. This convention has been followed primarily for mathematical convenience in the lack of substantial evidence to the contrary, but use of complex wave number rather than complex frequency would clearly be more representative of the spatial rather than temporal growth characteristic of the meanders (Fig. 6) during much of this sequence of observations. The envelope of these paths increases downstream in approximately linear rather than exponential fashion, but an equivalent spatial growth constant is on the order of ki = 2±1 x 10~3 km-1. It has been shown by Gaster (1962) that, as may be expected from energy consider- ations, for small growth rates the disturbance group velocity affords an approximate link between the temporal and spatial growth problems. Because there is no way apparent to me of inferring group velocity from these stream path observations, the maximum temporal growth rate, o-j, obtained from each of these theoretical investi- gations has been divided by the respective group velocity to obtain the corresponding Gulf Stream meanders between Cape Hatteras and the Grand Banks 509 spatial growth constants, ki, in Table 1. All appear still to be somewhat large, but are generally better than the corresponding temporal growth rates. Although Lipps' barotropic theory leads to the best approach to the observed growth constant, baro- clinic theories yield better approximation to other characteristics of Gulf Stream meanders. Inclusion of friction in Tareev's model with a horizontal eddy viscosity equal to that used by Munk (1950) in modelling the North Atlantic gyre leads to considerably improved agreement with observed wavelength and growth rate. Add- ition of topographic effect and horizontal convexity in the velocity profile can be expected to further stabilize and reduce the phase velocity of the fastest growing wave component. Likewise, Orlanski's model may benefit from truer representation of Gulf Stream parameters and topography. 75° 70° 65° 60° Fig. 6. Composite plot of nine consecutive positions of the 15°C isotherm at 200 m depth. The very rapid development of extreme meanders in June and July may be more consistent with the growth rates in Table 1, but details of their evolution remain unclear, and it is doubtful that meanders of such amplitude should be considered from the viewpoint of pertubation theory in any case. The rapid development of extreme meanders during this period suggests that temporal growth of meanders at times dominates the more usual spatial growth pattern, and that the temporal growth at such times may not be at great variance with theoretical estimates. It is of interest to compare the approach to the climatologic Gulf Stream (Fig. 6) with the turbulent spreading of a plane jet in homogenous non-rotating fluid. The theory developed by Tollmien ( 1 926) and applied to the Gulf Stream by Rossby (1936) describes linear spreading at an angle of 22-3°. The envelope of paths increases linearly over much of its downstream extent, with a spreading angle of about 20°. The mixing length proportional to downstream distance postulated in the theory is 1-13 km, and the associated eddy viscosity is 1-2 x 107cm2/sec, or about 2CM0% of the value required in Munk's (1950) model of the general circulation of the North Atlantic, and has a generally similar increase with distance offshore. Use of this value of eddy viscosity in Tareev's model results in a minor departure from the inviscid case. 510 Donald V. Hansen CONCLUSIONS From these observations it appears that none of the presently available theoretical models satisfactorily account for all major features of Gulf Stream meandering. It appears safe to predict however that the successful model will involve instability of a baroclinic current with some bathymetric effect. The topographic-beta effect invoked by Warren for development of his stationary wave model is consistent with the stationary aspect of the stream, its mean path, but the stability of such a topographically steered flow has not been investigated. The magnitude of the topographic variation is insufficient to account for details of individ- ual paths in terms of the stationary model, and the theory has not been extended to encompass the now very evident variation of meanders with time. Viewed as a dynamic wave theory, for real topography Warren's model predicts a wave of greater length and smaller phase velocity than is observed. On the other hand, if the Gulf Stream extends to the bottom as strongly as seems likely, this topography must at times exert a considerable influence on the meanders. While none of the published analyses of dynamic instability of the stream satis- factorily account for all identifiable wave parameters of the stream meandering, two baroclinic models yield good approximation to the length of the most unstable wave, and Orlanski's model yields a good approximation to the phase speed as well. The excessive growth rates obtained in all of these analyses become somewhat more realistic when interpreted as spatial rather than temporal growth, but a proper analysis for spatial amplification has not yet been done. It would be of interest to have the results of stability analysis using complex wave number perturbation of a baroclinic flow extending to a bottom with a depth gradient. From the point of view of observations, considerably greater resources or a new technique will be required for more definitive documentation of Gulf Stream meanders. Observational or modelling studies should anticipate an iteration interval of the order of 10 days for unambiguous resolution of the evolution of meanders. To document the propagation of disturbance energy through the region at the disturbance group velocity may require almost daily sets of paths. In lieu of several years of such obser- vations, it may be possible to infer from historical data whether the extreme meander development observed during the summer of 1966 is part of an annual cycle or a random event. Acknowledgements — The data reported in this paper have drawn upon the thoughts and efforts of a considerable number of people. I particularly wish to acknowledge the contributions of Mr. F. C. Fuglister of the Woods Hole Oceanographic Institution who provided much guidance in planning and accomplishing the stream tracking mission, Mr. R. L. Pickett and Mr. J. C. Wilkerson of the U.S. Naval Oceanographic Office whose special efforts to obtain ART data along the stream were most helpful in interpretating some of the month to month variations of the stream path, Dr. Bruce A. Warren of the Woods Hole Oceanographic Institution who gave valuable comments on the manu- script, and finally, the officers and crew of the U.S.C. and G.S.S. Explorer, to whose perseverence and resourcefulness in all seasons the continuous sequence of Gulf Stream pathlines is testimony. REFERENCES Barkley R. A. (1968) The Kuroshio-Oyashio front as a compound vortex street. J. mar. Res., 26 (2), 83-104. DeAngelis, R. M. (1967) North Atlantic tropical cyclones, 1966. Mariner's Weath. Log, 11 (1), 10-16. Gulf Stream meanders between Cape Hatteras and the Grand Banks 511 Duxbury A. C. (1963) An investigation of stable waves along a velocity shear boundary in a two-layer sea with a geostrophic flow regime. /. mar. Res., 21 (3) 246-283. Fuglister F. C. (1863) Gulf Stream '60. In: Progress in Oceanography, (M. Sears ed.), Pergamon Press, 1, 265-383. Fuglister F. C. (1967) Cyclonic eddies formed from meanders of the Gulf Stream. Paper presented before the Am. geophys. Un. in April 1967. Unpublished. Fuglister F. C. and A. D. Voorhis (1965) A new method of tracking the Gulf Stream. Limnol. Oceanogr., 10 (Suppl.), Rl 15-R124. Fuglister F. C. and L. V. Worthington (1951) Some results of a multiple ship survey of the Gulf Stream. Tellus, 3(1), 1-14. Gaster M. (1962) A note on the relation between temporally increasing and spatially increasing disturbances in hydrodynamic stability. J. fluid Mech., 14, 222-224. Hachey H. B. (1939) Temporary migrations of Gulf Stream water on the Atlantic Seaboard. J. Fish Res. Bd. Canada, 4 (5), 339-348. Haurwitz B. and H. A. Panofsky (1950) Stability and meandering of the Gulf Stream. Trans. Am. geophys. Un., 31, 723-731. Ichiye T. (1955) On the variation of oceanic circulation — V. Geophys. Mag., 26, 283-342. Lipps F. B. (1963) Stability of jets in a divergent barotropic fluid. /. atmos. Sci., 20, 120-129. Munk W. H. (1950) On the wind-driven ocean circulation. /. Met. 7, 79-93. Niiler P. P. and A. R. Robinson (1967) The Theory of free inertial jets — II. A numerical experiment for the path of the Gulf Stream. Tellus, 19 (4), 601-618. O'Brien, J. J. and R. O. Reid (1967) The nonlinear response of a two-layer, baroclinic ocean to a stationary, axially-asymmetric hurricane — I. Upwelling induced by momentum transfer. /. atmos. Sci., 24 (2), 197-207. Orlanksi I. (1969) The influence of bottom topography on the stability of jets in a baroclinic fluid. /. atmos. Sci. 26 (6), 1216-1232. Robinson A. R. and P. P. Niiler (1967) The theory of free inertial currents — I. Path and structure. Tellus, 19 (2), 269-291. Rossby C. G. (1936) Dynamics of steady ocean currents in the light of experimental fluid mechanics. Pap. Phys. Oceanogr. Met., 5 (1), 43 pp. Tareev B. A. (1965) Unstable Rossby waves and the instability of oceanic currents. (In Russian) Fisika Atmosfer. Okean. Izvest. Akad, Nauk, SSSR. Translation: 1 (4), 250- 256. Tollmien W. (1926) Berechnung turbulenter Ausbreitungsvorgange. Z. angew. Math. Mech., 6, 468^178. Warren B. A. (1963) Topographic influences on the path of the Gulf Stream. Tellus, 15 (2), 167-183. Warren B. A. and G. H. Volkmann (1968) Measurement of volume transport of the Gulf Stream south of New England. /. mar. Res., 26 (2), 1 10-126. 61 .«»6NTo», ^/f/VCF StR^tVSV U.S. DEPARTMENT OF COMMERCE Maurice H. Stans, Secretary ENVIRONMENTAL SCIENCE SERVICES ADMINISTRATION Robert M. White, Administrator RESEARCH LABORATORIES Wilmot N. Hess, Director ESSA TECHNICAL REPORT ERL 164-AOML 1 Correlation of Movements in the Western North Atlantic DONALD V. HANSEN ATLANTIC OCEANOGRAPHIC AND METEOROLOGICAL LABORATORIES MIAMI, FLORIDA May 1970 For sale by the Superintendent of Documents, U. S. Government Printing Office, Washington, D. C. 20402 Price 30 cents TABLE OF CONTENTS Page ABSTRACT 1 1. INTRODUCTION 1 2. RELATION TO CURRENT METER RECORDS 2 3. RELATION TO MOVEMENT OF CURRENT EDDIES 10 k. RELATION TO SWALLOW FLOAT MEASUREMENTS 12 5. DISCUSSION lh 6. ACKNOWLEDGMENTS Y] 7. REFERENCES 18 CORRELATION OF MOVEMENTS IN THE WESTERN NORTH ATLANTIC Donald V. Hansen A search was made for correlation of current meter records, movement of geo- strophic eddies, and Swallow float measure- ments with Gulf Stream meandering. Data of all these kinds are too few to permit strong conclusions, but some evidence is found indi- cating that passage of Gulf Stream meanders is accompanied by fluctuations of meridional flow extending an indeterminate distance outside the stream. 1. INTRODUCTION The path of the Gulf Stream between Cape Hatteras and the Grand Banks of Newfoundland was delineated at approxi- mately monthly intervals between September 1965 and April 1967. The position of the stream was delineated by following the position of the 15°C isotherm at 200 meters depth. Most of the operation was accomplished by the U.S.C.&G.S. ship Explorer using temperature and pressure sensors mounted on a ballasted fiberglass depressor, produced by the Braincon Corporation of Marion, Massachusetts, and sold as the V-Fin NAVITHERM system. Bathythermograph observations were made on return tracklines to confirm the basic observations and to obtain further information on thermal conditions on either side of the main thermal front. Figures 1 and 2 show typical pathlines from this set of observations . The major wavelike features of this sequence of pathlines have been interpreted (Hansen, 1970) as quasi-geostrophic waves on the order of 320 km wavelength propagated or ad- vected eastward at net speeds of 5 to 15 cm/s. Figures 3 and h, taken from that report show the propagation of phase inferred for these waves. The horizontal axis in these figures is the rhumb line through 37°30'N, 70°W; I+0°N, 60°W. The question of possible influence of these translations of the stream position on currents outside the stream itself is of considerable observational and theoretical interest, so an attempt was made to correlate these translations with the few other pertinent measures of water movements available from the North Atlantic. Although the data are too few and of too disparate types to yield firm conclusions, some in- teresting correspondence has been found, and these findings are summarized here. 2. RELATION TO CURRENT METER RECORDS The best available direct measures of transient currents in the Western North Atlantic during the period of pathline observations are from current meter buoys maintained near the stream by Woods Hole Oceanographic Institution (Fofonoff , 1968). The greatest number of useful records have been o o o o co 1 / \^ / A / J f ^ /x / 1 rr*r\ /*! 1 \ 1 o O ( i / V III X. >0 sO \ 1 / \. \X J ^*"»^ Vi/ ^^^.^ N 1 N ) s / X *+ / at \. / < ^ / S - w A / \ 00 i o / \ •^ V \ \ \ \ \ v i \ 1 \ / \ / :;^*>s * / y A IX o O ( \ V \ *\ v \ m \\ \ i;i\ 1:1 \ o iO K | . #^ / M . C o o ^0 H -p £ o CO o ■H ^H Td 5 y -p &q •H Cm ,2 C O 05 O O m X3 o CI -P co g O M •H £ CO CD -P jU -P X •H ^ 0 T3 ■H vO o O vD •H W O T3 •H r4 •H O M O CD 4-H lT\£l o ,H O -P fcuO Cm O c o o •H CO 0 CO d CO • O C -H o N tx O M O •H CJ O CO -P o CD m •H -H M "P CO CO O co CD ^ ft CD +3 M O O ? o o a -p £ 2 CD CD EH w n3 m o m CM Q) •H I 1 1 1 h- 500 KM SEPT 11-18 PHASE PROGRESSION SEPTEMBER 1965-MAY 1966 Figure 3. Interpretation of evolution of Gulf Stream meanders, September 1965 - May 1966. Dashed lines denote postulated phase progression, solid lines denote phase progression supported by other evidence . JUNE 15-20 JULY 15-23 AUG 16-23 NOV 15 PHASE ^ JUN Figure h . Interpretation of evolution of Gulf Stream meanders, June-November 1966. obtained from Site D. This site (39°20rN, 70°00TW) is gener- ally 100-200 km north of the near surface core of the Gulf Stream, and low frequency fluctuations of the north current component above 200 m are shown by Thompson (1969) to have significantly greater kinetic energy density than fluctu- ations of the east component. At this level the north and east components are only poorly correlated, but the princi- pal axis of the low frequency fluctuations lies about north- south as would be the case for a Rossby wave with wave number lying nearly east-west like the Gulf Stream meanders. Possible relationships between these energetic north-south current fluctuations and the fluctuating position of the nearby Gulf Stream are of particular interest here. Observed and inferred meridional positions of the thermal front associated with the Gulf Stream on 70°W during the Explorer cruises is compared (fig. 5) with the integral of the daily mean of the north component of current metered in the upper 200 m at Site D (Webster, 1968* ) . Each seg- ment of the integrated current meter record has been ad- justed meridionally for the best visual fit to the tempera- ture data. Only the gravest mode of the major meander * These and other data from the buoy project were presented in a seminar given by Dr. Webster during the Geophysical Fluid Dynamics Program, Woods Hole Oceanographic Institution, Summer, 1968. 7 ,-• 1 < \ ^. "*-- ^N ^** f -■ -^ + f / s 2 -J + -: s • + ^ u_ I =' + \ ~3 - Q 1 V —J -« _">-—.„ J 1 z ■^ - <** ,JT + > fc^s_-— o A Q *X ~ E 0) - \ CO O '35 - O ♦- 4 CJ a "* o e c - e o o k. k. 3 t * —3 0 CM o ^ -, -C ^^^^^^^^^^^^ ^B ■4— + o O o • ~3 <*=- C c • - o o ■m o ID c o o C o £ £Zh 2 o c o ++^^-Tr < c o **— o £ jC k» - •«™ c a> o —j*" o Q. a > o e e <~ 2 TJ o > a. T3 k. O Ll. (A O < c 0) c / -3 fe. ~-^5^^ _ • + ,-? Q f r — \ /_ M«M — ^ Z ) o ' |- - N .J 1 -. 1 1 CO CO co m to CO en (D O fH H S O EH CO .-I fr] a H P- Q -H O • d -H -P •H CD -P Ch -P |S CO CO CH 'H 0 -H (m OWOi3 U O- CO H d -P H -h O CO CI CO en O CD •h -p a >5 Ph a g Ph > CO CD CO O CO ftfn OPS Bh hh O 2 -P -H >, CJ) O 0Q CO p lf> CD ^ buD ■H fe o © ro O o o o features can be inferred from the temper a ture data; even for this the amplitude of north-south movement can only be estimated in most months, and no estimate has been attempted for the midsummer period due to the difficulty of interpre- ting evolution of the complicated thermal structures shown in figure h. However, aside from large transients in November of 1965 and 1966, the sense and magnitude of the north component of current appears to reflect meridional movements of the Gulf Stream. There is some indication that movement of the thermal front on 70°W may lead the current meter data in phase, most notably during the autumn of 1966. This phase shift is suggestive of the meander structure described by Webster (1961) from observations off Onslow Bay and reproduced in a mathematical model by Orlanski (1969) • On the other hand a phase lead on the order of 6 to 10 days is to be expected if the perturbation structure is essential- ly normal to the mean path of the stream rather than strictly north-south, but the data are insufficient to warrant further speculation about cross stream variation of phase. The mean of all current observations at this site has a negligible meridional component, which is of course also true of movement of the thermal front. A set of simultaneous current measurements was obtained from opposite sides of the Gulf Stream, at sites D and J (36°N, 70°W) in the spring of 1966. At 10 m depth, 9 fluctuation of currents with a north component on the order of 10 cm/s and a gross periodicity of about two weeks oc- curred essentially in phase at the two sites, and, as shown in figure 5? in phase with lateral movement of the Gulf Stream. 3. RELATION TO MOVEMENT OF CURRENT EDDIES At the outset of the stream path monitoring project, two cyclonic current rings or geostrophic eddies were discovered freshly separated on the south .side of the Gulf Stream and were observed (Fuglister, 1967) for the next several months. Figure 6 shows the meridional movement of these eddies 200 to 300 km to the south compared with the local meridional movement of the 15°C isotherm inferred from figure 3» Observations of the eddy position suffer from the same lack of resolution in time as the sequence of pathlines, and the already imprecise indication of possible relationships between their positions is further obscured by zonal movement of the eddies. Particularly at 66°W, it can be argued that the sequence of eddy latitudes is just as well represented by a random distribution about a linear trend. On the other hand, there is indication of a systematic relation to me- ridional movement of the nearby Gulf Stream, in that although meridional movements of the eddies are small, in every case where a clear judgment can be made, they are in 10 Latitude of I5°C isotherm @ 200 m oj oa, a"' ° > ,-—o ~-o— ... c~^ ,-~-~ o *-- i I 1 <""o o N — 1 1 0\ OJ OJ 00 © Latitude of eddies » oj 0) o _ CD 0) Z 01 (0 0> Figure 6 Meridional movement of detached eddies (open circles), and observed (dark points) and inferred (dashed lines) meridional movement of Gulf Stream at (a) 66°W and (b) 63°W. 11 the same direction as the inferred frontal movement. At 63°W both the sense and magnitude of the eddy movements are in reasonable agreement with those of the stream movements. k. RELATION TO SWALLOW FLOAT MEASUREMENTS If the positions of the thermal front summarized in figure 3 are approximated by 0T = 0m(x)+0p(x)cos k(x-ct) , (1) where 0t denotes the latitude of an isotherm in the main front as a function of eastward distance x, and time t, 0m is the time average latitude, and 0p is the amplitude of a progressive wave disturbance of the mean, the few suitable observations suggest the existence of an identifiable meridional flow that, aside from a possible ambiguity of phase, behaves as u = 3_0T = ck0n sin k(x-ct) . (2) at p While no direct evidence is available to indicate how far from the stream this disturbance may be felt, Iselin (1961) has suggested an association with transient currents revealed by the well known Swallow float measurements near Bermuda. As summarized by Crease (1962), these were a predominantly meridional motion with an apparent time scale 12 of 10 to 100 days and an rms amplitude of approximately 6 cm/s. Between 65°W and 70°W, the longitude of the float measurements, meander amplitudes are on the order of 100 km. The period and rms amplitude of the meridional movement described by (2) are therefore 2Z~ 1+6 days , and fL_P. all cm/s , ck ^2 both in order of magnitude agreement with values cited by Crease . Crease also computed a current structure function, [ u(x)-u(x+<£) ] , for simultaneous float measurements separated a distance^, the overbar denoting time or ensemble average. For the flow specified by equation (2) the normal- ized form of this function is, Sjt = 2 [ 1- cos(kZcosG) ] . If jL is taken normal to the current structure, then S/ is simply, S = 2[ 1-cos ki] . I judge however from Crease's figure 1 that the separation of his float pairs was more or less randomly oriented, in which case (3 ) becomes , S = 2[ 1-J0(ki)] , where J0 is the conventional notation for Bessel's function. 13 His values normalized by the mean square velocity fluctuation and a mean meander wave-length of 320 km, are plotted for comparison with these estimates (figure 7)« The small amount of data available from the float measure- ments as well as the meander observations prohibits confi- dence, but it is clear that the float measurements are quantitatively suggestive of an attenuated effect of Gulf Str e am me andor s . 5. DISCUSSION The evidence offered here is for the existence of meander scale current structures outside the stream proper, rather like the radiated geostrophic wave obtained in a mathematical model of Gulf Stream meanders by Robinson and Niiler (1967)* They estimate cross stream current components on the order of 10 cm/s for a stationary meander pattern, but differing by 180° from the phase relation between meridional currents and frontal movement suggested by figures 5 and 6. An alternative interpretation is that Gulf Stream meanders may in fact be a manifestation of quasi-geostrophic oscil- lations arising in mid-ocean independently of the stream, as has been suggested by Phillips (1966), as a result of fluctu- ating wind stress. The amplitudes of both the meridional movements of the Gulf Stream and the transients sampled by the Swallow floats are well above those computed by Phillips Ik Figure 7. Structure function computed from (h) (solid line), (5) (dashed line), and float measurements (dark points). 15 from wind stress of plausible magnitude. Phillips suggests that the oscillations generated by fluctuating wind stress interact with and extract energy from the Gulf Stream as part of the Gulf Stream meander inducing mechanism. It is difficult to reconcile the westward phase speed of about 8 cm/s expected of the mid-ocean oscillations with the eastward phase speed of the same magnitude observed in the meanders. Unfortunately, there are no observations to indicate phase speeds of the fluctuations in the float measurements . It appears feasible to test the existence of the suggested relation of currents outside the stream to Gulf Stream meandering by means of shallow Swallow floats or parachute drogue observations while monitoring the position of the Gulf Stream. One such experiment using a single parachute drogue was attempted near 71°W on 30 March 1967. Figure 5 snows that the currents at Site D changed from southerly to northerly at about this time. Unfortunately the anticyclonic section of meander whose leading (eastern) edge was selected for the experiment site did not develop sufficient amplitude to provide a useful result. The drogue, set initially in slope water, moved south across the edge of the stream becoming entrained in the stream, and thereafter acquiring a predominantly eastward motion. The drogue must have been influenced to some extent 16 by northerly winds of 25 knots. In view of the relatively weak (~10 cm/s) expected of the systematic flow, it is to be expected that a number of such experiments would be required for a clear result to show above the random variations. 6. ACKNOWLEDGMENTS The correlations attempted in this note have drawn upon the efforts of a considerable number of people. I particu- larly wish to acknowledge the contributions of Dr. Ferris Webster and Mr. Frederick Fuglister of Woods Hole Oceano- graphic Institution who kindly provided the current meter and eddy position data, and Mr. R. L. Pickett and Mr. J. C. Wilkerson of the U. S. Naval Oceanographic Office whose special efforts to obtain ART data along the stream were most helpful in interpreting some of the month to month variations of the stream path. Finally, the labors and long days at sea required of the officers and men of the U. S. Coast and Geodetic Survey vessels Explorer , Pierce , and Whiting to obtain the Gulf Stream paths is acknowledged. 17 7. REFERENCES Crease, J. (1962), Velocity measurements in the deep water of the western North Atlantic, J. Geophys. Res. 62 (8), 3173-3176. Fofonoff, N. P. (1968), Current measurements from moored buoys, 1959-1965? Summary Report, Woods Hole Oceano- graphic Institution, Ref. 69~30 (Unpublished manu- script . ) Fuglister, F. C. (1967), Cyclonic eddies formed from meanders of the Gulf Stream, Abstract of paper pre- sented before Am. Geophys. Un. in April 1967* Trans. Am. Geophys. Un. ^+8, (l), 123. Hansen, D. V. (1970), Gulf Stream meanders between Cape Hatteras and the Grand Banks, Deep-Sea Res. (in press) Iselin, C. O'D. (1961), An interpretation of the deep current measurements, Oceanus 2. (3)» 9« Orlanski, I. (1969), The influence of bottom topography on the stability of jets in a baroclinic fluid, J. Atmos- pheric Sci. 26 (6), 1216-1232. Phillips, N. (1966), Large scale eddy motion in the Western Atlantic, J. Geophys. Res. 71 (16), 3833-3892. 18 Robinson, A. R. and P. P. Niiler, (1967), The theory of free inertial currents, I. Path and structure } Tellus XIV (2), 269-291. Thompson, R. (1969), The search for topographic Rossby waves in the gappy current records at Site D, Technical Rpt., Woods Hole Oceanographic Institution Ref . 69-67. (Unpublished manuscript.) Webster, F. (1961), A description of Gulf Stream meanders off Onslow Bay, Deep-Sea Res. 8, 130-1^3. Webster, F. (1968), Observations of time dependent ocean currents, JEn course lectures and abstracts of seminars, 1968 Summer Study Program in Geophysical Fluid Dynamics, Woods Hole Oceanographic Institution Ref. No. 68-72, 115-122. Webster, F. (1969), Vertical profiles of horizontal ocean currents, Deep-Sea Res. 16, 85-98. 19 Reprinted from The Science Teacher 37 » No. k, 96 go A Co:is(;il I'oml — Sliiflii'fl by Oicauograpliic Method-;. K. O. Finery. 80pp. S.V50. American Elsevier Publishing Company, Inc., 52 Vandcrbilt Avenue, New York 10017. 1969. This small but thoroughly scientific hook is the biography, anatomy, and physiology of Oyster Pond, one of the many small csltia- rine ponds on Cape Cod. Hecause of its proximity to Woods Hole Oceanographic Institution, it was selected for study in un- usual depth. The history of the pond is traced from ice impounded in the Buzzards Bay moraine, through colonial settlement, to modern times. Geology, topography, and sediments of the pond arc described in considerable detail. Forty percent of the book, however, is devoted to quantitative evaluation of many qualities of ihe water itself and of the environmental factors that determine and modulate them. These factors range from the general influence of climate on water level, temperature, and ice cover to the influences on water chemistry, pri- marily inflow from the ocean and biological processes. Among the interesting revela- tions are evidence of pollution by human excrement and the conclusion that this pond, which is some 12,000 years old, can remain a pond another 4,000 years if the sea level remains about the same and if man's ac- tivities do not materially alter the pond. It is the kind of study on which to base the socio-economic-political decisions sorely needed in many larger coastal regions under- going rapid development and degradation. For the student and teacher, it shows the potential for interesting "neighborhood" scientific inquiry. Although frequently in- voking methods well beyond the average secondary student and using fairly esoteric language, Emery points the way to some easy observations to reveal patterns in and heighten awareness of the geophysical en- vironment. It is only through such aware- ness that Emery's "hope that for some of these years this and similar ponds will re- main to be enjoyed in scientific studies as well as for esthetic and recreational pur- poses" will be realized. Donald V. Hansen Director, Physical Oceanography Laboratory Environmental Science Services Administration Miami, Florida 63 Reprinted from Remote Sensing of Environment J_, No. 3, 161-164 A Note on the Use of Sea Surface Temperature for Observing Ocean Currents DONALD V. HANSEN and GEORGE A. MAUL Environmental Science Services Administration. Miami. Florida Abstract Bathythermograph data from 100 crossings of the Gulf Stream between Cape Hatteras and the Grand Banks were used to investigate the relationship between the surface temperature front and the deeper thermal front previously identified with the core of the Gulf Stream. Although relatively much weaker in summer than in winter, an identifiable surface front was found in all seasons. The mean sep- aration between the surface front and the maximum horizontal temperature gradient at 200 m is 14.5 km, and has no important temporal or geographic variations in this region. Both the mean and the variance of the separation are greater in regions of anticyclonic curvature than in regions of cyclonic curvature. The net result of this variance is to lend ambiguity to observations of meanders of ampli- tude less than 35 to 40 km so far as interpretation as variation of the Gulf Stream is concerned. Introduction It is by now well known that sea surface temperatures can be mapped with interesting resolution by satellite-borne infrared sensors, and numerous temperature maps purporting to show the Gulf Stream or other major currents have been published (cf. Rao, 1968). U.S. Navy aircraft have for some time been making regular flights to define the northern edge of the Gulf Stream by radiation thermometer measurements (U.S. Naval Oceanographic Office). Most applications, however, require knowledge of conditions in more than the thin layer at the ocean surface presently sensible from satellites, and mere exis- tence of the stream is not useful information. It has not been shown just what behavior of currents like the Gulf Stream and their associated deeper thermal structures can be usefully de- fined by remote sensing of surface effects. This paper presents some results from an attempt to clarify these matters with respect to the Gulf Stream. The analysis is similar in spirit to an earlier study by Strack (1953), but is done in the context of detailed knowledge of the configuration of the stream. Variation of Frontal Strength with Depth and Season The geographic position of the 15C isotherm at a depth of 200 m was delineated between the offing at Cape Hatteras and the Grand Banks at approximately monthly intervals during a systematic study of Gulf Stream meandering (Hansen, 1970). Figure 1 shows typical stream path delineations from that pro- ject. The philosophy of this project is readily understood when it is realized that the Gulf Stream is not so much a current of warm water in the ocean as a baroclinic flow along a frontal region between warm and cold water masses (Fig. 2). The 15C isotherm at 200 m depth was selected as an indicator for the major thermal front associated with the Gulf Stream. Twenty-one pathlines were observed during 1965-1967 using equipment and procedures essentially as described by Fuglister and Voorhis (1965), who also give a more detailed discussion of the relation of the thermal front to the Gulf Stream. Bathy- thermograph soundings and surface temperature observations were made at an average interval of 8.7 km on 100 nearly right- angle crossings of these pathlines to obtain further information on the variability of the deep front. This front was found to be a very reliable feature of the oceanographic situation ; invariably it was sharp (about 5°C in 20 km or less) and bracketed the 15CC isotherm at 200 m depth. The average temperature at the center of the strongest horizontal temperature gradient was 14.7 + 1. 5C(±1 std. dev.). A temperature front was found also at the surface in asso- ciation with the deep front in all of the crossings. The strength of this surface front varies considerably with season (Fig. 3), ranging from a temperature differential of about IOC in March to 2 C in August, but values in any particular set of obser- vations vary with sampling distribution because sea surface temperatures on the cold side of the front tend to be quite variable. The sharpness of the transition in individual cros- 75° 7(1° 65° 60° Fig. 1. Left, a typical Gulf Stream path as defined by the position of the 15C isotherm at 200 m (solid line). The dashed line is the return BTtrackline; the crosses mark places where the 15 C isotherm at 200 m was reencountered. Right, superposition of nine monthly positions of 15°C isotherm at 200 m; note the downstream growth of meander amplitude which became appreciable primarily east of 70°W. Remote Sensing of Environment 1 (1 970), 1 61-1 64 Copyright © 1970 by American Elsevier Publishing Company, Inc MAXIMUM 200 m TEMPERATURE GRADIENT Fig. 2. Thermal cross section of the Gulf Stream from west to east, 350 km SSE of Cape Cod, September 1966. Flow is into the plane of the page ( Vertical exaggeration 500 : 1 ). sings is known, from occasional thermistor recordings, to range from nearly discontinuous to a transition in several steps, but nonetheless the temperature contrast (difference between the average on the warm and cold sides) across the edge of the stream provides an objective measure for the relative sen- sitivity required of remote sensors at various times of the year (Fig. 3b). Relation of Surface Effect to Deep Front We address next the question of what variations of the Gulf Stream can be expected to be revealed when sufficiently pre- cise measurement of sea surface temperature can be obtained. The phenomenon of primary interest is variation of the mean- ders, or wavelike perturbations (Fig. 1), that develop in the stream, leading to ultimate loss of identity of the stream as a coherent flow, and sometimes to separation and cutoff of cur- rent rings or eddies (Fuglister, 1967). The parameter of value here is the horizontal distance L between the strongest hori- zontal temperature gradient at the surface and that at 200 m, taken as positive to the right when facing downstream. The pre- sumed normal component L„ was computed using the crossing angle to the known orientation (generally smoothed over down- stream distances of 10 to 20 km) of the thermal front at 200 m. The majority of the crossings were 75° to 90c intersections. All intersections of less than 30° or at times when the stream posi- tion was changing too rapidly to allow a reliable estimate of its local orientation were excluded from the analysis. Figure 4a shows the distribution of L„ for all 100 crossings. Remote Sensing of Environment 1 (1970) 161-164 200 METER TEMPERATURE 26 MARCH 1967 1 - *■ 10 KILOMETERS BUCKET TEMPERATURE SURFACE THERMISTOR RECORD 200 METER TEMPERATURE- 22 AUGUST 1966 1 4-i , , I ) 12- f_ uO < 10- / 0 U B- -> 6 < Qt 5 ■" 0 ■ MONTH J FMAMJ JASOND NUMBER OF CROSSINGS 2 515152 7 77 16 1545 (b) Fig. 3. (a) Surface thermistor record across the maximum surface gradient (upper, March 1967; lower, August 1966). (b) Average temperature contrast across the surface thermal front. The vertical bars are ±1 standard deviation. Donald V. Hansen and George A. Maul 162 f 30- J 25- z r* 01 20- o U O 1 5 - 0 >. 10- u z D 5- u tt "- r»J (a) MEAN 14 5 w -H 20 -10 0 10 20 30 40 50 60 70 Ln (km) 30 25 2 0 I 5 10 5 24 ^22 20 J8 6 I (C) 35- 30- 1 25n J 2 0 1 5^ 10 MONTH J FMAMJ J A 5 O N D (km) Fig. 4. (a) Histogram of distribution of distances between positions of maximum temperature gradient at the surface and at 200 m. (b) The temporal variation of distances between positions of maximum temperature gradient at the surface and at 200 m averaged by months. The vertical bar through each point denotes ±1 standard deviation, (c) The longitudinal variation of distances between positions of maximum temperature gradient at the surface and at 200 m averaged by 3° intervals of longitude. The vertical bar through each point denotes ±1 standard deviation, (d) The structure function for the displacement of the Gulf Stream surface front from that at 200 m. It has a mean value of 14.5 km, a standard deviation of 11.8 km, and a slight positive skewness (Table I). Negative values were observed in four instances; this is somewhat surprising in view of the structure of the stream as described by Fuglister and Voorhis (1965). In each of these instances, however, the weather was heavy enough for the ship to be hove to just before the crossing, suggesting that wind stress may be a major feature in displacing the surface front, by either vertical mixing or advection. The negative L„ was associated with a strong rever- sal in the upper 50 m of the customary inclination of isotherms across the stream, indicating strong wind-induced current shear. Table I Relationship of L„ to Curvature Anti- Path curvature Cyclonic Inflection cyclonic lntnl Number of crossings 19 21 44 100 Mean of L„(km) 11.3 14.2 16.2 14.5 Standard deviation (km) 8.1 9.7 13.4 11.8 Skewness" of Ln + 0.11 -0.78 + 0.94 + 0.53 "Computed as Pearsonian skewness = deviation. 3x (mean-median) standard At greater depths the inclincation did not differ significantly from the average for all 100 crossings (one in 85). An attempt was made to relate these events to the synoptic situation, but in all cases the storm passage was too rapid and too poorly docu- mented to permit any useful conclusion. There is no clear evidence of a seasonal variation in L„ cor- responding to that of the strength of the surface front (Fig. 4b). Likewise there is no strong dependence on longitude of either the mean or variance of/.,, (Fig. 4c). The apparently decreasing mean value of L„ with distance eastward from Cape Hatteras is mildly surprising in light of the increasing amplitude of meandering and relatively more diffuse nature of the stream, but the small differences shown in Fig. 4c are not statistically sig- nificant. Because the distribution of L„ is so weakly related to season or longitude, its spatial variation was further investigated by means of the structure function, S = [L„(x)-Ln(x + l)]2/LJ, where x is the reference position and / is the spatial displace- ment along individual Gulf Stream paths, and the overbar de- notes ensemble averaging. A Note on the Use of Sea Surface Temperature for Observing Ocean Currents 163 Remote Sensing of Environment 1 (1 970), 1 1 6-1 64 This function (Fig. 4d) reveals an expected downstream growth of variance independent of simple longitude, but is strongly modulated by a quasiperiodic variation of scale near 400 km. The mean wavelength of meanders is about 320 km, but the lags were taken along the curvilinear path length, and meander amplitudes are of the correct magnitude for the modu- lation to be interpreted as a meander-scale pattern in the variance of L„. By this interpretation the pattern disappears for lags greater than 1200 km because the sampling density is no longer adequate to resolve it and because such long lags necessarily involve heavy reliance on data from the eastern part of the sampled area where, owing to occurrence of more irregular and large amplitude meandering, the ratio of path- length to wavelength becomes both greater and more variable. To investigate this meander-scale pattern further, the L„ were visually classified and averaged according to the local curvature of the stream path. There is necessarily some arbitrariness in assigning curvature to many of the crossings. It was done by assigning anticyclonic curvatures to crossings visually deter- mined to lie within -J wavelength of a crest of the meander waveform, cyclonic curvatures to those within i wavelength of a trough, and zero curvatures to those near inflection points of the path. Sixteen crossings that did not fall clearly into any of these classes were excluded from the analysis.1 The pattern that emerges (Table I) is for values of the mean, variance, and skew- ness to be larger in regions of anticyclonic curvature than in regions of cyclonic curvature. Although the number of observations entering the subsets of Table I is less than satisfying, the pattern is consistent. The effect of this aspect of the variance is to enhance rather than to mask the underlying Gulf Stream behavior of interest. Discussion The mean value of L„ and the implied slope of the thermal front, 14.5 km and one in 72, do not differ significantly from the values 15 km and 1 in 75 given by Fuglister and Voorhis (1965) on the basis of a considerably smaller sample. Present data indicate, however, the existence of a meander-scale variation of the frontal slope from 1 in 80 in anticyclonic parts of the stream path to 1 in 55 in cyclonic parts. This may be a reflec- tion of the dynamically destablizing influence of anticyclonic curvature. The pattern'is also in qualitative agreement with the 'Crossings in inflection points were also separated as to leading or lagging the waveform crests, without revealing any significant differences. behavior of a mathematical model of a stable, potential vorti- city-conserving, baroclinic jet developed by Robinson and Niiler (1967), however. The major conclusions reached from this analysis are: 1. A surface temperature front bearing essentially the same relation to the deeper thermal structure associated with the Gulf Stream is found in all seasons, but varies seasonally in strength. 2. The axis of the Gulf Stream occurs about 15 km to the warm side of the surface front, with no important seasonal or geographical variations of the displacement. 3. The variance of the separation between the surface front and the deeper structure is nearly as large as the mean and oc- curs over distances short compared to a typical meander wave- length. Although it is difficult to assess precisely the effect of the relatively greater contribution with positive skewness to the variance occurring on the meander wave crests, it appears that the variance is sufficient to mask meanders of amplitude less than plus or minus twice the standard deviation on meander troughs or inflection points, or ±35 to 40 km. Inasmuch as meanders of greater than this amplitude occur primarily eastof70°W (Fig. 1), this is a region in which satellite-borne sensors offer promise for monitoring Gulf Stream meanders. Acknowledgments Support for this research was provided in part by the National Aeronautics and Space Administration's Earth Resources Survey Program through the National Environmental Satellite Center's Environmental Science Group. References Fuglister, F. C. (1967), Cyclonic eddies formed from meanders of the Gulf Stream, paper presented before the American Geophysical Union in April 1967 (unpublished). Fuglister, F. C, and A. D. Voorhis ( 1 965), A new method of tracking the Gulf Stream, Limnol. Oceanogr., 10 (Suppl.), Rl 15-R124. Hansen, D. V. (1970), Gulf Stream meanders between Cape Hatteras and the Grand Banks, Deep-Sea Research (in press). Rao, P. K. (1968), Sea surface temperature measurements from satellites, Mariners Weather Log, 12 (5), 152-154. Robinson, A. R., and P. P. Niiler (1967), The theory of free inertial currents. I. Path and structure, Tel/us, 19 (2), 269-291. Strack, S. L. (1953), Surface temperature gradients as indicators of the position of the Gulf Stream, Woods Hole Oceanographic Insti- tution Reference No. 53-53 (unpublished manuscript). U.S. Naval Oceanographic Office, The Gulf Stream, Published monthly at Washington, D.C. Received January 26, 1970 Remote Sensing of Environment 1 (1 970). 1 61-1 64 Donald V. Hansen and George A, Maul 164 64 Reprinted from International Hy d rog r a ph i c Bureau Review XLV II, No. 2 , 93" 1 06 MEAN SOUNDING VELOCITY. A BRIEF REVIEW by George A. Maul Environmental Science Services Administration, Atlantic Oceanographic and Meteorological Laboratories, Miami, Florida and James C. Bishop, Jr. Environmental Science Services Administration, Coast and Geodetic Survey, Seattle. Washington. INTRODUCTION In the three decades since the publication of J.D. Matthews' Tables of the Velocity of Sound in Pure Water and Sea Water for use in Echo- Sounding and Echo-Ranging (1939), numerous improvements have been made in the techniques of deep water echo-sounding: stabilized, narrow- beam transducer systems capable of resolving ±1 fathom in 4 000 fathoms are operational (Hickley, 1965); velocimeters able to measure acoustic velocity in situ with a repeatability of ±0.02 metre/second have been developed (Bissett-Berman Corp.); the equation for the velocity of sound in sea water has been significantly improved (Wilson, 1960); and high- speed computer technology has been applied to the problems of collection, reduction, and assimilation of bathymetric data (Karo, 1963; Bernstein, 1966; Maul, 1969). Present day requirements for precise depth determinations are rapidly approaching third-order accuracy (1/5 000): Luskin et al. (1954) proposed one part in 3 000 for bathymetric mapping; marine geodesists computing the Bouguer gravity anomaly introduce more than 0.1 milligal error for each fathom of depth error; slant range echo-sounders capable of sounding wide swaths of the sea floor require knowledge of variations in sound speed behavior over long oblique distances; and deep sea taut-wire mooring installations require precise depth information for accurate deployment of sensors. In view of modern capabilities and requirements, it appears profitable to review from time to time certain simplifying assumptions which can 86 INTERNATIONAL HVDROGRAPHIC REVIEW become a significant source of error. Incorrect methods of calculating the "mean sounding velocity", (also referred to in the literature as "sounding velocity", "mean sound velocity", or "mean vertical sound velocity") are in this category. MATHEMATICAL DEVELOPMENT Historically, echo soundings have been made by assuming a conven- tional value for the velocity of sound (1463 or 1500 metres/second) and then correcting for variations of this assumed value in the actual water column (Matthews, 1939; Jeffers, 1960). It must be recognized that echo-sounders are time measuring devices, and the problem is to convert half of the round-trip travel time of a sound pulse to depth by multiplying by a suitable mean velocity. Required is the vector quantity, the mean sounding velocity (MSV), which by definition is the quotient of the distance (Z) a sound wave travels in the vertical and the length of the associated travel time interval (T) : MSV = - (1) T This definition does not say "mean velocities from the surface to the stated depth" (Sverdrup, et al., 1942) nor "mean values for velocity of sound through the vertical water column" (Baker, et al., 1966). In correcting for sound velocity variations, the water column is considered to be divided into a series of layers (figure 1), each with thickness AZ4 and an associated velocity \(. The time interval AT, for the sound wave to pass vertically through the z'th layer is : AZ, AT,= — '- ' v, Summing the time intervals of all n layers in the water column from the surface (Z = 0) to depth (Z), " " AZ, <=1 i=\ yi For a continuous function V(Z), in the limit as AZ approaches zero, Substituting into equation (1) and rearranging terms we have the correct expression for the mean sounding velocity : btsT MSV= - / — (3) Zi-1 + Zi MEAN SOUNDING VELOCITY _j [^ V Velocity of sound 1 Vi AZi <—ZL itn interval of /i intervals Z Depth Fig. 1. — The ocean is considered to be composed of a series of finite layers AZ, with an associated Vt, which in the limit are the infinitesimal layers dz. Equation (3) is the integral form of the harmonic mean, that is, the reciprocal of the mean of the reciprocals. The equation used by Matthews to prepare his tables, as discussed by Dietrich (1963), is Sv -u: VdZ (4) where Sv is the "sounding velocity". Equation (4) is the integral form of the arithmetic mean which introduces a small error because the mean velocity required is not the thickness weighted average of the speeds, but is the total distance traveled divided by the total travel time. Because small velocities contribute more strongly, the harmonic mean will always be less than the arithmetic mean except when the velocity is constant, in which case the two types of mean value are equal. To illustrate the concept, consider a two layer ocean with layer thickness and associated velocity values as shown on figure 2. From equations (3) and (4) : MSV = V, / = ! I AZ, / = ! 1 km 2 km - + 2 km/s 1 km/s 1 km + 2 km -i = km/s 2.5 8K INTERNATIONAL HYDROGRAPHIC REVIEW Sv = S V V (km/s) AT, -0. 5 sec AT2=2.0 sec \ \ \ A \ \ \\\ \\ \ Bottom Z (km) Fig. 2. — Two layer model of the ocean. The layer thicknesses are AZ, and AZ2, the associated velocities V! and Vj, and the travel times AT, and AT^ where the subscripts 1 and 2 refer to the upper and lower layers respectively. The travel time of the sound wave is 2\ seconds. From equation (1) : 3 Z (using MSV) = - — km/s x 2.5 s = 3 km Z (using Sv) = — km/s x 2.5 s = 3 1/3 km Although this is a very hypothetical case and not representative of actual oceanic conditions, it clearly demonstrates the validity of equation (3), since the correct depth is 3 km by design. In the "standard ocean" (35°/no, O'C), which is approximated in polar regions where there is a near linear increase of sound speed with depth, the magnitude of this error is approximately 0.1%. This is significant in comparison to the 1 part in 4000 (0.025%) capability of modern echo- sounders. On the average, however, the error is anticipated to be less than 0.1%, because in middle and low latitude typical profiles of the speed of sound with depth have a mid-depth minimum which reduces the range of variation and hence the difference between harmonic and arithmetic means. MEAN SOUNDING VELOCITY 89 DISCUSSION As is well known, the velocity of sound is a slowly varying function of depth; for this reason the error introduced by the use of equation (4) has, until recently, been acceptable (Matthews; Officer, 1958; and Crease et al., 1964). Other authors (cf. Gabler, 1961; Dietrich, 1963; Maul, 1969) have ignored the subtlety entirely. Computer integration of velocimeter output is easily accomplished. The analog output of this instrument can be digitized at a high enough rate that the integral in equation (3) can be very closely approximated by finite differences. If classical sampling techniques are employed, the integral can be evaluated by assuming a linear change of the velocity of sound between sample points, by the trapezoidal rule. In figure 3 for example, the velocity Velocity of sound G = AV AZ Fig. 3. z Depth - Linear approximation of the change of the velocity of sound between standard oceanographic depths. 90 INTERNATIONAL HYDROGRAPHIC REVIEW of sound Vj, V2 is computed at the standard oceanographic depths Zlt Z2 respectively, from temperature and salinity observations at these points. The time for the sound to travel the distance AZ is given by equation (2) integrated from Zx to Z2, .z. T f 2 dL J-, v The equation for the straight line connecting the points (Vj, Zx) and (V2, Z2) is V = Vi + GZ* where G(=AV/AZ) is the velocity gradient, and Z* = Z1 - Z in the interval (Z, ^ Z ^ Z2). Substituting dZ 1 r " dL i = / = - In (V. + GZ*) \ V, + GZ* G ' Since V, + GZ* = V, at Z = Zt and V, + GZ* = V2 at Z = Z,, T=-^(lnV2^-lnV1)=-!rln^2. (5) which is in agreement with Ryan and Grim (1968). Equation (3) can be evaluated by Simpson's Rule. This requires the assumption that the velocity of sound varies from point to point in a smooth manner which can be approximated by a parabola. Observations in the ocean (cf. Woods, 1967) indicate that a layered structure exists which implies that the variables essentially change like a step-function. With this uncertainty, the reasonable approximation seems to be by the trapezoidal method. In Matthews' method, as adopted by the U.S. Coast and Geodetic Survey (Jeffers), the temperatures and salinities at Zx and Z2 are averaged, and a velocity is calculated for the mid-depth of the layer; it is assumed that this "mean velocity" is applicable over the entire layer. This introduces a small error, because the velocity of sound is a non-linear function of temperature, salinity and pressure. If Matthews Tables are used, as in Dishon and Heezen (1968), errors of 12 metres in 5000 metres of water depth are introduced because Matthews' equation for sound speed is used instead of Wilson's equation (Capurro, 1963). Furthermore, if true depth is used as the entering argument as in Matthews or Jeffers, instead of echo-sounder depth (also called "recorded depth"; Krause, 1962) an error of the order of 2.5% is introduced in the independent variable. This source of error is easily avoided in machine processing by using time as the independent variable and true depth as the dependent variable. CONCLUSION It is recommended that hydrographers re-evaluate mean sounding velocity corrections in the light of new instrumentation and more stringent requirements on bathymetry for economic and scientific activities. The MEAN SOUNDING VELOCITY 91 abundant sources of errors in marine surveys make it imprudent to add others that require no additional labor to eliminate. Electronic sampling and calculating techniques can remove many of the uncertainties imposed by the point source data of classical oceanography. The work of Matthews should be updated to reflect our vastly increased knowledge of the distribu- tion of the oceanic variables and how thev behave. REFERENCES Baker, B.B., Jr., W.R. Deebel, R.D. Geisenderfer, Editors : Glossary of Oceanographic Terms, Second Edition, U. S. Naval Oceanographic Office, Washington, D.C., p. 104, 1966. Bernstein, R. : Data Processing at Sea, Geomarine Technology, Vol. 2, No. 5, pp. 11-15, 1966. Bissett-Berman Corporation, Specification Sheet, Model 9045 Deep Sub- mersible S-T-D System, San Diego, 1968. Capurro, L.R.A. : Velocity of Sound in Sea-Water, International Hydro- graphic Review, XL, No. 1, pp. 47-48, 1963. Crease, J., A.S. Laughton, and J.C. Swallow : The Significance of Precision Echo Sounding in the Deep Ocean, International Hydrographic Review, XLI, No. 2, pp. 63-72, 1964. Dietrich, G. : General Oceanography, Wiley, New York, p. 69, 1963. Dishon, M. and B. Heezen : Digital Deep-Sea Sounding Library, Inter- national Hydrographic Review, XLV, No. 2, pp. 23-40, 1968. Gabler, H.M. : Limits of Accuracy of Echo Soundings in Ocean Regions, International Hydrographic Review, XXXVIII, No. 2, pp. 7-24, 1961. Hickley, T.J. : Some Recent Systems Development by U.S. Coast and Geodetic Survey, Internatiomd Hydrographic Review, XLII, No. 1, pp. 41-56, 1965. Jeffers, K.B. : Hydrographic Manual, Publication 20-2, U.S. Coast and Geodetic Survey, Washington, D.C., p. 182 tf, 1960. Karo, H.A. : Hydrographic Automatic Data Processing, International Hydrographic Review, XL, No. 1, pp. 141-147, 1963. Krause, D.C. : Interpretation of Echo Sounding Profiles, International Hydrographic Review, XXXIX, No. 1, p. 116, Eqn. (295), 1962. Luskin, B., B.C. Heezen, M. Ewing, M. Landisman : Precision Measurement of Ocean Depth, Deep-Sea Research, 1, pp. 131-140, 1954. Matthews, J.D. : Tables of the Velocity of Sound in Pure Water and Sea Water for use in Echo-sounding and Echo-ranging, Second Edition, H.D. 282, Hydrograhic Department, Admiralty, London, p. 52, 1939. Maul, G.A. : Precise Echo Sounding in Deep Water, Technical Report C&GS 37, Environmental Science Services Administration, Rockville, Md., 9 p., 1969. 92 INTERNATIONAL HYDROGRAPHIC REVIEW Officer, C. B. : Introduction to the Theory of Sound Transmission, McGraw-Hill, New York, pp. 229-230, 1958. Ryan T.V. and P.J. Grim : A New Technique for Echo Sounding Corrections, International Hydrographic Review, XLV, No. 2, pp. 41-58, 1968. Sverdrup, H.U., M.W. Johnson, R.H. Fleming : The Oceans, Prentice-Hall, Englewood Cliffs, N.J., p. 79, 1942. Wilson, W.D. : Equation for speed of sound in sea-water, Journal of the Acoustical Society of America, 32, p. 1357, 1960. Woods, J.D. : Wave-induced Shear Stability in the Summer Thermocline, Journal of Fluid Mechanics, 32, Part 4, pp. 791-800, 1968. 65 Reprinted from International Hydrographic Bureau Revi ew XLV II, No. 2, 85" 92 PRECISE ECHO SOUNDING IN DEEP WATER by Lt. Cdr. George A. Maul, USESSA Paper reproduced from ESSA Technical Report C&GS 37, Rockville, Md., January 1969, with kind permission of the USC&GS. IHB Note. In view of the increasing importance to bathymetry of accurate determination of the velocity of sound at the present time, we think it useful to reprint the present article — quoted in the references for the preceding article so that readers may be able to make a comparison between the arithmetical weighted mean and the harmonic mean methods. ABSTRACT The advent of narrow-beam stabilized echo sounders and shipboard digital computers is revolutionizing bathymetry measurements in the deep ocean. New and more precise procedures for obtaining and correcting depth measurements are described, and the application of these methods aboard the USC&GS ship Discoverer is presented. EQUIPMENT The United States Coast and Geodetic Survey ship Discoverer is equipped with a Narrow-Beam Echo Sounder (NBES) designed and built by the Harris ASW Division of General Instrument Corp. The performance specifications were provided the corporation by the Coast and Geodetic Survey. Among the specifications was that this echo sounder is to project a 12 kHz narrow sound beam to be effectively 2f degrees total beam (3 dB) down). The sound beam is gyro stabilized to ± 1 degrees of the local gravity vertical within the limitations of ±10 degrees pitch and ± 20 degrees roll. The depth resolution is ± 1 fathom at 4 000 fathoms. The sounding is displayed on a digital display to the nearest whole fathom, as well as on the conventional analog readout, a McKiernan-Terry Corp. Mark XV Precision Depth Recorder (PDR). The digital display of the NBES aboard the Discoverer was adjusted to provide an automatic correction for the average draft of the transducers. 94 INTERNATIONAL HYDROGRAPHIC REVIEW The Data Acquisition System (DAS) of the Discoverer is a Westing- house Prodac 510 processor utilizing a UNIVAC 1218 computer. The system is designed to collect, process, display, and store environmental data such as bathymetry, gravity, magnetics, wind speed and direction, and air and surface water temperatures; control data such as ship's course and speed, and position; and on-station data which includes water temperature, salinity, and velocity of sound as a function of depth. OPERATING PROCEDURE Prior to departure on a cruise, anticipated values of the velocity of sound are provided to the Coast and Geodetic Survey by the National Oceanographic Data Center. Computations are made from historical data using the empirical equation of W. D. Wilson [1]. The values provided to the ship are divided into applicable geographic zones. As the survey progresses from zone to zone, the values of the velocity of sound are changed to conform with the particular area of operations. An example of the geographic zones for a project is shown in figure 1. Fig. 1. — Geographic zones for velocity corrections. Corrections to soundings, as read from the sounding instrument, are changed as the trackline progresses from zone to zone. NARROW-BEAM ECHO SOUNDING [2 In this paper, the term sounding means the uncorrected reading of the echo sounder; depth means the vertical distance from the water surface PRECISE ECHO SOUNDING IN DEEP WATER 95 to the bottom. The term automatic depth input as used in the description of the data acquisition system means automatic sounding input. The narrow-beam echo sounder projects a signal at a repetition rate which is a function of the depth. If the water depth is in the range of 0-400 fathoms, a signal is projected once every second; if the depth is 400-800 fathoms, the signal is projected every 2 seconds, etc. This echo sounder is designed to receive the projected signal before the next sound burst is triggered. The first wave form of the returning sound pulse that exceeds a preset threshold level is used to measure the elapsed traveltime of the projected signal. The time count, which began with the trigger pulse, is stopped when the trend of the amplitude of this wave form is reversed (see figure 2). The elapsed time is converted to fathoms and is displayed on the digital readout. The mark on the precision depth recorder begins after the returning signal exceeds a preset threshold level, but before the amplitude is reversed, and lingers past the point of amplitude reversal until the threshold level is again reached. This produces a mark on the graphic recorder which varies from light to dark to light again as the signal passes. The change in density is not discernible to the eye. This implies that the digital sounding is not necessarily coincident with the leading edge of the mark on the recorder. This is illustrated in figure 2. Threshold level Point of amplitude reversal — — ■*— Receiver output PDR trace 1140 fm 1180 fm 1164 fm Fig. 2. — Superposition of the oscilloscope trace of the detected, filtered, and amplified receiver output over a section of PDR trace. The difference in digital and analog values depicted in figure 2 was taken from a test conducted aboard the Discoverer. The 3-fathom draft correction was subtracted from the digital value prior to the comparison. The apparent difference in soundings may be due to many factors among which are bottom slope, paper distortion, and instrumental error. It should be recognized that a 1-fathom difference will occur if the time from the threshold to amplitude reversal is 2.5 milliseconds. The digital value, with the draft correction, is automatically read into the data acquisition system when automatic depth input (ADD is initialized. For the sake of continuity, the digital readings are used to obtain soundings whenever the narrow-beam echo sounder is in operation. 96 INTERNATIONAL HYDROGRAPHIC REVIEW The narrow-beam echo sounder is a gated instrument. The gating switch is divided into ranges of 400 fathoms. This provides coordination with the scales on the precision depth recorder. If this switch is set at a range less than the sounding, the digital readings become erratic. If the setting is greater, the digital readings remain correct; however, the signal- to-noise ratio will decrease. A time-varied-gain (TVG) effectively provides greater receiver sensitivity with increasing depth. The echo sounder gating provides positive identification of the correct 400-fathom multiple, hence scale checks on the precision depth recorder are not necessary with the narrow-beam echo sounder operation. Scale checks may be easily accomplished on the Narrow-Beam Echo Sounder — Precision Depth Recorder by switching to the 0- to 4000-fathom scale on the graphic recorder; the gain on the Precision Depth Recorder usually must be reduced during this operation. The recording procedure is as follows : At the prescribed intervals, the sounding is read from the echo sounder digital display, and written on the graphic recorder trace for cross reference on the appropriate time mark. If automatic depth input is initialized in the data acquisition system, the sounding record is checked as the survey progresses. Manual entry requires check scanning at a later time. DATA REDUCTION Reduction of the soundings is accomplished by the data acquisition system on a real-time basis. The reading of the echo sounder is entered into the system either manually or automatically; manual entry is necessary when operating conditions require the manual override of the time-varied- gain. After processing for the velocity of sound, the depth is displayed on a Nixie tube readout, printed on the hydrographic and geophysical report typeouts, and stored on magnetic tape. Definitions of sounding velocity [3] and echo sounder depth [4] are now in order. Sounding velocity (Sv) is the weighted mean (Mn) of the velocity of sound (Vs) with depth (Z); that is, integrated velocity from the surface to the stated depth. Echo sounder depth (Ze) is the sounding the instrument will read in a water column whose sounding velocity is not identical with the instrumental velocity of 800 fathoms per second. The computer corrects the sounding for acoustic velocity in the follow- ing manner : The entered reading of the echo sounder is converted to time by dividing by the instrumental velocity of 800 fathoms per second. The computer then searches a listing of sounding velocity versus echo sounder depth; a linear interpolation is performed between the tabulated values for the applicable sounding velocity. The corrected depth is calculated by multiplying the sounding velocity by time. The sounding velocity may be derived from the basic equation for the weighted mean [5] of any parameter : PRECISE ECHO SOUNDING IN DEEP WATER 97 Mn = l=n 2 X,Q, i = \ (1) where Q{ is any variable and X{ is the interval over which Q( is applicable. In order to determine the mean velocity from the surface to a stated depth, it is assumed that linearity exists between the point sources of the data as shown in figure 3. VELOCITY Or SOUND "VT; a. A2 • < ■ ■■ ■ A r > 7 v». i v»m Vso u 0 Zi-l- Zi ■ JJ- 1 r Fig. 3. — Point to point distribution of velocity of sound versus depth. Consider the case of Z< to Z<_1, the mean velocity can be written : The bounded interval over which this value applies is : Z( must always be greater than Z{_1. Substituting into equation (1) : Mn = I AZ,Vs, i=n 2 AZ, = Sv. (2) 98 INTERNATIONAL HYDROGRAPHIC REVIEW The denominator when expanded : 2 AZ, = AZ, + AZ2 + AZ3 + • • • + AZ„ = z, - z0 + z2 - z, + z3 - z2 + • • • + z„ - z„_t = - Z0 + (Z, - Z,) + (Z2 - Z2) + . . . + z H = - z0 + z„ but Z,„ the su rfaee = o, therefore 2 az, = z„ Rewriting (2) 2 v*/ AZ< z„ 1 /=n _ = 7"2 V5,AZ, (3) The summation is from Z = 0, the surface, to Z — n, the depth to which the integration is desired. The function Vs is continuous on the closed interval 0 ^ Zt ^ Zn, hence the definite integral exists, and the equation may be written : 1 rz- Sv = - / Vsdz (4) Z ''o The integral is evaluated numerically be means of the trapezoidal rule. The entering arguments of Vs and Z are the tabulated values at the standard oceanographic depths. The standard oceanographic depths are enumerated in appendix 1. The average velocity of sound (Vs) is calculated for the standard oceanographic layers. An example of these calculations is shown in appendix 1. A graphic illustration of sounding velocity, velocity of sound, and instrumental velocity is shown in figure 4. Computer programming of sounding velocity is accomplished by substituting into equation (3) the expressions for Vs{ and AZ( above, and developing the following algorithm : Sv = 4~ 'f (Z, - 1i-, ) (V*, + VVl ) (5) The echo sounder depth (Zs) is derived from the basic equation : Distance = time (T) x speed. For an instrument calibrated for a standard speed of sound in sea-water of 800 fathoms per second : Zs = T x 800 fm/s = Tx 1463.04 m/s (6) The metric conversion is based on the U.S. Survey Foot which by definition equals 1200/3937 metre exactly. PRECISE ECHO SOUNDING IN DEEP WATER 99 0000 1460 VELOCITY ( Meters per second ) 1480 1500 1520 1540 1000 2000 T £ 2 3000 in • a 5 4000 5000 t+f^ y ? > /J o > _L "5 O _i hi > 2 z Ul % .3 \ ^ t y q * \ v^ 6000 Fig. 4. — Velocity as a function of depth. True depth <*' (Zt) has the same relationship to time : Z, = T x Sv Solving the simultaneous equation for echo sounder depth : Z, x 1463.04 Z. = Sv (7) (8) The sounding velocity in equation (8) is the applicable value for the true depth. These calculations are shown in the example in appendix 1. (*) "True depth" is understood to mean precise in the theoretical sense; the accuracy of the value is not implied. 100 INTERNATIONAL HYDROGRAPHIC REVIEW An example of the computer listing for the calculations in appendix 1 is shown in appendix 2. A gradient is applied to best fit the historical data beyond the deepest tabulated value. The original data acquisition system programming would not allow the numerical value of the depth to exceed the value of the sounding velocity in the listing. Effectively this meant that the gradient had to be linear from 1500 metres to the bottom. The data acquisition system software was changed to correct this situation. The use of sounding velocity computations is a computer application of the basic method of hand corrections outlined in Pub. 20-2, Hydrographic Manual [6]. Sounding velocity computations have been used aboard the Discoverer since she went into operation in July 1967. The refinement of interpolating with echo sounder depth as the entering argument, as suggested by Ryan and Grim [7], is now in effect. LIMITATIONS IN SHOAL WATER The procedure of adding the draft of the transducers to the echo sounder depth prior to processing the sounding for acoustic velocity will introduce an error in shoal water. It is desired to keep all errors less than | of 1 percent of the depth. That is : 0.5 % = % error = hZll x ioO (9) Z where Zc is the computed depth. The true depth and the computed depth may be written in the following form : + d (10) 1463 - ("> where d is the draft of the transducers in metres. Substituting equations (10) and (11) into equation (9) and solving for echo sounder depth, it can be stated that an error that exceeds | of 1 percent of the depth will be introduced if : [294063 200~~~s7~J (12) Consider the case of a Class I Oceanographic Survey Vessel whose draft is approximately 6 metres. If the sounding velocity is a rather high 1 542 metres per second, an error that exceeds ^ of 1 percent of the depth will be introduced when the fathometer depth equals 55.8 metres (30.5 fathoms). Due to signal blanking, the narrow-beam echo sounder is not usable PRECISE ECHO SOUNDING IN DEEP WATER 101 in depths less than 40 fathoms. Furthermore, current project instructions require the use of a shoal water echo sounder in depths less than 100 fathoms. Hence, the narrow beam sounder coupled with the data acqui- sition system will not under even these extreme conditions, inadvertently introduce this error. FUTURE REFINEMENTS Many of the refinements suggested by Ryan and Grim [8] in area surveys recognize the fact that off-line postsurvey processing is necessary. On-line, real-time processing depends on the use of historical data. This is an obvious shortcoming of the Discoverer's method. It must be recogniz- ed, however, that a practical limit may have been reached with the present sate-of-the-art that warrants additional equipment and processing un- economical. A compiler language program for the Westinghouse Prodac 500 of the sounding velocity and fathometer depth is given as appendix 3. This program can be adopted to provide on-station, real-time, calculation of these parameters for multisensor data input, as well as off-line processing of historical data or Nansen cast data. The addresses in the program were arbitrarily chosen and will have to be changed for use with the present data acquisition system on-station programs; the scale factors (B4 for velocity of sound, and B0 for depth) conform to the scaling in the present system on-station program. This scaling satisfies the accuracy of the data input. CONCLUSION This report represents a cohesion of ideas into a working system. The equipment and methods presented will reduce the labor of processing, and improve the accuracy of deepwater soundings. REFERENCES [1] Wilson, W. D. : Equation for speed of sound in sea water. Journal of the Acoustical Society of America, Vol. 32, p. 1357, 1960. [2] Technical Manual, Narrow-beam Echo sounder, Vol. 1, System Descrip- tion, General Instrument Corp. [3] Sverdrup, H. U., Johnson, M. W. and Fleming, R. H. : The Oceans, Prentice-Hall, Englewood Cliffs, N.J., p. 79f, 1942. 102 INTERNATIONAL HYDROGRAPHIC REVIEW [4] Ryan, T. V. and Grim, P. J. : A new technique for echo sounding corrections. International Hydrographic Review, Vol. XLV, No. 2, pp. 41-58 (1968). [5] James, G. and James, R. C, Editors, Mathematics Dictionary, Van Nostrand, Princeton, New Jersey, p. 380, 1949. [6] Jeffers, K. B. : Hydrographic Manual, Publication 20-2, U.S. Coast and Geodetic Survey, Washington, D.C., p. 182 ff, 1960. [7] Ryan, T. V. and Grim, P.J. : Op. cit., ref. [4]. T81 Ibid. PRECISE ECHO SOUNDING IN DEEP WATER 1(13 APPENDIX 1 z, Vs AZ Vs AZx Vs ZAZ x Vs ZAZ x Vs Ztx 1463.04 z, = — ' Sv OK z, 0 1542.0 10 1542.1 15421 (1542.0) 0 10 1542.2 10 1541.9 15419 15421 1542.1 9.5 20 1541.6 10 1541.2 15412 30840 1542.0 19.0 30 1540.7 20 1539.8 30796 46252 1541.7 28.5 50 1538.8 25 1538.2 38455 77048 1541.0 47.5 75 1537.5 25 1536.6 38415 115503 1540.0 71.3 100 1535.8 50 1533.7 76685 153918 1539.2 95.0 150 1531.6 50 1529.8 76490 230603 1537.4 142.7 200 1527.9 50 1526.4 76320 307093 1535.5 190.6 250 1524.8 50 1523.9 76195 383413 1533.7 238.5 300 1523.0 100 1521.2 152120 459608 1532.0 286.5 400 1519.5 100 1516.8 151680 611728 1529.3 382.7 500 1514.1 100 1510.8 151080 763408 1526.8 479.1 600 1507.6 100 1505.2 150520 914488 1524.1 576.0 700 1502.7 100 1500.0 150000 1065008 1521.4 673.1 800 1497.3 200 1494.6 298920 1215008 1518.8 770.6 1000 1492.0 200 1491.8 298360 1513928 1513.9 966.4 1200 1491.6 300 1492.3 447690 1812288 1510.2 1162.5 1500 1493.0 500 1495.6 747800 2259978 1506.'/ 1456.5 2000 1498.3 500 1500.2 750100 3007778 1503.9 1945.7 NOTE. — Z, is the standard oceanographic depth in meters. Vs and Si» are in meters per second. 104 INTERNATIONAL HYDROGRAPHIC REVIEW z, Vs AZ Vs AZx Vs £AZ x Vs 2AZ x Vs <\v — Z,x 1463,04 Z. = — — ' Sv z, 2500 1502.2 500 1507.0 753 500 3757878 1503.2 2433.2 3000 1511.7 1000 1519.7 1519700 4511378 1503.8 2918.7 4000 1527.7 1000 1536.2 1536200 6031078 1507.8 3881.3 5000 1544.7 7567278 1513.5 4833.3 APPENDIX 2 Interpolation Computer Listing Sv z, DVP(') 1542.0 0 1542/0000/ 1541.0 47.5 1541/0048/ 1540.0 71.3 1540/0071/ 1539.0 100.3 1539/0100/ 1535.0 203.9 1535/0204/ 1532.0 286.5 1532/0286/ 1529.0 394.3 1529/0394/ 1527.0 471.4 1527/0471/ 1524.0 579.6 1524/0580/ 1521.0 688.1 1521/0688/ 1519.0 763.1 1519/0763/ 1514.0 962.4 1514/0962/ 1510.0 1179.3 1510/1179/ 1507.0 1481.7 1507/1482/ 1504.0 1928.2 1504/1928/ 1503.2 2433.4 1503/2433/ 1504.0 2966.8 1504/2967/ 1508.0 3914.7 1508/3915/ 1513.0 4749.5 1513/4750/ Gradient = _ T2 G/+.00599/ z2-z, _ 1513.5- 1507.8 " 4833.3 - 3881.3 = + 0.00599 (*) The computer listing will accept integers only for the values of sounding velocity and echo-sounder depth. To minimize error, interpolations for integer values of sounding velocity are performed; only values of echo-sounder depth are rounded to the nearest meter. The program will accept up to nineteen points in the form of four-digit numbers. The left column of the computer listing is the sounding velocity; the right column is the depth. The gradient is applied at depths greater than 4 750 meters. PRECISE ECHO SOUNDING IN DEEP WATER 105 APPENDIX 3 Address Instruction Remarks 33333 ELC 1234 arbitrary non-zero constant 33334 JLZ 3344 33335 STZ 3410 clear register 33336 STZ 341 1 Do 33337 STZ 3412 Do 33340 STZ 3413 Do 33341 ELC 0 33342 ENB 3341 33343 STB 3333 3333 ELC 0 33344 ENL 3411 Vs,_, scaled B4 33345 JLZ 3367 33346 ADD 6010 + Vs, scaled B4 33347 STL 3414 Vs, + Vs,_, 33350 ENL 6011 Z, scaled B0 33351 SUB 3410 — Z,_, scaled B0 33352 JLN 3402 33353 JLZ 3402 33354 MPL 3414 x Vs, + Vs,_, 33355 ADA 3412 + 2 33356 STU 34131 2 (Z, - Z,_,) (Vs, + Vsy_,) scaled B4 33357 STL 341 2 J 33360 ELC 2 33361 MPL 601 1 x Z, 33362 STL 3416 2Z, 33363 ENL 3412 33364 ENU 3413 33365 DIV 3416 *2Z, 33366 STL 3415 = Sv scaled B4 33367 ENL 6010 33370 STL 3411 new Z,_j 33371 ENL 6011 33372 STL 3410 new Vs,_l 33373 ENL 3415 33374 RSL 4 33375 STL 3420 = Sv scaled B0 33376 ELC 2667 26678 = 146310 33477 MPL 6011 x Z, 33400 DIV 3420 * Sv scaled BO 33401 STL 3417 = Z, scaled BO 33402 1000 STOP 36010 36011 Program Input Addresses Vs, scaled B4 (input from the multisensor Z, scaled BO ) during on-station operations 106 INTERNATIONAL HYUHOGRAPHIC REVIEW List of Mnemonics Mnemonic Meaning ELC Enter AL with constant Y JLZ Jump on (AL) zero to Y STZ Set (Y) to 0 ENB Enter B with (Y) STB Store (B) in Y ADD Add (Y) to (AL) STL Store (AL) in Y ENL Enter AL with (Y) SUB Subtract (Y) from (AL) JLN Jump on (AL) negative to Y MPL Multiply (AL) by (Y) ADA Add (Y + 1 , Y) to (A) STU Store (AU) in Y ENU Enter AU with Y DIV Divide (A) by (Y) RSL Right shift (AL) by k positions Where AL is the lower accumulator AU is the upper accumulator A is the AU and AL (36 bit word) B is the B register (Y) is the contents of Y Y is the address 66 .-^ENTo^ Sc'tMC[ StR^tVS>" U.S. DEPARTMENT OF COMMERCE Maurice H. Stans, Secretary ENVIRONMENTAL SCIENCE SERVICES ADMINISTRATION Robert M. White, Administrator RESEARCH LABORATORIES Wilmot N. Hess, Director ESSA TECHNICAL REPORT ERL 167-AOML 2 An Oceanographic Investigation Adjacent to Cay Sal Bank, Bahama Islands ROBERT B. STARR ATLANTIC OCEANOGRAPHIC AND METEOROLOGICAL LABORATORIES PHYSICAL OCEANOGRAPHY LABORATORY MIAMI, FLORIDA June 1970 For sale by the Superintendent of Documents, U. S. Government Printing Office, Washington, D. C. 20402 Price 55 cents. TABLE OF CONTENTS ABSTRACT 1 1. INTRODUCTION 1 2. PROCESSING AND DISPOSITION OF THE DATA 4 3 . SETT ING 8 i+. OCEANOGRAPHIC BACKGROUND 9 5. TIDES AND TIDAL CURRENTS 12 6. OCEANOGRAPHY 17 7. THE SURFACE CIRCULATION 30 8. THE SUBSURFACE CIRCULATION 32 9. SUMMARY AND CONCLUSIONS 44 10. REFERENCES 47 APPENDIX A DRIFT BOTTLE RECOVERY RECORD 49 APPENDIX B SUMMARY OF SHIP'S DRIFT, WIND DATA, AND WIRE ANGLES ON OCEANOGRAPHIC STATIONS 51 ILL AN OCEANOGRAPHIC INVESTIGATION ADJACENT TO CAY SAL BANK, BAHAMA ISLANDS Robert B. Starr Forty^-seven oceanographic stations were occupied in the Cay Sal Bank region of the Straits of Florida to investigate the water structure in the straits here and in the entrances to Nicholas and Santaren Channels. The water exchange through Nicholas Channel appears to be negligible; Santaren Channel contributes water to the northern Florida Straits below 3 50-m depth. Evidence of a possible south-flowing countercurrent in the Straits of Florida is also presented. 1. INTRODUCTION An investigation of the physical and geological oceanogra- phy of the area of the Straits of Florida adjacent to Cay Sal Bank was conducted from June 20 through 26, 1962. This study consisted of k-7 oceanographic stations and bathythermograph observations. There were 22 bottom sediment cores taken and a release of 10 drift bottles at each station. The locations of the stations are shown in figure 1 and were planned to investigate the water structure across Nicholas and Santaren channels, as well as the Straits of Florida to determine the effect of Cay Sal Bank on this structure and to learn the nature of the bottom in the area. * The layout and numbering of sections (see figs. 7_ll) are shown in figure 1. 80° CUBA ^Z? OCEANOGRAPHIC STATIONS O NANSEN CAST — BOTTOM SAMPLE NAUTICAL MILES To ! 20 KILOMETERS 30 80° _1_ 30' Figure 1. Chart of station locations, section locations, and general bathymetry (in meters). The observations were made from the USC&GSS HYDROGRAPHER by the writer and Dr. Robert E. Burns, assisted by the officers and crew. The HYDROGRAPHER was commanded by Captain Raymond E. Stone. Ship's navigation was by Loran A, radar, and visual fixes The depths of 100 fathoms along the Florida Keys and 200 fathoms elsewhere were used as a secondary control when it was desired to position stations relative to the banks bounding the area. Fixes were taken every 15 min while the ship was on station so that when Loran reception was good or when the ship was close to land relative positions for deter- mining the ship's drift were good to one-quarter mile. The plotted locations of the stations are accurate to 1 n mi, except when Loran reception was poor well away from land (see fig. 1). The oceanographic stations consisted normally oT 2-8 bottle Nansen casts with modifications for shallow depths. These were taken starting from the surface to as near bottom as possible. A 180 lb steel ball was used as the Nansen cast weight to keep wire angles at a minimum. A bathythermograph observation to 900 ft or the bottom was taken at the time of each shallow cast. All Nansen bottles were equipped with two deep-sea reversing thermometers, except one had three. Five unpro- tected thermometers were used on each cast for thermometric depth determinations. The thermometers had been recently calibrated at the Naval Oceanographic Instrumentation Center and were periodically exchanged among the bottles to reveal malfunctions or erratic operation. The water samples for salinity analysis were bottled in aged citrate of magnesia bottles and shipped to Washington, D, C, where their salinities were determined by dual analyses on a South African conductive salinometer. Check analyses on a selected batch of samples were run on a HYTECH inductive salinometer. 2. PROCESSING AND DISPOSITION OF THE DATA Processing of the serial oceanograph:' c data included plotting station profiles of temperature and salinity against depth, the plotting of individual Temperature- Salinity (T-S) curves, and the comparison of these against a composite T-S curve. This composite curve is shown in figure 2. The verified station data were then transmitted to the National Oceanographic Data Center, where standard depth interpolations for the stations were made and the dependent parameters computed. A machine listing of the station data was then reviewed, density as sigma-t (a-^) was plotted as a check, and hand interpolations of tempera- ture and/or salinity were made where the machine ones were unacceptable. The final listings are available from NODC. 35.0 35.4 SALINITY 35.8 %, 36.6 37.0 28 24 20 u 16 Q. 12 ] i 1 i jy ai— i "XtT^ — -^ " ~ts . 23^ - 50 ^ 1/ £s 9>0^ ^^ 150 // <§ - y^ 300 - Ob^ - ^l> jr^^y/ ^y^ /& - ¥\ 800 - i x i 1 l i Figure 2. Composite Temperature-Salinity (T-S) Diagram. Depths Nlcwln mf fS;, ?° yth Atlantic Cent^l Water shown by line marked NACW, and South Atlantic Central Water shown by line marked SACW. The NODC reference number is 310I+2. Except where questioned, the depths of the individual observations are considered to be accurate within 5 m, the temperatures to ±0.02°C, and the salinities to -0.01& with relative accuracy to 0.003%» Where two protected thermometers were paired, the average was used in most cases, but where the thermometers differed by more than 0.05°C, the more reasonable value was used. This some- times happeded with observations in the steep thermocline, probably because of different thermal responses of the thermometers . The bathythermograph observations taken on the oceano- graphic stations are available from NODC as cruise number 5296. The individual traces at the station locations are re- produced in figure 3* The 28 returns from the L+60 drift bottles released are listed in appendix A. These amount to a 6.1% recovery, all of which came from only 11 of the h6 locations where bottles were released. The nine bottles recovered from station 38 account for 32.1% of all returns. Twenty-two bottom sediment cores were taken with 60- and 80- pound Phleger Corers with 3~foot barrels. Immediately after recovery, the cores were preserved with 5ml of alcohol and sealed. Their visual physical characteristics were logged, and they were stored in the ship's refrigerator. These cores were transferred to Florida State University and used by Figure 3. Bathythermograms taken at the o ceanographic stations. Donald Milligan as part of a Master's thesis (Milligan, 1962). 3. SETTING Cay Sal Bank may be considered an outlier of the Florida- Bahama Province. This province is not a continuous platform now but consists of extensive shallow water areas of general- ly less than 20 m depth transected by narrow, relatively deep channels of which the Straits of Florida and Santaren and Nicholas channels are examples. These are shown In figure 1 with their general bathymetry. The Cay Sal Bank area is located where the trend of the Straits of Florida changes from generally east-west to north- south. This change in conjunction with the bank and its associated Santaren and Nicholas channels significantly influneces the Florida Current. Since the current probably reaches to the bottom in this part of the straits, a knowledge of the general bathymetry (fig. l) and the con- trolling sill depths is necessary for understanding the structure of the current in this area. Recent Coast and Geodetic Survey soundings in the northren Straits of Florida have established that depths increase gradually from a sill of 730 m at Latitude 27°20°N., Longi- tude 79°3I+,W. This southward gradient increases appreciably west of Cay Sal Bank. The straits are also considerably wider from this point to the west (fig. l). The sill of the 8 Yucatan Channel between Cuba and Mexico at 2,100 m (C&GS Chart 1007) is so deep that it does not restrict the water properties of the straits. The relatively wide and shallow Santaren Channel joins the Straits of Florida northeast of Cay Sal Bank, while the deeper but narrower Nicholas Channel connects with the straits southwest of the bank (fig. 1). At the southeast end of Cay Sal Bank, Santaren and Nicholas channels merge into the Old Bahama Channel that separates the Great Bahama Bank from Cuba. The sparse sounding data from these channels indicate that their controlling sill depth occurs in the Old Bahama Channel and is roughly ^10 m. This channel also is considerably narrower than either Santaren or Nicholas Channel (C&GS Chart 1002). if. OCEANOGRAPHIC BACKGROUND The water masses occurring in the Cay Sal Bank area are defined best by referring to the composite Temperature- Salinity (T-S) curve of the oceanographic stations (fig. 2). This reveals the admixture of several water masses of diverse origin. The scatter in the plot to about 75~^ depth reflects the influence of locally generated modifications, particular- ly a secondary salinity maximum at 50 m, which is apparently caused by the sinking of relatively dense bank water intro- duced into the Bahamian and Florida Keys margins by tidal currents . Below this surface layer the main salinity maximum of 36.60 to 36.77%oat an average sampled depth of 150 m com- prises a relatively thin stratum of water that Wust (1961+) calls the Subtropical Underwater. This is water that has passed through the Yucatan Channel from the Caribbean Sea. It appears likely that the maximum salinity of this stratum lies closer to 125~m. depth, but this level was not sampled frequently enough for this to be established. The 100-m salinity of 36.99%oin this layer at station 10 appears anomalously high, but it has been retained because there appeared to be no evaporation from the sample bottle and because there was a 0.07°C. temperature inversion at this depth established with paired reversing thermometers and the BT observation. Furthermore, the density determined from these data did not imply instability. The lower salinities evident at 150 m occurred in the stations taken in the center and left-hand side of the Florida Current. These correspond to the Continental Edge Water of Wennekens (1959), which he interprets as being derived from the surface waters of the northern and eastern Gulf of Mexico and having sunk to their equilibrium level after winter cooling. Below 300 m, local and seasonal effects disappear from the composite T-S plot so that from 300 to about 700 m the curve reflects, for the most part, the result of a mixture 10 of North Atlantic Central Water with some South Atlantic Central Water. The influence of the South Atlantic Central Water appears to be most prominent at about 550 m (27*0 cr+. level) where it comprises up to 30% of the water type (fig. 2), but most of the water in this range is of North Atlantic origin. In particular, stations 2, 9, and h2 (see fig. l) appear to have relatively high percentages of North Atlantic Water at some levels. The minimum salinity evident in the T-S curve at roughly 800 m indicates the influence of Antarctic Intermediate Water. This water, which is also known as Subantarctic Intermediate Water, is considered to be formed at the Antarctic Convergence by mixing and sinking of Antarctic and Subantarctic surface waters. As the resulting water mass moves north it gradually mixes with adjacent waters so that by the time it reaches the North Atlantic at about 27° N. Latitude, the salinity minimum used to trace this water is gone. Its presence in the Straits of Florida with a value of 31+«87 ^indicates an appreciable quantity of water of South Atlantic origin at about 800 m. The observations below the salinity minimum show a posi- tive gradient in the salinity to the greatest depths sampled. This reflects the presence of Upper North Atlantic Deep Water with possibly the traces of an admixture of Mediterranean Water. These depths were attained at only the stations west 11 of Cay Sal Bank, and were well below the sills to the north and east. While for any level above the minimum, salinity increases to the right in the Florida Current, below the minimum it increases to the left. Temperature apparently always decreases to the left. 5. TIDES AND TIDAL CURRENTS Because the channels of the Cay Sal Bank area are rela- tively restricted, there is an appreciable bathymetric influence on the currents. Since tides and tidal currents become amplified in restricted waters, their effect probably influences the oceanographic station observations signifi- cantly; consequently, some of the irregularities evident in the charts and sections of properties may reflect tidal modification of the water column depending on the time of the individual station relative to the tidal cycle. The predicted and observed tides at Key West, the nearest reference station, were compared for the period of the oceanographic stations and were in good agreement. These, in turn, were compared with the tide predictions nearest the oceanographic stations at Elbow Cay on Cay Sal Bank and Tennessee Reef on the Florida Keys side of the straits. While Key West has a mixed tide, the tide at Elbow Cay and Tennessee Reef is predominantly semidiurnal. According to Dietrich (1963) the tide wave progresses upstream against 12 OJ P. or 03 O) -p ■H -UOOfsJ UOO|\| -UOO|s) UOO|\| — uoo|s| C£ CO CO LU Z z UOO|s| ■ UOOfsl u Z> Q < > o z o _ o 0 c o P o) "I d o •rH P 03 +J CO cO OJ P oj ^! C • Cfl P PQ X OJ l-H +J CO 00 o) >> 4-> CO u d •r-l 0) ,d T3 -P OJ d d T-l •i-l CO I-H CO CL <1) X > OJ (-1 o OJ X) •r-l P OJ OJ P CJ •r-l OJ 0) P OJ u •l-l 13 the flow of the Florida Current. Tidal current data in the area are available as pre- dictions only, and these are restricted to the Florida Keys side of the straits. In figure h, the predicted tide at Tennessee Reef is presented with the closest tidal current predictions at a point east of Long Key Drawbridge and at Lcng Key Viaduct. The direction of flood current at these sites is north and of the ebb current, south. Also included in this figure are the messenger times of the shallow casts of the oceanographic stations taken adjacent to the margins of the channels and of those that show the shallow, secondary salinity maximum. This secondary maximum has its greatest areal development along the Florida Keys but is more saline by approximately 0'3%oal°ng "the Bahama Banks. Along the Florida Keys the salinity gradient indicates a source from the west, but the gradient along the Bahama Banks indicates a warm saline tongae with a probable northern source. This is corroborated by the ship's drift at station 7 (fig- 5) • Station 3 along the Bahama Banks that would be expected to show the shallow maximum but did not was outside of this tongue. This salinity distribution is evident on the 50-m depth chart (fig. 6). None of the southern stations along Cay Sal Bank and the Cuban coast show the secondary maximum. This is due possibly to the phase and speed of the tidal currents during 14 81° 30' 80° 30' ( r / - Q \ \ \ \ ► .."' J / 1 1 A *\ / l 0 \ \ \ 25° 30' vjra / J / k ^ ^ ■■jL..J>V> / / \ \ 0 „ '- £<=" 7 °v / 7- / •6- 'O' i rn • r-, 1 ... /\/.o'^ /: 1 ■. on / ■■ "1 * .r ■■/' A ( t / / 1/ / / '■■-. > a 24° / \ U '; J < ' 7/ : fc » ~ .." 24° /...'■ , D cV tf K- 1 \ \ \ / ■■■■ /// /// / / // \ \ \ 23 2°V •• \ \ \ 30' ■■■■■■■y V , N,c^ 30' X* r °c — TEMPERATURE - SALINITY • DENSITY (Sigmo-t) •26.0°C .-y — > 28c SURFACE —. CURRENT SPEED SCALE NAUTICAL MILES 0 10 20 30 KILOMETERS VUD^^^ ^i...^! 0 12 3 KNOTS 0 20 40 60 81° 30' 80' 30' Figure 5. Distribution of temperature, salinity, and density at the sea surface. Arrows are vectors of ship's drift. Zero indicates no discernible drift. 15 81° 30' 80" 30' / d i T \ "X y / Q \ \ P- /*• if A ^\ / i 0 \ \ 25° 30' J1* / ( / k <7* p- / / \ \ 0 i; ? ? / : o ' *• . 1 I / \Z 1b .c / t/CA / V\ ,< ...-•■ /,'••' ,>>7... . \ ""<< / /-■■ ) ...23.8a; _ o -•23.8a,-- •;• f/:\\ •-•..« Vff a 3 24° ^^ / \ •• b1 * V'H- 3 o -^ 24° a1 ^^ -A y' to _.-' ;/ /$?". / I ^-260° si>1 B * ^ K. \ \ \ \ \ \ 'Z- <^ <^ -1. 30' ../' / : \ \ 30' .■••:'Jfi \s^ : —, CURRENT SPEED SCA LE 3 KNOTS V - SALINITY gma-l) TW 50 METER DEP 50 meters = 27.3 fart NAUTICAL MILES 0 10 20 30 KILOMETERS ^^ *£,**■ i 0 20 40 60 8 1° 30 80° 30' Figure 6. Distribution of temperature, salinity, and density at 50 m. Arrows are vectors of ship's drift. Zero indicates no .discernible drift. 16 the time these stations were occupied (fig. h) , but it is more likely due to the lack of a shallow area of adequate size for evaporation to produce high salinities. The higher average velocity and longer duration of flow of the ebb current compared to the flood current at Long Key indicate that the net transport of water is from the Gulf of Mexico side of the Keys into the Straits of Florida. The water introduced into the western, side of the straits by this net transport is probably the source of the secondary salinity maximum found here. 6. OCEANOGRAPHY The results of the HYDROGRAPHER oceanographic stations are presented in the accompanying charts and sections of the distribution of temperature, salinity, and derived sigma-t (cr-f)*. Isopleths of sigma-t are a convenient ex- pression for the density of water at surface pressure for a given temperature and salinity. They approximate the distribution of potential density very closely and may be considered as defining quasi-isentropic surfaces. Since these isopleths indicate the variation of density at any given level, they are useful for determining the approximate * The layout and numbering of sections (see figs. 7-ll) are shown in figure 1. 17 STATION 46 45 44 43 M- ' l TEMPERATURE NUMBER Figure 7a. Distribution of temperature (in degrees Celsius) along section 1. SALINITY STATION 46 45 44 43 J I L NUMBER II 10 5 4 3 I _ I _ J I ■ II Figure 7b. Distribution of salinity (in parts per thousand) along section 1. 18 STATION 46 45 44 43 1 I L SIGMA - T NUMBER 11 10 5 J L Figure 7c. Distribution of density (as Sigma-T) along section 1. 19 TEMPERATURE a 500 5 •y 600 J L J L J I I L Figure 8a. Distribution of temperature (in degrees Celsius) along section 2. SALINITY STATION 29 24 _1 I I 5 2 600 - J L J L _L 1 1 J I I I I I Figure 8b. Distribution of salinity Cin parts per thousand) along section 2. STATION 29 24 23 _l I L SIGMA - T NUMBER 12 9 z 600 J I Figure 8c. Distribution of density (as Sigma-T) along section 2. 2] TEMPERATURE 22 20 J | I .J J 600 - J ! L J L J I I L Figure 9b. Di of salinity C In parts per thousand) alo J 600 z x 700 a. UJ Q 800 J I I L J I L Figure 9c. Distribution of density (as Sigma-T) along section 3. en 1- 7—1 0 (1) ■F-l ) 4-» CJ U) ■< 0) ■/: 0) 03 u e 3 bO SM313W Nl Hid3Q 24 m o) 11 to (1) u bl W) e a 0 a hfl 4J • r-J o m b 1) in u. m b N-' S8313W Nl Hld3Q 25 relative velocity of currents that are related to the distri- bution of mass by applying the rule that, except for near- surface anomalies, in the northern hemisphere the lighter water lies on the right side of a current. The relationship of the water properties and the deduced currents in the vicinity of Cay Sal Bank to those near the adjacent banks is seen best on the charts (see figs. 5, 6, 12, 13 & l*+)> while the sections (see figs. 7~ll) illustrate the distribution of properties and the characteristics of the water masses in the Florida Straits and adjoining channels. The layout and numbering of the sections are indicated in fig. 1. These are drawn at a vertical exaggeration of approximately 120 to 1. The charts present the distribution of properties and sigma-t at the surface, 50, 150, 300, and 600 m. Levels below 600 m are not shown, because greater depths exclude over h0% of the stations including all of those in Santaren Channel. The surface and 50-m depth charts include current velocities derived from the ship's drift on station when the positioning was considered reliable and wind speeds, for the most part, were 12 knots or less. These wind speeds were read from the ship's anemometer. Wind velocities up to 20 knots were accepted on stations where the ship drifted into the wind or where the ship was in the high velocity core of the Florida Current. The current and wind velocity data for 26 81° 80° U B A ^^ Figure 12. Distribution of temperature, salinity, and density at 150 m. 27 Figure 13. Distribution of temperature, salinity, and density at 300 m. 28 Figure 14. Distribution of temperature, salinity, and density at 600 m. 29 the acceptable stations are summarized in table form in appendix B with the wire angles and directions of the oceano- graphic casts. 7. THE SURFACE CIRCULATION In the central portion of the Straits of Florida the high drift velocities found correspond to water temperatures above 28.0° C, except for station 20 (see fig. l) which appears to be influenced by upwelling (fig. 5)« The distri- bution of surface salinity does not correlate as well with the deduced current, except perhaps for a low salinity tongue associated with a southeastward drift in the entrance of Santaren Channel. Here low salinities at stations 6, 7 and 10 (see fig. 1 and 5) are possibly analogous to those associ- ated with the high velocitycore of the stream, but at these stations they seem to coincide with a zone of transition between Straits of Florida waters and those found in Santaren Channel. This zone of transition is defined by the 36.2%c salinity band on the surface chart (fig. 5) and is apparent in the near-surface layering evident in the BT traces at these stations (fig. 3). In Santaren Channel a thin film of slightly warmer surface water is apparent at the southern stations along the Bahama Banks side, and there is an appreciable salinity increase toward the banks as well (see fig. 7 and fig. 5). A much 30 more varied temperature and salinity distribution is evident here than in Nicholas Channel. Along the western side of the Florida Straits, the cause of a relatively low salinity at station ^0 (fig. 5) is unknown but it is not from rain or contamination from ship overboard discharge. A decrease in velocity near Cay Sal Bank in the Straits of Florida is apparent in the reduced drift at stations 19 and 22 and by the absence of a detectable current at station 16, while a northwesterly drift was found at station 15 (see fig. 1 and 5)« These stations were all within visual bearing and radar range of the cays on Cay Sal Bank. The high surface density at station 19 and configuration of the adjacent isopycnics suggest upwelling, which appears on section k (see fig. 10) to be from a depth of about only *+0 meters. This probably reflects a damming effect on the subsurface high velocity core of the Florida Current by Cay Sal Bank. The ship's drift, surface temperature and salinity, and density structure evident in the western entrance to Nicholas Channel agree, in that, except for a possible southward drift at the three eastern stations north of Cuba (fig. 5), little appreciable surface current appears to exist here. This southward drift may be the eastern side of a weak anti- cyclonic gyre. Santaren Channel, however, as noted previous- ly, does not seem to be quite so passive. Here the velocity decrease indicated by the reversal of slope of the near 31 surface isopycnics along the Bahama Banks extends to a depth of only about 20 m, as is evident in sections 1, 2, and 3 (see figs. 7, 8, and y) . The associated surface salinity gradient is the result of high salinities generated on the bank in the lee west of Andros Island (Cloud, 1962). The low salinity tongue with corresponding relatively low temperatures and resulting 23A isopycnic extending north- east from Cay Sal Bank (fig. 5) not only separates the northerly flow of Santaren Channel from the Florida Straits water but appears to represent a zone of mixing and a path of southerly flow toward Cay Sal Bank. Unfortunately most of the ship's drift observations in this area were unaccepta- ble, but those at stations 1, 2, and 3 (see figs, 1 and 5) support the interpretation of a slow northerly flow decreas- ing in velocity toward the banks, while observations at stations 7, 15, 1^, and 13 indicate that this zone may be the eastern side of a gyre between the Florida Current and the Santaren Channel outflow (fig. 5) • This inference is also upheld by the sigma-t structure in sections 1, 2, and 3 (see figs. 7, 8, and 9) which indicates that this circu- lation is more than 100 m deep. 8. THE SUBSURFACE CIRCULATION The 50-m depth was chosen as one of the levels to show the distribution of properties because its proximity to the 32 surface permits correlation with the drift measurements and it reflects the oceanographic conditions associated with the highest current velocities, but it is deep enough to be out of the influence of short term meteorological factors. In addition, this is the level of most of the secondary salinity maxima and is near the top of the high gradient of the pycnocline. It can be seen on the composite T-S plot (fig. 2) that his level posseses considerable variability in the T-S relationships. The Straits of Florida at the 50-m level exhibit a pattern considerably different from the surface chart in detail but similar in general features. The core of the current at this depth appears to be delineated by a sigma-t of 23«8, which hugs the Cay Sal Bank side of the channel in the vicinity of Nicholas Channel but trends toward the western side of the straits north of Cay Sal Bank (see fig. 6). The distribution of the temperature, salinity, and sigma-t isopleths along the Florida Keys side of the straits reflects the effect of the influx of water from the Gulf of Mexico with its associated secondary salinity maximum. The sources and characteristics of these maxima have already been discussed. The absence of this feature at station 3 along the Bahama Banks reflects the dominance of the northward-moving Santaren Channel flow at this point over the Florida Straits counterflow, which carries the high 33 salinities generated on the Bahama Banks in the lee of Andros Island, as previously indicated. This Santaren Channel water, which is colder at 50 m than the water to the north, appears to have its core at station 5 (see fig. 6). As it travels north it mixes with the warmer, more saline south- ward-flowing Bahama Banks water and becomes part of the anti- cyclonic eddy suggested in the discussion of the surface circulation. This pattern is defined by the 25° C. and 2!f.6 sigma-t isopleths in sections 1, 2, and 3 (see figs. 7, 8, and y) . The high salinity found at the 100-m level of station 10 may be a remnant of the secondary salinity maximum caused by tidal currents, a salinity maximum that has descended as it moved southwestward in the eastern arm of the gyre. In the western entrance to Nicholas Channel at the 50-m level a slight penetration of the Florida Current appears as the anticyclonic eddy mentioned previously. This extends to about 100 m depth (see fig. 8). It is well defined by the 2'7»0° C. temperature and 23 .8 sigma-t isopleths and shows up also as a core of minimum salinity (fig. 6). The available reliable drift determinations at stations hh, k5, h6 and 30, shown in figures 1 and 6, are in agreement with this. As far as the water budget in the area is concerned, this gyre does not appear to be particularly significant, and ap- parently very little net water transport is occurring in 34 Nicholas Channel above 100 m. The average depth of the main salinity maximum, and therefore the core of the Subtropical Underwater, is close to 150 m. For this reason and because 150 m is in the lower part of the high gradient of the main pycnocline, this level was chosen to display the distribution of properties. Al- though this is the depth of the salinity maximum, there is still a considerable spread evident in the composite T-S curve (fig. 2). The lower salinities at 150 m evident in this plot result from an admixture of Gulf of Mexico water described previously. In the Straits of Florida the 150 m level is the first to show a sinuous pattern in temperature, salinity, and sigma-t (see fig. 12) that continues to deeper levels. The vertical displacement of the 20° isotherm equivalent to the meander evident on this level is approximately h-5 m, and that of sigma-t, 30 m, neither of which are excessive amplitudes for internal waves or tides. However, the fact that the disturbance is uniform across the channel suggests that it is not caused by short-period fluctuations. This pattern does seem to be associated with a marked change in trend of the depth contours along Pourtales Terrace, as shown by Jordan et al. (l96Lt-) and as evidenced by the 600- and 800- m isobaths of figure 1. Sections h and 5 (see figs. 1, 10, and 11) cross the straits immediately downstream from where 35 it changes in direction from east-west to northeast-south- west. These sections also follow the maximum constriction in width of the straits, at the surface by Cay Sal Bank to roughly 65%, and at 600 m by Pourtales Terrace and Cay Sal Bank to approximately ^0% of what it was west of the bank. It is evident from the trend of the plotted variables at 150 m and other depths that the Florida Current is already flowing toward the northeast before it reaches sections h and 5 (see fig. 12). This is probably due to the hydraulic block caused by Cay Sal Bank and the relatively inert water of Nicholas Channel. Because these changes in the configu- ration of the straits are upstream from the two lines of stations, the undulation evident in the properties is most probably an expression of the accommodation of the Florida Current to the change in direction and to the widening of the channel downstream from the constriction. The extreme gradient evident in the properties at 150 and 300 m along the Florida Keys (see fig. 12 and 13 ) is not apparent in the 50-m or 600-m charts. The depth interval between 150 and 300 m includes most of the area of Pourtales Terrace (see figs. 1, and 11). The gradient in the water properties may be due in part to their accommodating them- selves to the transverse component of the sinuous wave as it interacts with the shoaling surface of Pourtales Terrace, but there appears to be another factor operating as well: 36 Below 150 m, the water at oceanographic stations 39 and *+0 was isothermal, isohaline, and of indifferent stability. The bathythermograms obtained at these stations (fig. 3) illustrate the isothermal structure very well. The depth range of 150 to 300 m is the depth at which the principal artesian aquifer (Floridan) of Florida is expected to out- crop in this area (Stringfield and LeGrand, 1966; Kohout, 1967). It is therefore suggested that the strong gradients evident in the charts and the absence of isopleths near the bottom at stations 39 and ^0 in sections h and 5 (fig- 10 and 11) respectively reflect the introduction of artesian water into the Straits of Florida. This possibility has been suggested by Stringfield and LeGrand (1966). From Kohout ' s (1967) interpretation of the hydrology and thermology involved, it is impossible to judge whether relatively fresh artesian water is expected to be relatively warm or cold. Jordan et al.(l96Lf) present bathy- thermograph sections obtained by the HYDROGRAPHER in the area in 1953* These give a more detailed thermal picture of this phenomenon. The unusual layer at station 39 is colder, fresher, and less stable than that at station k-0. This suggests that the source of the anomalous water is closer to station 39 and is being absorbed as it moves northeast with the Florida Current. The bathythermogram obtained at station 38 on Pourtales Terrace also shows this structure 37 from 530 feet (160 m) to the bottom. Unfortunately the Nansen cast observations at depth differ from the BT temper- atures because biological fouling of the oceanographic wire required the bottom bottles to be relowered; meanwhile the ship drifted out of the immediate area of the BT cast. It should be noted that this is the only BT observation (see fig. 3) that shows appreciable hysteresis in the thermocline between the times of lowering and raising the bathythermo- graph. The particular area of Pourtales Terrace over which station 38 was begun is one of Karst topography (Jordan et aL 196*+), so that the anomalous water found there could possibly have originated from a sink hole. At 150 m both Nicholas and Santaren channels appear to lack any appreciable circulation (fig. 12). In Nicholas Channel the isopleths of the physical properties and sigma-t suggest a possible slight inflow along the Cuban coast. At 150 m in Santaren Channel the anticyclonic eddy described previously apparently dominates the entire entrance to the channel and probably blocks any effective circulation between the channel and the Straits of Florida at this level. The next depth chosen to show the distribution of proper- ties is at 300 m. This is below the steep gradient of the pycnocline and is approximately the level at which the curves of the composite T-S plot (see fig. 2) converge, indicating that external influences are minimal and that the 38 water masses here and below have uniform properties except for several special cases. The 300-m chart (see fig. 13) is the first to show an appreciable reduction in the width of the Straits of Florida other than that caused by Cay Sal Bank itself. This contraction is due principally to the presence of Pourtales Terrace along the Florida Keys. At 300-m, the structure of the physical properties of the Straits of Florida is very similar to that at 150 m. The isopleths of properties are still quite closely packed and continue to trend northeast-southwest, while the sinuous pattern they display persists in the same region and at about the same magnitude that it did at 150 m. Cay Sal Bank station 19 shows an anomalously low salinity at this level on the composite T-S plot, (fig. 2). This low salinity possibly results from upwelling caused by blockage of the Florida Current by the northern flank of Cay Sal Bank. Nicholas Channel, at 300 m, exhibits slight evidence in section 1 (see fig. 7) of a possible weak anticyclonic eddy that appears to exist from this depth to the bottom. Since the sill depth at the eastern end of Nicholas Channel is approximately *+10 m, this gyre probably has no connection there but is driven by a segment of the Florida Current that is deflected into Nicholas Channel by the steep western end of Cay Sal Bank. There is an indication of this deflection 39 in the trend of the isopleths of temperature and salinity in the northern half of the entrance to Nicholas Channel on the 300-m chart. In Santaren Channel, the 300-m depth appears as part of a transition between the distribution of properties above and below. According to these (fig. 13) the core of the anti- cyclonic eddy that has dominated the upper layers of the entrance to the channel seems to be located at station 6. The last trace of this gyre apparently dies out at about « 350 m at this station (sec. 2, fig. 8) and at approximately this same depth in sections 1 and 3 (fig* 7 and 9). At 300 m the isopleths of properties and sigma-t indicate a probable northwesterly flow into the Straits of Florida between the eddy and the northeastern end of Cay Sal Bank. Between 3 50 and 550 m, the northwesterly flow appears to become more northerly and to occupy the entire width of Santaren Channel. This is evident in sections 1, 2, and 3 where the reversal in gradient along the eastern half of the channel and steepening of the isopleths, particularly that of sigma-t, indicate a zone of high shear that suggests a probable considerable outflow reaching close to the bottom, Apparently the major contribution of water from Santaren Channel to the Florida Current occurs in this interval. This outflow of water is defined best by its range of properties rather than an average depth range. These are 40 temperatures between 17*5 and 10.5° C., salinity between 35*3 and 36. *+%<», and sigma-t between 26.5 and 27.1. A comparison of these values with those found in the Straits of Florida between the average levels of 350 to 550 m is shown in table 1. Table 1. Comparison of Physical Properties of Florida Straits and Santaren Channel Waters Temperature Salinity Sigma-t (° C.) ( %) Santaren Channel 17. 5 - 10.5 36. h - 35-3 26.5 - 27-1 Straits of Florida l;+.5 - 09.0 35-8 - 35-1 26.7 - 27-2 It is clear that at these depths the water in Santaren Channel is about 2.0° C. warmer, 0.3%c more saline, and 0.2 sigma-t units less dense than in the Straits of Florida. This flow extends beyond section 3 (fig* l) and obviously contributes to the flow along the eastern side of the Florida Current along the Bahama Banks. The markedly increasing temperatures and salinities to the north and east at any given level apparently result from the Santaren Channel water accommodating itself to the increasing depth as it moves northward into the Straits of Florida. In the core of this flow, station 9 deviates from the composite T-S curve (see fig. 2) in most of the observations below ^00 m because of a consistently high salinity anomaly 41 of about 0.1%cor low temperature anomaly of about 0.5° C At this station, the values at h of the 5 depths sampled from ^00 m to the bottom of the cast produced this deviation so that there can be little question as to the validity of the observations. The resulting T-S curve is very close to that of North Atlantic Central Water (Sverdrup et al., 19^2), except for the observation at 558 m that agrees with the composite T-S curve. The deepest level chosen to be charted is that at 600 m. Below this, at 700 m, the bottom excludes almost 50% of the stations, including all of those in the entrance to Santaren Channel. The reduction in area of the straits between Cay Sal Bank and the Florida Keys relative to the upper levels, and to the straits to the west and north is very evident on the 600-m chart (fig. 1*+). This level is well down in the intermediate gradient of the pycnocline and is about 200 m above the salinity minimum. In the Straits of Florida, the northeast trend paralleling the isobaths and the curvature of the isopleths is as evident here as at the upper levels (fig. 1*+). In sections h and 5 (see fig. 10 and 11) it can be seen that the cross-stream gradients of the properties and sigma-t from about 500 m to close to the bottom intensify markedly. The increased shear that this intensified gradient implies suggests an increasing velocity to compensate for the narrowing and 42 shoaling of the straits. It has been reported that there is a south flowing counter-current along the bottom of the Straits of Florida (Hurley and Fink, 1963 ). Because of' the extreme difficulty of sampling the water immediately adjacent to the bottom in the high velocity core of the Florida Current, it is diffi- cult to assess the oceanographic regime in this very critical part of the water column. However, in section 5 (see fig. 11) where the sampling was deepest, the 27.6 sigma-t isopleth does indicate a decrease in cross-stream gradient. Possibly of more significance, however, is that from 600 m to the bottom of the cast, the water at station k-2 (fig. 1 and l1!) is significantly colder at a given level than at any other station and that at 500 m, which is just above the maximum depth sampled by station 37> the cold water at station h2 relative to station 37 reverses the sigma-t gradient. On the T-S plot (fig. 2) station h2 is the line to the right of the main group of curves between 600 and 800 m and is very similar to North Atlantic Central Water. Whether this cold water and reversed gradient are indicative of a southerly flow along the continental slope here is conjectural, but a southerly flow along the slope to the north has been reported (Stewart, 1962). In addition, from 700 m to the bottom of the casts, the salinity, which above this normally decreases to the left of the Florida 43 Current at any given level, consistently increases from the middle of the channel to the Florida Keys side of the straits. There is not, however, a cross stream reversal of the density gradient, as described for stations 37 and h2 . In the entrance to Nicholas Channel, the pattern of the isopleths on the 600-m chart (fig. 1*+) clearly suggests an anticyclonic gyre. This appears to extend from the 300~ni level to the bottom, which, at the entrance to the channel is slightly over 100 m. In Santaren Channel, the 600-m level is very close to the bottom. Consequently the isopleths of the properties and sigma-t reflect the influence of the bathymetry, particu- larly a midchannel ridge. A relatively warm, saline tongue of water appears to be moving north and sinking along the Bahama Banks side of the channel, as it does at shoaler depths (fig. 1^-). Most of it enters the Straits of Florida, but some appears to recurve southward to the west side of the ridge. The final destination of this south flowing water is unknown, but it has properties intermediate between the north flowing tongue and the Straits of Florida water with which it is mixed. 9. SUMMARY AND CONCLUSIONS Forty-seven oceanographic stations taken in the vicinity of Cay Sal Bank across the Straits of Florida, Nicholas, and 44 Santaren channels provide an insight into the effects of these features and the change in direction of the straits on the Florida Current. The deep, relatively narrow Nicholas Channel appears to have very little net circulation. An anticyclonic eddy, driven by the Florida Current, occupied its entrance. The Florida Current changes from east flowing to northeast flowing before it reaches Nicholas Channel. The structure of the Florida Current indicates that along the Cay Sal Bank side between 200 and 500 m, the velocities probably are much less than above and below. Along the Florida Keys side, overlying the Pourtales Terrace, the structure of the water column near the bottom indicates the possibility of artesian water seeping into the straits from sink holes in the terrace. East of the terrace there is some indication of a possible south flowing undercurrent along the bottom on the Florida Keys side of the straits. Santaren Channel, from the surface to 300 m, appears to be blocked by an anticyclonic eddy driven by the Florida Current. There appears to be a considerable net transport into the straits below this to the bottom. 45 10. REFERENCES Cloud, P. E., Jr. (1962), Environment of calcium carbonate deposition west of Andros Island, Bahamas, U.S. Geo- logical Survey Professional Paper 350, 138 p. Dietrich, G. (1963), General Oceanography, ( Interscience Publishers, John Wiley and Sons, New York, 588 p.). Hurley, R. J., and L. K. Fink (1963), Ripple marks show t:iat countercurrent exists in Florida Straits, Science, 139, 6O3-605. Jordan, G. F., R. J. Malloy and J. W. Kofoed (196^0, Bathymetry and geology of Pourtales Terrace, Florida, Marine Geology, 1, 259-287- Kohout, F. A. (1967), Ground-water flow and the geothermal regime of the Floridian plateau, Trans, of the Gulf Coast Assoc, of Geol. Soc. 12, 339~35l+. Milligan, D. B. (1962), Marine geology of the Florida Straits, M.S. Thesis, Florida State University, 120 p Stewart, H. B., Jr. (1962), Oceanographic cruise report USC&GS Ship EXPLORER-196O, (U.S. Government Printing Office, Washington, D. C), 162. Stringfield, V. T. and H. E. LeGrand (1966), Hydrology of limestone terranes in the coastal plain of the south- eastern United States, Geol. Soc. Amer. Special Paper 93, ^6 p. Sverdrup, H. U., M. W. Johnson and R. H. Fleming (19^2), The Oceans, (Prentice-Hall, New York, 1087 p.). U.S. Coast and Geodetic Survey (1967), Hydrographic Chart: Straits of Florida and Approaches, C&GS 1002. U.S. Coast and Geodetic Survey (1968), Hydrographic Chart: Gulf of Mexico, C&GS 1007. Wennekens, M. P. (1959), Water mass properties of the straits of Florida and related waters, Bull. Marine Science of the Gulf and Caribbean, 9, 1-52. Wust, G. (196^), Stratification and Circulation in the Antillean-Caribbean Basins (Columbia University Press New York, 201 p. ) . APPENDIX A DRIFT BOTTLE RECOVERY RECORD Rel ease Recovery- Sta. No. Latitude Longitude Date Latitude Longitude Date Days Before Found J une 1962 39 21+°38,N 80°^5'W 23 25°00'N 80°31'W 25 2 38 2lfo30,N 80o)+0'W 23 26°1I+IN 80°05'W 26 3 27 23°55'N 80°52'W 25 26°52'N 80°03,W 28 3 27 23°55'N 80°52'W 25 26°I+9,N 80°02'W 29 k 27 23°55'N 80°52'W 25 26°52'N 80°03'W 29 k 38 2Lf°30'N 80ol+0»W 23 26°21'N SO^'W 27 h 38 2Lf°30'N 80°i+0'W 23 26°03'N 80°07'W 27 h 38 2If°30'N 80oLfO'W 23 26°lLf'N 80°05'W 27 h 38 2I+°30'N 80°^0'W 23 26°09'N 80°06'W 29 6 38 2Lf°30,N 80°^fO'W 23 26°20'N 80°0If'W 30 July 7 39 2I+°38'N 80ot+5'W 23 25°00'N 80°31'W 1 8 38 2^°30'N 80°^0'W 23 26°1+1+,N 80°02'W 2 9 39 2l+°38'N 80OI+5'W 23 2I+°56'N 80°37'W 9 16 38 21+°30'N 80°^0'W 23 27°15'N 80°13'W 11 18 38 2I+°30,N 80OI+0'W 23 27°09'N 80°09'W 12 19 39 2I+°38,N 80ol+5'W 23 25°00'N 80°31,W 23 Oct. 30 ^5 23°2I+'N 80°31+,W 2\ 29°55'N 8l°17'W 12 110 9 2V)21'N 79°38'W 21 2Lf°If3w 6 2I+°25'N 79°28'W 21 23°0I+'N 7^°5^-'W 1+0 21+°^0'N 80°38'W 22 25°25'N 80°19'W 28 23°I+1+,N 80°50'W 26 32°20'N 6k°kVW 13 21+°29'N 79°!+8'W 21 2501^N 78°08'W 33 23oLfl'N 8l°05*W 25 39°05'N 28°03'W 1+0 21+°1+0'N 80°38'W 22 25°16'N 80°l8'W 2 2*f°28'N 79°19'W 20 59°20'N 6°00'E h0 21+°1+0,N 80°38'W 22 25°29'N 80°20'W LfO 2I+oI+0,N 80°38'W 22 25°29'N 80°20»W Nov. 6 135 1963 Jan. 1 19^ Mar. 20 271 Apr. 2 280 Sept. 8 ^3 Oct. k i+66 Dec. 1 556 196^ Oct. 19 851 Nov. 29 918 Dec. 6 925 APPENDIX B SUMMARY OF SHIP'S DRIFT, WIND DATA, AND WIRE ANGLES ON OCEANOGRAPHIC STATIONS Sta. Current Wind Wire Wire No. Speed Direction Speed Direction Angle Direction (knots) (deg. T) (knots) (deg. T) (degrees) (deg. T) 1 0 — 10 180 3 220 2 0.7 007 2 200 10 3 0 7 200 5 k 0 7 205 3, 17 --- 7 1.5 13>+ 12 180 12 13 1.2 033 7 160 8 180 1>+ 1-3 009 5 135 15 155 15 1.9 302 5 150 23 — 16 0 — 6 1^+0 0 — 18 1.0 0^1 7 135 Ik 185 19 1.2 070 10 120 9 — 20 3-5 0>+9 12 100 10 125 21 2.5 028 l^f 090 18 110 22 1.5 039 12 090 9 23 0 12 085 6 070 26 3.8 066 20 090 9 080 27 3-2 060 12 090 23 205 29 1A 303 12 090 li+ 100 30 0.5 286 12 090 30 095 APPENDIX B (cont.) Sta. Current Wind Wire Wire No. Speed Direction Speed Direction Angle Direction (knots) (deg. T) (knots) (deg. T) (degrees) (deg. T) 32 2.7 OMf 16 110 26 33 1.8 038 18 110 36 3^ 0.8 093 16 077 6 0^+0 35 0.7 101 12 050 12 Oh 5 36 1.0 057 12 090 31 37 2.6 0^8 lit 090 0.25 39 2.2 028 7 120 3 ^0 3A 032 8 115 19 230 kl 3-5 051 10 13 5 32 185 1+2 2.3 0^+2 7 120 29 180 ^3 0 9 120 17 110 hU 1.0 215 7 120 15 110 h5 0.6 197 9 090 15 030 he 0.5 210 9 075 22 060 GPO 859-256 Reprinted from E®S 51, No. 5, ^-^O 67 Reprinted from E©S Vol. 51. No. 1, January 1970 International Geophysics International Symposium on Earth Tides The Sixth International Symposium on Earth Tides was held in France at the University of Strasbourg, September 15- 20, 1969. It was organized by the Perma- nent Commission on Earth Tides, Inter- national Association of Geodesy, 1UGG. Although many aspects of the meet- ings were comparable to previous earth tide symposia in that the papers again dealt primarily with instrumentation and data analysis, there was a greater degree of open-mindedness and willingness to discuss new procedures that added con- siderably to the value of the meetings. With regard to instrumentation, con- siderably greater emphasis is being placed on possible contributions by various po- tential sources of error, on calibration, on the interchange of instruments between stations, and to simultaneous observa- tions using multiple sensors at the same site. With this increased sophistication, there has come an awareness that the geophysical interpretation of the observa- tions may hinge on a high degree of accuracy and therefore there is now a related willingness to consider new sug- gestions in regard to instrumentation. A similar change has come about in data analysis in that there is now an active program to use longer series to achieve both more accurate results and a high degree of resolution. Thus, the fixed 29-day analysis is no longer the ultimate end-product, and least-square analysis of data that may not be continuous and equally spaced in time is accepted as a basic tool. With this has come an interest in other frequency bands, not only the long-period tides but also high frequency tides as well. There is considerable in- terest in M3, and frequencies as high as 8 cycles per day are being investigated. There is also greater interest in net- works of stations, in particular to permit careful consideration of ocean tide ef- fects, both loading and attraction. Evalua- tion of ocean co-tidal and co-range charts for use in earth-tide analysis was of great importance in many papers, thus provid- ing a great deal of support to the rela- tively new international effort in deep-sea tide measurements and to hydrodynamic model studies. One particularly enthusi- astic speaker even suggested that earth- tide measurements may supply the neces- sary data for the calculation of ocean-tide charts. American participation was somewhat greater than at previous meetings. The presentation by John Kuo (A trans- continental tidal gravity profile across the United States, J.T. Kuo, R. C. Jachens, G. White, and M. E. Ewing) created a considerable stir, partly because this was the first systematic earth-tide network in the United States and even more because the long series of stations at about the same latitude made possible a study of loading effect from both the Atlantic and Pacific oceans. Professor Lecolazet, chair- ing the meetings, was particularly enthusi- astic in congratulating the speaker at the conclusion of the presentation. W. E. Farrell's paper (Instrumental aspects of tidal gravity measurements) also received considerable interest and comment. At the request of Professor Marussi, President of I AG, each member nation was asked to designate an official repre- sentative to the Permanent Commission on Earth Tides. It is the intent of the Commission to deal directly with the national delegate in the future rather than with national committees. The resolutions were presented by the Resolution Committee to a second meet- ing of the Commission at an evening meeting on September 1 9 and adopted by vote at the final meeting on September 20. The six resolutions are included as the Appendix. The USSR was not represented at the meetings, but a number of USSR papers proposed for the symposium were sum- marized by other speakers on the final day. All papers will be published in the Proceedings of the symposium. Bernard D Zetler Atlantic Oceanographic and Meteorological Laboratories ESSA Miami, Florida Appendix 1 . The permanent Commission for Earth Tides, taking note of recent instru- mental developments and of progress made towards a better understanding of the physical theory and calibration of instruments generally, recommends that, wherever possible, long term observa- tional series should be planned as regular observatory-type programs in a number of different regions of the world. This program is considered to be essen- tial to ascertain many phenomena that effect movements of the earth's surface in the Chandlenan period, in the tidal fre- quencies and as secular trends, moreover the possibility of higher resolution analy- sis should now be practicable. 2. The Commission recommends the establishment of several complete earth- tide stations along the equatorial regions and in the southern hemisphere, partic- ularly in Africa, South America and in Australia. 3. Considering the worldwide impor- tance for the science of the globe to establish a close network of observing stations, the Commission recommends the achievement, as soon as possible, of 9 the station started in Schiltach, Black Forest, Germany. By the installation of this station, it would be finally possible to fill a gap in the net between France, Belgium, and Luxembourg stations on the one hand and the stations of Berchfesgaden, Czech- oslovakia, and Austria on the other hand. 4. The Commission recommends that earth-tide stations send, as soon as possi- ble, their numerical results of measures to the International Center in Brussels. 5. Inasmuch as ocean loading and ocean attraction effects on earth-tide observations have become significantly important in earth-tide studies, the Per- manent Commission on Earth Tides en- dorses efforts now underway in the oceanographic community to develop more accurate co-tidal and co-range lines through deep-sea observations and hydro- dynamic model studies. 6. The Permanent Commission for Earth Tides wishes to commend the President, Professor Lacroute, and all members of the Organizing Committee for the excellence of the arrangements provided for the Sixth International Symposium on Earth Tides and for the very generous hospitality that has been offered to all participants. 10 Reprinted from E®S 51, No. 5, 479-^80 68 Reprinted from E©S Vol. 51, No. 5, May 1970 International Geophysics International Tsunami Symposium The International Symposium on Tsunamis and Tsunami Research was held in Honolulu, Hawaii, October 7- 10, 1969. Australia, Canada, Germany, Japan, New Zealand, USSR, and the United States sent representatives. There were three seminars: (1) Seis- mic Source and Energy Transfer, con- vened by S Soloviev; (2) Tsunami In- strumentation, convened by Vitousek; and (3) Tsunami Propagation of Run- up, convened by K. Kajiura. Many of the scientific findings were of considerable significance. With respect to tsunami generation, papers by lida, Watanabe, and Hatori provided vital statistical correlations of tsunami sources and tsunamigenic earthquakes. The theoretical dependence of gravity- wave parameters on source parameters was reported by G. Podyapolsky. In the discussion on instrumentation, an automatic, remote, vocal-type gauge was described by G. Dohler. K. Terada reported on the progress in Japan for both remote analog and remote digital tide gauges. Four submerged long-wave recorders were used to study seiche in Oofunato Bay, which was severely da- maged by the 1960 Chilean tsunami. An offshore ocean-wave meter has been modified to report for the tsunami period range. Design, development, and utilization of a Bourdon-tube, deep-sea, tide gauge and of a Snodgrass vibration system repackaged in glass spheres were meticulously described by J. Filloux and M Vitousek, respectively. The plans for the Pacific Tsunami Warning System were reviewed by L. Murphy and R. Eppley. R. Johnson proposed a method for using a hydro- phone array to record T -Phase data suitable for estimating fault characteris- tics. The suggested method is designed to eliminate from consideration those events for which no significant tsunami has been generated. The propagation of tsunamis was analyzed both analytically and numeri- cally. Analytical studies of point-source generation, significance of Coriolis ef- fect, the effects of heterogeneity and vis- cosity of the fluid medium were pre- sented by S. Voit and B. Sebekin. A. Nekrasov analyzed the transformation of waves by a step model of the conti- Day Topic and 1:12,500 was used to quantitatively study deep-ocean tsunami propagation by M. Krivoshey. The tsunami inunda- tion was evaluated as to extent and depth by a larger scale, distorted model of 1:5000 and 1:350. The effects of such extreme scale distortion on wave param- eters were studied in a flume. Recent progress towards solving the problem of storing and quickly retriev- ing relevant tsunami facts in documents was reported by J. Walling. A digital computer is used for analysis of indexed properties of documents stored in mi- crofiche form on a five-second, random- access, display file. This International Symposium was sponsored by the International Union of Geodesy and Geophysics Tsunami Committee and the East-West Center. The Proceedings will be edited by Wm. Mansfield Adams and will be published by the East-West Center Press. At this meeting the committee adopted a number of resolutions. Among them the committee proposed that an Interdisciplinary Symposium on Tsunamis and Earthquakes be arranged for the IUGG meeting planned for Mos- cow, USSR, during August 1971. It was suggested that the symposium have the following days, topics, and conveners. Convener First Tsunami Committee Meeting B. D. Zetler Second Redefining Tsunami Magnitude I. lida Third Prediction of Tsunami Inundation: Short Term G. R. Miller Fourth Prediction of Tsunami Inundation: Long Term S. S. Voit nental shelf. The tsunami response of a uniform-depth model harbor connected to an ocean by a channel was considered by G. Carrier and R. Shaw. The numeri- cal studies were also represented by a dynamic-programming approach for improving prediction of arrival times de- vised by R. Braddock R. Reid and C. Knowles described the estimation of the deep-water tsunami form by an inverse ransformation of a marigram obtained near the island. Several laboratory model studies were reported; local geometry effects by L. Hwang and A. Lin; wave intrusion into a harbor by R. Whahn and D. Bucci; and a verification of the Carrier-Greenspan transform the- ory, as applied to a double-humped wave, by J. Williams. An unusually small, distorted scale model of 1 65,000 The Committee endorsed and en- couraged the use of offshore and deep- sea tsunami gauges (in particular the re- establishment of the offshore gauge at Wake Island), intercalibration tests of these gauges, and studies involving the utilization of focal source mechanisms as significant steps toward more effec- tive tsunami warnings. The Committee recommended that whenever a tsunami exceeds two meters anywhere, records from representative stations should be submitted from all cooperating nations to the World Data Centers. It also suggested that agencies distributing questionnaires relative to earthquake information include a re- quest for information on sea state. The Committee endorsed the effort by the International Tsunami Information 479 Center to compile a collection of photo- graphic copies of marigrams showing tsunamis. It urged that this effort be continued and, if possible, accelerated, deferring a decision on publishing an at- las of these marigrams until the next meeting while requesting all members to investigate the possibility of publishing such an atlas in all or part of their re- spective countries. The officers of the committee were re-elected at the meeting to serve until the Moscow meeting. Five additional scientists are being invited to serve on the committee which is presently con- stituted as follows: B. D. Zetler, Chair- man, USA; S. L. Soloviev, Vice Chair- man, USSR; K. Iida, Vice Chairman, Japan; W. M. Adams, Secretary, USA; J. W. Brodie, New Zealand; K. Kajiura, Japan; C. Lomnitz, Mexico; L. M. Mur- phy, USA; G. L. Pickard, Canada; R. O. Reid, USA (IAPSO representative); E. F. Savarensky, USSR. Those invited to join me Committee are: R. D. Brad- dock, Australia; E. Gajardo, Peru; G. R. Miller, USA; V. S. Moreira, Portugal; S. S. Voit, USSR. Bernard D. Zetler Chairman Wm. Mansfield Adams Secretary 69 Reprinted from Bulletin of Marine Science 20, No. 1, 5 7 - 6 9 TIDES IN THE GULF OF MEXICO— A REVIEW AND PROPOSED PROGRAM B. D. ZETLER and D. V. HANSEN Physical Oceanography Laboratory, Atlantic Oceanographic & Meteorological Laboratories, Miami, Florida Abstract A study of tides in the Gulf of Mexico is proposed as part of the pro- gram for Gulf Science Year (1970). There are several existing hypotheses explaining the diurnal tides in the gulf. These are described and discussed and a new hypothesis is suggested. The semidiurnal tides are generally small, and therefore have had less attention; nevertheless, there are several hypotheses that are quite contradictory. A program of tide and tidal cur- rent observations is proposed which should permit discrimination among the various hypotheses. Introduction A number of federal oceanographic agencies are cooperating with GURC (Gulf Universities Research Corporation) in a Gulf Science Year in 1970. This study of tides in the Gulf of Mexico was requested in connection with the development of a program by the Panel on General Circulation, Gulf Science Year, with specific instructions "(a) to list and review the existing literature, (b) to identify the scientific problems to be solved, and (c) to propose a program aimed at solving these problems, with special emphasis on the cooperative aspect of this effort." A review of the literature and data available on the subject leads to the conclusion that the problems are un- usually well defined; furthermore, instrumentation has been or is being de- veloped that will permit obtaining necessary observations to resolve these problems. Existing Theory It has long been known that the tide at many places in the Gulf of Mex- ico is diurnal (one high tide and one low tide each lunar day of 24.84 hours), or mixed (a large inequality between the heights of the two high waters and/or between the heights of the two low waters in a lunar day). This is in sharp contrast with the tide on the east coast of the United States, where the tide is semidaily with little inequality between the heights of either the two high waters or the two low waters in a lunar day. The diurnal regime of the gulf has been the subject of numerous studies and there have been important differences in the conclusions. The Gulf of Mexico is a basin connected to the Atlantic Ocean by the Florida Strait and to the Caribbean by the Yucatan Channel. The opening 58 Bulletin of Marine Science [20(1) between the Bahamas and Cuba contributes negligibly to volume transport because of its shallow depth. Early researchers (Harris, 1907; Endros, 1908; and Sterneck, 1921) suggested that the diurnal tide in the gulf is some form of co-oscillation with the tide in the nearby Atlantic, but essentially opposite in phase. This implies a standing wave entering through one or more connecting channels, the Florida Strait or the Yucatan Channel, or both. Grace (1932, 1933) studied both the diurnal and semidiurnal tides in the Gulf of Mexico in terms of the response of the gulf to astronomic tide- generating forces and of a co-oscillation with the tide in the Atlantic, ex- cited in the gulf by periodic flow in the channels. Using observations at various places in the gulf and representing bathymetry of the gulf by a small number of rectangular boxes, he concluded that the diurnal tide is primarily co-oscillating, entering the gulf through the Florida Strait and exiting through the Yucatan Channel about 5 or 6 hours later. Grace's model is therefore consistent with the ideas of the earlier workers, although he based his work entirely on tidal data from within the gulf. Marmer (1954) attributed the diurnal tide in the gulf to the resonance period of the basin. He summed up his analysis along these lines: "Quali- tatively, the simplest explanation of the relatively large diurnal component in the Gulf is that the length and depth of its basin are such that its free period of oscillation approximates 24 hours; that is, it approximates the period of the diurnal tide-producing forces and therefore responds better to the diurnal forces than to the semidiurnal forces." Von Arx et al. (1955) calculated the diurnal tidal current in the Florida Strait, using the cross section of the strait and the tidal prism in the gulf and assuming no tidal exchange through the Yucatan Channel. However, this calculation was done as part of a possible interpretation of results from another study, and the constant rate of inflow through the Yucatan Chan- nel was used merely to simplify the calculation. The semidiurnal tides in the Gulf of Mexico are generally small, but the tidal regime appears to be more complex, so much so, that Dietrich (1963) showed a question mark in the gulf in his world cotidal chart. Harris (1904) explained the M2 tides observed along the periphery of the gulf as due to a progressive wave entering from the Florida Strait; the later lunitidal in- tervals in the northeast corner of the gulf he attributed to the slow move- ment of a progressive wave over a long shallow shelf. Grace (1933) found that his mean error in amplitude was halved and the mean error in phase significantly reduced by omitting Cedar Keys and St. Marks from his calcu- lations. He justified the omission "because of local conditions which have not been allowed for in the discussion," such as the shallowing in the areas of these stations. His cotidal chart shows a counterclockwise rotation about 1970] Zetler & Hansen: Tides in the Gulf of Mexico 59 j| rTi/o^oj* Bp/J, is' ? j* s^B HR GULF OF ^B A >-CV ■|8}'-1,«- "■«»•© ©i.j5s- A ^ \ MEXICO ~ ,„. ^ * < X$I3,Z4' Jm^^ '^^ IhHhk^i. /8.M" - i_ ^\ Jfk ?<^B Bib J£^ k '(5)/2 9,335' ?35.?«/' ''^ ^| H 9^ ^^J lHk» 27,«4"(S^H ^^^^^^^^^^ Hgct «. v JBm- mm ^Pj.^to" Figure 1 . Kx harmonic constants. Circled numbers correspond to numbers of tidal stations in Table 1; amplitude is given in cm, and phase in degrees referred to Greenwich transit. Circled letters with arrows correspond to letters of tidal- current stations in Table 2; amplitude is given in cm/ sec, and phase of indicated direction is in degrees referred to Greenwich transit. an amphidromic point south of the Mississippi River Delta with very rapid changes in phase along the delta and along the north side of the Yucatan Peninsula. Sterneck (1920) also found an amphidromic point near the cen- ter of the gulf, but he postulated a clockwise rotation of the cotidal lines. Discussion Manner's hypothesis for a resonant diurnal tide does not seem to match the tidal harmonic constants. In a resonant basin, one expects to find an amphidromic point somewhere near the middle and the phase angle to be opposite on either side of the basin. It is clear from Figure 1 and Table 1 (representing all available Ki harmonic constants on or near the coast) that the diurnal tide is essentially in phase throughout the basin. Furthermore, Royer & Reid (1966) estimated the fundamental period of the gulf at less than eight hours, contrary to Mariner's hypothesis. Grace's calculation also M) Bulletin of Marine Science [20(1) 0 - 0 c < < D •i o^£ a E E u < c X) u ^-^ 5j £ E < cfl 0 — -J o 60 < 0 ' to I? <- 60 1) O^ - 'B o i- i- — — i— ■— — C3 C^ ?] til fl C3 d i >% >* >^ >* >> >. l_( l^ C3 u >* S^NO >^ On NO r<-| NO <"<1 r«-) NO NO c*i <"<") m in On ON ON On On OOOnOnOnONOO V-l Tf ON ON n— 'NCrnnrl inmmm — i — M — > m m tT rl r) on © r~ in, i— i rl m r<~i ^m-t ^-^Orl r^inND^i- oo oo oo m on t-~ r-- O "^ -h — in in (Nmr<~iTl- NNMN m m © ^ rl --^ on — <-» d r° S-g-o J2 60 d a> O iS oo 03 c N >N |_ - 2 ^ eg -J "3 "3 «j >-, >. ON ON — ri n — _ -t m i 1 c 1 ON © r<~, >n m, \0 r«-| oc On On ON ON r- ON rj- rl on Tt- m, — rl rl -r — ^ On m ^j- m, — ri ri m On tj- nO © m, NO (^1 — c rl © rl on rl m oo ON ON no — r- in co -^l- 00 ON ON (N ri ri 55 ^ < „ S.S < o §.a ? r> co tiXIO 3 60"3 — rl ci rf in r- oo on © — 1970] Zetler & Hansen: Tides in the Gulf of Mexico 61 -J < 0 •o £ oit 1? O-o JJ w Ml Ih Ih >, [h u- i— "-> Ih Ih > Ih Ih In - ca r3 a a tD - -, ~ 03 n, - 0> O — > P^ >-. >, >%m --. > >, ^. > 0< O 0> — — (N — — ' — ' ^H ~ — fN) — — — r- o m r~ r- y. = c m m i -t -t -t -r i/". in i NO OO OO N^iOO^ hmON i r*l r*"i in m rt in rt O * rt m -+ -i- o On ON On ON ON ON On ON On On On 3N ON Nlfl^ h^iOooO OM» 3> r-~ no r-~ m in rt ON CO r-~ in rt rl rl rl rl cl (N rl rl rl rl m cj t~- rl ^m* NO D NO r~ no in n (N rl O m Tf ^H -h in rt rt r~ r- N N (N N rl o -t- -t * r-- r- r- r i o * oo r~ r- on oo n no WO\rt £ in * o o rl rl rl rl -> rt m rl m — i n n on m rj rj rn rn n m no in m n n m in rt oo r~ rt ON in rt O rt O O in O £ 0 S c ca "3 oj _c P G /. 0 Ih 0 u ~ri G Z So < UJ H ty rt Ara dre Isl mpico racruz atzaco mpech agreso < CQ -J U ivana rapach silda* U o Ih O rt ° < « h-, U <—> P-, Ph M u o a t H>UUPh J5 OS C3 sou 3 0 e- o r~ oo' On O rt rl m rt in NO r-' od ^H ' 1 rt rl n n n n n n r\ n 62 Bulletin of Marine Science [20(\) Figure 2. M2 harmonic constants. Same method of notation as in Figure 1. showed that the direct tide contributes only a very minor part of the K] tide in the gulf. Although Grace's method appears to be fundamentally sound, his repre- sentation of gulf geometry was quite approximate, and the phase progres- sion southward through the Yucatan Channel cannot be reconciled with the available Kx tidal constants in the Caribbean Sea. Many of the latter were not available when Grace made his study. Dietrich's (1963) Ki cotidal chart of the world shows the tide progress- ing northward through Yucatan Channel and arriving in the Gulf of Mex- ico essentially in phase with the Ki wave coming through the Florida Strait. His cotidal lines match reasonably well the phases at additional tide sta- tions in the Caribbean, analyzed subsequent to his paper. Since an understanding of the tidal regime in the gulf requires informa- tion on the tidal currents in the Florida Strait and Yucatan Channel, an in- tensive search was made for records of tidal-current observations in the two channels. Only some old observations by Pillsbury and some surface ob- servations in 1965 off Hollywood, Florida, by the General Dynamics Mon- ster Buoy were found. General Dynamics furnished these data; the first 15 1970] Zetler & Hansen: Tides in the Gulf of Mexico 63 c u X UJ s 0 u- - o o H u Z < OS h Z LU H < w a: ac U < O H Z < Z o U y 7. o S a: < I h d «-> On u •a y 5 <-> % Q3S ley 60 U u -a j= 3 " •- o -2 "3 o O 73 73 ir, i/", r~ r~ r~ >£ iC cc cc ec 0> cc 'S. cc :c O oo 285 >r. -t- 00 252 m r-; -ji ^ vi \ vr ri o 00 I — ri <■<■> On m O O 00 ■* r^ — ! — ia, -t vC 3^ ri sC r^ r- ce CC — en oc ^c « © m m rn O o o o o -c IT) m — — n ci n c so n ri »5 _=a , , c C t-> e — c c U 73 D o ■ > CO U Q "J 64 Bulletin of Marine Science [20(1) days appeared to be most suitable for analysis (Smith et ai, 1969). The available Ki and M2 tidal harmonic constants for the Florida Current and the Yucatan Channel are listed in Table 2. Computation of Tidal Amplitude. — For an irregular basin with surface area, 5, and incoming currents, uh normal to the basin boundaries at cross sec- tions, au volume continuity requires the rate of change of surface elevation, h, with time, /, to be: Since currents enter the gulf only through the Florida Strait and the Yucatan Channel, u is non-zero only at cross sections ax and a2 of these channels, and the mean current speeds in these channels are denoted by Cii and f/o, the bar representing an average over the pertinent area. Then S — = ii1a1 + tioflo. (2) dt At this point, the current speeds include both permanent flow and tidal current but, in a consideration of an oscillating tidal current, the permanent currents that flow in through the Yucatan Channel and out through the Florida Strait more or less cancel each other, the relatively small difference being related to river drainage, rainfall, and evaporation in the gulf. Considering now the harmonic tidal current through the two channels, with w the angular speed of Kl5 <£i and 4>2 the phase lags in the two chan- nels, and iii and u2 representing the mean amplitudes of the tidal currents, the height becomes h(t) — [(i/i<2i sin ! + u2a2 sin <£?)2 + (ui«i cos i + u2a2 cos 4>2)2]- (3) Ui_ax sin x + u2a2 sin 2 x (Sw)- wt + tan~ UiOj cos i + u2a2 cos 2 Sufficient data are not available to evaluate this expression for compari- son with tides observed on the coasts of the gulf, but Grace's theory is nec- essarily consistent with it. Grace computed the tidal currents in the chan- nels by fitting his dynamical model to the available tidal constants from around the gulf. He noted that his Ki results do not match well the current observations by Pillsbury, in either amplitude or phase. In addition to the question of how reliable harmonic constants from such short series may be, Grace noted that the observations may not be representative of the average tidal currents in the channels. If the Ki tidal current in the Yucatan Channel is assumed to have the same phase (as suggested by the tidal constants) and amplitude as in the 1970] Zetler & Hansen: Tides in the Gulf of Mexico 65 Florida Strait, where some current measurements are available, equation 3 simplifies considerably to h(t) =hsin(wt + i), (4) where * _ (fli + a2)ui wS The area of the Gulf of Mexico is estimated to be 1.7 x 1012 m2, and the cross-sectional areas of the Florida Strait and Yucatan Channel are 4.8 x 107 m2 and 25.8 x 107 m2, respectively. The computed amplitude of the A Ki constituent in the gulf is therefore h — 15 cm, which is in good agree- ment with the amplitudes listed in Table 1 for the periphery of the gulf. Standing-Wave Hypothesis. — Figure 1 and Table 1 show that the ampli- tudes for the diurnal constituents are very small in the Florida Strait at Miami and Bimini. In many areas, the associated diurnal tidal current is even less significant under such circumstances, as may be understood from the amplitude portion of equation 4, A whS «i = ; • This indicates that the tidal amplitudes are weighted by their relative fre- quency in regard to currents in such a closed region. Thus the semidiurnal tide has relatively twice the associated current that the diurnal tide has. However, the diurnal tidal current is definitely not small in the Florida Strait, which suggests the possible existence of a standing wave node in this area. Schmitz & Richardson (1968) found Ki and Oi each comparable to M2 in transport measurements for the Florida Current. Steinberg & Birdsall (1966) and Clark & Yarnall (1967) reported a large diurnal variation in their spectral analysis of phase changes for an acoustic signal continuously monitored across the strait. The analysis of the Monster Buoy surface- current data showed Ki and d somewhat larger than M2. The K: and Oi amplitudes and phases for the first four tide stations in Table 1 confirm that there is a standing-wave oscillation in the strait, with a node close to the latitude of Miami. The tidal harmonic constants for the western part of the Caribbean Sea also show small amplitudes and rapid changes in phase, thereby indicating a comparable regime in that area. It is not difficult to visualize the two regimes as one, with Cuba's mass serving as a barrier to connecting the cotidal lines. The Kx tidal regime in the Florida Strait can be documented more ade- quately by analyses of tidal observations at additional points along the east coast of Florida between Vero Beach and Key West. The rapidly changing Kx phase along this coast has not been a problem to the Coast and Geodetic 66 Bulletin of Marine Science [20 (1) Survey in terms of supplying tidal predictions for navigational purposes, because the amplitude is so small. However, these harmonic constants are important to studies of variability of the Florida Current, as well as the na- ture of the tide in the Gulf of Mexico. With reference to the observed phases of the current relative to the tide, an approximate Greenwich phase of the Ki tide for the entire gulf is 20°. The maximum flood at the node should precede this by 90°, or a phase of about 290°. The phase of 284° by Smith et al. (op. cit. ) fits this very well. Harris' analysis of the Pillsbury data off Rebecca Shoal and Yucatan Chan- nel gives Greenwich phases of 252° and 335°, respectively, approximately 40° from the anticipated value in opposite directions. Variations of this amount are reasonable for harmonic constants from 2- and 4-day series of current observations. Grace's cotidal chart shows the tidal wave entering the gulf through the Florida Strait and exiting through the Yucatan Channel about 5 hours later. The agreement between phases of his expected maximum currents and the phase of Pillsbury's observations is considerably poorer: variations of 141° and 75°, respectively. Semidiurnal Tides. — Grace compared the available observations of tidal currents in the entrance to the Florida Strait and in the Yucatan Channel with currents calculated from his theoretical development. The fit was found to be poor, and Grace pointed out that even the two sets of observed data in the Yucatan Channel "appear to be very different, unless the cur- rent data are unreliable." If Harris' hypothesis of a progressive wave en- tering the gulf through the Florida Strait is correct, the west current should be in phase with the high tide. At current station B (off Fowey Rocks) and at C (between Rebecca Shoal and Cuba), the tidal current is about an hour later than the tide. This is a reasonably good fit in phase from short rec- ords, particularly when allowance is made for some contribution by a sta- tionary wave oscillating east-west in the basin. It appears that the tidal cur- rent to the north at station E (Yucatan Channel) may also be about an hour later than the high tide, but the latter must be inferred from data for sur- rounding points and is not well determined. The controversial interpretations of the available semidiurnal harmonic constants are most likely to be resolved by bottom measurements of the tide in the gulf. In selecting the exact locations for installing the tide gauges, consideration should be given to the areas of greatest disagreement between Harris and Grace. Proposed Program Observations of Currents. — It is imperative that at least one series of ob- servations of currents, suitable for tidal-current analysis, be obtained in the 1970] Zetler & Hansen: Tides in the Gulf of Mexico 67 Yucatan Channel. On a somewhat lower priority, it is desirable that addi- tional series of such observations be obtained in the Florida Strait. The Institute of Marine and Atmospheric Sciences, University of Miami, attempted to obtain a good series of measurements of currents from a ship anchored in the strait in the spring of 1968, but heavy seas contributed so much noise to the observations that they do not seem to be sufficiently reli- able to warrant tidal analysis. In the authors' opinion, the greatest possi- bility for good tidal-current data lies in hanging a current meter from a buoyant float on a short tether (about 10 meters) off the bottom. This will minimize the effect of waves and simplify the anchoring problem. It is within the present state of the art (Knauss, 1965), but thus far reliability of the package, including release mechanism, has been a problem. Tidal Observations. — The coverage of tidal constants for the gulf appears to be reasonably adequate to our needs. The real need is for offshore tidal observations in various parts of the gulf, which can be made by pressure sensors on the bottom (Munk & Zetler, 1967). An implicit assumption of equal amplitudes in the deep portion and the shelf was made in deriving equation 4. It will be surprising if the phases for the diurnal constituents differ significantly from those of nearby stations ashore, but such informa- tion is essential to complete a description of tides in the gulf. As indicated previously, the information for phases of the semidiurnal tides is very im- portant because of the different offshore projections of phases by Harris and Grace. The proposed program of bottom observations of the tides in the gulf could be an excellent proving ground for an international program in deep-sea tides presently being organized. Tidal observations should also be obtained in the Caribbean in the vi- cinity of the Yucatan Channel along the east coast of the Yucatan Peninsula and, if possible, along the nearby south coast of Cuba. Bottom tidal gauges could be used effectively in this area, as well. Summary The following observational programs are necessary for a comprehensive study of tides in the Gulf of Mexico. They are listed in order of decreasing priority. 1. Tidal current observations in the Yucatan Channel. A period of 15 or 29 days would be best, but shorter periods of a few days would be use- ful, particularly if chosen near the dates of maximum declination of the moon. 2. Tidal measurements in deep water in various portions of the gulf and nearby areas of the Caribbean. 3. Tidal current observations in the Florida Strait. The comment made under point 1, concerning duration, applies here as well. 68 Bulletin of Marine Science [20(1) 4. Analysis of tidal observations for more places on the east coast of Florida between Key West and Vero Beach and in nearby areas of the Car- ibbean, generally for at least 15 days and hopefully for longer periods. Sumario Mareas en el Golfo de Mexico — Revision y Proposicion de un Programa Se propone un estudio de las mareas en el Golfo de Mexico como parte del programa Aho Cientifico del Golfo (1970). Existen varias hipotesis que explican las mareas diurnas en el Golfo. Estas se describen y discuten y se sugiere una nueva hipotesis. Las mareas semidiurnas son generalmente pequehas y por tanto han tenido menos atencion; no obstante, hay varias hipotesis que son bastante contradictorias. Se propone un programa de observaciones de mareas y corrientes de mareas que permitiria discriminar entre las distintas hipotesis. BIBLIOGRAPHY Clark, J. G. and J. R. Yarnall 1967. Long range ocean acoustics and synoptic oceanography, Straits of Florida results. Proc. 4th U. S. Navy Symposium on Military Ocean- ography, Vol. 1: 309-365. Dietrich, G. 1963. General oceanography, an introduction. John Wiley and Sons, New York, 588 pp. Endros, A. 1908. Vergleichende Zusammenstellung der Hauptseichesperioden der bis jetzt untersuchten Seen mit Anwendung auf verwandte Probleme. Petermanns Mitt., 54: 86-88. Grace, S. F. 1932. The principal diurnal constituent of tidal motion in the Gulf of Mex- ico. Mon. Not. R. Astr. Soc. Geophys. Suppl., 3(2): 70-83. 1933. The principal semi-diurnal constituent of tidal motion in the Gulf of Mexico. Mon. Not. R. Astr. Soc. Geophys. Suppl., 5(3): 156-162. Harris, R. A. 1904. Manual of tides, IV B. Rep. U. S. Cst geod. Surv. for 1904, Appen- dix No. 5: 313-400. 1907. Manual of tides, V. Rep. U. S. Cst geod. Surv. for 1907, Appendix No. 6: 231-545. K.NAUSS, J. A. 1965. A technique for measuring deep ocean currents close to the bottom with an unattached current meter, and some preliminary results. J. mar. Res., 25(3): 237-245. Marmer, H. A. 1954. Tides and sea level in the Gulf of Mexico. Fishery Bull. Fish Wildl. Serv. U. S., 55(89): 101-118. Munk, W. H. and B. D. Zetler 1967. Deep sea tides: A program. Science, 158( 3803) : 884-886. 1970] Zetler & Hansen: Tides in the Gulf of Mexico 69 Pillsbury, J. E. 1891. The Gulf Stream. Rep. U. S. Cst geod. Surv. for 1890, Appendix No. 10: 461-620. ROYER, T. C. AND R. O. REID 1966. Gravity waves in a rotating basin — normal modes. Dept. of Ocean- ography, Texas A&M Univ., Proj. 471, Ref. 66-27T: 85 pp. SCHMITZ, W. J. AND W. S. RICHARDSON 1968. On the transport of the Florida Current. Deep-Sea Res., 15(6): 679- 693. Smith, J. A., B. D. Zetler, and S. Broida 1969. Tidal modulation of the Florida Current surface flow. Jour. Mar. Tech. Soc, 5(3): 41-46. Steinberg, J. C. and T. G. Birdsall 1966. Underwater sound propagation in the Straits of Florida. J. acoust. Soc. Am., 39(2): 301-315. Sterneck, R. 1920. Die Gezeiten der Ozeane. Sber. Akad. Wiss. Wien, 129: 131-150. 1921. Die Gezeiten der Ozeane. Sber. Akad. Wiss. Wien, 130: 363-371. Von Arx, W. S., D. F. Bumpus, and W. S. Richardson 1955. On the fine-structure of the Gulf Stream front. Deep-Sea Res., 3: 46-65. 70 Reprinted from Monthly Weather Review 9_8_, No. 6, 462-^78 Vol. 98, No. 6 UDC 651.466.755:551.465.557:551.515.21 462 MONTHLY WEATHER REVIEW "BOTTOM STRESS TIME-HISTORY" IN LINEARIZED EQUATIONS OF MOTION FOR STORM SURGES ' CHESTER P. JELESNIANSKI 2 Atlantic Oceanographic and Meteorological Laboratories, ESSA, Miami, Fla. ABSTRACT A transient Ekman's transport equation, in which bottom stress is formed as a convoluted integral in terms of surface stress and surface slope, and a continuity equation are used as predictors to compute storm surges in a model basin. Driving forces in the basin are analytically computed, using a model storm to represent actual meteorological conditions. A coastal boundary condition that relates surface slope to surface stress is developed by balancing slope and drift transports normal to a vertical wall. At interior grid points of the basin, sea-surface heights are computed by numerical means, using the prediction equations. These sea-surface heights are then extrapolated to the coast to agree with the coastal surface slope given by the boundary condition. Coastal storm surges computed in this manner are compared with observed surges to test the model developed in this study. CONTENTS 1. Introduction 462 2. Prediction equations in component form 463 3. Bottom stress as a convolution integral 464 4. Approximating the kernels KF, KQ for numerical compu- tations 466 5. Coastal boundary conditions 466 6. Model basins and storms, open boundaries, initial condi- tions 468 7. Testing the model 469 8. Summary and conclusions 471 Appendix A 472 Vertical current profiles and bottom stress solutions for large TH 472 Bottom stress solutions for small TH 474 Appendix B 475 Lebesgue's theorem 475 Appendix C 475 Appendix D 477 Interior points 477 Open boundaries 477 Coastal boundary 477 Acknowledgments 478 References 478 1. INTRODUCTION A mathematical model for storm surges could begin with the theory of drift and slope currents as developed by Ekman (1905, 1923). This theory, though based on simplifying assumptions of shallow-water theory, hydro- static pressure, homogeneous sea of infinite horizontal extent, constant Coriolis parameter, constant eddy vis- cosity coefficient, and neglect of lateral stresses and non- linear interaction terms, is still superbly useful for many investigations. Most of these assumptions are too severe for deep seas of large areal extent where variation of the Coriolis parameter, density stratifications, and lateral stresses are important physical processes. However, the equatious may be of sufficient generality to compute ' This study is in partial fulfillment of the requirements for the degree of Doctor of Philosophy of Engineering Science in the School of Engineering and Science of New York University. * Now affiliated with the Techniques Development Laboratory, ESSA, Silver Spring, Md. storm surges along shallow continental shelves of limited areal extent where variation of Coriolis parameter is negligible and lateral stress is much smaller than the vertical stress. Following Ekman, one can write the equation of motion in complex form dv)_ -ifw+q-\-v dhv 6V* (1) where w=u-\-iv, horizontal components of current, /= Coriolis parameter, g=-g[(d(h-h0)/dx)+i(d(h-h0)/dy)], g = gravity, h = storm surge height, v=constant vertical eddy viscosity coefficient, 2'=vertical coordinate positive upward, prime symbol in anticipation of nondimensionalizing, and h0= inverse barometric height from atmospheric pressure, and in a more convenient form to nondimensionalize the vertical coordinate as (1+*) w=) H'-e+y-iS dw Hdz~l (3) June 1970 Chester P. Jelesnianski 463 where W=H f wdz, Q=Hq, and F=b>/H)(dw/dz)\!=0- The vertical coordinate in equation (3) has not yet been completely eliminated. It appears implicitly in the vertical gradient of velocity on the bottom, that is, the bottom stress.3 By assuming intuitive forms for bottom stress that are not based on Ekman's theory, the vertical coordinate can be eliminated. Such investigations have been carried out by Hansen (1956) and Miyazaki (1965; . Instead of treating bottom stress as an extrapolation of present forces, Platzman (1963) considered the time history of present and past forces using Ekman's theory and derived a differential operator for bottom stress in series form. Jelesnianski (1967) used a modification of this scheme in numerical computations of hurricane- generated storm surges along coastal areas. The results appeared to explain some salient features of storm surges. Platzman's series expansions, designed to act separately on transport and driving forces, had inherent conver- gence difficulties. The difficulty disappeared only when the two series were truncated to first order for the trans- port field and zeroth order for the driving forces; thus, the truncated form implies that immediate time-history of forces is sufficient to express bottom stiess. This restric- tion on time history was sufficient motivation for investi- gating the possibility of using an integral operator for bottom stress that incorporates all the time history of the system. Using Ekman theory, Welander (1957) suggests that bottom stress can be determined from the local time- histories of wind stress and surface slope by means of an integral operator in the form of a convolution integral. In this approach, there is a lag in time between the appearance of wind stress or surface slope and the con- sequent bottom stress. The operator includes the entire time-history of driving forces indefinitely into the past. Welander also suggests a single prediction equation to compute the surface heights or storm surge, but only his first suggestion is followed in this study. The exact analytical form for bottom stress is approximated by an integral form and computed by numerical techniques. Thus, the transport equation of motion and a continuity equation are used in this prediction scheme. In Platzman's and Welander's schemes, the vertical coordinate is fully eliminated at the expense of consider- ing a new form for the variation of bottom stress in terms of quantities that are not dependent on the vertical coordinate and time. Ekman's equation cannot satisfy physical boundary conditions at a wall or coastline, that is, vanishing currents or vanishing current normal to the wall. However, van- ishing transports normal to the wall can be used as representative boundary conditions. The case of zero depths at a coastline introduces singularities in the equa- tion of motion that can be treated mathematically and 3 In a stratified deep sea, it is assumed that the velocity vector vanishes at some distance below the surface because of mass adjustments; thus, bottom stress also vanishes. In this case, lateral stresses are important dissipation forces. computationally for certain types of depth profiles gener- ally encountered in nature. It appears from equation (2) that the vertical current profile is a function of driving forces at local points without regard for neighboring points, and similarly the transports in equation (3). This is not true, for we have yet to satisfy the continuity equation dt dx dy (4. where W= U-\-iV defines the components of the complex transport. The surface slope Vh will be called the dynamic slope to distinguish it from the inverted barometer effect. The dynamic slope is treated as a driving force 4 in this study. The driving forces, F and Q in equation (3), have been regarded as independent functions of time, even though they do vary in space and are interdependent. This has been done purely for convenience, but with the under- standing that the momentum equation is spatially connected through the continuity equation. In this study, a model basin and model storm are used with the prediction scheme to compute surges. The computations are performed numerically using finite- difference equations. Comparisons of observed and com- puted surges are made for three hurricanes that passed Atlantic City with tracks more or less parallel to the coast. The surge from this type of storm passage is very compli- cated in that several resurgences occur after storm passage, in addition to the peak surge which occurs during storm passage. 2. PREDICTION EQUATIONS IN COMPONENT FORM For convenience, the momentum equation (3) is now written as Q-t + if)w=Q+F-(eQ+eF) (5a) where QQ, QF is notation for complex convolution inte- grals representing bottom stress in terms of surface slope (dynamic and atmospheric pressure) and surface wind stress, respectively. The form of these integrals is given in a later section. In component form, the above becomes and dU dt~ dV= dt V+*>F+gn^- dx bh dx dh0 3 . '1 (5b) .gn%-ju+»F+gn^-ge«* where WF, 'V)F are components of surface stress. There are six G's in the above equations, the real (rs) and imaginary (ij) part of Q. for each of three driving forces, where j=l, 2, 3 means dynamic slope or storm surge, slope due to atmospheric pressure, and wind stress driving force, respectively. 1 Platzman (1963) treated transport as a driving force in his series expansion, for conven- ence in numerical computations. His method could equally well treat Q as a driving force . 464 MONTHLY WEATHER REVIEW Vol. 98, No. 6 The surface stress F in this study is given by F=Opa |Fj|Fj p where Vs=complex wind, pa, p = air, water density, C the drag coefficient is assumed constant, and C/)a/p=3X10-6 ft2/sec2. Equation (5b) and the continuity equation (4) are the prediction equations used in this paper. Boundary condi- tions must be specified to complete the system; these are given in later sections. The numerical scheme for computa- tions is given appendix D. The numerical scheme was tested; comparisons were made between it and known analytical solutions without bottom stress for resonance phenomena (Reid 1958) — that is, traveling (edge) waves. For comparison purposes, only basins with shallow slopes and small coastal depths were used. The computed periods and/or wave lengths agreed with the fundamental mode of the analytically derived dispersion equation to within a few percent. No com- parisons were made of the computed amplitudes of the surge since the driving forces of this study are not equiv- alent to the ones used in known analytic solutions (Greenspan 1956, Munk 1956). 3. BOTTOM STRESS AS A CONVOLUTION INTEGRAL The bottom stress convolution integral is a mathemat- ical statement that the fluid not only senses present forces but also remembers past forces, that is "time history." For formulating the bottom stress (v/H){dw/dz)\z,-i in (3), equation (2) is solved for w, the current profile, as an exact convolution integral in terms of the local driving forces F and Q. A boundary condition for the bottom is needed to complete the transport prediction equation; a simple one5 is w|z=_i = 0. With this boundary condition, a solution of equation (2) gives bottom stress as v dw :-i H2Uo F(t-r)e-"'KF(T)dT + £Q(t-r)e-^KQ(r)dr'j (appendix A), where Kf(t), Kq{t) are appropriate kernel functions. Note that v\W- can be used as a time scale for the kernel functions; thus, TH=(v/H2)t is a convenient nondimensional parameter. For large TH, one form for the kernels is ^')-S(-i)v(n+|).«p{-[(»+J),Jr,} ^(0=2 exP {-[("+;>) T~]T»\ ; and (6) 'Other bottom boundary conditions may be preferable, such as WH) (cto/dz) 1 1— 1 = sw\,— i or (p/H)(dw/dz)|i~i=«|w|it>|i—i, where s is a slip coefficient. The solutions have forms that are laborious for computations; hence, they are not considered in this pre- liminary study. and for small TH, another form is ^)=^s(-i)nH)exp r K^t)=^TW-\ 1+2 S (-D" exp H)' (7) The characteristic or reference time TH varies considerably in this study due to variable depths in the basin. Com- parisons of the two time scales associated with v/H2 and / in the bottom stress convolution integrals suggest the latter time scale to be of small importance in shallow water. The graphs of the kernels, with TH as the independent variable, are shown in figure 1. The kernels are uniformly continuous for all positive values except in the neighbor- hood of TH = 0. From equation (7), the structure of the kernels for TH-^0-\- (small time or deep water) can be studied, noting that x"e~z^>0 as x— ><*> for all n, KQ^> {TH)-ln, and KF^0 as Tff->0 + . The kernel KF has an essential singularity at TH = 0; this is demonstrated by considering the coefficients of a Taylor's expansion of (7) where dkKF/dT^TH=0 = 0 for k=0, 1,2,. . . , that is, the power series expansion for KF vanishes although KF does not. Since this study deals with shallow water, the form (6) is preferable to (7). For large values of TH, TH>0.3, the kernels given by (6) converge rapidly, and only the very first few terms are required in computations; for small TH, 7#<0.3, the series converges very slowly, and many terms would be required. For convenience in numerical computations, either kernel is represented by means of a finite series of exponentials consisting of the very first few terms of equation (6) plus correction terms. The kernel can then be written as N K=J^ant 7!=1 (8) where N is finite and an, bn are to be specified. If at each time step in computations the entire convolu- tion integral is recalculated at each surface grid point, an inordinate number of computations and amount of ma- chine core storage are required. By taking advantage of an "exponential" kernel, a recursion formula can be developed to update or modify the integral, using previous values and newly generated data that appear at each time step. To develop a recursion formula, let G be any of the three driving forces of the convolution integral. Represent its exact kernel by equation (8), then define eGw=TJi£ G^-^~ttT s v-wr. o) Letting t=mAt and Q. a(mAt)= Ga, one can rewrite the June 1970 Chester P. Jelesnianski 465 LINEAR SCALE — LOG SCALE Figure 1. — The kernels KF, KQ as functions of the nondimensional parameter TH. above as 9„ N frnM (?3=-&iSo- G{mM-T)e-lt'+tn*dT. tt n=i Jo (10) The summation and integration operators have been inter- changed; this is permissible for finite sums. The inter- change can also be made for the exact kernels given in equation (6), even though the series are not uniformly convergent at TB=0; the proof of the interchange comes from Lebesgue's theorem as given in appendix B. Now consider any nth term in equation (10) and form and £1 n = l (ID m-1 fik+Dit CS=anJZ G(mA«-r)e-(,"+")*. (12) 4=0 Jk/U To process (12) into a numerical form, let 6(ffli(-T)~a-(mAI-r)j3 (13) where a=Gm~k, fi=[Gm-"-l — Gm-k]lM, and G'imAt—r) = — j8. Here, an assumption is made that the driving forces can be represented by a linear function in the small time interval At. Suppose now that equation (12) is integrated by parts. Then " *=0 L On + lJ On + %J X G'(mAt-T)e-l,>"+")TdT. JkM Applying (13) to the above equation gives C3=I2 (AnY[BnCh-*-l+EHG"-*\ (14) " *=o where An=e-^+inA<; ( )*=ith power; Bn=J~~®".,\ A„+,, ,*"v\A4 ' and b„+ij[_ (bn+if)AtJ V - a" l~i i A*~l "1 " bn+ijli + (bn+iJ)MJ By suitable contraction on limits in the summation opera- tor, equation (14) can be written as m— 1 CS =Jn 2 (An)kG"-k+Bm(A»)m-lG<'+EnGm (15) where yn=Bn(An)-1+Ett. In (15), G°=0 since all driving forces are initially zero. Suppose now that time increases from mAt to (m-\-l)At. Then m C5+1=7n S {An)*G»+1-*+E>G"+1, (16) or after some rearrangement {OT-l "^ 7* S {An)*G~~*+ EnG>* V +BnG^+EnGm+\ (17) With the aid of equation (15), the above becomes CS^l=AnCSH+BnGm+EnGm+l. (18) Returning to equation (11), one obtains e2+l=W2 £ Co+,=% £ [A,C3n+BnG»+EHG»+l] (19) which is a simple recursion formula for the convolution integral. Since the convolution integrals are zero at t=0, then for initialization Co=0 and C"£n=0. To break (19) into real and imaginary parts to fit (5b), consider equation (11) at time t=mAt. Then e.T.+^-raSK^.+ttfyJ, J=l-2,3, (20) 466 MONTHLY WEATHER REVIEW Vol. 98, No. 6 where +EMnG™ .) —Eit) nG ("> and (21) and where G^p, Gup means real and imaginary parts of the jth driving force and the subscripts (r)n, (i)n mean real and imaginary parts of the complex coefficients An, Bn, and En. The complex coefficients given by equation (14), although formidable in appearance, can be computed once and for all when an and bn from (8) are specified for each kernel separately. Note that j=l, 2 have the same kernel KQ, but different driving forces. 4. APPROXIMATING THE KERNELS KF, KQ FOR NUMERICAL COMPUTATIONS ft is very difficult to form the kernels KF, Ka with great accuracy throughout the positive TH axis when using the finite sum of exponents given by equation (8). This difficulty arises because of the nonuniform conver- gence of the kernels at the point TH=0. For shallow water, where bottom stress is most important, the kernels can be adequately represented for moderate to large time intervals with the first term of the series (6) ; consequently, it is desirable to consider this first term as the major part of the kernel, and if any other terms are used they will be appropriate corrections of insignificant value except when TH is small. The corrections, if any, should be in exponential form to take advantage of the recursion formula given by (19). For KF, no finite number of terms in (8) will adequately represent the kernel as TH— >0 + . For convenience, equa- tion (8) is approximated by using the first term of (6) in its exact form and altering the coefficient of the second term so that Kr=A\{e- 'TH/i_--9^THH-\ (22) where A is a normalizing factor given by the ratio of the integrals (6) and (8) as _ 1/2 =0.8835. Although (22) does not accurately represent the kernel KF for small TH, it does have the property of starting off with zero value, reaching a peak value, and then decreasing monotonically and exponentially to zero as TH—*<*> , all in conformity with the character of the exact kernel. For KQ also, no finite sum of terms given by equation (8) will adequately represent the kernel as TH— »0 + . The character of the curve, however, can be represented by taking only the first term of the series (6) with altered coeffi cients in the form KQ^Be-2T"ii where B rsexp{-[H)-»^ /."«p(-ir')dr- 1/2 "4/n-2 (23) = 1.2337. The approximation for KQ given by (23) is finite as TH— »0 + , whereas .£CQ— >°° in equation (6). However, the integrals of these kernels enter the computations and converge whether using the exact or approximate kernel. Although the approximations for the kernels do not accurately agree with the exact kernels, the integrals with respect to time for large t or small H do agree. In any case, the approximations have the characteristics of time history in the convolution integrals and should shed some light on bottom stress time-history. 5. COASTAL BOUNDARY CONDITIONS In formulating boundary conditions, the artifice of a vertical wall placed at the coast is used. This is done applying the argument that the bottom slope at and near a coast is two or three orders of magnitude greater than the average slope of the Continental Shelf. In Ekman's equations, for basins with small sloping bottoms, horizontal viscosity at neighboring points is considered small compared to vertical viscosity. This condition no longer holds at coastlines having large bottom slopes and /or the infinite slope of a vertical wall. Thus, to satisfy boundary conditions of a vertical wall placed in the fluid, we would have to consider at least the effects of vertical motion to balance the horizontal viscosity. If Ekman's equation is to be used with coastlines, then compromises are in order. A physical boundary condition at a coast with a vertical wall has vanishing normal velocities, that is, ii(x,y,z,t) x=0 = 0. For transport equations of motion, we settle instead for a more relaxed boundary condition represented by vanishing normal transport, that is, U(x,y,t)I=0=0. This relaxed condition permits a useful interpretation of Ekman's equations at the coast. It is possible to postulate a balance between wind and drift transports normal to a vertical plane, and this plane can then be regarded as a coastline. The separate Ekman spirals, drift, and slope currents in the vertical differ, and for finite depths there can be June 1970 Chester P. Jelesnianski 467 Figure 2. — Computed coastal surge profiles at the time of peak surge for various sums of the convolution integrals in the predic- tion equations. Observer is at sea, facing land; abscissa is the coastline. at most only a finite number of points in the vertical where the total current has vanishing components in a given horizontal direction. This means that, if bottom stress is considered in Ekman's equation, it is impossible to have both vanishing transport and bottom stress normal to the boundary. We insist, therefore, on vanishing normal transports, dU(x,y,t)/dt\I=0 = 0, at the coastline and accept the resulting bottom stress values computed by the convolution integrals in (5b) to form -gH^+fV+«>F+gH^-°-± e is 1, so that the behavior has the form of a Dirac function. Hence equation (5a) becomes h->o \ dt (<$W=_i ,fwy (25) (The same result follows if v— ><».) The solution to equa- tion (25) depends on initial values of W, which are zero (or the transports become zero by definition for zero depths); hence, the transport is zero for all times. Now (24) is the same as Re(dW/dt)=0; so for H->0, the boundary equation reduces identically to zero. To determine a coastal boundary condition for coastal H—>0, we consider the structure of the vertical current profile for small depths. The exact form for the drift current (after division by H) is given by equation (40) as =4 S cos (2B+1) \ z P [^F(t-r) Irif! tl 71 = 0 ^ JO X cos fT + iv)F(t-T) sin/r] X exp / -[(271+1) iJ-^Adr. As H—*0, the limiting form behaves like a Dirac function so that u 1 lim 11, (l+z)"F(t) (26) drill 468 MONTHLY WEATHER REVIEW Vol. 98, No. 6 since |"2Scos(2,+ l)^J;exp{-[(2n+l)g2^<} dt 8 » cos (2n+l)-2 1 =^? § (2w+l)2 =v (1 + 2)- (See Dwight 1961.) Interpreting equation (26) for shallow water, we see that the current varies linearly with depth and the stress as MF(t) ; also, the Coriolis parameter is no longer significant. From equation (53), the exact form for the slope vertical current profile (after division by H) is given as !;oPr^S(^+iw2cos(2w+1)^ X P Vz)Q(t-r) C0SJT + WQ(t-r) sin fr] Xexp^-[(2n+l)|J^r\ dr. As H— >0, the limiting form also behaves like a Dirac function, so that lim TJ H->o ti 2v (l-z2)(I,Q«) (27) j;exp{-[(2,+i);g^}^ wti(2n+l)l/2COs(2n + l)W2Z X Jo L =BS(fcS-3Cos(2,+ l)|2=l(l-^). (See Dwight 1961.) Interpreting (27) for shallow water, we see that the current varies parabolically with depth; the stress is zero on the surface and varies as wQ(t) on the bottom; the Coriolis parameter is no longer significant. For vanishing transports normal to a coast, we then form lim H->0 tl ffJ_i(«„,/,+Ms^)-j;|_^2_ + ^— |-0 wQ(t)=-^"F(t). (28) Ekman derived the above result for the equilibrium case (Neumann and Pierson 1966). A useful interpretation of the last equation could be as follows. If the characteristic time TH is 1, then t0=H2/v is a measure of time to reach equilibrium state. But shallow depths imply t0—>0, which means that, even near zero, time is large relative to the time required for the equilibrium state to occur. It is emphasized that the 3/2 factor for the coastal boundary condition in (28) occurs only in conjunction with the no-slip bottom boundary condition w2=_, = 0. For no bottom stress, that is pure bottom slip and H— >0, it COASTAL '''//yy&r. DEPTHS Figure 3. — Rectangular one-dimensional variable depth model basin. follows that (I><2= — ™F as given by equation (24), and the factor is 1 . The form of the surge in the neighborhood of the seaward boundary is strongly influenced by the depth profile. Suppose at the boundary H=ax9; a and /3 are constants. Then taking U)Q=Hdh/dx, it is seen that the surge h at the boundary would be finite or infinite as /3 is less or greater than 1.' In particular if (3=1, there is a logarithmic singularity in h. Nonlinear effects, no doubt, take precedence as //— >0. These effects are not within the scope of this study. Because of this, and since singularities are introduced in the equations of motion, the case of zero boundary depths is not considered in the computational methods of this study. When the coastal depths are finite, it is possible to determine Q in terms of f as a boundary condition (appendix C). This form of the boundary condition may be preferable to equation (24), for example for Welander's suggested numerical scheme; both forms are identical to within an initial constant, and the initial constant is zero for an initially quiescent sea. 6. MODEL BASINS AND STORMS, OPEN BOUNDARIES, INITIAL CONDITIONS The model basins of this study correspond to that given by Jelesnianski (1966) consisting of a rectangular-shaped variable depth basin, open to the sea on three sides. Only one-dimensional depth profiles are used since the con- tinental shelves of the oceans vary predominantly in one direction. Except for reprogramming, the need for extra machine core storage, and extra machine time, there are no essential or insurmountable difficulties in the model preventing two-dimensional bottom specifications if such detail is desired. Figure 3 illustrates the idealized basin used in this study. 6 Natural coastlines generally have 0<1. June 1970 Chester P. Jelesnianski 469 For any grid scheme in numerical computations, the grid distance must be fine enough to portray not only the storm surge but also the driving forces of the storm. This distance may be determined by empirical tests. Due to computer core limitations and economics of machine operations, it is impossible at this time to consider an entire ocean as a basin; open boundaries are therefore used in this study. On the two lateral, open boundaries normal to the coast, the boundary condition used is dV/dy=0. This condition 7 is arbitrary and used purely for convenience. In any case, reflections from these boundaries eventually corrupt the interior of the basin. However, if the boundaries are placed sufficiently far from an area of interest along the coast, there will be a time interval before it is corrupted by reflections from the boundaries. The placement of these side boundaries are determined by empirical tests. The deep water open boundary is placed somewhat arbitrarily near the juncture of the continental shelf and slope. In deep water away from coastal influences, the dynamic surge is small, and the surface heights correspond very closely to the inverse barometric effect. The boundary condition used is h = h0. The model storms used in this study are analytically described using simple meteorological parameters pre- sumably available at weather stations. For the formulation of the model storm, see Jelesnianski (1966). The fluid in the basin is initially quiescent. The storm is allowed to grow to maturity in a continuous but rapid manner. Initial positioning of the storm is unimportant if the placement of the mature storm lies in deep water beyond the Continental Shelf. For storms traveling more or less parallel to the coast and along the Continental Shelf, initial placement must be at least sufficiently distant from the area of interest so that the surge has time to form; this can be operationally determined by empirical tests through variation of initial storm placement, growth time of storm, basin length, etc. 7. TESTING THE MODEL Prior to testing the model with actual observations, a value for the eddy viscosity coefficient v is required. To see how the coastal surge profile varies for different values of v, consider a particular model storm traveling normal to the coast of a model basin. Figure 4 is a plot of computed surge profiles at the time of peak surge. For small v, the profile 8 approaches the no bottom stress profile. By com- paring the observed surges from tide gages against com- puted surges of the model, it is possible to choose a value of v to adequately match the observed surges. The most complicated coastal surge phenomena occur for storms moving more or less parallel to the coast. It was decided, therefore, to test the model for such storms by 7 One could postulate radiation properties, such as making the two boundaries trans- parent to waves, say traveling parallel to the coast. For example, it is possible to form traveling waves with phase speed equal to the speed of the storm traveling parallel to the coast (Jelesnianski 1966). » The profiles computed by Platzman's method (Jelesnianski 1967) behave somewhat similarly except for the important difference that the peak surge for small » exceeds the peak surge of the no bottom stress case. Figure 4. — Coastal storm surge profiles for different eddy viscosity values. All other variables are the same; abscissa is the coastline. comparing it with observed storm surges off Atlantic City. Only on the Atlantic Seaboard do historical storms have tracks nearly parallel to a coast, and Atlantic City is the only station in this region that has a tide gage well exposed to the sea. Figure 5 shows the paths of three storms on which computations made in this study were based. The plan view of the model basin is 560X65 mi. The depths of the model basin vary in one dimension only and are equivalent to the mean depths in the region off Atlantic City. Ini- tially, the storms were placed at the + points in the figure, with zero strength. While traveling along their tracks, they were allowed to grow to maturity in a rapid but continuous manner over 2 hr. The observed meteorological storms varied in strength, size, and speed of motion along their tracks. The meteorological parameters used to de- scribe the model storms were supplied by the Hydro- meteorological Branch, Water Management Information Division, Office of Hydrology, ESSA, Silver Spring, Md. ; they are not listed in this study. For computational con- venience, the fixed storm parameters in the model were altered only once every hour to correspond with the ob- served or extrapolated synoptic data of the storms. Figure 6 shows an observed tide record for the Atlantic City tide gage during passage of the September 1944 storm. It was necessary to put the raw observed tide data in suitable form before effecting comparisons between observed and computed data. The sequential numbers on the tide record represent hourly times of tide heights reported by the Coast and Geodetic Survey. The hourly records do not adequately portray the low-frequency oscillations; data between the hourly records were there- fore supplied by smoothing the high-frequency oscillations of the tide record by eye. The astronomical and seasonal tides were then subtracted from the prepared tide record using methods described by Harris (1963). This type of processed data will henceforth be referred to as observed data. Figure 7 compares computed versus observed tides at Atlantic City for the 1944 storm whose path is illustrated 470 MONTHLY WEATHER REVIEW Vol 98, No. 6 in figure 6. The peak tide, computed with and without bottom stress, agrees very well with the observed peak and time of occurrence. This is to be expected, since the peak is directly associated with the storm center and for fast moving storms the characteristic Ekman time t=H2/v is too large for bottom stress to be significantly felt under the storm center. After passage of the storm center and with the passing of time, the resulting waveforms or resurgences in the basin are then affected by bottom stress as demonstrated by the figure. The resurgences computed with and without bottom stress have almost equal ampli- tude and phase until contaminated by reflections from the false open-boundaries. With bottom stress, the resurgences decrease in amplitude with time, but with very little phase change9 as compared to no bottom stress. Figures 8 and 9 show computed results for the two remaining storms. In all these computations, v was given the value 0.15 ft2/sec (139 cmVsec). On the eastern seaboard, there are insufficient tide gages to determine the character of the observed coastal surge profile. Figure 10 illustrates the time history of the com- puted surge profile on the coast for the September 1944 storm. The directly generated crest and trough associated with the storm center, and moving with it, decrease in amplitude with time due to decreasing storm strength. The nature of the following resurgences are not discussed except to point out that phase speeds are not equal to storm speed. Traveling waves, with phase speed equal to storm speed, can form for the storm sizes in the model of this study, but they depend in part on the nearshore bottom topog- raphy. To demonstrate this, consider the model basin off Atlantic City modified now to a shallow linear depth as shown in the insert of figure 11 ; when the September 1944 storm surge is recomputed in this modified basin, the resurgences (fig. 11) appear to be traveling waves with phase speed equal to storm speed. The resurgences computed with bottom stress in this study agree in essence with the observed resurgences, but there are unexplained phenomena. For example, in figure 8 (hurricane Donna), there is an observed spike at 1400 est that was not reproduced in the computations; a similar but less pronounced spike exists in figure 7. The driving forces of a storm can excite certain wave forms that become trapped in a basin ( Longuet-Higgins Figure 5. — Observed paths of three storms along the Atlantic Seaboard. The model basin position is shown by a rectangle. * In Platzman's method (Jelesnianski 1967), there are significant phase changes. Scale [feet] 3r Atlantic City, N.J. September 1944 Figure 6. — Recorded tide traced from original gage record, and predicted astronomical tide (smooth curve) at Coast and Geodetic Survey Tide Station, Steel Pier, Atlantic City, N.J. The integers are hourly reported tide heights (.reproduced by permission of Harris 1963). June 1970 Chester P. Jelesnianski 471 \ „ ^ .-.. // / \ I \ / / \s/j /. \ i \ / / y if\ l /*\ \ \ , /\ > a\ ~~^\ I I I . \\ 'a ^ J / 1 1 ' 1 > \ 1 //I--- I I I I MA r3 'A I. /I// 1 06SERVEO \\ j / \ ' NO BOTTOM STRESS BOTTOM STRESS TIA. emistoryA y Figure 7. — Comparing the observed and computed surges at Atlantic City for the September 1944 storm (zero time at initiali- zation for computations) . Figure 8. — Observed and computed surges hurricane Donna. at Atlantic City for Figure 9.- -Observed and computed surges hurricane Carol. at Atlantic City for Figure 10. — Time history of the computed coastal surge profile for the September 1944 storm. Arrows show the path of the storm relative to the coast (storm initially 40 mi from bottom boundary). *s ^ ■v&C^'ife ^ ^ '■- ';<■ _ "^ 0o — §J. ^ Figure 11. — Same as figure 10, but using the shallow, linear depth basin shown by the broken line depth profile in the insert. 1967), and these trapped waves produce resurgences. The phenomena of trapped waves is beyond the scope of this study. It is suggested that the application of geometric optics, or ray theory, could be a fruitful venture to shed light on possible trapped waves for any given basin (Shen and Meyer 1967). Many simplifying assumptions are used in the model. No account is taken of the interaction between transient surges, the basic flow of the general oceanic circulation, and the astronomical tides. Curvilinear boundary coasts, estuaries, and two-dimensional depth profiles have been ignored. Notwithstanding the simplified treatment, there is reasonable agreement between observed and computed surges. 8. SUMMARY AND CONCLUSIONS A model storm described analytically with simple meteorological parameters is used to represent observed tropical storms and thereby to compute driving forces that generate storm surges. These surges are computed by numerical means in a rectangular-shaped model basin with depths varying in one dimension, and open to the sea on three sides. To test the model used in this study, computed surges for three storms traveling parallel to the eastern seaboard of the United States are compared with observed surges at Atlantic City. Ekman's equation of motion in transport form was found to be very useful when bottom stress was put in a convoluted form to take into account its time history at local points of the basin. The exact form of the integral is cumbersome to work with, but a simple repre- sentation of the kernel in the convolution integral gave a recursive relation in convenient form for numerical computations. The computed results do not differ greatly from those of a differential form for bottom stress given by Platzman (1963) and computed by Jelesnianski (1967), except that tegral form was better behaved for small values of the eddy viscosity and there were smaller phase changes in the post storm resurgences following passage of the 472 MONTHLY WEATHER REVIEW Vol. 98, No. 6 model storm. The integral form is not truncated as is the differential form, and it retains all the time-history bottom stress generated by driving forces; this serves to eliminate awkward questions on convergence properties of bottom stress formulation. For more realistic modeling of bottom stress, extra machine computations are required for the preliminary application of this study. A time-dependent coastal boundary condition was de- veloped by balancing drift and slope transports normal to a vertical wall. This boundary condition was then specialized in a form containing bottom stress and con- venient for computations; it cannot, however, handle zero boundary depths. A separate time-dependent bound- ary condition that agrees with Ekman's classical equi- librium case was formed for zero depths. A defect at the coastal boundary is that Ekman's equation uses vanishing transport that in turn does not imply vanishing current. Thus, the boundary condition is only a first approxima- tion that is hopefully acceptable for the present state of the art in storm surge computations. The results of .this study explain many of the observed phenomena of storm surges, but there are some unex- plained anomalies. These anomalies may in part be due to unknown or unobserved meteorological activity in the storms, the gross simplicity of the model basin, and initiali- zation or starting procedures in the basin. Of equal signifi- cance may be the coarseness of the grid spacing, which cannot recognize small-scale resonance phenomena re- stricted to a small region about the coast. Even within the linear equation limitations of this study, further research is required to include the effects from curvilinear coast- lines, two-dimensional variable depth basins, the effects of open boundary conditions on interior points of the basin, and the errors introduced by nonvanishing currents normal to a coast with finite depths. Further insight may also be gained by considering a bottom slip condition rather than vanishing bottom current. APPENDIX A A bottom stress formulation, necessary in equation (2), can be determined rather easily by means of a table of Laplace transforms, without requiring an explicit solution of the vertical current profile. However, the transport vertical current profile is directly formulated to analytic- ally investigate special problems such as transport forma- tion in deep and shallow waters, the formation of coastal currents, the transient surface slope, and comparisons with Ekman's equilibrium cases. The vertical current profile is composed of drift and slope currents. In this section, separate solutions in con- voluted form are given for these currents in terms of surface slope and surface wind stress. A superposition of the solutions gives the general vertical current profile. The vertical gradient of this current on the bottom then gives a form for the bottom stress. Coastal boundaries are not considered since special techniques, given in the main report, are used to handle these boundaries. It is convenient to form the solutions in terms of a nondimensional char- acteristic time parameter, TH=(v/H2)t. VERTICAL CURRENT PROFILES AND BOTTOM STRESS SOLUTIONS FOR LARGE T„ Pure drift current — Ekman's equation for pure drift current is, with the notation of equation (2), dw_ ., v d2w —_-lJW+— — (29) with boundary conditions I 1 ..1 r, " dw I ■my, d"w W =0, n=0, 1. The Laplace transform of (29) is sw(z, s) = — ijw(z, s) + v d2w(z, s) W 6V (30) with remaining boundary conditions A, . . n v dw(z,s) =F(s). For preliminary considerations, and comparisons with classical solutions, let the surface stress be a suddenly applied constant force iF0 and let the resulting current for this special case be w0. The solution to equation (30) is * iHF0sinha(l+z). HE* (31) vsot cosh a \ v/H'' A solution for the above, using an inversion integral, is w0(z, t)==—. . es'w0(z,s)ds = 'Z residues. (32) 2lrt Ja-ib The poles of (31) are all simple. The residues from these poles are given in table 1 where n = 0, 1,2, ..., y—(l-\-i) EH, E=-yJJ/2v (Ekman's parameter), and 0n=[n+(l/2)]T/H. A solution for equation (31) is then iHF0 sinh [7(1+2)] cosh 7 w0(z, t)=- -§s^c4KH (33) where An=2% , fif; 0„=,[2t-£2+«]=;/+w^. /3i+4.E4 Equation (33) may also be written as ir(n+i)«]{l-e-»»'} (34) «>o(z, o=m? 2 a„ cos vtl n=0 2)>=iS A cos [(.+!).*] vy cosh 7 vH n = on setting ^=0 in equation (33). Equation (33) is identical to the solution given by Nomitsu (1933a) using other methods; Nomitsu plotted hodographs for different depth basins with Ekman's number as a parameter. Similar solutions have been obtained by Fjeldstad (1929) and Hidaka (1933) using integral equations. June 1970 Chester P. Jelesnianski 473 Table 1. — Residues of the poles of equation (SI) a =0 i7/F0sinh[y(l+;)] vy Sillh y *..- -MM)'-'] cos[(n+^\ir:~\e-'<'-^ Before proceeding to more general cases of variable surface stress, it is interesting to compare the equilibrium transport of equation (34) with Ekman's classical solution for the case of infinite depths. To do this, (34) is integrated in the vertical to form ^•«=Sst^5{1-_w}- (35) In the above, the operations of summation and integration were interchanged ; this is permissible since the series (34) is uniformly and absolutely convergent in the range of integration. Equation (35) can be now written as V 71=0 (-l)-2[(n+i)jg-4ig , X^l-exp [-ift] exp{-[(W£)7rJ ^2} }• (36) At this point, there is a choice in limit procedures. Consider J _K y iF0 - -(-l)HiE2 hm W0= — 2 - —rk -K) and if->» v rt=0 4£,4 x(«+i) / [l-«-"']. (37) The first limiting case is Ekman's classical solution for transport in an infinite depth basin. The second limiting case demonstrates that, in limiting procedures, care must be exercised on how the question of limits is asked. A simple physical interpretation could be as follows. Ekman assumes that a balance between input momentum and dissipation exists without specifying how the balance was reached. In the latter equation of (37), the depths are too large for bottom stress to act as a dissipating mechanism; hence, the only way remaining to balance momentum is for the fluid to work against the surface stress cyclically with time. This suggests that, for deep water systems, an internal dissipating mechanism should be considered. A very simple one could be the Guldberg-Mohn assump- tion where internal friction is given by — rw, r a constant. Equation (29) could then be written as —=-%fw+ww,f=f-ir. (38) Replacing/ with/' in (36), one finds that the sequence H, t — > ro , or t, H — * oo is now irrelevant. The transport, of course, is now no longer 90° cum sole to the wind stress, but skewed by the angle tan-1 r/f. Since / » r, except at or very near the Equator, internal viscosity is not very important in transient solutions except at small latitudes or large depths. In this study, only the shallow continental shelf is used so that for practical considerations internal viscosity effects are small compared to bottom stress during transient conditions. It is desirable to remove the restriction of a constant wind stress. Suppose the wind stress varies with time, but with the initial property of F(0)=0 and dF/dt\t=0= 0. Then the solution to equation (30) is A A A w(z,s)=sF(s)w0(z,s). (39) The solution to the above can immediately be written as dF(t- w(z,t)~- -/: Wa(Z,T)d,T. Inserting equation (34) into the above, integrating by parts, and noting that An6n=2v, one finds the drift current to be w(z,t)-- iS co. [(«+!) «]j;j?Xl-r).-Wr. The drift transport is 1^=2 2 (-1)" B=o H(3 - f F{t~ n Jo T)e~B^dr. (40) (41) From equation (40), the drift current bottom stress becomes v dw Hdt z=-i H Jo t-r) S (-l)"A,e-«»'dr v dw Hdz~ where KF(t)=T, (-1 =Jp £ F(t-r)e-^KF(r)dr (42) Slope current — Ekman's equation for slope current is, with the notation of equation (2), dw ., v d2w with boundary conditions , . v dw H2 dz2 d"w (43) -O'wLr0'71^'1- Let the surface slope q0 be constant and the current for this special case w0. When using Laplace procedures as 474 in drift current, MONTHLY WEATHER REVIEW Vol. 98, No. 6 Suppose now that the surface slope varies with time and the initial conditions 10 are g(0)=0 and dq/dt\,=0=Q. a ^SoTi cosh as"! , lif+s ,... Then u "" ' w(z,s)=sq(s)w0(z, s). (52) The inversion integral of the above, with identical poles The solution to the above can be immediately written as as in drift current, gives a solution of , .. C'dq(t-T) ^r_cosh72-j V L cosh 7 J w0{z, t) = w0(z, r)dr. (jo (-l)M- When inserting equation (47) into the above and inte- When setting t = 0 in the above, cosh yz' n+^Vz \e~e"'. (45) grating by parts, the slope becomes IT cosh72"| 1 i (-1)«A» [Y ,1\ "I if (46) Equation (45) can then be written as l-e~ (47) W0(t)=%±( l£A* [l-e"»-«]. If-- then 'vHt=o PI <->«, vtl n=o Pn (48) (49) If (46) is integrated in the vertical, then 1. , . ijH>-(-l)*An - tanh 7=1—^ — 2-, & 7 v n=a Pn Substituting the above into equation (48) gives limWo^ri-^anhTp^ c- x -i+ and 1 sinh 2EH+ sin 2EH 2EH cosh 2EH+ cos 2EH i - sinh 2EH+ sin 2£'fl*] 2Ei?' cosh 2EH+ cos 2.EH J 1 (50) lim U0=Sj=,> (51) tl „ = 0 P ^ cos [(n+^) *zj P q(t-r)e-^dr. (53) The slope transport is ^(*)=4s4 f 2(t-r)«-'.'rfr. (54) " n=o P„ Jo From equation (53), the slope current bottom stress becomes " Jo 71=0 This solution is identical to the one given by Nomitsu (19336) using other methods. Before proceeding to more general cases of variable where surface slope, it is interesting to compare the equilibrium transport of equation (47) with Ekman's classical solu- tion for infinite depths. For one to accomplish this, equation (47) is integrated in the vertical to form H dz v dw Hdz~ =|i j'oQ(t-r)e^KQ(r)dr ^w-S««p{-[(«+s)*Tbi*}- BOTTOM STRESS SOLUTIONS FOR SMALL T„ (55) Pure drift current — Consider equation (31) with a variable wind stress so that where w(z,s) = F(s)G(z,s) £., , .£/" sinh a( 1+2) s-\-if G(Z,S)=— j >a = — 7E72 va cosh a v ti' (56) If a solution for bottom stress only is desired, it is not necessary to solve for the vertical current profile. Bottom stress is given as v dw\ _ v pdt7| Hdz~\!=-~H dz~\ =Fsech a. (57) The inversion of sech a, from Laplace transform tables, immediately gives equation (42) for large TH. To consider small TH, rearrange sech a as sech a= 2e- l+e- The following inversions o =2 2(-l)Vl2"+"«. (58) 77=0 X^le-^h e-a2/il and X~'[, . . ' r 1° For initial conditions, care must be taken that g = 0 for t<0. In appendixC.lt is shown If the above limiting procedure had been reversed, then that the dynamic slope at a coastal boundary for an initially quiescent sea and surface there would be a factor (1— e~tft) lUSt as in the pure stress F(o' jumps immediately to «(0) = -F(0)/H. Thus it is required that F«)=0 for ' r t<0;i(F is a constant, then it is required to consider a step function that changes in value drift-current case. fromotofat£=o. June 1970 Chester P. Jelesnianski 475 from any table of Laplace transforms applied to (58), gives for equation (57) where KF{t)=- v dw\ _ 2v V5 w) 3/2 f F(t-r)e-'frKF(T)dT s(-i)bH) Xexp[-(n+^y(^///2)]- (59) The interchange of summation and Laplace inversion is justified, since the series in (58) is absolutely convergent on the lines (Re (s) = constant) on which the inversion in- cegral is defined. The convergence properties of the above kernel are discussed in the main report. Pure slope current — Consider equation (44) with a variable surface slope so that where w(z,s) = Q(s)G(z,s) (60) * . H I" cosh as") , is i /'/ Bottom stress is given as v dw | _ fi tanh a (61) The inversion of tanh a/ a, from Laplace transform tables, immediately gives the expansion of (55) in terms of large TH. The expansion in terms of small TH is obtained by rearranging tanh a/a as tanh a l — ( a a(l + e 2q) The following inversions 4[ 1+2 2 (-1) n = l "«> Ja J a rt— X" Ja Since the exact kernels are uniformly convergent for all ranges of positive t except neighborhoods of t = 0, then only a small range, say 0 to 1, needs to be retained in the limits of integration. Consider now only the pertinent form of the exact kernel KF in equation (6) n N exp T-U+o) t\ Ci S(-n* — K v 1N ; Jdt=\ ut)dt. Jo -o ^n+Vj Jo To develop the summable function g(t), consider \fM)\-> .7(0 = -t-'^)~2tjoa$^dr=2-H-'T(e) dr (65) The convergence properties of the above kernel are discussed in the main report. where r(e) is standard notation for the gamma function that is finite when t>0. But then \J„(t)\9(. Note that the above differs from the boundary condition where (24) where Re(d/dt) (Wdr,fl+WllaJ = 0. To start, one writes equation (66) in terms of the approximate kernels given by (22) and (23); later, the „, ,. ._,. . , * i i n\ ■ i a v *■ tA-i\ Then equation (71) impi exact kernels will be considered. J^rom equations (41) and (54), F=W cosMe~bl'-e~m')> ■ ■ ■ etc IPS Wdrtft+Wslope=2 2 (-Dn — [(2n+l)|] x£ F(t-r) exp (-t/r) exp {- [(2n+l) gJ§J-(/» -2S rUf> t— t) exp (— i/r) "=°[(2n+l)|J X exp {- [(2/1+1) gjjp}*-. M9(Q «> where ( ) means ( )= I ( )e~s'dt. After some braic manipulation, X)9T-646?e-Wir cos/r— ^ (64&?+2f)e-9l"r /r"|^r-/r'(",$«-r)e-'"^r. (74) X sin (69) ^r~ -n2 exp J = (271+1) 1 1 ^ f V Then equation (67) can be written as If the above is used in computations, then recursive relations could be formulated as in the main report. The presence of iv)Q in the last term is a complication; however, the Coriolis coefficient reduces this term several i— exp ( — bit), orders of magnitude compared to others, so that it can 0i 0=Re (61) Jo \26x l F(t-r) COs/r B be ignored. For the case H—*0, it follows that lim[lI)Q(t) = -U)F(t)- i ("' [U)F{t-T) cos fT 9 Jo -wF(t-r) sin fT]5(r)dT], ff-x) + <")F(t-T) sin /rl[«-"r-«-9»"]+^ lMQ(t-r) cos/r 01 5(t) =Dirac function, or wQ{t) = -^x)F(t). (75) + ""Q (t-r) sin/r]€-6'r \dr. (70) This relation is different from that given by equation (28) in the main report, where the exact kernels KF, KQ were used. The boundary condition applies to the coastal 0=ix)9(F*(I)F+w9{F*lv)F+U)9(o*xp(-47rV-^/)- Applying the above to equation (76) gives tl 71 = 1 X f'Q(t-T)T exp (-t/r) exp (-45r2n2^-2r\/r- (79) The limit of the above as H—>0 gives Q(t) = -±F(t) -TR-ir2^ tn2 exp ( —4ir2n2^j-2t \it - (80) w2lhin2 3 This is another derivation of equation (28) in the main report. APPENDIX D In numerical computations with finite differencing, we use Shuman's (1962) notation: u',~ [u?y-u?.-/y, ^"""=^12 11 2 1 2 4 2 1 2 1 Jjm U I.* Uz 8As 1 0 1 2 0 2 1 0 1 DT.rf.rfcrr-gL 1 2 1 0 0 0 -1 -2 -1 (81) Uf.j. INTERIOR POINTS The momentum prediction equations given by equation (4b) in finite-difference form are U^-gH.-hT+fV^+^F+gH^-teio] and (82) Tt=-gH,,XXV-fU"',''+[MF+gH^-pie(ii)] ' . The terms MF, WF, (gH) (dh0/dx), and (gH)(dh0/dy) are driving forces computed from the model storm; the derivative of the inverted barometric effect (atmospheric pressure gradient) is given and need not be set in finite- difference form. Equations (20) and (21) are used to evaluate 2 G (r,), 2 Q (ij) at time m At. The dynamic surface slope gradients in (21) are not given, therefore they are set as hx , hy ■ Empirical tests without the smoothing operator ( ) gave small spurious waves in the basin in the vicinity of the storm center. This could be the result of the atmos- pheric pressure driving force (and other variables of the storm model) computed with an error of position as great as half a mile at grid points of the basin. The smoothing operator applied to the driving forces of the storm did damp out the small spurious waves, and for convenience in computations was also applied to the Coriolis and bottom stress terms. Except for the small spurious waves, the results were nearly the same with or without the smoothing operator. The continuity equation (4) becomes t=--f:v-vi OPEN BOUNDARIES (83) With open boundaries, it is impossible to use the nine- point difference forms of equation (81). The centered difference form Ux was used for gradients along the boundaries, and the uncentered form bU 1 1-3U7.j+4UT+x.j-UT+2.j] (84) dx 2As was used for gradients normal to the boundary. COASTAL BOUNDARY The centered difference form is used to compute trans- port parallel to the coast. The boundary equation (24) is used to compute surges on the coast in preference to the continuity equation (4). To display the dynamic slope at the boundary, we rewrite the boundary equation with 478 MONTHLY WEATHER REVIEW Vol. 98, No. 6 the aid of (2) at the time rnAt as { In Gm(r1), there is a term containing (dh/dy)m which cannot be determined explicitly, but it is multiplied by a small coefficient and can be safely ignored or else replaced with known slopes at interior points. Iterative tests show that the coastal surge is insensitive to this term in the boundary equation. The term {2v/H-) (E{r)t) in the di- visor approaches 1 as H—>0, which is readily seen by examining equation (14); therefore, zero depths cannot be used. An extrapolation scheme is now used where surge heights on interior grid points of the basin are connected to the boundary in conformity with the slope given by the left side of equation (85) ; this is done using the uncen- tered difference form (84). Because the depths vary, the following identity is used // dm h dx' (86) Empirical tests show that the right side is preferable when using uncentered difference forms. For notational conven- ience, we denote the right side of (85) by JK™j and use the right side of (86) with (84) to form hm — }.m dary ~2As . 9 -H4ff, 11: (87) Although analytic solutions satisfying the boundary equation (24) do satisfy continuity conditions on the boundary, there is no guarantee that the numerical scheme of this study satisfies continuity on the boundary. Stability studies for mixtures of centered, uncentered, and nine-point difference forms lie beyond the scope of this study. Empirical comparisons between computed and observed results are used as an indicator of the effective- ness of the numerical scheme. ACKNOWLEDGMENTS The author is sincerely grateful to Prof. Willard J. Pierson, Jr., for his invaluable guidance, criticism, and encouragement during the course of this investigation. Appreciation is also due Professors Gerhard Neumann, Albert D. Kirwan, Jr., and Richard M. Schot- land for their many kind advices and helpful suggestions. Special thanks are expressed to Dr. Albion Taylor for the many friendly hours of conversation we spent together during the investigation as well as his critique and proofreading of the manuscript. REFERENCES Apostol, T., Mathematical Analysis, Addison- Wesley Publishing Co., Inc., Reading, Mass., 1967, 552 pp. (see p. 459). Dwight, Herbert B., Tables of Integrals and Other Mathematical Data, The Macmillan Co., New York, 1961, 336 pp. (see p. 90). Ekman, Vagn W., "On the Influence of the Earth's Rotation on Ocean Currents," Archiv fur Malemalik, Astronomii, och Fysik, "Vol. 2, No. 11, K. Svenska Vetenskaps-akademien, Stockholm, 1905, pp. 1-53. Ekman, Vagn W., "Tiber Horizontalzirkulation bei Winderzeugten Meeresstromungen" (Concerning Horizontal Circulation in Con- nection with Wind-Generated Ocean Currents), Archiv fur Malemalik, Astronomii, och Fysik, Vol. 17, No. 26, K. Svenska Vetenskaps-akademien, Stockholm, 1923, pp. 1-74. Fjeldstad, Jonas E., "Ein Beitrag zur Theorie der Winderzeugten Meeresstromungen" (A Contribution to the Theory of Wind- Generated Ocean Currents), Gerlands Beilrage zur geophysik, Vol. 23, No. 3, Akademische verlagsgesellschaft M. B. H., Leipzig, 1929, pp. 237-247. Greenspan, H. P., "The Generation of Edge Waves on a Continental Shelf," Journal of Fluid Mechanics, Vol. 1, No. 6, Dec. 1956, pp. 592-674. Hansen, von Walter, "Theorie zur Erreehnung des Wasserstandes der Stromungen in Randmeeren nebst Anwendungen" (Theory of Calculation of the Water Level and Currents in Marginal Seas, with Applications), Tellus, Vol. 8, No. 3, Aug. 1956, pp. 287-300. Harris, D. L., "Characteristics of the Hurricane Storm Surge," Technical Paper No. 48, U.S. Weather Bureau, Washington, D.C., 1963, 139 pp. Hidaka, Koji, "Non-Stationary Ocean Currents, Part I," Memoirs of the Imperial Marine Observatory, Vol. 5, No. 3, Kobe, Japan, 1933, pp. 141-266. Jelesnianski, Chester P., "Numerical Computations of Storm Surges Without Bottom Stress," Monthly Weather Review, Vol. 94, No. 6, June 1966, pp. 379-394. Jelesnianski, Chester P., "Numerical Computations of Storm Surges With Bottom Stress," Monthly Weather Review, Vol. 95, No. 11, Nov. 1967, pp. 740-756. Longuet-Higgins, M. S., "On the Trapping of Wave Energy Round Islands," Journal of Fluid Mechanics, Vol. 29, Part 4, Sept. 1967, pp. 781-821. Miyazaki, M., "Numerical Computations of the Storm Surge of Hurricane Carla 1961 in the Gulf of Mexico," Ocean Magazine, Vol. 17, Nos. 1-2, Nov. 1965, pp. 109-140. Munk, W. H., Snodgrass, F., and Carrier, G., "Edge Waves on a Continental Shelf," Science, Vol. 123, No. 3187, Jan. 1956, pp. 127-132. Neumann, G., and Pierson, W., Jr., Principles of Physical Ocea- nography, Prentice-Hall Publishing Co., Inc., New York, 1966, 545 pp. (see p. 212). Nomitsu, Takaharu, "A Theory of the Rising Stage of Drift Cur- rent in the Ocean: I. The Case of No Bottom Current," Memoirs, Ser. A., Vol. 16, No. 2, College of Science, Kyoto Imperial Uni- versity, Japan, Mar. 1933a, pp. 161-175. Nomitsu, Takaharu, "On the Development of the Slope Current and the Barometric Current in the Ocean: I. The Case of No Bottom Current," Memoirs, Ser. A., Vol. 16, No. 2, College of Science, Kyoto Imperial University, Japan, Mar. 1933b, pp. 203-242. Platzman, George W., "The Dynamical Prediction of Wind Tides on Lake Erie," Meteorological Monographs, Vol. 4, No. 26, Sept. 1963, 44 pp. Reid, R. O., "Effect of Coriolis Force on Edge Waves: I. Investi- gation of the Normal Modes," Journal of Marine Research, Vol. 16, No. 2, 1958, pp. 109-144. Riesz, Frigyes, and Sz.-Nagy, B., Functional Analysis, Frederick Ungar Publishing Co., New York, 1955, 468 pp. (see p. 37). Shen, M. C, and Meyer, R. E., "Surface Wave Resonance on Continental and Island Slopes," MRC Technical Summary Report No. 781, Mathematics Research Center, University of Wisconsin, Madison, Sept. 1967, 64 pp. Shuman, Frederick, "Numerical Experiments With the Primitive Equations," The Proceedings of the International Symposium on Numerical Weather Predictions, Tokyo, Japan, November 7-13, 1960, Meteorological Society of Japan, Tokyo, Mar. 1962 pp. 85-108. Welander, P., "Wind Action on a Shallow Sea: Some Generaliza- tions of Ekman's Theory," Tellus, Vol. 9, No. 1, Feb. 1957, pp. 43-52. [Received July 2J,, 1969; revised February 3, 1970] Reprinted from Applied Optics 9_, No. 12, 2697" 2 705 "71 Reprinted form APPLIED OPTICS, Vol. 9, page 2697, December 1970 Copyright 1970 by the Optical Society of America and reprinted by permission of the copyright owner A Radiometric System for Airborne Measurement of the Total Heat Flow from the Sea E. D. McAlister and W. McLeish An airborne system for measurement of the total heat flow from the sea has been developed and used successfully during the BOMEX exercises in May 1969. Details of the system are described, and its operation is illustrated by one day's results at Barbados, W. I. Continuous recalibration of detector sensitivity was a major improvement which permits measurement of sea surface temperature to 0.01 °C. Introduction For the past several years this laboratory has been developing a system for direct measurements of the total heat flow within the ocean to the surface. This quantity represents the total heat loss from the water and is important in the dynamics of the ocean. In addition, it represents the total energy available to the marine atmosphere from below and is of considerable value for meteorological predictions. No direct method of measurement has previously been demonstrated. The principle of the method is to measure the vertical temperature gradient in the top 0.10 mm of the sea sur- face wherein the heat flow is dominated by molecular conduction. This is accomplished with a two-wave- length infrared radiometer especially designed for the purpose. From this temperature gradient and the conductivity of seawater the total heat flow may be determined. The first breadboard model and successful results ob- tained with it were described by McAlister.1 This resulted in U.S. Patent2 3,373,281 of 12 March 1968. Subsequently a radiometer designed for airborne use was obtained. After repeated trials and extensive modification this radiometer successfully measured the output from a laboratory water surface having a known heat loss. These and other studies were described by McAlister and McLeish.3 The use of an airborne digital data recorder is neces- sary to reach the accuracy of water temperature mea- surement required. Such a recorder was added to the system just prior to departing for Barbados, W. I., to participate in the bomex exercises in May of 1969. In spite of severe weather conditions at Barbados, three weeks of flying established the feasibility of air- borne measurements of total heat flow from the sea. The results obtained there will appear in a separate publication. Principle of Operation The principle of this method depends on the physical and optical properties of water, namely its molecular heat conductivity and absorption coefficient for in- frared radiation. Figure 1 shows the absorption co- efficient K, and the optical depth l/K, of water* in the infrared to 8 m- K ranges in value from 1.0 at 1.2 n- to 7360 at 2.96 p. This curve was drawn from data assembled by Irvine and Pollack.4 The intensity of radiation by emission from the water is a function of the underwater temperature pro- file. Once this profile is known, an effective depth from which all radiation of a particular wavelength originates can be defined. A linear profile is found3 where conduc- tion of heat predominates. Equating the intensity from the effective depth to the intensity integrated over the linear profile, it is found that the effective depth is l/K, where K is the absorption coefficient for the particular wavelength of interest. The right-hand scale for Fig. 1 is l/K, i.e., optical depth in millimeters. K is in reciprocal centimeter units. E. D. McAlister is with the University of California at San Diego, Scripps Institution of Oceanography, La Jolla, California 92037; W. McLeish is with ESSA, Atlantic Oceanographic and Meteorological Laboratories, Miami, Florida 33130. Received 27 April 1970. * Measurements with the wavelengths used show the absorp- tion coefficient and reflectivity of seawater the same as pure water within 1%. December 1970 / Vol. 9, No. 12 / APPLIED OPTICS 2697 10 20 Fig. 1. Absorption coefficient and optical depth of water in the infrared. Absorption, scattering, and emission in the atmo- spheric path used must be small and measurable. Three atmospheric windows are marked with a W in Fig. 1. Thus, there are available wavelength regions of 2.0 n to 2.4 /J., 3.5 n to 4.1 /j, and 4.5 n to 5.1 /*, pro- viding optical depths in water of 0.5 mm, 0.075 mm, and 0.025 mm. The 2.0-2.4-/X region can be used only at night because reflected solar radiation exceeds emission from the sea at this wavelength. Energy Transfer at the Sea Surface The amount of heat flowing from the sea surface by evaporation and air conduction is lost at the interface. The radiation loss comes from the top 0.02 mm. The total loss is , transported upwards by the molecular conductivity of water and by the vertical components of convective and turbulent flows. Because the vertical components of these flows are zero at the surface, there is a depth at which the flow of heat upward is dominated by conduction. Under calm conditions this depth is near 1 mm, and for a wind of 10 m sec-1 it is about 0.2 mm. These details are described by McAlister and McLeish3 and McAlister.8 The optical depths 0.025 mm and 0.075 mm provided by the regions 4.5-5.1 n and 3.5-4.1 /j. are within the upper layer, where the temperature gradient is linear and heat flow is by conduction.3 Also the 0.025-mm depth is below the radiating layer.3 Consequently, using these wavelengths the total heat flow is measured by the radiometer, since the energy lost by radiation flows upwards by conduction to a depth near 0.020 mm, where the radiation loss starts. The Radiometer The radiometer as now used has the following param- eters : instantaneous field of 25° cone view scan rate 133 sec-1 sampling time (1°) 20 X 10 ~6 sec detectors two PbSe two cooled multilayer filters providing optical depths of 0.075 mm and 0.025 mm cooler (195 K) reference blackbodies 3.5-4.1 M (channel 1) 4.5-5.1 M (channel 2) thermoelectric two The radiometer unit is shown schematically in Fig. 2, which pictures the optical system and arrangements of components. A thermoelectric device cools the de- tectors and filters to 195 K, and the spherical front sur- faced mirror allows the detectors to view a 120° cone at 195 K, which increases their sensitivity. The detec- tors are side by side, 2 mm X 5 mm each, and are covered with the appropriate filters. This combina- tion makes a square 6 mm X 6 mm, which is imaged unmagnified just inside the mouth of the blackbodies. The beam then forms a 25° cone which is used to scan the sea surface and the sky as the mirror rotates. The mirror angle is such that this beam is 20° forward of vertical to prevent the detectors from viewing the air- craft by reflection from the water surface. The two reference blackbodies are viewed on each revolution of the mirror, thus providing a continuous calibration of detector sensitivity. The temperatures of the blackbodies are recorded continuously. During a cycle of the scanning mirror, the detectors respond to the radiation intensity of the sky, blackbody 1, water, and blackbody 2 as received through the FLIGHT DIRECTION THERMO-ELECTRIC COOLER DETECTORS T AND 2 BEHIND FILTERS 1 AND ') SPHERICAL MIRROR' RELAY LENS INSULATION REFERENCE BLACKBODY 1 INSULATION REFERENCE BLACKBODY ; SCAN MIRROR SCAN MIRROR MOTOR MAGNETIC PULSE SAMPLING TIPS PREAMPLIFIERS 1 AND 2 Fig. 2. Schematic of two-wavelength radiometer. 2698 APPLIED OPTICS / Vol. 9, No. 12 / December 1970 optical filters. The waveform of the detector signal approximates four abrupt steps separated by constant value regions representing the four target intensities. These intensities are sampled at the correct time deter- mined by the angular position of the four magnetic pulse tips. A preamplifier for each detector is con- tained in the radiometer housing. The response char- acteristics of the preamplifiers, 0.02 Hz to 2500 Hz (£ power), were based on calculations of the response necessary to duplicate such a waveform within accept- able error limits. The radiometer is mounted in a pod ahead of the aircraft nose as sketched in Fig. 3. The control unit and digital data recorder are in the aircraft cabin. Figure 4 shows the action curves for the filter detector combinations. The normalized ordinates are the product of filter transmission, detector sensitivity, and relative energy for a 290-K blackbody. No infrared transmitting windows are used to cover the ports through which the sea and sky are viewed. Motor driven covers keep these openings in the pod closed at all times except when measurements are made. Thus, the optical system used to view sky, water, and blackbodies has identical transmission in each case. The net effect of absorption scattering, and emission in the atmospheric path, is measured by flights at several altitudes (see Fig. 5). Reference Blackbodies Each reference blackbody was constructed of two aluminum blocks, machined to give an 8° wedge cavity when joined. The use of a wedge instead of a cone permits the detectors to view the reference as the mirror rotates for a much longer period of time before the reading is taken. Construction of the bodies in two parts allows the apex to be made as sharp as desired; also the bodies can be disassembled for cleaning. Solid aluminum was used to minimize temperature differ- ences within the blocks. A controllable heating pad was attached to each face of the blackbodies, and they were insulated with wool felt. The blackbodies are mounted within chambers containing a cooled air stream, and their temperatures are maintained as desired with the heating pads con- trolled by separate sets of thermistors within the metal blocks. The blackbody cavities are black anodized to reduce surface-interior temperature differences. The surfaces were given a smooth, specular finish, so that external radiation entering the cavity parallel to its axis would undergo more than twenty (180°/8°) reflections before being returned. The anodized surface had a measured reflectivity in the present infrared region ranging from 2-4% at normal incidence to 15% at a 70° angle of incidence. The entire cavity surface was not anodized; instead, the outer one-third of each surface was polished to a mirror appearance. The surface temperature fluctua- tions along the cavity are presumed to be greatest near the opening, and the mirrored surface prevents these from influencing the instrument readings. DC-3 AIRCRAH NOSE RADIOMETER POD DUAL INFRARED RADIOMETER Fig. 3. Line drawing of pod and DC-3 nose. too f\ r^\ 80 / i) / \eo - / I O 40 - / 20 "./,.! J i . i , 3.8 4 2 4 8 Wavelength, microns Fig. 4. Action curves for the two filter-detector combinations. The temperature of each blackbody is measured by two thermistors connected in series, installed within the metal blocks on opposite sides of, and each 3 mm from, the radiating surfaces. The distance of the thermistors from the apex of wedge is 21% of the depth of the cavity, a value found by calculation to minimize errors due to temperature gradients within the block. These thermistors are calibrated against a mercury thermom- eter which can be read to 0.01 °C and which has been checked against a Bureau of Standards standard ther- mometer. The glass encased thermistors are held in contact with the thermometer mercury bulb in a stirred water bath. The temperature of the water bath is then changed, in about 0.2° steps, through the range of ocean temperatures expected, 10°C to 30°C. During each step the output of the resistance bridge is moni- tored with the data logger described below. In this way coincidence in time is obtained in reading of the temperature and of the output of the bridge. Ten December 1970 / Vol. 9, No. 12 / APPLIED OPTICS 2699 50 100 ALTITUDE - METERS Fig. 5. Intensity difference received at altitude vs altitude. graphs of such a series of measurements, each one for a 2°C range, constitute the calibration charts for the blackbodies. Temperature differences between them can be read to 0.001 °C from these charts. Extensive recalibration of the system as used in Barbados has shown that the radiometer's two internal blackbodies are more accurate than the external refer- ence blackbodies used for calibration. They give more reproducible results, since changes in their temperature can be read, to 0.001°C. Temperature differences be- tween Bi and Bi are quite accurate because they are geometrically identical. This temperature difference is used in determining total heat flow. However, the absolute value of sea surface temperature does depend on the inner black surface temperature of the black- bodies. Therefore, a correction determined by calibra- tion with external blackbodies is needed to obtain correct values of sea surface temperature. This correc- tion is difficult to determine. Present tests show it to be near 0.01 °C positive. Digital Data Recorder The various readings from the radiometer are con- verted to digital form and recorded on a computer compatible magnetic tape by means of a digital data recording system designed specifically for use with this instrument. The functioning of the data system is shown schematically in Fig. 6. At each mirror position indicated by a pulse tip spike, the recorder samples the signals from both detectors during a 20-jusec period. The amplitudes are stored in sample and hold circuits until released through a multiplexer into an analog- digital converter. The digital reading then is stored in a summation register. Since there are four identified mirror positions in each rotation and two detectors, the recorder contains a set of eight summation registers. The eight readings from the succeeding rotation of the mirror are added to the corresponding readings from the first rotation, and this continues until a total of thirty-two readings have been accumulated in each summation register. The most significant twelve bits of each sum are then transferred to one of ten output buffer registers. Also at this time the two reference blackbody thermistor signals are read and placed in output registers. The contents of the register are then transferred to a magnetic tape. One field of data is written for each thirty-two rota- tions of the mirror. Each field contains four readings from each of two radiation channels (sky, blackbody 1, sea, blackbody 2) plus two blackbody thermistor read- ings. Each reading contains twelve bits accuracy, but offscale readings are represented by a special char- acter. In addition, each field contains a coded identifier at the beginning and the count of a one per second clock at the end. In recent use, one record consisted of one hundred fields and required 32 X 100/133 = 24 sec. The functioning of the instrument is monitored con- tinuously in flight with display lights on the digital data recorder, and any offscale readings or recognized tape errors are noted during each record or immediately after it is completed. In addition the detector channels are monitored with an oscilloscope to detect excessive noise and to insure that the reference blackbodies are at the proper temperatures compared with the apparent sea temperature. HEFERENCE BR TEM MUX CRYSTAL ADDRESS •-ADVANCE MASTER COUNTER TIMING TIME COUNTER INCREMENT TAPE RECORDER O Fig. 6. Schematic of data recorder. 2700 APPLIED OPTICS / Vol. 9, No. 12 / December 1970 Reduction of Random Noise The noise in the preamplifier output signal is often comparable in amplitude to the signal differences be- tween the different targets, so that the random instru- ment noise must be reduced to an amount on the order of 10 ~4 of the original noise. Since the filter bandpass is specified by the limitations on inherent systematic errors, random noise reduction is accomplished by averaging a series of readings. The 1// noise power spectrum of the analog signal within the electronic filter bandpass requires that most of the noise spectral energy be concentrated in the region of low frequencies. This is, unfortunately, the region where averaging is least effective in removing noise, and the present noise level would require averages over hours or days to be reduced sufficiently. However, the rapid recalibrations in the present mode of operation shape the noise spec- trum into a form that can be reduced by averaging over about 1 min. The influence of the recalibration on the spectrum is evaluated by considering the calcula- tion of the results to be performed in several steps, each of which produces a modification to the spectrum which has previously been established. Blackman and Tukey6 describe the influence of dif- ferent data manipulations on power spectra of signals, and show that complex operations may be treated as combinations of elementary operations. A block aver- age is considered as a smoothing followed by decimation, the selection of one value in each averaging length. Subtraction of the reading of one blackbody from the other readings can similarly be considered as a high pass filtering followed by decimation. The digital sampling of a 20-Msec segment of the 2 msec between readings is also a decimation. A white spectrum will remain white through the present operations, and even a 1// spectrum will become very nearly white as a result of the low frequency rejection filter introduced by the subtraction. With a 1// spectrum, the variance in water temperature measurements can then be given by a1 oc ln(/u//i)/length of average. This equation shows the advantage of restricting the preamplifier bandpass to that necessary for accurate readings. Also, since the two infrared channels contain essentially parallel electronics and show similar wave- forms, electronic errors other than noise in one channel will also occur in the other, so that they will largely cancel in the ocean heat flow calculation. Calculation Procedures The infrared radiance from the water surface at night Iw is the sum of two parts : Iv(\ — r) from immediately below the surface ; and Is • r from the sky by reflection from the water surface, i.e., Iw = Iu(l - r) +Is-r, (1. where Iv and Is are the underwater and sky radiation intensities and r is the reflectivity of the water surface. The radiometer compares this total with that from the reference blackbody, IB- In Ref . 1 it is shown that (Iv - Is)e = (Iw - Ib) - (Is - Ib>\ iii channel 1 this is ,, j . (Iwi — Ib\) — (Is, - lBi)ri (lui - Ibi) = = Ai, (2) and in channel 2 this is II I \ (IW2 ~/jl) ~ {Is'~ lB*)ri A CU (lU2 — Ibi! = = At. (6) The difference in intensity coming from the two depths is then Iv, — Iu2 — A, — A2 (4) The temperature difference in the water at the two depths is therefore where A71 = (.4, - At)C, C = (TBl - TBi)/(JBl - It (5) (0) and IBl, IB2, TBl, and TBi are the average intensities and temperatures for the two blackbodies during the time interval of interest. This approximate relation holds with sufficient accuracy when water temperature and the blackbody temperatures are no more than 2° or 3° apart. The Effect of Sea State The 25° beam averages the intensity over a 50-m diam area of the sea surface from an altitude of 100 m. This spot size is of the order of a wavelength of surface waves. Therefore the instantaneous effect of waves in changing the reflectivity and emissivity of the sea surface is reduced, i.e., the effect approaches that of a flat surface. In addition, the temporal variations due to waves is effectively reduced by integration over a 1.6-km path (30-sec flight). This was pointed out by Saunders.7 In calculations using Cox and Munk's data on wave slopes, he comes to the conclusion that for wave conditions up to a = 0.3 (35-knot winds) the ocean is essentially flat. Therefore the small residual effect of sea state is not considered in the present state of development. Twenty degrees is the angle of emergence of the radiation coming into the radiometer from just below the water surface. It is also the angle of reflection of sky radiation. The best value at hand for the 20° reflection has been obtained from Potter's8 measure- ments at 30°, 40°, 50°, etc., combined with McAlister's1 values at 4° angle of incidence. These values were plotted on rectilinear coordinates and a smooth curve drawn through them. The 20° values read from this curve are 2.68% and 2.10% for the 3.5-4.0-M and 4.5-5. l-/i wavelength bands, respectively. December 1970 / Vol. 9, No. 12 / APPLIED OPTICS 2701 Calculation of the Temperature Difference Between the Two Depths There is an appreciable amount of absorption, scat- tering, and emission of radiation in the atmospheric path to the ocean even in the wavelength regions of the atmospheric windows used. This effect renders the intensities measured at altitude less than what they are just above the water surface, and the loss is greater at the longer wavelength (channel 2). Fortunately, this net atmospheric effect can be measured by flights at three or more altitudes, and plotting the radiation intensity differences from the two depths as observed at altitude [Eq. (4)]. Since the absorption and emis- sion are small in an atmospheric window for the path lengths used, the data so obtained fall on a straight line which can be extrapolated down to zero altitude, the ocean's surface. This extrapolation is shown in Fig. 5 for the 27 May data, where an intensity difference of 1.4 is found for zero altitude. The temperature differ- ence AT is then calculated using Eq. (5). The actual temperatures at the two depths cannot be obtained as accurately as the difference in temperatures, as just described. This is because during the half hour or more of time necessary to obtain several readings at three or more altitudes, the temperature of the water flown over usually does change a few hundredths of a degree centigrade, i.e., as much as the difference in temperature at the two depths. Consequently, a plot of the temperatures at the two depths shows a larger spread in values and an uncertain intercept at zero altitude. Also, since the difference in radiation inten- sity coming from the two depths [Eq. (4) ] changes only slightly (a small fraction of 1%) for a 0.1 °C change in water temperature (from, say, 300.0 K to 300.1 K) the temperature difference as obtained from Eq. (5) is accurate. Operation The operation of the system is illustrated by a set of records obtained during the Barbados exercises (bomex) and by the interpretation of these records. As mentioned previously, the losses in the atmospheric path to the sea are determined by two nights, each at four altitudes: 50 m, 100 m, 150 m, and 200 m. These are made in a series of flights in a racetrack course around Scripps' vessel Flip, on which was re- corded the vertical profiles of temperature and humid- ity above the water along with other meteorological and oceanographic data. Successive flights of 30 sec (yielding data for ~1.6 km of sea surface) were made upwind 300 m north of Flip and then downwind 300 m south of Flip. On 27 May, from 0852 to 0946 Zulu time, twenty-two flybys were made and the computer printout of the average of part of the one hundred entry records is shown on Fig. 7, along with the black- body temperatures and the water surface temperature from channel 1. Note that the water temperature is between the blackbody temperatures. Each one of the entries in this figure is the average of 3200 individual readings (100 X 32). Notice the small variation in the average temperature of the black- bodies and also that for the water temperature at 0.075 mm depth, the latter being the average tempera- ture for a 1.6-km path on the sea surface. The computer is programmed next to calculate Ah the right-hand side of Eq. (2), and A2, the right-hand member of Eq. (3). Some of the steps in this calcula- tion are printed out in Fig. 8. The first column is the record (flight) number, the second column is IVl — lBl, then i^ — IBt for channel 1. The fourth column is Iu2 — Ib1 (channel 2), then IBl — IBl, then TBl — TB^ in degrees Celsius, next is a column of flight altitudes, and finally Ax — A-2 in intensity units. The first number in column 2 is the numerator of Eq. (2). The next number down (also record 8) is the above number divided by ex (which makes it Ai). Numbers in the third and fifth columns are the intensity differences in channels 1 and 2 for the temperature dif- ferences (column 6) between the two blackbodies. The first number in column 4 is the numerator of Eq. (3). The next number down this column is the first one divided by e2 and multiplied by the sensitivity ratio of column 3 over column 5. This number is Ao. Col- umn 7 is the altitude of flight in feet. Column 8 is A\ — At, Eq. (4), for the different altitudes of flight, column 7. A progressive change in intensity difference from the two water depths (column 8) is apparent as the sea surface is approached in equal steps of 50 m. These values of Ax — A2 are plotted against altitude in Fig. 5. Each value plotted here is an average and is derived from 6400 readings in the two channels. The circled points are average values for the four different flight altitudes, and are derived from 38,000 readings for the 50-m and 100-m altitudes, 51,000 readings for the 150-m altitude, and 12,800 readings for the 200-m altitude. The intercept at zero altitude shows a difference of 1.40 intensity units. Using Eq. (6), C (the calibration constant) is calculated from the average of the numbers in column 6 divided by the average of the numbers in column 3. This ratio is 0.0188CC per intensity unit in channel 1 for the exercise. The average temperature difference between the depths of 0.025 mm and 0.075 mm, during this time interval, is obtained from Eq. (5), and has a value of 1.40 X 0.0188 = 0.026°C. The heat flow equation Q = KAT/d per unit area gives the amount of heat energy flowing from 0.0075 cm to 0.0025 cm as 0.086 X 0.026 0.0050 = 0.45 cal cm 2 min '. This then is the average value of the total heat flow from the sea surface for the period 0842 to 0956 Zulu time on 27 May 1969 near the latitude and longitude of Flip. The upwind and downwind legs of the racetrack course were separated laterally by about 600 m, and the results from the two legs were averaged separately. 2702 APPLIED OPTICS / Vol. 9, No. 12 / December 1970 SCANNF* NO-l SCANNED NO. 2 REFERiNCE TiM». BBl 25.2150 BB2 27.Q300 "£<-, StAd) Rd (1) SKT(l) BB <2) SSM2) B8 (1) S*Y(2> SB (2) TBB(l) TBB(2) OEC. IV lrtt>2 , 71 lifJ2. BB<1)-B8<2) SEA12)'BB11) BB(1 ).BB(J ) (T81-TB2) • 64, 7708 •66,51*6 79.7700 .73.2122 .97,9637 102.2700 -1.4330 •64.16V6 .65,9022 80 ,4800 .70.3970 .8^9029 102.8700 -1.4469 •64.18/2 •65,9202 80.5200 .74.5662 .59.0137 103,2700 -1.4654 •62,2385 • 63.91.V0 81 .0700 ■73.43g2 .88.1352 103,9500 •1.4887 •61,8286 •63, 4980 79.7400 ■76.13J0 .59.6370 103,3300 -1 .5009 •63,5282 •65,2434 81.0700 ■76.4397 .60.6337 103,7400 -1.5120 •61.6995 •63,3654 81 .4800 -67.4796 •53.7504 103 , 8300 -1.5184 15 15 •61.2291 •62,8823 80.3700 .66.6752 ■92.5126 103,5800 -1.5180 •62,8257 -64,5220 81.3600 ■72.2530 ■ 5/. 6623 103,4800 -1.5C75 •65. 7931 •67.5695 81.1300 ■75.8100 .40.0629 103,9400 -1.5154 •64,6786 •66,4249 79 .9300 .7/ . 7997 61.610s 102,4500 •1.5C20 -64, 7515 •66,4998 79.8400 77 . 9682 61.6507 102,4900 -1.5C01 ^0 20 •63,2875 •64,9962 79,8400 ■70.5369 56. 0645 1 01 ,9600 -1.5C47 21 Zl •62.67V2 •64,3716 79.9000 ■70.2218 55.6540 102,3300 -1.5C10 22 22 •62, 7994 >»64,4950 79,3200 •74.5P95 58.7787 102,0600 -1 . 49J9 23 -63,0110 •64.7123 78.9000 73.9933 66.5616 101,1900 -1.4V12 24 i* •60.5814 ■62,21/1 77 .4500 75.2417 98.8683 100.4800 -1.4807 25 25 •61.1286 -62.7790 76.2600 75.0601 58.2646 99.7200 -1 .4794 26 26 •58. 77V0 -60.3660 76.6600 66.5081 91.8034 99,9000 -1.4765 27 27 -59. 7536 •61,36/0 75.7200 6/.5613 52.0985 99 , 6700 -1.4«61 .•8 28 -57,2425 • 58. 7880 74 ,9900 61. 0033 46.6769 99, 4800 -1.4484 29 it •59.0782 •60.67J3 75.6500 63.9175 49. 06}0 100,0400 -1 .4360 Fig. 8. Computei - printout of radiation intensity differences. Alt. A L"A2 • 8 .5559 • 9 ,9993 • 6 . 9066 • 5 .7B3B • 3 .8610 -4 .6097 .9 .6150 .10 .3697 •6 8597 -7 .5067 -4 8141 -4 .8491 •8 931' -8 7l76 -5 7163 "6 150/ -J 348V -4 5144 •8 5626 -9. 2685 1?. 1112 11 . 6123 and viewing the ocean at 20° and 60° from the vertical. With higher system sensitivity these two optical path lengths to the sea surface should be sufficient. This will require two additional reading positions, controlled by magnetic switches on the mirror shaft, one for the 60° look at the sky and one for the 60° look at the sea. Also, two more entries in the data reduction system, or else time sharing for the present one, will be necessary. Conclusions (1) The present system has demonstrated the feasibil- ity of airborne measurements of total heat flow from the sea surface. Laboratory tests show an average error of ±S% in measuring heat flow.3,6 This is the first time that such direct measurements have been made. (2) Continuous recalibration (with two blackbodies) in the present mode of operation shapes the noise 2704 APPLIED OPTICS / Vol. 9, No. 12 / December 1970 spectrum into a form that can be reduced by averaging over about 1 min. (3) A new order of accuracy in sea surface tempera- ture measurement has been shown. The present sys- tem has surpassed the accuracy of oceanographic mer- cury thermometry for ocean surface temperature. (4) A redesign of the system to decrease the time needed for one heat flow measurement to about 3 min is possible. We are indebted to E. Corduan, engineer in charge of our tests at Barbados, and our technical crew, D. Dixon, H. Grow, F. Mansir, pilot D. Harvey, and co-pilot B. R. Jacquot for outstanding performance in complet- ing these difficult tests in darkness and often severe weather. We are further indebted for the technical assistance of F. G. Brown in the development and laboratory testing of the instrument during the years 1962-1968. This research was supported by the Office of Naval Research, codes 461 and 481 ; the Naval Oceanographic Office, code 7007 ; and the National Science Foundation, Atmospheric Sciences Section, under grants GA-1491 and Ga-1 1975. References 1. E. D. McAlister, Appl. Opt. 3, 609 (1964). ( 2. E. D. McAlister, U.S. Patent No. 3,373,281, 12 March 1968. 3. E. D. McAlister and W. McLeish, J. Geophys. Res. 74, 3408 (1969). 4. W. M. Irvine and J. B. Pollack, Icarus 8, 324 (1968). 5. E. D. McAlister, Oceans from Space (Gulf Publishing Co., Houston, Tex., 1969). 6. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1958), Sees. B. 15-B. 17. 7. P. Saunders, 1966 Symposium on The Remote Sensing of En- vironment (Univ. of Mich., Ann Arbor, Mich.), pp. 815-826. 8. R. F. Potter, Corona Laboratories; private communication. 9. E. B. Kraus and C. Rooth, Tellus 13, 233 (1961), Fig. 2. 10. S. L. Hastenrath, Limnol. Oceanog. 13, 322 (1968). 11. Yu. M. Timofeev, Izv. Atm. Oceanic Phys. 2, 772 (1966). December 1970 / Vol. 9, No. 12 / APPLIED OPTICS 2705 72 Reprinted from Journal of Geophysical Research 75, No. 33, 6872-6877 Spatial Spectra of Ocean Surface Temperature William McLeish National Oceanic and Atmospheric Administration Atlantic Oceanographic and Meteorological Laboratories Sea-Air Interaction Laboratory, Miami, Florida 33180 One-dimensional variance spectra of radiometric ocean surface temperature are similar at small wave numbers to horizontal spectra within the upper ocean. The variance densities in both surface water and upper ocean water decrease continuously with increasing wave numbers. However, at wave numbers greater than 2-5 X 10"5 cycle cm"1 the spectra within the water continue to decrease, but the surface spectra often become nearly constant. The additional variance density there is attributed to alteration of the surface temperature by patches of compacted organic films. This compaction is produced by convergences in the turbulence within the water. Thus small-scale temperature patterns on the ocean surface often represent only a superficial consequence of the water circulation rather than bulk temperature variations. The 'surface temperature' of the ocean is commonly measured with a bucket thermom- eter at depths of 10-30 cm, whereas the surface temperature recorded by an infrared radiation thermometer (IRT) occurs at a depth of only 0.02 mm. A mean temperature difference be- tween these depths commonly exists and can be predicted approximately [Saunders, 1967] ; but there are also horizontal variations in sur- face temperature that are not found at greater depths. In IRT surveys interpreted as tempera- ture patterns of the ocean mixed surface layer, these variations are assumed to be confined to small amplitudes. Our results give estimates of the scales at which the differences may become significant. Methods The surface temperature measurements were obtained with a 7- to 12-/J. wavelength IRT with an effective field of view of about 0.2 rad. An electronic low-pass filter with a time con- stant of either V2 or 1 sec was used to reduce aliasing; the power transfer functions of the filters were measured and applied in subsequent calculations to remove the influence of the filters from the results. The variance spectra in Figure 1 were cal- 1 The data and calculations in this paper were obtained while the author was at the University of California, San Diego. Copyright © 1970 by the American Geophysical Union. culated according to Blackman and Tukey [1958] through autocovariance functions ex- tending to 100 lags. Each record contained 1024 readings at y2-sec intervals with the exception of the spectra from the ship which contained 600 readings at 1-sec intervals. Trends were not removed. Two blank spectra were obtained with the radiometer directed toward a blackbody of nearly constant temperature. The mean spec- trum of instrument noise so obtained, spectrum A, was subtracted from the initial results to give the ocean spectra C-L. The stability of an individual estimate of spectral density (ratio of standard deviation of estimate to mean value) for a white spectrum is predicted to be 0.32. The mean stability in a series of successive spectra of the same region, spectra C, is 0.35. Spectrum B is the mean of two spectra of air temperature variations encountered in flight within the marine moist layer. The airborne ocean spectra were obtained under similar atmospheric conditions. The operating condi- tions under which the spectra were obtained are given in Table 1. Figure 2 shows original IRT and simultaneous bulk temperature records obtained from a moving ship. The IRT was mounted on a plat- form forward of the bow, and a thermistor was suspended from the platform to remain in the water at a depth of about 5 cm. Each record required one minute; during this time the ship advanced at 1.5 m sec"1. The platform was brought in for radiometer calibration at time A, 6872 BRIEF REPORT 6873 + 4 + 3 + 2 + 1 0 E V '>. +3 U "5 +2 °- +1 CM ^ x O o 0 i 3 + 2 -I- 1 0 Instrument Noise t Ocean T (Ship) Ocean T -6 -5 -4 -5 -4 -5 -4 -5 -4 log10> 1 4-> ' 0 U CD £-1 N_ _ \ \ ^ \ 1 ^' 1 1 ^ / ^ / s / \ \ \ \ 1 1 1 1 1 . . , . ■ ill 0 12 LOCAL TIME 18 24 Figure 1. Diurnal variation of the mean specific humidity in the moist layer below the trade wind inversion (curve 1). Curve 2 shows unoorreoted specific humidities obtained during ATEX (see text). Miami area were compared to establish as well as possible the total error and to use these data to provide corrections to existing data. The majority of tests were made during typical fair- weather cumulus conditions that represent the undisturbed trade wind regime, although some were made during cloudy conditions and at night. The standard pulse type 40 3 MHz radiosonde was compared with modified versions that, we believe, have significantly reduced the radiation error caused by solar heating. There were two types of modifications, the first type consisted of a minimal change and could be accomplished within a few minutes. Adhesive aluminum foil was placed on the top of the humidity duct to block the transmission of solar radi- ation, the inside of the duct was sprayed with black paint (nonglossy) to prevent scattered and reflected radiation from reaching the black carbon element (see fig. 2) . The second modifica- tion was more drastic because the duct was completely re- configured. Since there was no intention to fly the sondes in conditions of ac- tive precipitation, a verti- cal tube was attached to the radiosonde. It was manufac- tured from 1/4-inch styrofoam and covered on the outside with adhesive aluminum foil. The inside of the duct was sprayed with black, nonglossy paint except for the top 2 inches, which were left white. The sensors were in the lower third of the tube (see fig. 3) where they were shielded from radiation and had excellent ventilation. Figure 2. Diagram of the 403 mu ■ , • c ■ . ■ j MHz radiosonde with probable This modification was used „ , , . K, , , sources of heattng of the for all comparison flights hygristor at 2. Styrofoan <-- Black Coating Carbon Hygristor except the one on February 10 , 19 70 , in which aluminum foil was used over the hygristor and a flight on February 16, 19 70 that intercompared both modifications . The following proce- dure was established for all of these flights . Each flight train consisted of a 600 g balloon inflated to give at least a 300 m per minute rate of ascent, a parachute, a train regulator, a standard WB 40 3 MHz pulse modulated sonde, and a modi- fied sonde, as described _ , . , j./.« j above (was below the stan- F%gure 3. Rad%o sonde mod%f%ed to minimize solar and inter- dard) . In general, the nal heatinq of the hygristor . . , , , y J yy standard sonde was trans- mitting on the off-set fre- quency of 40 7 MHz, and the modified sonde was transmitting on 403 MHz. On the ground two receivers recorded the respective sondes and the two recorders were synchronized closely by time tics. On several flights the position of the sondes on the train was reversed to determine whether relative position would cause any bias. None was apparent. The results of these flights are presented in the appendix. Rod Thermistor 2.1 Comparison Between the Standard and Minimum Modification Sondes The modification consisted of covering the top with aluminum foil and of blackening the duct (from here on referred to as alu-modification) . This minimum modification indicates that the largest error contribution comes from direct radia- tional heating. For example, at 900 mb the alu-modification sonde records RH values 10 percent higher than the standard sonde. Therefore, an ascent was made that compared the alu- modification with the vertical duct type modification. On the average, the difference did not exceed 5 percent RH with the duct type sonde recording still higher RH values during high humidity conditions (surface to 960 mb , 760 to 680 mb) and lower RH at low RH values (9 40 to 750 mb) . This indicates that the better ventilation of the vertical duct improves the response time of the sensors. This effect is discussed later in section 3.3. All further test flights were made with the vertical duct modification. 2.2 Comparison Flights Between Standard Sondes and Vertical Duct Sondes These comparison flights were made under various day and night conditions. An example of typical trade wind con- ditions on February 19, 1970, may be found in the appendix. A temperature inversion of 6°C between 910 mb and 880 mb acts as a lid on the moist layer. Below the inversion the standard radiosonde reported 70 percent RH while the modified duct sonde showed 90 percent RH, a difference of 20 percent RH or from 9.1 g/kg to 7.0 g/kg in corresponding mixing ratio. Similar results can be found in the other daytime observations (see appendix) . These latter ascents from April 18 to April 24, 1970, were performed somewhat differently in order to obtain simul- taneous humidity readings. In the earlier flights, due to small differences in the baroswitches of the two sondes, one sonde reported temperature while the other reported humidity or reference. The modified duct type sonde was rewired to report humidity continuously, interrupted only by the reference signal at every fifth contact point. Hence, the appendix also shows values of RH that were measured exactly at the same time. These tests were made to obtain sufficient simultaneous data to develop the correction procedure (see sec. 5) that will be applied to the ATEX data. As expected, flights during thick overcast conditions and at night showed little humidity differences or nearly identical readings between the two sondes (within the sensor accuracies) . All data are presented in the appendix. 3. LABORATORY TESTS Several tests were made in the laboratory. Due to limited resources these tests should be considered as only providing rough estimates of some other possible errors not directly attributable to solar heating. For these tests a 6-foot vertical chamber with a 2 foot x 2 foot cross section was built and was provided with fans to generate a vertical wind of about 5 m/sec, or the average rate of ascent of a radiosonde . 3.1 Electronic Heating The radiosonde was placed in the vertical wind tunnel with thermocouples at basically two places. Continuous temp- erature readings were obtained, from the center of the entrance to the humidity duct of the regular radiosonde and from the carbon element itself. A thermocouple junction was attached to the carbon element and covered by a drop of silicone grease, At the same time dry- and wet-bulb temperatures were measured in the vertical wind tunnel some 12 inches above the suspended radiosonde for control purposes. The battery was activated and the radiosonde was pre- pared in the same way as before actual releases. The measure- ments started 30 min after the radiosonde was activated, a normal time span for baseline checks and flight preparation. The tests ended after 2 hours of operations. No attempts were made to test the radiosondes under other than surface atmos- pheric pressure. The ventilation effect under reduced atmos- pheric pressure is not known. A number of different radiosondes were tested, which included the types used during BOMEX. Although these sondes differ in transmitting frequency and location of battery or transmitting electronics, they all have the same configuration as far as the humidity sensor exposure is concerned. Also, the plastic material of the radiosonde housing, is the same. Table 1 shows the results. Also, some tests were made by changing the temperature of the air flow to determine the temperature time lag of the carbon element (see sec. 3.2). Finally, the modified vertical duct type radiosonde used for the environmental comparison flights (see sec. 2) was similarly tested and no heating effects detected. Table 1. Heating of Hygristor in Various Radiosondes due to Electronics and/or Battery . Radiosonde Type 403MHz 403MHz Transponder Pulse AM 1680/403MHZ 72MHz Temp. °C +0.3 +0.4 +0.7 +0.2 3.2 Humidity Response Time of the Radiosonde System Two separate attempts were made to determine the time constant of the humidity sensor under variable temperature conditions. For these tests the carbon element was removed from the radiosonde housing and exposed directly to the air stream. Temperatures (and in one experiment the RH) were changed, with the resistance change of the carbon element being transmitted to the radiosonde receiver and recorded con- ventionally on the .strip chart recorder. The experimental set-up for the first series of tests is shown in figure 4. Two different air masses were available. The laboratory air had a temperature of about 20 °C and a relative humidity of 4 8 percent. A large storage box was supplied with air from an air conditioning duct having a temperature of about 10°C and a RH of 68 percent. The air was drawn at about 5 m/sec by a fan through a channel containing the carbon element and a number of ther- mocouples. Temperature and humidity were observed in the cold storage box by calibrated mercury thermometers. Figure 5 is an example of a typical humidity trace. The ventila- tion rate at the sensor was 5 m/sec. It is clearly evi- dent that when the cold air comes in contact with the carbon element the recorded "RH" drops at first by roughly 5 percent and after about <\ir Conditioner I Warm Air Storage (~20°C,48RH) Scale 12 in. Exhaust Fan <- TX T Carbon Cold Air Storage (~10°C,68RH) Figure 4. Experimental arrange ment for response time deter- mination. 10 — 2 min — 1 min 0 min 80 ord. Figure 5. Apparent humidity decrease during rapid temperature decrease at 5 m/sec ventilation rate. 5 sec acquires its original value. The time constant was deter- mined as the time required to attain 64 percent of the new value. An average value of 17 sec was observed at 5 m/sec ventilation rate. However, at 1.5 m/sec the time constant increased to 45 sec (see fig. 6) . These are approximate values because the time constant was determined from the re- corded signal without taking the nonlinearity of the resis- tence vs. RH curve into account (Marchgraber and Grote, 1965). However, the error may not be exceedingly large because be- tween 50 percent RH and 6 5 percent RH this relationship can be approximated to the first order by a straight line. This preceeding test involved two air masses with both parameters, temperature and humidity, changing. The experiment 11 1 1 1 1 - - - - - Cold Air 0 min 4Q 1 1 1 b J ( HO 1 1 1 1 Figure 6. Apparent humidity decrease with sudden temp- erature drop at 1.5 m/sea ventilation rate. was repeated by attempting to create two air masses differ- ing only in temperature and with identical RH. This was accomplished by means of an environmental chamber. The experimental arrangements are outlined in figure 7. The air in the environ- mental chamber was heated to several degrees above room temperature while the RH was kept equal to that in the room. A small fan kept the air circulating rapidly. Temper- ature, humidity (by means of carbon element) , and air movement (hot wire anemometer) were monitored. Adjacent to the chamber, a horizontal duct was placed containing another carbon element, temperature gauge, and hot wire anemometer. When RH, (room humidity) equalled RH_ (chamber humidity) , the chamber cover was removed rapidly and room air with T, < T_ was blown at a speed of about 5 m/sec over the carbon element in the environ- mental chamber. Again, the signal from the carbon element was Blower Environmental Chamber Receiver & Recorder 12 in. Figure 7. Experimental arrangement for response time with the same temperature but different humidities . 12 transmitted from a 40 3 MHz transmitter to a nearby re- ceiver and recorded by the radiosonde recorder. Figure 8 shows an example of these tests. This second test con- firmed the findings of the previous tests, namely, a time constant of the humidity radiosonde system of about 16 sec, if a ventilation rate of 5 m/sec is maintained. For this test two different air 5 min 4 min 3 min — 2 mm 1 mm 40 T1= 26 3° T2= 29 3C 80 ord Figure 8. Record for tests with equal relative humidity and different temperatures . masses were generated with the following properties: T (°C) RH (%) e (T) s (nib) a (mb) air mass 1 29 .3 50 air mass 2 26 . 3 50 40.755 20.378 34.209 17.105 The carbon element is held in air mass 1 until ther- mally adjusted. When suddenly exposed to air mass 2, the element will acquire the new temperature very slowly due to its heat capacity. Therefore, in the close vicinity of the element the saturation water vapor pressure e (at T = 29.3) will change at a rate similar to the thermal property of the element. Hence, at the time of air mass 2 arriving at the element, the RH is given by the ratio e (air mass 2) a e (T = 29.3°C) s 17.105 mb 40.755 mb = 42% RH. 13 This means that under these test conditions because of the 3°C higher surface temperature of the carbon element, the recorded relative humidity will be 8 percent lower than the actual humidity associated with air mass 2. In this test a reduction of RH by 9 percent was found (see fig. 8) thus confirming the expected effect. Further- more, the test shows that the actual time constant of the carbon element measuring RH is determined primarily by the effect of changing temperature, which is quite different from the time constant of the carbon element at constant environ- mental temperatures. Furthermore, if 3°C/30 0 m is the average lapse rate and the balloon's rate of ascent is 300 m/min, the AT temperature change experienced by the radiosonde is t^t = 3°C/ min. Also, if the thermal time constant of the carbon ele- ment is approximately 20 sec, the carbon element will be operating thermally at approximately 1°C higher temperature than the environmental temperature. The apparent reduction in the humidity reading can be calculated for an air parcel with 80 percent RH and 22°C as follows : e (21°, 80%) 19>889 "• = ~ 7R9- DU es (22°, 100%) 26.430 Oo resulting in an underestimate of 5 percent in RH value. This effect should be present in day and night flights due to the heat capacity of the carbon element. 3.3 Flow Rate Tests To provide some estimates about the ventilation rate in the standard radiosonde humidity duct, we suspended the radiosonde housing in the vertical chamber and measured air speed with two hot-wire anemometer probes (TSI model 1051-2, 14 with linearized output) . Figure 9 shows the locations, numbered 1 through 5, where wind speeds were measured. The reference speed was ob- tained 6 inches above the radiosonde housing. At this reference height, wind obser- vations were made all across the chamber (24 inches by 24 inches) and no appreciable variation was found except very close to the chamber walls . The results of the mea- surements are summarized in a Reference 6" < ■ Carbon sis hygristor s A A A I 12 3 4 i A 5 Sea i e ^ 1 in. Figure 9. Cross section of humidity duot showing loca- tion of hot wire anemometer probes at points 1, 2t Z, 4, and 5. Air flow is toward the reader. table 2. Each value represents percentage of flow reduction with respect to the reference speed. Each location had a mean of about 10 observations. These tests seem to indicate that due to the peculiar configuration of the humidity duct the ventilation rate may be reduced to about 30 percent of the assumed rate of ascent. Normally, the balloon is inflated in such a way that is rises 300 m per min or 5 m per sec. It is possible that the actual Table 2. Measurements of Air Flow in Humidity Duot Location Average Flow Reduction (%) 71 65 67 70 72 15 ventilation rate may be as low as 1.5 or 2 m per sec. In addition, the radiosonde train swings as it rises, which may add further difficulty in estimating the true ventilation rate and its possible variation through the humidity duct. The modified sonde that was used in the comparison flights described in section 2.2 was also subjected to these tests with the results indicating very little flow reduction (about 7 percent near the carbon hygristor location) . In view of the results on the time constant of the humidity recording system (see sec. 3.2) , we may conclude that due to all these effects, such as the sensor temperature and sensor exposure, environmental conditions, and recording sys- tem, the actual time constant may be as large as 30 to 40 sec. 4. COMPARISON TESTS BETWEEN THE U.S. RADIOSONDE AND THE GERMAN RADIOSONDE After ATEX in March 1969, the German research vessel Meteor anchored at the equator and 30 °W longitude for 4 weeks to conduct primarily an ionosphere program in connection with the active sun year. During that time a comparison program was carried out consisting of the U.S. 40 3 MHz pulse type radiosonde and the German M60 radiosonde. Both were attached to the same balloon. A total of 10 daylight ascents and five nighttime ascents were made. The German sonde differs considerably from the U.S. sonde, both in configuration and in sensor. The configuration for sensor exposure is similar to the modified U.S. sonde used in the Miami comparison flights. As the humidity sensor, a rolled human hair is used, which is described by H.G. Muller (1965) . Presumably, its characteristics at temperatures above 16 freezing and at high humidities are quite good, and it deter- iorates quickly at -55°C. Between 0°C and -20°C the time con- stant increases which, according to Muller, is 10 sec for high humidities and temperatures above 0°C. The data were grouped in four categories: (1) humidity data above 0°C, (2) humidity data below 0°C, (3) daylight flights, and (4) night flights. Figure 10 shows the relative frequency distribution at daytime (1000 local time) and temperatures 20 U.S. sonde (carbon) ---German sonde (hair) u c 13 cr o 10 u i. 0 y.„ __ _i /percent relative humidity *' I ■ I , 1 i— I 20 40 60 80 100 Figure 10. Daytime observations of relative humidity frequency distribution of the U.S. and German sonde. 17 above 0°C for the German M60 humidity recordings and the U.S. 403 MHz sonde. Figure 11 shows the same statistics for the night flights (2200 local time). As seen from figure 10, only a few relative humidities above 80 percent were recorded with the U.S. sonde and the relative frequency maximum has shifted from 75 percent RH , as recorded by the hair hygristor, to 65 percent RH , as recorded by the carbon element. At night, distributions are similar, especially at high humidities. At low humidities the hair II C r- ^ ^ A r\ 1 r- n i^ K r\ n \ U . J . JUMUC \ ^ U 1 1-> u s= a> Z3 A cr CD s- <4- ' \ A 4- O 10 r ' \ / \ 1 / \ / \ +-> c CD a i_ / / \/ \ 1 / \ 1 / i 1 / \ / \ Q. I \ I I / I / percent relative humidity | / 1 . 1 . J . 1 . 1 20 40 60 80 100 Figure 11. Relative humidity frequency distribution of U.S. and German sonde night observations . 18 A RH ARH = : h a i r - ca r b on 20 1 T 1 l / T 1 l /' 1 10 i 1 1 J. 0 -10 , RH 1 I 1 20 4 0 60 80 hygristor values are lower at daytime as well as at night- time. This may be due to the poorer response of the hair hy- gristor to lower humidities or the relatively long time con- stant of the carbon hygristor system due to poor ventilation (see sec. 3.2) or both. The difference in RH be- tween the hair hygristor read- ings minus the carbon element readings was plotted against the reported humidity from the Figure 12. Frequency of occur- ence of difference between carbon element, both for the oarbon and hair RH for daji daytime ascents (fig. 12) and observations . the nighttime ascents (fig. 13) . The vertical bars indicate the standard deviation. Although there were not nearly enough cases for the nighttime values, the results as shown in figure 13 support the assump- tion that little error is pre- sent in the nighttime ascents. Therefore, no attempt was made to correct the nighttime read- ings . The Meteorological Insti- tute of the University of Ham- burg (Prof. K. Brocks, Director) developed a special sonde that is used for flights up to about 20 40 60 so ioo 21,000 feet. The sonde consists Figure 13. Frequency of oc- of a vertical aluminum tube (2 curence of difference be- inches x 2 inches x 12 inches) tween carbon and hatr RH for night observations . containing a dry thermistor ARH ARH = hair •ca rb on 20 T I 10 T I l 1 I 0 1 T I i I i \ T I 1 J. T 1 J. 1 -L i 1 J. l i i 1 V T A -10 i % RH , i -L 1 1 19 bead, wet thermistor bead, and the carbon hygristor. The altitude is determined by radar tracking. These sondes were used during ATEX on the German R/V Meteor and Planet. The RH as recorded by the carbon hygristor and as derived from the dry- and wet-bulb temperatures were similar. This is further evidence that the solar radiation contributes most to the daytime humidity errors on the U. S. 40 3 MHz sonde. 5. ATEX DATA CORRECTIONS All daytime radiosonde ascents that were made from Discoverer j Meteor3 Planet 3 and Hydra during ATEX with the U. S. 40 3 MHz radiosonde will *be corrected according to amounts presented in figure 14. Curve 1 was derived from the compari- son flights from the Meteor (sec. 4). Independently, curve 2 was constructed from the comparison flights in Miami (sec. 2.2) . In figure 14 the deficiency in RH, ARH, is plotted Figure 14. Correction curves for carbon hygristor due to solar heating . Curve 13 based on the German hair hygrometer 3 in- cludes data for temperatures below 0°C. Curve 23 based on SAIL's modified radiosonde 3 is for temperatures above 0°C. 20 against the RH reported by the regular 40 3 MHz sonde. These data were obtained under clear sky conditions with a few small trade wind cumuli, a good simulation of the general weather conditions during ATEX. An example may illustrate the application of the graph. If the regular 403 MHz sonde reports, say, 80 per- cent RH , then to this value RH = 11 percent is added to give 91 percent RH . For 70 percent RH reported, the corrected value reads 85 percent, etc. Test calculations showed, how- ever, that at very low altitudes (up to about 995 mb) this correction leads to over estimates. During the baseline check of the modified and regular radiosonde, each was exposed to the same humidity conditions and calibrations were adjusted to show this. Upon release and exposure to solar heating, the transmitted humidity values diverged such that after about 40 sec the solar heat- ing effect stabilized. This level averaged out near 200 m or 995 mb for the test data. A family of curves similar in shape to curve 2 in figure 14, but with decreasing ampli- tude from 200 m to the surface, has been developed to correct values during the period of divergence due to initial heating . It should be emphasized most emphatically that these corrections may be applied confidently only for the condi- tions comparable with those under which they were derived, namely, the undisturbed trade wind conditions as prevalent on ATEX. To verify the validity of the correction curve, we plotted the 32 day and 32 nighttime radiosonde observa- tions made in the subtropical Atlantic during July and August. As shown in figure 15, corrections were applied to the daytime humidity values and the resulting curve matched the nighttime values quite closely. 21 650 700 750 800 850 900 950 1000 J3 DAY (observed) DAY ' (corrected NIGHT mixing ratio: g/kg jL 10 1 2 14 16 Figure 15. Data for 32 day and 32 night radiosonde observa- tions made during July and August 1970 in the Atlantic. 22 6. CONCLUSION The relative humidities obtained by the U.S. radiosonde with the carbon element humidity sensor may indicate values that are incorrect by a substantial amount. The principal reason for this error is the temperature of the element it- self. If the element for any reason operates on a higher (or lower) temperature level than the environmental temperature, the air over the surface of the element will be heated (or cooled); therefore, the saturation water vapor pressure will be raised (or lowered) , resulting in a lower (or higher) RH. The carbon element may acquire a different temperature than the environmental temperature during the daytime, prin- ciply because of radiative heating. A second source of error is the heat capacity of the carbon element itself, which leads to a temperature lag while the radiosonde is rising through the atmosphere. With an adiabatic lapse rate this process will also tend to indicate humidities that are too low. In an inversion the result is opposite. Considerable improvement could be achieved by changing the exposure of the carbon element to provide a radiation shield and better ventilation. 7. ACKNOWLEDGEMENTS We express our appreciation to Mr. 0. Scribner of the Field Research Projects Office for calling our attention to the problem and Dr. A. Glaser of BOMAP for suggestions regard- ing the study. Although all of the Sea Air Interaction Lab- oratory staff were involved in the study, particular thanks are due Messrs. D. Waters, M. Poindexter, P. Connors, and Dr. W. McLeish for their contributions. We are grateful to Dr. C. Pflugbeil of the Deutscher Wetterdienst Seewetteramt at Hamburg (German Marine Weather Office) for generously providing the Meteor data used in this study. 23 8. REFERENCES Marchgraber, R. M. , and H. H. Grote (1965) , The dynamic behavior of the carbon humidity element ML-476. Humidity and Moisture I_ (Reinhold Publishing Corpora- tion, New York, N. Y.). Morrissey, J. F. , and F. J. Brousaides (1970), Temperature induced errors in the ML-476 humidity data, J. of Applied Meteorology 9, No. 5, 805-808. Muller, H. G. (1965), Humidity sensors from natural materials, Humidity and Moisture I_ (Reinhold Publishing Corpora- tion, New York, N. Y.). 24 APPENDIX A Radiosonde Temperature and Humidity Data The following 50 figures illustrate the data gathered during these experiments at Miami . Both the modified and unmodified sondes are included. 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V I— CS u- s « as s +i K Q co • is is « 3 K CO s 64 f~i « 0 VI +i is ^ 0) g S a ^ Dq fr? +i o V a E s ■w 1 a o -Q^ 1 ■o £ 05 « is iSi +i V* t-~i> 0} 3 K 0) O o is • 0) «"S ■tj o Vi S K "qj a w o is «••! 0) +* Ss V fej 46 © o o o o 47 s E +s K O CO • « 3 K CO r-i <3 O •^ +i Jh T3 0) £ ^ « tel as s« 4i © o •^ s 0) CO ^ K £ a o 0 & OS CO +5 • rt3 O 1 fc +i 1 d o ^ T3 <0 s 0) a Sh iS} +i •^ t-^ to 3 S o Sh f . 0) LQ ns O ^J1 K £ ^ <3 0) © Ss c* 05 q> o> Jifl'S s s . *T3 O 1 Sn +i 1 a o *y ^ i * se 0) « ^ Si S-i •^ ^ to 3 K 03 O o S^ • 03 ix "X3 O •sji c e ^C « 03 © 03 03 03 Ss -Q fe. 49 50 "11 Reprinted from IEEE Transactions on Geoscience Electronics GE-8 , No. k, 326-336 IEEE TRANSACTIONS ON GEOSCIENCE ELECTRONICS, VOL. GE-8, NO. 4. OCTOBER 1970 Laser and Microwave Observations of Sea-Surface Condition for Fetch-Limited 17- to 25-m/s Winds DUNCAN B. ROSS, VINCENT J. CARDONE, and JACK W. CON A WAY, JR. Abstract — The variability of sea-surface conditions has been observed from a low-flying aircraft by a laser-wave profiling system and a scanning horizontally polarized 19.35-GHz passive microwave radiometer for fetch-limited wind speeds of 17 to 25 m/s in the North Sea. Wave profiles obtained with the laser system have been analyzed and show that wave growth occurs simultaneously at all frequencies and that an equilibrium value for the higher frequency components is eventually reached, but not before substantially higher (overshoot) values are obtained. Simultaneous observations of the microwave brightness temperature at vertical incidence show an increase with wind speed (or roughness of the sea surface) of 'l°K/m/s. This increase, not in accord with theory, is shown to be a function of the percentage of foam coverage of the ocean surface. Introduction FOR a number ot years various scientific organiza- tions have been concerned with developing tech- niques to remotely observe ocean-surface parame- ters of wave height and wind speed in a quantative manner. The purpose of these efforts is to provide in- formation about the "state of the sea" in support of operational requirements and to improve environmental forecasts. During March, 1969, a study of the active and passive microwave characteristics of the ocean surface under the influence of various wind speeds and wave heights was staged out of Shannon, Ireland. This experiment was a cooperative effort of several scientific organiza- tions and included three aircraft and scientists from the Naval Oceanographic Office; NASA, Goddard Space Flight Center; NASA, Manned Spacecraft Center; NASA Ames Research Center; New York University, New York; and the University of Kansas, Lawrence. The three aircraft were equipped with a variety of re- mote sensors capable of measuring the microwave brightness temperature, radar backscattering cross section, surface temperature, and wave heights. Between March 6 and March 13, five coordinated flights were conducted over Atlantic weather stations I and J which are located within about 720 km off Shannon and are routinely occupied by British and French weather ships. During these flights the highest winds encountered averaged about 16 m/s, an unfortu- nate development as the sites were selected due to the Manuscript received May 18, 1970. This paper was presented at the 1970 IEEE International Geoscience Electronics Symposium, Washington, D.C., April 14-17. D. B. Ross is with the Naval Oceanographic Office, Department of the Navy, Washington, D. C, 20390. V. J. Cardone is with New York University, New York, N. Y. J. W. Conaway, Jr., is with NASA, Goddard Space Flight Center, Greenbelt, Md. 20771. Fig. 1. Geodolite 3A laser prohlometer. high probability of occurrence of winds greater than 20 m/s and seas greater than 8 meters. The weather situation was particularly interesting to the local Irish meteorologists who marveled at the "mildest weather in twenty years!" As time was running out, a weak meteorological dis- turbance formed just south of Ireland and moved slowly eastward while a building high-pressure system moved eastward from Iceland into Norway between March 12 and March 14. As a result of these develop- ments, the pressure gradient in the North Sea gradually increased and by 2300 GMT, March 13, offshore winds in the North Sea reached 20 m/s. By early morning, March 14, it became apparent that these winds would hold or increase during the day, and plans were made to conduct a flight experiment be- tween the coast of Denmark and Scotland, the area of highest winds. The plan of the experiment was to observe the be- havior of the microwave signature of the surface under steady-state wind conditions, but varying (growing) wave conditions. The NASA Ames Research Center Convair 990, a four-engine jet aircraft, equipped with a scanning 19.35 GHz microwave radiometer, a laser- wave profiler, and a medium-resolution infrared ra- diometer was utilized to obtain data from a distance of 160 km off the coast of Denmark to the vicinity of the Shetland Islands. The NASA MSC P3A aircraft, equipped with an active radar scatterometer, was uti- lized to obtain radar cross-section data at a point mid- way between the coasts of Denmark and Scotland. This ROSS et ah: LASER AND MICROWAVE OBSERVATIONS OF SEA SURFACE 327 CW LASER TUNED CRrSTAL RANGE SELECTOR SWITCH :RrsTAL f AMPLIFIERS OSCILLATOR OSCILLATOR 1 v I 1 "^ V MODULATOR VOLTAGE DIVIDER k. REFERENCE MIXER REFERENCE IF AMPLIFIER (4 916 kHz) \ I ANALOG OUTPUT * < 1 L J PHASE DETECTOR SYSTEM » SIGNAL y\ r ► DIGITAL OUTPUT PHOTO- MULTIPLIER SIGNAL MIXER SIGNA IF AMPLIFIER (4 916 kHz) y SIGNAL T TELESCOPE VIEWING EYEPIECE SIGNAL STRENGTH MONITOR Fig. 2. Geodolite block diagram. SPECTRA PHYSICS LASER T 61 M i Fig. 3. Comparison of laser and wave-staff recordings of surface waves from a fixed ocean platform. paper describes a portion of the results obtained with the scanning microwave radiometer and the laser-wave profiler aboard the Convair 990. Instrumentation Laser-Wave Profilometer The laser wave profilometer is a standard modle Geodolite 3A airborne altimeter manufactured by Spectra Physics, Inc., Mountain View, Calif. (Fig. 1). Fig. 2 is a schematic diagram of the instrument [l ]. The ranging technique consists of amplitude-modulating a continuous-wave helium neon laser of red light centered at 6328 A. The reflected light is collected by an 8-inch Schmidt-Cassegrain telescope, detected by a photo multiplier, amplified, and phase-compared with the modulation frequency of the transmitted beam. The phase difference between these two signals is propor- tional to the transit time of the light, and hence the range. This range is directly proportional to the wave- length of the modulation frequency. The highest mod- ulation frequency available is 49.17 MHz with a wave- length of 3.048 meters. A total of five modulation fre- quencies are available, yielding range selections of 101, 102, 103, 104, and 106 feet. By means of a range-extender circuit each of these selections may be extended depend- ing on the variability of the terrain. For wave measure- ments only the full-scale increments of 3.048, 6.096, and 30.48 meters are used (see [l] for more details). Static tests of the laser system have been conducted aboard an offshore tower [2]. Figs. 3 and 4 are excerpted from [2] and show good agreement with a reference resistance wire wave staff. Initial flight tests of the system were conducted off Atlantic City, N. J., and in the vicinity of Argus Island, a U. S. Navy research tower located near Bermuda, British West Indies, in 60 meters of water. Fig. 5 is an example of profiles of surfaces waves as they shoal and break on the beach shown in conjunction with simul- taneous strip photography [3]. Fig. 6 presents a com- parison of averaged wave spectra obtained from three 2-minute tracks flown near the Argus Island tower with that derived from a 20-minute sample of wave measure- ments obtained from the tower's resistance wire wave staff. Since the aircraft is a moving reference, it is necessary to convert the observed wave spectrum to fixed co- ordinates. The conversion technique used involves ac- counting for the speed of the aircraft relative to the phase speed of each wave-frequency component and IEEE TRANSACTIONS ON GEOSCIENCE ELECTRONICS, OCTOBER 1970 .418 1 1 1 1 J-\I,J 1 I.J 1 1 1 1 1 1 1 / v A / \ / ^' \ \ 1 V — | - \ ' \l V v i l .372 - 1 v \_' 125 SAMPLE LENGTH -7 MINUTES 1 SAMPLE INTERVAL- 1.25 SEC 1 j NUMBER OF LAGS ■ 120 | : j< — LASER COHERENCE ►' .279 1 1 M: ' ~~ 232 1 1 1 1 1 IP 1~ .186 WAVE STAFF—* | i /; 1; t- 1 '.9 I li l\ A S \ ■ \ -'A"" .093 046 \ J L_L J L CPS .016 .032 048 .064 .080 .096 .112 .128 .144 .160 Fig. 4. Comparison of wave-energy spectra derived from laser and wave-staff recordings of surface waves. assumes that all waves are traveling in the direction of the wind [4]. Since this is an approximation, the pres- ence of swell and the spreading of wave energy with dis- tance can lead to errors. In the case presented little swell was present, and the errors associated with direc- tional spreading appear to be minimal for most pur- poses. Another source of error is that of aircraft motions of heave, pitch, and roll. Fig. 7 depicts the energy spec- trum of heave motions, mapped to fixed coordinates, of the type of aircraft involved (a Lockheed Super Con- stellation) during the Argus Island experiment when the surface winds were 12 m/s. It can be seen that essen- tially all of the aircraft heave (vertical) motions are concentrated at equivalent wave frequencies of less than 0.07 Hz. The time series of roll angles experienced during this same 3-minute track averaged about + 1.5°. For flight altitudes of 200 meters this corresponds to range (wave-height) errors on the order of 0.15 meters. From these data it can be seen that the majority of range errors associated with aircraft motions are small within the wave-frequency passband. As a result, the most convenient technique for removing these errors is simply high-pass filtering, where the low-frequency cutoff selected depends upon the turbulance and, for most cases, is less than that associated with a true wave frequency of 0.07 Hz. For extremely precise measure- ments, additional effort must be expended. For the data presented in this paper, the filtering technique was em- ployed with apparently good results. ■ WHITE WATER CREST -WHITE WATER CREST Fig. 5. Airborne laser profiles of surface waves obtained in conjunc- tion with simultaneous continuous strip photography. Microwave Radiometer The passive microwave radiometer utilized for obser- vations of microwave brightness temperature presented herein is a horizontally polarized 19.35 GHz (A = 1.55 cm) scanning (slotted-waveguide, phased-array) system developed by Aerojet General Corporation as a proto- type for a proposed Nimbus D satellite experiment [5]. The instrument scans + 50° from nadir with an instan- taneous field of view of 2.8°. A cold- and a hot-load cali- bration reading is obtained at the beginning and end of each 2-second scan. Operating at an altitude of 180 meters, the surface resolution is about 7.0 meters. Since the duration of measurement of each increment of viewing angle is 0.02 second, an effective resolution cell on the order of 15 meters is obtained at typical air- craft velocities. Meteorological Situation As noted in Section I, the general synoptic situation was a result of a weak disturbance moving eastward from Ireland simultaneous to an eastward displacement of a high-pressure system located over Iceland. These two events caused a gradual tightening of the gradient in the North Sea, and corresponding surface winds in- creased slowly but steadily to a maximum average of ROSS el a/.: LASER AND MICROWAVE OBSERVATIONS OF SEA SURFACE l2i — i — i — i — i r 0° 5° 10° PERIOD (SEC) 30 20 15 12 FREQ.(CPS) 033 .05 .067,083 Fig. 6. Comparison of wave-power spectra obtained with the laser profiles aboard a U. S. Navy aircraft with that obtained from an in-situ wave staff. .20 25 FREQUENCY(HZ) Fig. 7. Aircraft heave displacement spectrum showing energy contribution in the surface-wave pass board. 25 m/s by 1200 GMT, March 14, as reported by the German beacon vessel LHHT, located at 57.7°N, 03°E (Fig. 8). Since only one of the reporting ships shown in Fig. 8 was equipped with an anemometer (the rest being Beaufort estimates), it was felt necessary to derive the surface wind field by constructing isotachs of the geo- strophic wind from a fine-scale analysis of the surface pressure field. Surface pressure data was obtained from a consider- able number of British and continental shore sites, and isotachs of the geostropic wind were drawn relying heavily on the ship reports. Near the ship LHHT, a ratio of surface (20 meters) to geostropic winds of 70 percent gave good agreement, although in nearby re- gions of large shear, higher geostropic wind ratios are apparent. This is reasonable considering the effects of lateral turbulent momentum transfer. The preceding analysis considered the effects of stability after the technique of Cardone [6]. In order to verify the validity of the inferred surface wind speeds, Table I was constructed. This table shows wind speeds computed from the Litton model LTN 51 inertial system aboard the aircraft. The flight-level winds reported are 1-minute averages computed approx- imately every 5 minutes during the lower altitude tracks. These values were averaged over 20 minutes of Fig. 8. Ship reports in the vicinity of the North Sea, 1200 GMT, March 14, 1969. Dashed line is flight track of the NASA CV990. The digit adjacent to each report is the wind speed to the nearest knot within the 5 knot range indicated by the bar or flag. flight time (shown in brackets) and reduced to the equivalent 20-meter anemometer height assuming neu- tral stability and a logarithmic wind profile extending to an altitude of at least 43.3 meters [7]. The rather consistent agreement between the wind speeds derived by this technique, the geostropic surface winds, and the ship reports, lends considerable confidence to the pre- sumed wind fields. Observations of Wave Growth The intent of the experiment was to begin the down- wind flight track as near to the upwind shore as possible and then to fly downwind until the wave spectrum was essentially fully developed. This was not entirely prac- tical, however, as clearance procedural problems of the aircraft prevented approaching the shoreline within less than about 157 km. Further, due to previous limited success because of relatively low wind speeds, the re- ported winds were greeted with some scepticism. As a result, the flight track (dashed line of Fig. 8) was planned to best accommodate several possible metero- logical situations which might be present, and events seem to confirm the final plan selected as a good com- promise. Fig. 9 presents plots at their appropriate fetches of all available measurements of significant wave height Hs-1 The fetch was measured as simply the distance from the coastline in the direction of the implied sur- 1 Hs is defined as the average value of the highest one-third waves. S30 IEEE TRANSACTIONS ON GEOSCIENCE ELECTRONICS. OCTOBER 1970 TABLE I A Comparison of Winds Obtained from the NASA CV990 over the North Sea and 20-Meter Level Winds Reduced from Geostrophic Winds Based upon the Analysis Shown in Fig. 3 Flight Level Reduced Geostrophic Time (GMT) Latitude Longitude Altitude (meters) Wind Direction Wind Speed (m/s) Wind Direction Wind Speed (m/s) 1338 54°40'N 06°02'E 152 085° 23.7 110° 22.7 1345 55°15'N 06°01'E 152 112° 25.8[25]22.0 110° 22.7 1350 55°34'N 06°01'E 146 110° 23.1 110° 22.7 1355 55°56'N 06°03'E 116 110° 26.8 110° 22.7 1400 56°07'N 05°24'E 122 110° 22.7 110° 22.7 1407 56°13'N 04°30'E 152 098° 26.8 110° 23.7 1414 56°25'N 03°33'E 152 105° 27.3 [27.3] 25 2 110° 24.7 1417 56°28'N 03°12'E 152 107° 22.7 110° 25.8 1420 56°39'N 02°57'E 146 105° 29.9 110° 26.8 1435 57°35'N 02°17'E 152 107° 28.3 110° 25.8 1440 58°02'N 01°32'E 152 105° 25.8 [27.8] 25 8 110° 25.2 1445 58°14'N 01°10'E 152 110° 27.3 110° 25.2 1450 58°30'N 00°36'E 152 110° 30.4 110° 24.7 1455 58°48'N 00°01'E 152 108° 25.8 110° 23.7 1500 59°04'N 00°31'W 152 107° 24.7 [24.2] 22 1 110° 23.2 1505 59°23'N 01°06'W 152 108° 25.8 110° 22.7 1510 59°46'N 01°27'W 152 112° 21.6 110° 21.6 Note: Flight-level winds averaged over approximately 20-minute legs shown in brackets. The second value italicized is the aircraft value reduced to the 20-meter level after Moskowitz [7]. face wind direction. It is seen that Hs generally in- creased with fetch to about 370 km but decreased there- after. As a reference, a theoretical relation (Inoue— Cardone) is plotted for 22 m/s, a suitable wind speed for much of the data as determined from the analysis of all available wind inputs [6]. The wind speed for the particular location of each Hs plotted was obtained from the geostropic analysis and is shown below each value. Up to 370 km the varitaion of Hs with fetch is in good agreement with the theoretical relation, which ap- plies for infinite-duration fetch-limited seas. Beyond 370 km, the measured wave heights are considerably below the theoretical relation and depart increasingly with fetch. This latter behavior is generally explainable by duration effects, because the latter measurements plotted are from a wind field that exhibited considerable variability in wind duration. In particular, the durations are considerably longer in the near shore (southernmost portion of the first downwind run) area. An inspection of the previous 6-hourly sea-level-pressure analysis indi- cates no significant variation in the pressure gradient there for the 24 hours preceding the flight. Considering that the winds prior to 24 hours were only slightly lower, these durations are probably sufficient for the seas to be fully developed at their respective fetches. From the vicinity of LHHT northwestward, however, the durations are extremely limited. The 3-hourly wind reports at LHHT, Fig. 10, suggest that the duration of 20-m/s winds was only about 12 hours and that the duration of 23-m/s winds (or higher) was only about 3 hours. Toward the end of the last downwind run, dura- tions were probably more limited, considering the way in which the synoptic scale pressure gradient was chang- ing. The behavior of the data below 370 km suggests that these data might be employed to study growth, because THEORETICAL 23.2 M/SEC I I I L 300 400 FETCH (KM) Fig. 9. Observations of significant wave height (Hs) as a function of fetch. Wind speeds observed in meters per second are shown next to each value. the wind field there might be considered to be reason- ably steady and homogeneous. Results A convenient way to study the gross behavior of a developing sea in this case is presented in Fig. 11 which shows the plots of spectral density (m2-s) as a function of frequency (true) and fetch. This contour analysis is based upon spectra computed for 160-, 176-, 203-, 231-, 268-, and 323-km fetches. Though the resolution is not as great, the analysis is conveniently comparable to that obtained in the radar altimeter fetch-limited study at lighter winds by Barnett and Wilkerson [8]. The analysis in Fig. 11 is considerably smoother than that of their study, largely due to the decreased resolution. ROSS el al.: LASER AND MICROWAVE OBSERVATIONS OF SEA SURFACE 26 1 1 1 1 1 1 1 1 0 *" UJ in 1 22 — - 18 1 1 1 1 1 1 1 1 - 0600 0900 GMT (HOURS) Fig. 10. Wind speeds reported by the German ship LHHJ (57.5CN, 03°E) on March 14, 1969, at 3-hour intervals. The following are the major features to be deduced from this figure. 1) At frequencies above about 0.13 Hz, the spectral density does not change significantly with fetch. Thus these spectral components are already saturated, or fully developed, and in equilibrium with the wind field. 2) Below about 0.13 Hz all spectral components are increasing in intensity with fetch simultaneously. 3) The spectral peak generally moves toward lower frequencies (as indicated by the dashed line) with in- creasing fetch, in general agreement with existing con- cepts of spectral development. A rather surprising feature, however, is that the magnitude of the spectral density at the peak does not increase markedly with fetch beyond about 185 km. 4) A given spectral component will overshoot its eventual equilibrium value. That is, if the development of a single frequency component is followed fetchwise, it is seen that the spectral density increases rapidly to a maximum value at a given fetch and then decreases gradually to a lower equilibrium value at greater fetch. The effect is most noticeably between frequencies of 0.095 and 0.115. The overshoot effect at higher fre- quencies is not observed but presumably occurred at shorter fetches (< 160 km), because the data suggest that the fetch at which the effect occurs increases with de- creasing frequency. This striking feature of the North Sea spectra is perhaps the most remarkable because it implies the operation of mechanisms in wave generation not yet treated satisfactorily by existing theories. The overshoot effect has been reported in wave-tank studies and in the field experiment of Barnett and Wilkerson, and its appearance here lends support to the fact that this is a real phenomenon [9], [10]. The magnitude of the overshoot effect observed in the Barnett and Wilker- son study, that is, the ratio of spectral density at even- tual equilibrium to that at the peak of the overshoot, was scattered between 0.35 and 0.75. For the North Sea mission this ratio could only be computed for fre- quencies of 0.111, 0.108, and 0.105 Hz where values of 0.38, 0.50 and 0.41 occurred. Some of the features discussed previously are evident if the spectral density is plotted versus fetch for selected frequencies. Thus Fig. 12(a) shows a saturated fre- quency. Superimposed upon the data is the spectral 200 250 FETCH (KM) 300 350 Fig. 11. Contours of equal spectral density (m2-s.) on a frequency-fetch diagram. behavior for the Inoue-Cardone growth theory which is based upon a modified Miles- Phillips resonance insta- bility growth mechanism and the Pierson-Moskowitz fully developed spectrum [6]. It is seen that generally in Fig. 12(a)-(f), the equilibrium value observed is 30-40 percent less than that indicated by theory. This is largely explainable by the different equilibrium range constant B = 0.52 X 10~2 found for the North Sea spectra as compared to 0.8X10-2 used in the Pierson-Mosko- witz spectra. The overshoot effect is clearly evident in Fig. 12(b)-(h). The theoretical growth, of course, does not indicate overshoot, because it is based upon the relation (in the early stages of growth) d{S) it A + BS (1) where 5 is spectral density, / is time, A is the resonance mechanism parameterization, and B is the instability mechanism parameterization. Dissipation effects are included by allowing the growth rate to decrease as the fully developed spectral value is approached. For in- finite-duration limited-fetch growth, (1) is written Cg dSjf) dX A + BS(f) where X is the fetch and Cg is the group velocity of each wave frequency /. Disregarding the effect of the over- shoot, it may be said that the Inoue-Cardone growth (which predicts the variation of Hs fairly well) is too fast for frequencies above 0.078 Hz and too slow for frequencies below 0.069 Hz. The rapid growth of these frequencies is surprising, especially considering that these spectral components should be under the influence of dissipation by bottom friction. IEEE TRANSACTIONS ON GEOSCIENCE ELECTRONICS, OCTOBER 1970 90 -,. 34 1 I I " U 60 " s.o " u< 1 ioo 200 FETCH (KM) 300 115 1 1 1 - - " t • " J 1 100 1 200 FETCH (KM) 1 100 200 300 FETCH (KM) (a) (b) (c) -f= 108 - 100 200 300 FETCH (KM) (d) ' I 1 -- 105 - y , i 102 1 / I 1 - " 0 100 200 FETCH (KM) 300 (e) (f) 100 200 300 FETCH (KM) (g) 100 200 300 FETCH (KM) (1.) 90 1 = 091 1 ^ HI - *? if 30 -^ 1 100 200 300 FETCH (KM) 0) 10 - I 1 = 087 1 1 jjj«0 *? 5 30 " 0 1 1 100 200 300 FETCH (KM) <)) 100 200 300 FETCH (KM) (k) 100 200 300 FETCH (KM) (1) 90 - f° 074 1 1 1 - y 6o - JO - °I 1 1 100 200 m 100 200 300 FETCH (KM) (m) (n) Fig. 12. Plots of spectral density versus fetch for selected frequencies. ICO 365 300 FETCH (KM) (o) It is possible to quantitatively compute the values of A and B from plots Fig. 13, (a)-(o), provided dissipa- tion effects can be considered to be small. As a rule, these effects can be considered small (not considering bottom friction) if the spectral density is less than 30 percent of its eventual equilibrium value (after Barnett and Wilkerson [8]). Within this restriction the compu- tation can be performed on frequencies 0.087, 0.083, 0.078, 0.074, 0.069, and 0.063 Hz and will be performed on spectra recomputed for greater fetchwise resolution. Microwave Observations As with the observations of wave growth with the laser profilometer, the intent of the microwave portion of the experiment was to determine the effect of chang- ing gravity-wave conditions on the observed measure- ments of brightness temperature. Instrumental diffi- culties prevented collection of useful information during the initial lower level flight pattern which included the downwind track. Between 1419 GMT and 1435 GMT, during a short excursion to higher altitudes, the diffi- ROSS el a].: LASER AND MICROWAVE OBSERVATIONS OF SEA SURFACE 170 160 — )33 150 — 140 5 130 120 110 — 100 1 1 ' 1 ' 1 ' 1 ■ 1 ' 1 ' ' ' ', ! V = '9.4 KMC / 1 - 1 / 1/ . - // - - // / ; - A*^ ;ytfrrr^^^^--~^^^ r- w=i4m/sec ^^^ ^^ '^Cv^-^ V" w=8M/SEC S / 1 \ / ' \ - Vn^^^ ^-w = 4M/SEC *— SPECULAR / 1 \ ' / / / / SURFACE - , 1,1,1,1,1.1 , 1 , 1 10 20 30 40 70 40 SO t,0 (DEGREES) Fig. 13. Temperature of horizontally polarized radiation as a function of angle (upwind case) •t» ?■» culties were resolved and valid data were obtained dur- ing the remainder of the flight. Fig. 13 shows the expected increase in brightness temperature, TB versus viewing angle one would expect for a microwave frequency at 19.4 GHz [ll]. From the curves an increase in TB of about l°K/m/s would be expected for a view angle of 50°. However, no increase would be expected at the vertical incidence (0°). This theory is based on the work of Cox and Munk [12] and involves the use of wave-slope statistics and geometric optics neglecting the influence of white caps, foam, and spray. Fig. 14 shows the observed values of brightness temperature TB, (where * denotes the data that were not corrected for an atmospheric contribution) at ver- tical incidence in conjunction with simultaneous mea- surements of surface wind speed Uio and significant wave height Hs, as determined by the technique previ- ously discussed. From this figure it can be seen that during the period 1435 GAIT to 1450 GMT there was little change in either Uzo, Hs, or TB*. At 1500 GMT as the flight track neared the proxim- ity of the Shetland Islands, Z720 and TB* steadily de- 1420 1430 TIME (GMT) Fig. 14. Comparison of significant wave height (Hs), wind (£/), and brightness temperature (Tb*). speed creased, while a similar but slight decrease in Hs was observed. At 1512 GMT the aircraft purposely flew in the lee of the Shetland Islands to observe the effect of a drastic change in wave height while maintaining essentially the same wind speed. A change in TB* of about 4 percent was seen while changes in U20 and Hs were 20 percent and 95 percent, respectively. From these results it can be concluded that the predominent mechanism producing a change in TB* is more associ- IEEE TRANSACTIONS ON GEOSCIENCE ELECTRONICS, OCTOBER 1970 - 150 i30r FLIGHT 8 5m/sec Fig. 15. Comparison of brightness temperature Tb* versus wind speed. ated with changes in wind speed rather than the height of the longer gravity waves. Because the range of winds during this flight was re'-atively small and since no low-wind-speed condition was available, data from other flights conducted were examined and a plot of wind speed versus brightness femperature at vertical incidence was constructed (Fig. 15). Most of the data presented are derived only from data taken when the aircraft was flying in the immediate vicinity of weather stations I and J, which are equipped with anemometers located at a distance of 19.5 meters above the sea surface. The exceptions are the values for low (<5-m/s) wind speeds which come from near the coast of Ireland, and wind speeds used were obtained from the inertial navigation system while flying at an altitude of 180 meters and reduced to standard anemometer height. The points plotted are average values of the total number of measurements ob- tained for each wind-speed increment. The wind-speed increments were 0-7, 7-10, 10-12.5, 12.5-15, etc. The average value obtained for each wind-speed increment usually included data from different days or locations. As a result of this averaging process, the assumption can be made that the atmospheric contribution is the same for each increment of wind speed, thus minimizing potential errors. Nevertheless, it cannot be assumed that no error is present. From the best-fit line shown in the figure, a wind- speed dependence of 1°K m/s can be seen. This result is not in agreement with the theoretical prediction of Stogryn [ll]. A similar result has been reported previ- ously by Nordberg et al. [13], however, using the same instrument. Since these findings show a change in TB at vertical incidence which is not in agreement with the theory, a more extensive treatment of the data was indicated. Readings as high as 300°K have been observed by Williams [14] from artificially generated foam in a swimming pool with a radiometer mounted in a NASA MSC Convair 240 aircraft. Hollinger [15] has confirmed a foam dependence at 19.46 GHz with observations from the Argus Island research tower. His data showed increases of as great as 70°K for the artificially generated foam patches, while excursions (spikes) of 30°K above background levels were observed for foam patches r- rLibM I e 5M/itc ^FLIGHT 6 'M/SEC I— CI IPUT O U wAff 110L- FLIGHT 8 , '*M/SEC 150 Fig. 16. Nadir looking 19.3 GHz brightness temperature. generated by a 15-m/s wind. Moreover, Droppleman [16] has developed a model for microwave brightness temperature which predicts a foam dependence [18]. The work of Williams [17] also predicts a foam sensi- tivity. Fig. 16 shows the character of the time series of the radiometer output at vertical incidence for several wind speeds. Large spikes can be seen which could be asso- ciated with large foam patches nearly filling the antenna beam.2 This is not too difficult to imagine since the effective illumination of the surface is about 15 meters when flying at an altitude of 180 meters. Conaway [18] has identified a time series spike ob- served simultaneous to photography of a large white cap where the amplitude of the spike measured 202°K, Fig. 17. The highest spike observed during this flight mea- sured 220°K. If one assumes that the value of 220°K is representative of 100-percent foam (or at least char- acteristic of a white cap), all that is needed to establish a first-order curve for TB versus percent foam is a repre- sentative value for the no-foam situation. Munk [19] has suggested that the onset of whitecapping occurs at a wind speed of about 5-7 m/s. If 7.5 m/s is chosen as essentially foam free (< 1-percent white caps), a value of Tb for the foam -free condition may be obtained from Fig. 15 (approximately 120°K). By connecting a straight line between these two values Fig. 18 is obtained. Using the linear relationship (by design) between Tb* and percent foam cover of Fig. 18, the nadir brightness tem- perature as a function of wind speed, as shown in Fig. 16, may be expressed as percent foam cover as a func- tion of wind speed. The result is shown in Fig. 19 and is compared with the results of other workers [6], [20], [21]. Good agreement is seen for wind speeds to 20 m/s. 2 In this discussion a white cap is considered to be a multilayered foam phenomena, whereas a wind streak, while composed of foam, could be single layered. ROSS et at.: LASER AND MICROWAVE OBSERVATIONS OF SEA SURFACE 335 FLT 8 19 3 GHz RAD. SCANS 10 36:08 10:36 10 10:36:12 118 117 110 114 119 104 118 126 112 124 127 111 123 129 111 129 124 115 125 127 109 123 137 118 129 179 117 126 186 118 125 199 123 127 195 121 132 153 122 130 132 127 132 125 121 132 127 121 133 126 120 131 126 120 125 123 123 121 122 125 126 121 124 121 124 118 123 116 123 115 115 120 118 111 116 Fig. 17. Simultaneous observation of a brightness temperature spike and photography of a large white cap. An analysis of photography obtained during this ex- periment, while consistent with the above findings, sug- gests that the amount of wind streaking (thin lines of foam oriented in the direction of the wind) must be taken into account in any estimation of percent foam coverage, particularly when considered in terms of the emissivity. Quantizing these streaks is a difficult and subjective task because much depends upon the quality and orientation of photography. It is not suggested that the curve of Fig. 19 depicts the precise behavior of foam coverage with wind speed, particularly since the effects of fetch, duration, and stability likely play a significant role in foam density [6]. Nevertheless, the agreement is remarkably con- sistent. Conclusions By the use of active and passive remote-sensing instru- mentation it has been possible to measure ocean-surface waves and wind speeds. From observations of wave growth with a laser pro- filometer, the following were found. 1) Existing wave theory can be used with reasonable results to predict the rate of growth of the signifi- cant wave height with increasing fetch. 2) A migration of the spectral peak toward lower fre- quencies with increasing fetch is observed. 3) All wave frequencies are receiving energy simul- taneously. 4) The spectral density of a particular frequency component will overshoot its eventual equilib- rium value by as much as 50 percent. From observations of sea-surface conditions with a microwave radiometer the following conclusions can be made. 1) Measurements of brightness temperature are not particularly sensitive to large changes in energy 140 150 160 170 180 190 BRIGHTNESS TEMPERATURE ( TB«) Fig. 18. 15 20 25 WINDSPEEO (M/SEC) 35 Fig. 19. Percent foam coverage determined from the brightness temperature {Tb*) relationship compared to observations and to semiempirical calculations of Cardone [6]. density of the low-frequency gravity-wave spec- trum. 2) An increase in Tb* at vertical incidence is seen in disagreement with theory, but can be explained as a dependence of percent foam coverage. 3) While a dependence of Tb* on foam coverage has been shown, exploitation of this finding depends upon establishment of a unique relationship be- tween percent foam and wind-wave conditions. Furthermore, the atmospheric sensitivity must be lessened, perhaps by multifrequency techniques. Nevertheless, airborne measurements of surface wind speed of a very useful degree of accuracy are seen to be feasible. Acknowledgment The authors wish to thank J. W. Sherman, Dr. W. J. Pierson, and Dr. W. Nordberg, for their aid and en- couragement during all aspects of this effort; the Irish meteorologists at Shannon International Airport, whose interest, assistance, and spirit contributed significantly to a successful and memorable experiment; and the scientific and flight crew of the CV909, who responded IEEE TRANSACTIONS ON GEOSCIENCE ELECTRONICS, VOL. GE-8, NO. 4. OCTOBER 1970 to extremely short notice and made the North Sea flight possible. References [1] H. Jensen and K. A. Ruddock, "Applications of a laser profiler to photogrammetric problems," presented at the Amer. Soc. Photogrammetry, Washington, D. C, 1965. [2] D. B. Ross, R. A. Peloquin, and R. J. Sheil, "Observing ocean surface waves with a helium neon laser," Proc. 5th Symp. on Military Oceanography, Panama City, Fla., May 1968. [3] V. E. Noble, R. D. Ketchum, and D. B. Ross, "Some aspects of remote sensing as applied to oceanography," Proc, IEEE, vol. 57, pp. 594-604, April 1969. [4] M. St. Denis and W. J. Pierson, "On the motions of ships in confused seas," Trans. Soc. Naval Arch. Marine Eng., 1961. [5] C. Catoe, W. Nordberg, P. Thaddeus, and G. Ling, "Prelimi- nary results from aircraft flight tests of an electrically scanning microwave radiometer," NASA, Goddard Space Flight Center, Greenbelt, Md„ Tech. Rep. X-622-67-352, August 1967. [6] V. J. Cardone, "Specification of the wind field distribution in the marine boundary layer for wave forecasting," Geophys. Sci. Lab., New York University, New York, Rep. TR69-1, Decem- ber 1969. [7] L. Moskowitz, "Reduction of ocean wind data by use of drag coefficients with application to various wave forecasting tech- niques," U. S. Naval Oceanographic Office, I MR 0-66-64, Jan- uary 1965. [8] T. P. Barnett and J. C. Wilkerson, "On the generation of ocean wind waves as inferred from airborne radar measurements of fetch-limited spectra," /. Marine Res., vol. 25, pp. 292-328, September 15, 1967. [9] A. J. Sutherland, "Growth of spectral components in a wind- generated wave train," J. Fluid Mech., vol. 33, 1968. [10] H. Mitsuyasu, "On the growth of the spectrum of wind-gener- ated waves, pt. II," Rep. Res. Inst. Appl. Mech. (Kyushu Uni- versity, Fukuoka, Japan), vol. 17, no. 59, 1969. [11] A. Stogryn, "The apparent temperature of the sea at micro- wave frequencies," IEEE Trans. Antennas Propag., vol. AP-15, pp. 278-286, March 1967. [12] C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Marine Res., vol. 13, February 1954. [13] W. Nordberg, J. Conaway, and P. Thaddeus, "Microwave ob- servations of sea state from aircraft," NASA, Goddard Space Flight Center, Greenbelt, Md., Tech. Rep. X-620-68-414, 1968. [14] G. F. Williams, "Microwave radiometry of the ocean and the possibility of marine wind velocity determination from satellite observations," J. Geophys. Res., vol. 74, p. 18, 1968. [15] J. Hollinger, private communication. [16] J. D. Droppleman, "Apparent microwave emissivity of sea foam," /. Geophys. Res., vol. 75, January 20, 1970. [17] G. F. Williams, "Microwave radiometry of the ocean," pre- sented at the Ninth Meeting AD HOC Spacecraft Oceanography Advisory Group, Texas A&M University, January 1968. [18] J. Conaway, "Microwave radiometric observations of sea state in March 1969," Proc. Rev. on Microwave Radiometry, U. S. Naval Oceanographic Office (to be published). [19] W. Munk, "A critical wind speed for air-sea boundary pro- cesses," /. Marine Res., vol. 6, p. 203, 1947. [20] H. Murphy, "Percentage foam versus wind velocity," Univer- sity of Miami, Coral Gables, Fla., May 1968. [21] D. C. Blanchard, "The electrification of the atmosphere from bubbles in the sea and its meteorological significance," Tellus, vol. 9, p. 145, 1947. 75 Reprinted from Meteorological Ponographs JJ^, No. 33, 29^-301 STATUS OF INSTRUMENT DEVELOPMENT FOR SPECIALIZED MARINE OBSERVATIONS WlLLARD W. SHINNERS Atlantic Oceanographic and Meteorological Laboratories, ESSA, Miami, Fla. A number of representative data acquisition systems are presented under three general categories: 1) ship- board, 2) airborne, and 3) buoys. The Research Triangle Institute developed a system aboard the research vessel Eastward using both analog strip chart and digital tape recording of up to 24 channels of meteorologi- cal and oceanographic data. To overcome problems inherent in operating from a large ship, Florida State University successfully used an extensible boom extending forward from the bow of the ESSA Discoverer. To obtain time series and profile data within the gradient level, ESSA's Sea-Air Interaction Laboratory uses a five-channel multiplexing system. Resistance-controlled oscillators modulate I RIG channels 5-9 on a 403- MHz carrier frequency. The University of Hamburg uses three modulated audio frequencies in their three- channel sonde on the 403-MHz carrier frequency to acquire data at sea. Bead thermistors, carbon humidity strips, aneroid cells and light weight anemometers are used. For data at the ocean-atmosphere interface the TRITON buoy developed at Florida State University has performed successfully while moored in water depths of 8000 ft. A spar buoy configuration 112 ft in length is placed in 75 ft below the surface. On-board recording and radio telemetry of data may be programmed. A much smaller spar buoy, 40 ft in length and 300 lb in weight, has been operated from the Discoverer as a tethered system while the ship is hove to. A hard wire link is used for data collection. 1. Introduction Specialized marine observations are considered to be those which require a greater accuracy or more frequent time and/or spatial sampling than general synoptic observations obtained from cooperating ships at sea. Let us examine briefly some of the problems of obtaining representative data at sea. Ships of a few hundred to several thousand tons displacement are the usual platforms from which the marine scientist operates in investigating deep water areas of the oceans. These vessels create a micro- climate in their immediate vicinity due to heat from the ship and the obstruction by the ship to the normal wind and water movements. A large research vessel will use up to 7000 gallons of fuel per day, which produces approximately 9.5 X 108 Btu. If all the energy were dissipated only within the water, it would be enough to warm the water displaced by such a vessel ~120F. A substantial amount of the heat generated aboard is dissipated directly into the environment in the Fig. 1. Observed air flow and wave pattern with ship drifting. exhaust through ventilators, by conduction and radia- tion. Water used for cooling the engines and dis- charges from the sanitary system add additional heat and pollutants to the environment of the ship. Turbu- lent mixing soon distributes the heat dissipated to the atmosphere, but the fact remains that tempera- ture and humidity measurements made from any location other than one well exposed and to windward may be seriously biased and not representative of ambient conditions. Water temperatures may be er- roneous if taken close to the hull or near any discharge from the ship. For large-scale synoptic observations, i.e., for areas in the order of several thousand square kilometers, temperature and humidity data taken at bridge level on the windward side of the ship will generally be adequate. For small-scale investigations involving areas of a few hundred square kilometers, particularly for energy fluxes between the ocean and the atmo- sphere, such data would not usually be suitable. A major difficulty is caused by the disruption of the air flow by the ship itself. A ship, like a large building or a hill, will cause a horizontally moving wind to be deflected upward with vortices developing both wind- ward and leeward of the vessel under certain condi- tions. Sea gulls commonly observed soaring over a vessel are riding a standing wave caused by the ship. To obtain visual delineation of the airflow over a vessel, smoke flares and neutral buoyancy balloons were released upwind and downwind at the sea sur- 295 METEOROLOGICAL MONOGRAPHS Vol. 11, No. 33 face and up to 10 m above the surface. From motion pictures taken of the trajectories, the air flow was developed and is shown in Fig. 1. Under neutral stability conditions with the ship broadside to the wind and the smoke source 250 ft directly abeam, a deflection upward was noted at an upstream distance of about twice the beam of the ship. There was a significant acceleration as the smoke passed over the ship. A small vortex formed on the windward side, and an elongated vortex was observed on the leeward side. A change in the sea surface wave from normal conditions at A (Fig. 1) was noted at B where the counter wind of the vortex reduced the size and shape of the waves. This phenomenon was more pronounced at F on the leeward side. When the source was moved so that the smoke passed forward of the bow, the smoke remained near the surface. Diffusion and mechanical mixing increased the size of the plume in an undisturbed manner as it passed the ship. In addition to the self-induced problems of the ship as an instrumental platform, the marine environment requires instrumentation which can function depen- dably when exposed to high humidities, airborne salt particles, strong winds and sometimes rather violent wave and ship movement, and be deployed without danger to the equipment or personnel. New techniques and materials are needed for work in the marine environment. Only a few of the many different approaches to data acquisition at sea are discussed below, for there are as many approaches as there are specific data requirements. These systems do not meet all require- ments in the marine area, since each was designed or adapted for a specific program ; however, they are generally indicative of present procedures and hardware. 2. Meteorological oceanographic surface data acqui- sition system To meet a requirement for observations on a scale between microscale and synoptic, the Research Triangle Institute developed a data acquisition system for use abroad the research vessel (R/V) Eastward- operated by Duke University (Smith and Tommer- dahl, 1966). The sensors are essentially off-the-shelf items and available through commercial sources in most instances. The method of recording meteorologi- cal, oceanographic and ship data in analog and digital form provides considerable information for a variety of users in the physical and biological sciences. Sensors include a dew cell, thermistor, and an infrared radiometer mounted on a short mast at the bow. Fig. 2 illustrates the mounting of these instru- FlG. 2. Bow mounting of dew cell, thermistor and infrared radiometer aboard R/V Eastward. ments. The air temperature sensor is that used in a standard W3 radiosonde (left, Fig. 2). The dew cell is mounted in the conical shaped housing. The IR radiometer is mounted in the segmental circular tube. On an A-frame, forward at 10-15 m above the sea surface, additional air temperature thermistors are mounted. Wind direction, wind speed, and solar radia- tion sensors are located on yard arms extending from the A-frame. An encapsulated bead thermistor (Fig. 3) is towed from a boom on the starboard side so that the sensor remains a few centimeters below the sea surface and well away from any water discharges from the ship. The Thermilinear system, built by Yellow Springs Instruments, is a semi-conductor with associated electronics which provides a linear response to tempera- ture change. Units built for use aboard ship have Fig. 3. Thermilinear probe for water temperature measurements. The sensor tip is immediately above the centimeter scale. October 1970 METEOROLOGICAL MONOGRAPHS 296 WIND VELOCITY TRANSDUCER COUPLER UNIT 1 a, 2t| CHANNEL SELECTOR SWITCH 0-=^MV p ANALOG RECORDER - -► 1 10 BIT SHAFT ENCODER BUPPER and PARITY CIRCUITS DIQITAL TAPE RECORDER AIR TEHP WATER TEMP ' : t \ i , .. SHIP SPEED GEAR TRAIN MICRO- SWITCHES CONTROL SIGNAL TIMING AND FORMAT CONTROL PRINT . • t MOTOR CONTROL * TAPE ADVANCE MANUAL DATA 4 • SYNCHRO- NOUS MOTOR REFERENCES Fig. 4. Diagram of the oceanographic-meteorological data acquisition system aboard the R/V Eastward. plastic covered leads up to 50 m in length, terminating at the thermistor bead tip which measures about 0.6 cm in diameter. Response time with the protective coating is ~ 7 sec. With a 10 ixV (°C)~1 sensitivity, one can obtain a detailed set of measurements of surface temperature variability while the vessel is underway. The unweighted line will remain just below the surface at speeds of 10-15 kt and wave heights < 4 ft. By adding weights, the sensor may be towed at deeper levels in the water to obtain a continuous tem- perature profile. Additional information on the pitch and roll of the vessel, speed and heading, atmospheric pressure, time, and visually determined cloud, weather, visibility, and sea state are recorded. Fig. 4 illustrates the ar- rangement of the system components. Fig. 5. Instrument boom in extended position aboard the USC&GS Ship Discoverer. Data logging is accomplished by routing the sensor signal output to a coupling unit. The coupler scales the basic signal as necessary to provide a proper output over the ranges of ambient conditions expected. From the coupler the signal is transmitted to a 24-channel strip chart recorder programmed to sample a channel every 2 sec. Selected sensors are sampled twice during each 48-sec sequence, and a number or reference signals are included in the recording. The strip chart record permits immediate use and monitoring of the data. An incremental digital, mag- netic tape record is made for use in computer processing of several days later. By means of a 10-bit shaft encoder, data signals are carried through buffer and parity circuits to the tape recorder. Ship's speed and heading are recorded by mechani- cally coupling a precision potentiometer to the pit log and the gyro compass. Relative wind direction is obtained in the same manner with a shaft encoder potentiometer technique. With values for the relative wind and ship's heading and speed, one can calculate true wind speed and direction. 3. Instrument boom and surface data system One approach to the investigation of energy fluxes is to determine the temperature, humidity and wind gradient by taking data at discrete heights above the sea surface. From Fig. 1, it is apparent that an air parcel at the surface ~ 100 m upwind would cross over the ship at 20-30 m above the sea; hence, data taken at discrete heights on the ship may not be representative of ambient conditions at those heights in undisturbed air. Obviously, the smaller the vessel the better are the prospects of obtaining valid data. Since vessels operat- ing in deep ocean areas must be of sufficient size for safety and range purposes, and since these vessels must perform other functions in which the modifica- tion of the immediate environment is of no conse- 297 METEOROLOGICAL MONOGRAPHS Vol. 11, No. 33 quence, the meteorologist and physical oceanographer must devise means of overcoming the problems of data acquisition caused by the presence of the ship. A number of investigators faced with the problem of ship interference have taken the approach of mount- ing sensors on supports extending horizontally and/or vertically from the ship so as to place the sensors in representative air. Florida State University used this method aboard the oceanographic survey ship Dis- coverer during their Barbados studies in 1968. The system, with modifications, consists of a 40-ft boom (Fig. 5) which is extended forward of the ship's bow and retracted for servicing. Fig. 6 indicates the major components of the instrumented boom system in a block diagram. Thermistors are used for air wet- bulb and water temperatures. The wet bulb is aspirated to provide adequate and continuous ventila- tion. A 75-ft lead permits the water temperature thermistor to be extended from the boom to the water. A combination of weights and a float keeps the sensor at the surface. This procedure is used only when the ship is hove to or underway at very low speeds. A lithium chloride humidity sensor is used for direct humidity measurements and for comparison with the wet/dry bulb method. A standard Weather Bureau model F420C wind speed transmitter is used. The wind direction transmitter is modified to operate a linear potentiometer, producing a variable voltage representative of the relative wind direction. This equipment has proven to work well for extended periods aboard ship. Sealed bearings and non-corro- sive materials are used. Radiation data are obtained by mounting a net radiometer well out on the boom so as to view the water surface and sky with a minimal effect from the ship. A sensor calibration connection at the bow junction permits one to check individual sensors during the servicing of the boom instruments. instrument booh BOM/LAB ARi *-M WIND DIRECTION *~ " 1 I 1 1 1 * - RELATIVE HUMIDITY BOOM JUNCTION THERMISTOR BRIDGE, AIR TEMPERATURE WATER TEMPERATURE WIND SPEED WET BOLB TEMPERATURE RADIOMETER A C POWER J t SENSOR BON STATION TERHIHAL JUNCTION I ANALOO TAPB STRIP CBART RECORDERS Fig. 6. Schematic of the surface data instrument boom system. FM recording is used in the 0.5-5.0 V range. Since the thermistor and radiometer outputs are in the millivolt range, signal amplification is done at the bow before the signal is carried to the oceanographic laboratory aft for recording on tape and strip charts. A dc voltage is fed to the humidity and wind direction sensors to provide an output in the 0.5-5.0 V range. Data are recorded in analog form with the A to D conversion of the tape record being done ashore. Strip chart records serve for on-board monitoring of the system and provide real-time data as may be required. 4. Atmospheric boundary layer system To obtain detailed information in the lower few hundred meters of the atmosphere over the ocean, ESSA's Sea-Air Interaction Laboratory (SAIL) de- veloped a five-channel multiplexing tethered telemetry system. The basic requirement was to obtain repeated AIRBORNE TRANSDUCER-TRANSMITTER P — PRESSURE H — HUMIDITT m — kind T — TIRPERATURE R»d- RADIATION 0-ZOOOn, PATH SHIPBOARD RECORDING STATION P ANALOG SIGNALS H ANALOG SIGNALS W ANALOG SIGNALS T ANALOG SIGNALS R«d ANALOG SIGNALS J DISCIMINATOIS * p TAP* RECORDER N ALTERNATIVE ] SIGNAL RATH EOR I SHIPBOARD I RECORDING STRIP RECORDER Fig. 7. Five-channel airborne multiplexing telemetry system. October 1970 METEOROLOGICAL MONOGRAPHS 298 Fig. 8. Instrument cage for tethered airborne telemetry system. vertical profiles as well as time series data within the gradient level. Five separate sensors are monitored continuously by using the 395-410 MHz band as a primary carrier frequency, and IRIG channels 5-9 as data channels multiplexed in the carrier frequency. Fig. 7 illustrates the functioning of the system in which resistance- controlled oscillators in each sensor circuit vary the sub-carrier frequencies. The sub-carrier frequencies are fed through a mixer to the primary transmitter. When received at the ground station, the carrier frequency is fed to a discriminator which separates the sub- carrier data channels. The data are then recorded in analog form on magnetic tape with a time code signal. Analog data may also be recorded on strip charts for real-time monitoring and as a back-up record. The "bird cage" pictured in Fig. 8 is flown on a tethered balloon and provides protection for the anemometer as well as supporting the housing for the temperature and humidity sensors. Wires from the instruments are run to the radio transmitter which is usually carried well above the "bird cage" and closer to the supporting balloon. Arrangement of the thermistors and carbon hygristor within the sensor housing and radiation shield is shown in Fig. 9. The resistance range of the thermistors is 200,000 to 80,000 Q for a temperature range of 10-30C. The carbon humidity element ranges from about 20,000 tt at 30% relative humidity to 700,000 Q at 90%. The response time of the thermistor beads is ~ 1 sec, while the carbon element responds almost ten times as fast. These are production hygristors used in standard Weather Bureau radiosondes. An aneroid cell operating over a variable resistance provides a measure of pressure-altitude. For nighttime radiation observa- tions, a Suomi-Kuhn infrared radiometer is flown. Wind speed values are obtained by use of a light- weight generating anemometer. To place several sensors aloft to a height of 1000 m requires a sizeable lifting device. Unfortunately, most research ships have their deck areas filled with winches, cranes, stanchions, antennas, etc., and handling a balloon on the open deck even under light-to-moderate winds is a difficult task. Two types of balloons have been used ranging in size from 250 to 1500 ft3. An aerodynamic V shape gains additional lift with in- creased wind speeds and will remain stable at moder- ately high speeds. However, its relatively greater width for a given static lift (or cubic volume) re- quires more deck space for handling. The conven- tionally shaped balloon, i.e., blimp or dirigible, is a little easier to handle in restricted launch and recovery areas, and performs quite well at the lower wind speeds. Proper rigging of shroud and tether lines, tail assembly, and adequate inflation are essential for satisfactory flight. Parafoils (kites) have proven quite useful under steady moderate winds. Shaped in the form of an airfoil section, the parafoil develops tremendous lift in winds from 20-40 kt. Power winches are necessary to handle both bal- loons and parafoils. Line loads in excess of 100 lb may be encountered in gusty winds with even the 250 ft3 balloons or the smaller 42 ft2 parafoils. Braided nylon line, which has good elasticity, has been found to work well for this type of operation. Fig. 9. Sensor housing and radiation shield for thermistors and carbon humidity strip. Two panels are pictured to illustrate the wet-bulb mount in the upper unit and the carbon hygristor and dry bulb in the lower unit. 299 METEOROLOGICAL MONOGRAPHS Vol. 11, No. 33 5. Three-channel sonde The Meteorological Institute at the University of Hamburg (Stilke el al., 1967) uses three audio fre- quencies carried simultaneously on a 403-MHz carrier frequency to obtain data continuously aboard the research vessels Meteor and Planet. Designed for tethered flight and for free flight in the lower 6-7 km, the sonde uses a number of variations in sensor com- binations and methods of flight. A free-flight version uses thermistors for dry- and wet-bulb temperatures in the range of 30 to -IOC. The FM/FM system uses a frequency range of 6.5-10.7 kHz for dry bulb and 250-500 kHz for wet bulb. A third channel is modulated by a carbon hygristor over the range of 0.5-2.5 kHz. With this version of the radiosonde using dry bulb, wet bulb, and a carbon hygristor, altitude is deter- mined by using a shipboard wind-finding radar. In the event radar tracking is not available, a pair of aneroid cells operating a linear potentiometer is sub- stituted for the wet bulb or carbon strip in order to obtain height data. A second alternative is to fly the three-channel sonde in conjunction with a standard radiosonde. The three Censors each modulate a different fre- quency band as a function of the ambient tempera- ture, wet-bulb temperature, and relative humidity or pressure. The three sub-carrier frequencies are imposed upon the primary carrier with radio telemetry to the shipboard receiver. On board ship, the signal is impressed on a dual-channel magnetic tape recorder. The composite signal of the three channels is logged on one track while a 10-kHz signal is recorded on the second track. With a standard 10-kHz signal as a reference, tape speed may be corrected during decoding. On-board monitoring is accomplished by using a variable bandpass filter to decode individual channels and record the analog signal on a strip chart. Each channel is checked periodically to verify that valid data are being obtained, with the magnetic tape record of all data being retained for final processing ashore. On the return to port, the analog signals for the three data channels are obtained by filtering the com- posite taped signal through three bandpass filters for the respective frequencies involved. Each filtered signal is fed through a frequency counter from which a digital record is made. The digital data are then available for computer processing. The three-channel sonde shown in Fig. 10 weighs ~ 300 gm with batteries. Shown in the flight position the dry-bulb thermistor is at the upper left of the center unit ; the wire frame midway holds the carbon humidity element ; and the wet-bulb wicking with Fig. 10. 300-gm three-channel radiosonde developed by the Institute for Meteorology, University of Hamburg, for low-level atmospheric studies at sea. water reservoir is immediately below. The aluminum housing (far left unit in Fig. 10) covers the sensors during flight so that air is ducted past the sensors. During tethered flight the sonde is flown with the sensors oriented horizontally below the sonde and directly into the wind. 6. TRITON buoy The TRITON buoy developed by Florida State University (Garstang et al., 1967) under an ESSA grant has proven to be an effective tool in the investi- gation of the energy exchange at the sea-air interface. Moored east of Barbados for approximately two months in water over 8000 ft deep, TRITON obtained data from both the ocean and the atmosphere. Dan W. Clark, Inc., of Woods Hole, Mass., con- structed the buoy illustrated in Fig. 11, the overall length of which is 112 ft. The sub-surface portion is composed of two cylindrical sections, 2 ft in diameter and 21 ft in length, and a similar section with two spheres 5 ft in diameter. The lower two sections are flooded to bring the buoy to a vertical position when anchored. Compressed air is carried in the spheres for buoyancy and for evacuating the flooded sections during recovery. The instrumentation and power supply are mounted in fiberglass tubs 16 inches in diameter and 24 inches high, inserted at the platform level just above the spheres. October 1970 METEOROLOGICAL MONOGRAPHS 300 METEOROLOGICAL SENSORS WAVE SENSOR TRITON BUOY VERTICAL AND ROTATIONAL DAKPINO PLATES PRESSURIZED SECTION 21 FEET Li FLOODED SECTIONS U2 FEET 1 Fig. 11. TRITON buoy used to obtain oceanographic and meteorological data by Florida State University. The buoy has been moored in 8000 ft of water by using a combination of 4000 ft of plastic coated steel cable and 6000 ft of nylon line. A 50-ft, 550-lb chain secures the cable to the buoy, and the bottom terminal includes chain, a 300-lb clump weight, and a 300-lb Danforth anchor. With a 1.2 slope for the anchor line, the buoy remained in position with winds up to 50 kt and moderate seas. The sensors and the data acquisition and telemetry system were procured from Geodyne. The system is compatible with the Odessa buoy system, a joint development of the Coast and Geodetic Survey and Geodyne Corporation (Anonymous, 1968). Fig. 12 is a schematic block diagram of the TRITON buoy instrumentation circuits. A programmer, timer and digitizer are the heart of the system. Signals from transducers such as thermistors, pulsed anemometers, accelerometers, strain gages, magnetic compass, etc., are programmed to the digitizer. Both the sequence and the sampling interval may be varied to meet particular research requirements. Wave data, for example, are sampled at the rate of 12 times per second. From the digitizer the data are recorded on tape for later processing. Data may also be relayed to a ship or shore station by radio telemetry for monitor- ing or real-time use. The triangular tower structure supports the several meteorological instruments, navigation beacon, radio beacon, antenna, wave sensor, and a large wind vane to maintain buoy orientation. At-sea servicing of the buoy by use of rubber boats has proven feasible in up to 10-ft seas. The buoy is quite stable with a 1.5° movement from vertical noted in a 3-ft sea. ,Wtl ■Ult THEIMISTOI DRY BUtB THERMISTOR ( ANEMOMETER RAIN GAUGE DRV BULB THERMISTOR} ANEMOMETER WIND DIRECTION WATER TEMPERATURE THERMISTOR WAVE PRESSURE SENSOR 7. Sea-air interaction buoy To obtain near-surface gradient values under light sea conditions, SAIL instrumented a small spar buoy. The buoy (Fig. 13) is commercially available and constructed of aluminum for the surface float and sub- surface section. Fiberglass is used for the mast section Fig. 12. Schematic of the TRITON data acquisition and telemetry system. Fig. 13. Sea-air interaction buoy for tethered operations. 301 METEOROLOGICAL MONOGRAPHS October 1970 above the water. Overall dimensions of the buoy are : parabolic surface float, 36-inch diameter and 14-inch central thickness ; sub-surface ballast and battery unit, 20 ft in length with a 6-inch diameter; instrument mast, 20 ft in length and a 3-inch diameter. The total weight of the buoy in air with lead ballast is ~300 lb. Two modes of deployment and operation may be used. The buoy may be set adrift and data collected by radio telemetry, or it may be tethered to the ship and the data collected by hard-wire link. The latter method worked quite well during sea trials with the ship in a drift mode. Due to the considerable freeboard and rapid drift of the Discoverer from which the buoy was operated, the buoy remained well upwind at the end of a 200-yard tether. A 2000-lb test electro- mechanical cable is used for the tether. Floats are attached at intervals to the line to maintain slight positive buoyancy. During recovery, the electro- mechanical cable is brought in by capstan. The data acquisition system is similar to the air- borne multiplexing system used by SAIL. Since weight and power were not as restrictive as in the airborne version, larger battery capacity and heavier sensors were used. Plastic cylindrical sensor mounts ~ 8 inches in length and 2 inches in diameter were con- structed to house the air temperature thermistor, wet thermistor, and a carbon hygristor. Aluminized mylar shielding is used to minimize the radiational effects. The sensor housing is mounted to face directly into the wind. Buoy orientation is controlled by a fixed vane attached to the lower portion of the mast. In the tethered modes, the mooring line strain-parallels the action of the vane. 8. Conclusion The various data acquisition systems discussed above must really be considered as systems still under development. From the efforts of the meteorologist and oceanographer working together in the ocean environment and aided by the physicist, the electron- ics engineer, and others, greatly improved systems and techniques will become available to the marine research scientist in the future. In situ sensor methods have limitations, and hopefully an acceleration of development in indirect techniques such as the use of infrared radiometry, microwave refractometers, and lasers may provide the means for obtaining accurate information at sea rapidly and inexpensively. REFERENCES Anonymous, 1968: ODESSA small buoys with big voices. Ocean Industry, 3, No. 10. Garstang, M., P. F. Smith and K. E. Perry, 1967: An unattended buoy system for digital recording of air sea energy exchange parameters. Trans. Second Intern. Buoy Tech. Symp., Marine Tech. Soc. Smith, J. R., and J. B. Tommerdahl, 1966: Oceanographic data logging system for air-sea interaction studies. Final Rept. Phase I, Res. Triangle Inst. Stilke, G., K. Mollnhaur and L. Jahnke, 1967: Dreikanal- Radiosonde zur kontinuierlichen Messung der Temperatur, der Feuchte und des Luftdrucks. Meteor. Forschung., Bl, 54-63. GPO 837 - 964 \)