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Reprinted from Quarterly Journal Royal 50 Meteorological Society 95_, No. 403 , T 20 - >4 7 551.543.1 (265/266) : 551.576.31 : 551.577.31 : 525.624 Tropical cloudiness and rainfall related to pressure and tidal variations By G. W. BRIER and JOANNE SIMPSON Environmental Science Services Administration (Manuscript received 20 October 1967; in revised form 9 September 1968) Summary A definitive statistical relationship is established between tropical cloudiness and rainfall and the semi- diurnal solar (S2) atmospheric tide, as manifested in the semi-diurnal surface pressure variation. Pressure and weather data are used from Batavia (seventy years) and Wake Island (twelve years). The S2 tidal effect is shown to enhance cloudiness and rain near sunrise and sunset, and to suppress them shortly after midday and midnight. The analysis is based on (a) the fact that the S2 amplitude varies by 15-20 per cent between months and by more than 100 per cent from day to day and (b) the amplitude of the S2 wave as computed from the pressure data at a station is closely related to the 5-6 hourly pressure changes during the periods around 4-5 a.m. to 10 a.m., from 10 a.m. to 4 p.m., etc. The crux of the analysis is the demonstration that days with large 5-6 hourly pressure changes during these periods have large cloudiness changes (in the sense described above) during these same periods relative to days with small 5-6 hourly pressure changes. Possible mechanistic connections between S2 pressure tendencies and cloud properties are examined. The varying convergence-divergence field is suggested as the main link. It is shown how the concentration of active cloud updraughts in the Tropics can permit cloudiness to be extremely sensitive to small divergence fields. Finally, large-scale simultaneous pressure changes over the Pacific Ocean area are shown and related to cloudiness changes. A need for re-examination of the nature and origins of tropical disturbances is shown to exist, using the concept that possible small (terrestrial or extra-terrestrial) triggers may set off significant changes in weather both locally and on the synoptic and global scales. 1. Introduction Tropical cloudiness and rainfall patterns exhibit different time and space scales and different relationships to the other atmospheric variables than do those in temperate latitudes. For many years it has been suspected that tropical oceanic clouds and rain exhibit maximum amounts and frequency during the hours of darkness, compared to the hours of daylight. This suspicion has been confirmed by recent studies from a research vessel (Garstang 1964; Holle 1968) and several tropical atolls (Lavoie 1963). In addition to a diurnal periodicity, a superimposed semi-diurnal periodicity has been increasingly indicated by observational analyses (LaSeur and Garstang 1964; Kiser, Carpenter and Brier 1963; Malkus 1964). The main features of the semi-diurnal effect appeared to be a cloudiness and rain maximum near dawn, with a weaker maximum near sunset. The existence, causes and distribution of tropical cloudiness and rainfall variations are important to seek and document, not only for forecasting local weather in the Tropics but for understanding disturbance growth, the energy sources of the large-scale global circulation and for progress towards eventual weather modification. The frontal and air mass models of cloud and precipitation control were long ago shown inapplicable to the Tropics (Palmer 1951). More surprisingly, the satellite era has begun to suggest that progressive travelling waves or vortical perturbations in the wind field, while often present and of major importance, may not be the main or most common controls upon tropical cloudiness and rainfall variability (Simpson, Garstang, Zipser and Dean 1967). It is timely to re-examine these controls and their degree of predictability. We have chosen the semi-diurnal variation in the belief that the documentation and greater understanding of this one scale of variation, which is currently tractable, may open the door to under- standing and prediction of cloudiness on other important but currently less tractable scales. Various causes, all radiative, have been advanced for the diurnal cloudiness cycle (e.g. Kraus 1963). The semi-diurnal cycle has been more controversial and more difficult 120 121 TROPICAL CLOUDINESS AND TIDES to establish. The reasons are, firstly, that its amplitude is small compared to interdiurnal changes, amounting to a range of roughly 5-15 per cent in cloudiness and perhaps a slighter larger percentage in rainfall. This low signal to noise ratio requires many years of data to form an adequate sample. Secondly, nearly all observations have been made from land masses; even small islands introduce their own daily regimes which vary as the large- scale flow varies. Thirdly, visual cloud observations are very difficult at night. Systematic bias can be argued related to the phase of the moon, for example, no matter how long the data sample. Numerous workers have hypothesized a relationship between the 12-hour atmospheric solar tidal oscillation, called the S, wave, and the cloudiness and rainfall cycle (Gold 1913; Riehl 1947; LaSeur and Garstang 1964). The semi-diurnal S2 surface pressure wave is one of the outstanding features of the tropical atmosphere. It has pressure maxima near 10 a.m. and p.m. local time and minima near 4 a.m. and p.m. The mean annual amplitude is about 1-2 mb, decreasing with higher latitude and varying with season (Stolov 1955; Haurwitz and Sepulveda 1957). This regular twice-daily barometric change is clearly due to the sun but it has become established practice in meteorology to refer to it as ' tidal ' without specifying what portion is thermally or gravitationally induced. A small associated tidal wind variation in the tropical easterlies can be extracted by statistical analysis from long series of wind data. An example is the surface tidal wind at Eniwetok Atoll (11-30N; 162-15E) presented by Lavoie (loc. cit. 1963). The tidal wind range was about 30 cm sec-1, with easterly wind maxima and minima corresponding to those in pressure. Putting together these indications, Malkus (1964) postulated the pressure-convergence-cloudiness relation illustrated schematically in Fig. 1. Maxima in cloudiness correspond with maxima in convergence or pressure tendency which lead the pressure maxima by three hours or 45° in phase. Two main problems faced the evaluation of the proposed relation between the S2 wave and cloudiness. The first lay in the factual demonstration that the relation exists, which is difficult due to the high noise level and several types of data inadequacy. The fact that the low-level convergence associated with the S2 tidal wave is not likely to be greater than 1-5 X 10-7 sec -1 led most meteorologists to dismiss its importance for many years, since storm and sea-breeze scale convergence exceed this amount by 1-3 orders of magnitude. The main purpose of this paper is to establish a conclusive relation between the S2 wave and semi-diurnal cloud and rainfall variations. The matter of mechanism is still not resolved; some suggestions will be considered in the closing Sections. If the diurnal march of cloudiness and rainfall is affected by the S2 wave, a midday suppression should be noted around the hours of noon and early afternoon and another suppression shortly after midnight. The noon and early afternoon suppression is strong and readily detectable on ships and most small islands, but on larger land masses it is usually at least partly obscured or overcome by the sea-breeze and land effect (Riehl 1947, 1954; LaSeur and Garstang 1964; Holle 1968). Verification of the after-midnight suppression was regarded as critical in confirming the S2 relationship; neither a radiative nor sea-air exchange hypothesis of cloudiness variations could account for a mid-nocturnal diminution in cloudiness or rain. Unfortunately, documenting this nocturnal suppression in cloudi- ness faced the problem of observer bias, while no oceanic rainfall records were available until the R. V. Crawford cruises by Garstang (Garstang 1964; LaSeur and Garstang 1964). These cruises, albeit with a small data sample, showed a very large after-midnight diminution in both rainfall and 3 cm radar echoes. Oceanic satellite radiation measure- ments reported by Merritt and Bowley (1966) provide confirmatory evidence in diminished cloudiness and heights of tops just after midnight. Despite these encouraging pieces of evidence, the S2-cloudiness relation still lacked firm statistical support. The demonstration has now been made possible and forms the main subject of this paper. The key links are (i) documentation (Holloway, Holt, Mauchly and Woodbury 1955) of fairly large monthly variations in the amplitude of the S2 wave, (ii) the demonstration by Brier (1967) of a statistical relation between these monthly variations and the magnitude of the six-hour pressure changes (from 0400-1000 hr, G. W. BRIER and J. SIMPSON 122 1000-1600 hr local time, etc.) and (iii) the establishment of a correlation between pressure change and clouchness variations of proper magnitude and direction consistent with the observed S2-cloudiness relation. This paper is mainly concerned with this link. The data at Batavia show differences of 15-20 per cent in S2 amplitude between the same month of different years and for single days amplitude variations may exceed 100 per cent. Wake Island and other typical stations show similar variations. Very little is known about the nature of these changes, their spatial distribution and propagation as a wave phenomenon, or the extent to which they may represent variations in either the ' migratory ' or ' standing ' component of the S2 wave. Present theory has little or nothing to say about them. It is known that the diurnal component Su which is smaller in amplitude, is quite variable and influenced by local weather. However, since by mathematical defini- tion St and S2 are orthogonal, it does not seem possible to account for long term variations in S2 as a direct consequence of variations in S1. For the present, many of these questions must remain unanswered, and here we shall refer to the semi-diurnal pressure oscillation at a station as a tidal or S2 component, without attempting to specify what portion is thermally induced or results from resonance phenomena of the atmosphere. Although the amplitude of the S2 pressure wave as determined from the data at a particular station shows considerable variation in time, the phase of the wave remains remarkably constant. This means that a month with an average S2 amplitude higher than normal will have larger than normal pressure rises from 4 a.m. to 10 a.m., larger pressure falls from 10 a.m. to 4 p.m., etc. This, of course is the reason for the statistical relationship reported by Brier (1967). But it is also clear than on an individual day a rise in pressure during a six hour period, say from 4 a.m. to 10 a.m., will increase the amplitude of the S2 wave estimated by harmonic analysis, even though the variation in pressure is not sinusoidal Mbs 0 2 4 6 B 10 12 14 16 18 20 22 2< - \ Pressure \ / 24 LMT CONV DIV CONV L H L H at 4 ie>0 at 0700 10 1300 16 i£>o at 1900 Figure 1. Schematic illustration of hypothesized relations between diurnal pressure wave, convergence field and cloudiness over tropical oceans or small atolls. Top curve shows observed mean annual diurnal pressure oscillation at Eniwetok atoll (after Lavoie 1963) as a function of local mean time. Arrows above bottom diagram show qualitative predicted (Stolov 1955) and observed (Shibata 1964) varia- tion in the tropical easterlies due to the S2 component of the atmospheric tide and the associated convergence- divergence. Diagram shows lows (L) and highs (H) spread around the clock (or globe) and associated pressure tendencies. See Bjerknes (194S) for diagrams explaining antibaric character of tidal winds. Cloud symbols below indicated cloudiness variations and local times of extremes if maximum cloudiness is in phase with maximum convergence and vice-versa. 123 TROPICAL CLOUDINESS AND TIDES in wave form or may be produced by non-tidal perturbations. However, if large six hour pressure changes were distributed uniformly and randomly throughout the day, there could be no net contribution to the mean S2 wave and the pressure changes could not be considered as tidal since they are not phased in with the 24 hour clock. The statistical relation between the magnitude of the S2 wave and the six hour pressure changes means, on the average, a larger six hour pressure change is associated with a larger value of S2, but it does not necessarily imply that an anomalous change during a particular six hour period is tidally produced. The six hour pressure change is a convenient measure or index of the amplitude of the S2 wave but, more important in the analysis here, it makes it possible and easy to study in greater detail the fluctuations that take place in periods much shorter than 24 hours. The pressure-convergence-cloudiness relation postulated earlier and illustrated schematically in Fig. 1 requires that rising pressure from 4 a.m. to 10 a.m. (4 p.m. to 10 p.m.) should be associated with increasing cloudiness. If this view is essentially correct, then one should expect to find a greater increase in cloudiness on days when the pressure rise during this period was greater than normal, and a smaller increase in cloudi- ness on days when the pressure rise was smaller. Likewise, during the period 10 a.m. to 4 p.m. one should expect to find the greatest suppression of cloudiness on days when the fall in pressure was relatively greater. If a statistically significant relation is found between cloudiness (or rainfall) and the magnitude of the pressure changes during these intervals, then strong support is provided for a physical link between S2 and weather, regardless of whether we know the direction or the mechanism of the causality or reason for variations in the amplitude of S2. The evidence would be even more convincing if the relationship was pronounced, suggesting that the tropical atmosphere was very sensitive to small pressure changes. 2. The data used and the analysis procedure Two data samples were used in this study, the first from Batavia (now called Djakarta) and the second from Wake Island. Pressure trends are to be correlated with trends in cloudiness and rainfall for selected 5 and 6-hour periods of the 24-hour day. Batavia (6-80°S; 106-45°E) is located at the north-west extremity of Java, in the Malay Archipelago. Fig. 2 shows that Java is a mountainous island extending about 600 miles approximately east-west and about 100 miles north-south. Numerous peaks exceed 2,000 m and several exceed 3,000 m elevation. The mean annual rainfall at Batavia is 184 cm per year. Java is in the south-east monsoon in its winter which is the dry season. The rainy season occurs in summer (October through March) when Java lies in the equatorial trough. The surface pressure at Batavia is practically always rising from 4 a.m. to 9 a.m. local time and from 4 p.m. to 10 p.m. The pressure is always falling from 9 a.m. to 4 p.m. 6*8 8"' LOCATION OF BATAVIA ON JAVA 4'S 6"S e's bATAVIA (\ J"TK>wJ l.f'i?h .■■- / — jV, ioc Mi 0 M CONTOUR BOVE 2000 M • MT. PE4K A 10 |"E 106*E ioe"E IIO'E 112'E IH"E II6"E I20*E Figure 2. Location of Batavia on island of Java in Malay Archipelago and schematic illustration of orography. G. W. BRIER and J. SIMPSON 124 WAKE ISLAND I66~6'E I66°37' I66"38'!; I66°39'E 19° 19 N I9°I8' N 19° I6'N Figure 3. Outline map of Wake Island (after Kiser et al. 1963). Dark areas depict dry land; clear outlines show outer margins of barrier reef. Numbers in boxes are elevations in ft. Six hour changes may be nearly 6 mb at times or as small as 2 mb at other times. The annual mean amplitude of the semi-diurnal pressure variation is about 1-38 mb. The average diurnal march of cloudiness and rainfall shows a dawn and sunset maximum, with a secondary maximum just after noon. For presentation, we have analysed a sample from 16 months of summer season data for the years 1924-1944, used earlier by Brier (1966). The dry season has also been studied; it shows similar but less pronounced results. Wake Island (19-29°N; 166-65°E) typifies a contrasting tropical situation. Fig. 3 shows that it is a truly oceanic atoll, less than 4 by 3 miles in total extent. The atoll lies in the northeast trades the year round, but disturbances of temperate origin occasionally affect it during the drier winter season. The mean annual rainfall at Wake is 94 cm per year, about half that at Batavia. Twelve years of data were available on magnetic tape, subdivided into four seasons. Winter is defined as December through February, spring as March through May, etc. The mean semi-diurnal variations in these data had previously been related to mean atmospheric tides by Kiser, et al. (loc. cit. , 1963). The surface pressure at Wake is normally rising between 5 a.m. and 10 a.m. local time and also between 4 p.m. and 10 p.m. The annual average amplitude of the semi- diurnal pressure wave at Wake is 0-93 mb, or only 67 per cent of that at Batavia, in poor agreement with the 79 per cent ratio calculated from the cosine-cubed decrease with latitude found empirically by several workers (Haurwitz 1956; Simpson 1918). The ratio of daily and monthly variations to the mean are comparable at both locations. The mean cloud cover at Wake shows peaks at dawn and sunset, with a weak midday suppression. In contrast with most other small tropical islands (e.g. LaSeur and Garstang 1964; Lavoie 1963) the mean visually recorded cloudiness is smaller during the night-time than during the daylight hours. The mean rainfall frequency shows a maximum between 0300-0600 with a secondary peak near sunrise. Figs. 4 and 5 illustrate the reason why a definitive relation between weather and S, wave has been so difficult to establish. In the mean daily marches of the weather variables, land-sea effects and their interaction with synoptic disturbances cannot be subtracted out, nor can the night versus day observers' bias in cloudiness be assessed. 125 TROPICAL CLOUDINESS AND TIDES 1012.0 BATAVIA 1 1 i 1" 101 1.0 /~x uj 10100 / 5 10090 - UJ 2: iooao \nri7Ci ' i i 7.0 z| 100 1 T i arte Q n " " 6 AM 6 PM 12 Figure 4. Diurnal marches of pressure, cloudiness and rain amount and duration at Batavia, Java. Averaged over the year for 70 years of data. Rain amounts are hourly. Rain duration (in minutes) was summed for each hour for each month for the seventy years. The curve shown is the average of all monthly curves. Note that on this and succeeding figures the abscissa value at the origin (left) is 1 a.m. An interesting example of ' heated island ' effect is seen by comparing the cloudiness and rainfall curves in Fig. 4. The cloudiness curve has a strong midday peak, absent in the rainfall. Experience suggests the midday island-produced clouds are less likely to precipitate due probably to the rise in cloud base height resulting from the heating (Malkus 1964). The primary means by which the present study attempts to establish a definite relation between atmospheric tides and weather variables is to segregate days of abnormally large from days of abnormally small S2 pressure component and to compare the semi- diurnal cloudiness and rainfall variation on these two classes of days with each other. This is accomplished by selecting days on the basis of pressure change during 5-6 hour periods, since we are interested in studying pressure-weather relationships on a much shorter time scale than an entire day. Furthermore, this avoids the serious ambiguity in interpretation that would result from a direct comparison between the amplitudes of the semi-diurnal components of pressure and weather computed from a 24 hour period. It would be possible, for example, for a large S2 pressure component to result from an anomalous rise in pressure from 4 a.m. to 10 a.m. while a large semi-diurnal component in cloudiness might be produced by a large rise in cloudiness from 4 p.m. to 10 p.m. Since any correlation resulting from such an analysis might be misleading or spurious, it makes more physical and statistical sense to concentrate on weather variations concurrent G. W. BRIER and J. SIMPSON 126 iOI50 WAKE ISLAND rr 0.0 Figure 5. Diurnal marches of pressure, cloudiness and rain frequency at Wake Island. Averaged over the year for twelve years of data. BATAVIA CO 10.0 9.0 - CO CO LU ? 8.0 O o _J u 7.0 6.0 1 1 i -^ ~|AP i i i SMALL /\ **" 1 / ! / i \ A. / i \ .— 1 1 1 /\ N 1 / \ \ IS / N 1 A \ 1 / \ ^-~s It \ LARGE/ N — ' \ i / V s // \ h-1 T ^> J \i/ \ . 1 / — \ N 1/ \ i ! I 6 AM 12 6 PM Figure G. Comparison of diurnal marches of (summ:r) cloudiness at Batavia for large pressure talis (solid and small pressure falls (dashed) in midday period from '» a.m. to 4 p.m. local time. 127 TROPICAL CLOUDINESS AND TIDES with the pressure changes. Statistical averaging over a number of samples will reduce the effect of local variations, or noise due to pressure changes that are non-tidal or random with respect to the time of day, since they cannot contribute, in the long run, to the average S2 pressure oscillation determined at a station. 3. Results and discussion Table 1 summarizes the analysis procedures and results. Three periods of the day were examined for Batavia and two for Wake, corresponding to both S2 tidal pressure rises and including the midday fall period for Batavia. Large and small pressure changes are defined as follows for Batavia: From 0400 to 0900 increases equal to or exceeding 3 mb were called ' large.' Increases equal to or less than L8 mb were called ' small ' changes. TABLE 1. Statistical results Differences in weather variations with large and small pressure changes at Batavia and Wake Island. Pres- sures normally rise in morning and evening and fall during midday hours. Greater cloudiness-precipitation increases in morning and evening and decreases during midday are found on all large pressure change days than on small pressure change days except the one (very small) exception in parenthesis Identification Number of cases Weather variations A Period Initial Large Small Difference Difference > Difference Difference of cloud pressure pressure of of in in day conditions changes changes pressure cloudiness change mean (tenths) change changes in precipi- (mb) in probability tation period of rain from beginning to end amount during period (mm) 4 a.m. period 4 a.m. period Batavia to (6-0S°S; 106-45°E 9 a.m. 4 p.m. to 94 82 1-28 0 06 733 10 p.m. 178 87 2-11 0-1S 8-65 9 a.m. 1, 2, 3 10 11 2-31 550 to 4, 5, 6 7 4 1-49 2-20 4 p.m. 7, 8, 9 15 15 2-18 1-80 (all groups) (all groups) 10 17 18 250 2-10 0-29 6-5S Wake Island (19-29°N; 166-65°E Winter 5 a.m. 54 54 1-96 013 003 Spring to 54 54 232 0-42 004 Summer 10 a.m. 54 54 1-81 084 009 Autumn 54 54 2-13 (0-08)* 0-03 Winter 4 p.m. 54 54 215 056 0-06 Spring to 54 54 2-03 0-38 003 Summer 10 p.m. 54 54 1-80 1-29 0-03 Autumn 54 54 2-11 0-25 0-11 Change in opposite sense For the p.m. rise period the corresponding boundaries were 4 mb and 3 mb, respectively. For the midday fall period, the three greatest pressure falls in each month were classified as ' large ' changes, while the three least falls were called ' small ' changes. For Wake, only the rise periods were studied. The three greatest rises in each month were called ' large ' changes while the three smallest rises in each month were called ' small ' changes. G. W. BRIER and J. SIMPSON 128 To understand the pressure- weather relationship established by Table 1, it is necessary to keep in mind that the entries under ' Weather variations ' are the differences between the cases of large and small pressure change. For example, during the morning pressure rise period at Batavia, the ' large rise ' days exhibited a greater increase in cloudiness between 4 a.m. and 9 a.m. than did the ' small rise ' days, by 1-28 tenths; they exhibited an in- crease in rain occurrence probability 0-06 greater than the ' small rise ' days and a 7-33 mm larger rainfall amount in the five-hour period. We define the rain occurrence probability as the number of rain occurrences divided by the total number of cases. Qualitatively similar relationships are inferred for both rise periods in both locations. During the falling pressure period of the day at Batavia, the S2 effect should act to suppress cloudiness and rainfall if the tide- weather relationships work as hypothesized in Fig. 1. However, Java is a large land mass. Sea-breeze effects are working in the midday hours to build clouds against any suppressive influence. The best method of isolating the S2 effect is to compare weather trends on the large and small pressure change days in the same location. From the work of Haurwitz (1955), it could be argued that the heated land mass effect is uncorrelated with the amplitude of the S2 wave and is cancelled out in the com- parison just described. Haurwitz's work, however, concentrated on the small island of Bermuda (32.18 N; 64.78 W). The greater size of Java suggests a possible feed-back relationship between the land mass effect and cloudiness. Because clouds diminish insolation at the ground, a three-way coupling between disturbances, sea-breeze and S2 effect ccaid occur. This might also involve an interaction with the Sx component of pres- sure. We cope with *;his problem by sub-dividing the cases by initial cloudiness conditions. The results are striking, as shown in Table 1 for the 9 a.m. to 4 p.m. period at Batavia. Relatively much greater suppression (or smaller enhancement of weather by the heated land mass effect) occurs on large pressure change days than on small ones. When the initial cloudiness is 1-3 tenths at 0900, the cloudiness decrease is more than five tenths greater during the large pressure change middays than during those with small pressure falls. Clearly this means that small S2 days have midday increases in cloudiness, since cloud amount cannot decrease below zero tenths. This result implies that most cases of greatly increasing daytime cloudiness at Batavia are days of weak S2 wave. That is, ' island ' effect and S2 amplitude are inversely related. Fig. 6 shows that the sea-breeze or island effect is able to produce a noon cloudiness peak at Batavia on both classes of day, but when the S2-associated divergence is strong at 1300 hours, the cloudiness is not able to go on developing during the afternoon as it does on weak S2 days. Conversely, Table 1 shows that days which start off disturbed (10 tenths cloudiness at 0900) show midday suppression due to the S2 effect. Physically, these initially disturbed days contrast with the initially fair days in experiencing a minimal heated island effect. Therefore large S2 effect superimposes upon disturbances to suppress cloudiness during the day by two tenths more than small S2 effect dees. Wake Island also exhibits a significant and similar relationship between the S2 tidal component and the weather variables. But the difference in cloudiness changes at Wake are much less than those found at Batavia; they are in fact relatively much smaller than the one-third decrease in amplitude of the S2 pressure wave at Wake compared to Batavia. It may be that the interaction of land mass effects with S2 (or S,) variations increase the cloudiness sensitivity to the latter. However, it is likely that a factor in the difference is simply the larger mean cloudiness at Batavia in summer. To explain the difference further it may be necessary to assess the relative frequency of cloud types and elevations. In the morning the autumn season at Wake shows a very small S2-cloudiness relation in the opposite sense from that generally prevailing. Even in that case, however, the relation- ship for rain occurrence turned out positive, consistent with the rest of the lesults. Thus the one negative value in Table 1 might well be a statistical accident that a larger data sample would reverse. It is noteworthy that only in summer does the S2-\v ather relation- 129 TROPICAL CLOUDINESS AND TIDES WAK 3LAND 7.0 30 3. SUMMER 4. AUTUMN J L 6 AM 12 6 PM Figure 7. Seasonal change in daily marches of pressure and cloudiness at Wake Island. On the cloudiness (lower) curves note the seasonal migration of the mean peak Irom morning to afternoon in good agreement with the slopes of the pressure (upper) curves. Pressure curves not plotted on absolute scale. Interval is 1 mb (see Fig. 5). ship at Wake exhibit comparable strength to that shown at Batavia in summer. Fig. 7 compares the seasonal change in the march of mean pressure wave and cloudiness at Wake. Surprisingly, the pressure wave shows maximum amplitude in winter. Haurwitz and Sepulveda (1957) in fact showed that in January the S2 wave has its maximum amplitude at 15CN while in July it is a maximum at the Equator. Thus the maximum S2 amplitude is displaced latitudinally from both the overhead solar position and that of the equatorial trough in all seasons, a mystery which has not been explained. For present purposes, it is most important to note only that the strength of the S2-cloudiness relation at any place is dependent upon factors other than the mean amplitude of the S2 wave. Fig. 7 shows these factors are more complex than just the average cloudiness, since at Wake the autumn cloudiness is greater than that in spring. The autumn cloudiness, however, is likely both to occur at higher levels and to exhibit a greater ratio of stratiform to cumuliform than in spring. Section 4 on mechanistic linkages suggests ways to pursue these interesting ques- tions further. The seasonal trend in Fig. 7 which shows the main cloudiness peak advancing with season from morning in winter to late afternoon in summer seems to be at least partially explained by a similar trend in the slopes of the pressure curves. This indicates that variations in the S{ pressure component are related to cloudiness in the same way that S2 is related, thus confirming the relationship between pressure trends and cloudiness- changes. The main result of Table 1 is that out of the 28 entries in the last three columns, 27 G. W. BRIER and J. SIMPSON T 130 Figure S. Comparison of daily march of summer cloudiness at Batavia for large (solid) versus small (dashed) morning (4 a.m. to 9 a.m. local time) pressure rises. The lower curve is the difference between the two upper curves and shows the greatest increase during the 4 a.m. to 9 a.m. period when pressure was increasing the most rapidly in the large Ap group compared with the small Ap group. Note absence of any noticeable 24- hour trend in the variables. of them are positive. By chance one would expect one-half of them to be negative. Four- teen separate or independent groups (six for Batavia and eight for Wake) were analysed for cloudiness and only one of these shows a negative value (which is very small or close to zero). The chances are less than one in ten thousand that one or fewer negative signs will turn up in 14 randomly distributed differences. Thus there is no doubt about the 6.0 - 0.0 LARGE SMALL \ / \ SMALL / I ^- — i £ -J X 6 A M 6 PM "Figure 9. Comparison of hourly summer rainfall amounts for large (solid) and small (dashed) morning pressure rises at Batavia. As indicated in Table 1, the difference in precipitation amount was 7 '33 mm while the ratio of the amounts during the 4 a.m. to 9 a.m. period is 14 to 1 ! Note also the downward trend in amount for the small pressure rise cases, in contrast with the upward trend in the large pressure rise cases. 131 TROPICAL CLOUDINESS AND TIDES statistical significance and physical reality of the relationship between pressure change and weather. Significance would have been attained if only 6, instead of 14, separate groups had been analysed. The values in the two rain columns in Table 1 are not inde- pendent of the results of the cloudiness column since more frequent rain and greater amounts will tend to be associated with increasing cloudiness. However, the functional and quantitative relationship between cloudiness, vertical cloud development, rain fre- quency and rain amount are just beginning to be documented in the Tropics (LaSeur and Garstang 1964; Holle 1968). If there is no entry in the table, it means that the analysis was not performed either because the data were not conveniently available or because it was felt that the data sample was too small give meaningful results. For example, the rainfall analysis was made only on the combined groups for the Batavia 9 a.m. to 4 p.m. period because of the few cases and high natural variability in rainfall. A second important result of this study is that with this separation into large and small pressure change cases (correlated to large and small S2) the S2-weather relation becomes so pronounced and consistently above the noise level that it is apparent from visual inspection of the graphs and can be demonstrated even with relatively few obser- vations. Figs. 8-15 show a few selected graphs from the Batavia results. Differences between individual curves are generally highly significant but standard errors are not 0.20 Figure 10. Comparison of hourly rainfall probability for the summer season in Batavia for large (solid) and small (dashed) morning pressure rises. The lower curve is the difference between the two upper curves. The greatest increase in rainfall probability is during the period of rising pressure. The abscissa refers to the rainfall measured up to the end of the hour. G. W. BRIER and J. SIMPSON 132 Figure 11, Rainfall amount comparison for the evening pressure rise period for Batavia in summer. The rise period considered is 4 p.m. to 10 p.m. local time. Large pressure rise cases (solid) show much more precipita- tion in the period than do the small pressure rise cases (dashed). 10! 5. 1014.0 1013.0 10120 (MB) 101 1.0 10 1 0.0 1009.0 Figure 12. Diurnal march of pressure at Batavia on large (solid) and small (dashed) pressure fall days. Note that the pressure falls between 9 a.m. and 4 p.m. local time on both classes of uays, but about 67 per cent more on ' large' fall days. Note that ' large' midday fall days are also days of large rises in the a.m. and p.m. periods, graphically illustrating Brier's (1967) correlation between S2 amplitude and 5-6 hourly pressure changes. Other pressure regime curves are similar. 133 TROPICAL CLOUDINESS AND TIDES (MB) Figure 13. Difference in cloud regimes on days with large versus small midday pressure at Batavia in summer, when the 9 a.m. cloudiness is 1-3 tenths. The period considered is 9 a.m. to 4 p.m. local time. The upper curve is the difference in the pressure fall between the large fall and small fall cases (Fig. 12). The lower curve is the difference in cloudiness change between the two sets of cases. Note that the greatest and in fact the only consistent and large decrease in cloud anomaly is during the period of falling pressure anomaly. Since cloudiness cannot decrease by five-tenths if it is initially three-tenths or less, the results are contributed mainly by the increased cloudiness that takes place when the pressure falls much less than it normally does during the period 9 a.m. to 4 p.m. (see Fig. 6). given because they would be misleading in view of the lack of independence of the obser- vations from one hour to the next. Fig. 8 compares the diurnal cloudiness march for large and small pressure rises in the morning period from 4 a.m. to 9 a.m. Both cases show the three peaks of Fig. 4, but the large morning pressure rise cases show a higher rate of cloudiness increase in the morning and a less sharp noonday cloudiness peak. It is important to note that there is relatively little change in 24 hours in all curves, so that situations with long period trends are not influencing the results. Very small or zero 24-hour trends were found for all data sub-divisions reported in Table 1. Fig. 9 compares the corresponding daily marches of mean hourly rainfall amounts for Batavia. The aggregate mean rainfall for the period is in the ratio of 14 to 1 for the case of large . versus small pressure rise. For the ' small ' pressure change, the trend in precipitation is downward during the period, indicating a suppression of activity. The same G. W. BRIER and J. SIMPSON 1.54 (MB) Figure 14. Difference in cloud regime on days with large versus small midday pressure tall at Batavia in summer when the 9 a.m. cloudiness is 10 tenths. A greater midday suppression is found on the large pressure fall days. suppression was found in rainfall probability (Fig. 10). Fig. 9 and the location of Batavia (Fig. 2) suggest that a late nocturnal land-mountain breeze dominates the precipitation regime in the early morning hours on 'small' pressure change days. The island effect is largely overcome by the tidal effect on ' large ' pressure change (large S2) days. Fig. 11 shows the corresponding rainfall amount comparisons for the 4 p.m. to 10 p.m. pressure rise period. The dominance of the island effect is striking on the 'small' pressure change days, as is the dominance of the S2 effect on the ' large ' pressure change days. Figs. 12-15 examine the midday regimes at Batavia with very low and very high initial cloudiness at 9 a.m. Fig. 12 illustrates graphically the correlation between 5-6 hour pressure change and semi-diurnal S2 amplitude which was established statistically by Brier (1967, loc. cit.)- Even with only 10-18 cases making up each graph, the strikingly greater suppression on the ' large ' pressure fall (large S2) days is obvious. Fig. 13 illustrates the different effect of large versus small S2 on the midday cloudiness peak on days which start off fair. The midday cloudiness peak has five-tenths more sky cover on weak S2 days. Fig. 14 examines the same midday differences on days which start off overcast. Large Sz days show a noonday reduction in sky cover two-tenths more than do small S_. days. Fig. 15 compares midday rainfall amounts. The amount of rain from °> a.m. to 5 p.m. during the ' small ' pressure falls exceeds that during the ' large ' pressure falls by a factor of three. This ratio again supports the hvpothesis regarding the varying relative strengths of tidal versus island effect. 135 TROPICAL CLOUDINESS AND TIDES 12.0 Figure 15. Comparison of rainfall amounts at Batavia in summer during days ol large midday pressure fall (solid) and small midday pressure fall (dashed). Note the far bigger afternoon peak on the small pressure fall days. WAKE ISLAND -0.05 AM Figure 16. Comparison for Wake Island. Differences in pressure rise, cloudiness increase and increase'in rain for the morning pressure rise period from 5 a.m. to 10 a.m. Small rise values have been subtracted from large rise values (all seasons). G. W. BRIER and J. SIMPSON 136 2.0 1.0 - 0.0 / \/i 1 1 l\ WINTtR - / 1 \ ; 1 H : 1 1 \ ■ i Figure 17. Cloudiness comparison for Wake Island for morning pressure rise period, broken down by seasons. Small rise values have been subtracted from large rise values. Note pronounced excess in cloudiness increase on large pressure rise cases for all seasons except autumn. Diagrams for Wake Island for the morning (5 a.m. to 10 a.m.) pressure rise period are shown in Figs. 16-18. In Fig. 16, it is important to note that the pressure difference curve does not necessarily mean that the pressure fell from midnight to 1 a.m. It means that days with large pressure rises from 5 a.m. to 10 a.m. had lower initial pressures than the small pressure rise days. Most noteworthy is the observation that when the pressure stopped rising rapidly around 10 a.m., the cloudiness and rainfall stopped increasing and actually decreased. This emphasizes that we are dealing with variations on a time scale of a half day or less and not twenty-four hour trends, for if the latter were involved the cloudiness and rainfall would have continued to increase, or at least levelled off, past 10 a.m. The morning relative cloudiness peak for the 'large' pressure rise days is pro- nounced in all seasons except autumn. The latter season, nevertheless, has a strong relative peak in rainfall. This peculiarity is equally evident in the afternoon diagrams for autumn (not shown). At this time no explanation is evident, but if the peculiarity were confirmed in a larger data sample, a reason might first be sought in the seasonal changes in cloud types, elevations and origin. Some evidence of 24-hour trends is present in the autumn data at Wake. Climatologically, this season might be the most prone to travelling disturbances. 137 TROPICAL CLOUDINESS AND TIDES 0.10 Figuic IS. Ram frequency comparison for Wake Island, for morning pressure rise period, broken down by seasons. Small rise values have been subtracted trom large rise values. Pronounced excess in increased rain probability is found for the large rise cases for all seasons. 4. Possible mechanistic: connections between S2 atmospheric tide and cloudiness AND RAINFALL Fig. I hypothesized a physical connection between the S2 pressure wave and clouds by means of the convergence and divergence concomitant with the rising and falling pressure. It was also mentioned that most meteorologists have regarded the magnitude of the S2-associated convergence as too small to affect clouds and precipitation. However, the hypothesized S2-weather relationship has now been established statistically. It there- fore becomes desirable to examine possible mechanistic links and to inquire about their necessary magnitude and method of operation. We shall first estimate the magnitude of the convergence-divergence likely to be associated with the S2 wave and then inquire as to how it might affect clouds and precipitation. A basic physical relation is found in the tendency equation, viz : ft = - J & v • v» dz z A g v7/ . VH p dz + gpwz . B C (1) The symbols have their usual meanings; 3p/3t is the local pressure tendency at level z (for example as measured by a barograph). A is the horizontal velocity divergence term. B is the horizontal density advection term. C is the vertical motion term where wz is the vertical air motion at level z, positive upwards. At the surface (z = 0), id = 0. Density advection G. W. BRIER and J. SIMPSON 138 plays no part in the semi-diurnal pressure cycle. Since the tropospheric density p has only one maximum and one minimum around the globe, we must explain the surface pressure oscillation in terms of the vertically integrated divergence field. From Eq. (1) an average divergence field (from the surface to levels of 12-15 km) of the order of 10-7 sec-1 would produce a surface pressure oscillation with an amplitude of about 1 mb at the surface. Since the atmosphere is commonly divided into superimposed layers of divergence and convergence the net integrated value, however, may tell us little about what a given layer is experiencing. Average cloud layer divergences of 1-3 X 10-7 sec-1 are in good agreement with results from tidal theories and observations, as reviewed by Shibata (1964). If the main tidal divergence producing the pressure change were confined to the lowest three kilometers, it would average about 3 X 10-7 sec-1 for Batavia and 2 X 10-7 sec-1 for Wake. Thus for the ' large ' pressure change days at Batavia, the cloud layer convergence could be in the neighbourhood of 6 X 10-7 sec-1, or more if there were compensating layers aloft. Clearly the magnitude of the S2-associated convergence cannot be resolved without a determination of the tidal ' wind.' These S2 winds have been studied successfully with rockets and meteor trails in the ionosphere where they are large (Elford 1959; Greenhow and Neufeld 1961; Kashcheyev and Lissenko 1961). But in the high density troposphere, whence the main contributions to surface tendencies must originate, the measurement problem has been very difficult. The mean horizontal tidal winds corresponding to a divergence field of about 2-5 X 10-7 sec"1 are about 80 cm sec-1. The surface wind evaluated by Lavoie (1963) at Eniwetok atoll (11-30°N; 162-15°E) is much smaller than this, but the magnitude might well be expected to increase upward away from the surface. It is necessary to determine the amplitude and phase of the S2 tidal wind as functions of altitude, a very difficult task. Small wind variations must be isolated from far bigger inter-diurnal changes. A large around-the-clock sample must be sought on one or more atolls. This sampling presents a nearly impossible data requirement since rawinsondcs are normally made at 12-hour intervals. One of the rare opportunities with more frequent soundings was provided at Lajes Field, Azores, in 1956-1958. Using these data, Harris, Finger and Teweles (1962) made a fine study of the semi-diurnal tidal winds (and other variables) at thirty levels between the surface and 10 mb. The east-west component increases rather uniformly from about 28 cm sec"1 at 850 mb to about 1 m sec-1 at 15 mb (29 km) with little change in phase. Unfortunately, the Azores are extra-tropical (38.73 N; 27.07 W). The only opportunity for a similar study on a tropical atoll was provided by the Marshall Island bomb tests in the 1950's, when a series of six-hourly upper wind measure- ments were made. There was also a helpful shift in observation time within the series, permitting an adequate 3-hourly sample over the 24-hour period at some stations. These data were analysed, in most detail for Eniwetok, by Shibata (1964, loc. cit.). He found mean tidal winds consistent with Fig. 1 and the mean divergence figures quoted here. A maximum east-west component of 80 cm sec-1 was found at 1 km (just above mean cloud base) with a probable error of i 9 cm sec-1. There was also some evidence of a phase shift beginning above 2 km. By 3 km, the tidal wind had apparently reached a 6-hour phase lead relative to that in the lower cloud layer, although the data were rapidly thinning with height. It would be important to determine whether this difference from the results of Harris et al. (1962) is real and due to location difference, or whether it is fictitious. Some upper atmospheric studies (cf. Greenhow and Neufeld 1961) suggest that the iono- spheric (80-100 km) tidal wind and pressure oscillation are, in some seasons, almost exactly out-of-phase with those at the surface. From Fig. 1, this implies that the upper divergence field may be out of phase with that lower down. Tropical studies (e.g. Riehl 1954) have shown that the most favourable conditions for clouds and rain consist of con- vergence in the lower cloud layer and divergence at its top. Thus determination of the existence and height of any phase shifts in semi-diurnal tidal wind and pressure 139 TROPICAL CLOUDINESS AND TIDES oscillation is important. Harris et al. (1962, loc. cit.) show that a two-year series of six- hourly wind soundings could provide the necessary information. We must next ask whether and how these small convergence-divergence fields could cause the documented variations in cloudiness and rainfall. A divergence of 1CT6 sec-1 is roughly the value of the prevailing mean divergence in the trade-wind cloud layer, associated with an average subsidence of several hundred metres per day. The subsidence was shown (by Riehl et al, 1951) to be a major brake against cloudiness. Thus if the large S2 days are associated with oscillating divergence-convergence magnitudes of 25-75 per cent of this amount, we might expect a significant effect upon cloud growth. The prevail- ing divergence is to a large extent removed near sunrise and sunset and greatly increased during the midday hours. In the equatorial trough zone, mean convergence prevails and analogous reasoning would apply. To understand the effect of these small changes on clouds, however, we must keep in mind the concentration of convergence and active cloudiness in the Tropics. A study of the equatorial trough by Riehl and Malkus (1958) suggested that the mean ascent there is not a gradual, widely spread slow movement of all the air, but that the up motion is highly concentrated in a few active cloud groups, and within these in a few active cloud towers. An analysis by Kuo (1961) provides an important theoretical foundation for this concentration. He showed that if the stratification is unstable for ascending motion over an infinite area and stable for descending motion, and small random perturbations of various scales are introduced, the final disturbance evolved will have the dimension of a cumulus cloud. The stable stratification in the descending region has the effect of in- creasing the critical lapse-rate and narrowing the ascending region and making the descend- ing motion widespread, so that centres of the ascending region are further apart. The distances estimated from Kuo's theoretical analysis agree favourably with cloud row spacing obtained from satellite observations. In this way the weak, large-scale tidal perturbation can cause the atmosphere to react on the cumulus scale. We postulate that this concen- tration of vertical motion is a key to the relation between S2 tidal convergence and weather. In the quantitative calculations, we shall be conservative and consider the effect of a convergence-divergence amplitude of only 2-5 X 10~7 sec-1. This amplitude agrees with the mean tidal winds found by Shibata (1964) at Eniwetok and also with theoretical values and the observed mean pressure changes in the Marshall Islands region. By continuity, a convergence field of 2-5 X 10-7 sec-1 would be associated with an overall average ascent of 0-1 cm sec-1 at 3 km (near the top of the normal undisturbed cloud layer in the trade- wind region). The mean cloudiness at this level is 35 per cent and the mean is made up by about half the sky being clear and the other half being occupied by cloud groups with about 70 per cent cloudiness. We assume that the average ascent of 0*1 cm sec-1 over the whole area is brought about by no ascent in the clear zones, with 02 cm sec-1 confined entirely to the cloudy zones. Table 2 shows how an oscillation of ± 02 cm sec"1 in the average vertical motion can lead to a 10 per cent cloudiness variation. The figures in Table 2 are based on typical values taken from years of aircraft observations by Malkus (1958a). A small mean addi- tional vertical motion is able to contribute such a relatively large cloudiness change because of the concentration of the active updraughts into 2-3 per cent of the whole area, so that most clouds seen or photographed are inactive or decaying. This concentration of active updraught has in fact been confirmed by years of observations and has also been found in tropical hurricanes (Malkus 1958b; Malkus, Ronne and Chaffee 1961). The calculations in Table 2 are intended to be illustrative rather than definitive; they are both conservative in assumptions and insensitive to reasonable variations in them. Examining the results in more detail, we find that they depend on the following three features of cumulus clouds, which have been documented observationally. (i) Comparable vertical speeds in active updraughts and active downdraughts, which together occupy only a small per cent of the total cloudy area. In the example, the G. W. BRIER and J. SIMPSON 140 TABLE 2. Cloudy area (3 km elevation) Average over 24 hours 5 per cent Active updraught 274 cm sec-1 5 per cent Active downdraught — 150 cm sec-1 60 per cent Inactive cloud — 8 cm sec-1 30 per cent Intercloud spaces — 1 cm sec"1 uJ = + 1-1 cm sec"1 Max. conv. (2-5 X 10~7 sec-') 5-5 per cent Active updraught 274 cm sec-1 5-5 per cent Active downdraught — 150 cm sec"1 66 per cent Inactive cloud — 8 cm sec-1 23 per cent Intercloud spaces — 1 cm sec-1 w = + 1"3 cm sec-1 Max. Div. (2-5 X 10"7 sec"1) 4-5 per cent Active updraught 274 cm sec-1 4-5 per cent Active downdraught — 150 cm sec-1 54 per cent Inactive cloud — 8 cm sec-1 37 per cent Intercloud spaces — 1 cm sec-1 TU = + 0-9 cm sec"1 updraught speed is not quite twice that of the downdraught, which is a typical lifetime average for the upper parts of a cloud (Malleus 1954; 1955). (ii) Equal or nearly equal areas on the average occupied by active updraught and downdraught (not necessarily in the same cloud). (iii) Nearly constant ratio between area occupied by active cloud draughts (up and down) and inactive or decaying cloud matter. Table 2 suggests that a 20 per cent cloud-group cloudiness variation, or an overall 10 per cent variation, can readily result at 3 km from a convergence amplitude as small as 2-5 X 10~7 sec-1. Aircraft observations suggest that the cloudiness variation at 1-2 km would be as large or larger. Active updraughts and downdraughts have very nearly the same r.m.s. amplitude near cloud base, since the updraughts increase upward and the downdraughts downward. Therefore, at lower levels a smaller mean updraught may permit as large a cloudiness increase as that shown by Table 2 for about 3 km. There is also evidence of a 'tidal' variation in the height of the trade-wind inversion and the thickness of the moist layer, which vary as the pressure tendency*. These variations are probably caused by the semi-diurnal variation in the vertical development of trade cumuli and are thus unlikely to be a critical link in the causal chain between S2 tendency, cloud- iness and rainfall. A semi-diurnal variation in the cloud base height, however, could be a critical link in the causal chain, if the cloud base were found to be lower near sunrise and sunset and higher just after noon and after midnight. Some evidence of a systematic semi-diurnal variation of about 100 m in magnitude was found by Holle (1968) analysing photographs from the R. V. Crawford (13-00°N; 5500°W). Cloud base had double minima near dawn and sunset. This variation could be explained in terms of sea-air transfer effects, if substantiated. No night-time cloud base information was available with which to see whether the critical post-midnight rise was present. Holle's sample was only 3 weeks, moreover, and the error in cloud base measurement may have been comparable to its variation. A further study of oceanic cloud base variations is important. The reason is that on most typical tropical soundings a 100 m (10 mb) lowering of cloud * Personal conversation with Professor Herbert Riehl of The Colorado State University. 141 TROPICAL CLOUDINESS AND TIDES base would result in tops that are higher by 0'5-LO km and buoyancies increased by 50-100 per cent, if the in-cloud lapse rates are unchanged. Without the necessary observations, it is only possible to inquire here whether a convergence- divergence of roughly 2-5 X 10~7 sec-1 in the sub-cloud layer could cause a variation of the order of 100 m in the height of cloud base and how it would operate to do so. Convergence of this magnitude in the sub-cloud layer corresponds to a net inflow of about 10 per cent of the air which is ascending through cloud base, if at this level one- tenth of the area is occupied by ascent at 25 cm sec-1 or if one-twentieth of the area is ascending at 50 cm sec-1. In any case it is noteworthy that a fairly conservative estimate of the average tidal convergence represents a significant fraction of the air rising through cloud base. Although this does not explain how cloud base is or could be lowered by tidal effects, it does point to a need for systematic investigation of oceanic cloud bases and the mechanisms controlling their height. At present it appears probable that dynamic factors (horizontal wind convergence) are an important mechanistic link in the relation between S2 tendency and cloudiness and rain. It can be postulated that the convergence acts to produce slightly stronger updraughts, lower cloud bases, greater vertical development and a higher cover of cumuli. Thus our proposal to assess the variation in cloud levels and types with season at Wake is clarified. Stratus-type clouds should be less affected by these mechanisms, as should very tall cumulonimbus in disturbed situations, particularly if the tidal convergence shifts phase above about 3 km. None of these links is as yet firmly established. The next Section attempts to discuss the questions concerning mechanisms relating tropical weather and pressure tendency by a brief look at variations on different time and space scales. 5. Scales of tropical pressure changes and their relations to cloudiness A major result of this study is the confirmation that cloudiness increases with rising 5-6 hour pressure tendency and decreases with falling 5-6 hour pressure tendency. This relation was found statistically at two widely separated tropical stations with different orography and climatology. Although tropical forecasters have long used the relation between rising pressure and increasing clouds, this correlation may surprise some temperate- latitude meteorologists who associate increasing clouds and rainy weather with the approach of travelling low pressure centres. In the Tropics, the hierarchy of pressure change scales, their causes and their relations to weather show increasing dissimilarities to those in higher latitudes as knowledge of them increases. The most obvious scales of pressure change as seen on a tropical barograph (not in order) are: the 12-hour S2 wave, the 24-hour St wave (smaller than S2), large-scale inter-diurnal changes, progressive inter-diurnal changes due to travelling synoptic-scale windfield perturbations and sub-synoptic or meso-scale variations. Preliminary tests indicate that the relation between rising pressure and cloudiness can be expected to be valid statistically on all scales, although many more detailed studies need to be made. The relative contribution of the different scales of pressure variations to tropical weather has not been specifically documented. The advent of satellites will now permit this to be begun in the case of cloudiness. Twenty years ago it was a common belief that most tropical rain occurred in wave-like or vortical perturbations travelling with speeds com- parable to those of the ' basic current ' in which they were embedded or with the equatorial trough and its fluctuations. The well-known ' easterly wave model' of a class of travelling disturbances does indeed predict convergence and maximum cloudiness on the east or rising-pressure side of the easterly wave. The passage of travelling disturbances, however, did not contribute significantly to the results in this paper. The relation between the time of disturbance passage and local time is random. Furthermore, we showed that 24-hour changes were negligible in almost all of our figures. Satellite implementation of tropical weather analysis (e.g. Simpson et a\. 1967, loc. cit.) has suggested that many large rain-producing disturbances in the Tropics are not G. W. BRIER and J. SIMPSON 142 recognizable as travelling perturbations in the low-level windfield. Instead, they grow and die in situ with no major change in the three-dimensional windfield as represented by the synoptic networks, even when those networks with the best coverage, such as in the Caribbean area, are further supplemented by research aircraft and other special obser- vations. This puzzle together with the S2-weather relation established here led to the construction of Figs. 19-21. Fig. 19 shows the surface pressure at the midnight observation during July 1955 for three Pacific islands. Eniwetok is about 900 km from Wake Island and Kwajalein is about 1,100 km from Wake. The general trend in pressure at all three stations is downward to about 14 July, upward to about 24 July, downward to 26 July and upward again to the end of the month. The peaks and tendencies appear to be in phase at all three stations with little evidence of disturbances progressing with the winds. Fig. 20 shows the cloudiness at the same stations for the same period. There is a general downward trend in mean daily cloudiness until around the 13th or 14th. After that the trend is upward, reaching a maximum around 22 July and then decreasing to a minimum around the 25th or 26th. Comparison with Fig. 19 shows clearly that the cloudiness is decreasing in the pressure fall periods and increasing in the pressure rise periods. Nor is there evidence of any substantial or consistent time lag between events at the three stations. Finally Fig. 21 shows simultaneous hourly pressure anomalies at even more widely separated Pacific stations. These anomalies are still largely in phase, despite a longitudinal 1015.0 1014.0 1013.0 1007.0 1006.0 WAKE IS. - ENIWETOK IS. - KWAJALEIN IS. I 10 15 20 25 30 JULY 195 5 Figure 19. The surface pressure at the midnight observation during July 1955 for the three Pacific atolls of Wake (19-29°N; 166-65°E), Eniwetok (11-30°N; 162-15°E) and Kwajalein (9-15°N; 167-30°E). Eniwetok is approximately 900 km from Wake and Kwajalein is about 1,100 km. 143 TROPICAL CLOUDINESS AND TIDES UJ 5 0.0 WAKE 13. ENIWETOK iS. KWAJALEIN IS. 10 15 20 25 30 JULY 1955 Figure 20. The mean daily cloudiness at the three Pacific island stations of Fig. 19 during July 1955. Note the similarity in cloudiness and pressure trends. JUNE 1955 Figure 21. Simultaneous hourly pressure anomalies 1-15 June 1955 for Kwajalein Island, Eniwetok Island and Luzon, Philippines. The diurnal and semi-diurnal variations have been removed by using departures from the monthly means of hourly values. G. W. BRIER and J. SIMPSON 144 separation of 47 degrees and a latitudinal separation of 6 degrees. The latter precludes a northward surge of the equatorial trough, another frequent synoptic-scale cause of change in tropical pressures and weather. Similar in-phase changes over widely separated (by latitude and longitude) Caribbean and Atlantic stations were carefully documented by Frolow a quarter century ago (Frolow 1942). A stationary 6-day period was analysed but not explained by him. Nor do we have any explanation for the changes shown in Figs. 19-21 in terms of either a terrestrial or extra-terrestrial origin. We do postulate, however, their importance to tropical weather and suggest a further study using satellite observations. Nor do we deny the existence or importance of migratory perturbations in the wind- field. These play an important role in the atmosphere's water, momentum and energy budgets, and in their severe form both wreak destruction and bring important rainfall as tropical storms. It is, however, time to reassess quantitatively the controls upon tropical weather and the pressure change-weather relations on a hierarchy of scales. Furthermore, we believe that the tendency-weather relationships that we have documented on one scale and suggested on others may be an important step to a further understanding of tropical disturbances. 6. Concluding remarks A statistical relation between S2 atmospheric tide and a semi-diurnal variation in tropical cloudiness and rain has been established. 'Large' 5-6 hour pressure change days have been shown to have larger semi-diurnal variations than ' small ' 5-6 hour pressure change days at Batavia and Wake Island. Using a previously established correlation between 5-6 hour pressure changes and S2 amplitude (see Brier 1967 and Fig. 12 (a)) we deduced that the S2 effect acts to increase cloudiness and rain near sunrise and sunset and to suppress them near midday and just after midnight. The pressure- weather relation- ship demonstrated here shows that pressure changes of around two or three millibars, associated with the mean S2 oscillation, are quite adequate to account for the observed in- crease of 5-15 per cent in mean cloudiness and rainfall near dawn and sunset. Statistically significant relations were found for per cent cloudiness, rain probability and rain amount for each station for each season, except for cloudiness at Wake in Fall. The mechanism relating S2 and weather is not yet resolved although a strong obser- vationally-based argument exists in favour of its being dynamic, through the effect of the changing tidal convergence-divergence field upon cloud development and possibly upon cloud base height. The direction of the causality is not yet firmly established, since anomalies in the S2 variation (cf. Haurwitz and Sepulveda 1957) imply a feedback to S2 amplitude from atmospheric variables, possibly from the clouds themselves. Cloudiness variations could be at least partially controlled by other factors, such as sea-air interaction. The causal linkages must be left open for further investigation, building upon the firm association established here. We do not know of any physical theory to support the alternative suggestion that the mean S2 pressure wave is primarily a consequence of the semi-diurnal cloudiness cycle. Any such theory must explain how a semi-diurnal cloud- iness cycle with an amplitude of 5-15 per cent can produce a S2 oscillation with an ampli- tude of 1-2 millibars and at the same time show for example, why stations with a pronounced midday cloudiness peak like Batavia fail to show a corresponding pressure maximum a a few hours later. We have also briefly presented data suggesting important linkages between larger-scale pressure rises and increased cloudiness. These pressure changes are found to occur almost simultaneously over wide belts of latitude and longitude and their possible effects would have to be considered in a synoptic or statistical investigation of the world-wide distribution and propagation of the St and S2. These relationships are among a number of factors compelling reassessment of the definition, nature and origin of tropical disturbances and how these might be forecast or controlled. 145 TROPICAL CLOUDINESS AND TIDES A possibly important clue is provided by Brier's (1967) study of the cause of the amplitude variation in the S2 wave. He showed that S2 amplitude variations are correlated with lunar gravitational tides, in a beat fashion, so that large amplitude S2 occurs when the lunar tide acts in phase with the S2 tide and small amplitude S2 occurs when they are out of phase. Although the mechanism of this interaction between the thermal and gravi- tational tides is not understood, the important point is that a small trigger can force a large response in marginally balanced atmospheric systems, as demonstrated in a different context by Brier (1965). Evidence has also begun to come in (Brier and Carpenter 1967) which suggests that the tropical atmosphere may be more prone to the development of synoptic-scale disturbances when the S2 wave has a large amplitude. It is important to explore these tide-weather relations further and also to inquire whether any significant contributions to the large-scale pressure anomalies shown in Fig. 21, or documented much earlier by Frolow (1942), may be associated with lunar or solar tides or their interaction. Increasing evidence favours the association of very large scale as well as large amplitude response to very small forcing functions. For example, the 26-month shift in upper winds around the whole tropical belt may be related to a beat frequency between solar and lunar tides, in which a mechanistic linkage has been suggested via the latent heat release by large tropical clouds (Brier 1966). An important start at pursuing many of the questions raised here has been made using rainfall records and re- sults from a hierarchy of special field programmes on Barbados in the West Indies (Garstang and Visvanathan 1967). Undoubtedly there are inherent and perhaps even unpredictable instabilities in the ocean-atmosphere system itself, which contribute some or possibly even most of the tropical pressure and weather variations. Nevertheless, if any predictable outside forcing functions, such as tides, can be shown to cause even a measurable fraction of the variations, then some aspects of tropical weather become more understandable, predictable and even perhaps controllable than they were previously. Furthermore, if a predictable small-scale, small amplitude trigger can be shown to interact with and set off large-scale instabilities in the atmosphere itself, such as synoptic- scale storms or a 26-month shift on global upper winds, then those globally important phenomena become more tractable to modelling, prediction and conceivably modification through understanding the small triggers and how they operate. Acknowledgments We wish to thank our colleagues Thomas H. Carpenter and William L. Kiser for their assistance with the data analysis and computations. Mr. Robert N. Powell drafted the drawings and Mrs. Peggy M. Lewis prepared the manuscript. We are grateful for their contribution. References Bjerknes, J. 1948 ' Atmospheric tides,' /. of Marine Res., 7 (3), pp. 157-162. Brier, G. W. 1965 ' Diurnal and semi-diurnal atmospheric tides in relation to precipitation variations,' Mon. Weath. Rev., 93, pp. 93-100. 1966 Evidence for a longer period tidal oscillation in the tropical atmosphere,' Quart. J. R. Met. Soc, 92, pp. 284-289. 1967 Reply to J. R. Probert-Jones on ' Evidence for a longer period tidal oscillation in the tropical atmosphere,' Ibid., 93, pp. 127-131. Brier, G. W. and Carpenter, T. 1967 Comment on ' A study of a non-deepening tropical distur- bance,' /. Appl. Met., 6, pp. 425-426. Elford, W. G. 1959 ' A study of winds between 80 and 100 km in medium latitudes,' Planet. Space Sci., 1, pp. 94-101. Frolow, S. 1942 ' On synchronous variations of pressure in the tropics,' Bull. Amer. Met. Soc, 23, pp. 239-254. G. W. BRIER and J. SIMPSON 146 Garstang, M. 1964 Garstang, M. and Visvanathan, T. R. 1967 Gold, E. 1913 Greenhow, J. S. and Neufeld, E. L. 1961 Harris, M. F., Finger, F. G. and 1962 Teweles, S. Haurwitz, B. 1955 1956 Haurwitz, B. and Sepvilveda, G. M. 1957 Holloway, L., Holt, A., Mauchly, J. 1955 and Woodbury, M. Holle, R. L. Kashcheyev, B. L. and Lissenko, I. A. Kiser, W. L., Carpenter, T. H. and Brier, G. W. Kraus, E. B. Kuo, H. L. LaSeur, N. E. and Garstang, M. Lavoie, R. L. 1968 1961 1963 1963 1961 1964 1963 Malkus, J. S. 1954 1955 1958a 1958b 1964 Malkus, J. S., Ronne, C. and 1961 Chaffee, M. Merrit, E. S. and Bowley, C. J. 1966 Palmer, C. E. 1951 Riehl, H. 1947 ' The distribution and mechanism of energy exchange between tropical oceans and atmosphere,' Dept. of Met. Florida State Univ., Tallahassee, Florida, U.S.A. Doctoral Dissertation. ' Solar and lunar influences on rainfall,' Final Rep. Part I to the U.S. Environmental Science Services Admin., Grant No. E-18-67(G). Discussion of S. C. Russell's ' Results of monthly and hourly cloud form frequencies at Epsom 1903-1910,' Quart. J. R. Met. Soc, 39, pp. 271-293. ' Winds in the upper atmosphere,' Ibid., 77, pp. 598-626. ' Diurnal variation of wind, pressure and temperature in the troposphere and stratosphere over Azores,' /. Atmos. Set., 19, pp. 136-149. ' The thermal influence on the daily pressure wave,' Bull. Amer. Met. Soc, 36, pp. 311-317. ' The geographical distribution of the solar semi-diurnal pressure oscillation,' Met. Pap., 2 (5), pp. 1-36. New York Univ. ' Geographical distribution of the semi-diurnal pressure oscillation at different seasons,' /. Met. Soc. of Japan, 75th Anniversary Vol., pp. 149-155. ' Topics in statistical meteorology,' Final Rep. Met. Statistics Project, Inst. Cooperative Res., Univ. Pennsylvania. ' Some aspects of tropical oceanic cloud populations,' /. Appl. Met., 7, pp. 173-183. ' Investigation of atmospheric circulation at the height of 80-120 km,' (In Russian), ' Ionospheric Researches,' No. 9, Acced. Sci., U.S.S.R. ' The atmospheric tides at Wake Island,' Mon. Weath. Rev., 91, pp. 566-572. ' The diurnal precipitation change over the sea,' /. Atmos. Sci., 20, pp. 546-551. ' Convection in conditionally unstable atmosphere,' Tellus, 13, pp. 441-459. ' Tropical convective and synoptic scale weather systems and their statistical contribution to tropical meteorology,' Final Rep. on the Observational Field Programme to U.S. Army Electronics Res. and Devel. Lab. Grant No. DA-SIG-36-039-62-G23 and U.S. Army Res. Office Grant No. DA-ARD-49-092-63-G23. ' Some aspects of the meteorology of the tropical Pacific viewed from an atoll,' Hawaii Inst, of Geophysics, Rep. No. 27. ' Some results of a trade cumulus cloud investigation,' /. Met., 11, pp. 220-237. ' On the formation and structure of downdraughts in cumulus clouds,' Ibid., 12, pp. 350-354. ' On the structure of the trade-wind moist layer,' Pap. Phys. Ocean. Met., Woods Hole Ocean. Inst, and Mass. Inst. of Tech., 13(2), 47 pp. ' On the thermal structure of the hurricane core,' Proc. Tech. Conf. on Hurricanes, Miami Beach D3, 1-2 (1958). ' Convective processes in the tropics,' Proc. Symposium Tropical Met., W.M.O. and Int. Un. of Geodesy and Geophysics. Rotorua, New Zealand, Nov. 1963, pp. 247-277. ' Cloud patterns in hurricane Daisy, 195S,' Tellus, 13, pp. 8-30. ' Analyses of diurnal variations in Tiros VII S-12 n window radiation over Indonesia and Malaysia,' Second Quarterly Rep., Contract No. NAS-10151, N.A.S.A., Goddard Space Flight Centre, Greenbelt, Maryland, U.S.A. ' Tropical meteorology,' Compendium of Meteorology, Amer. Met. Soc, Boston, Mass., U.S.A., pp. 859-880. ' Diurnal variation of cloudiness over the subtropical Atlantic Ocean,' Bull. Amer. Met. Soc, 28, pp. 37-40. 147 TROPICAL CLOUDINESS AND TIDES Riehl, H. Riehl, H., Yeh, T. C, Malkus, J. S. 1951 and LaSeur, N. E. Riehl, H. and Malkus, J. S. Shibata, E. Simpson, G. C. Simpson, J., Garstang, M. Zipser, E. J. and Dean, G. Stoiov, H. L. A. 1954 Tropical meteorology. McGraw-Hill Book Co., New York, Toronto, London, pp. 392. The northeast trade of the Pacific Ocean,' Quart. J. R. Met. Soc, 77, pp. 598-626. 1958 ' On the heat balance in the equatorial trough zone,' Geo- physica, 6, 3-4, pp. 503-538. 1964 ' The atmospheric tide hypothesis on the diurnal variation of cloudiness in the tropics,' M.A. dissertation, Dept. of Met. Univ. of California (Los Angeles), 82 pp. 1918 ' The twelve-hourly barometer oscillation,' Quart. /. R. Met. Soc., 44, pp. 1-19. 1967 ' A study of a non-deepening tropical disturbance,' /. Appl. Met., 6, pp. 237-254. 1955 ' Tidal wind fields in the atmosphere,' /. Met., 12, pp. 117-140. 51 U.S. DEPARTMENT OF COMMERCE Environmental Science Services Administration Research Laboratories ESSA Technical Memorandum ERLTM-AOML 4 THE EFFECT ON RAINFALL OF CLOUD CONDENSATION NUCLEI FROM VEGETATION FIRES OVER SOUTH FLORIDA DURING SPRING DROUGHTS Ronald L. Holle Experimental Meteorology Laboratory Atlantic Oceanographic and Meteorological Laboratories Miami, Florida October 1969 TABLE OF CONTENTS Page ABSTRACT 1 1. INTRODUCTION 1 2. CHARACTERISTICS OF FIRE-PRODUCED CCN IN THE ATMOSPHERE OVER SOUTH FLORIDA 6 2.1 Sources of Smoke During South Florida Droughts ° 2.2 Effectiveness of Common South Florida Vegetation as CCN Sources During Fires '' 2.3 Estimation of Amounts of Fire-Produced Nuclei Over South Florida During Spring, 19&7 5. CONCLUSIONS AND SUGGESTIONS b 7. REFERENCES 3. RAINFALL AND SYNOPTIC SITUATION IN SOUTH FLORIDA DURING SPRING OF 1967 l8 4C POSSIBLE EFFECTS OF FIRE-PRODUCED CCN ON INDIVIDUAL CLOUDS 32 kO ACKNOWLEDGMENTS ^3 kk APPENDIX - MRI FINAL REPORT - CONDENSATION NUCLEI MEASUREMENTS ON FOUR TYPES OF COMBUSTIBLES FROM THE FLORIDA EVERGLADES by William D. Green ^7 1 1 1 THE EFFECT ON RAINFALL OF CLOUD CONDENSATION NUCLEI FROM VEGETATION FIRES OVER SOUTH FLORIDA DURING SPRING DROUGHTS Ronald L. Hoi le ABSTRACT Cloud condensation nuclei (CCN) at cloud base strongly affect the droplet concentration at cloud base, which in turn influences the life history of a cloud. Continental nuclei counts are much higher over large fires, which thereby may keep much of a cloud's water in small droplets that do not grow to raindrop size during a cloud's lifetime. Considera- tion of the vegetation cover in South Florida led to the choice of four sources of most smoke particles produced during droughts: (1) muck (peat), (2) algae, (3) saw grass, and (k) mixed leaves from common trees and bushes These were burned at 0.75 percent supe rsa tura t i on in the laboratory and al were found to produce between 1 0^ and 10 nuclei per g burned. A sample calculation assuming reasonable burn rates for these materials resulted in 4600 CCN cm-^ when mixed uniformly to cloud base. The extreme dryness between 1 April and 15 May of 1 96 7 over Florida was found to be related predominantly to synoptic-scale dryness and northerly winds aloft. There was no significant large-scale lag in rainfall caused by lingering CCN from fires, since dynamic causes easily explain the timing of rainfall. Individual cloud rainfall may have been affected by high CCN counts, as suggested by cumulus height populations and cumulus model calculations. Liquid water fallout from small clouds is affected to a greater degree than from tall clouds. 1. INTRODUCTION Cloud condensation nuclei (CCN) have been considered an impor- tant factor in determining several aspects of cloud growth. It is general Is recognized (Mason, 1962; Braham, 1 968) that the available CCN count at cloud base determines to a significant extent the cloud droplet concentration at cloud base. Twomey and Warner (1967) found a correlation coefficient of over 90 percent between airborne measurements of these two parameters. Cloud droplet concentration subsequently influences cloud growth by changing the diffusive growth rate of cloud-size particles (10 to 20 fl ) and by determining partially their later potential for collision and coalescence growth, and thus their ultimate size. Nuclei concentrations are major vari- ables in matheTnat ical models of droplet growth by Howell (19^9), Mordy (1959), and Twomey (1959) • As the concentration of CCN, and thereby the cloud base droplet con- centration, grows several important changes occur in the cloud. Less water grows to raindrop size (general 1 y >k00fi ), and more remains as cloud droplets that have low terminal velocities and collection efficiencies (Twomey, 1959). In this context, Kessler (19&5) has referred to "cloud conversion", where in a uniform cloud of cloud-sized droplets, such droplets may collide with one another to form raindrops, even when no larger drops are available initially. This is, however, a slow process. If the original nucleus is a large 500^/ salt particle, by contrast, the condensed droplet may have a large terminal velocity - while a small droplet may hardly fall at all. Under these circum- stances the coalescence time for a raindrop to form, when many CCN are present to share the available water, may greatly exceed the lifetime of the cloud. Twomey (1959) showed most clearly that in a simplified model with 1 g m"^ liquid water and starting with a normal d i st r i but ion of droplet radii, less than one-tenth as much water is collected by coalescence for a "drought" CCN count of 1350 cm"-' compared with a "maritime" value of 50 cm"-*. His model also predicted that precipitation only could be initiated heterogeneous ly by salt particles, for example, in a continental cloud with 4-00 droplets cm J and 1 g m~3 liquid water. For clouds of 800 droplets cm--5 or more, inordinately long times and depths are necessary. The highest published count of CCN is 4300 cm"^ near the Marshall Islands (Twomey and Wojc iechowski , 1969). Usually, numbers do not exceed about 2800 cm .. This approximate figure is the highest reported by Squires and Twomey ( 1 966) over the Australian continent, by Meteorology Research , I nc .3 (MRl) over Puerto Rico in July 1967 (unpublished notes from Experimental Meteorology Branch (EMB) project), and by both MRl and Naval Research Labora- tory (NRL) aircraft during May 1 968 over Florida (unpublished notes). -3 Average continental CCN counts are often several hundred cm , but variable. Squires and Twomey ( 1 966) found counts over Colorado in summer to vary from 13 to 1309 cm"-* (at 0.75 percent supersaturat ion) in the first 6,000 feet above surface. Comparable numbers over the Caribbean during August ranged from 60 to 360 cm"-'. These do not include Aitken nuclei, which at times 4 -3 reached over 10 cm . Such particles, however, are too small to become activated and condense water that will later grow to raindrop size under normal ambient supersaturat ions . It is generally agreed that natural mechanisms of CCN formation over land are (as yet) much more important than anthropogenic production around the world (Twomey, I960; Twomey, 1963; and Twomey and Wojc iechowski , 1969). However, on a smaller time and space scale the counts are much more variable. Schaefer (1969) convincingly presents observations of many types of inadvert- ent weather modification that are brought about through changes in CCN, freezing nuclei, and Aitken nuclei. During a flight over Africa, Schaefer (1958) saw clouds reaching 35,000 feet that did not produce any surface rainfall. These clouds were in the vicinity of large bush and forest fires occurring before the rainy season began. Schaefer hypothesized that the clouds did not rain because so many CCN were being entrained into them that coales- cence was ineffective among the numerous small droplets, and thus no raindrop- sized particles developed. No data were presented for this case con- cerning the type and amount of material burned, its effectiveness as CCN, or the observed CCN concentrations in the area. Sugar cane fires are prolific sources of CCN, which Warner and Twomey (1967) found to reach a maximum of 2580 cm near cloud base during a fire in Australia. Their concentrations measured over the sea were lower than over land when fires were occurring, but still higher (average of 280 cm ) than normal maritime counts. Hobbs and Radke (1969) measured airborne CCN caus' e>d by a simulated forest fire in Washington. They found that CCN increased -3 -3 from 100 cm before ignition to well over 1000 cm a few hours later. Feininger ( 1 968) suggests that rainfall over the Amazon has been reduced over the last 15 years because the natural tree cover in the region has been ex- tensively cut. This may have allowed an increase in CCN because of wind trans- port from exposed ground, which thereby affected precipitation. The widespread forest fires over Alaska shown by Parmenter (19&9) also may reduce summer rain- fall to some degree. These studies suggest situations where larger CCN counts may have af- fected rainfall when events on the surface caused large amounts of pollutants to enter the atmosphere. Warner (19b8) found apparent rainfall reductions over several decades that resulted from cane fires increasing the CCN counts downstream over parts of Australia. An interesting comparison to these re- sults can be made during a drought period over the Florida peninsula. In this region prolonged shortages of rain in spring sometimes change the surface k from mostly water-covered swamp to rather continental, as surface water evap- orates and the water table lowers. There also is extensive radar, rain gage, and radiosonde information available. In particular, the period of April and May 1967 was extremely dry over Florida. Since the preceding winter also had been rather dry, surfaces that normally were wet became quite continental with respect to potential for CCN production, and numerous fires occurred until the drought effectively was ended by rainfall in mid-May. The question is asked then whether the fires produced effective CCN that were active at realistic supersaturat ion values, and whether such nuclei can be detected to have had any effect on rainfall. This could be effected by (1) prolonging the drought over a large region through mixing the CCN produced by all fires up to cloud base, for example, or by (2) reducing the amount of rain that might have fallen from individual clouds that formed near CCN-produc i ng fires during the drought. We will examine first the nuclei in terms of their source, effectiveness, and amount. Then we will study the synoptic conditions to delineate time periods when CCN could have had an effect on the physics of clouds, real or hypothetical, during the drought. Although droughts over South Florida initially result from reduced rainfall, the extent of fires in recent drought years apparently has been greater than during previous years. In 1 968 again, numerous fires occurred during several dry weeks in late April and early May. Whited ( 1 968) suggested that "it isn't really the lack of rain that's drying up and burning up the Everglades. It's man." He continues, "We are lowering our level of ground water outside the Everglades National Park. We are drying the muckland... and the stuff is catching fire more often. As the muckland burns, heavy 5 smoke pollutes our air." This is then a rather unique variation on the many types of possible inadvertent weather modifications by man. 2. CHARACTERISTICS OF FIRE-PRODUCED CCN IN THE ATMOSPHERE OVER SOUTH FLORIDA It is not true that during a drought, a steady increase in CCN count occurs over land only, until rainfall clears the air. Concentrations depend on time and location of fires, wind trajectories, and ultimately location of the clouds. During the spring of 19&7, however, there was a much more con- tinental character to the sky than is often the case over Florida. Visibility was sometimes reduced in the horizontal direction by heavy haze in the lower levels, which usually indicates an inversion and trapping of small particles and water droplets. Such haziness was probably greater than normal in Miami between 1 April and 15 May 1967. Smoke particles spread over populated areas on several days during the drought. Such instances were noted by the author in Coral Gables on 19 April and 10, 27, and 28 May. Figure 1 shows the 10 May late afternoon sky over Coral Gables. At this time a layer of dense smoke was sufficiently heavy to obscure the sun in the absence of clouds about 2 hours before sunset. The smoke is not uniform, shown by the lighten- ing in the upper left corner. 2.1 Sources of Smoke During South Florida Droughts What are the available sources of smoke in South Florida during a drought? Figure 2 shows the natural vegetation cover in Florida drawn by Davis (1967). Only five major types that occur within 100 n mi are portrayed here. Table 1 explains the characteristics of the major plants growing in the lettered areas. Saw grass covers a very large area. Based on descriptions XI ro CD O CJ >- i/l >- o E CO en COLLIEtf Figure 2. Location of counties and natural vegetation cover types over South Florida within 100 n mi of Miami (after Davis, 1967). Description of types is given in table 1. 8 in table 1 saw grass of some extent (types A and E) covers about 3,000 5quare nautical miles. Grassland and pasturelands of other grasses (C and E) cover 2 a total of about 750 n mi . Non-hardwood trees, bushes, and palmettoes cover 2 part of the 3000 n mi of types B and D, while pine, cypress, and other tropical hardwoods in hammocks then comprise the rest of the area. This analysis of vegetative areas does not show completely the pro- portional amounts of combustibles in droughts. Conversations with members of fire control agencies in South Florida ht*i/e led to the addition of two impor- tant biological sources of smoke: peat(muck) and algae. The Everglades Fire Control (state agency) specializes only in control of muck fires, mostly in Broward and Palm Beach counties. Mr. Charles Rogers (personal communication) of EFC indicated that when the water table lowers, or the surface of the muck dries out, up to 6 in. may burn off, with an average fire burning about 2 or 3 in. deep. The muck is 10 to 50 percent decomposed organic materials and contains its own oxygen (Howard, 1965), such that muck will burn under, in, and floating on water. Further evidence of its unusual character is that the muck evaporates (oxidizes) at a rate of about 1.5 in. per year (besides fires) in the Lake Okeechobee region. According to Howard (1965), rainfall of less than 0.25 in. has little effect on a muck fire, while over 1 in. may stop a shallow fire. Estimation of the land area with muck is difficult. In figure 2 we see that parts of all vegetative types, except B, have muck at the surface. It is always present to some extent in saw grass, pasture, and other grass lands, since these plants grow from nutrients in the muck. These areas alone 2 comprise about 3,^+50 n mi . There is also muck in cypress and marshes with trees and bushes, but these areas do not burn easily or often. 9 Table 1. Area and Description of the Five Major Vegetation Types within 100 n mi of Miami (After Davis, 1967) Letter Area Vegetation A 2635 n mi2 EVERGLADES MARSHES. Some of these areas consist only of saw grass marshes of varying density, while some other regions have herbs and bushes mixed with saw grass. Some tree islands, sloughs and other marshes also. B 2500 n mi2 PINE FORESTS. Open woodlands of pine, partly on rock. Many herbs, saw palmettoes, shrubs, other hardwoods and tropical hammocks. Also includes some cypress swamps, prairies, and bay tree swamps C 650 n mi2 GRASSLANDS OF PRAIRIE TYPE. Includes wet prairies on seasonally flooded lowlands, and dry prairies, on seldom flooded flatlands. Much has been con- verted to pasture land. D 500 n mi2 REGION OF OPEN SCRUB CYPRESS. Mostly on rock and marl soils that are often flooded. Some palm and hardwood hammocks. E 1105 n mi2 WET TO DRY PRAIRIE-MARSHES ON MARL AND ROCKLAND. Some are mostly thin saw grass; also other bushes and grasses Algae are also significant smoke sources in saw grass areas. When the surface is covered with water, algae can cover up to 50 percent or more of the water to a depth of about 1 in. When drought comes and the water table lowers, the algae dries, clings to, and then burns with the saw grass. Since the area involved is sometimes quite large in grass fires, algae must also be considered significant smoke sources. 10 2.2 Effectiveness of Common South Florida Vegetation As CCN Sources During Fires The effectiveness of smoke particles from vegetation fires as CCN sources will be presented in terms of results of laboratory tests made on samples, wh i ch were supplied to MR I . The only previous comparable data were collected by Warner and Twomey (1967) and Hobbs and Radke (1969), who gave CCN counts which were caused by vegetation burning but did not include any specific data on the combustibles. Four samples of vegetation were collected in the Dade County Everglades on 9 May 1969 to represent the combustibles during droughts in the area. Based on actual fire reports for 1967, it was decided that hardwoods did not comprise a significant proportion of the smoke that was produced. Also, the pasture grass and other non-saw -grass plants in flatlands were considered sufficiently similar to saw grass to warrant testing only that kind of grass. Data concerning the four samples are shown in table 2. The "mixed leaves" category represents several rather different, but common, plants found in ham- mocks among many of the vegetation types listed in table 1. They may not, in fact, be the best three in terms of volume burned. The "peat" entry is repre- sentative of only one of three different common types of muck found in South Florida. The complete test procedure is given in the report by Green (1969), in- cluded as the appendix to this paper. Briefly, the test instrument is similar to the aircraft-borne condensation nuclei (CN) counter developed by MR I and used for the 1967 EMB project, as described by Mee and Takeuchi (1968). The four samples were first dried out completely at MRI. Then two burn modes were 1 1 Table 2. Source and Composition of Four Samples Collected in Everglades to be Tested for Effectiveness as CCN Sample Locat ion Remarks Algae Shark Val ley Rd., Everglades National Park Mixed Near intersection leaves of US 41 and 27 (bushes) Muck Frog City on (peat) US 41 Saw Near canal along grass US 41 Collected from canal surface among saw grass plants. Combination of leaves from 3 common bushes : 1 . About 40 percent of samples from leaves and branches of coastal plain willow tree (Sal ix long! pes) . 2. About 40 percent from saw palmetto fronds (Serenea repens) . 3. About 20 percent of sample from leaves and branches of southern wax myrtle, or bayberry tree (My r ica cer i fera) . Collected from edge of road in swampy saw grass region. Some live and dead blades, some tips and roots mixed. tried, one with abundant oxygen supplied and the other was a partially-covered fire with smoldering combustion. These were designed to simulate open and con- fined burning in the real atmosphere. The samples were burned in a large chamber with a volume of 100 liters, then either 20 or 100 cirr of gas and smoke were taken from this volume and put into a smaller chamber with an 11 -liter volume. Air from this chamber was injected into the MRI CN counter (volume of .024 cm-') , where between 20 and 100 nuclei were found for each sample. Results are remarkably uniform for all materials in both modes of burning. The particles were found to be between 0.4 and 1.2/i in diameter, which is with- in the normal range of CCN. Test results are shown in table 3. 12 Table 3. Average and Standard Deviation of the Number of Condensation Nuclei Active at 0.75 Percent Supersaturat ion for Four Types of Combustibles^ Saw Grass Mixed Leaves Peat Algae (2)T~ (2) " (2) " 72j Rapid 2.9* 1 . IxlO9 CN/g 3.5±0.1xl09 2.9-0.2xlOy 4.8l0.9x109 Burn i ng GO (3) (2) (2) Smolder- _ ing or Slow 5.85- 5. Ixl0y 4.9-1 .6xl0y 4. 7^3 • 7x1 0y 11.5- 0 .7x1 09 Burn i ng Ash 5% 5% 35% 50% *(after Green, 1969). t Number of samples burned shown in parentheses The immediate impression is that all of these materials are significant q ] o producers of activated CCN. The counts range from 2.9 x 10^ to 1.15 x 10 CN per gram of burned material, active at 0.75 percent supersaturat ion . The materials were not particularly good sources of Aitken nuclei. Algae are twice as productive as the other three combustibles, perhaps because they contain some of the limestone that usually underlies the water containing the algae. Rather small numbers of samples were burned for most materials, hence the large standard deviations. These deviations were not mass-weighted, although some samples were smaller than others. More samples should have been tested, but part of the materials was used to bring the CN count to within the range of the instrument. Ash content was estimated visually and applies to both burn modes. 13 Several variables must be considered when applying table 3 to the atmosphere. A choice is available between rapid and slow burning rates in that a hot flame will reignite the smoke and remove it from the CCN count. A lower burn temperature produced larger particles; nevertheless, the tests show more CCN for smoldering fires. From personal conversation with forestry and fire-control personnel, it appears that most fires with these k materials burn rapidly at a high temperature. A greater potential variable is the change of CCN with supersaturat ion Twomey and Wojc iechowski (1969) have shown this variation with several param- eters, but when only one value of supersaturat ion could be used ,0.75 percent was chosen becaust CCN counts are considered most accurate then. Also they indicated that for an updraft of 3 m sec" (reasonable for continental Florida cumuli) the supersaturat ion is about 0.75 percent. Numerous studies have shown that as supersaturat ion increases by a factor of 10 the CCN count increases by 5 to 10. Hobbs and Radke (1969) showed that different super- saturation spectra of CCN existed before and during their simulated forest fire, with kj percent more CCN present during than before, at 0.75 percent supersaturat ion. Data from real clouds are needed to learn the proper value for Florida cumuli in spring droughts, however. 2.3 Estimation of Amounts of Fire-Produced Nuclei Over South Florida During Spring, 1967 The most difficult link in the chain of reasoning, which starts with knowing surface vegetation distributions and ends with how many CCN may have entered a cloud, is how to handle the data on observed fires in a certain period. Information is difficult to obtain, interpret, and summarize. Most 14 of the fire data used here came from the Everglades Fire Control (EFC) . Original ranger reports were scanned for location, duration, area, and type of fire whenever such facts were reported. Their data were searched for fires of 3 acres or more in April and May of 1 967 for the count ies, whi ch cover most of the land area within 100 n mi of Miami. Additional data for Dade County were obtained from the Florida Forest Service (FFS) for all fires larger than 1 acre. Most of these were small fires in wooded land near populated regions. One interesting variable is the diurnal variation of observed fires during these 2 months. The highest fire frequency is at 1600 EST, during highest temperature and lowest relative humidity on a drought day. This coincides with the highest cloud tops in the late after- noon (see fig. 1^) over Florida and suggests that maximum CCN counts can affect cumuli when they are at their most active stage of the day. Some idea of the area involved in fires can be gained from table k, which shows the FFS data for Dade County and EFC reports for all counties within 100 n mi of Miami. Clearly, there is not a monotonic increase of fire activity with time. Although this gives an average of 55 acres per fire, 70 of the 95 fires were 100 acres or less in size, and only 6 were over 1,000 acres. These 6 contributed 80 percent to the total area burned. Figure 3 shows that four of them were in northern Broward County and two in southern Palm Beach County. It should be noted that all six were located in the area of vegetation type A (figure 2),which is the Everglades marsh with saw grass and tree islands. Figure 3 also shows the location of most of the other large fires during April and May 1967 that are listed in table 4. The larger fires in Broward and Palm Beach Counties are again found mostly in saw grass and 15 1 to 1,000 ACRE FIRE OVER 1,000 ACRE FIRE Figure 3. Locations of fires over South Florida during April and May 1967. Dates and acreages of the 6 largest are shown. 16 Table 4. Number of Fires and Acreage Burned in April and May 1967 within 100 n mi of Miami Apri 1-15 16-30 May 15 16-3 Tota Acreage Burned 1,973 30,264 Number of F i res 1 2 33 16,864 2,801 51 ,902 Acres 33 17 95 Fires muck areas. During the spring of 1967 EFC personnel estimate (personal communication) that 5 percent of the private land and 10 percent of the public land with muck bottoms burned in these two counties. One of the six large fires on May 13th (10,000 acres) is identified on the ranger report as "mostly saw grass and some muck," but no others are this specific. The exact composi- tion of the combustibles is not critical, however, since the test data show that a fire in mixed undergrowth alone, for example, produces about the same number of CCN as saw grass or muck; or 80 percent of the area burned produces about 80 percent of the CCN in smoke, regardless of vegetation. It should be noted that the estimated area of a large fire is only the area inside a peri- meter enclosing all smaller fires that are out of control during the lifetime of the large major fire. The following computation, nevertheless, places into perspective how much a large-scale approach can contribute to CCN production, and how easily an order of magnitude may become lost. The factors are chosen to be reasonable values but are far from being well established. Consider a 5,000-acre fire. Assume 0.33 g of muck actually burns for each cm of moist peat, which is only a guess, then table 5 shows a sample calculation based on estimates and the test data of how many CCN are produced. 17 Table 5. Sample Calculation of CCN Produced by a 5,000- Acre Fire Based on Assumed Burn Rates and Test Data for CCN Production Assumed Total CCN Produced Rate of Burn Burn Volume (g) for Rapid Burn ing (CN/g) Total Nuclei (CN ) Muck 1 in. deep* l.^xlO10 2.9xl09 Saw Grass 1 ton/acre 4.54xl09 2.9xl09 Algae 1/10 ton/acre 4.54xl08 4.8xl09 Mixed leaves 1/10 ton/acre 4.54x10 3.5x10^ Total : 5 .63x ;10<9 1 .32* lO19 1 .57* ;1018 2 . I6x 18 .10 7 .33 x 1019 '-''More likely would have 3 in. of muck burning over 1/3 of whole area. Then assume that the 7.33x10 J CN calculated in table 5 to have been produced over the 5,000 acres are spread evenly up to a 700 -m cloud base. 1 A i "K The total volume of air is 1.60 x 10 cm , which results in 4600 CN per cm. It should be very clear that these assumptions are uncertain. Never- theless, even if the concentration is 460 cm , this is probably greater than the average background CCN count over South Florida. At any rate, knowledge of the test figures removes some doubt from one step of the calculation. There is obviously no substitute for measurement of CCN in the real atmosphere during a drought. Actually, high concentrations may well be limited to small regions near the active fires, as will be discussed in section 4. 3. RAINFALL AND SYNOPTIC SITUATION IN SOUTH FLORIDA DURING SPRING OF 1967 In terms of rainfall the months of April and May are quite variable from year to year over South Florida. Normals over the south half of Florida during April range from 2.5 to 4.4 in. and during May from 4.0 to 6.5 in. 18 Some idea of the cloud populations and their variability can be gained from radar data summarized in figures 4 and 5. The curves show the cumulative daytime maximum tops within 100 n mi of Miami in daytime (07-18 EST) and are a fairly good measure of the rainfall. For April (fig. k) there have been 2 years markedly wetter than the average, two years drier, and three years near the average; 1967 was the driest April since at least 1963. In general, the same is true for figure 5 and the month of May, although May was drier in 1965 than in 1 967. Spring of 1967 will now be examined in detail. Figure 6 shows the cumu lative normal and observed rainfalls from 22 March to 31 May 1967 f°r two portions of Florida within 100 n mi of Miami. An average of six stations with 30-year means was used for the "Lower East Coast" and five such stations for the "Everglades and Southwest Coast" as found in the Monthly Climatologi- cal Data of the U. S. Weather Bureau. The normal mean rainfall from 22 March to 31 May is 10.15 in. for the Lower East Coast and 7.75 in. for the other area. (Monthly means were linearly distributed from the start to the end of each month.) Observed rainfall in 1967 fell at only two times of conse- quence: once in late March and again during the last half of May. Average observed precipitation from 1 April to 16 May was between 0.15 and 0.30 in., which is extremely low. Starting on 16 May, a line drawn to the end of the month is little different from the slope of the normal, thus the drought can be considered to be confined to 45 days from 1 April to 15 May. This drought in Florida was probably greater in extent during 1967 than the previous severe one in 19^+5. 19 o o O I- UJ < X < 60 55 50 45 40 I- 35 30 25 20 15 10 APRIL 100 90 80 70 60 50 40 30 20 10 0 Figure k. Cumulative daytime (07 to 18 EST) maximum tops in thousands of feet within 100 n mi of Miami during each April from 1963 to 1969, and the average of these years- 20 100 90 80 70 60 50 40 30 20 10 Figure 5. Cumulative daytime (07 to 18 EST) maximum tops in thousands of feet within 100 n mi of Miami during each May from 1963 to 1969, and the average of these years. 0 21 11 10 CO LU X < or LU > < 3 O Lower East Coast ( 6 Stations ) Everglades and Southwest Coast (5 Stations ) CUMULATIVE NORMALS CUMULATIVE OBSERVED, 1967 22 27 MARCH 01 05 10 15 20 25 30 05 10 15 20 25 31 APRIL- MAY- I igure 6. Cumulative normal and observed (1967) rainfall over South Florida during late March, April, and May. 22 Observed precipitation over the entire state is shown for April (fig. 7), 1 to 15 May (fig. 8),and 16 to 31 May (fig. 9). Areas with less than 0.05 in. are lightly shaded, while those with more than 2 in. are heavily shaded. In April, many stations reported no rain or a trace, and few exceeded 0.50 in. except to the north. Some of the rain along the east coast probably fell from shallow cumuli during easterly flow. But the absence of significant rainfall in the western two-thirds of the peninsula, except at one station, indicates that almost no large afternoon cumuli developed all month from land heating. Rainfall north of 29 was caused by a frontal system. Virtually no rain fell from 1 to 15 May south of 28° (fig. 8). North of 28° there were spotty heavier rains, but no organized systems prevailed. Figure 9 shows that the areas with less than 0.05 in. during 16 to 31 May were small, while some locations exceed- ed 2 in. This pattern is more typical of a summertime map for half of one summer month in Florida, except that amounts are still somewhat low. How much of this great reduction in rainfall could have been effected by increased CCN counts caused by the fires discussed in the previous section? Is the relation direct, indirect, or obscure? Much insight can be gained by considering the large-scale circulations and then the vertical time-sections for Miami. A strong ridge at 700 mb was centered in the eastern. Gulf of Mexico during April, and extended eastward across the peninsula in May to form a long ridge centered at 25°N from the Gulf to the Central Atlantic. Heights at 700 mb over South Florida were 50 to 100 ft above normal in April and 30 ft above in May (Stark, 1967; and Green, 1967). Northwest or west-northwesterly flow is indicated on mean charts for both months. It is interesting to note that 23 80* 30e APRIL 1967 OBSERVED PRECIPITATION %^ 25° i 80° Figure f . Observed precipitation during April 1967 over peninsular Florida . 2k F i gure 8 Observed precipitation for the period over peninsular Florida, to 15 May 1967 25 80° 30° MAY 16-31,1967 OBSERVED PRECIPITATION <^S 25* <: 80° Figure 9. Observed precipitation for the period 16 to 31 May 1967 over peninsular Florida. 26 coincident with the end of the Florida drought on 16 May, "Great circulation changes occurred from the first half of May to the last half..." over much of North America (Stark, 1967; p. 591). Time-height cross sections at Miami were constructed for wind direction and dew-point depression from the surface to 40,000 ft between 27 March and 31 May 1967 with data at 10 wind levels and 3 moisture levels. Besides giving some idea of the nature of the wind and moisture structure during the drought, the charts were prepared to show whether there were any effects of the smoke- produced CCN on rainfall. It may be hypothesized that if CCN were effective in inhibiting rainfall, the beginning of more normal rains in Florida would come later than the dynamic changes of wind and temperature. By this hypothesis, then, a wetter and less subsident regime would move in, but little or no rain would fall, possibly for a day or two because of large CCN counts preventing precipitation-sized droplets from growing in large numbers. Two key representative factors were found to be reasonably well related to rainfall during the period. These two are (1) presence of winds with a northerly component above about 15,000 ft, which probably were subsiding and (2) a dew-point depression of 20°C or greater at 700 mb . Frank and Smith ( 1 968) also found that the humidity at 650 mb is related to Florida radar echoes better than at any other level. These factors are often closely related. From 27 to 31 March the 700-mb dew-point depression was 10 to 20 C, except that it de- creased from 15°C on the 28th and 30th to 1°C on the 29th. At the same time as the moisture intrusion, west-southwest winds occurred from 10,000 to 18,000 ft, and rainfall was observed. It is important to note, however, that two days earlier, no moisture accompanied extensive southwest winds and no rain fell (see fig. 6). Northwesterly winds were increasingly 27 common in April and early May; so much so that from 21 April to 10 May, winds were from the northwest during 95 percent of the time above 15,000 ft and often reached near the surface. Strongest winds were at 200 mb and sometimes reached 75 k or more from the west-northwest. The dew-point depression at 700 mb between 21 April and 5 May was seldom less than 18 C. In general, then, rainfall was well related to moisture and accompanied winds with a southerly component fairly closely. With these general comments of the time cross sections in mind, we examine the section at Miami from 11 to 20 May. Figure 10 shows wind direc- tion and 700-mb dew-point depression during this period of onset of rainfall (see fig. 6). Isogons in upper figure 10 show a basic northwesterly current aloft, with northeast and southeast winds between it and the surface easterlies. The satellite photographs during the dry period for several days up to 15 May are quite similar; for example, figure 11 shows that there was no significant cloudiness near South Florida on 15 May. On this date no radar echoes were reported over peninsular Florida, but southwesterly flow ahead of a trough was moving into northern Florida (Halter, 1967). By comparison, note that south- west winds (with speeds under 20 k) are found through a 15,000 ft depth on 16 May. Lower figure 10 usually shows a dry layer above 700 mb , except that dew-point depressions down to 6°C at 700 mb are found on the 1 6th and 17th. The time sections show that winds with a southerly component advected a deeper moist layer over Miami on 16 May. The ESSA 3 picture on 16 May, figure 12, shows a large band of cloudiness over South Florida, which was associated with a frontal trough. Numerous we 1 1 -developed cumuli and some cumu Ion imbi were observed (Halter, 1967). Since this band of cloudiness and the onset of 28 45 1 1 1 1 P NW i I r n 1 p i 1 p 11 MAY 12 MAY 13 MAY 14 MAY 15 MAY 16 MAY 17 MAY 16 MAY 19 MAY 20 MAY 1967 45 40 35 -30 T i — r T T T -i — r T i — i — r T 15 20 20 10 15 20 t ! j I i i_r i I l i ,5 i .10 i*0?^ 11 MAY i gure 10 . 12 MAY 13 MAY 14 MAY 15 MAY 16 MAY 17 MAY 18 MAY 19 MAY 20 MAY Time cross section at Miami of dew-point depression in degrees C (lower panel) and wind d i rect ion (upper panel)from 11 to 20 May 1967. 29 Figure 11. ESSA 3 photograph at 17^2 GMT on 15 May 1967 Florida is in upper left portion of picture. 30 Figure 12. ESSA 3 photograph at 1833 GMT on 16 May 1 967 Florida is in center of picture. 31 moisture and southwest wind coincides with the onset of rain, it is clear that no lag whatsoever existed that may be caused by the hypothesized CCN effect, at least on a large scale approach. The rapid return to dryness at 700 mb on the 1 8 t h is accompanied by more northwest winds (fig. 10) as the trough moved offshore, and no rain of consequence fell from 19 to 23 May (fig. 6). (Most of the rain on 18 May came early in the morning.) No "lag effect" of CCN in large scale terms apparently occurred in mid-May 1967. since the dynamic changes were quite strong. Large CCN counts did not have much opportunity to act on clouds nevertheless, because winds over southeastern Florida up to 5,000 ft were from the open ocean for many days before May 16. Fire records show that from ]k to 15 May a total of only 30 acres burned. The larger fires of 10,000 acres on 13 May in Palm Beach County and 5,000 acres on 12 May in Broward County came several days before changes in dynamics took place, such that the smoke had probably settled and been diffused by the wind, mostly to the northwest. It is interesting to speculate that a CCN effect could only have been important on a large scale if (1) large fires were burning on the day when meteorological conditions changed?and (2) these conditions kept the smoke over land and carried the CCN into the clouds which began to grow. Such a combination on a large scale is rather unlikely to occur on the particular day when a drought is ending, as on 16 May 1967. k. POSSIBLE EFFECTS OF FIRE-PRODUCED CCN ON INDIVIDUAL CLOUDS The result of the previous section does not negate the possibility that fire-produced CCN reduced rainfall from individual clouds during spring of 1967. How much rain a cloud produced during a drought versus what it may have 32 made with no smoke in the vicinity only can be determined by theoretical models, direct aircraft measurements, or calibrated radar studies. In fact the very premise that the cloud forms first and then is modified by the greater CCN count is uncertain. Some photos have shown large cumuli that formed over forest fires because of the fire location (see cover pictures of Weatherw i se , August 1962; and Sc ience , 17 January 1969). The concept of influencing an individual cloud over a fire may be understood better by considering the Gaussian plume numerical diffusion model of Milly et al. (1969). This model was developed originally to predict the diffusion of cloud seeding nuclei produced by ground generators. Since we are interested in CCN counts at a cloud base of 700 m, while their results showed distributions at 1500 m, only qualitative comparisons may be drawn. Nevertheless, a fire over South Florida would be a sort of seeding in reverse, and distributions would be quite analogous to their low-stability, high output rate case. For the 10-mph wind used in this diffusion model, considerable variation was found which depended primarily on rate of output from the gener- ators, number of generators and stability in the lowest k m. Applied to a single forest fire under Florida meteorological conditions, this model would imply that a strong CCN concentration would be produced at 700 m fairly near to the fire, downstream, and in only one area. The distribution of concentra- tions cannot be estimated but maximum values over a small area certainly would exceed the subcloud layer figure of 4600 CN cm" , which resulted from the large scale approach given in section 2.3. It is quite possible that a CCN count much smaller than the maximum would effectively reduce precipitation fallout. Much could be learned by running such a model as that of Milly et al. (1969) 33 for one generator, a comparable output rate, and stability as is found in Florida, and for a 700-m height, although some consideration must be made of the different fall velocities of CCN compared to Ag I particles. Some idea of the effect that larger CCN counts have on individual cumuli, regardless of whether they form over a fire or simply entrain some of the ambient CCN in the general vicinity of the fire, may be gained by varying the nuclei count in a cumulus model that includes both dynamics and cloud physics. The model described by Simpson and Wiggert (1969) was run for Miami soundings on 15 and 17 May 1967. Variations were made in N, , the con- centration of drops at cloud base, from 50 to 5000 cm . This concentration is closely related to CCN concentrations, as mentioned earlier. The relative dispersion D^ was taken to be 0.1083, a smaller value than that used in the "Berry Florida" version of the model, since for large Nl most nuclei would be from one source and of one size over a fire. For the dry day of 15 May at -3 1200 GMT only calculations for N, = 50 cm were made. Even for this marine- type cloud there was no fallout of liquid water (summed over all height steps of the buoyant element) because of the very dry sounding (fig. 10). For a 700-m cloud base, the cloud top for a radius of 500 m was only 1 450 m, while for a 1500-m radius, the top was 2500 m. Nothing short of a huge radius apparently would have made a significant cumulus on this day, and no rain was observed to fall over the southern two-thirds of Florida. It is interesting to note, however, that at 1 600 EST on 15 May a cloud reached 12,000 ft over water within 100 n mi of the Miami WSR-57 radar. Either the dry layer aloft was missing near this cloud, or a meso-scale convergence had produced a very large radius. 34 The calculations for Miami on 17 May at 1200 GMT were made for a cloud base of 600 m and Db = 0.1083. The Berry Florida version always had Db =0.1460 and N^ = 500 cm"3. Table 6 shows the results for liquid water and table 7 shows top heights. Calculations for a cloud base of 700 m gave somewhat Table 6. Fallout of Liquid Water for Varying Tower Radii R and Cloud Base Drop Concentrations N5 for Miami on 17 May 1 967 at 1200 GMT R 500 m 000 m 1500 m 50 cm" Nb 500 cm' 5000 cm -3 2.13 g m 1.21 0.44 -3 4.17 3.87 3.37 4.26 3.88 3.27 Berry Florida 1 .28 3.83 3.86 Table 7. Same as Table 6, Except for Cloud Heights 500 m 000 m 500 m 50 cm N, 500 cm"3 5000 cm -3 4400 m 4250 m 4200 m 7150 m 7000 m 6800 m 8850 m 8700 m 8500 m Berry Florida 4250 m 7000 m 8700 m 35 smaller values than in tables 6 and 7, but did not change the relationships in any case. On 17 May rainfall was reported to exceed 0.50 in. almost everywhere in Florida. Tops reached 40,000 ft over land within 100 n mi of Miami at 1^00 EST, and tops over water exceeded 20,000 ft every hour of the day. Even with this moist sound i ng, however , some reduction in top heights is seen when CCN are numerous. Particularly interesting is the liquid water fallout being greatly affected for small radii. In this situation a 10 increase in N, reduced the fallout to 20 percent of the fallout for a maritime CCN count. Perhaps this is why clouds of 10,000 to 15,000 ft over land seem to rain less sometimes than clouds of a similar size over water. Because of their smaller volume small clouds may entrain proportionally more CCN into their core region of ascent. Radke and Hobbs (1969) indicated that growing clouds also may absorb CCN from the surrounding area. Then a larger proportion of the liquid water in a 500-m radius cumulus may be condensed onto the numerous CCN and little water can grow to raindrop size. Note also that fallout from the larger 1500-m cloud is reduced by 23 percent. It may be possible to see some effects of occasionally larger CCN counts during fires over land by comparing 1967 populations to those during a wet year. A quick review of population statistics shown in Holle ( 1 968) can be gained by examining figures 13 and ]k. The distributions of daytime maximum tops within 100 n mi of Miami in May of 1 966 and 1 967 Bfe divided into those tops occurring over land and over water in figure 13. May 1 966 was a wet month (see fig. 5) and the land curve shows, for example, that heights exceeded 20,000 ft in daytime on 80 percent of those May days. 36 LU UJ 60 55 C/) CO 50 X I- 1 100 90 Figure 13. Cumulative percentages of maximum cumulus heights during daytime (07 to 18 EST) over land and water during May 1966 within 100 n mi of Miami (after Holle, 1968). 37 Clouds over water also were fairly large, but had fewer tops over 20,000 ft than clouds over land areas. In 1967 clouds over water were definitely smaller, but the curve does not differ from 1 966 by more than 15 percent above 20,000 ft and 25 percent down to 10,000 ft. Clouds over land in I967 show a large reduction in frequency for tops below 30,000 ft. In May 1 966 a cloud over land reached 15,000 ft on every day, whereas the clouds were this high on only kO percent of the days in 1967. Figure ]k shows the diurnal frequency of land and water clouds in 1 966 and 1967 in terms of echo presence. Some echoes were seen over water during about 85 percent of all hours in May 1 966 and about 50 percent of May 1967 hours, a reduction to 60 percent of 1 966 values. Land clouds in 1967, how- ever, reduced to between 30 and 50 percent of 1 966 frequencies. From 1200 to 1800 EST, when fires were most frequent , echoes were seen on kO percent of the days in 1967 over land compared to 90 percent in I966. In other words, the "drought" was more pronounced over land in 1967 than over water. Similar conclusions were found in Holle (I968) comparing another dry year (1965) to 1966. Since figure 13 shows that smaller clouds formed proportionally less often over land in 1967 (compared to large clouds) than in 1966, it should be recalled that large CCN counts affect smaller clouds more than large clouds (see tables 6 and 7). It does not appear possible, nevertheless, to expect that a large CCN count could stop some clouds completely from growing to precipitation stage, which might have grown otherwise. The 15 May calcula- _3 tion showed no fallout even for an oceanic N, of 50 cm , since the environ- ment was unfavorable for any cloud growth on that day. The 17 May calculation showed that on a moist day more CCN only reduced the liquid water fallout 38 -a c 03 vO v£3 CTi 03 en c 03 -o • c --^ 03 00 \£> "O c — 03 OJ L_ . — o O IE ^ 1- o a» C 4-> 4- U 03 cr^—- 1_ — 4- E 0) o — o 03 -C 03 2 c 1- 1^ — CTi Q — o o o o o o o o o o 0) 00 r^ Computations of the growth by condensation of a population of cloud droplets, Tellus _M_, 16-44. Parmenter, F. C. (1969), Picture of the month - Alaskan forest fires, Monthly Weather Rev. 97, 683. Radke, L. and P. Hobbs (1 969) , Measurement of cloud condensation nuclei, light scattering coefficient, sodium-containing particles, and Aitken nuclei in the Olympic Mountains of Washington, J. Atmospheric Sci. 26, 281-288. Schaefer, V. (1958), Cloud explorations over Africa, Trans. N.Y. Acad. Sciences JO, 535 . Schaefer, V. (1969), The inadvertent modification of the atmosphere by air pollution, Bull. Amer. Met. Soc. 5_0, 199-206. Simpson, J. and V. Wiggert (1969), Models of precipitating cumulus towers, Monthly Weather Rev. 97, 471-489. Squires, P. and S. Twomey (I966), A comparison of cloud nucleus measurements over Central North America and the Caribbean Sea, J. Atmospheric Sci . 23j_ 401-404. Stark, L. P. (1967), The weather and circulation of May 1967 - strong blocking and record cold in the East, Monthly Weather Rev. 95, 587-592. Twomey, S. (1959), The influence of droplet concentration on rain formation and stability in clouds, Bull, de L'Obs. du Puy de Dome, 33-41. 45 Twomey, S. (I960), On the nature and origin of natural cloud nuclei, Bull, de L'Obs. du Puy de Dome, 1-19. Twomey, S. (1963), Measurements of natural cloud nuclei, J. Rech. Atmospher iques 1, 101-105. Twomey, S. and J. Warner (1967), Comparison of measurements of cloud droplets and cloud nuclei, J. Atmospheric Sci. 24, 702-703. Twomey, S. and T. A. Wojciechowski (1969), Observations of the geographical variation of cloud nuclei, J. Atmospheric Sci. 26, 684-688. Warner, J. (1968), A reduction in rainfall associated with smoke from sugar- cane fires - an inadvertent weather modification? J. Appl . Meteorol. 7, 247-251. Warner, J. and S. Twomey (1967), The production of cloud nuclei by cane fires and the effect on cloud droplet concentration, J. Atmospheric Sci. 24, 704-706. Whited, C. (1968), What's really drying Glades, Miami Herald, 1 May 1 968 . 46 APPENDIX CONDENSATION NUCLEI MEASUREMENTS ON FOUR TYPES OF COMBUSTIBLES FROM THE FLORIDA EVERGLADES by W i 1 1 iam D . Green INTRODUCTION The objective of the tests described in this report was to determine the number of cloud or meteorological condensation nuclei produced by the burning of four types of combustibles from the Florida Everglades. PROCEDURES The four types of mater i al s , 1 i sted below, were burned in a closed chamber under conditions simulating open burning with abundant oxygen or confined burning resulting in slow combustion or smoldering. Following the burning, a measured sample of the smoke and gases was withdrawn from the chamber and injected into a second dilution volume containing filtered air. The sample to be counted in the MRI Cloud Condensation Nuclei Counter was drawn from this chamber. The four types of materials submitted were Sawgrass Mixed Leaves Mud-Peat Algae The materials, as received, were dried in an oven at 120°C for 2k hours before processing. One-half to two grams of the material was weighed out in a glass dish and the dish was then placed in the combustion chamber. A fragment of the hi sample was ignited outside the chamber to avoid a contribution of nuclei from the match or torch. The fragment was then blown out and the glowing coal was placed on the sample in the dish. The chamber was closed and an oxygen line in the chamber was used to ignite the sample. In the slow burning or smoldering mode, the resulting fire was rapidly extinguished and the oxygen was used only to maintain the smoldering of the resulting brands. In the open or rapid burning mode, the oxygen was used to maintain open flames and combustion. After 50 to 75% of the sample had burned, the combustion was smothered by covering the dish. The combustion chamber had a volume of 105,000 cubic centimeters. From this volume, either 20 or 100 cc of gas and smoke were withdrawn with a syringe and injected into a volume containing 11,200 cc of filtered air. After corrections for the small background in both chambers, the resulting concentration of condensation nuclei in the last chamber was about equal to 3 the natural background of 10 nuclei per cc. Within the counting volume of the condensation nuclei counter (0.024 cc) , the count was in the range of 20 to 100 for each of the samples. The above dilution procedure was calibrated several times with both the CN counter and an Aitken Nuclei counter and the contributions from residual nuclei in the chambers were always less than 10 percent. The final results were corrected for this small background. k8 RESULTS CN Measurements The number of condensation nuclei per gram of material burned (loss of weight) is reported in the following table. In all cases, the number was 9 1 0 between 10 and 10IU CN per gram. The number in parentheses is the number of individual samples burned in the particular mode. An estimate of the ash or unburnable fraction is given at the bottom of the table. With the exception of the algae, which produced about twice as many nuclei per gram burned, all the materials were comparable. The higher count for the algae may be due to a close association with limestone or calcium carbonate which might be activated by the burning process. Table I CONDENSATION NUCLEI ACTIVE AT 0.75 PERCENT SUPERSATURAT I ON FROM FOUR TYPES OF COMBUSTIBLES CN/Gram (Burned) x 1 0 9 Sawgrass Mixed Leaves Peat Algae Rapid Burning (2) (2) (2) (2) 2.9 t 1.1 3-5 ± 0.1 2.9 - 0.2 4.8 - 0.9 Smoldering or (4) (3) (2) (2) Slow Burning 5-8 ± 5.1 4.9 ± 1.6 4.7 ± 3-7 11.5 - 0.7 Ash 5% 5% 35% 50% NOTE: The large deviations noted on smoldering of sawgrass and peat are due to errors introduced by the burning of one small sample (0.2 - 0.3 grams) in each case. 49 Slow burning, as suspected, produced more smoke and nuclei. S ize D i st r i but ion The maximum size of the particles produced can be calculated from the relationship N _7rv^p = 1 assuming all the sample burned is converted g to nuclei active at 0.75 percent. Assuming p = 1.5, 5 x 10 particles per gram would have an average diameter of 6 microns; 11 x 1 o" particles per grar would average 2 microns. Since it is unlikely that more than 20 percent of the samples were converted into nuclei active at 0.75 percent, the particles would average between 0.4 and 1.2 microns in diameter, or within the range for cloud or meteorological condensation nuclei, 0.4 were falling down- 159 Vol. 50, No. 3, March 1969 Fie. 6. Cloud hole A at about 0925 EST; picture taken from down town Miami. ward fiom the central cirrus formation, thus removing water from this zone. These falling crystals soon evaporated below, the innermost falling farther before evaporation, thus pro- ducing the characteristic tapering cirrus tail illustrated in Fig. 1. The observations suggest that the central tuft may not have completed conversion to ice, so that the central (.loud may have, in fact, remained partly a water droplet cloud. Figs. 2 and 4 of hole A show fairly well the approxi- mately radial appearance of the lateral cirrus at two stages of this hole, ft is noteworthy that most of the photographs illus- trating the holes reported in W'eatherwise and the Bulletin also show this radial cirrus structure, and show as well that cirrus extends below the altocumulus. At least three processes appear to be of major importance in detei mining the lateral growth of the holes and their ultimate size. The first, already mentioned and most easily observed, is the radial propagation of cirrus filaments as water droplet altocumulus is converted into ice crystal cirrus. This process appears to go rapidly at first, then more slowly, finally becoming generally ineffective so that it pro- duces little or no additional cirrus. During this last stage the cirrus already formed decreases or disappears, presumably by descent and evaporation of the ice crystals. Thus the visible cirrus filaments may be considered to be the net result of two opposing processes, one generating and the other decreasing the cirrus. The second, or cirrus reducing, process would appear to be dominant during the last stage (of ineffective net production). The third process became clearly evident during this 1 December case when the circular boundaries of the two holes met and then overlapped. At this time the fact that the hole diameteis were increasing was made evident not by the advancing outward limit of the lateral cirrus filaments and the associated altocumulus edge, as previously, but instead by the process of overlapping, and the advance of an apparent "edge," a quasi-discontinuity or marked change in cellular pattern of the altocumulus. Within the zone of overlap no cirrus was observed, and for the most part the altocumulus did not dissipate but persisted and remained little changed. Thus the outer limits or "edges" of the circles, only partly "holes" at this time, were revealed at the overlap zone not by the presence and absence of altocumulus, as formerly, but by distinct structural differences within the altocumulus. I hese well-marked limits were clearly still increasing during the observation period. They were moving outward slowly as a wave-like progression of a minor dis- continuity or anomaly in the otherwise remarkably homo- geneous cellular altocumulus pattern. Possibly what was moving outward was merely a progressive extension of the zone of weak downwaid motion that surrounded, and partly compensated for, the central zone of weak ascent. However, near the perimeters of the circles these downward motions should be extremely weak. Thus it is notable that the moving "edge" appeared to be a small but real wave perturbation propagating outward from a central initiation area, as along an interface, and may well have been such a wave. It would appear that holes of this type represent a rather complex combination of thermodynamic and dynamic conditions, which remain, as yet, not properly measured and inadequately understood. The sequence of events described above could conceivably be initiated by entirely natural "seeding" processes, or could be a result of the activities of man. Ice crystals falling from overlying cirrus formations with well-developed tails have been observed by one of us from aircraft on several different occasions to produce similar but smaller near-circular open- ings in the cellular altocumulus below. Thus seeding from cirrus can initiate such holes. Cirrus tails have also been observed to initiate development of a substantial convective system, producing precipitation, by seeding supercooled altocumulus (Braham, 1967). However, during the period of observation on 1 December no cirrus of any kind was visible above the altocumulus. Ice crystals falling from almost in- visible thin cirrus, or persisting from dissipated cirrus rem- nants, might possibly have provided the necessary nuclei. Such initiation would appear to be unlikely, though the Miami sounding does show a fairly pronounced moisture maximum and a significant temperature inversion at about 28,000 ft, and a lesser moisture maximum at 33,000 ft (so that a thin cirrus layer could have been present), and though cirrus crystals have been observed to fall considerable dis- tances through quite dry air and still effect nucleation of middle clouds (Braham and Spyers-Duran, 1967). Initiation by other natural falling particles also remains a possibility, as does initiation by particles due to activities of man. Since the holes began to form just west of Coral Gables, neither rockets nor vertically-moving aircraft appear to have been involved. Approximately horizontally-moving aircraft might have produced suitable freezing nuclei either while in flight above or while passing through the cloud layer. Such aircraft were not observed near the area of interest during the 90-min observation period, nor were any holes observed to the north where air traffic was fairly heavy. No aircraft were observed for over an hour above or near the initiation point of the third hole. Natural nucleation, perhaps by a chance concentration of sufficient appropriate nuclei, would appear to be the most likely alternative. 160 Bulletin American Meteorological Society Fie. 7. A view of both cloud holes A (left) and B (right) as they appeared southeast of Coral Gables at about 0930 EST. In summary, it may be noted that a basic requirement for circular hole development appears to be a very particu- lar type of cloud — a high, thin, cellular, rather homogeneous, relatively strongly supercooled, water droplet cloud. A second basic requirement is successful initiation by appropriate nuclei. Although the details of initiation remain undeter- mined, initiation is clearly a rare event, quite possibly a rare natural event. Once initiation occurs a central cirrus head develops quite rapidly, giving rise to a central zone of weak upward motion, a gradually widening surrounding zone of weak descending motion, a lateral propagation of cirrus filaments, and a central tail of falling ice crystals. A slowly outward-moving wave-like perturbation is also present. The holes, and these associated conditions, would appear to be observed rarely because the required altocumulus conditions occur infrequently, at least where most observation takes place, and because even when these conditions are present the required initiation events occur rarely. Acknowledgments. The authors are grateful to the follow- ing individuals whose photographs add much to this note and led to its preparation: Thomas E. McCaughan of the National Hurricane Center, ESSA, Coral Gables, Fla., for Figs. 2, 3, 4 and 7; Charles True of the National Hurricane Research Laboratory, ESSA, Coral Gables, Fla., for Fig. 5; and Bill Kuenzel of the Miami Herald for Fig. 6. References Braham, R. R., Jr., 1967: Cirrus cloud seeding as a trigger for storm development. /. Almos. Sci., 24, 311-312. , and P. Spyers-Duran, 1967: Survival of cirrus crystals in clear air. /. Appl. Meteor., 6, 1053-1061. 161 53 Reprinted from Tellus Vol . XXI, No. 3, 331-340. The transport of moisture into the antarctic interior By B. LETTAU, ESS A, Silver Spring, Maryland (Manuscript received June 25, \l ABSTRACT The magnitude of the moisture transport by the atmosphere into the Antarctic interior is determined from a mass transport model which allows a longitudinal variation in the annual flux values. It is indicated that the use of monthly mean transport and tem- perature values underestimates the annual moisture transport required by observed accumulation values in the interior, consequently a relatively much larger fraction of the annual moisture transport must occur in conjunction with positive temperature deviations from mean monthly values. This relation is examined at Byrd station where it was found that during the austral summer 1957-8 the threeday period with the highest 700 mb temperature accounted for nearly 20 % of the annual moisture transport. The variation of the moisture transport with altitude is examined and its effect as a constraint upon the maximum central height that the ice sheet may attain is brieflv discussed. Introduction One of the more important, but heretofore generally neglected aspects of Antarctic mete- orology is the mechanism by which the large amounts of precipitable water required to nour- ish the inland ice sheet are transported into the continent. Since the annual increments of the net snow accumulation are fairly easily identified by stratigraphic methods (e.g. Gow, 1965), estimates of the annual ice mass budget are generally made without reference to mete- orological or climatological conditions, although their inclusion would very likely give a better definition of the dynamic situation which is interacting with the underlying surface. The problem that will be considered here is simply to determine how and where the mass of water enters the Antarctic continent and is car- ried into the interior. This will involve analysis of the mass flow over the continent and con- sideration of the probable moisture content of the air. Some implications of the results will also be discussed, particularly with reference to the problem of whether the total ice mass is presently increasing or decreasing. The flow of air over the Antarctic continent also is an important parameter in the study of a number of related questions concerning the heat balance of the continent and the role that the continent plays in affecting the climate at lower latitudes. Since the routine measurement of atmospheric moisture content at very low temperature is both difficult and imprecise, the direct evalua- tion of the total moisture transport will not be attempted, except for a short analysis of the actual temperature-moisture covariance at one station, but rather the feasibility of moisture transport will be considered in combination with various Antarctic circulation models. Such a general treatment of course only yields limit- ing conditions and possible mechanisms, but does provide an insight into the ice mass balance of the Antarctic interior. The two-layer circulation model The most recent treatment of the mass budget of the Antarctic atmosphere is that of Rubin & Weyant (1963), which presents a consistent pattern of outflow in the lower troposphere and inflow in the upper troposphere and stratos- phere, involving a balanced flux of 65 x 1012 gm/ sec. This conceptually simple model of upper level inflow, sinking motion, and low level out- flow is similar to one proposed for Greenland by Hobbs (1945), and is in agreement with that Tellus XXI (1969), 3 332 B. LETTAU postulated for the Antarctic from ozone trans- port values (Wexler et al., 1960). Furthermore it provides an adiabatic heat source to offset the large continental radiative losses. However such a model cannot be reconciled with the transport of water vapor since on the average it suppresses precipitation, and assigns the mass influx to such a high altitude that little moisture can be ransported into the interior. Apparently the peripherally averaged situation is never actually realized, and the mathematically de- termined mean state may not be equated to a physical equilibrium or steady state. The Rubin-Weyant model utilizes a cir- cuit equivalent continent with a radius of 2000 km, and was developed from coastal sta- tion data. It therefore includes an edge effect which places the boundary between inflow and outflow at a much lower altitude than can be expected in the interior. As one goes inland from the coast, the zero net transport level should rise approximately as the ice surface, and the already difficult moisture transport pro- cess will be confined to more hostile altitudes. An alternate hypothesis, which seems more reasonable from a synoptic point of view is that large deviations of the meridional wind com- ponents from their average values exist in space or time. Either supposition however, produces a mass transport pattern that is unlike the mean peripheral pattern. The tabulated values of the circumferential monthly mean meridional winds given by Rubin & Weyant allow a determination of the temporal variability, although not of the spa- tial variability of the mean mass flux. These show that there was, on the average, outflow at and below 700 mb and inflow at and above 500 mb around the periphery of the Antarctic continent in every month included in the study. It follows therefore that longitudinal variations in the mass flux must exist, and that there must be preferred sectors of inflow and outflow on the Antarctic continent. A consideration of the water vapor transport required to produce the observed snow accumu- lation in the interior leads to the conclusion that the preferred sectors of inflow must ne- cessarily transport relatively large amounts of water vapor and that the inflowing air must therefore be relatively warm. This of course is also required from considerations of the total atmospheric heat budget. If it is assumed that the mean annual precipitation amount over the Antarctic interior is roughly 10 cm of water, then a flux of 0.04 x 1012 gm/sec of water vapor into the equivalent continent is required. In conjunction with the previously given value of the mass flux, this loss implies a decrease in mixing ratio of 0.62 gm/kg for the inflowing air during its residence time over the continent, which is an appreciable change in the Antarctic. Mean conditions at Amundsen-Scott station for example produce a saturation mixing ratio at the surface of only about 0.66 gm/kg, thus stated very simply, air flowing into the interior must be saturated, while air flowing out of the interior must be dry, a condition that is difficult to achieve in practice. Peripheral variation of the mass flux The peripheral variation of the mean annual mass flux was computed for Rubin and Wey- ant's equivalent circular continent, using actual radial wind components rather than meridional wind components, although this refinement is only of moderate importance since the greatest angular difference between the radial and meri- dional direction does not exceed 23°. The analy- sis was carried out from the surface to 50 mb in three increments: Sfc to 600 mb, 600 to 350 mb, and 350 to 50 mb. The mean annual, vertically integrated mass flux values for the peripheral stations are given in Table 1. Since the stations are not spaced equally on the perimeter of the equivalent continent, mass flux values are presented for a unit area defined as a one centimeter wide strip extending from the top to the bottom of each layer. Mass outflow has been defined as positive. The distribution of the annual net mass flux is also shown in Fig. 1 with the stations identified by their number in Table 1. Examination of Table 1 shows that preferred sectors of inflow and outflow definitely exist. On the average the mass flux is positive in Wilkes Land and in the Weddell Sea region, and negative in the eastern Ross Sea. Marie Byrd Land and much of East Antarctica. Maxi- mum values of mass inflow occur at Byrd and Mirny, while maximum values of mass outflow occur at Hallett and Dumont d'l'rville. The outflow at Hallett could be due to the large angle between the boundary of the equivalent TollusXXI il i10 3 E o Fig. J. Histogram of the monthly net moisture transport through the Byrd sector during the austral summer 1957-8. Also shown is the cumulative total moisture transport. only once during the summer of 1957-58. There is however no reason to suppose that it cannot recur one or several times during one summer, but on the other hand, there is also no reason to assume that it need to occur at all. Then, because of the great influence of this situation on the total annual moisture transport, one would expect a high interannual variability in the moisture transport values. Furthermore it would follow that the observed annual accumu- lation amounts, which represent a rough mea- sure of the annual moisture transport, should similarly be highly variable. This latter effect is indicated in a study by Giovinetto & Sehwerdt- feger (1966), who found that the one-year lag correlation in the snow accumulation record over 200 years at the South Pole was very nearly zero, so that the annual succession of snow accu- mulation amounts is very nearly random. The accompanying standard deviation values indi- cate that individual annual values may vary from the mean, by a factor of 2, producing a relatively large range of observed values, in accord with the moisture transport thypothesis at Byrd. Effect on ice mass balance The mass balance of the interior ice sheet is a function of the ablative effects at its edge and its surface, and the accumulative effects of the precipitation pattern on its surface. Since nei- ther its rate of gain nor its rate of loss can be calculated very precisely, the difference in the two rates, which determines whether the ice mass is increasing or decreasing is also not very well defined. It is however possible to place rough limits on the amount of ice that can be accumulated. The detailed moisture transport values at various pressure levels at Byrd show that to a very good approximation these vary logarithmi- cally with pressure, such that the transport is halved for a pressure decrease of 100 ml). This empirical observation is related to the fact that at Byrd a 100 ml> pressure decrease corresponds to an increase in altitude of approximately 1500 m, through which distance the moist adiabatie lapse rate will produce a temper! tiro decrease of approximately 10C which in turn corresponds approximately to a decrease in the Tellus XXI (lutisi). ;? TRANSPORT OF MOISTURE INTO THE ANTARCTIC INTERIOR 339 saturation mixing ratio of a factor of 2. On the further assumption of horizontal flow, and be- cause of the generally sloping surface, one can say that for every 100 mb decrease in the surface pressure on a track from Byrd station to Amundsen-Scott the total annual moisture transport will be decreased by a factor of two. Since the mean pressure difference between Byrd and Amundsen-Scott is 126 mb, the moisture transport at Amundsen-Scott will be roughly 40% of that at Byrd. In the present case that would be 0.12 x 1018 gm/year, which somewhat exceeds the amount necessary for a mean precipitation rate of 5 cm/year computed previously. The mean precipitation rate may be greater than 5 cm/year however, and the com- puted transport value at Amundsen-Scott is a slight overestimate because the simple model that has been postulated above is not strictly correct. It does not, for example, take into ac- count the fact that some moisture will be ad- vected through the sides of the volume extend- ing inland from Byrd and so will be lost as far as this analysis is concerned. Although the assumptions which underlie this simple latitudinal transport decrease model are open to question, the model itself is quite useful for rough calculations. The highest ice surface elevation in the Antarctic interior is about 4000 m (550 mb) which, if it were uni- formly applicable to the Amundsen-Scott- Vostok-Plateau area, would reduce the mois- ture transport to 10% of that at Byrd, ana pro- duce a mean annual precipitation value of about 1 cm. This value is so small that it ap- pears very unlikely that the ice sheet could maintain itself at such an altitude for very long before wind-produced ablation and the out- ward movement of the ice sheet would initiate a thinning process. The existence of an appre- ciably thicker ice sheet than the present one seems therefore excluded on meteorological grounds. This conclusion of course assumes a climate not much different from the present one. Clima- tic amelioration does occur and should be con- sidered in any discussion of such a slow process as the variation in thickness of the interior ice sheet. In general, the moisture transport will vary directly with the temperature, although the atmospheric mass flux may change with the climate and must also be considered. It should be noted however, that an increase in the mean temperature, for example, must occur at least throughout the troposphere for the moisture transport to increase by a noticeable amount, and that climatic variations which are confined to the surface layers will have a negligible effect on the mass balance of the ice. Resume La magnitude du transport de vapeur de l'eau dans l'interieure de l'Antarctique par l'atmos- phere est determinee par une modele du trans- port de masse qui permette une variation longitudinale en le valeur de la fluxe annuelle. II est indique que l'usage des moyennes men- suelles en le transport et la temperature sous- estime le transport annuel de vapeur de l'eau exiges par les valeurs observes de l'accumula- tion de glace en l'interieure. Par suite il faut que la plupart du transport annuel de vapeur de l'eau se trouve avec les deviations positives de la temperature a partir des moyennes mensuel- les. On examine ce rapport pour le station Byrd oil on trouve qu'en ete austral 1957-8 l'espace de trois jours a la temperature la plus grande a 700 mb produisee a peu pres 20% du transport annuel de vapeur de l'eau. On examine aussi le variation altitudinal du transport de vapeur de l'eau et on discute en peu de mots son effet comme eonstrainte sur la elevation centrale que peut atteindre la mer de glace REFERENCES Astapenko, P. D. 1964. Atmospheric Processes in the High Latitvdes of the Southern Hemisphere (tr. by Israel Program for Scientific Translations, Jerusalem), 286 pp. Giovinetto, M. B. & Schwerdtfeger, W. 196b. Ana- lysis of a 200 year snow accumulation series from the South Pole. Arch. f. Met. Oeophys. and Biokl., 15, 2, 228-249. Gow, A. J. 1965. On the accumulation and seasonal stratification of snow at the South Pole J. Glaciology, 5, 40, 467-478. Hobbs, W. H. 1945. The Greenland glacial anti- cyclone. J. Meteorology, 2, 3, 143-153. Loewe, F. 1962. On the mass economy of the in- terior of the Antarctic ice cap. J. Oeophys. Res., 67, 13, 5171-5177. Tcllus XXI (1969), 3 340 B. LETTAU Rubin, M. J. & Weyant, W. S. 1963. The mass and heat budget of the Antarctic atmosphere. Monthly Weather Review, 91, 487-493. Wexler, H. 1961. Ice budgets for Antarctica and changes in sea level. J. Glaciology, 3, 29, 867-872. Wexler, H., Moreland, W. B. & Weyant, W. S. 1960. A preliminary report on ozone observations at Little America, Antarctica. Monthly Weather Review, 88, 43-54. nEPEnoc BJiArn bo bhytfeiiiimk OBJIACTM AHTAPKTMKM OnpeAf-nneTCH BejiniinHa nepeHoca BJiam b aTMOC(J>epe BHyTpb AHTapKTHKH nyTeM HcnoJib- riOBaiiHH MOfleJiH nepenoca Maccw, KOTopan yiiHTbinaeT jroJiroTHbie M3MeHeHHn B roAOBbix BeJiHMHHax noTOKOB. ynasano, mto HcnoJib30- BaHHe cpeflHeMecHHHbix sHaneHHti nepeHoca Maccbi h TeiwnepaTypbi saHHwaeT rosoBofi ne- peHoe Bjiarw, TpefiyeMbitt HaGjiioaaeMbiMH 3Ha- HeHHHMH aKKyMyjIHIIMH BO BHyTpeHHIlX ofl- jiacTHX. CjieflOBaTejibno, cymecTBeHHan nacTb roflOBoro nepeHoca BJiarn AOJiwHa npoHcxojiiTb npw HajiH4HH nojiomHTejibHbix OTKJioneniiii Te\i- nepaTypbi ot cpeAHeMecHMHbix 3HaHeHHii. 3tb cBH3b npoBepnjiacb sjih CTaHUHM Bapa, rje 6buio HafiAeno, mto b TeneHiie JieTa 1957-58 rr. jtjih Tpex flHeft c nan6ojibiunMH TeivinepaTypaMn Ha noBepxHocTH 700 m6 nepenoc BJiarn cocTaBH.i noHTH 20% ot roAOBoro nepenoca. HccjieAyeTCH H3MeHeHHe nepeHoca BJiarn c bhcotoh h KpaTKo oScywflaeTCH orpaHmniTejibHoe ero B.uiHnne Ha MaKCHMajlbHyK) BblCOTy, KOTOpOH MOHteT AOCTHHb jieAHnort nonpoB. Tellua XXI (1969). 3 54 Reprinted from Annalen der Meteorologie NF No. 4, 30-34. — 30 — DK 551.510.522:551.554 Wind structure in the equatorial maritime friction layer von B. LETTAU Abstract The vertical wind structure in the equatorial maritime friction layer is related to para- meters derived form pressure and density gradients, frictionalstresses, and the rotation of the Earth. The analytic expressions for the free-air wind and wind shear, obtained by latitudinal differentiation of the geostrophic approximation, are used to define surface wind components analogous to the midlatitude surface geostrophic wind and gestrophic deviation vectors. Two assumptions are made in the analysis: 1. The free-air wind and vertical wind shear vectors are determined by macro-scale meteorological patterns which are persistent for relatively long periods of time, and 2. The vertical wind structure of the equatorial friction layer is determined by the momentum exchange mechanism at the air-sea interface and by local synoptic temperature (density) variations. The use of the latitudinal gradients of the coriolis force and the pressure gradient force obviates the problem of a vanishing coriolis parameter at the equator, and as a result the model in its detailed application is analogous to that of the wind structure in an extra-tropical baroclinic boundary layer. The model is tested with observed surface temperature values and wind profiles obtained in the Arabian Sea by the 1967 "OCEANOGRAPHER" expedition, and in the equatorial Atlantic Ocean by the 1925 — 7 "METEOR" expedition. Relevant climatological pressure and tempera- ture fields have been taken from published summaries and atlases. The observed behavior of the wind profiles can be related quite well to the ambient distributions of thermodynamic parameters: The observed shear vectors may be separated into a thermal component related to local synoptic temperature variations, and a frictional component related to the vertical variation of the shearing stress. Since these generally oppose one another, and the fric- tional shear vectors decrease with height, the total shear vector increase to a non-zero asymptote, producing the typically observed maritime pattern. Zusammenfassung Die vertikale Windstruktur in der aquatorialen maritimen Reibungsschicht hangt ab von Parametern, die aus den Druck- und Dichte-Gradienten, den Reibungskraften und der Ro- tation der Erde abgeleitet sind. Die analytischen Ausdrucke fur den Wind in der freien Atmosphare und die Windscherung, die durch breitengerechte Differenzierung der geostro- phischen Naherung erhalten wurden, werden benutzt, um die Bodenwind-Komponenten ahnlich den Vektoren des geostrophischen Bodenwindes und der geostrophischen Abwei- chung fur die Mittelbreiten zu bestimmen. Zwei Annahmen werden in der Analyse gemacht: 1. Die Vektoren des Windes in der freien Atmosphare und der vertikalen Windscherung werden bestimmt durch ein makro-meteoro- logisches Feldgeprage, das iiber relativ lange Zeitabschnitte andauert, und 2. Die vertikale Windstruktur der aquatorialen Reibungsschicht wird durch den Mechanismus des Impuls- Austausches an der Grenzflache Luff — See durch lokale synoptische Temperatur-(Dichte-) Anderungen bestimmt. Die Benutzung der Breiten-Gradienten der Coriolis-Kraft und der Druckgradient-Kraft beugt dem Problem eines am Aquator verschwindenden Coriolis-Para- meters vor, und es ergibt sich, daB das Modell in seiner Anwendung im einzelnen dem der Windstruktur in einer aufiertropischen baroklinen Grenzschicht ahnlich ist. Das Modell wird an Hand der Bodentemperaturen und Windprofile gepriift, die im Arabischen Meer auf der „Oceanographer"-Expedition 1967 und im aquatorialen Atlantischen Ozean auf der „Meteor"- Expedition 1925 — 27 beobachtet wurden. Hinreichend belegte klimatologische Druck- und Temperaturfelder wurden den veroffentlichten Zusammenstellungen und Atlanten entnom- men. Das beobachtete Verhalten der Windprofile kann recht gut zu den umgebenden Ver- teilungen der thermodynamischen Parameter in Beziehung gebracht werden: Die beobachte- ten Scherungsvektoren konnen aufgeteilt werden in eine thermische Komponente, die zu den lokalen synoptischen Temperaturanderungen in Beziehung steht, und eine Reibungskompo- nente, die zu der vertikalen Anderung der Scherungskraft in Beziehung steht. Da diese im allgemeinen einander entgegengesetzt sind und die reibungsbedingten Scherungsvektoren mit der Hohe abnehmen, so wachst der gesamte Scherungsvektor asymptotisch gegen einen von null verschiedenen Wert und lafit die beobachtete, fur maritime Verhaltnisse typische Form entstehen. — 31 It is the purpose of this report to examine the vertical wind distribution within the maritime friction layer both in geostrophic terms, that is in a rotating system with a welldefined Ekman layer, and in non-geostrophic terms, that is in an equatorial non-rotating system in which the analytical framework is not as simply defined. Additionally it is intended to examine the manner in which the system passes from the geostrophic to the non-geostrophic mode. It has been established that in middle and high latitudes of the northern and southern hemisphere, where the coriolis parameter has an appreciable magni- tude, the effect of the surface stress is to produce a satisfyingly veering wind vector through the boundary layer, although quite often the simple spiral is distorted by an accompanying geostrophic wind shear (JOHNSON (1), B. LETTAU (2)). Essentially the same technique has been used by CHARNOCK et al (3) with reasonable success. The obvious next step then was to attempt similar analyses at approximately 10°N, and at the equator. The results reported here at 10°N are not successful if success is defined as obtaining inconsistent answers with standard techniques; the results at the equator on the other hand indicate that it is possible to interpret some of the observations within a new framework fitted more reasonably to the ambient conditions. In the spring of 1967 a series of wind profiles were obtained by USCGS OCEANOGRAPHER off the Somali coast in the region of a persistent wind maximum within the boundary layer, which had been called the Somali Jet by BUNKER (4). Although the individual wind velocities observed on this cruise did not reach the high values observed by Bunker, the general decrease in the wind speed with height was observed and appears in the mean wind profile. The wind as a function of height is given in figure 1 in a coordinate system oriented parallel and normal to the surface wind vector. In such a coordinate system the _^ Compcrenl parnlei l< component (mps) Fig. l Wind components observed in the boundary Layer off the Somali coast and hodograph of the associated shear vectors over 200 m interval. The thermal wind vector is derived from the shear of the geostrophic wind. determination of the shearing stress with height by the geostrophic departure method is particularly simple and straightforward. I shall not go into the details of the method here since it has been described in a number of publications, particularly in H. LETTAU and HOEBER (5). The shearing stress is described in this situation by the progressive (and additive) deviation of the observed wind profile from the geostrophic wind profile, down to the surface stress, x,„ which is proportional to the total integrated profile deviation. The weakest point of this technique is the deter- mination of the shape of the geostrophic wind profile. The hypothesis that the wind at the top of the planetary boundary layer is in fact geostrophic offers one con- straint, while a second is obtained from the characteri- stics of the shearing stress profile in the chosen coordi- nate system. In the absence of further information (e.g. the surface pressure gradient) it is safest to assume a linear geo- strophic profile as has been done here, resulting in an angle of 17° between the observed surface wind and the surface geostrophic wind. The computed surface stress value is 0.11 dynes/cm2, the geostrophic drag coefficient is 0.4 x 10-3, and the friction velocity is 9 cm/sec. All of these are of course equivalent, derivable from each other, and only subject to personal preference. The values are low as surface friction parameters go, but fall reasonably well into the summaries of these parameters as given by ROLL (6). Occasionally independent observations either of the surface pressure distribution (surface geostrophic wind) or of the temperature distribution (thermally produced wind shear) are available which indicate that the true situation is likely to be more complex than that shown here. For example the average wind profiles obtained by CHARNOCK, FRANCIS, and SHEPPARD (3) at Anegada included the surface geostrophic wind as an observed parameter. An examination of their diagrams shows quite clearly that a linear geostrophic profile will not satisfy all three constraints, hence the geostrophic profile must be curved. It is encouraging to note however that the curvature of the profile decreases upward indicating that the horizontal temperature con- trast is greatest at the surface. In their case the surface stress is higher at 0.32 dynes/cm2, the angle between the geostrophic and observed wind at the surface is less at 13°, while the geostrophic drag coefficient is nearly the same at 0.3 x 10-3. One can see from this that results which do not conflict with previous experience can be obtained from techni- ques involving the coriolis parameter in regions where the geostrophic approximation can no longer represent the observed wind field. The situation changes somewhat however at the equator itself. Here the equivalence between geostrophic departure and shearing stress no longer holds because neither the geostrophic wind nor the factor of propor- tionality are defined. It is however possible to apply those concepts and techniques that are independent of latitude. For example, it is reasonable to assume that a free region and a friction layer exist and that their boundary lies at approximately the same altitude as in mid-latitudes. The following analysis is based on a series of pilot balloon ascents from the 1925-7 METEOR expedition, between 5° N and 5° S latitude in the Atlantic Ocean. The data are old but usable, and illustrate the relevant dynamic processes very well. An examination of the individual ascents showed that the variation in wind direction decreased with height, orlooking from the top down, the wind at 2000 m was typically from the northeast; the wind at 1000 m from somewhat south of east, with the surface wind from a variety of directions. As a first step therefore it was decided to group the profiles by surface wind direction at two point intervals, and to construct mean profiles by averaging the component parallel and nor- mal to the surface wind at standard levels. The gross structure of the five resultant classes is shown in figure 2 which gives the surface wind vector, the sfc- 32 Fig. 2 Surface wind vectors (solid), surface — 1000 m shear vectors (dotted), and 1000 — 2000 m shear vectors (dot-dashed), in the atmospheric boundary layer of the equatorial Atlantic Ocean. 1000 m shear vector, and the 1000-2000 m shear vector for each group. Quite plainly there is a tendency for the shear to increase with veering of the surface wind, and also for the shear vector to increase with height. This last effect is quite generally observed in the trade wind zone where it is due to the opposition of the pressure and temperature gradient, producing anti- parallel wind and wind shear vectors. In the equatorial region however one must look for an alternate explana- tion since the normal thermal wind is not defined. It seems reasonable however that the extremely variable deriation of the sfc wind vector from the 200O m wind, vector, which ranges roughly from 0° to 180° among separate groups is caused by an equally variable ther- modynamic parameter within the boundary layer; and it is difficult to imagine this parameter to be anything other than the horizontal temperature distribution. One may say then that there exists an as yet undefined equatorial thermal wind which has the same characte- ristics as the normal midlatitude thermal wind. \ \ \ \J 1 I I U I PARAllEl COMPONENT NORMAL COMPONENT |m.1,,,/..„„d| OBSERVED SHEAR VECTOR 0-200 M Fig. 3 Wind components in the equatorial boundary layer and asso- ciated shear vector. The mean azimuth of the surface wind is 201°. Figure 3 shows the mean profiles of the group with the individually largest sfc deviation (a = 201°). The components of the profile are again parallel and normal to the surface wind. The parallel component decreases continuously and nearly linearly from a sfc value of 6mps to 5mps at 2000 m. The normal component is compara- tively small and is directed to the right of the sfc wind in the lower part of the profile and to the left in the upper part. The lower part of the diagram presents the smoothed shear vector one two hundred meter inter- vals in hodograph form, and shows clearly its increase in magnitude and veer with height. Since the shearing stress very likely does not increase with height, and in fact most likely has gone to zero at 2000 m, the observed shear vector from 1800 to 2000 m has been arbitrarily taken as the equatorial thermal wind and has been assumed constant through the boundary layer. The vector difference between the 1800-2000 m shear and the observed shear then represents an effect which is large near the surface and goes to zero at 2000 m which looks very much like the effect of surface stress. The stress vector turns to the right with height in this case, and as you may note appears to reach a non-zero asymptotic value, indicating that the assumption of a constant thermal wind is not quite correct. The next group with a mean surface wind azimuth of 168° (fig. 4), looks very much like the previous one \. \ \ A, \ OBSERVED SHEAR VECTOR 0 200 M OBSERVED SHEAR VECTOR 1800 2000 M / / Fig. 4 Wind components in the equatorial boundary layer and asso- ciated shear vector. The mean azimuth of the surface wind is 168°. except that the turning of the stress vector with height is not quite so great as for the first group, and that its magnitude goes smoothly to zero at 2000 m. The third group, with a mean surface wind azimuth of 146° (fig. 5), again is very similar to the other two except that the wind shear is not as great. Although the slope of the profiles appears to be the same or greater than the others, the wind scale has been ex- panded by a factor of two. The observed shear still increases with height, however the stress vector has practically no curvature, but again goes smoothly to zero at 2000 m. 33 OBSERVED SHEA VECTOR 1800 2000 M / / Fig. 5 Wind components in the equatorial boundary layer and asso- ciated shear vector. The mean azimuth of the surface wind is 146°. boundary layer (the first shear vector) should be roughly the same as that of the surface wind. If the top of the boundary is taken as approximately 1200 m, then the azimuths of the two vectors agree quite well. / / ./ PAHAllEl COMPONENT NORMAL COMPONENT ,cor>d| OBSERVED SMEAR l^\ VECTOR Figure 6 shows the mean wind profiles of the fourth group in which the mean surface wind azimuth approa- ches that of the upper winds, and the wind speed varies \. \ ^A PARAILEL COMPONEN NQRMAl COMPONENT Fig. 6 Wind components in the equatorial boundary layer and asso- ciated shear vector. The mean azimuth of the surface wind is 124°. relatively little, particularly in the parallel component. The observed shear decreases with height which is something new and there is some doubt that the 1800 — 2000 m shear vector is the appropriate one to define as the thermal wind since the stress vector turns first to the right and then to the left with height. Directional consistency may be preserved if the top of the boundary layer is taken to be approximately 1200 m, and the curvature in the upper part of the profile is assumed to be due to vertical variating in the equatorial thermal wind. It is possible to reach the same conclusion by considering the idea that the direc- tion of the stress vector is the lowest 200 m of the Fig. 7 Wind components in the equatorial boundary layer and asso- ciated shear vector. The mean azimuth of the surface wind is 79°. The fifth group (fig. 7) has generally the same profile curvature for the parallel component, but a quite dif- ferent normal component. The direction of turning is generally to the right, with the shear increasing with height, although the mean shear over the 2000 meter height interval is quite small. There is again some doubt that the 2000 m level is in fact the top of the boundary layer, the azimuth of the near-surface stress vector becomes 80°, again in good agreement with the surface wind direction. We may summarize the so-called stress vectors on one diagram (fig. 8) and examine the vertical variation of the shearing stress. To a certain extent this is illu- sory because the shift from a shear vector to a stress vector involves the unknown eddy dynamic viscosity. In a limited situation such as this one cannot hope to do better than to apply uniformly a typical value, and this has in fact been done. This scheme has some merit however, since it allows comparison with shearing stress values obtained in other experimental situations. The typical value incidentally was 15000 cm2'sec for the eddy dynamic viscosity or Austaugh coefficient, or alternatively 0.4 X 10-s for the shear stress coefficient The surface stress values obtained here, ranging from 0.12 to 0.28 dynes/cm2, are of a reasonable magnitude and compare quite well to those found by Charnock at Anegada, under presumably similar conditions, but from the geostrophic departure method. The peculiar inflection point at about 800 meters in two of the profiles is directly related to the previously mentioned possible error in the height of the boundary layer, and would disappear if the height were adjusted. Returning now to the equatorial thermal shear mentioned previously, it became apparent in this study that the surface wind direction was highly sensitive, in a predictable manner, to variations in the surface temperature. Figure 9 shows the surface wind direction as a function of the observed station temperature, and — 34 SHEARING STRESS |d^ Fig. 8 Vertical variation of the stress vector for the five separate groups. The values shown represent the difference in shear between any level and the top of the boundary layer. + 27.0 O + Fefc) Temperature Ay = 7 5 deg latitude + + + „ ■D § \o i» 26.0 25.0 1 . 1 . 0 \ Station Temperature \ 0 \ . . \ °> . . i to the vertical temperature structure. The salient para- meter is <52T/<5y2 interpreted as a local deviation from a linear meridional temperature gradient in the equa- torial region. The sense of the relationship is such that a local hot spot will produce an eastward directed shear, that is, the wind at height is more westerly than at the surface, while a local cold spot will produce a westward directed shear, that is, the wind at height is more easterly than at the surface. The magnitude of the zonal shear is proportional to the relative intensity of the temperature deviation. If now the second derivative is replaced by a finite difference, and as a first approximation it is assumed that the observed station temperatures are the result of a uniform but unknown field temperature minus a deviation due to local causes, then the local deviation, over a suitable horizontal distance, is the only unknown in the equatorial thermal wind equation. This scheme has been applied to the zonal components of the five individual thermal shear vectors with the results shown in the same figure. With a horizontal scale of 7.5 degrees of latitude — roughly the dimensions of traveling disturbances in tropical regions — the computed deriation in each case brings the field temperature to an approximately uniform value, which is a gratifying result in itself. In addition, this value is quite close to the climatological surface temperature of the region under consideration. In conclusion I would like to state that the analysis presented here suffers greatly from lack of supporting data. On the other hand it seems reasonable to conclude that the structure of the boundary layer in equatorial regions is not very much different from that in mid- latitudes, and that even if the geostrophic departure method of obtaining the shear stress vector is invalid at the equator, the free air wind vector, the stress vector, and the boundary layer all retain theier normal meaning. It should also be remembered that this has been a heuristic examination — ■ that the conclusions follow from the assumptions, and that only the similarity between deduction and observation can be pointed out. One can only hope that future expeditions will have the foresight to plan for detailed enough appropriate observations so that the relationships suggested here may be adequately tested. References Surlace Wind Direction Fig. 9 Conjectural field temperatures (see text) as a function of ob- served mean surface temperatures and mean surface wind directions. it is quite evident that the direction veers by roughly 60° for every degree centigrade decrease in the station temperature. For surface temperature near 27° C (the climatological mean value), the surface wind direction is approximately parallel to that at the top of the boundary layer, while by extrapolation for a tempera- ture of 24° C, the surface wind is oppositely directed to the upper winds. One can obtain an analytic expres- sion for the horizontal wind in equatorial regions by differentiating the geostrophic relationship with respect to latitude. If both the horizontal wind shear and the horizontal density gradient are small, the result is an equatorial wind, analogous to the geostrophic wind, with /? as the angular parameter and <5p/c5y as the stream function. It is possible to obtain the vertical variation of this equatorial wind in terms of the hori- zontal variation of <5p/<5y, which may then be related (1) JOHNSON, W. B., Jr.: Climatology of atmospheric boundary layer parameters and energy dissipation. Studies of the three-dimensional structure of the planetary boundary layer. Dept. Meteor. Univ. Wisconsin (1962). (2) LETTAU, B.: Thermally and frictionally produced wind shear in the planetary boundary layer at Little America, Antarctica. Monthly Wheater Rev. 95 (1967) S. 9. (3) CHARNOCK, H.; FRANCIS, J. R. D.; SHEPPARD, P. A.: An investigation of wind structure in the trades. Phil. Trans. Roy. Soc. London A 249 (1956). (4) BUNKER, A. F.: A low-level jet produced by air, sea, and land interactions. In: Proc. Sea- Air Inter- action Conference, Tallahassee, Florida. Techn. Note 9-SAIL-l (1965). (5) LETTAU, H. H. ; HOEBER, H. : Uber die Bestimmung der Hohenverteilung von Schubspannung und Aus- tausch-Koeffizienten in der atmospharischen Rei- bungsschicht. Beitr. Phys. Atmosph. 37 (1964) S. 2. (6) ROLL, H. U.: Physics of the marine atmosphere. New York (1965). 55 MONTHLY WEATHER REVIEW VOLUME 97, NUMBER 9 SEPTEMBER 1969 UDC 551.511.2 ON THE KINETIC ENERGY SPECTRUM NEAR THE GROUND ABRAHAM H. OORT Geophysical Fluid Dynamics Laboratory, ESSA, Princeton, N.J. ALBION TAYLOR Atlantic Oceanographic Laboratory (SAIL), ESSA, Silver Spring, Md. ABSTRACT For hix stations in the northeastern United States, the spectrum of horizontal wind speed was analyzed using 10 yr of 1-min averaged, hourly surface reports. The fast Fourier transform technique was employed to estimate the spectrum between 1 cycle/2 hr and 1 cycle/2 yr. The kinetic energy spectra show two major spikes at periods of 24 hr and 1 yr. However, most of the energy is contained in the traveling cyclones and anticyclones with periods between 2 and 7 days. The apparent discrepancy between Van der Hoven's results and our results concerning the existence of an important diurnal cycle in the kinetic energy can be explained by Blackadar's theory of the diurnal wind variation with height. Van der Hoven's spectrum represents conditions near the top of the surface layer, while our data were taken well within the surface layer. A line-by-line investigation of the diurnal peak reveals a very sharp line at 2400 hr with two side lobes 3.9 min away from the main line. These side lobes are probably caused by an annual modulation of the diurnal cycle. The spectra tentatively corrected for aliasing give some indication of the existence of a spectral gap between small-scale turbulence and mesoscale phenomena. 1. INTRODUCTION Van der Hoven (1957) made a detailed analysis of the power spectrum of the horizontal wind speed in which he analyzed measurements taken at Brookhaven National Laboratory, Long Island, at a height of about 100 m. By piecing together various sets of observations, he was able to present a composite picture of the contribution to the total variance of the wind speed from different frequency ranges. The kinetic energy spectrum thus determined covered periods from 4 sec to about 2 mo. He convincingly showed that mqst of the variance of the wind speed can be explained by the passage of large, synoptic scale pressure systems with periods of about 4 days. Turbulence of the order of minutes also gave some contribution, although it was much smaller. However, between these two regions he found a broad section of the spectrum centered near the period of 1 hr with very little energy connected with it; this last portion of the spectrum was therefore called the "spectral gap" region. His analysis further showed a small rise in the spectrum for periods of about 12 hr, but surprisingly there was not much energy near the 24-hr period. More recent investigations by Bysova et al. (1967) using 40 hr of wind speed data from a 300-m tower at Obninsk (U.S.S.R.) also show a pronounced minimum in the spectrum between the turbulent and .mesometeor- ological wind fluctuations. Recently, 10 yr of hourly wind records have become available on magnetic tape for several weather stations in the United States. This made it feasible to repeat and extend Van der Hoven's analysis to include the spectrum from periods of a few hours up to a few years. Another contributing factor was the advance in data analysis made possible by the introduction of the "fast Fourier transforms" (FFT), recently developed by Cooley and Tukey (1965) for calculating the Fourier components directly from a long time series in very little computation time. This practically eliminates the difficulties connected with the piecing together of various portions of the spectrum. In contrast to Van der Hoven's work, our analysis shows a major spike in the wind spectrum at a period of 24 hr. Therefore, an important part of this paper will be concerned with an investigation of the diurnal vari- ability in the kinetic energy. 2. DATA AND DATA ANALYSIS In 1965, records of hourly surface data for several U.S. stations covering the period Jan. 1. 1949. through 623 624 MONTHLY WEATHER REVIEW Vol. 97, No. 9 Dec. 31, 1958, were stored on magnetic tape at The Travelers Research Center, Inc., Conn., under contract for the U.S. Air Force. DATA A group of three stations (Caribou, Old Town, and Portland) in Maine, representing the northeastern part of the United States, and another group in the Great Lakes Region (Detroit and Sault Sainte Marie, both in Michigan, and Duluth, Minn.) have been investigated. The climate at all of these stations is influenced to a high degree by the proximity of water, with the exception possibly of Caribou. As we shall see later, there appear to be no major differences in the shape of the spectrum at the stations considered. Therefore, in this paper we have arbitrarily selected Caribou for a more detailed study. In a future study we intend to include other groups of stations having a more continental climate as well as stations at a lower latitude. The wind observations were taken 1 hr apart and represent 1-min averages. The height of the wind sensor is not the same for all stations but varies from 30 to 80 ft above the ground. Other factors that make the results for the different stations not strictly compatible are 1) differences in station elevation above sea level and 2) differences in exposure of the wind sensor due to, e.g., neighboring buildings. In some cases the location of the wind sensor was appreciably changed during the 10 yr of record. However, we have included all 10 yr in our analyses. Although Caribou is located only 150 mi from the Atlantic coast, its climate can be classified as a typical continental type. Old Town and Portland have an "east coast" maritime climate; the winds are generally light. The climate of the group of stations in the Great Lakes Region has some maritime characteristics because of the location of the stations close to the Great Lakes. Rather frequent changes in the weather pattern occur, since nearly all atmospheric disturbances that move eastward across the country pass close enough to affect the weather. Further climatological information is given in table 1. DATA ANALYSIS In the present study we are interested in the contribu- tion from different frequency bands to the variance of the horizontal wind speed (i.e., in the kinetic, energy spectrum). The contribution from each frequency range is estimated by calculating the sum of the squares of the coefficients in the cosine and sine transforms (the Fourier coefficients) at the particular frequency. Recently a method for efficiently computing these coefficients, called the fast Fourier transform (FFT), has been reported by Cooley and Tukey (1965). This method produces savings of up to 99 percent of computer time over conventional methods of finding the Fourier coefficients. The FFT apparently not only reduces the computation time but also slightly reduces round off errors associated with these compu- Tablk 1. — Climatological information from "Local Climatological Data — With Comparative Data" published by the U.S. Weather Bureau (1958) Caribou, Maine Old Town, Maine Portland, Maine Detroit, Mich Sault Ste. Marie, Mich. Duluth, Minn Station identi- fication CAR OLD PWM DET SSM DLII Lat. (°N.) 46.9 44.9 43.7 42.4 46.5 46.8 Long. (°W.) 68.0 68.7 70.3 83.0 84.4 92.2 Station elevation above sea level (ft) 620 124 61 619 721 1409 Wind in- struments above ground (ft) Reported changes in exposure of wind in- struments none (') none none (!) (3) 1 We could find no reports on the height of tiie wind instruments before 1954. It is, however, more likely that the height was not changed during the 10 yr of record. - On June 15. 1949, the wind instruments were relocated on another building. The elevation above ground was changed from 43 ft to 33 ft on the same date. 3 On July 1, 1950, the wind-recording equipment was moved from the city to the Duluth Airport. tations. The computation time is reduced by a factor of (\og2N)/N where N is the number of data points in the time series (Group on Audio and Electroacoustics (G-AE) Subcommittee on Measurement Concepts, 1967). For further details the reader is referred to the papers in a special issue of the IEEE Transactions on Audio and Elec- troacoustics (June 1967), entitled "On Fast Fourier Transform and Its Application to Digital Filtering and Special Analysis." A fast Fourier transform subroutine was coded for the Univac 110S. This subroutine replaces a time series of length 2m (m an integer) with the Fourier coefficients for the time series. Since the maximum value of m allowed by the program equals 14, the time series may contain a maximum of 16,384 data points. In the case of hourly data, one can analyze a series of at least 1 yr in one pass (8,760 points). In order to analyze a series of 10 yr, we shall replace the values in the original time series by the averages over 6 hr. The number of data points is then reduced from 87,600 to 14,600. Because of the finite length record, it is impossible to resolve Fourier coefficients corresponding to frequencies separated by less than a certain amount. This limit of resolution measured by AF has the value of 1 over the period of the entire data record, i.e., 1 cycle/1 yr or 1 cycle/10 yr, according to whether a 1-yr or a 10-yr period is being analyzed. In order to clarify these statements, let us follow the reasoning given by Bingham et al. (1967, pp. 57-58). The finite Fourier transforms resolve exactly any combination of sine terms and cosine terms of frequencies F0, I1\, F2, . . . , F„ . . . ( = 0, AF, 2AF, . . . , jAF . . .). Thus, if a component c; cos(2tt Fjt-{-j) were added to the time series, the transform would be affected in the coefficients as and b} (the coefficient a} would be replaced by aj + Cj cos 4>j, ii"d b} by bj+Cj sin j), but the other coefficients ak and . „, where k^j, would not be affected. However, if a component c cos(2irFt-\- ) were added to September 1969 Abraham H. Oo.t and Albion Taylor 625 the time series, with F not equal to one of the Fj} all Fourier coefficients would be affected by an amount pro- portional to (\F-Fj\lAF)-1 for \F-F,\>2AF. Thus the influence of a sinusoidal term at frequency F is largest for frequencies Ft nearest F, although its influence extends to coefficients at frequencies F} many times AF away. This "spill-over" of the influence may be decreased by de- creasing AF (which means considering longer records). Another means of sharpening the resolution lies in a filtering procedure known as "hanning" the Fourier coefficients (see Blackmail and Tukey, 1958, pp. 14-15). This may be done directly by applying the hanning weights — ){, Yi, —Yt to the coefficients at frequencies F—AF, F, F-\-AF, respectively, or indirectly by multi- plying the original time series by a data window function before processing the data. If the time t runs from 0 to T, a data window can be obtained by multiplying the data series by a cosine bell: (l-cos2irf/T)/2. This curve has a maximum value of 1 in the middle of the series and falls off smoothly to 0 at the beginning and at the end of the series. After applying the window, the influence of a sinusoid of frequency F on the other coeffici- ents tends to (\F-F,\/&F)-* for \F—Ft\>A^F. That is, the influence of a line at frequency F is now restricted to a smaller neighborhood of that frequency. Prior to applying the data window, the mean of the series and a least-squares linear trend were computed and subtracted from the series. The presence of such long-term variations would tend to bias the spectrum by introducing extra variance in the lower frequencies. After the data were conditioned by the mean and trend removal and by the data window, the time series was extended by adding sufficient zeros to attain the number of 2U data points required by the subroutine. As a result, the number of Fourier components computed increased from half of 8,760 (or half of 14,600) to 8,193 at frequencies that divide the frequency interval 0< F < 1/(2 At) into 8,192 equal parts (in our case At equals 1 hr or 6 hr). Thus, we have an apparent increase in resolution over this interval. The increase in resolution is not real, however, since the Fourier coefficients are no longer independent, but must be related to each other in such a manner as to produce the extra zercs. This introduces an interaction between components similar to the spill- over mentioned above and emphasizes the need of hanning the data with the cosine bell. A plot of the individual power estimates versus fre- quency will in general be very "rough" showing many individual small peaks. Often, the location and magnitude of these peaks is climatologically insignificant, being due to sampling fluctuations rather than any systematic physical interaction. It is thus desirable to average out these peaks to obtain a more useful presentation. Of course, we then give up much detail in resolution. How- ever, with a long time series covering nearly three decades of frequency, the resolution is generally one or two orders of magnitude greater than required in any case. There are two possible means of performing the aver- aging to account for sampling fluctuations. One method is to break up the entire record into several parts of equal length, next to compute spectral estimates for each part, and finally to average these estimates at the cor- responding frequencies. In effect, this corresponds to taking several samples. An alternative method, which we actually use here, is to calculate the Fourier coefficients and then to average estimates in several frequency bands (Hinich and Clay, 1968). Incidentally, the loss of resolution in the frequency domain produced by this averaging tends to compensate for the fictitious increased resolution produced by the subtended zeros. In our case, we have split up the frequency scale into about 80 bands. We distributed the band limits according to a logarithmic scale between the lowest and highest frequencies attainable. The lowest frequency is evidently l/(NAt), and the highest (the Nyquist or folding) fre- quency 1/(2 At), where N is the total number of observa- tions and At is the time interval between observations. For example, for a 10-yr record the resolution in the vicinity of 1 yr is about one-tenth of a year or 36 days ; however, near periods of 1 day the resolution is approxi- mately 1/3650 day or 24 sec. In our logarithmic scale with 80 bands, the power in the band near 1 day repre- sents the average over several hundred individual esti- mates (see table 3 in the Appendix), while in the bands near 1 yr only one or two estimates are included. In order to have some assurance that significant in- formation is not being averaged out along with variations due to sampling fluctuations, some form of confidence statistics would be useful. If the individual estimates within each band are distributed very tightly around the mean for the band, more confidence would be attached to that mean than if the individual estimates were widely scattered. Again, more confidence is attached to a mean if many estimates are used to compose it. A statistic with these properties is given by DF=n M*/(M*+V) where n is the number of estimates in the band, M is the mean, and V the variance. The quantity DF is referred to as the number of equivalent degrees of freedom and. according to Blackman and Tukey (.195S, pp. 21-25) the chi-square distribution with DF degrees of freedom has the same mean-variance relation as the estimates in that band. It should be emphasized that a low number of degrees of freedom does not mean that the data in this band is unreliable, but merely that the computed mean does not represent the estimates in the band very well. Thus, if resonance, for example, produces a very large, narrow peak inside the band, say at the 24-hr period, the degrees 626 MONTHLY WEATHER REVIEW Vol. 97, No. 9 HOURLY KINETIC ENERGY Figure 2. — Spectrum wind speed at Brookhaven National Lab- oratory, Long Island, at about 100-m height (after Van der Hoven, 1957). Frequency F in cycles/4096 days. Figure 1. — Hourly kinetic energy at Caribou, Maine, for the first 10 days of January 1949. of freedom estimate for that band is sharply reduced (see, e.g., table 3 in the Appendix of this paper). In such cases a close, line-by-line examination of this band may be indicated. 3. THE ALIASING PROBLEM As mentioned earlier, the reported wind speeds represent 1-min averages and are spaced 1 hr apart. Figure 1 shows a plot of the reported hourly kinetic energy for Caribou, Maine, for the first 10 days of January 1949. The graph gives evidence of high-frequency fluctuations in the data. This intuitive conclusion is backed up by Van der Hoven's results at Brookhaven (fig. 2) which show that the energy in wind fluctuations below 2 hr cannot be neglected. The power in the frequency range between 1 cycle/2 hr and 1 cycle/1 min causes an aliasing problem. However, the aliasing is not as bad as it might appear from figure 2. The observations in the high-frequency part of the spectrum were taken during the passage of a hurricane near Brookhaven. A more normal situation would certainly give lower values for the maximum in the minute range; a maximum value between 0.5 and 1.0 m2 sec-2 might be expected (table 2) instead of the value of 3.0 m2 sec-2 shown in figure 2. In the present data sample the power in the non- resolvable frequencies between 1 cycle/2 hr and 1 cycle/1 min is added to and cannot be distinguished from the real power in the resolvable range of frequencies between 1 cycle/10 yr and 1 cycle/2 hr. The higher frequencies that are aliased into a resolvable frequency F are: 2FN-F,2FN+F, 4FN-F, 4FN+F, QFN-F, 6FN+F, etc., where ipAr = Nyquist or folding frequency=l cycle/2 hr. For example, the power in periods of approximately 72, 51, 33, 28, 21, 19, 15.6, 14.4, 12.4, 11.6, 10.3, 9.7, 8.8 min, etc. will be added to the power in a period of 6 hr. Table 2. — Spectral intensity in small-scale turbulence maximum as a function of roughness length Cari- bou Old Town Port- land De- troit Sault Ste. Marie Du- luth 2 (ft) 33 27 55 81 33 55 V (m sec-') 5.75 3.85 4.59 4.95 4.61 6.35 {PXF)m, i (m! sec-2! (zo=20cm) .36 .18 .18 .17 .23 .34 (PXF)„„ , (m2 sec-2 (zo=50 cm) .60 .31 .28 .26 .39 .53 <.PXF)m„ , (m2sec-2 (zo=100cm) 1.00 .54 .42 .38 .64 .82 z =observation height above ground. V =mean horizontal wind speed. (PXF)m„t =product of power density and frequency in small-scale turbulence maximum. io r=oughness length. Before going into more detail, let us first discuss the form in which the spectra in this paper will be presented. For each frequency band, the value of the product of the mean power density (P) and the mean frequency (F) will be plotted as the ordinate and the natural logarithm of the mean frequency (\ogeF) as abscissa. This commonly used scale gives perhaps a better illustration of the con- tribution of the various ranges of meteorological interest than a curve of simply the mean power density versus the frequency. In both cases, the area under the curve between the two frequencies Fx and F2 gives that portion of the total variance (kinetic energy) that is explained by phenomena in this frequency range I iog.F, log.F, (PxF)dlogeF PdF. In our graphs we chose to let the frequency decrease from left to right, in order to have the time scale increase in that direction. Let us assume that the aliased part of the spectrum between 1 cycle/ 1 min and the folding frequency of 1 cycle/2 hr resembles white noise, i.e., the power is not a function of frequency. The effect of aliasing will then be to add to the true power between the folding frequency September 1969 Abraham H. Oort and Albion Taylor 627 and 1 cycle/2 yr a constant amount, independent of frequency. Aliasing as described above is, of course, independent of the way in which the spectrum is repre- sented. However, different representations of the spectrum might give different impressions of the effect of aliasing. In the graphs in this paper, the product of the power and the frequency (not the power itself) is plotted along the y-axis. Each time that one decreases the frequency by e (in other words, the value of the ^-coordinate in the graphs is decreased by 1), the contribution to the y-coordi- nate (power X frequency) due to aliasing will decrease by e, simply because the frequency decreases by e. Thus, the effects of aliasing tend to show up mostly near the folding frequency of 1 cycle/2 hr. If the true spectrum were to show a decrease of power with increasing frequency near the folding frequency instead of being independent of frequency, the effects of aliasing would be still more concentrated near this frequency. For a better understanding of the aliasing effect, we have performed two experiments for Caribou, Maine. In the first experiment we used all hourly surface reports and analyzed the spectrum in the range from the Nyquist frequency of 1 cycle/2 hr up to 1 cycle/2 yr. In the second experiment we only used one observation every 6 hr and could, therefore, determine only the spectrum between the new Nyquist frequency of 1 cycle/12 hr and 1 cycle/2 yr. In this last experiment, the power between 2 hr and 12 hr is aliased further into the rest of the spectrum. The results shown in figure 3 indicate that most of the distor- tion is confined to the spectrum in the vicinity of the Nyquist frequency, i.e., to the range from 12 hr up to about 2 days. In the next section we shall make use of this result in order to make a rough correction to the spectrum of Caribou for the effects of aliasing from the range of periods of 1 min to 2 hr. 4. THE KINETIC ENERGY SPECTRUM In this section, power spectra of the surface wind speed will be presented which cover cycles from 1 cycle/2 hr to 1 cycle/2 yr. A split up of the spectral analysis in two parts was necessary because of the limitation in the total number of data points in the computer program for the fast Fourier transform. METHOD OF ANALYSIS OF THE SPECTRUM The spectrum for periods of 24 hr and up was obtained by an analysis of the 10 yr of record. The hourly data were first averaged over nonoverlapping 6-hr intervals. Next, these 6-hr averages were used as input data for estimating the spectrum from 12 hr and up. The averaging process reduces the amplitude of each wave in the spectrum by R(F) = sm(irFT)/(irFT) where R(F) = the response function for a wave with frequency F, F= frequency in cycle/hr, and 7 = the filtering interval=6 hr (Holloway, 1958). The original 009013027 0. Figure 3. — Example of the effects of aliasing on the wind speed spectrum. Dashed line gives the spectrum at Caribou, Maine, if power between 2 and 12 hr is aliased. Frequency F in cycles/4096 days. spectral power was restored by multiplying the computed power at each frequency by l/R2(F). The spectrum for periods between 2 hr and 1 day was obtained by analyzing each year of the 10 yr of record separately and then averaging the spectral estimates thus obtained. In general, the effects of aliasing are most severely felt in this part of the spectrum, i.e., close to the Nyquist frequency. THE HIGH FREQUENCY PART OF THE SPECTRUM Our concern at this point is to estimate what the most probable shape of the spectrum will be between periods of 2 hr and 1 min. Since Van der Hoven made his study, further evidence has been accumulated that there exists a broad gap in the spectrum. For example, Bysova et al. (1967) analyzed a continuous record of 40 hr of wind velocity fluctuations measured at Obninsk (U.S.S.R.). Their analysis shows at all levels (25, 75, 150, and 300 m) a pronounced spectral gap between periods of about 15 min and 7 hr. This gap, which separates the mesoscale phenomena (periods of the order of a few hours) from the high-frequency turbulence (periods of the order of minutes), appears to be centered at a period of about 1 hr. The value of the high-frequency maximum of PX.F can be estimated using a general relationship found by Busch and Panofsky (1968) for the maximum (PXF)/u*2^l where u*=friction velocity =kV/ (log, z/z0) in neutral air, fe=von Karman constant =0.4, 20=roughness length. 2= height observation above ground, and V = mean wind speed. For simplicity, effects of stability have been ne- glected in the formula for the friction velocity. Table 2 gives the calculated values of PXF in this maximum, assuming several different values of the roughness length. In the case of Caribou, we rather arbitrarily selected a value of O.Snr sec"- in the high-frequency maximum 628 MONTHLY WEATHER REVIEW Vol. 97, No. 9 - V. 579 - 35 SPECTRUM WIND CARIBOU , MAINE SPEED 30 25 a2° FOLDING FREQUENCY -H S 1 5 A - 1 0 l\ nJ '"X POSSIBLE SHAPE SPECTRUM y 0 5 AT VERY HIGH FREQUENCIES /- / 1 00 \ ,-'''' -*- LOG F _j — * e "T~^ i i i 1 14 | ,3 | ,2 j „ j | ,o | • | a t ' t 6 5| i I' I 2 1 VI 2 M 1 5 M 10 M 20 M 1 HR 2 HR 3 HR 6 HR 12 HR 21 HR 1 3D 1 6D 1 10 D 1 30 D 1 1/2 YR 1 1 YR Figure 4. — Results of an attempt to correct the spectrum at Caribou, Maine, for the effect? of aliasing from periods between 1 min (the basic averaging period of the wind reports) and 2 hr (the Nyquist frequency). Frequency F in cycles/4096 days. corresponding with a roughness length between 50 cm and 100 cm. The location of the maximum does not seem to be very well fixed. For higher wind speeds it generally shifts to higher frequencies. Again arbitrarily, but perhaps not unreasonably, we selected a location of about 1 cycle/2 min. Having fixed the height and the location of the high-frequency maximum, we drew freehand a hypothet- ical line for the "true" spectrum (see dashed line in fig. 4). This line gives our estimate of how the spectrum would look if measurements were available for 10 yr with a 1-min instead of a 1-hr separation. In drawing the dashed curve, we used the following guidelines: 1) The conservation of variance of the wind speed. In other words, the area under the dashed curve between the basic averaging frequency of the data (1 cycle/ 1 min) and the folding frequency FN (1 cycle/2 hr) should be approximately equal to the area between the solid (com- puted) and dashed curves to the right of FN. 2) The assumption of an approximately white power distribution in the aliased portion of the spectrum to the left of FN. The contribution to the spectrum at the right of FN due to aliasing will then decrease by e, if F decreases by e (see discussion in section 3). This consider- ation rather limits the range of acceptable possibilities in drawing the true spectrum curve to the right of FN. If one would assume, e.g., significantly more power to the left of FN than is done in figure 4, the dashed curve would become negative near the folding frequency — an impossible situation. After having drawn the dashed curve in the way described, the total amount of aliased power is directly determined. However, considerable freedom is still left in constructing the shape of the spectrum between the folding frequency and 1 cycle/1 min; more information is needed. 3) The assumption of the existence (which seems to be well proved, Busch and Panofsky, 1968) and next of the magnitude and location of the high-frequency maxi- mum as tentatively derived above in table 2. Finally, one can infer that very little energy is left to be distributed between the high-frequency maximum and the folding frequency. Although our method of estimating the true spectrum is of course very approximate, the final curve in figure 4 shows that our results using a very long time series are certainly compatible with the existence of a spectral gap in the vicinity of 1 cycle/2 hr. DETAILED DISCUSSION OF THE SPECTRUM Starting on the left side of figure 4 for Caribou, Maine, one notices first the rise in the spectrum in the vicinity of a period of 2 min due to small-scale turbulence with a maximum value of 0.8 m2 sec-2. Then there follows the spectral gap region with intensities of the order of 0.1 m2 sec-2 or less between roughly 10 min and 2 hr. Next, in the range from 2 hr up to 2 days, the level of activity starts to rise from the low values in the spectral gap up to a very high level in the "cyclone rise." Superposed on this part of the spectrum is a minor peak at 12 hr and a major peak at 24 hr. A high, broad plateau of activity of about 3 m2 sec-2 connected with the travel- ing cyclones and anticyclones is found at periods between approximately 2 and 8 days. After this, the level of ac- tivity drops quite rapidly and shows only minor (probably not significant) bumps near periods of 1 and 2 mo. Finally, we reach periods of one-half and 1 yr where again im- portant peaks are found. A striking feature of the "cyclone rise" is the appearance of spikes. By making the resolution coarser (or by a little September 1969 Abraham H. Oort and Albion Taylor 629 smoothing on the spectrum) it is relatively easy to get rid of the spikes. However, we think the picture as it is may give the reader more insight into the inaccuracies (or rather the effects of sample fluctuations on the spectrum). These fluctuations play a role even when one analyzes a very long sample such as 10 yr of data. It is clear that one should not interpret the peaks (at 3.1, 3.9, and 5.5 days) as true periodicities comparable to the diurnal and annual periods or to their higher harmonics. If one looks at the hundreds of individual power estimates that make up each peak, one soon realizes that each band consists of a large number of peaks and valleys. The high average value in a band means only that the general level of activity is high in that portion of the spectrum. If one studies the spectra for individual years, spikes seem to occur each year but not necessarily at the same frequencies. Averaging of the 10 individual years would largely smooth out these spikes. 17 & more detailed information on the spectrum for Caribou, e.g., the number of equivalent degrees of freedom for each band, the reader is referred to table 3 in the Appendix. In figure 5, the measured kinetic energy spectra for the six stations considered in the present study are plotted, both with (full line) and without (broken line) applying a correction for aliasing. The area under each solid curve was normalized; and, because the total variance is not the same for the different stations, the scale along the y-axis is also different. The general shape of these spectra is quite similar, in spite of apparent differences in detail. For example, in the case of Caribou and Duluth the intensity in the cyclone rise appears to be much larger than in any of the other stations. On the other hand, Detroit shows an exceptionally pronounced annual cycle. The intensity in the cyclone rise for Caribou and Duluth has a value between 2 and 3 m2 sec-2, while for the other stations the intensity is only 1 to 1.5 m2 sec-2. According to the description in the Local Climatological Data — With Comparative Data (U.S. Weather Bureau, 1958), Caribou Airport is located on the top of high land which is about on the same level as most of the surrounding, gently rolling hills. The exposed location of this airport probably causes the greater activity in the cyclone and anticyclone scale, while in the case of Duluth Airport the large value must be related to its high elevation above sea level (see table 1). The differences in intensity can thus be explained by assuming that the observations at Caribou and Duluth are more representative of the conditions at higher levels in the atmosphere. One can expect that, in general, the annual period in the kinetic energy will show up most prominently at continental stations and at stations located at high latitudes. Since the six stations considered in this study are located in a relatively narrow latitude belt between 42° N. and 47° N., only the effect of continentality might be noticeable. However, there is no clear indication of this effect in the graphs given in figure 5, possibly because the stations are all located close to either the Atlantic Ocean or to the Great Lakes. One other important point is that — if one allows for the effects of aliasing (see dashed curves in fig. 5) — all spectra tend to show low values near the Nyquist frequency of 1 cycle/2 hr. COMPARISON WITH VAN DER HOVEN-S RESULTS If we compare figures 2 and 4, good qualitative agree- ment is generally found between the spectrum at Brook- haven, Long Island, determined by Van der Hoven, and our spectrum for Caribou, Maine. As we have pointed out before, the small-scale turbulence maximum in the minute range has an abnormally large' value in the case of Brookhaven, due in part to hurricane conditions present in its determination. The difference in magnitude of the cyclone peak, i.e., 5 m2 sec-2 for Brookhaven and less than 3 m2 sec-2 for Caribou, could be related to the difference in location. However, it appears more likely that it is mainly due to the difference in elevation above ground level at which the observations were taken (respectively, 100 m and 10 m). Another contributing factor may be that Van der Hoven's observations were made during the winter half year, while ours are representative of the entire year. One important qualitative difference, however, is the surprising lack of a diurnal peak in the Brookhaven data even though there is a semidiurnal peak of comparable magnitude. The most probable reason for this discrepancy lies in the fact that the Brookhaven observations were taken at a height of 100 m, which is near the top of the surface layer (see fig. 6, taken from a report by Singer and Raynor, 1957), while ourdata represent conditions with- in the surface layer. Both Van der Hoven's results at the top of the surface layer and our results within the surface layer are in very close agreement with Blackadar's description (1959) of the typical diurnal wind variation with height. 5. THE DIURNAL CYCLE IN THE KINETIC ENERGY In table 4 (see Appendix) the hourly kinetic energy averaged for each of the 10 yr is given as a function of local time (see also fig. 7). For each station and for each year there is a large and systematic diurnal variation. The maximum value is found between 2 and 3 p.m., and the minimum in the early morning. The phase of this diurnal variation changes rather rapidly with height. Singer's measurements (fig. 6) show that around 120 m the phase of the diurnal cycle is shifted by 180° compared to the phase at the surface. At this height the maximum wind speed is observed at night, and a minimum around midday. The change of wind speed with elevation and time of the day was clearly explained by Blaekadar 1 19591 as being related to the coupling and decoupling of the surface and upper layers. Because of the frictional drag exerted 630 MONTHLY WEATHER REVIEW Vol. 97, No. 9 009 015 0 27 0 47 081 009 015 027 0 47 08 Figure 5. — Spectra wind speed determined from 10 yr of hourly wind reports. The dashed curves represent a rough estimate of the spectrum corrected for the effects of aliasing. Frequency F in cycles/4096 days. on the air by the earth's surface, the wind speed generally increases with height above the ground. During the day, convective mixing will transfer momentum from higher levels to the surface layer. The wind speed in this layer will thus increase until an equilibrium is reached between the supply of momentum from above and the loss due to friction with the earth's surface; but this same process will slow down the upper layers during the daytime. However, at night convective mixing stops; and the sur- face and upper layers become effectively decoupled by the formation of a temperature inversion. The air near the surface then slows down, while the air in the upper layers speeds up. The spectra presented by Bysova et al. (1967) for heights of 25, 75, 150, and 300 m seem also to show an important contribution at frequencies near 1 cycle/24 hr, the highest contributions being found at 300 m. The diurnal variation presented in table 4 for the different stations shows a remarkable variability from year to year. We have the impression that all this varia- bility cannot be explained away by changes in exposure of the wind instruments and that there may well be a September 1969 Abraham H. Oort and Albion Taylor 631 EST 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 I 2 3 4 5 I MIDDAY MIDNIGHT Figure 6. — Diurnal variation of wind speed (m sec-1) with height at Brookhaven National Laboratory, Long Island (after Singer and Raynor, 1957). KINETIC ENERGY - / / y '""* "N \ \ \ ' / \ ' :;--- :s£7 Xv " ■ Figure 7. — Ten-year average of the kinetic energy as a function of local time at Caribou, Old Town, and Portland, Maine; Detroit and Sault Sainte Marie, Mich.; and Duluth, Minn. 009 0.15 027 047 081 144 2 51 PERIOD (DAYS) - 437 762 133 212 404 707 t22 2C m - SPECTRUM U CARIBOU . MAINE (|75-I49M2SEC'2) - - - - - L0GeF 1 ' \y^ 0.0 SPECTRUM U+ SPECTRUM V _ CARIBOU, MAINE {cP-t- v^-joom'sec*2) - 6.0 - - " - - - 2.0 -^^^^y w A - v VA, , - LGGe F 1 1 1 >^ long-term cycle superposed. However, we do not want to pursue this topic further since this is beyond the aim of our present investigation. Our purpose in showing the results for the different years is to make clear that the diurnal cycle shows up in the results for each year. THE LACK OF A DIURNAL CYCLE IN THE SPECTRUM OF THE ZONAL AND MERIDIONAL WIND COMPONENTS It may be of interest to compare the present results with the spectrum obtained from separate analyses of the west-to-east (it) and the south-to-north (v) components of the wind (fig. 8). In the second type of analysis there is a significant increase (by a factor of 3) in total variance because the wind direction adds a new degree of freedom. However, the most interesting difference (compare figs. 4 Figure 8. — Spectra of the west-to-east (u) and the south-to-north (v) components of the wind for Caribou, Maine, determined from 10 yr of hourly wind reports. Frequency F in cycles 4096 days. and 8) lies in the fact that the diurnal peak does not show more prominently in the ;/- and r-spectra. The lack of an important diurnal cycle in the zonal and meridional wind components is indeed very surprising. The interpretation is probably that the wind direction at the stations considered is — at least near the surface — highly variable and that it does not change systematically during the course of a day. The 10-yr mean u- and r- components and the total wind speed as a function of the time of the day are shown in figure 9. If stations with strong land- and sea-breeze effects had been selected 632 MONTHLY WEATHER REVIEW Vol. 97, No. 9 6 - CARIBOU. MAINE NOON 12 14 16 EST (HR ) 20 22 24 Figure 9. — Ten-year average of the zonal (u), the meridional («) wind component and the total wind speed (|v|) as a function of local time. in this study, the diurnal cycle would certainly have been more prominent in their u- and I'-spectra. We might also mention the strong annual periodicity in the ^-component of the wind, which does not show up in the u-component. The same is true for the other stations in Maine (not shown here). However, in the cases of Detroit and Sault Sainte Marie the annual period is most dominant in the u-component, while for Duluth both the it- and y-components show an important annual cycle. It is not obvious what causes these differences in the u- and y-spectra. THE DIURNAL SPIKE IN THE KINETIC ENERGY SPECTRUM From the kinetic energy spectra as shown in figure 5, the diunial band was selected for further study. The logarithm of the individual power estimates (not multi- plied by the frequency) is graphed on a linear frequency scale in figure 10. A sharp spike at exactly 24 hr dominates the picture. However, a little distance away from this spike the in- tensity drops off rapidly. In addition to the main peak, there are on both sides secondary maxima of about equal intensity. A plausible explanation for the occurrence of these side lobes, which are located at a distance of about 4 min from the peak, seems to lie in an analogy with the "beating" phenomenon in acoustics. Our basic assumption is that the amplitude A of the diurnal cycle in the kinetic energy is not constant throughout the year, but has an annual variation A=At+A2 cos(2wt/T), where t is measured in days and T= 365.25 days. A spectral analysis would show at 24 hr the intensity of that part (Ai) of the diurnal cycle which is constant. However, the remaining signal would be interpreted as being the sum effect of two cycles at (1 + 1/365.25) and (1 - 1/365.25) cycles per day, corresponding with periods of respectively 24.066 hr and 23.934 hr. These frequencies are indicated in figure 10 by arrows. A cos(2tt<) = (/1i+^2 cos(2irt/T)) cos(2irf) =AX cos(2*0 + (l/2)vl2 cos 2wt(l + l/T) + (l/2)A2cos2wt{l-l/T). With some imagination one can also detect a weaker semiannual modulation of the diurnal cycle at periods of 24.13 hr and 23.87 hr. The meaning of this effect is that the modulation during the year is not a pure sine wave but that also higher harmonics are involved. In order to test our hypothesis for this beating phe- nomenon, we investigated the diurnal cycle in January and in July (fig. 11). Indeed, the results show that there is a strong annual modulation of the diurnal cycle. The largest amplitude is found during July, when there is the strongest convective exchange between the surface and higher levels. Finally, we would like to comment on one other inter- esting feature shown in figure 10, i.e., the close cor- respondence in magnitude and shape of the diurnal spike and to a lesser degree of the side lobes between the differ- ent stations. One would expect that the intensity in the diurnal cycle would be strongly dependent on the latitude and longitude of the station, in the sense that the intensity would increase with decreasing latitude and also with increasing continentality. However, the stations used in this study are not particularly suitable for investigating these questions. 6. SUMMARY AND CONCLUSIONS The spectrum of horizontal wind speed was analyzed using 10 yr of 1-min-averaged hourly surface reports for a group of stations in the northeastern United States and another group near the Great Lakes. The fast Fourier transform technique was used to estimate the spectrum between periods of about 2 hr and 2 yr. The results were compared with the earlier work of Van der Hoven (1957) for Brookhaven, Long Island. It was found that most of the effects of aliasing are confined to frequencies between the folding frequency of 1 cycle/2 hr and 1 cycle/ 12 hr. After assuming a reasonable shape for the small-scale turbulence maximum in the September 1 969 Abraham H. Oort and Albion Taylor 633 2407 2400 2393 (HR J i i 2407 2400 2393 (HR ) 1 ^T 4060 4080 4100 4120 4140 F (CYCLES /4096 DAYS) 0.001 0.0001 i i L SAULT STE. MARIE DIURNAL PEAK 001 0.001 0.0001 L LlI CO 0.01 %- 0.001 o CL 0.0001 i r — i 1 ii 4060 4080 4100 4120 4140 F (CYCLES /4096DAYS) 0.001 0.0001 Figure 10. — Plot of the individual power estimates (m2 sec-2 per elementary frequency interval) versus frequency near the diurnal period minute range, the spectrum for Caribou, Maine, was corrected for the aliasing from frequencies between 1 cycle/1 min and 1 cycle/2 hr. With regard to the final form of the spectrum as shown in figure 4, the following comments can be made: 1) Any reasonable method of correcting for the effects of aliasing seems to lead to quite small values for the spectrum near the folding frequency of 1 cycle/2 hr. This finding is compatible with the existence of a wide spectral gap between the small-scale turbulence maximum near a period of 2 min and the mesoscale phenomena at periods of a few hours. The existence of such a gap in the spectrum was first discussed by Van der Hoven (1957) and has been most extensively documented by the atmospheric turbu- lence group at The Pennsylvania State University under Professor Hans A. Panofsky. The present study shows that there is some evidence for a spectral gap even if one uses a very long time series. 2) Most of the variance of the wind speed is explained by the activity of traveling cyclones and anticyclones at periods roughly between 2 and 7 days. This agrees quite well with Van der Hoven's results. 3) A large peak in the kinetic energy spectrum was found at the diurnal period and a minor peak at the semi- 634 MONTHLY WEATHER REVIEW Vol. 97, No. 9 KINETIC ENERGY CARIBOU , MAINE ® JANUARY X JULV NOON L Table 3. — Continued 8 10 12 14 16 18 20 22 24 EST (HR ) — Figure 11. — Ten-month mean kinetic energy for January and for July as a function of local time at Caribou, Maine. Table 3. — Data on the power spectrum of the horizontal wind speed at Caribou, Maine. Hourly data cover the period Jan. 1, 1949, through Dec. 31, 1958. Band N PE (days) Log.F P PXF (m2 sec-2) DF 1 8630 0.09 10.75 0.03 1.33 4346 2 7710 .10 10.64 .03 1.22 3923 3 6900 .11 10.53 .03 1.13 3287 4 6180 .12 10.42 .03 1.00 2929 5 5520 .14 10.30 .04 .99 2796 6 4950 .15 10.19 .04 1.02 2388 7 4420 .17 10.08 .04 .98 2236 8 3960 .19 U.97 .0o .98 1945 9 3540 .21 9.86 .05 .90 1752 10 3170 .24 9.75 .05 .94 1567 11 2840 .27 9.64 .06 .86 1351 12 2530 .30 9.53 .07 .91 1284 13 2270 .33 9.42 .08 1.00 989 14 2040 .37 9.31 .08 .92 996 15 1810 .42 9.19 .08 .83 883 16 1630 .47 9.08 .12 1.03 777 17 1450 .52 8.97 .19 1.47 243 18 1310 .58 8.86 .14 .96 614 19 1160 .65 8.75 .17 1.04 618 20 1040 .73 8.64 .19 1.07 508 21 940 .81 8.53 .28 1.41 476 22 830 .91 8.42 .29 1.30 388 23 442 1.03 8.29 1.45 5.79 6 24 396 1.15 8.18 .45 1.61 201 25 354 1.29 8.07 .45 1.42 182 26 317 1.44 7.96 .55 1.56 148 27 284 1.61 7.85 .68 1.49 129 28 253 1.80 7.73 .77 1.76 142 29 227 2.01 7.62 .93 1.89 104 Band N PE (days) Log.F P PXF (m2sec-2) DF 30 204 2.24 7.51 1.07 1.96 99 31 181 2.51 7.40 1.38 2.26 98 32 163 2.80 7.29 1.71 2.51 82 33 145 3.13 7.18 2.32 3.04 65 34 131 3.50 7.07 2.05 2.41 66 35 116 3.91 6.96 3.08 3.23 63 36 104 4.37 6.84 2.61 2.45 55 37 94 4.88. 6.73 2.46 2.06 55 38 83 5.46' 6.62 4.10 3.08 44 39 75 6.10 6.51 3.15 2.12 32 40 67 6.82 6.40 2.88 1.73 34 41 59 7.62 6.29 4.03 2.17 35 42 54 8.52 6.18 2.90 1.40 29 43 48 9.52 6.06 4.29 1.85 25 44 42 10.6 5.95 2.57 .99 22 45 39 11.9 5.84 3.05 1.05 21 46 34 13.3 5.73 3.28 1.01 23 47 31 14.9 5.62 2.78 .77 21 48 27 16.6 5.51 2.92 .72 11 49 25 18.6 5.40 2.96 .66 17 50 22 20.8 5.29 1.68 .33 11 51 19 23.2 5.18 1.49 .27 11 52 18 25.9 5.06 2.22 .35 10 53 16 29.0 4.95 3.14 .44 8 54 14 32.4 4.84 4.61 .58 9 55 12 36.1 4.74 2.58 .29 5 56 12 40.4 4.62 3.53 .36 8 57 10 45.3 4.50 2.33 .21 7 58 9 50.6 4.39 4.65 .38 5 59 8 56.6 4.28 5.42 .39 4 60 7 63.1 4.17 3.44 .22 4 61 7 70.7 4.06 4.84 .28 5 62 5 78.8 3.95 4.93 .26 4 63 5 87.2 3.85 2.o! .12 5 64 5 97.6 3.74 5.17 22 4 65 4 109. 3 62 4.54 .17 66 4 122. 3.51 2.11 .07 67 3 3 137. 152. 3.40 3.29 3.86 1.83 .12 .05 68 69 3 171. 191. 3.18 3.07 2.34 10.70 .06 .23 70 71 2 210. 2.97 9.80 . 19 72 234. 2.86 .65 .11 73 2 265. 2.74 2.22 .03 74 2 304. 2.60 9.50 .13 75 1 1 1 1 1 1 1 341. 372. 410. 455. 512. 585. 683. 2.48 2.40 2.30 2.20 2.08 1.95 1.79 48.94 80.85 7.97 6.01 3.40 2.51 10.86 .59 .89 .08 .05 .03 .02 .01 76 77 78 79 80 81 JV=number of spectral estimates in frequency band. 7^5= mean period in band (days). F=mean frequency in band (cycles per 4,096 days). P=mean power density in band (m2 sec-2 per elementary frequency interval, where elementary frequency interval =1 cycle/4,096 days). PxJ'=mean spectral intensity in band (m2 sec-2). Log, F = natural logarithm of mean frequency in band. DF = number of equivalent degrees of freedom for estimate of P in band and = NTVpi (see Blackman and Tukey, 1958, p. 24). Note that the following relation should hold: 81 81 /_ _\ total variance windspeed=y^ NjX.Pj = 0- 1 1 1 S ( -PX^ ) ' where the constant o.m represents the band width in log.F units. diurnal period. Van der Hoven (1957) did not find the diurnal peak, probably because his data were taken near the top of the surface layer (about 100 m). Blackadar's September 1969 Abraham H. Oort and Albion Taylor Table 4. — Hourly kinetic energy (m.2 sec~2) 635 Station Year 1 15.7 18.7 13.4 10.9 11.7 11.4 11.6 10.3 11.8 12.5 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Daily average CAR 1949 15.1 18.2 13.5 10.8 11.2 11.8 11.9 11.2 12.0 11.8 14.4 18.1 13.0 10.6 10.7 11.0 11.7 11.6 11.6 11.2 15.1 19.0 12.3 10.4 10.9 11.4 12.2 10.3 11.5 11.5 15.2 18.7 12.5 10.8 10.7 10.8 11.8 10.7 11.7 11.6 15.2 19.3 12.7 10.7 10.5 11.7 11.6 10.7 11.4 11.1 16.3 21.0 13.7 11.7 11.5 12.2 11.9 11.6 13.2 11.6 17.9 22.2 14.9 13.5 13.7 13.8 13.4 12.8 14.0 14.4 21.3 26.5 17.4 15.6 16.2 15.5 15.5 16.3 16.4 15.6 23.6 29.1 19.3 17.8 17.6 16.9 17.7 17.6 18.1 18.6 24.2 31.2 19.7 18.9 19.7 18.9 19.9 19.9 20.0 20.1 25.6 33.6 20.9 20.1 20.0 19.6 21.2 20.8 22.4 21.7 27.0 34.7 21.6 21.6 20.8 20.2 22.6 21.0 23.4 21.8 27.0 35.5 22.1 21.5 21.0 21.3 21.8 21.8 24.2 22.6 27.9 32.6 22.2 21.9 21.9 19.9 20.9 21.3 24.1 22.5 25.7 33.1 21.0 20.1 21.0 18.7 18.6 20.3 23.2 21.4 23.7 29.6 19.4 18.4 18.9 17.3 18.1 19.1 20.0 18.9 20.7 25.7 16.5 15.5 16.0 15.8 15.3 15.9 17.0 17.3 17.9 22.1 14.9 13.6 13.4 14.5 13.9 12.5 14.7 15.2 16.7 22.1 14.4 13.0 13.7 14.2 13.1 12.4 13.1 14.7 15.7 21.3 14.3 11.8 13.0 12.7 12.5 11.0 12.7 13.9 15.3 22.5 12.9 11.9 12.2 12.5 12.1 11.1 12.3 13.0 15.5 ilS. 0 19.5 46.9° N. 68 0° W 1950.. 1951 21.0 13.0 11.6 19.3 12.9 11.0 24.8 16.2 (est) 1952 14.7 1953 11.8 11.0 12.1 11.3 11.1 11.2 10.5 10.7 11.8 11.5 15.0 1954 14.8 1955. 1956 --- 15.1 14.6 1957 15.9 1958 10-yr average. 1949 1950 1951 12.2 12.2 15.7 12.8 12.7 4.0 5.9 5.2 4.7 3.6 3.7 4.3 3.4 4.3 4.6 12.4 12.4 3.7 5.6 4.9 5.0 3.4 3.4 4.5 3.4 4.2 4.9 12.5 12.5 13.5 15.1 5.5 9.5 7.0 7.5 5.9 5.9 6.6 5.2 6.0 6.2 17.6 7.1 11.1 8.7 8.5 7.3 7.1 8.3 6.4 7.4 7.5 19.6 21.2 22.7 23.5 23.9 23.5 22.3 20.3 17.6 15.3 14.7 13.9 13.6 13.1 12.6 16.6 OLD 44.9° N. 68.7° W. 3.9 5.7 4.5 4.6 3.7 3.5 4.3 3.6 4.2 4.8 3.6 5.8 4.8 4.6 3.5 3.8 4.5 3.4 4.1 4.8 3.8 6.0 4.8 4.8 3.4 3.7 4.8 3.4 3.8 4.7 4.0 6.3 5.0 5.2 3.6 3.7 5.1 3.6 4.1 4.8 5.0 7.3 6.1 5.8 4.3 4.5 5.5 4.3 4.5 5.1 7.9 14.3 10.6 10.2 8.3 8.5 10.7 7.6 8.3 8.8 8.6 15.4 11.9 11.8 10.8 9.2 11.4 9.1 9.3 10.3 9.4 16.5 13.0 12.5 10.7 10.1 13.0 10.0 10.5 10.9 10.2 18.6 13.4 13.5 11.6 10.3 13.5 10.3 11.1 11.9 10.7 17.4 13.9 13.9 11.8 10.5 14.3 10.6 12.2 11.8 11.0 17.9 13.2 13.2 11.8 10.7 13.2 10.8 12.0 11.3 10.5 17.1 11.8 12.4 10.4 9.8 13.0 9.9 11.5 11.0 9.4 14.2 10.4 11.3 9.6 8.2 11.2 8.7 10.4 10.2 7.5 12.0 8.6 8.8 8.0 7.0 9.1 7.5 8.7 8.9 6.1 9.7 6.5 7.4 6.1 6.0 7.1 6.2 7.1 7.9 5.0 7.7 6.0 6.9 5.9 4.9 6.6 5.5 6.6 6.9 4.6 7.6 5.3 6.1 4.7 4.7 5.7 4.9 5.4 5.8 4.2 6.8 5.1 5.8 4.4 4.2 5.1 4.3 4.8 5.4 3.6 6.7 5.2 5.0 4.2 3.9 4.6 3.9 4.7 5.5 3.9 6.3 4.9 4.8 3.7 3.8 4.2 4.1 4.6 4.9 6.4 10.5 7.9 (est) 1952 1953 8.1 6.7 1954. 1955 6.3 7.9 1956 6.3 1957 7.1 1958 10-yr average.. 1949 1950... 1951 1952... 1953 7.5 4.3 4.0 5.0 6.3 6.5 7.9 8.2 8.2 7.1 9.1 11.8 4.4 4.1 5.4 6.3 6.7 8.2 7.9 8.2 7.3 9.0 11.9 4.3 4.3 4.6 5.3 6.8 6.7 8.1 7.6 8.4 7.1 9.3 11.9 4.3 4.5 4.2 5.2 6.8 6.3 7.7 7.9 9.0 7.1 9.2 12.0 5.2 6.5 7.9 6.8 7.2 9.5 9.4 11.5 11.5 12.4 9.3 12.5 16.8 9.5 10.7 8.5 9.6 11.5 12.2 15.8 14.8 15.7 12.2 17.4 20.7 11.6 12.4 10.9 11.8 13.7 14.3 17.8 16.4 18.5 13.9 21.3 21.6 12.7 11.1 12.5 14.6 14.1 18.2 17.7 18.4 13.6 22.3 23.8 12.5 10.7 12.0 14.2 14.2 18.3 17.3 18.1 13.5 22.3 24.1 11.7 10.4 8.6 7.0 6.2 5.5 4.4 6.3 7.4 7.2 9.2 8.7 10.3 8.0 10.3 13.3 5.0 4.7 4.5 7.5 PWM 43.7° N. 70.3° W. (EST) 4.3 5.2 6.6 6.6 7.8 7.5 8.7 7.0 8.5 11.9 4.4 5.6 7.0 6.3 8.1 7.8 8.4 6.7 8.4 11.7 4.7 5.7 7.1 6.9 8.3 8.7 9.2 7.3 9.6 13.2 5.6 6.7 8.3 7.9 0.5 9.6 11.1 8.6 10.6 14.0 8.1 8.2 10.9 10.9 14.5 13.6 13.5 11.1 14.6 18.9 9.5 10.4 13.2 12.9- 16.7 16.4 17.5 13.4 19.7 21.0 10.4 12.0 13.4 13.5 16.2 15.9 17.3 12.8 21.7 22.6 8.4 10.4 11.7 11.9 14.5 14.2 15.5 11.8 19.8 21.1 6.3 8.7 10.0 9.7 13.1 11.7 12.4 10.5 16.7 18.7 5.0 7.7 8.9 8.7 10.9 10.3 11.0 9.4 13.7 15.4 4.9 6.7 7.8 8.1 9.7 9.2 10.8 8.5 12.5 13.6 4.7 6.2 7.0 7.0 8.5 8.5 9.2 7.5 10.2 12.4 4.2 5.7 6.7 6.8 8.5 8.7 9.0 7.4 9.6 12.8 4.0 5.8 6.3 6.8 8.1 8.7 8.3 7.1 9.0 12.3 6.4 7.7 9.2 9.2 11.5 1954 - 1955 11.1 12.0 1956 1957 1958 10-yr average. 1949 1950 1951 9.5 13.6 16.1 7.4 7.5 9.4 9.1 8.8 8.6 9.9 9.5 8.8 9.0 10.7 11.7 7.4 7.6 7.4 7.5 8.1 9.2 10.7 11.7 10.5 9.8 10.8 10.7 11.4 11.2 10.9 12.8 12.8 12.4 13.8 15.1 16.1 16.6 16.5 15.6 13.9 11.8 10.1 9.2 8.5 8.1 7.9 7.7 10.7 DET 42.4° N. 83.0° W. 9.6 9.3 9.3 8.9 9.4 10.1 9.1 8.8 11.3 12.0 10.0 9.2 8.8 8.3 9.3 9.5 8.4 8.7 10.4 11.7 9.5 8.4 9.0 8.5 8.9 9.0 8.4 8.5 10.6 11.5 9.1 9.1 8.6 8.4 9.3 9.4 8.9 8.7 10.2 11.1 9.5 8.6 8.3 8.4 8.9 8.8 8.6 8.8 10.3 10.7 9.3 9.0 8.5 8.6 9.3 9.7 9.0 9.0 10.6 11.0 10.3 9.8 9.0 9.1 10.2 10.3 9.7 9.7 11.2 11.3 13.3 11.3 11.4 11.8 11.8 13.6 12.3 12.2 13.7 14.3 14.7 12.3 12.6 13.4 12.8 14.7 13.7 13.6 15.1 16.3 15.4 13.1 12.9 13.9 13.9 15.3 14.5 14.5 16.9 18.3 16.6 13.9 14.0 15.0 14.7 15.6 15.3 14.8 17.7 19.4 18.0 14.6 14.5 16.0 15.8 16.9 16.5 15.9 17.9 20.6 18.1 15.0 14.4 16.2 16.1 17.6 16.8 15.8 18.7 21.1 17.4 14.8 14.2 15.9 16.0 18.0 16.3 15.9 18.7 20.9 16.9 14.3 13.8 15.4 14.8 16.9 15.8 15.1 18.3 21.0 14.7 13.6 13.4 14.9 13.6 15.7 15.0 14.1 17.1 20.2 14.2 12.4 11.6 12.5 12.2 13.7 13.0 12.7 15.8 18.2 11.7 11.1 10.7 11.7 11.6 12.1 11.7 11.1 14.0 16.7 10.6 10.7 9.7 11.0 10.7 11.0 10.7 10.5 13.3 15.1 10.8 9.8 9.9 10.2 10.4 11.0 10.6 10.0 12.5 13.6 10.7 10. -j 9.8 9.5 10.2 10.3 9.6 9.4 12.2 13.2 10.0 10.2 9.6 9.7 9.6 10.3 9.3 9.3 11.6 12.3 12.6 11.3 10.9 (EST) 1952. 1953 11.5 11.7 1954 12.5 1955 11.8 1956 11.5 1957 13.8 1958 15.2 9.8 8.9 7.9 7.7 7.8 7.7 7.7 7.7 7.3 9.1 8.9 9.6 9.4 8.0 8.1 7.9 7.3 7.8 6.9 8.1 6.9 8.4 7.9 9.2 9.3 9.1 9.4 10.0 9.4 8.7 7.5 7.6 7.5 8.1 8.1 7.6 8.8 8.4 11.2 12.6 13.9 14.9 15.7 16.7 17.0 16.8 16.2 15.2 13.6 12. 2 11.3 10.9 10.5 10.2 12.3 1949 1959 1951.. 1952 1953 1954 1955. 1956 1957 1958 SSM 46.5° N. 84.4° W. (EST) 8.5 8.6 7.7 7.0 7.3 7.3 7.6 7.4 8.6 9.0 7.9 26.7 20.6 13.4 15.1 14.6 16.1 17.3 16.1 14.7 15.7 8.5 8.1 7.5 6.9 7.3 6.7 7.8 7.2 8.3 7.9 8.3 7.7 7.8 7.4 7.8 7.2 7.3 7.1 8.2 7.8 8.4 8.1 7.8 6.9 7.4 7.5 7.3 7.2 8.1 7.7 8.6 7.8 7.5 7.3 7.4 7.6 7.4 7.5 8.5 7.9 9.9 8.7 8.1 8.6 8.3 8.9 9.0 8.4 9.6 9.5 11.0 10.6 9.6 9.6 9.5 10.2 10.2 9.1 11.0 10.4 12.6 11.6 10.4 10.8 10.5 11.1 11.4 10.6 12.5 12.0 14.8 13.1 11.8 12.5 11.7 12.3 12.8 11.9 13.8 13.4 16.4 13.7 12.9 13.8 13.0 13.8 14.1 12.8 16.6 15.3 16.9 14.9 13.6 14.9 14.0 15.3 14.9 13.2 17.4 16.8 17.1 14.7 15.1 14.9 14.5 15.2 15.8 13.7 19.0 18.0 17.1 14.7 14.4 14.8 14.3 15.0 16.0 14.6 19.2 18.6 17.0 13.9 13.9 14.5 14.0 14.8 15.5 14.6 18.8 18.7 15.4 12.3 12.7 13.2 13.0 13.1 13.1 12.5 17.0 17.2 13.1 10.9 11.1 11.2 11.1 11.6 11.3 11.3 15.3 16.1 11.8 9.8 9.8 10.0 10.1 10.4 10.2 10.4 13.8 14.7 10.3 9.5 8.7 8.6 9.0 8.7 9.3 9.1 11.9 11.6 9.9 8.8 8.8 7.9 8.3 S. 0 8.7 8.5 10.8 10.6 9.9 8.3 8.3 8.1 8.0 7.7 S.4 7.8 10.0 10.4 8.9 7.9 7.6 7.7 7.5 7.6 8.3 7.6 9.5 9.6 11.7 10.3 9.9 10.0 9.9 10.1 10.4 9.8 12.3 12. 0 10-yr average 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 10-yr average 8.1 25.6 20.7 13.5 14.3 14.9 16.8 17.8 16.4 15.2 15.3 7.7 7.6 7.7 7.7 7.8 8.2 8.9 10.1 11.4 12.8 14.3 15.2 15.8 15.9 15.6 13.9 12.3 28.2 23.9 16.6 18.1 20.5 20.9 20.1 21. 9 20.5 21.9 11.1 9.7 9.1 8.7 .1.2 10.6 DLH 46.8° N. 92.2° W. (CST) 26.4 21.2 13.3 13.7 14.2 15.4 17.0 16.5 14.3 16.5 26.4 22.3 12.8 14.3 14.4 15.5 17.0 16.9 14.8 17.1 26.6 23.7 12.7 15.0 14.8 16.1 16.5 16.5 15.4 16.2 26.5 22.9 13.3 14.7 14.0 15.9 16.5 16.4 14.9 15.8 26.9 23.6 13.9 13.9 14.5 16.0 16.8 17.5 15.6 16.2 26.8 24.8 14.2 15.0 16.1 17.3 17.3 18.1 16.3 17.1 28.8 25.6 15.1 15.6 18.3 19.1 19.1 19.5 17.4 17.9 30.7 25.8 16.4 17.9 19.7 20.6 19.7 21.6 18.6 19.3 33.3 26.1 19.0 20.0 22.0 23.3 21.5 22.6 20.8 21.1 34.7 27.4 20.6 21.4 22.9 '23.8 23.5 24.2 22.5 23.1 34.8 27.8 20.7 21.9 23.4 24.3 24.5 24.7 23.6 24.9 36.7 27.9 21.7 23.3 24.4 25.0 25.1 26. 2 25.0 25.5 36.9 27.7 21.2 22.3 24.7 25.6 24.1 25.1 24.3 25.0 36.7 27.9 21.1 23.1 24.4 24.4 24.7 25.1 24.8 25.5 35.5 28.4 20.4 22.4 24.1 24.6 24.4 25.1 24.3 24.7 31.8 26.5 18.8 20.4 22.5 22. S 22.0 23.1 ::. s 23.3 27. 1 22.4 15.2 16.2 18.4 19.3 IS. 7 19.9 lv 1 19.3 24 0 20.1 13.5 14 ■! 16.1 16.9 it. : 15 4 16.3 16.4 24. S 20. 7 13.0 14.8 15.6 16.5 17.0 17.8 15.4 15.3 26.2 21.8 13.8 14.4 15.5 16. 5 17.3 17.6 16.1 15.7 24.8 21.3 13.4 14.0 15.0 16.3 17.7 IP. 7 is .; i?. i 29.4 24. 2 16. 2 17.4 18.5 19.5 19.7 20. 2 IS. 6 19.3 17.0 17.0 16.9 17.1 17.4 17.1 17.5 18.3 19.6 21.1 23.0 24.4 25.1 26.1 25.7 25.8 25.4 23.4 21.3 19.4 17.4 17.1 17..=. 17.0 20.3 636 MONTHLY WEATHER REVIEW Vol. 97, No. 9 theory (1959) adequately explains the differences between Van der Hoven's and our results. 4) At low frequencies in the spectrum beyond the cyclone rise, most activity is found in the annual and semi- annual periods. The stations used in this study are confined to a latitude belt between 42° N. and 47° N. One may expect that there will be a general shift in importance of the diurnal and annual peaks and of the cyclone rise, if one would study stations at a different latitude. Through a comparison with the spectra of the zonal and meridional wind components, it is shown that the diurnal cycle in the wind speed is not accompanied by a similar cycle in the wind direction. The diurnal variation in the kinetic energy near the surface with a maximum between 2 and 3 p.m. is in evidence at each of the six stations and for each of the 10 yr. A closer look at the individual estimates that make up the diurnal peak in the spectrum shows, in addition to the mean spike at 24 hr, side lobes which are probably due to the annual modulation of the diurnal cycle. The diurnal cycle is found to be more pronounced in July than in January. This is what one might expect with a more intense vertical exchange of kinetic energy between the surface and upper levels during the summer. APPENDIX Table 3 supplies more detailed information on the spectral estimates and their accuracy for Caribou, Maine. Table 4 gives the average kinetic energy as a function of time of the day for the six stations and the 10 yr studied. ACKNOWLEDGMENTS Copies of the data tapes used in this study were kindly supplied to us by Mr. Howard M. Frazier of the Travelers Research Center, Inc. We would like to acknowledge the help of the following people at the Geophysical Fluid Dynamics Laboratory, ESSA: Mr. Henry Stambler for writing the unpacking program for the data tapes, Mr. Richard Stoner for drawing the figures, and Mrs. C. T. Morgan for typing the manuscript. REFERENCES Bingham. C, Godfrey, M. D., and Tukey, J. W., "Modern Tech- niques of Power Spectrum Estimation," IEEE Transactions on Audio and Electroacoustics, Vol. AU-15, No. 2, June 1967, pp. 56-66. Blackadar, A. K., "Periodic Wind Variations," Mineral Industries, Vol. 28, No. 4, College of Mineral Industries, The Pennsylvania State University, University Park, Jan. 1959, pp. 1-5. Blackman, R. B., and Tukey, J. W., The Measurement of Power Spectra, Dover Publications, Inc., New York, 1958, 190 pp., (see pp. 14, 15, and 21-25). Busch, N. E., and Panofsky, H. A., "Recent Spectra of Atmospheric Turbulence," Quarterly Journal of the Royal Meteorological Society, Vol. 94, No. 400, Apr. 1968, pp. 132-148. Bysova, N. L., Ivanov, V. N., and Morozov, S. A., "Characteristics of the Wind Velocity and Temperature Fluctuations in the Atmospheric Boundary Layer," Proceedings of the International Colloquium on the Fine-Scale Structure, Moscow, June 15-22, 1966, Izdatvo Nauka, Moscow, 1967. pp. 76-92. Cooley, J. W., and Tukey, J. W., "An Algorithm for the Machine Calculation of Complex Fourier Series," Mathematics of Com- pulation, Vol. 19, No. 91, Apr. 1965, pp. 297-301. Group of Audio and Electroacoustics, Subcommittee on Measure- ment Concepts, "What Is the Fast Fourier Transform?" IEEE Transactions on Audio and Electroacoustics, Vol. AU-15, No. 2, June 1967, pp. 45-55. Hinich, M. J., and Clay, C. S., "The Application of the Discrete Fourier Transform in the Estimation of Power Spectra, Co- herence, and Bispectra of Geophysical Data," Reviews of Geo- physics, Vol. 6, No. 3, Aug. 1968, pp. 347-363. Holloway, J. L., Jr., "Smoothing and Filtering of Time Series and Space Fields," Advances in Geophysics, Vol. 4, 1958, pp. 351-390. Singer, I. A., and Raynor, G. S., "Analysis of Meteorological Tower Data April 1950-March 1952 Brookhaven National Laboratory," Brookhaven National Laboratory Report No. BNL 461 (T-102), Contract No. (AFCRC-TR-57-220), Upton, N.Y., June 1957, 93 pp., (see p. 34). U.S. Weather Bureau, Local Climalological Data — With Com- parative Data, for the stations Caribou, Maine, Portland, Maine, Detroit, Mich., Sault Sainte Marie, Mich., Duluth, Minn., published in Asheville, N.C., 1958. Van der Hoven, I., "Power Spectrum of Horizontal Wind Speed in the Frequency Range from 0.0007 to 900 Cycles Per Hour," Journal of Meteorology, Vol. 14, No. 2, Apr. 1957, pp. 160-164. [Received February 24, 1969; revised April 10, 1969] CORRECTION NOTICE Vol. 97, No. 3, March 1969, p. 286, next to the last sentence: "Moscow Airport in Idaho reported — 50°F, on the 30th, the coldest December tem- perature of record in the State." is incorrect and should be deleted. Reprinted from Journal of Applied Meteorology, The American gg Meteorological Society, Vol. 8, No. 1, 92-104. 92 JOUR N A L OK APPLIED MF.TKOROI.O G Y Volume 8 The Importance of Natural Glaciation on the Modification of Tropical Maritime Cumuli by Silver Iodide Seeding Robert I. Sax Atmospheric Physics avd Chemistry Laboratory, l-.SSA , Coral Gables, h'la. (Manuscript received 21 August 1%8, in revised form 7 November I%8) In order to determine if natural glaciation proceeds rapidly or extensively enough in tropical maritime cumuli to influence attempts to modify their dynamical behavior by seeding with silver iodide, a detailed study was made of the clouds observed during the 1965 Project Stormfury experiments. Krom photographic coverage, notes on visual observations, and instrumentation on-board penetrating aircraft, data were compiled on cloud liquid water content, volume-median drop size, in-cloud temperature profile, and the dynamical life histories of both seeded and non-seeded clouds. The validity of applying Koenig's numerical splintering model to t ropical maritime cumuli, as well as an assessment of the effectiveness of silver iodide seeding, were determined by comparing the dynamical behavior of paired seeded and non-seeded clouds with glaciation times predicted by the model. Dynamical studies were initiated on two independently developed parametrized numerical cumulus models, and an excellent correlation between predicted and observed cumulus growth was found if no natural glaciation at temperatures > — 15C was assumed. The results of this study suggest that natural glaciation does not proceed rapidly and/or extensively enough in the critical cloud updraft areas to alter the effectiveness of modifying tropical maritime cumuli bv causing artificial glaciation with silver iodide. 1. Introduction The technique of modifying supercooled cumuli by silver iodide seeding is based on the idea that silver iodide particles will act as freezing nuclei at a much higher temperature than naturally-occurring nuclei. Instead of remaining liquid until temperatures of the order of — 25C have been reached, the seeded cloud can freeze and release its latent heat of fusion in the tem- perature range of -4 to -8C, thus gaining additional buoyancy. The cumulus growth resulting from the in- creased buoyancy can best be demonstrated on days when an existing inversion layer is strong enough to prevent penetration by the natural, unseeded cumuli, but not sufficiently strong to prevent penetration by the warmed, seeded cumuli. Explosive cumulus growth can occur if the atmosphere above such an inversion is un- stable and not too drv. Such a seeding modification hypothesis based on a growtli increase caused by buoyancy from fusion heat- ing fundamentally assumes that the organized updraft region of the cloud remains essentially liquid until the time of seeding. 1 ne effectiveness of artificial seeding would be drastically reduced if a significant portion of the water content in an updraft area is rapidly consumed by ice from natural glaciation at temperatures> - 15C. In the extreme case of rapid natural glaciation of up- draft water content near temperatures of — 5C, no change in growth behavior between seeded and non- seeded clouds could be expected. From a cumulus modification viewpoint, therefore, observations of ice particles existing in cumuli topping below the —ISC level are particularly important. A great deal of evidence has accumulated during the past decade giving credence to the idea that ice occurs far more frequently at temperatures > — 15C in the free atmosphere than previously thought possible, and ap- parently in greater concentrations than can be ex- plained by the presence of nattiral freezing nuclei. Murgatroyd and Garrod (1960) found significant quan- tities of ice in British cumuli whose tops were no colder than —11C. Koenig (1963) showed evidence from the University of Chicago's Project Whitetop experiments indicating that approximately 30% of the cumulus clouds sttidied in Missouri completely glaciated, ap- parently naturally, at temperatures > — IOC. Mossop el al. (1968) report finding ice crystals in an Australian cumulus cloud which never reached a temperature <— 4C. Koenig (1968) sampled ice particles in Cali- fornian orographic clouds which failed to grow above the — 9C isotherm. The author himself has observed evidence of ice particles al "warm" temperatures during an ESSA cloud physics project in Puerto Rico during the summer of 1967. Although the presence of some isolated large ice particles at temperatures > — IOC can be explained by a stochastic freezing process (Gokhale, 1965), a com- plete and rapid glaciation of natural clouds would certainly require a more efficient process. Hypothesizing that large water droplets eject splinters of ice as they freeze, and that such splinters can act as freezing nuclei for other liquid droplets which, in turn, eject more splinters as they freeze, Koenig (1966). using laboratory I-EBKUAKY 1969 ROBERT I . S A X 93 Table 1. Theoretical time for natural cloud glaciation by the ice-splintering mechanism as a function of cloud liquid water and mean drop size (after Koenig, 1966). % of cloud LWC glaciated Cloud LWC , (g/m)3 Average Drop Diom. (microns) Time (seconds) Average Drop Diam. (microns) T ime (seconds) Average Drop Diam. (microns) Time ( seconds) 10 0-5 30 760 60 550 90 500 10 1-0 30 420 60 320 90 300 10 20 30 240 60 Not Computed 90 180 50 0-5 30 860 60 640 90 600 50 1-0 30 460 60 380 90 340 50 2-0 30 270 60 Not Computed 90 210 95 0-5 30 1280 60 910 90 880 95 1-0 30 660 60 520 90 500 95 2-0 30 400 60 Not Computed 90 280 data on splinter production as studied by Latham and Mason (1961), devised a numerical model for a chain- reaction type of ice-multiplication glaciation in cumuli topping at temperatures > — IOC. His computed glaci- ation times are a function of the cloud's liquid water content and drop-size distribution, but turn out to be remarkably insensitive to the number of initial ice par- ticles present in the cloud. A summary of his results, based on an initial 10 ^ ice particle concentration of 1 m~3, is given in Table 1. The above computations have strong implications on dynamical cumulus modification by silver iodide seed- ing. The predicted time for 95% glaciation by a natural ice-multiplication mechanism in a cloud with a broad drop-size distribution is within the 5-10 min needed for complete artificial glaciation by silver iodide seeding. It would appear to follow that trying to induce artificial glaciation by seeding clouds possessing a broad drop size distribution, such as tropical maritime cumuli, should be ineffective in altering the life history of such clouds since almost complete natural glaciation by an ice-multiplication mechanism is predicted to occur in approximately the same time interval. This study is an attempt to determine if natural glaciation occurs both significantly and rapidly enough in tropical mari- time cumuli to impair the effectiveness of cumulus modification by artificial seeding techniques. 2. Analytical procedure and acquisition of data All data were obtained from the 1965 Project Storm- fury cumulus modification experiments during which randomized seeding operations were conducted on 23 tropical maritime cumuli in the Caribbean. Only 14 of the clouds were actually seeded, the remainder being used as control clouds. Two ESSA DC-6 aircraft, equipped to measure such physical parameters as liquid water content, volume-median drop size, ambient tem- perature, humidity, wind speed and direction, and ver- tical accelerations, made cloud penetrations at 10,000 and 1Q,000 ft, and a Naval Research Laboratory air- craft, equipped with a Formvar replicating device (Averitt and Ruskin, 1967) penetrated clouds at the 17,000-ft level. The cloud's life history was carefully analyzed from 16-mm color motion pictures taken from the command and control aircraft (a radar-equipped WC-121) and from 35-mm movies taken from both sides of the two DC-6 penetrating aircraft. Color slides and Hasselblad pictures, along with the original notes taken by meteorologists on board the various partici- pating aircraft provided a clear reconstruction of the cloud's growth from time of first visual sighting. The liquid water data were obtained by means of a Johnson-Williams meter in combination with a hot wire instrument described in detail by Levine (1965). Es- sentially, this system consists of a nickel-iron wire loop cloud unit sensitive to drops<100/u in diameter, and a rain instrument made of the same kind of wire wound on a grooved ceramic cone and sensitive to drops> 100 fj. in diameter. Because the responses of the two instru- ments are dependent upon drop size, the volume-median drop diameter can be determined if a drop distribution is assumed.1 In order to test the applicability of the splintering model to the Stormfury clouds, it was necessary to focus attention on an analysis of physical parameters such 1 An exponential log-normal distribution was assumed, both for calibration of the instrument and for the actual clouds. In this case the volume-median corresponds closely with the mean, and the two terms can be interchanged without introducing a large error. 94 JOURNAL OF APPLIED METEOROLOGY Volume 8 Table 2. Liquid water contents and volume-median drop sizes for nine clouds studied during Project Stormfury. (JW refers to the Johnson-Williams meter.) Dot* (1965) Cloud Run Seed or No Seed Average JW LWC (g/m3) Average Total LWC (g/m3) SLWC greater than JW size drops Average Volume Median Drop Size (microns) Maximum LWC (total) g/m3 Flight Altitude (feet) 28 July 1 1 No Seed 0-31 107 71 67 31 19,000 3 1 Seed 0-27 0-79 66 83 1-6 19,000 29 July 1 2 Seed 0-31 113 73 85 21 19,000 1 2 Seed 013 108 88 99 1-7 10,000 2 1 No Seed 0-12 0-50 76 132 10 19,000 3 August 4 2 Seed 0-14 0-46 70 109 0-6 19,000 5 August 3 1 Seed 013 0-43 70 120 1-6 19,000 1 1 No Seed - 015 - - 0-3 19,000 10 August 2 1 No Seed 0-29 1-30 78 89 2-1 19,000 3 1 Seed 0-19 0-79 76 105 1-8 19,000 J as cloud liquid water content profile, volume-median drop size, cloud life history, and environmental con- ditions. This also served to point out any internal physical differences between the control and seeded Stormfury clouds. In order to determine if natural glaci- ation is important enough to alter the effectiveness of silver iodide seeding in tropical maritime cumuli, the behavior of the Stormfury clouds was analyzed by using two independently developed dynamical models, both of which assumed no natural glaciation at temperatures > — 15C. If natural glaciation is as rapid and wide- spread in the updraft regions of tropical maritime cumuli as the splintering model seems to imply, the dy- namical models would not be expected to give a good correlation between predicted and observed cloud top heights, particularly for the non-seeded cases. 3. Discussion of the physical analysis Reliable physical data from the Levine instrument could only be obtained at the 19,000-ft penetration level for nine of the Stormfury clouds, five of which were seeded.2 A complete summary of the data obtained is shown in Table 2. With the exception of the 5 August control cloud, these cases had water contents and vol- ume-median drop sizes comparable to those used in Koenig's calculations (Table 1), thus enabling their time of glaciation by an ice-multiplication mechanism to be easily predicted. A good test for the validity of Koenig's model could be made by determining if natural 2 Because of the abundance of large drops in tropical cumuli, the Levine cloud instrument wire frequently broke and data were lost; the problem of preventing such breakage is currently being studied by ESSA's Research Flight Facility. glaciation occurred in these clouds in the time and to the extent predicted by the model. Because the NRL aircraft could not fly above 17,000 ft, the Formvar replicator was sampling at temperatures too warm for mixed phase conditions except on 5 August when the freezing level was exceptionally low and the sampling took place at — 4C. Except for 5 August, therefore, direct evidence of the extent of cloud glacia- tion could not be obtained, and an indirect deductive means of determining natural glaciation had to be used. If a cloud fails to grow above a certain level for a sub- stantial period of time (15-20 min), and is then seeded, any sudden growth of the cloud can most likely be attributed to additional buoyancy caused by the latent heat release of freezing water. Significant growth can only occur if a large percentage of the cloudy updraft area is supercooled liquid water at the time of seeding. Also, if a seeded cloud can grow, while an unseeded cloud, possessing the same physical properties, is unable to grow in an identical environment, such behavioral difference can most likely be attributed to fusion heat release and rules out the possibility of rapid natural glaciation in the unseeded case. Such an analysis of the dynamical behavior of the Stormfury clouds was used as the primary means of assessing the rate and impor- tance of a natural glaciation mechanism and its effect on the modification of tropical maritime cumuli by silver iodide seeding. 4. The cloud data Table 3 summarizes the important data analyzed for each of the nine clouds thought to have reliable Levine water measurements. Fig. 1 gives the temperature pro- February 1969 ROBERT I. SAX Table 3. Supercooling times and cloud growth histories for nine clouds studied during Project Stormfury. 95 Dots (1965) Action Time of First observotion To (GMT) Top Temp at To CO Time of Action Tl (GMT) Top Temp at Tl (°Q Time Supercooled until Action Time (min) Growth to Action Time (to Growth after Action Time (ft) Totol T ime of Supercooling Control Coses (min) 28 July Control Seed 2010:00 2202:30 -60 -7-5 2033 00 2217:30 -80 -5-0 23-0 150 1500 -1500 2500 17500 30-0 (Seeded) 29 July Seed Control 1755:00 1920:00 -90 -9-0 1810:30 1929:30 -190 -140 15-5 9-5 4000 2500 14000 None (Seeded) 150 3 August Seed 2142:00 -19-0 2158:30 -22-0 16-5 2500 10500 (Seeded) 5 August Control Seed 1641:00 1747:30 -90 -120 1657:30 1805:30 -140 -180 16-5 18-0 2000 4000 4000 11000 210 (Seeded) 10 August Control Seed 1913.00 1940:00 -110 -8-0 1916:00 1957:30 -110 -17-0 Unknown 17*5 None 4000 None 14000 Unknown (Seeded) file through each cloud (except for the 5 August con- the center, thus accounting both for its extreme dryness trol) as measured at 19,000 ft by the vortex thermom- and for the temperature profile omission. The following eter onboard the DC-6. The 5 August control cloud was brief analysis of each cloud has been given in much penetrated incorrectly at the edge instead of through greater detail by Sax (1967). •7-0 7-5 •8-0 8-5 SEEDED CASE 28 JULY STARTING TIME 2202:00 CONTROL CASE 28 JULY STARTING TIME 2033:00 4-0 -SEEDED CASE 29 JULY ^-v 4-5 -STARTING TIME 1817:00/' N. 5-0 / V 5-5 / \ 6-0 / ^ •6-5 -7-0 J 1 1 ■ 1 1 1 1 1 7-0 ■8-0 CONTROL CASE 29 JULY STARTING TIME 1926:00 SEEDED CASE 5 AUGUST STARTING TIME 1759:00 40 -CONTROL CASE 10 AUGUST 4-5 -STARTING -^ — S. 5-0 -time r \ 5-5 -1916:00 / \ 6-0 / X. 6-5 / A^ 70 7-5 1 1 I 1 I i i 10 20 30 40 50 00 TIME IN SECONDS 10 SEEDED CASE 10 AUGUST STARTING TIME 1953:00 10 20 30 40 50 00 TIME IN SECONDS Fig. 1. Temperature profiles at the 19,000-ft level for eight of the Stormfury clouds. 96 JOURNAL OF APPLIED M K T KOKOI.OGY Vol v mk 8 MAXIMUM 3-1 g.m3 28 JULY 1965 ALTITUDE 19,000' NO SEED •VOLUME MEDIAN DROP SIZE fi •TOTAL LWC (g,'m3) •JW LWC (g/m3) _L 2-8 2-4 2-0 - 1-6 -1-2 0-8 - 0-4 - 0 -60 -40 2033:30 50 00 TIME (SEC) Fig. 2. Physical profile at the 19,000 ft level; 28 July control cloud. a. 28 July Good physical measurements were obtained for both a seeded and a control cloud on this day, the control cloud's 19,000-ft physical profile being shown in Fig. 2. This cloud was observed to exist with its upper level at a temperature < — 6C for 23 min prior to penetration, and a further 7 min after penetration, but the cloud could grow no higher than to the 24,000-f t level (— 18C). The steadiness of the temperature profile (Fig. 1) indi- cates the absence of a strong warm updraft in the upper 28 JULY 1965 ALTITUDE 19,000 SEED MAXIMUM 1'6 g/m3 AVERAGE LWC 079 g/m3 ■ VOLUME MEDIAN DROP SIZE // — TOTAL LWC (g/m3) ■" JW LWC (g/m3) 2202:00 30 40 TIME (SEC) 16 12 0 8 0-4 140 120 100 80 60 40 Fig. 3. Physical profile at the 19,000-ft level; 28 July seeded cloud (before seeding). portion of the cloud. Assuming that a few "primary" ice particles (1 m-3) were able to form early in the cloud's existence as it approached the —IOC isotherm, the splintering calculations predict that about 9 min would be sufficient time for this cloud to achieve 95% glaciation. If such glaciation actually did occur in this short time interval in the control cloud, then 24,000 ft should represent an upper limit to the growth of a seeded cloud possessing similar physical characteristics STORMFURY CUMULUS 1965 SEEDED CLOUD 28 JULY AFTER SEEDING < 2.5 mm radius should freeze at — 10C in 25 sec, and 50% of such drops should freeze in the same time at — 14.5C. The large volume- median drop sizes in both the seeded and control cases (Fig. 5 and Fig. 6) would seem to indicate that such large droplets should have been present in these clouds to provide an adequate source of primary ice particles for ice-multiplication initiation. This would be par- ticularly true in the case of the seeded cloud with its strong supporting updraft. The failure of the seeded cloud on this day to exhibit much growth prior to seeding, and the failure of the control cloud to grow at all, even though both clouds were supercooled at temperatures < — 10C for a suffi- cient amount of time to completely glaciate according to the splintering model, indicates that the model cal- culations greatly overpredicted the extent and/or rate of natural glaciation in these clouds. The 15.500-ft growth increase in the seeded turret indicates that natural glaciation does not proceed efficiently enough 3 AUGUST 1965 ALTITUDE 19,000' SEED ■VOLUME MEDIAN DROP SIZE /i •TOTAL LWC (g/m3) ■JW LWC (g/m3) J_ 1 2 0-6 - 160 -140 120 - 100 - 80 2157,00 20 30 TIME (SEC) 40 50 00 Fig. 7. Physical profile at the 19,000 ft level; 3 August seeded cloud (before seeding). to interfere with the effectiveness of the artificial seeding of tropical maritime cumuli. c. 3 A agnst The only case available for this day was a seeded cloud which had its upper 4000 ft supercooled well below — 15C for 16^ min prior to seeding, but managed to grow only 2500 ft during that time. After seeding, however, the seeded turret grew 10,500 ft in 14 min and separated from the main cloud mass. Comparing the cloud's physical profile shown in Fig. 7 with the splintering criteria i;; Table 1, it can be seen that this cloud should have been 95% glaciated at least a full 3 min before it was seeded. The dynamical behavior of the cloud, how- ever, strongly refutes the idea that it had completely glaciated before seeding. The sudden increase in cloud buoyancy shortly after seeding can reasonably be attri- buted to warming caused by a mass amount of fusion heat release, an impossible condition for a cloud already fully glaciated. The cloud's long supercooling time at such a low temperature should theoretically insure a primary ice concentration of 1 irr3, but the ice ap- parently could not propagate throughout the cloud as rapidly as predicted by the splintering model. The ex- tent of natural glaciation in this cloud was apparently not sufficient to interfere with the effectiveness of the silver iodide seeding. February 1960 ROBERT I . SAX 99 5 AUGUST 1965 l\ ALTITUDE 19,000' SEED kl AVERAGE LWC . 1 1 0-43 g,m3 ' — wn M ,M? y we si y CENTRAL •v h / VOLUME MEDIAN DROP SIZE u TOTAL LWC (g/m3) i i JW LWC (g/m3) 1 1 1 1 I 1759:20 40 50 00 TIME (SEC) -1-6 - 1-2 - 0-4 Fig. 8. Physical profile at the 19,000 ft level; 5 August seeded cloud (before seeding). d. 5 August The control cloud for this day topped at 26,000 ft (— 14C) and was supercooled below — 9C for at least 21 min. Unfortunately, the DC-6 penetration of this cloud was incorrectly made through an extremely dry edge instead of through the center, thus making it im- possible to compare the physical characteristics of this cloud with the splintering criteria presented in Table 1. In contrast, a great deal of work has already been published about the seeded cloud for this day (Ruskin, 1967; Simpson 1967). As can be seen from Fig. 8, this cloud possessed two distinct turrets, a rather wet western turret and a dry central turret. The central turret was the oldest part of the cloud and had existed above the 21,000 ft level (-12C) for at least 18 min before beginning to dissipate near the time of seeding. As can be seen from Fig. 9, the western turret was a young, growing area which had existed above 19,000 ft (— 7C) for 6 min at the time of seeding. The splintering calculations (Table 1) predict that, at the time of seed- ing, the central turret should have been 95% glaciated while the western turret should have been about 10% glaciated. Formvar replication data were available for the western turret at the 17,000 ft level ( — 4C) shortly before the time of seeding. Using a method similar to Averitt and Ruskin (1967), a detailed ice-to-water per- centage area analysis was made from the Formvar sec- tions which did not contain large graupel pellets or shattered liquid droplets. As P"ig. 10 indicates, the average concentration of ice in the western turret just before seeding time was 20%, but a localized pocket of up to 50% ice existed in a small area near the cloud edge. This is roughly in agreement with a similar analysis on the same cloud performed by Ruskin (1967). The low water content of the central turret made a quantitative estimate of ice impossible for that portion but, in small areas where good data were available, the central turret appeared somewhat more glaciated than the western. The presence of significant quantities of ice in the young western turret lends support to a multiplication mechanism since the number of natural freezing nuclei active at — 8C cannot account for the large amount of ice throughout the turret. However, the old central B GROWTH OF 5 AUGUST SEEDED CLOUD o CENTRE TOWER (NOT SEEDED) o— l-o RADAR o--o — o PHOTO D WESTERN TOWER (SEEDED) O-J-O RADAR 0---CJ--0 PHOTO * SEEDER AIRCRAFT REPORT 10 12 TIME 26 28 Fig. 9. Growth of the 5 August seeded cloud. 100 J O U R N A L OF A P P L I E D M E T E O R O L O G Y Voi.umk 8 i TOTAL TIME 10 SEC , r* AVERAGE ICE TO WATER RATIO 21% "' 50% 5 AUGUST 1965 A MAXIMUM ICE/WATER 50% FORMVAR DATA A 40% at IU •- 30% < o UJ y 20% /#— A — ■ h\ L'' \ n \ I \* k n \x A' / \ s 1 x 1 \ * //A/ \ * // y \ C\ A' \ / **A If \ / 10^ 10 FRAME AVERAGE 0 1 1 1 1 30 FRAME AVERAGE I I l I i i i < 12,350 380 410 440 470 500 530 TIME 30 FRAMES SEC 560 590 620 12.650 Fig. 10. Ice-to-water area percentage from Formvar data for 5 August seeded cloud. Abscissa is in frame number, 30 frames being equivalent to 1 sec or 100 m. turret had reached the — 18C level by the time of the Formvar sampling, and there is a possibility that the western turret was contaminated by ice particles filter- ing down from above. It is also not clear just how much of the observed ice was actually liquid freezing on impact with the cold Formvar. Although not conclusive, the presence of small pockets of up to 50% ice concen- tration in this cloud at — 4C may be indicative of a multiplication mechanism working on a localized scale near the edges of the cloud, but not necessarily spread- ing throughout the entire cloud. In any event the dynamical behavior of the two turrets works against an efficient large scale natural glaciation theory. According to the formvar evidence from a penetration just after seeding, the western turret was able to completely glaciate within 5 min after the silver iodide was released, and it managed to grow 10,500 ft higher than the unseeded central turret. If natural glaciation proceeded as rapidly and as extensively through tropical maritime cumuli as envis- aged by the splintering model, it would be very difficult to explain the failure of the central core to grow in a similar manner as the seeded turret. It is interesting to observe that arguments for some kind of an ice-multiplication process working on a less extensive scale and proceeding less rapidly than en- visioned by Koenig can be advanced from a study of this cloud. This is especially significant in view of the fact that this was the only Stormfury case that had good Formvar replication data at the required temperature. e. 10 A ugust Although the only two Stormfury clouds randomly selected for intensive studv on this dav were both seeded, excellent physical data were obtained on a penetration through a non-seeded cloud. Particularly noticeable in this control cloud's physical profile shown in Fig. 11 is the large volume-median size of the drops. This is consistent with observations of rain falling from cloud base during the entire 5 min it was under observa- tion. Although the cloud topped at — 11C (about — 7C in the active, warm updraft core) when first observed, it quickly rained out and began to dissipate. Unfortu- nately, the cloud's history prior to the first observation is not known, thus making it impossible to determine the total time of supercooling and relating its behavior to the splintering hypothesis. Good physical data were not obtained on penetra- tions of this day's first seeded cloud, but the second seeded case provided the profile shown in Fig. 12. First observed topping near — 8C, this cloud grew 4000 ft to the — 17C level in the 18 min leading up to the time of seeding. In 30 min following seeding, the cloud's growth rate accelerated as it grew an additional 14,000 ft. The splintering calculations predict that this seeded cloud should have been 95% glaciated some 8 min be- fore the time of seeding. However, the cloud's dynami- cal behavior is not consistent with such a prediction. The pronounced acceleration of cloud growth after seeding strongly implies fusion heat release through silver iodide nucleation, a condition requiring an essen- tially supercooled liquid state in the seeded area at the time of seeding. The large height increase of the seeded cloud again serves to point out the effectiveness of artificial glaciation under the right conditions in tropical maritime cumuli. February 1969 ROBERT I . SAX 101 5. Discussion of the dynamical modeling Although it is both useful and interesting to try to evaluate the efficiency of ice multiplication by physi- cally and dynamically examining a cloud's life history in retrospect, a much more effective way of deter- mining the importance of natural glaciation on cumulus modification is to predict beforehand the behavior of a certain size cloud in a given environment assuming the complete absence of natural glaciation and then testing the predictions on actual clouds. Likewise, from a suitable numerical model of cumulus dynamics it should be possible to predict the effects of seeding before the actual seeding experiment is conducted. Tf the clouds, after seeding, behaved as predicted by a model that assumes no natural glaciation at a tem- perature warmer than — 15C, and if the unseeded clouds also behaved as predicted by such a model, it would be very hard to understand how natural glaciation at temperatures warmer than — 15C could be a significant process in altering the dynamics of cumuli. Two such independently developed numerical models were used to predict the behavior of all 23 clouds studied in the 1965 Project Stormfury experiments. The model used by the Experimental Meteorology Branch (EMB) of ESSA has been described by Simpson et al. (1965). MAXIMUM 21 g/m3 H AVERAGE LWC 1-30 g/m3 -2-0 1-6 1-2 10 AUGUST 1965 ALTITUDE 19,000' NO SEED VOLUME MEDIAN DROP SIZE TOTAL LWC (g/m3) 0-8 0-4 JW LWC (g, „3, 160 140 120 - 100 - 80 60 -40 J_ 191600 10 20 30 40 50 Ot TIME (SEC) Fie. 11. Physical profile at the 19,000 ft level; 10 August control cloud. MAXIMUM 1-8 g/mJ H AVERAGE LWC 0-79 g/m3 10 AUGUST 1965 ALTITUDE 19,000' SEED •VOLUME MEDIAN DROP SIZE fX ■TOTAL LWC (g/m3) ■ JW LWC (g/m3) 1-8 1-2 0-8 - 0-4 - 0 160 140 120 100 80 60 40 _L. 1953=00 20 30 TIME (SEC) Fig. 12. Physical profile at the 19,000-ft level; 10 August seeded cloud (before seeding). The model used at The Pennsylvania State University (PSU) is a steady-state modification of a time-depen- dent model developed and described bv Weinstein and Davis (1968). Essentially, the EMB model calculation consisted of integrating the vertical equation of motion for the rising cloud tower, which is assumed to behave as a rising plume with a vortically circulating cap, entrain- ing environmental air at a rate inversely proportional to its horizontal dimension. The vertical acceleration of the center of the cloud tower is expressed as the dif- ference between buoyancy and drag forces. The buoy- ancy force is a function of the temperature excess of the cloud over the environmental air, and is reduced by entrainment and by the weight of the condensed water within the cloud. The drag forces consist of momentum exchange from entrainment and a small aerodynamic effect. One-half of the cloud's liquid water was assumed to fall out of the cloud at each integration step. The model has recently been modified to include micro- physical interactions (Simpson et al., 1968). The PSU model does not deal directly with the verti- cal acceleration of a cloud turret, but rather with con- version of kinetic energy to updraft velocity. The pro- duction of energy is again a function of the temperature excess of the cloud over the environmen'al air, the drag of the cloud's liquid water, and an entrainment param- 102 JOURNAL OF APPLIED METEOROLOGY Volume 8 eter. A constant vertical mass flux through the cloud is assumed, thus allowing the updraft radius to be a func- tion of the vertical velocity. The cloud's liquid water is partitioned into cloud water and hydrometeor water by assuming autoconversion and accretion rates, and all of the hydrometeor water is carried until the cloud reaches its maximum height, at which time it is released. Although the two models approach the energetics of cloud growth from slightly different directions, the thermodynamic and entrainment calculations are handled in roughly the same manner. Both models re- quire an environmental sounding, cloud base height, and the appropriate cloud radius as input data, and both compute cloud temperature excess, liquid water content, vertical velocity profiles, and maximum cloud height as output. In practice, neither model assumes glaciation to occur naturally at temperatures > — ISC. If the cloud were seeded, a subroutine was introduced which allowed the latent heat of fusion to be released linearly between — 4 and -8C (EMB model), or completely at -6C (PSU model). Both models then assumed ice saturated con- ditions, thus accounting for additional warming as water vapor sublimed onto the ice instead of condensing into water. Given an environmental sounding and the cloud base height, it was thus possible to predict cloud top heights of both the seeded and the non-seeded Storm- fury clouds on both models if an in-cloud updraft radius could be chosen for the PSU model corresponding to the turret radius used in the EMB model. 6. Results of the dynamical modeling A composite summary of the modeling results is given in Table 4. The chosen PSU model radius is an extrapolation into the cloud body of the turret radius Table 4. Comparison of the EMB cumulus model with the PSU model : Results from he 1965 Project Stormfury experiments. Cld Radius EMB Model Predict PSU Model Predict Obs Max EMB Diff (km) PSU Diff (km) Time Cloud Action Unfroz Seed Unfroz Seed Top EMB (m)PSU Cld Ht (Km) Cld Ht (Km) (Km) 28 July 2058 1 Contr 500 1400 6-4 9-8 14-2 14-4 6-3 .0-1 .7-9 2217:30 2 Seed 550 2850 6-7 10-5 15-6 15-7 10-5 0 »5-2 2033 3 Contr 650 2000 7-8 11-9 14-9 15-1 7-4 -0-4 *7-5 29 July 1810:30 1 Seed 1150 1700 7-6 12-4 6-6 12-1 11-6 .0-8 .0-5 1929:30 2 Contr 1100 1700 7-0 11*9 6-6 12-1 6-8 -0-2 -0-2 2044:30 3 Contr 1150 2000 7-6 12-4 8-2 12-9 7-8 -0-2 *0-4 2126:30 4 Seed 800 1350 5-4 5-4 5-2 5-2 5-4 0 -0-2 2205:30 5 Seed 800 1350 5-4 5-4 5-2 5-2 50 .0-4 • 0-2 1 August 2013:30 1 Seed 800 1500 60 6-0 5-7 5-9 6-2 -0-2 -0-3 3 Auqust 2158:30 1 Seed 1000 1800 9-4 11-1 10-0 11-2 11-2 -0-1 0 4 August* 1825:30 1 Contr 950 1500 8-5 10-4 8-2 10-2 9-9 -1-4 -1-7 2144:30 2 Seed 650 1100 6-3 7-1 6-7 7-5 7-4 -0-3 • 0-1 5 August 1657:30 1 Contr 1000 1500 8-4 12-9 7-5 12-9 8-4 0 -0-9 1805:30 2 Seed 850 1250 7-0 11-9 6-3 11-9 11-0 ♦ 0-9 .0-9 8 August 1636:30 1 Contr 1200 2300 7-2 8-6 6-1 7-0 7-0 .0-2 -0-9 1703:30 2 Seed 900 2100 6-4 6-5 5-9 6-4 6-4 -0-1 0 9 August 1727:30 1 Contr 700 1200 8-4 9-8 8-7 11-1 8-3 ♦ 0-1 • 0-4 1740:30 2 Seed 850 1250 9-5 11-2 9-2 11-4 11-2 0 ♦ 0-2 1847:30 3 Contr 1200 1400 6-8 7-5 5-3 5-3 6-5 »0-3 -1-2 1944:30 4 Seed 700 2100 8-4 9-8 13-7 13-9 10-2 -0-4 .3-7 2022:30 5 Seed 1300 2000 7-1 9-2 5-8 6-8 8-7 .0-5 -1-9 10 August 1813:30 1 Seed 900 1300 8-6 10-6 7-9 10-2 10-2 ,0-4 o 1957:30 2 Seed 1100 1 1500 9-7 12-0 8-3 11-2 11-4 -0-6 J -0.2 _ at - lie- inT^^f Z PAfP bS 7" " °^le,f m Predl**f 'he 4 August control case could he resolved if the cloud naturallv glaciated at 15C, in that case he EMB model pred.cts a top height of 10.0 km, while the PSU model predicts a top heiaht of 98 km The cloud grew to 9.9 km. This is the only case for modeling support for natural glaciation at temper UureO- V February 1969 ROBERT I . S A X 103 used by the E1IB model. Although admittedly this is a very subjective technique, it was performed prior to the model calculations to eliminate bias. As can be seen from Table 4, the PSU model cloud top heights were generally in good agreement both with those predicted by the EMB model and with the actual observed cloud heights, with the notable exception of the three clouds on 28 July. A careful re-examination of the cloud photographs for this day revealed that the radii chosen for the PSU model were almost a factor of 2 too large, and this error was compounded by an un- stable environment above 20,000 ft which allowed very buoyant clouds at that level to grow naturally all the way to the tropopause. Because the cloud's buoyancy, computations are a function of entrainment, which in turn is a function of the cloud's horizontal dimension, the error in choosing the cloud radii on this day was critical and caused the PSU model to overpredict cloud growth by an embarrassing 50%. The statistical results of the modeling are graphically portrayed in Figs. 13 and 14. If the EMB model predictions are compared with the observed maximum heights of all 23 Stormfury clouds, a correlation co- efficient of 0.98 is established by the results. Excluding the three clouds on 28 July from the analysis, the corre- lation coefficient between the PSU model predictions and the observed maximum height of 20 Stormfury clouds is 0.92. Such results strongly imply that natural glaciation 9 10 11 OBSERVED HEIGHT (Km) Fig. 13. Experimental Meteorology Branch (EMB) model pre- dicted cloud top heights vs observed cloud top heights for all 23 Stormfury clouds. The correlation coefficient is 0.98. The triangu- lar symbols give the EMB model predicted cloud top heights for natural glaciation at — 8C (of the extent predicted by the splinter- ing model) vs the observed cloud top heights. Only the six Storm- fury clouds with long, documented life histories and good micro- physical data cloud were used in this particular analysis. The correlation coefficient between predicted heights and observed heights for these six cases is a rather poor 0.43, indicating that the splintering model glaciated these clouds too rapidly. C 13 12 o y 1 11 po ^ ■"" C l;l LINE t- X olO LU X Q £ 9 - PSU MODEL D PREDICTIONS UJ DC °- 8 - O D a VS. OBSERVED HEIGHTS ALL CASES 7 D O EXCEPT 28 JULY 6 /o D o SEEDED CASES D CONTROL CASES X) I D i l I i i i I 8 9 10 11 OBSERVED HEIGHT (Km) Fig. 14. Pennsylvania State University (PSU) model predicted cloud top heights vs observed cloud top heights; three cases on 28 July excluded from analysis. The correlation coefficient for these 20 clouds is 0.92. does not affect the dynamical behavior of tropical maritime cumuli, at least at temperatures > — 15C. Only for one cloud (control case of 4 August) do both models predict cloud heights better if natural glaciation is assumed at — 15C. Using a slightly different technique of analyzing the results of the model predictions, Simpson et al. (1967) demonstrate a very good correla- tion between seeding and growth which strongly indi- cates that natural glaciation is not nearly as efficient as artificial seeding by silver iodide in modifying the dy- namical behavior of tropical maritime cumuli. 7. Summary and conclusions In order to test the validity of Koenig's (1966) ice splintering model, and in order to determine if natural glaciation is important enough in tropical maritime cumuli to influence modification attempts by silver iodide seeding, a detailed study was made of cumuli observed during the 1965 Project Stormfury experi- ments. Physical data involving the water and tempera- ture profiles within the clouds were analyzed, and dy- namical studies were initiated on two independently developed numerical cumulus models. In the physical analysis it was found that all of the seeded clouds studied grew at least 10,000 ft higher than a paired control cloud in the same environment, thus indicating a strong cause-and-effect relationship be- tween seeding and growth. A very strong correlation between seeding and growth was later confirmed in the dynamical analysis. Some direct evidence of partial glaciation in a cloud topping at no colder than — 5C was found, but all of the clouds behaved dynamically in a manner indicating that their vital updraft areas 104 JOURNAL OF APPLIED METEOROLOGY VOLL'MI. 8 did not glaciate as rapidly as predicted by the splinter- ing model. The evidence suggested that the updraft core of a typical tropical maritime cumulus cloud can remain in a supercooled liquid state at temperatures of — IOC and colder for periods^ 20 min, and natural glaciation in such a cloud is not extensive enough to significantly influence its dynamical behavior. On the other hand, the results of the study indicate that artificial glaciation induced by silver iodide seeding is an effective means of modifying the dynamical behavior of such clouds by converting the cumulus updraft areas from supercooled water to ice at temperatures^ — 5C. The primary conclusion to be drawn from this study is that natural glaciation does not proceed rapidly and/ or extensively enough in the critical cloud updraft areas to alter the effectiveness of modifying tropical maritime cumuli by causing artificial glaciation with silver iodide. 8. Future studies Evidence now suggests that the occurrence of ice in clouds topping at temperatures near — IOC is far more prolific than can be explained by assuming a one-to-one relationship with active freezing nuclei. From the re- sults of this study, however, apparently the ice is not evenly distributed throughout the cloud body, as the vital updraft areas remain essentially supercooled liquid for long periods of time. It is possible that some kind of an ice-multiplication mechanism may be able to work near the cloud edge to glaciate local pockets, but cannot work effectively in the wetter updraft core. A better physical understanding of the behavior of freely-falling freezing water droplets in realistic atmo- spheric conditions is essential to the interpretation of an ice-multiplication mechanism. It now seems likely that the original laboratory work on splintering per- formed by Mason and Maybank (1960) may have greatly overestimated the efficiency of such a mecha- nism in the free atmosphere. Both Dye and Hobbs (1968) and Johnson and Hallett (1968) have failed to find copious splintering under more reasonable atmo- spheric conditions using rather large (1 mm) suspended drops, but more work now needs to be concentrated on both the freezing of small droplets in free fall and the importance of a riming mechanism on ice multiplication. Acknowledgments. The author is sincerely grateful to Dr. Joanne Simpson and the personnel of the Experi- mental Meteorology Branch for making the Stormfury data available for this study, and for offering much help- ful advice on a wide variety of topics related to the splintering mechanism and computer modeling. R. E. Ruskin and J. M. Averitt of the Naval Research Lab- oratory provided the Formvar tapes used in the analysis of the 5 August seeded cloud, and both devoted a great deal of their time in assisting with the interpretation of the data. The author wishes to express a special note of thanks to Dr. Larry G. Davis of The Pennsylvania State University faculty for initiating interest in the topic, and for providing much-needed encouragement and guidance on attacking the problem. REFERENCES Averitt, J. M., and R. E. Ruskin, 1967 : Cloud particle replication in Stormfury tropical cumulus. /. A ppl. Meteor., 6, 88-94 Dye, J. E., and P. V. Hobbs, 1968: The influence of environmental parameters on the freezing and fragmentation of suspended water drops. J. Atmos. Set., 25, 82-96. Gokhale, N. R., 1965: Dependence of freezing temperature of supercooled water drops on rate of cooling. /. Atmos. Sci., 22, 212-216. Johnson, D. A., and J. Hallett, 1968: Freezing and shattering of supercooled water drops. Quart. J. Roy. Meteor. Soc, 94, 468-482. Koenig, L. R., 1963: The glaciating behavior of small cumu- lonimbus clouds. J . Atmos. Sci., 20, 29-47. • , 1966: Numerical test of the validity of the drop-freezing/ splintering hypothesis of cloud glaciation. /. Atmos. Sci., 23, 726-740. , 1968: Some observations suggesting ice multiplication in the atmosphere. /. Atmos. Sci., 25, 460-463. Latham, J., and B. J. Mason, 1961 : Generation of electric charge associated with the formation of soft hail in thunderclouds. Proc. Roy. Soc. {London), A260, 537-549. Levine, J., 1965: The dynamics of cumulus convection in the trades: A combined observational and theoretical study. Woods Hole Oceanographic Institution, Ref. No. 65-43, 129 pp. Mason, B. J., and J. Maybank, 1960: The fragmentation and electrification of freezing water drops. Quart. J . Roy. Meteor. Soc, 86, 176-186. Mossop, S. C, R. E. Ruskin and K. J. Heffernan, 1968: Glaciation of a cumulus at approximately — 4C. J. Atmos. Sci., 25 889-899. Murgatroyd, R. J., and M. P. Garrod, 1960: Observations of precipitation elements in cumulus clouds. Quart. J. Roy. Meteor. Soc, 86, 167-175. Ruskin, R. E., 1967: Measurements of water-ice budget changes at — 5C in Agl-seeded tropical cumulus. J. A ppl. Meteor., 6, 72-81. Sax, R. I., 1967: Natural and artificial glaciation of tropical cumuli. NSF Rept. No. 9, Dept. of Meteorology, The Pennsylvania State University, 85 pp. Simpson, J., 1967 : Photographic and radar study of the Stormfury 5 August 1965 seeded cloud. /. A ppl. Meteor., 6, 82-87. , G. W. Brier and R. H. Simpson, 1967: Stormfury cumulus seeding experiment 1965: Statistical analysis and main results. /. Atmos. Sci., 24, 508-521. , R. H. Simpson, D. A. Andrews and M. A. Eaton, 1965: Experimental cumulus dynamics. Rn\ Geophys., 3, 387-431. , V. Wiggert and T. Mee, 1968: Models of seeding experi- ments on supercooled and warm cumulus clouds. Proc. First Natl. Conf. Weather Modification, Amer. Meteor. Soc, Albany, N. Y., 251-269. Weinstein, A. I., and L. G. Davis, 1968: A parametrized numerical model of cumulus convection. NSF Rept. No. 11, Dept. of Meteorology, The Pennsylvania State University, 44 pp. We.xler, R., and R. J. Donaldson, Jr., 1966: The spread of ice in cumulus clouds. J. Atmos. Sci., 23, 753-756. 57 Reprinted from Medical Opinion & Review Vol. 5, No. 10, 39-5) Science: Cloud Building and Breaking Joanne Simpson, Ph.D. Seeding clouds with silver iodide has been going on for more than twenty years, and, during all that time, controversy has been raging about it. Recently, the Experimental Meteorology Laboratory of the En- vironmental Science Services Ad- ministration (ESSA) jointly with the Naval Research Laboratory has been conducting research to clear up the controversy. To understand what is new and different about our approach to cloud seeding, we must know some- thing of the history of the subject. Cloud seeding dates back only to 1946, when Vincent Schaefer, at the General Electric Company, dis- covered that small pellets of dry ice could convert a supercooled water cloud into an ice cloud — at least, it could in his laboratory. The concept of supercooling is central to the theory of cloud seed- ing. Water may be cooled to a tem- perature below its freezing point but still not crystallize. When some nucleus is present around which the ice may grow, then crystallization will proceed in the familiar man- ner. After his laboratory work, Joanne Simpson is Director of the Experimental Meteorology Lab- oratory, U.S. Department of Com- merce Environmental Science Ser- vices Administration, and Adjunct Professor of Atmospheric Science at the University of Miami. Coral Gables October, 1969 Schaefer experimented in the real atmosphere, where he used dry ice to convert supercooled fogs and stratus clouds. He was frequently able to precipitate snow streamers, and many people still remember the impressive race-track patterns carved out by GE aircraft in super- cooled stratus decks. Silver Preferred Only a year later, in 1947, Ber- nard Vonnegut, also of GE, discov- ered that silver iodide was nearly as good a cloud nucleator as dry ice, presumably because its crystal structure so closely resembles that of ice. Vonnegut and his successors showed that silver iodide could be produced chemically in ground or airborne generators, making it lo- gistically more convenient than dry ice for seeding experiments. We are still using silver iodide. Schaefer and Vonnegut have ex- plained their cloud conversion in terms of the colloidal instability of a cloud of supercooled water. At temperatures colder than freezing, the saturation vapor pressure is higher over water than over ice, so that the introduction of ice crystals into a supercooled cloud releases the colloidal instability — that is, the ice crystals grow at the expense of the water drops until the cloud is glaciated. In the atmosphere, su- percooled clouds are common be- cause of scarcity of nuclei. The rain-making idea, originated CUMULUS EXPERIMENTS AIRCRAFT OPERATION LEVELS 30,000ft W-57 gX :^17-24.000ft 19,000ft_ 17,000ft^_ 10,000ft 2,000ft -H WC-121 A-3B DC-6 DC-4 Figure 1. Experimental design for cumulus-seeding experiment. Several aircraft are heavily instrumented with probes to measure temperature, hu- midity, winds, cloud water, rain water, particle habit and spectrum. Pyro- technic seeding-devices are dropped by jet aircraft at 100-meter intervals within bracketed arrows. 11.6km altitude by Schaefer and his colleague, No- bel Prize winner Irving Langmuir, went like this: in order for a cloud to rain, about one million tiny cloud drops, each about a thousandth of a centimeter in diameter, must some- how combine into one raindrop of about a millimeter in diameter. Rel- ative to the cloud, the drop can then fall and reach the ground without evaporation. One way to achieve this artificially would be to intro- duce one to ten artificial freezing nuclei per million supercooled drop- lets, or about one nucleus for each one to ten liters of cloudy air. The ice will fall as rain when it melts at a lower altitude. Let us call this the "static" theory of precipitation growth by seeding, since it ignores the motion structure of the cloud and possible cloud changes. Since an average cumulus might contain about ten trillion liters of supercooled cloudy air, and silver iodide generators provide roughly ten trillion nuclei per gram of ^l^i..^. 11,6km altitude ^-lkm altitude "EXPLOSION," FIRST PHASE "EXPLOSION," SECOND PHASE Figure 2. Scale outlines of the growth of a cloud fol- made every three to four minutes by photogrammetry lowing seeding. First phase of the explosion is shown from the command and control aircraft that were box- at the left: second phase, at the right. The outlines were ing the cloud. October, 1969 smoke, we need something like a few grams of silver iodide per cloud. This requirement is well within the capacity of the ground and airborne generators that have been in use for many years. One of the most carefully de- signed of the experiments based on the "static" hypothesis was Project Whitetop, a five-year program for seeding of summer cumulus clouds over Missouri. Project Whitetop was directed by an eminent meteo- rologist, Roscoe R. Braham, Ph.D., of the University of Chicago. Sta- tistical controls were applied both in space and time. Two disturbing results were ob- tained: first, the seeding apparently decreased rainfall by about 2 1 per- cent over an area of 1 00,000 square miles; second, Dr. Braham found that many rather warm, but still su- percooled, cumuli had plenty of natural ice already in them. In fact, he often found about one ice par- ticle per liter in unseeded clouds. Our ESSA group has duplicated these results over Florida and the Caribbean. Since the one ice particle per li- ter that Dr. Braham and we found was the amount supposed to be in- troduced by seeding, there should c D Figure 3. Explosive growth of same seeded cloud as shown in Figure 2. Typical GO cloud (A) is shown at time of seeding. 9 minutes later (B). 19 minutes after seeding (C), and 38 minutes after seeding (D), when the cumulonimbus is fully developed, top about 40,000 feet. have been precipitation. If the the- ory were correct, there would be no point to introducing much larger injections of ice nuclei, since these would result in "overseeding" the cloud. If too many ice nuclei were Figure 4. Typical ''cutoff" tower growth regime following seeding: A, cloud at seeding time: B. 10 minutes later: C, 18 minutes after seeding, when tower has reached 36,000 feet and cut off. October, 1969 introduced, it was believed, the cloud water would be shared among many small ice particles, and none of them would grow large enough to precipitate. In our own work, we chose a dif- ferent approach; ironically enough, overseeding was just what we de- cided to aim at because we intended to rapidly release the heat of freez- ing (fusion) in the supercooled water. We intended to increase the cloud buoyancy and hence enhance Figure 5. Typical "no-growth" re- gime. At 12 minutes after seeding, cloud looks unchanged except that top has glaciated. its updraft and vertical growth. When we first started our modifica- tion experiments, back in 1963, we were not directly concerned with increasing rainfall, although it was soon clear that increased rainfall was a likely by-product of the in- vigorated cloud dynamics. So we have proposed the "dy- namic" theory. From years of study of cumulus clouds, we had learned that their life cycle is a fierce strug- gle for existence, with the forces of growth and destruction in near bal- ance. Because it is very difficult to study by measurement a nearly bal- anced natural phenomenon, we wanted to upset the balance. This, we thought, would enable us to im- prove our numerical models of cumulus clouds. Floating on Air The main growth force in a cu- mulus is buoyancy. The air of the cloud has a lower density than the surrounding air. Gaseous water con- denses into the liquid droplets that make up the cloud; in the process, heat is released; thus the average tropical cumulus is warmer than its environment by about 0.5 to 1.0°C. Freezing its liquid water content of one to two grams per cubic meter can about double this excess and thereby double its buoy- ancy— if the freezing is done sud- denly in the cloud's ascending re- gion. A "seeding subroutine" that models this release of heat was in- troduced into our computer. For a real-life experiment, the technical means first appeared in 1963, when, for the first time, the massive-seeding techniques became available. These had been invented at the Naval Ordnance Test Sta- tion in California. The innovation consisted of generating silver iodide smoke by pyrotechnics or fireworks. These Navy pyrotechnic silver io- dide generators released 1.2 kilo- grams of silver iodide each. More- over, they could be dropped by an aircraft from above directly into the business portion of the cloud. In August, 1963, we conducted a preliminary pyrotechnic seeding experiment in the Caribbean area. Six clouds were seeded with about twenty kilograms of silver iodide per cloud — about one nucleus per cloud drop instead of one or a few per million, as the static theory re- quired. Four of the seeded clouds showed a spectacular or explosive growth following seeding; more- over, it appeared that our model could predict which clouds would grow, which would not. The validity of the results was viewed with some justifiable skep- ticism by the meteorological com- munity: there is a large, natural variability in clouds; the sample was small; and there was a possibil- ity of bias in the selection of clouds ( clearly, the clouds just might have grown as well by themselves, with- out seeding). Control System We had to apply statistical con- trol and randomization, in the same manner as in medical or biological research. The simplest randomiza- tion technique would be tossing a coin — heads you seed, tails you don't, but you do observe the cloud as a control. A series of sealed enve- lopes were prepared for us by a stat- istician and provided to the pilot of the seeder aircraft. He then fol- lowed the "seed-no-seed" instruc- tion without informing the project scientists what his action had been for any given cloud. In 1965, an extensive random- ized-seeding experiment was under- taken with seven aircraft in the Ca- ribbean area (see Figure 1 ). A stack of five instrumented aircraft make one penetration of the "GO" cloud before seeding and many penetra- Medical Opinion & Review tions after seeding to develop a com- plete picture of its before-and-af- ter structure. The jet seeder flies through cloud top between the first two measuring runs; it drops pyro- technics at 100-meter intervals, so that the smoke plumes completely fill the supercooled portion of the cloud top. A seventh aircraft (not shown in Figure 1 ) boxes the cloud and directs all the others on its ra- dar scope. It also takes radar and Figure 6. Development of tank "cloud" as function of time. Note circulationlike vortex ring as indicated by white streaks. The computer model of a cumulus — a set of equations predicting vertical rate of rise of a buoyant plume or bubble — was originally developed from laboratory experiments, such as this, carried out at the Imperial College in London and at the Woods Hole Oceanographic Institution in Massachusetts. Here a laboratory cloud, which consists of a blob of salt so- lution, is released into a resting tank of pure water. The cloud, being denser than its surroundings, moves downward. Its vortexlike circulation is made visible by neutral-density, white-painted particles. These ex- periments led to the laws of cloud-tower circulation and of mixing between cloud and its drier surroundings, which in nature is the main brake against buoyancy. October, 1969 49 motion pictures on time-lapse, so that the cloud growth can later be reconstructed ( Figure 2 ) . In 1965, we obtained twenty- three GO clouds, of which fourteen were seeded and nine were studied identically as controls. This experi- ment established definitively that massive silver iodide seeding could increase cloud growth, but under specifically initial conditions of the cloud-environment system. The ital- ics contain the meat of the result, which clarifies some of the seeding controversy. Seeding could lead to three quite different growth re- gimes, depending on the conditions ( Figures 3-5 ) . The first is explosive growth, where the cloud grows greatly in both height and size and becomes a full-fledged cumulonim- bus after twenty to thirty minutes ( Figure 3 ) . With this regime, we suspected that the rain falling from the cloud must have been consider- ably increased. In the second re- gime ( Figure 4 ) , the seeded tower grows to great heights, but it cuts off from the main cloud body, which may then dissipate prematurely. We suspected a decrease of rainfall in these cases. The third regime dis- plays little or no growth (Figure 5 ) , and so we might expect either no change or lessened rainfall from seeding. The version of the computer model we used in 1965 did very well in predicting the difference be- tween the growth and no-growth cases ( Figure 7 ) , however it was too simple to say anything about precipitation — but then, we had no way to measure rainfall over the Caribbean anyway. Since then, we have improved the model so that it begins to predict the growth and fallout of precipitation, and we can measure rainfall with the Univer- sity of Miami's calibrated radars. In May, 1968, our first overland experiment was run in South Flor- ida, again a cooperative venture of ESSA and the Naval Research Lab- oratory. The Air Force, the Univer- sity of Miami, and Meteorology Re- search, Inc., also participated. For a land experiment, ESSA had spe- cial pyrotechnic flares developed commercially. These burn out com- pletely by 10,000 feet and so are safe to use over populated areas. Extensive laboratory and field tests have been made of these flares ( Figures 8 and 9 ) , which put out fifty grams of silver iodide each. Their efficiency was sufficiently high so that twenty units per cloud were injected. This time, the results were even more successful. Thirteen of the fourteen seeded clouds grew ex- plosively following seeding. The seeded clouds grew an average of 1 1,400 feet higher than the control 2 6 10 14 Rates of Rise (m/sec) 0 12 3 Temp Excess °C Figure 7. Model results for cloud of Figures 2 and 3. Right-hand curves are temperature excess of cloud over environment, and are proportional to buoyancy. Left-hand curves are rate of rise of cloud tower as function of height. Growth ceases at level where rate of rise goes to zero. Unseeded- tower properties are shown by solid lines. Seeded properties are shown by dashed and dotted lines. Different seeded curves are results of slightly dif- ferent seeding subroutines, some allowing for tower expansion. Note in- creased temperature excess (buoyancy) caused by seeding. October, 1969 clouds. The odds against that being a chance occurrence are one in two hundred. A main reason for this im- provement was that the computer model was run each morning in ad- vance of the seeding operation. If the model predicted that all clouds would grow to great heights natur- ally— or that no clouds could grow even after seeding — the day's oper- Figure 8. Loading of pyrotechnic flares on rack under wing of jet seeder-aircraft. Rack is in down po- sition, aircraft nose is on left. Each of two racks carries 56 50-gm flares. Each flare is 3.75in long and about ISin in diameter. ation was cancelled; thus nearly all "dud" cases were avoided. Also, the cutoff growths were eliminated, presumably as a result of the "two- shot" seeding technique, where the seeder aircraft make two successive passes at right angles to each other. One of the most important re- sults of the experiment (Figure 10) is a combination theoretical, statistical, and observational graph plotting seedability against seeding effect. "Seedability" is defined in kilometers — it is the difference be- tween the model-predicted seeded top and the predicted unseeded top. A seedability of 4km means that the seeded cloud should grow 4km higher than the same cloud if left unseeded. "Seeding effect" is the dif- ference (again in kilometers) be- tween the observed maximum cloud top and the predicted unseeded top. If the data follow the model, the numerical results for the seeded clouds should be found to lie on a slanting line with slope one, be- cause for them seedability and seed- ing effect should be exactly equal. The unseeded control clouds, how- ever, should lie along the horizontal line with zero slope, because they should show no seeding effect re- gardless of their seedability. The two populations separate clearly, even to the satisfaction of the statisticians, and the effect of massive seeding on vertical cloud growth is again definitively estab- lished. But we were able to take a fur- ther important step and relate rain- fall to both cloud growth and pre- dicted seedability. To do this, first the water production in ten-minute intervals had to be calculated for all clouds, both seeded and un- seeded. A prerequisite for this eval- uation was a careful calibration of all components of the radar. A com- parison was made with the exten- sive rain-gauge network of South Florida, so that a measured radar- echo intensity can be read as a rate of rainfall ( Figure 11). There was a high day-to-day and cloud-to-cloud variability, but, on the average, the seeded clouds rained twice as much as the con- trols. The average difference was 100 to 150 acre-feet per cloud, which is quite a lot of water. Un- fortunately, the large variability and small sample reduced the sta- tistical significance of the rainfall increases, depending on the partic- ular test used, to where the odds were only one in five to one in twenty against the results having Figure 9. Nighttime test of five pyrotechnic flares. 1968 Florida st t d- ing-pro gram. Straight line is aircraft landing-light, left on for 4.000ft travel. Each flare falls 12.000ft be- fore burnout (SO seconds ): forward tranl is only about 1500ft. Medical Opinion 4 Review come about by chance. This level of significance is not adequate, and the experiment must be repeated one more time with the same result in order for it to be completely de- finitive. There is an important result of this experiment that pertains to rainfall modification — the vertical growth following seeding and the predicted seedability are both highly and significantly correlated to the production of water by a seeded cloud. This supports the dynamic theory of seeding, which hypoth- esized that invigorating the cloud growth was the way to increase rainfall. Quantity, ISol Quality Confirmation of this came from the detailed aircraft penetrations: the precipitation sampling instru- ments showed that the rainfall rate, spectrum, and structure were not perceptibly different in seeded and unseeded clouds, both at the 20,- 000-foot elevation and at cloud base. Rather, it was the increased size and prolonged life of the seeded clouds that caused them to rain more, and not the microstructural changes the older theories had sup- posed. Also, we now have the abil- ity to predict in advance the poten- tial water-production from seeding, since the numerical model can pre- dict seedability when atmospheric temperature, moisture, and initial cloud-diameters are known. In general, there is good seed- ability when there are just a few isolated thunderstorms over South Florida; both drier and much wet- ter days are generally less favor- October, 1969 able. The probable number of fa- vorable days in the various seasons is now being investigated. If ten clouds could be seeded on each suit- able day, then, at 100 to 150 acre- feet per cloud, the water production would be considerable. In an oper- ational seeding program, which would be much less expensive than our experimentation, each cloud could be seeded for less than $500, including pyrotechnics and aircraft time. With irrigation water costing about $48 per acre-foot, we would get about a ten-to-one cost-benefit ratio — z'/ these results can be ex- tended from single clouds to groups of clouds over a larger area. The implications of this experi- ment are more far-reaching, how- ever, than the immediate practical consequences of rain augmentation. We have learned to predictably and controllably manipulate one aspect of the convective, or buoy- ant, process, and that is a key pro- cess in the atmosphere. If we con- trol one aspect of cumulus activity, then why not others in the foresee- able future? Seedability (Predicted), in Km 0 10 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 Figure 10. Seedability versus seed- ing effect, Florida, 1968 (see text). Cumulus clouds are important in several ways equally as vital as their rain production. Clouds like these are the driving mechanism of se- vere storms such as the squall line, hailstorm, tornado, and hurricane. A hurricane-seeding program, Pro- ject Stormfury, is building on the techniques and models described here to seek a way to mitigate the destruction of the furious hurricane winds, which do nearly 300 mil- lion dollars damage annually in the United States alone, aside from a tragic loss of life and human suffer- ing, as hurricane Camille recently demonstrated. Forestalling Storms At present, in the Soviet Union, an area half the size of Switzerland is being protected from hail dam- age. There, rockets and artillery shells are guided by radar to fire massive quantities of silver iodide into the wettest part of potential hail clouds. An apparently spectac- ular reduction of hailstone size and damage has resulted. Finally, cumulus clouds play a crucial role in maintaining the large-scale wind systems in the at- mosphere— they drive the trade winds, convert the fuel in the global fire-box zone near the equator, and affect the earth's radiation budget over large portions of the globe, so that their effects must be incorpo- rated in the computer forecast-pro- grams that the weatherman uses daily to predict the air flow. The knowledge gained from controlled experiments and numerical cumu- lus models are being introduced into large-scale forecast schemes RAINFALL. AS DETERMINED BV CLOUD-BASE ECHO-CONTOURING Cloud 6. May 16. 1968 % >l Seeing _ff^ ' Begins ~^^B -14 mm -7 ^f 45 nautical miles Greater than 0.09 in/hr Greater than 0 45 in/hr Figure 11. Radar echo (at cloud base) for a cloud that exploded fol- lowing seeding. Time from seeding, in minutes, is under the echo tracing. leading to the more realistic sim- ulation of global weather changes. But what of possible large-scale weather and climate modification? Since cumulus clouds fuel large wind systems, drive storms, and control exchange of radiant energy, could not altering cumuli over wide areas perhaps change storm and weather patterns? This might sound today like a far-fetched science-fic- tion daydream, but that's the way a manned moon-voyage sounded in the 1930s. end 58 Reprinted from Deep Sea Research Vol . 16, Suppl . 447, 233-361 . Deep-Sea Research, 1969, Supplement to Vol. 16, pp. 233 to 261. Pergamon Press. Printed in Great Britain. On some aspects of sea-air interaction in middle latitudes Joanne Simpson* Abstract — Sea-air exchange is related to travelling frontal cyclones in middle-latitudes. The distri- bution of energy and momentum transfer relative to the cyclone model is first described. Then the role of sea-air exchange in cyclogenesis is analyzed in terms of the concentration and production of vorticity. Observational cases are supplemented by numerical model results. It is tentatively con- cluded that the direct effect of oceanic heating upon cyclone growth is small but that the indirect effect, via convection, may be very large. A beginning attempt is made to analyze how and under what conditions turbulent exchange sustains deep convection and how, in turn, the convection acts to produce or enhance cyclone development. 1. INTRODUCTION Like the weather, the main characteristic of sea-air interaction in these regions is fluctuation. A typical sample from Atlantic Station C (52°45'N; 35°30'W) is shown in Fig. 1. The graphs are time sequences of sensible and latent heat exchange, Qs and Qe, and shearing stress, t. These were computed from the ship's three-hourly observ- ations using the Jacobs exchange formulas in the form published by Malkus (1962). The figure shows that the exchange fluctuations are not random but quite organized. The main organization is on a time scale of 2-3 days, with superposed mesoscale variations of a few hours. In the period shown, 4-35 cm (net) of sea water evaporated into the atmosphere at Sta. C and 58 % of the evaporation took place in just one- sixth of the time intervals, while 84% was achieved in one-third of them. The shearing stress imposed on the ocean and the sensible heat flux were similarly concentrated. The significant air-sea exchange in mid-latitudes is thus restricted almost entirely into synoptic-scale " disturbances." It requires little daring to identify these with the travelling frontal cyclones which dominate the weather maps of these regions. This exchange pattern contrasts with that in the tropics, where the major energy exchange i s effected by the strong and steady trade winds. In Fig. 1 , the shape of the exchange curves permits deductions about the weather pattern and its stage of development. In the sequence February 2-4, a surge in stress (wind) coincided with negative heat flux abruptly changing to positive just before midnight on February 2. Then the evaporation and heating of the air persisted for about a day after the strong winds diminished. These features suggest a simple cold front or young warm-sector cyclone wave, with warm air flowing northward first, followed by a sudden cold outburst over the sea. Figure 2a shows that this was indeed the chain of events. A front is as much an " exchange discontinuity " as it is an air mass transition. A deeper, older and more occluded cyclone is suggested by the exchange pattern for January 27-29. The greater deepness is indicated by the stronger stress and the age by the lack of surface warm air advection (negative heat exchange) ahead of the ♦Environmental Science Services Administration and University of Miami, Coral Gables, Florida. 233 234 Joanne Simpson 3- HOURLY EXCHANGE AT SHIP C Fig. 1. Three-hourly exchange at Atlantic Ship C(52°45'N; 35°30'W) from Jan. 26-Feb. 16, 1954. Values of Qs (sensible heat flux), Qe (latent heat flux) and t (shearing stress) computed from ship observations using Jacobs-type formulas. Top curve is Q, in cal cm-2 sec-1 x 105; middle curve is Qe in same units; bottom curve is shearing stress in dynes cm-2. The " a " denotes time of weather map in Fig. 2a; the " b" denotes time of weather map in Fig. 2b. 40 SURFACE CHART FEBRUARY 2, 1954 1250 G. M T Fig. 2a. Surface weather map for February 2, 1954, 1230 GMT. Adapted from Daily Series Synoptic Weather Maps published by U.S. Weather Bureau. Only station shown is Weather Ship C. Sea temperature (°F) appears to lower right of station symbol. Remaining notation standard. On some aspects of sea-air interaction in middle latitudes 235 30 SURFACE CHART JANUARY 27, 1954 1230 GMT. Fig. 2b. Surface weather map for January 27, 1954, 1230 GMT. Adapted from Daily Series Synoptic Weather Maps published by U.S. Weather Bureau, in same way as Fig. 2a. storm. However, the skew-shaped Qs and Qe curves, with positive heat flux and evaporation lasting beyond the wind maximum, again suggests a cold-air outbreak behind the system. Figure 2b bears out these deductions. The deepening cyclone is an outstanding feature of the mid-latitude atmosphere. It both characterizes the instability of the westerly winds and releases the energy that maintains their motion. The cyclone problem has consumed the greatest minds and effort in meteorology. And this is rightly so. Cyclones are not only the elements of planetary energy exchanges across these latitudes and the solution to one of the most fascinating (unsolved) stability problems in geophysics, but they condition the natural environment of most of human civilization. Figure 1 suggests that they also control sea-air interaction over the extra-tropical oceans, at least on the short time scale. Models of the deepening wave cyclone were evolved early in the century by the great Norwegian meteorologists (see Petterssen, 1956, Chap. 12 and references). These models described and explained physically the three-dimensional distributions of wind, cloud and weather patterns as a " typical " frontal system goes through its life history. It is thus fitting that successors of these great Norwegians (Petterssen, Bradbury and Pedersen, 1962) have incorporated the sea-air interaction distribution into the cyclone model, so that exchange becomes quantitatively and coherently related to the developing disturbance and its processes. Perhaps even more exciting, a possibility has concomitantly emerged of an important feedback of sea-air interaction upon the growth of the cyclones themselves. The enhanced exchange which oceanic cyclones have at their disposal apparently can, under propitious circumstances, cause them to be unstable where they would not be 236 Joanne Simpson so over land. Thereby they may sometimes deepen violently and even disrupt the planetary flow pattern of an entire hemisphere. If further research substantiates this linkage, the oceans will indeed have become a vital part of still another crucial aspect of mid-latitude meteorology. As well as their long-recognized role in producing an anomalously warm Europe, they may through local sea-air interaction affect the stability of the planetary westerlies to disturbances. Before discussing this intriguing possibility, we shall first examine the relationship of exchange to the cyclone model. 2. HOW THE WEATHER PATTERN CONTROLS EXCHANGE Petterssen, Bradbury and Pedersen, (1962) constructed a composite oceanic cyclone in each stage of development and documented the distribution of exchange in relation to its winds and weather pattern. The synoptic situations were chosen to be typical of the various stages of cyclone development, as proposed by Bjerknes and collaborators (1918; 1922; 1933). These stages are: the nascent cyclone wave, the warm-sector cyclone, the partly occluded cyclone, the full occlusion, and the front- less cold core low. In addition, the typical features of arctic outbreaks were similarly investigated. Fifty-one individual cases during the winter of 1956-1957 were selected for the compositing. In each, analyses were drawn for the pertinent variables. The sea-air transfer was computed from these with the Jacobs formulas at grid points oriented with respect to the cyclone center. These were then transferred to a master grid constructed for each of the five stages of development. Charts A in Figs. 3-6 show the sequence of pressure distributions and frontal structures at sea level for the developing wave cyclone. Figures 7 and 8 show the same calculations for the frontless cold core low and arctic air outbreak. The young wave (Fig. 3) is generously supplied with tropical air dragged north from the trade wind belt, which is perturbed in tune with the wave disturbance. Charts B show the rate of kinetic energy dissipation at the ocean-atmosphere interface, or the surface shearing stress times the windspeed. The maximum stress is found in the warm sector of the open wave, while it increases and moves to the cold air in the rear as the storm develops, (cf. Fig. 1). The patterns of energy exchange (Charts C and D) exhibit remarkable peaks associated with the cold air. These peaks are developed by and locked into the cyclone pattern as it progresses. Typical maxima of the sensible flux were about 1 cal cm-2 min-1 (or 1440 cal cm-2 per day) and maximum isopleths of latent heat flux were about 1-4 times this. Still higher peaks were found in single cases. Except over the cold coastal waters (which prohibit large sea-air humidity differences), the fluxes Qs and Qe are highly correlated, as can be seen by comparing Charts C and D with Chart E which shows their sum. The net upward radiative fluxes from sea to air were computed to be in the much lower range of 000 to 0- 10 cal cm-2 min"1 (Godbole, 1961). Standing above any doubts about the Jacobs formulas, the main feature of cyclone exchange is its large size coupled uniquely to the moving system. In the extreme case the oceanic heat loss to the atmosphere amounted to 2-5 cal cm-2 min-1. This is about twenty times the average absorption of shortwave radiation at latitude 50°N in winter and more than forty times the net balance that the sea surface has in the radiation bank ! Consequences to the ocean of these huge spasmodic heat losses have On some aspects of sea-air interaction in middle latitudes LATENT HEAT ] > yv? ' 1 VWd (CAL CM"* MIN-1) ** * / 7 S— — — 1 — '• ' Jr$o\ -£-*-"■"" p>.i < ■J 0 6' ,/ "~^> •~N~— 'vy/xT®^ l^"**^^; o«^ - — ""t/^3 ^~-ol " / K 02 -VL __y- 1 * . 1 0,4 ~-Z " *° l0A 1 ,.v PREDOMINANT V "Yh/J J "S" WEATHER *J >\ PW^~~~Ij r'Aif 0 \ 5/ — / / 0 \\ q \ 100 \ .-r Fig. 3. (After Petterssen, Bradbury and Pedersen, 1962). Models of nascent cyclone waves. Note that the values in Chart B have been multiplied by 100. been difficult to isolate. Here we will be concerned mainly with the role of these exchanges in the cyclone processes themselves. 3. EXCHANGE AND CYCLONE STRUCTURE In the warm air, the figures show negligible sensible heat exchange and slightly positive latent heat gain by the atmosphere. As in the tropics, small cumuli prevail in 238 Joanne Simpson this sector, with their upward development stopped by the trade inversion. But here the tropical air is cooling at a rate of about 5°C per day! Computations by Godbole (1961) showed that this is effected by huge radiative losses at cloud top (~ 800 mb) which help in maintaining the steep cloud layer lapse rate and upward convective heat flow. In the cold air portion of the system, peak amounts of sensible and latent heat are absorbed, with consequences for European rainfall and perhaps for the future of the Fig. 4. (After Petterssen, Bradbury and Pedersen, 1962). Models of warm sector cyclones. On some aspects of sea-air interaction in middle latitudes Fig. 5. (After Petterssen, Bradbury and Pederson, 1962). Models of partly occluded cyclones. individual cyclone also. The most remarkable feature, however, of this series of diagrams is the comparison of the heating patterns with the weather patterns in Charts F. The latter draw upon the standard weather code to characterize the dominant sky type as: strong convective (heavy shower symbols); moderate con- vective (plain shower symbols) ; weak convective (fine weather cumulus symbols) ; fog or stratus (dashes) ; and frontal precipitation (hatched). The numbers inserted between the weather symbols in Charts F signify the 240 Joanne Simpson probability of occurrence of that weather type. The heavy lines which mark the border between neighboring predominant weather types represent the 50% prob- ability of occurrence of either of the adjacent types. The zone of transition between two adjacent types is normally quite narrow and the losing type soon drops below the 10% frequency level. The high probability within large regions and the remarkable continuity from one stage of development to the next are noteworthy. Even more noteworthy are the relationships on Charts C, D and E. The axes of SEA LEVEL % gg?^ PRESSURE " \y ^4^^ Mil l\W ~-/ 00 ' 710-^— \^ / a / 20 ^k**~s-~r^^ ^/NiV 1 ^_ / / \ 1 *~^\i i DISSIPATION OFJv^i^^-io- KINETIC ENERGY^ /\^Ty~~ /\ "^/Sjsu /7xv2 \ / I *A / T^4Jf — -^ /\ \ A \/V *°lz \V \ /V "/ / / " \ / ^^~ ZD — \V =0.1 /\ ^0.s / / "0 ~"T s. / / SJ0.07 / /I y iA \."'S \ B r Fig. 6. (After Petterssen, Bradbury and Pedersen, 1962). Models of full occlusions. On some aspects of sea-air interaction in middle latitudes 241 DISSIPATION OF ^*&T^-M. "^ C*^s. / y^ [/ / 7^ i " \ >^/s Fig. 7. (After Petterssen, Bradbury and Pedersen, 1962). Models of cold core frontless cyclones. the heavy convective areas are oriented at right angles to the heating pattern. The con- ditions shown in Fig. 3 are typical. A band of moderate to heavy convective activity is present to the northwest of the apex of the wave where the rate of heating is moderate. The convective activity decreases to moderate south of Newfoundland where the rate of heating is quite large. Still farther to the west only flat cumulus and stratocumulus develop although the heat inputs by exchange reach a maximum in this area. The features shown in Fig. 3 are maintained throughout the life history of the model cyclone except that the area with heavy convective activity enlarges as the storm deepens and moves toward Europe. Comparison of Charts F, E and A in Figs. 3-8 shows that heating from the under- 242 Joanne Simpson lying surface always results in some convective activity. However, unless the air takes part in a cyclonic circulation, moderate and heavy convection (with precipitation) will not take place even if the surface heating is very intense. Petterssen, Bradbury and Pedersen conclude that as far as the " state of the sky " is concerned, there is a greater difference between cyclonic and anticyclonic air masses than there is between those warmed versuscooled from below. A similar conclusion regarding tropical sky types was reached by Malkus and Riehl (1964). From aerial photographs over the tropical Pacific they devised a set of seventeen sky code numbers and found these could be better related to large-scale vorticity tendencies than to any other feature of the atmosphere. This dynamic control upon convection, when understood, could prove to have powerful implications to the oceans. Cyclonic disturbances form a critical link and here we shall examine the joint role of the oceans and of convection in their development. * "^-Jdl / tll\ |l^ - J Lift-- "C^Slw ^? /(\^\F/\ ^W V« n£\ ^*"L» /vs. 1 * / \ /*! \ / r»r GE0STR0PH1C STREAMLINES "/ AND ISOTACHS ( M SEC1) __ / \ ■< ^^"^^^ X m&JJ r fe fe J 1 1 fL-^iy °V— ^§=g§^ ***J\ 1 A ^ SUM OF C AND D v 0* ^ — 1 ~~Z^*f^ * os 1 (CAL CM"' MIN-1) °\. / \ Fig. 8. (After Petterssen, Bradbury and Pedersen, 1962). Composite chart showing the characteristics of outbreaks of arctic air in different parts of the North Atlantic region. 4. HEAT SOURCES AND THE GROWTH OF MARINE CYCLONES Cyclone development over the oceans apparently needs different ingredients than those usually found to catalyze it on land. Over continents, a proper setup for the concentration of vorticity by advection seems to precede most cases of deepening. Over the Atlantic, Petterssen, Bradbury and Pedersen, usually found that the setup for vorticity advection was not adequate to explain development. As compared with similar structures over the North American mainland, there was remarkably little On some aspects of sea-air interaction in middle latitudes 243 evidence of a well- developed upper trough with strong vorticity advection ahead of it which could overtake the young marine wave cyclone. Some other initial mechanism must then be sought in oceanic developments. It is our purpose next to as sess the possible role of sea-air interaction in this exciting puzzle. The question is to discover how cyclonic vorticity either creates or concentrates itself in the developing low-level disturbance. Petterssen develops the vorticity relations, beginning with the vorticity equation on a constant pressure surface derived directly from cross-differentiation of the horizontal equations of motion, viz: % — * CD where 77 is the absolute vertical vorticity (composed of the relative vorticity £ and the Coriolis parameter/), D is the two-dimensional velocity divergence in the pressure surface, nearly equal to the horizontal velocity divergence on a level surface. So far, only the twisting terms have been ignored.* The pioneer numerical forecasting models (see, for example, Thompson, 1961, Chap. 7) largely used this equation with the right side assumed zero, so that the absolute vertical vorticity is conserved and only redistributed by horizontal advection. As we mentioned, this appeared roughly adequate to predict cyclogenesis over continents. But much evidence points to the divergence D as somehow providing the missing ingredients for marine developments. It is clear from (1) that to grow a cyclone we want convergence at low levels, which from continuity implies divergence aloft. In several papers, Petterssen and his collaborators (1955; 1959) have been concerned with developing quantitative connections between heat source distri- butions, convergence and vorticity production. The development is implemented by postulating a level of non-divergence in the middle or high troposphere where dr,/dt — 0. Then if we break down all variables into surface and shear values, viz: \V= \V0 + |KS, D = Do + Ds-n = -no + 1), = £0 +/+ £. (2) where \V is the horizontal wind vector and the shear is taken between 1000 mb and the level of nondivergence, the vorticity equation at the level of nondivergence is ^ + V-V£s + Vs-Vw = A>*?o = -*» (3) it dt The vorticity advection is represented as /(,= -VV^5- V, • VVo. (4) Its evaluation in numerical forecasting models has been described at length (c.f Thompson, 1961). Therefore -&-»*-£-^ ♦The solenoid term does not appear explicitly in the vorticity equation in pressure coordinates, due to slightly different definitions of vertical vorticity £ in pressure vs. height systems. For clarifi- cation, the reader is referred to Petterssen (1956), p. 135 ff. 244 Joanne Simpson The right side of (5) is a measure of the rate of destruction of vorticity at the 1000 mb level. Since w is positive, development of the cyclonic absolute vorticity is pro- portional to the negative magnitude of the right side of (5). Following Sutcliffe and Forsdyke (1950), we use £>o as a measure of development and attempt to relate Do to sea-air interaction through <)£«/<>/. Petterssen (1955) set up a quasi-geostrophic, hydrostatic framework to relate its/it quantitatively to the heat source distribution. With these assumptions we have Zs = V2/i T (6) where h is the geopotential thickness between the level of nondivergence and 1000 mb and /is the Coriolis parameter. Using the integrated hydrostatic equation and the first law of thermodynamics we obtain >* = /Mn* 1 &Q + w(r-ar) + At (7) it p tCp dt Where p is the pressure at the level of nondivergence and p0 is 1000 mb. dQ/dt refers to the heating rate per unit mass. The vertical velocity is co = dp/dt, ra is the dry adiabatic lapse rate and r the actual lapse rate in pressure coordinates. At = iT iT u — — v — 7>x iy (8) where At is the thermal advection. The bars denote averages with respect to intervals of In p. And finally, since Hs = V2 (ih\ we have £-„A-^ In Po AT + --£ + cp dt o> (ra - n (9) (10) The immense complexity of the development process is apparent from (10). Develop- ment at the 1000 mb level comes out as an unbalance between the vorticity advection and the Laplacian of certain interrelated thermal contributions. The thermal contri- butions derive from advection, non-adiabatic heating, and vertical motion times stability or buoyancy. The last term is a measure of convective heat release when the air is saturated and conditionally unstable. Over the oceans, the first two terms may be established or controlled by the sea- air interaction. As the cyclone models showed (Figs. 3-8), dQ/dt and convection are related but not uniquely. For oceanic heating to set off intense buoyant convection in the overlying air, the initial vorticity must already be cyclonic. This additional requirement in terms of initial conditions perhaps accounts, at least partly, for the vast variety of marine developments. In the work described on Atlantic cyclones, Petterssen, Bradbury and Pedersen, (1962 be. cit.) computed the direct effects of heating upon the thickness On some aspects of sea-air interaction in middle latitudes 245 changes in the vicinity of ten cyclones, using equation (7). Specifically, they evaluated dQ/dt and w (Ta — T) and compared these with other factors causing thickness change. But drastic assumptions were required in so doing. For one thing, the depth of the heated layer and the vertical decay of the flux curve had to be assumed arbi- trarily. The latent heating had to be taken from an area-mean ascent rate, which would indeed be fortunate if it correctly approximated convective release. The main result of the ten computed cases was that the dQ/dt contributed non- negligible thickness changes, up to one-third or even one-half those from other sources. However, all were in a sense of height rises, or reduced falls. The tentative conclusion is that including sensible heating from the sea may be necessary for a good forecast, but that it does not contribute directly to cyclone intensification. On the whole the ten cases chosen contained rather small amounts of precipitation due to large-scale vertical motion, with the result that the height changes due to released latent heat were small. The main effects of sea-air interaction may lie in the instigation of large convective precipitation, or in more subtle dynamic convective effects via the forcing of an ageostrophic mass inflow (convergence). This effect probably cannot be explicitly studied in a large-grid, geostrophic hydrostatic framework as the foregoing; even the twisting term may become important in the vorticity equation at an early stage, as in tropical developments (cf. Yanai, 1961). Furthermore, the seaward position of Petterssen's growing cyclones may have obscured matters, since cyclonic vorticity would coincide with heating more fre- quently just off the American continent in the preferred planetary trough position. After leaving the coast, anticyclonic vorticity is more likely to dominate the cold air. We suggest that the coastal waters are cyclogenetic not just because of the thermal impact but because this impact frequently coincides with a trough position and initial cyclonic vorticity. Two contrasting sets of observational evidence are next introduced for preliminary evaluation of this hypothesis. 5. CONTRASTING OBSERVATIONAL CASES On January 22, 1955, the Woods Hole Oceanographic Institution's research air- craft flew from the island of Bermuda (32°20'N; 64°44'W) to a location in Rhode Island (41°38'N; 71°30'W) on the U.S. East Coast. The path of the aircraft (Fig. 9 inset) cut through a young wave cyclone that had generated on a cold front in the Gulf Stream area off Cape Hatteras and was accelerating over the ocean in a north- easterly direction. An opportunity was thus provided to measure the turbulent fluxes of momentum and heat directly and to relate them to the structure of the cyclone and its air masses. The work has been described in detail by Bunker (1957). All the observations and computations are summarized in Fig. 9. The outstanding feature of the cold air mass was its very high static stability,which must have been maintained by strong subsidence. Beneath the levels of the aircraft observations, great instability must have existed, since the ocean was 6°C warmer than the air. The only turbulence observation taken in the cold air showed decreased turbulence and a downward heat flow at 100 m elevation (80 km behind the cold front). The shearing stress measured was about 3 dynes cm-2. The downward flux of heat in an air mass flowing over 6°C warmer water requires comment in connection with Petterssen's cyclone models. It re-emphasizes that a 246 Joanne Simpson 00 ca t" o • - Iliia §e1sTc 0(N d ca^ 5 >>.ap ft- i3 c u S 23°^ ■shags EQ « O . „ .2 rt^-t; o sislS n>tm y «> 2- « = a'5 y U.S 5* 8 5 c «s «21« ia. O "2— ... . eo P, "S ^ 2.2 «aa *°"§.Ss.2 Sd-8^1 a E « a s 1- U «JJ C « § a o.^ C.Ecos on 9£ « qo ;— rj U C e SU313N '1H9I3H On some aspects of sea-air interaction in middle latitudes 247 large boundary transfer does not imply large heat addition to a deep air layer. Bunker's case permits quantitative estimation of the balance of the heat transfer processes at work, namely buoyant convection, mean subsidence and eddy diffusion. Using the method of Priestley (1954), Bunker estimated the maximum upflux of heat due to buoyant convection to be 0-4 m cal cm-2 sec"1. This flux was obtained assuming the mixing rates for momentum and heat to be equal and using the observed root-mean-square temperature deviations. At the same time, he computed a down- ward flow of heat by eddy diffusion of 1 m cal cm"2 sec1 with the conservative value of 50 g cm-1 sec-1 for the eddy conductivity. As the airplane detects the net heat flow in the vertical, it is apparent that a downward flux should be obtained from its records, as it was. Thus a strong mean subsidence behind the front preserved the great stability and resulted in a net downward flow of heat by advection and diffusion even under conditions of large sea-air temperature difference and slight turbulence. The very lowest air is heated by the ocean, becomes unstable and rises in small buoyant " thermals " which penetrate a short distance into the stable air. The heat transport by this convection process was, in this case, small compared to the downward flow. This air mass was heated more by warm stable air aloft than by the warm ocean ! It is noteworthy that Bunker's disturbance failed to deepen but died soon as an open wave. Restriction of the role of exchange by dynamic factors (subsidence) probably played a role in this failure. The exchange was working against strong anti- cyclonic vorticity in most of the cold air (cf. inset Fig. 9). We suggest that the anti- cyclonic vorticity worked its effect through subsidence, which prevented the heating from setting off deep convection. To support this we contrast a case where the exchange encountered an initially cyclonic planetary pattern, with a dramatically different outcome. The Gulf of Alaska is frequently the scene of rapid cyclone intensification. Many times the cyclogenesis occurs on such a large scale that the basic planetary wave pattern is radically altered in a few days, with effects even reaching half a hemisphere downstream toward the east. Namias and Clapp (1944) attributed this type of deepening to the rapid modification of cold Arctic air masses pouring over the warmer waters of the Alaskan Gulf. Winston (1955) pursued this suggestion in a fascinating case study. He used a violent development on February 1-4, 1950, to assess the role of sea-air interaction in cyclogenesis. The broad-scale circulation changes associated with this cyclone development were well portrayed by the five-day mean 700 mb charts (not shown). The new Gulf of Alaska trough developed in conjunction with the westward retrogression of a large ridge originally in the Eastern Aleutians. This resulted in a northerly flow bringing cold air over the Gulf of Alaska where it was exposed to rapid heating, as we shall examine later. The trough formation in the Gulf of Alaska abruptly shortened the downstream half wave length of the planetary waves in the westerly belt, with drastic consequences to the North American and Atlantic flow patterns. Prior to the development, a broad cyclonic flow dominated the Western and Central sections of the United States with attendant storminess and cold weather in the west. With the establishment of the new trough in the Gulf of Alaska and southward, heights rose rapidly over the 248 Joanne Simpson a. Feb. 1, 1950 Fig. 10. (After Winston, 1955). Sequence of daily maps for 500 mb (upper) and sea level (lower) portraying details of cyclonic development in Gulf of Alaska. Maps are reproductions from Daily Series Synoptic Weather Maps published by the U.S. Weather Bureau. 500 mb charts are for 1500 GMT and sea-level charts for 1230 GMT. On some aspects of sea-air interaction in middle latitudes 249 Fig. 10b. Feb. 2, 1950 250 Joanne Simpson Fig. 10c. Feb. 3, 1950 On some aspects of sea-air interaction in middle latitudes 251 Fig. lOd. Feb. 4, 1950 252 Joanne Simpson Western United States, anticyclonic circulation developed and consequently improved weather set in. Such major adjustments in the large-scale flow over North America are typical following cyclogenesis in the Alaskan Gulf. The cyclone growth is viewed in Fig. 10. At the surface the individual perturbation which triggered the development was a left-over occlusion which moved from the Bering Straits on February 1 (Fig. 10a) through Alaska and into the northern Gulf by February 2 (Fig. 10b). In this interval the occlusion transformed into a cold front with an icy Arctic air mass behind it. This front had just reached the Gulf by map time of February 2. The intensifying cyclone at sea level formed on this front and was not the same low which was in Northwestern Alaska in Fig. 10a. This new cyclone deepened to extremely low central pressure (985 mb) in the next two days (Figs. 10c and d). Aloft, the development of a new trough in this vicinity was qualitatively inferrable from the initial setup for vorticity advection. Winston's first step was to determine quantitatively how much of the development was accountable to this mechanism. Therefore equation (1) was tried out with the right side equal to zero, namely ^=0or^ = -V-Vr, (11) dt it where the vertical advection of vorticity w 'b-q/'ip has also been ignored. With the quasi-geostrophic approximation, (11) is expressed in terms of heights and height tendencies and the well-known methods of numerical forecasting with the barotropic model are utilized. The barotropic technique was applied at 700 mb to a large region surrounding the Alaskan Gulf. In the early period of development (Feb. 1-Feb. 2, 0300 GMT) the agreement between the barotropic forecast and the observed development was excellent, both in the magnitude of the height changes and in the location of the centers of maximum falls. In the period of most rapid deepening, the barotropic prediction failed most badly. At 1500 GMT February 2, the maximum computed twelve-hourly height fall of — 340 ft was found along the Southeastern Alaskan coast, while the observed peak height fall of — 530 ft was located farther west near the middle of the Gulf of Alaska. This was just the time when cold Arctic air had begun streaming out over the Gulf, thereby abruptly introducing a large heat source into the atmospheric circulation. By 0300 GMT February 3 a deep closed low had become established over the Gulf of Alaska at 700 mb. Barotropic computations from this flow pattern now indicated large height falls over the extreme Western Gulf of Alaska, whereas the observed fall center was farther east and weaker. This latter type of error in the barotropic computation persisted to the end of the period on February 4. The important results of this very interesting experiment are twofold: (1) Horizontal advection of absolute vorticity was responsible for much of the cyclone development in the Gulf of Alaska, particularly in the initial stages. (2) Pure advection could not explain the rapidity and exact location of the intense development. At the time of most rapid deepening, computed height falls were east of and weaker than the observed falls, whereas following the establishment of the deep closed low, the computed falls were to the west of and stronger than the observed falls. Winston attributed the main errors of the barotropic computation to the neglect On some aspects of sea-air interaction in middle latitudes 253 of the divergence term in the vorticity equation. He suggested that the oceanic heat source produced an ageostrophic thermal circulation, with inflow at low levels, ascent and outflow aloft. A negative divergence in equation (1) would create cyclonic vorticity adding to that advected and obviously acting qualitatively to correct the errors in the barotropic computation. It is noteworthy that the vorticity creation is greatest at the time and place where the cold air first reaches the warm waters of the Gulf. Manabe (1957) made a now classic study of cold air outbreaks over the Japan Sea. He found, among other things, convergence in the cloud layer of the polar air after travel over the warm waters. Fortified with this result and with Petterssen's weather patterns relative to heating in oceanic cyclones (Figs. 3-6), we suggest the role of deep convection in producing this convergent circulation, as it so often does in tropical developments. Most significant is the fact that cyclonic vorticity already existed over the Gulf of Alaska when the cold air outbreak began (cf. Fig. 10b). Thus a heat source was imposed upon a troposphere favorable to penetrative convection. Winston forged the first links in documenting this chain of reasoning by his vertical velocity and heating calculations. He computed the vertical velocities directly from equation (1) without further neglections, expanding it in the form rf = -V'ViJ-a. ^+V~- (12) it ip Up Here the divergence D on the pressure surface is written as — icofbp. Rearranging this equation, we have JM_j? + v v^ (13) ~bp \tj / ij2 which upon integration becomes ».*« - .h) fL— !<* (,4) Pi where p\ and po are arbitrary pressure surfaces. Winston used the surface chart and those for 700 and 500 mb for computing the integrand. Before the cold air outbreak reached the ocean, a broad area of ascent was found in and east of the developing trough. In the northwesterly flow to its rear (over Alaska and Bering Straits) pronounced sinking was computed. Twelve hours later when the heat source had just set in, upward motion increased over most of the Gulf of Alaska. Also now the ascent extended well back into the northwesterly flow behind the developing trough at both 700 and 500 mb. The peaks of upward motion were now located in the cold air behind the front. These were found over the middle of the Gulf of Alaska to the southwest of earlier maxima, even though the trough had moved eastward. Later, the vertical motion field once more took on a relation to the trough more familiar to continental situations. Generally pronounced downward motion de- veloped west of the trough and upward motion was now restricted to the area east of the trough. Apparently the usual effects of subsidence and horizontal divergence of 254 Joanne Simpson the cold air mass in its southward drift and lifting (with horizontal convergence) in the warm air east of the trough again dominated, although a pronounced heat source still operated as the cold air continued to stream out over the Gulf. Thus a main result of Winston's work is that the heating was most influential in this development for a short 12-24 hr period following the initial impact of the heat source. After the cold dome moved out over the ocean in greater depth, the more powerful effects of sinking and spreading of the cold air killed or overcame the convergence produced by the oceanic warming. This fits in beautifully with what we have learned from the studies of Manabe, Petterssen and Bunker; here the heat source lost its ability to create convergence because the convection was suppressed by the subsidence linked with planetary divergence. This inference is supported by Winston's heating calculations. He computed the net heat added to the air in twelve-hour intervals by the same trajectory method employed by Manabe (1957). The results are shown in Table 1, broken down into two layers. Table 1. Heating of air associated with Gulf of Alaska cyclogenesis, Feb. 2-4, 1950 (after Winston, 1955) \2-hr period dQ/dt dQ/dt dQ/dt beginning 10-5 10-7 7-5 1500 GMT, Feb. 2 [2210 + 1270 + 940 0300 GMT, Feb. 3 + 1430 + 1020 +410 1500 GMT, Feb. 3 + 1090 + 850 + 240 0300 GMT, Feb. 4 + 520 + 700 -180 1500 GMT, Feb. 4 + 400 + 500 -100 Subscripts 10-5, 10-7, and 7-5 refer to layers 1000-500, 1000-700, and 700-500 mb respectively. Units : cal/cm2 per day. It is interesting to compare Table 1 with Manabe's case. Presumably the radi- ational heat losses in the air columns should be nearly the same. If we also carry over Manabe's near balance between radiation loss and precipitation gain, the sensible heat supply from sea to air in the Gulf of Alaska must have reached about 2000 cal cm-2 per day in the peak twelve-hour period starting at 1500 GMT, February 2. The average oceanic sensible heating for the outbreak period of Table 1 would be about 1000 cal cm-2 per day, in good agreement with Manabe and confirming the results of both studies. Even more interesting is the vertical distribution of heating and its time sequence. In the first twelve-hour period (just after the cold air hits the Gulf) the upper air layer is warmed nearly as much as the lower layer. Subsequently the heating becomes more and more concentrated at low levels, until in the last two periods we find cooling between 700 and 500 mb. The oceanic heat source was still at work, but its effects just were not being propagated upward. Concomitantly, convergence was no longer creating vorticity to enhance the deepening process. The evidence points to penetrative cumuli as the linking mechanism between thermal and dynamic transformations here. We suggest convection as the means by which sea-air interaction can — in favorable (i.e. initially cyclonic) circumstances — act to aid marine cyclonic development, perhaps crucially in some cases. This would On some aspects of sea-air interaction in middle latitudes 255 indeed be a very subtle feedback mechanism between sea and air, involving the large- scale planetary vorticity patterns. The linkage between exchange, convection and storm deepening was explored further in the Gulf of Alaska case by Pyke (1965), as far as the pitifully sparse data permitted. The only ocean station in the Gulf is Ship P at 50°N, 145°W. The front is just passing the ship in Fig. 10c (1230 GCT, February 3). Figure 11 shows the calculated " before and after " picture of sea-air exchange at the ship, related to several weather parameters. An overall temporal connection between pressure fall, increased exchange and convective weather is obvious at first glance. Looking more closely, one can observe the approach and intensification of the storm quite easily by noting the relationships between the plotted variables. A sudden increase in to began at 1800 GCT, 2 February. Increased stress was accom- panied by showers and by an acceleration of the pressure fall and followed by a marked increase in To — Ta. It is at this time that the edge of the strong pressure gradient surrounding the deepening cyclone (visible on the surface map for 2 February in Fig. 10b) must have reached the ship. The mP air that had been over and east of the ship is replaced by the cooler mP air coming from the large high pressure area building over the Aleutian Islands. Between 0900 and 1800 GCT on 3 February there was another sharp increase in To — Ta, a further shift in wind, and an increase in con- vective precipitation associated with the actual cold front passage. Throughout the period, the sea temperature To remained nearly constant (within 1°C) so that the increase in To — Ta is mainly a reflection of the drop in the air temperature as colder air is advected into the region. 2 FEB. 3 FEB. 4 FEB Fig 11. (After Pyke, 1965). Computed sea-air energy exchanges, Q, (sensible heat) and Qe (latent heat) at Ship P (50°N; 145°W) for a period 0000 GCT, 1 February through 1800 GCT, 4 February 1950, plotted with sea-level pressure (p), air-sea temperature difference (T0 — Ta) eddy shearing stress (t0), observed weather and wind veolcity 256 Joanne Simpson Both latent and sensible heat exchange also rose by nearly an order of magnitude during the deepening of the cyclone. The increase is a joint consequence of the higher winds and the increased sea-air property difference as the cold, drier air moved in from the north. The maximum values of Qe computed at Ship P for this period are on the order of 400 x 10"5 cal cm-2 sec-1, with peak Qs running at about 250 X 10-5 cal cm-2 sec-1. Climatological mean values are about 70 x 10-5 cal cm-2 sec-1 for Qe and about 20-30 x 10~5 cal cm-2 sec1 for Qs. Clearly, the first four days of February 1950 were a period of much greater than normal sea-air exchange by about an order of magnitude. The peak exchange values obtained here, however, still fall far short of the maximum values that occurred in the Gulf of Alaska during this storm. Ship P is far to the south of the initial point of contact of the arctic air with the sea (Fig. 10b). At the point where the continental air first hit the warm sea, there was a far larger exchange than was experienced at P, as indicated by calculations from Table 1 . The dissipation of atmospheric kinetic energy, which can be computed from wind- speed and to, had a maximum value of 27 x 10-5 cal cm-2 sec-1, only an order of magnitude lower than the maximum value of Qs. This is in good agreement with the model of Petterson, Bradbury and Pedersen for the deep occluded cyclone (Fig. 6) and much higher than mean or undisturbed values. The onset of heavy shower symbols in Fig. 1 1 beginning at the cold front passage suggests an association between high exchange, convection and cyclonic vorticity. The drastic accompanying change in the ship's upper air sounding hammers home the association even more vividly (Fig. 12). The first sounding (Fig. 12a) shows as yet no effects of the cold outbreak. A well- mixed layer extends up to 900 mb, capped by a sharp inversion and dry layer aloft. The sea-air temperature difference is very small. The second sounding (Fig. 12b) 0300 GCT 2 FEB. 0300 GCT, 3 FEB. 0300 6CT, 4 FEB Fig. 12. (After Pykje, 1965). Upper air soundings at Ship P, surface to 300 mb and winds aloft, plotted on U.S. Air Force Skew-T, log p diagram. Solid lines are temperatures; dewpoint curves are dashed heavy lines. Sea surface temperatures are plotted in triangular symbols. The thin solid lines are dry adiabats; the thin broken lines are saturated adiabats. a. 0300 GCT, Feb. 2, 1950 c. 0300 Feb. 4, 1950 b. 0300 Feb. 3, 1950 On some aspects of sea-air interaction in middle latitudes 257 shows the first influence of the storm system on the weather at the ship. The winds have shifted considerably; there is an influx of moisture at high levels. Destruction of the marine inversion is beginning and the sea-air temperature difference is increas- ing as the cooler air from the northwest reaches the ship. The third sounding (Fig. 12c) depicts a complete air mass transformation; it is a typical deep convective sounding. A well-mixed moist layer of air now extends to great heights. The winds (especially in the lower levels) have veered to north-north- west and the tropopause has lowered to 406 mb. It had been above 300 mb on the two previous soundings. The sea-air temperature difference is now very large, with conditionally unstable air throughout most of the troposphere. Thus the oceanic heating extends its influence, via convection, to great heights. A saturated moist- adiabatic parcel starting with the temperature of the sea surface would penetrate above the tropopause before losing its buoyancy. Intense convective activity is in fact well documented by the fact that heavy cumulus (Low Cloud Code 2) prevailed at every observation after 1 500 GCT, 3 February. Showers dominated the past weather in every observation from 1200 GCT, 3 February until the end of the period. The sharp contrast between this explosive development case and the nondeveloping wave examined earlier emphasizes the role of convection (and conditions favoring it) as necessary to implement sea-air exchange in marine storm growth. The ways that circulation growth may be affected by convection is best illustrated using the vorticity equation in rectilinear coordinates with altitude as the vertical coordinate, namely fr = -(f+QD at 7)0. i>p t>a ip 7>x iy iy ix ~dw 7)V i)W i)U ~dx Iz iy "bz div. solenoid twisting + ~bx ly friction (15) Here a is specific volume; u, v and w are rectilinear velocity components, and Fx and Fy are frictional forces per unit mass. Physically, convection may influence disturbance growth in two ways, thermal and dynamic. Its thermal role is carried out by the effect of its heat release upon the mass field (density or specific volume). In the vorticity equation, this heat release alters or creates the solenoid term. The dynamic effects of convection arise from the fact that the convection changes the motion field. In the vorticity equation, these changes can enter via the divergence, twisting or even the friction term. The thermal role of convection in the tropical hurricane is well known. The cloud towers pump up the water vapor fuel and convert it into sensible heat, thus creating the density and pressure gradients that maintain the storm. In vorticity terms, the precipitation warming leads to a specific volume increase toward storm center, creating a positive solenoid term which acts to increase the vorticity. The dynamic effects of convection are less well understood and will be much more difficult to formulate. In particular, the causal chain between deep convection and the growth of low-level convergence with upper outflow cannot be stated quantitatively or even sequentially. The Gulf of Alaska evidence hints that the development of deep con- vection can be instigated by increased sea-air exchange, when conditions are favorable. 258 Joanne Simpson The convection then presumably produces increased low-level convergence and out- flow aloft, contributing to the increase of cyclonic vorticity, and so forth. In tropical hurricanes, the twisting term and the friction term may also be con- trolled by convection in a manner that implements deepening. Gray (1967) suggests that the vertical momentum transports by the huge cloud towers are essential to generate and maintain the high-level outflow, without which the storm could not remain viable. There is no reason why these effects should not operate in mid- latitudes. The dynamic interactions of convection with larger-scale circulations is an almost unbroken and probably crucial frontier in meteorology. Mechanistic under- standing of tropical storms and some aspects of how convection operates in them has been advanced by meticulous case studies using instrumented aircraft. A similar approach is advocated for higher-latitude oceanic cyclones, supplemented by the powerful new tools of satellites and instrumented buoys. Although it may appear difficult to catch and measure adequately a fast-deepening cyclone with current aircraft capabilities, a great advantage is provided to these endeavors by the highly sophisticated numerical models available to predict mid-latitude circulation features. 6. NUMERICAL MODELS Spar (1962) pioneered in designing a numerical model specifically to investigate the role of sea-air interaction in cyclogenesis. It was quasigeostrophic, vertically integrated and baroclinic (thermotropic). Dynamically, the model used the complete frictionless vorticity equation. The energy equation contained terms representing the effects of latent heat of condensation and heat flux from sea to air. The heat of condensation was computed from the derived vertical velocity w and humidity soundings. The oceanic heating was put in from a Jacobs-type formula, with an empirically determined proportionality constant. This constant was determined from calculated heating along trajectories during actual cold air outbreaks and thus allows for some other diabatic effects in addition to turbulent transfer from the sea. The computation program permitted four sets of predictions to be made for each case studied : (1) a barotropic forecast ; (2) a baroclinic prediction in which water vapor is neglected (dry baroclinic); (3) a baroclinic prediction including water vapor and latent heat of condensation, but without flux of heat or water vapor from the ocean (no flux), and (4) a " complete " baroclinic prediction including all the above effects. Results of twelve-hour forecasts for two Atlantic cases are reported by Spar, GERRiTYand Cohen (1961) and several more unpublished cases have been discussed in- formally. The major conclusions from Spar's work are that the direct effects of oceanic heating upon cyclogenesis are virtually negligible and that the indirect effects lie (1) in creating atmospheric baroclinity particularly at coast lines and (2) in instigating and driving convection. In the case studies Spar found that the main improvement in fore- cast occurred in progressing from a barotropic to a baroclinic model. In " wet " cyclones, a further improvement was gained by including latent heat release. Virtually no improvement was gained by progressing to the " complete " Ynodel with oceanic fluxes included. For our purposes, the main deficiency in Spar's model is that it is On some aspects of sea-air interaction in middle latitudes 259 quasi-geostrophic. Its consequent inability to treat the divergence term in (15) excludes the possibly important dynamic effects of convection. Additionally, bad truncation errors forced the forecasts to terminate after twelve hours. A hierarchy of nine-level hemispheric primitive-equation models have been developed by the staff of the Geophysical Fluid Dynamics Laboratory (G.F.D.L.) of the Environmental Science Services Administration (Smagorinsky, Manabe and Holloway, 1965; Manabe, Smagorinsky and Strickler, 1965; Manabe and Smagorinsky, 1967). These models can be either moist or dry and can include or exclude parameterized sea-air fluxes of heat, moisture and momentum. Particularly clever is their manner of treating cumulus precipitation by a method called " con- vective adjustment." When the lapse rate exceeds moist adiabatic and the relative humidity reaches a certain threshold (80 or 100%), the lapse rate is adjusted to moist adiabatic and the released heat is supplied to the air. Thus in this model heating from the ocean can play its role in sustaining convection through maintenance of an unstable lapse rate. The only aspects of convection wholly lost are its more subtle mesoscale dynamic effects and its vertical transports of momentum. The latter are being parameterized in a still unfinished stage of the model. The G.F.D.L. models have been tested for two two-week winter periods (Miyakoda, Smagorinsky, Stricker and Hembree, 1969). Predicted circulations showed good resemblance to observed throughout the test. Each case was run with a three-tiered model hierarchy : Experiment 1 was without sea-air exchange ; Experi- ment 2 had exchange and a 100% condensation criterion; and Experiment 3 had ex- change and an 80% condensation criterion.* Experiments 2 and 3 gave better results than Experiment 1, particularly for oceanic cyclogenesis. In these two experiments, three generations of Atlantic cyclones were identifiable corresponding almost one-to- one with observed cyclones. Hence we infer that marine deepening is at least fairly well predicted. Experiment 3 gave better results than Experiment 2, simulating an eighth day cyclone missed by Experiment 2. However, the results between the three experiments differed less than had been expected, possibly suggesting the dominant role of baroclinity in most developments. The foregoing series of computations was run using climatological mean sea surface temperatures. Later, an experiment was run by Miyakoda| using the actually measured sea temperatures during the period, which in the Western Atlantic happened to be anomalously warm by about 5°C. The latter prediction, after ten days, was much better than those of the previous experiments. The improvement was apparently due to the growth of a single deep cyclone which, while originating in the warm ocean area, disrupted the planetary flow as far away as Siberia! This result has instigated a series of experiments introducing assumed sea temperature anomalies and examining their consequences on air circulations. Such calculations provide, at least, a quantit- ative start in testing the brilliant but previously qualitative hypotheses of Namias (1959; 1963; 1965a; 1965b) and Bjerknes (1959; 1962; 1964) on the role of sea-air interaction in climatic change. To date, a case of explosive marine cyclogenesis has not been specifically selected and post-analyzed with the G.F.D.L. model hierarchy. A deterrent is the several ♦Other factors were also varied between experiments so they are not a strict test of the role of exchange. tWork not yet completed for publication. Kindly discussed with the writer by Dr. Miyakoda of G.F.D.L, ESSA. 260 Joanne Simpson man-years required to set up each experiment and then to interpret the results. Not- withstanding, the expense and labor is still smaller than that of a medium-scope observational program and is, in fact, a necessary prerequisite for the proper and well- guided use of future observations in unravelling a problem that is critical to both sea and air. Acknowledgments — The writer is deeply grateful for the generous help of her colleagues in the Geo- physical Fluid Dynamics Laboratory of the Environmental Science Services Administration, upon whose work the last section of this paper is largely based. Particularly stimulating conversations were held with Drs. J. Smagorinsky, K. Bryan, S. Manabe and K. Miyakoda. Much gratitude is also due to Professor J. Spar of New York University for generous help in interpreting his own work and other aspects of sea-air interaction. REFERENCES Bjerknes J. (1918) On the structure of the moving cyclone. Geofys. Publn, 1, 8 pp. Bjerknes J. (1959) The recent warming of the North Atlantic. In: The Atmosphere and the sea in motion, Rockefeller Inst., Oxford Univ. Press, London, 65-73. Bjerknes J. (1962) Synoptic survey of the interaction of sea and atmosphere in the North Atlantic. Geofys. Publn, 24, 115-145. Bjerknes J. (1964) Atlantic air-sea interaction. Adv. Geophys., 10, 1-82. Bjerknes J. and H. Solberg (1922) Life cycles of cyclones and the polar front theory of atmospheric circulation. Geofys. Publn, 3, 18 pp. Bjerknes V., J. Bjerknes, H. Solberg and T. Bergeron (1933) Physikalische Hydrodynamik. Springer- Verlag. OHG, Berlin. Bunker A. F. (1957) Turbulence measurements in a young cyclone over the ocean. Bull. Am. Met. Soc, 38, 13-16. Godbole R. V. (1961) A preliminary investigation of radiative heat exchange between ocean and atmosphere. LJnpublished manuscript on hie at the Geophysical Sci. Dept., Univ. of Chicago. Gray W. M. (1967) The mutual variation of wind, shear and baroclinity in the cumulus convective atmosphere of the hurricane. Mon. Weath. Rev., 95, 55-74. Malkus J. S. (1962) Large-scale interactions. The Sea: Ideas and Observations, M. N. Hill, editor, Interscience Publishers, 88-294. Malkus J. S. and H. Riehl (1964) Cloud Structure and Distributions over the Tropical Pacific Ocean. Univ. Calif. Press, 229 pp. Manabe S. (1957) On the modification of air-mass over the Japan Sea when the outburst of cold air predominates. J. Met. Soc. Japan. 35, 31 1-326. Manabe S., J. Smagorinsky and R. F. Strickler (1965) Simulated climatology of a general circulation model with a hydrologic cycle. Mon. Weath. Rev., 93, 769-798. Manabe S. and J. Smagorinsky (1967) Simulated climatology of a general circulation model with a hydrologic cycle. II: Analysis of the Tropical Atmosphere. Mon. Weath. Rev., 95, 155-169. Miyakoda K., J. Smagorinsky, R. F. Strickler and G. D. Hembree (1969) Experimental extended predictions with a nine level hemispheric model. Mon. Weath. Rev., 91, 1-76. Namias J. (1959) Recent seasonal interactions between North Pacific waters and the over- lying atmospheric circulation. J. geophys. Res., 64, 631-646. Namias J (1963) Large-scale air-sea interactions over the North Pacific from summer 1962 through the subsequent winter. J. geophys. Res., 68, 6171-6186 Namias J. (1965a) Short-period climatic fluctuations. Science, 147, 696-706. Namias J., 1965b : Macroscopic association between mean monthly sea-surface temperature and the overlying winds. J. geophys. Res., 70, 2307-2318. Namias J. and P. F. Clapp (1944) Studies of the motion and development of long waves in the westerlies. ./. Meteor., 1, 57-77. Petterssen S. (1955) A general survey of factors influencing development at sea level. J. Meteor., 12, 36-42. Petterssen S. (1956) Weather analysis and forcasting. Vol. 1, Second Edn. McGraw-Hill, New York. Petterssen S. and P. A. Calabrese (1959) On some weather influences due to warming of the air by the Great Lakes in winter. J. Meteor., 16, 646-652. On some aspects of sea-air interaction in middle latitudes 26 1 Petterssen S., D. L. Bradbury and K. Pedersen (1962) The Norwegian cyclone models in relation to heat and cold sources. Geofys. Publn, 24, 243-280. Priestley C. H. B. (1954) Vertical heat transfer from impressed turbulent fluctuations. Austral. J. Phys., 9, 133-143. Pyke C. B. (1965) On the role of sea-air interaction in the development of cyclones. Bull. Am. Meteor. Soc, 46, 4-15. Smagorinsky J., S. Manabe and J. L. Holloway, Jr. (1965) Numerical results from a nine- level general circulation model of the atmosphere. Mon. Weath. Rev., 93, 727-768. Spar J. (1962) A vertically integrated wet, diabatic model for the study of cyclogenesis. Proc. Int. Symp. Numerical Weather Prediction, Tokyo 1960, Met. Soc. Japan, 185-204. Spar J., J. P. Gerrity, Jr. and L. A. Cohen (1 961 ) Some results of experiments with an integrated, wet, diabatic weather prediction model. New York Univ., Sci. Report No. 2, Contract Nonr-285 (09), Dept. Meteorol. and Oceanography, 28 pp. (Unpublished manu- script). SuTCLiFFt R. C. and A. G. Forsdyke (1950) The theory and use of upper air thickness patterns in forecasting. Q. J. R. Met. Soc, 76, 189-217. Thompson P. D. (1961) Numerical Weather Analysis andPrediction. MacMillan Co. New York. Winston J. S. (1955) Physical aspects of rapid cyclogenesis in the Gulf of Alaska. Tellus, 7, 481-500. Yanai M. (1961) A detailed analysis of typhoon formation. J. Met. Soc. Japan, (2), 39, 187-213. 59 Reprinted from MONTHLY WEATHER REVIEW, Vol. 97, No. 7, July 1969, pp. 471-489. UDC 651.676.11:561.S77.11:561.674.1:5M.«09.617 MODELS OF PRECIPITATING CUMULUS TOWERS JOANNE SIMPSON and VICTOR WIGGERT Atmospheric Physics and Chemistry Laboratory, ESSA, Miami, Fla. ABSTRACT This paper presents a model of the growth of cumulus clouds. The water content and maximum height of rising towers are calculated using a buoyancy equation with consideration of effects of entrainment and water load. The latter is subject to effects of modeled microphysical effects. Precipitation growth is parameterized in terras of an autoconversion equation and a collection equation. A precipitation fallout scheme is devised that depends on water content, drop spectrum, and the vertical rise rate of the tower. Then "freezing subroutines" are devised to model the effects of silver-iodide seeding. A hierarchy of seeding routines, using different ice collection efficiencies and terminal velocities, is partially tested against the data of the Stormfury 1965 tropical cumulus-seeding experiment. Some preliminary numerical experiments on warm clouds are performed, assuming changes in drop spectra from hygroscopic seeding. 1. INTRODUCTION This paper reports a first step toward a long-standing goal, namely the joint dynamical-physical modeling of a cumulus cloud. The growth and fallout of precipitation interacts with the updraft, which in turn controls the amount and development of hydrometeors. The most sophisticated models of precipitation growth (e.g., Tel- ford, 1955; Twomey, 1964; Berry, 1967) have assumed a fixed water content and invariant or zero motion field. Few dynamical models have yet considered the effects of variable fallout upon either the ascent rates or sub- sequent particle growth. Kessler (1959, 1961, 1963) pioneered in introducing the effect of varying updraft into cloud physics. He evol ved parameterized equations for precipitation growth. He used these equations in combination with assumed vertical motion profiles and an assumed water generation function, set to approximate adiabatic condensation. We adopt his physical approach, introduced into a simplified model predicting dynamical variables as a function of environment and cloud-base conditions. This model is a direct outgrowth of model EMB 65 (Experimental Meteorology Branch, 1965) of an entrain- ing cumulus tower, discussed by Simpson et al. (1965). That treatment bypassed the cloud physics by arbitrarily dropping out one-half of the liquid water condensed, regardless of updraft speed or particle spectrum. Here, we introduce the basic concepts of Kessler regarding precipitation growth, summarized by him in a recent memorandum (1967). All water is initially condensed in small cloud particles which rise with the ascending air. A process called autoconversion creates some precipitation- sized particles, which then continue to grow by collecting small cloud particles. Precipitation-sized particles have a specified terminal volocity and continually fall out of the cloud tower. The fallout relieves some of the liquid water reduction of buoyancy and acts to slow down subsequent coalescence. Our cloud physics thus consists of an auto- conversion equation, a collection or coalescence equation, a terminal velocity law, and a fallout scheme. At all stages, the model development has been tested against field measurements on both natural and artifi- cially modified clouds. Silver-iodide seeding experiments have been particularly useful tests of cumulus models; the 1965 Stormfury series is particularly emphasized here (Simpson, Simpson, Stinson, and Kidd, 1966; Simpson, Brier, and Simpson, 1967). This modeling effort is de- signed to parameterize complex processes in such a way as to give realistic predictions of measurables, such as vertical tower growth, buoyancy, hydrometeor distribu- tion, radar reflectivity, etc., in both seeded and unseeded cumulus towers. A contrasting approach is exemplified by the brave attempts at much more sophisticated models (e.g., Ogura. 1963; Murray and Hollinden, 1966; Arnason, Greenfield, and Newburg, 1968) which integrate the full hydrody- namic equations of motion on a space grid in a series of time steps. So far, none of these have achieved sufficiently realistic relationships between vertical growth, buoyancy, size, velocity, and temperature for useful prediction in modification experiments. Among the major problems are the intractability of formulating turbulent entrainment, the limitations imposed by working within confined boundaries, errors and fictitious results introduced by finite-differencing schemes, and the restriction to two- 471 472 MONTHLY WEATHER REVIEW Vol. 97, No. 7 dimensional or axisymmetric coordinates. All these difficulties have been bypassed in the EMB series by observationally guided parameterizations so that the models give realistic and useful results despite their obvious crudities. We hope that the full hydrodynamic models can build upon the more successful of our para- meterizations as the recent work by Arnason et al. (1968) has built upon those of Kessler. 2. DYNAMIC ASPECTS OF THE MODEL The development of the numerical model, up to the EMB-65 version, is described in detail by Simpson et al. (1965). It involves integrating a differential equation for the vertical acceleration of a cumulus tower, where the acceleration is formulated as the difference between a buoyancy term and a drag term. Turner (1962) showed that the same form of the equation is applicable whether a cloud tower is idealized as a jet, a buoyant rising plume, or a "thermal" with vortical internal circulation. With the basic postulate that the internal circulation takes one, or a hybrid, of these forms, the differential equation for the rate of rise w is as follows: dw dw d /w2\ gB 3 /3 , ^ . „ \ w2 ,,, dt=w dlTdz (j)=l + -y-S (l K>+C°) R (1) where z is height and t is time; gB is the buoyancy force per unit mass; y is the virtual mass coefficient; K2 is the entrainment coefficient; CD is an aerodynamic drag co- efficient; and R is the radius or horizontal half-width of the cumulus tower. The derivation of this equation is discussed by Simpson et al. (1965), and in more detail in a thesis by Levine (1965). Here, we will emphasize the physical foundations. It is important to keep in mind that we are using a quasi- Lagrangian framework in tracing the rise of a single cloud tower and that the coordinate system follows the circula- tion center of the tower. Thus, the plots of w and other variables versus z represent properties of the tower as it rises through that level. The results can only be con- sidered cloud "profiles" in the roughest sense, during the interval that a steady-state condition might be expected to prevail. This interval may be different for the thermal- dynamic properties in comparison with the hydrometeors. In the cloud physics discussion to follow, we are treating the precipitation growth and fallout within and from a single vortically circulating tower, with a roughly spherical shape and radius R. We are not able to treat precipitation growth within the whole body of the cloud, nor the ulti- mate rainout from its base. The cornerstone of the dynamic modeling lies in the entrainment relation hypothesized, namely: J-; -j— —~d (laboratory result) and l_dM M dz 9 K -^7 = 09 ~n (theoretical result). (2a) (2b) The fractional entrainment rate per unit height is (l/M)dM/dz where M is the mass in the rising tower. The important point is that the entrainment or dilution is inversely related to dimension, a relationship derived in laboratory experiments on convection. Although airborne measurements are still too crude to test this relationship definitively, it was supported by a series of unpublished temperature and liquid water records made by aircraft measurements of the Woods Hole Oceanographic Insti- tution. Deductions from other aircraft measurements are apparently in conflict (Sloss, 1967). The proportionality constant in (2a) was found by Turner (1962) for laboratory plumes while (2b) was derived by Levine (1959) for a buoyant spherical vortex. The quantity K2 is evaluated from equation (2b) as 0.71; if necessary, this value can be adjusted from observational tests. The radius R of the cloud tower is determined empirically, from photogrammetry or aircraft penetra- tions. Together with an environment sounding and condi- tions at cloud base, this completes the input to the numerical calculation. Over the oceans, cloud-base condi- tions are assumed to be saturation at environment tem- perature at the observed cloud base when available, or otherwise at the lifting condensation level. Over land, cloud-base temperature excesses must be known, since re- sults are sensitive to as little as 0.5°C variation. On the other hand, the predictions are highly insensitive to the input ascent rate w at cloud base (Andrews, 1964), which is taken as 1 m sec-1 throughout this work. Thus for the oceanic cases considered here, the entire calculation could be made when the sounding becomes available, without reference to the actual clouds, with the exception of the tower radius R. The necessity for measuring R on the experimental clouds is a major shortcoming of this approach, since, so far, meteorologists have no way of predicting the cloud dimensions that a given situation will produce. Nor have the more sophisti- cated hydrodynamic models successfully faced this problem; an input initial dimension is still required. Here, we try to pick a characteristic active tower size for each cloud. As seen in equation (2), this size selection is merely a device to determine the entrainment rate. To date, a constant R with elevation has proved ade- quate. Above about 400 mb in the Tropics, entrainment becomes a less important brake on cumuli, due to lower saturation compared to actual mixing ratios. Hence, changes in R become decreasingly important with height. The buoyancy term is evaluated as follows: buoyancy =gB= g[AT-ATv (LWC)] T, (env) (3) where AT, is the virtual temperature difference between tower and surroundings and A71„(LWC) is the reduction due to the weight of suspended liquid water, as formulated by Saunders (1957), namely, AT, (LWC) = r, LWC (4) July 1969 Joanne Simpson and Victor Wiggert 473 Table 1. — Parameiera of the EMB cumulus models Parameter Meaning EMB 66 EMB 68 Remarks Entralnment Aerodynamic drag coefficient Virtual mass coefficient Liquid water retained 0.56 0.806 0.65 0 Lab. value 0.71 0 0.6 value=1.126 LWC yi condensate. Falloutscheme ._ Much Improved In EMB 68 where T, is the cloud virtual temperature and LWC is its liquid or solid water content in grams per gram. Ideally, mixing and condensation should be calculated at each height step, followed directly by the buoyancy determination and integration of equation (1). The cost and complexity of this procedure has led us, however, to the simpler method involving an entrainment calculation following the method of Stommel (1947) which is inde- pendent of (1). First, the entrainment calculation is performed on the computer, proceeding from cloud base upward between sounding points and assuming in-cloud saturation with respect to either water or ice. Output variables are cloud temperature, specific humidity, and liquid water condensed. These cloud properties are then available to calculate buoyancies at any interpolated vertical intervals in order to integrate equation (1) in ascending steps. To complete gB and undertake the inte- gration, it remains only to specify y, CD and a fallout scheme for the condensation products. The maximum top height achieved by the cloud is defined to be that level where w goes to zero. Table 1 shows the specification of dynamic parameters in the EMB-65 version of the model, which was prescribed in advance of the 1965 Stormfury cumulus-seeding experi- ments, and the modifications made in the current EMB 68. A major weakness in EMB 65 was the arbitrary assump- tion that one-half the liquid water condensed in the entrainment calculation has fallen out of the tower at each level. A fixed fractional fallout precludes any feedback between the model's physical and dynamical processes and prevents the model from even a crude prediction of precipitation growth. With this limitation, K2 was prescribed in the range 0. 55-0. 65 by numerous in-cloud temperature measure- ments, up to and including those from the Stormfury 1963 seeding experiments. A small value of CD was introduced to allow for the apparently greater vertical-momentum reduction than that due to entrainment. Turner (1964) suggested that a virtual mass coefficient would have achieved this end more realistically. However, since EMB 65 so mishandled the water retention, it did not appear worthwhile to refine the momentum relationships further until this weakness was ameliorated. It is clear that a smaller entrainment rate and a larger fractional retention of liquid water would have equally satisfied the momentum relations, but reducing the entrainment would have given in-cloud temperature excesses higher than those observed, and so was precluded. Despite its oversimplifications, EMB 65 gave an excel- lent prediction of the maximum cloud-top heights of the Stormfury 1965 seeding experiment and the growth or nongrowth of the seeded clouds (Simpson et al., 1967). The average absolute error in height prediction was only 166 m for unseeded clouds and 336 m for seeded coluds. These "errors" are within the accuracy to which top heights could be measured. Since cloud-top heights varied widely, often on the same day, this result supports the l/R entrainment relation as a useful first approximation. The model was also used by McCarthy (1968) to predict seedability distributions for Project Whitetop clouds in Missouri. 3. CLOUD PHYSICS ASPECTS OF THE MODEL Since the 1965 experiments, an improved version of the model has been developed, using parameterized equations for the growth and fallout of precipitation. This model series is called EMB 68. An intermediate model called EMB 67 was discussed by Simpson et al. (1968). It con- tained an error in logic in water budgeting, leading to the exhaustion of cloud water in some seeded clouds and hence will not be included here. The only important change in the dynamics from EMB 65 just described lies in the introduc- tion of a virtual mass coefficient of y — 0. 5 and the drop- ping of the aerodynamic drag CD (table 1). This change was made for two reasons. First, Turner's (1963) laboratory results suggested both that the turbulent boundary layer was continually swallowed by the rising convection ele- ment so that CD should be zero and that a virtual mass effect arose from the pushing of outside air around the rising plume. Turner measured a laboratory value of y of about 0. 5. Second, EMB 65 predicted too high ascent rates for the towers, at least in comparison with our some- what fragmentary photogrammetric measurements. Use of virtual mass instead of CD reduces rise rates while giving slightly higher cloud-top heights for the same bouyancy so that we could raise K? to 0.65 in the EMB-68 series. The latter figure is still consistent with the in-cloud temperature measurements and is now within 10 percent of the laboratory value of 0. 71. The figures in section 8 show that all EMB-68 cases have considerably lower and more realistic ascent rates than did the corresponding calculations in EMB 65. The main improvement in EMB 68 is that precipitation growth is predicted, and its fallout interacts with the vertical motions. All water is first condensed as cloud water, with small drop size (roughly 5-30m) and negligible terminal velocity. Then a process called autoconversion begins. This involves the formation of precipitation par- ticles either by the aggregation of several cloud particles or by the action of giant salt nuclei, or similar processes. We reconsider autoconversion in relation to ice growth by vapor diffusion (Bergeron effect) later in section 6. We have used two different autoconversion equations in most 474 MONTHLY WEATHER REVIEW Vol. 97, No. 7 of the EMB-68 cases, namely : dM dt or (autocon version) =Ki(m— a) gm m-3 sec l (m>a) (5) -j— (autoconversion) = at m' -(•+^S) gm m-3 sec (6) where equation (5) is due to Kessler (1965) and equation (6) is due to Berry (1968a). In both equations dM/dt is the rate of growth of the precipitation water content M in gm m-3 and m is the cloud water content in gm m~3. Kessler's linear equation was obtained intuitively. The parameter Kx is the reciprocal of the 1/e "conversion time" of the cloud water. Kessler chose Kt as 10~3 sec-1 to be consistent with a cloud lifetime of about 1000 sec. Existing cloud data probably preclude values one order of magnitude higher or lower. The "a" is a threshold cloud water content at which conversion is hypothesized to begin; we have followed Kessler in taking a=0. 5 gm m~3. Berry's equation (6) is developed theoretically from a model of initial cloud growth by condensation and coalescence of cloud-sized particles with each other. The early droplet spectrum near cloud base has a number concentration of Nb drops per cm3 and a relative dispersion Db due to the condensation spectrum. The relative dis- persion Db is denned as: D„= standard deviation of droplet radii mean droplet radius (7) The derivation of Berry (1968a) used the collection efficiencies of Shafrir and Neiburger (1963). Subsequently, Berry (1968ft) has redone the calculation for the Davis and Sartor (1967) collection efficiencies and, at our request, has modified his parameterization formula to suit a boundary of 200-/1 diameter between cloud and pre- cipitation particles. His thus modified values are given in equation (6). The choice of the 200-m boundary between cloud and precipitation was made for three reasons: 1) a drop with 200-ji diameter has a terminal velocity of 1-2 m sec-1 and is thus beginning to fall at a speed com- parable to cumulus updrafts, 2) our aircraft foil pre- cipitation sampler fails to size reliably drops much smaller than this, and 3) most 10-cm radars begin to show an echo of a cloud when numerous drops of about this size are present. An important feature of Berry's equation is that a different autoconversion rate is predicted for maritime and for continental clouds. For maritime clouds we have chosen a drop concentration of 50 cm-' at cloud base and a relative dispersion of 0.366. For extreme continental clouds we later use a drop concentration of-2000 cm"' and the smaller spectral dispersion of Z>»=0.146. These num- bers are consistent with measurements by Squires (1958), Battan and Reitan (1957), and MacCready and Takeuchi (1965, 1968). For the main comparison with the 1965 seeding data, only the maritime formulation is used. Although Kessler's equation is linear and Berry's approximately cubic, the predicted physics and dynamics of the clouds differ little enough that observational selection between them is difficult with existing data. By and large, it appears that the models using Berry's autoconversion formula give somewhat better height predictions and more reasonable liquid water distributions, although obser- vational tests of the latter are inadequate to date. Twomey (1959), Braham (1968a), and others have postulated that the entire history of coalescence pre- cipitation growth in a cumulus is largely controlled by the initial droplet spectrum at cloud base. Use of equation (6) in our physical-dynamical model permits a fascinating test of this hypothesis in section 10. The coalescence or collection rate is that derived by Kessler (1965, 1967) with the assumption that the pre- cipitation spectrum follows that of Marshall and Palmer (1948). The Marshall-Palmer spectrum is defined by a single parameter n0, namely : nD=n0e-XD (8) where D is the diameter, nDSD is the number of drops with diameter in the range between D and D+8D in unit volume of space, and n0 is the value of nD for D=0. The exponent \ is related to the precipitation water content by integrating over all diameters to obtain X=42.K25Af-°-M (9) or X= 3.67 in the gram-meter-second system of units. D0 is the median volume drop diameter or the diameter which divides the distribution into parts of equal water content. We use the following equation for terminal velocity of raindrops, namely: V= — 130DU2 msec-1 (D in meters) . (10) This equation was developed by Kessler (1965) from Gunn and Kinzer's (1949) data in the "Smithsonian Meteorological Tables" by List (1951). It gives slightly different values from those in the empirical table by Mason (1957). Both were used alternatively in the trial stages of our model with undetectably different results. Using equations (8) through (10) and physical reason- ing, Kessler obtains a collection equation, namely: ^ (collection) =6.96X10-4£'nSmmM0878 gm nr at 1 sec ' (ID where E is the collection efficiency of precipitation particles for cloud particles, with a value near unity for liquid clouds. Thus the collection rate depends on the July 1969 Joanne Simpson and Victor Wiggert 475 cloud water content m, precipitation water content M, and two parameters n0 and E. From the Marshall-Palmer spectrum, a terminal velocity V0 as a function of M is derivable as follows: Kro=-38.3n0-0'1MM0126 msec" (12) Physically, V0 is the terminal velocity of the median volume drop size D0. We also compute and print out the median volume diameter of the precipitation particles from A>=joq2 meters (13) or Z>„=.087 V 26Ma25 meters pants were from ESSA, the Naval Research Laboratory, and Meteorology Research, Incorporated, with dropsonde support provided by the U.S. Air Force. The main purposes of the program were investigation of natural glaciation in tropical cumuli and measurement of the cloud-physics properties of actively rising towers. Droplet spectra were measured on the M.R.I. Piper Aztec using a foil sampler (MacCready and Takeuchi, 1967), and liquid water contents were determined by joint use of several instrument systems. A major pertinent result was the testing of the Marshall- Palmer spectrum. Roughly, a dozen excellent penetra- tions through actively rising oceanic towers were obtained. The Marshall-Palmer spectrum verified to a good first- order approximation, as it also has verified in similar measurements in Project Whitetop clouds in Missouri , ... ,, (Braham, 19686). In all cases, n0 was 107 m-4 or slightly for comparison with aircraft measurements. , . ,, , , , , r] m, ,,, , . i , j • tut -j less; in no case would a larger value have been realistic. The fallout scheme is now simple to design. We consider T^-iL c j ,n, . , . ■ , , , ,, . .. .. ,. , . r", , , , , , With n0 specified as 107 m \ sets of trial model runs the average precipitation particle to be located at the , , , , T , ,___ , , , .. . , . , „ ... . , ■ ., „ Tl were made on some of the July 1967 clouds and on the tower center and to fall with terminal velocity V0. It , , , , , , , , ., ,.„, , , ,, .. „ , ,. , ,,_ ,J .. unseeded and preseeded clouds of the 1965 experiment and leaves the vortically circulating portion of the tower after , ..f n L t *• * tJ t i , „. ,, , , . ,. . , , n m. » A- i, ii compared with all pertinent observations. A K2 of no larger falling through a height interval K. The fractional fallout ., ««- X . ..i h.i*ai.ij u * e • -i. i- w° i i. • i. • . i • lL e than 0.65 was confirmed; at least half the clouds would not of precipitation M in each height interval is therefore , , , , , ... , . , . m, •• .. .r ..... , t 1.1. j. l-l u it reach observed levels with a higher value. The collection the ratio of the time for the tower to rise through the ~, . _, . ,. ,,,7? , , , „ , , . , . ,. , ,, . , ,. . °, . efficiency E in equation (11) is chosen as 1, following vertical height step over which the integration is being „ , „ , ,. , , ,. , , n . j /tm \ i. a i . ., , j. j- . Kessler. Present modeling and observational deficiencies made (50 m) to the time for the volume median diameter , ,, .... •:» . ij u j . .ii .. , j- /-ii i ^1 i lL we such that adjusting it for unfrozen clouds would not drop to fall through one radius. Clearly, the larger the , . . . J , .,,111 , , ., 1.1 .■. 1 ., . 11 be meaningful. The values of the cloud physics parameters drops and the weaker the rise rate, the greater the fallout , , ,,„.,„ -D ,. ., , , \_ . r, ,, n . , , , o , ., - „ °. , used for all EMB-68 liquid clouds are shown in table 2. per umt height, several other fallout schemes were attempted; but so far, only this one has given both Table 2. — Cloud physics parameters for liquid cloud* consistent and realistic results. From this point, the water-budgeting is straight forward. arameer All water condensed in the Stommel entrainment calcula- „ # m t ai tion in each vertical interval (z2—zl)=dz is first put into cloud water m. Then autoconversion and collection " calculations are applied to obtain AM in the interval Db where dt=dzjwi. Then AM is added to M and subtracted N from wi. Finally, a fallout calculation is applied to obtain AM fallout, which is subtracted from M. The fallout is "° summed with height in a separate column to give later e the total rainout from the tower. The final sum of m+M after conversion, collection, and fallout is used in the buoyancy correction to calculate w2, and this same sum is then exported upward to repeat the water budget in the next height interval. The basic assumption in the cloud physics modeling 0nce the precipitation water content and spectrum are is that the Marshall-Palmer (1948) spectrum, or some defined, the radar reflectivity similarly tractable distribution, prevails for precipitation 7=Tn 7> hD continuously during the active life of the tower. If true, this implies that the cloud processes are always restoring is readily predicted, namely: this spectrum in the face of the continuous fallout of the larger drops. Z=3.2X10"» n0-° ■» M1 7S (meters') (15) or Z=3.2X10»no-°"M1-7» (mm6 m"') and when n0=107 m~4 Z=1.8X10' AT" mrn'm-*.! (16) Meaning Autoconversion parameter Autoconversion threshold Spectrum dispersion Particle concentration at cloud base Marshall-Palmer Intercept Collection efficiency precipitation for cloud Value 10-' sec-' 0.8 gm m-» 0.306 maritime, 0.1« continental 80 cm-» maritime. 2000 cm-' continental 10'm-' 1 Remarkj Kessler value Ke.saler value Berry values Observed (see teit) Observed Kessler value 5. RADAR ECHO PREDICTION AND PRELIMINARY TEST OF MODEL (14) 4. AIRCRAFT DETERMINATION OF MODELING PARAMETERS A cooperative five-aircraft cumulus program was carried out in the vicinity of Puerto Rico in July 1967. Partici- 476 MONTHLY WEATHER REVIEW Vol. 97, No. 7 In EMB 68, we have also used the empirical relations between the rainfall rate R (mm hr_1) and radar reflec- tivity Z that, have been found useful in tropical areas (Gerrish and Hiser, 1964), namely: and with « UNSEEDED FALLOUT 4.5 gm/m> RADIUS ■ 1150 m "\ 'SLUSH ■ ■'■'■ ♦ {* BREAK 2 4 0 2 0 20 40 60 0 2 0 4 e 12 WATER CONTENT RADAR ECHO Tc-T. ASCENT RATE (gm par m*) K) LOG,. Z imnf/m') ro W (m/tac) Figure 7. — Predicted properties of seeded cloud 2, July 29, 1965, using model EMB 68 Kk. The observed seeded cloud tower (see figs. 10 and 13) grew vertically following seeding, cutting off from the main cloud body which dissipated. 8. PRECIPITATION CHANGES FOLLOWING SEEDING AND PHYSICAL-DYNAMICAL INTERACTIONS Columns 10-12 of table 3 deal with calculated pre- cipitation changes between seeded and unseeded clouds. The quantity AR is defined as the difference in the summed fallout between the seeded and the unseeded tower, while AR/R is the ratio of this difference to the unseeded fallout or the fractional change in precipitation fallout due to seeding. The number appearing in column 10 is the average percentage change in fallout for all seeded clouds (except 3 and 4, which were seeded above 0° C). The average AR/R does not mean much in itself since it is composed of large increases versus large decreases, with roughly the same number of clouds showing predicted increases as decreases. Figures 6-8 illustrate this point with model K. Figures 6 and 7 show results for seeded clouds 1 and 2. In all models, these clouds showed the largest positive values of AR/R. For example, cloud 1 (Kessler) showed a 19-percent increase in model A and a 51-percent increase in model F, the extreme cases. Figure 8 shows the results for seeded cloud 6, which showed the largest precipitation decrease. The correspond- AUGUST 3. 1965 SEEDED CLOUD © EMB 68 UNSEEDED EMB 68K SEEDED EMB 65 KESSLER CONVERSION SEEDED FALLOUT 3.09 gm/m> UNSEEDED FALLOUT 4.69 gm/m» RADIUS' 1000 m ; ;sa«s; — oes TOP 4 0 2 0 20 40 0 2 4 0 4 e 12 16 ER CONTENT RAOAR ECHO *-1» ASCENT RATE Igmwrm'l K} LOG. Z (mitrym*) PCI W laAltl Figure 8. — Predicted properties of seeded cloud 6, Aug. 3, 1965, using model EMB 68 KK. Note the relatively large top height predicted for the unseeded cloud and the smaller fallout predicted for the seeded cloud. The observed cloud (figs. 11 and 14) grew explosively following seeding. July 1969 Joanne Simpson and Victor Wiggert 483 ing range in its AR/R (Kessler) is from — 44 percent in model A to +12 percent in model F. Thus, the average values should be interpreted in this light. When the average is negative for a model, it simply means smaller pluses, one or two fewer clouds with increases, and larger decreases. Those clouds that showed large predicted precipitation increases from seeding in all models were those with low unseeded tops and large seeding effect EF, while those with large precipitation decreases were those with tall un- seeded tops and a smaller value of EF. The two clouds that failed to grow (5 and 9) after seeding showed neg- ligible precipitation change; these two are omitted from the correlations shown in columns 11 and 12. The inverse correlation between unseeded top heights and AR is, in nearly all models, significant at better than the 5-percent level. The positive correlation between seeding effect and AR is significant in all cases. Physically, this result means that if an unseeded cloud will grow naturally to heights of 8-10 km, seeding will probably decrease precipitation fallout by "hanging up" the precipitation particles in the ice phase. Little is gained by further growth above these levels since the condensation rate falls off to very small values at cold temperatures. The most promising cases for increased fallout from seeding are those clouds whose natural growth does not exceed 6-7 km and where a big seeding effect is predictable from the model. Since AR denotes only the fallout difference between seeded and unseeded towers, similar calculations to those in columns 10-12 were run for total precipitation produc- tion by the towers. The results were so nearly similar to the foregoing that they are not shown. The changes in precipitation fallout are on the order of 20-30 percent and generally in the range of about 1 gm m-3. This is about half an inch over 2 sq mi, or more than 50 acre-feet. This amount is of course not much, but we are considering only the rising period of a single tower. In an explosive growth case, many towers succeed each other over a greatly prolonged lifetime, so that conceivably we could obtain the half inch over as much as three times the area, or a total of perhaps about 160 acre-feet, which is not negligible. By the same argument, of course, an ex- plosive growth could overcome the calculated negative fallout difference computed only for the first tower in comparison with its unseeded fallout. It should be emphasized that we are not able to compute how much of the cloud fallout reaches the ground as precipitation. This potentiality will depend upon how much of the tower fallout descends through the cloud body and how much through the drier environment, hence upon environmental circumstances such as humidity, wind shear, and cloud-base height. Nevertheless, we hypothesize a proportionality between our calculated fallouts and potential rainfall production by seeding. In other words, circumstances of explosive growths of towers which are predicted not to grow high without seeding are most favorable, while cut-off growths are less so. Clouds which are predicted to grow to the cumu- lonimbus or near-cumulonimbus stage, unseeded, should show the smallest gains or even rainfall losses from seeding. We plan to test this hypothesis with the results of a 1968 Florida seeding program in which the precipitation at numerous levels, from cloud base upward will be evaluated with calibrated ground radars. Meanwhile, comparison of the clouds modeled in figures 6-8 illustrates very well the interactions between physical and dynamical features and perhaps explains some aspects of the difference between explosive growth and cut-off tower growth. Clouds 1 and 6 were observed to grow ex- plosively following seeding, while cloud 2 exhibited the cut-off tower regime. Figures 9-11 are photographs of these clouds; figures 12-14 show their scale outlines, re- constructed photogrammetrically. Two features dis- tinguish the cut off from the explosive cases. The first is the wider measured cloud body of clouds 1 and 6 compared to cloud 2. The second distinguishing feature lies in the calculated velocity, water, and temperature profiles. Note in figure 7 that the vertical ascent rate goes virtually to zero at 6 km, while it increases rapidly to above 8 m sec-1 between 7 and 8 km. The diminution of ascent rate causes a "dumping" of hydrometeors at 6 km, the level at which the break appears. The unloading of the tower permits it to accelerate rapidly, while the rather narrow cloud body below is apparently killed (fig. 10B) by the "fall-through" of the precipitation. A stable dry layer in the environment of cloud 2 gives rise to a strong negative buoyancy from just above 4 km to nearly 6 km. 9. MARITIME VERSUS CONTINENTAL CLOUDS AND WARM CLOUD EXPERIMENTS Figure 15 shows a typical maritime tropical cumulus and its extreme continental counterpart. The same sounding and radius are used for both clouds, as is the Berry conversion equation (6). For the maritime cloud, Nt=50 cm-3 and Db= 0.366. For the continental cloud, 7V»=20OO cm"' and D»= 0.146. The dynamics of the resulting clouds are virtually identical, although the continental cloud terminates about 100 m lower due to the 1 gm m-3 higher water content near its top. The physical properties and radar echoes of the clouds are utterly different. The precipitation fallout is nearly eight times as much from the maritime cloud as from the continental cloud! The vast predicted difference, particularly in precipita- tion, between maritime and continental clouds encourages experimentation on converting one type of cloud into the other, particularly by seeding with hygroscopic particles. Could a maritime cloud be inhibited from raining by the addition of very many small hygroscopic particles? More importantly, could a continental cloud be caused to rain more by broadening its cloud base spectrum? Figures 16 and 17 are preliminary numerical tests of these ideas. 484 MONTHLY WEATHER REVIEW Vol. 97, No. 7 Figure 9. — Photograph of seeded cloud 1, July 28, 1965, at seeding time (2217:30 gmt). Right-hand portion seeded. In experiment 1 (fig. 16), we hypothesize adding enough small hygroscopic particles to reach the continental concentration, but since we cannot remove the giant oceanic nuclei, we leave the relative dispersion unchanged. The results are striking. We predict a large (nearly 100 percent) increase in cloud water content and a 72-percent decrease in precipitation fallout. In experiment 2, we try to make a continental cloud more maritime and to increase precipitation by a hypo- thetical introduction of enough large hygroscopic particles to widen the relative dispersion to 0.488 while leaving the droplet concentration unchanged from 2000 per cm3. The results are successful, although less so than in experi- ment 1. We predict an increased precipitation fallout of 150 percent per tower which, however, amounts to only 0.29 gm m"3 or at most about 15 acre-feet. Thus, while hygroscopic seeding appears the most promising technique for rain increase under drought conditions, when only warm clouds are present, it is not as drastic nor as powerful a cloud modification technique as silver-iodide seeding, since it only affects the physics of the seeded tower itself, while silver-iodide seeding can affect the dynamics of the entire convective system over numerous life cycles of an individual tower. 10. CONCLUDING REMARKS A final supercooled seeding experiment was tried numerically, designed to test the Bergeron effect alone. Dynamic effects via latent heat release were assumed to be zero, and the only seeding effect was hypothesized to be increased autoconversion beginning at — 4°C in the seeded clouds. These experiments were performed with the Kessler formulation only. Values of Kiy 4 times and 10 times the value (10-3 sec-1) used for liquid clouds, were taken. The tiny increases in precipitation and fallout were too small to affect any of the significant figures in the predictions. This result confirms an earlier July 1969 Joanne oimpson and Victor Wi<3Sert 485 Figure 10.— Photographs of seeded cloud 2, July 29, 1905; (A) at ll: min after seeding (1812 gmt); (B) at 15J1 min after seeding (1S26 gmt) Note ii.ii -eedcd lowei nas *.iu off and is showering into main cloud body below, which is dissipating. 486 MONTHLY WEATHER REVIEW Vol. 97, No. 7 Figure 11. — Photograph of seeded cloud 6, Aug. 3, 1965, at 11% min before seeding (2147 gmt). conclusion by Kessler (1967) that large changes in auto- conversion do not affect precipitation growth after collection has become important in a cloud. Therefore, the main conclusion of this paper is that the main effect of seeding supercooled tropical cumuli is through the alteration of the cloud dynamics, which in turn alters the water carried and precipitated. The feed- back of the physics to the dynamics only changes the motion field critically in certain marginal situations, for example the cut-off case of figure 6. A hierarchy of quite different physical models, with widely different ice collection efficiencies and ice fall speeds gives results dynamically very similar to each other. Furthermore, the results with the new EMB-68 series arc qualitatively the same as with the simpler EMB-65 model — the clouds that grew significantly following seeding could not be made to fail to grow (and vice versa) with any reasonable permutations of the seeding subroutine nor of the ice regime. However, some selection among the physical models was possible with available measurements, suggesting a reduction of ice terminal velocity relative to that of water particles. The best EMB-68 models give reasonable predictions of precipitation growth, fallout, and radar echo intensity, which stand to be tested with results of the next obser- vational program. Both positive and negative precipitation changes of the order of 20-30 percent are predicted. These are equivalent to water amounts of 100-200 acre-feet per cloud of these dimensions, if precipitation falling from the tower reaches the ground. In any case, it July 1969 > s MAX GROWTH Joanne Simpson and Victor Wiggcrt 487 STORMFURY CUMULUS JULY 28. 1965 r '. vtNy (1 ^ - CLOU) ZOJOOMT Figure 12. — Scale outlines of seeded and control clouds on July 28, 1965, constructed using photogrammetry as described by Simpson (1967). STORMFURY CUMULUS JULY 29. 1965 MODEL CLOUD NINE — MARiNE FALLOUT 1.48 gm/m' BARBAD0S --LAND FALLOUT 0,9^ ^ ^ ^ -I R « 400 m TOTAL P c ■j \ - ; "--rN. — top . / L • /OBSI \ 7 ■ 1 r / / ■II 1 1 ■) - K, = 0 65 1 . E ■ 100 % / / ■ y / ■ . ymi ■ , i 1 1 1 i i i i WATER CONTENT RADAR ECHO Tc-T« ASCENT RATE (qm per m'l 10 LOG,. Z (mmVm') CCI W (m/i.cl CONTROL CLOUO I , MAX GROWTHS 1922 GMT SEEDED ClOUD C~^> 'TANGO iBlOGMT . ^ MAX GROWTH 1829 GMT CONTROL CLODD 2 =^^ "TANGO" 2044-30 GMT .___, MAX GROWTH 2054 GMT Figure 13. — Scale outlines of seeded and control clouds on July 29, 1965, constructed in the same manner as figure 12. STORMFURY CUMULUS AUGUST J. IS6S SEEDED CL OUD AT TANGO 2158 30 GUT CREW EXPLOSIVELY Figure 14.— Scale outline of seeded cloud 6, Aug. 3, 1965, at time of seeding. Due to aircraft radar failure, no photogrammetry was possible after seeding. is possible to predict with this model favorable and unfavorable situations for silver-iodide seeding;. The favorable situations are those of large vertical growth following seeding or large seeding effect, particularly if explosive growth occurs. The difference between explosive and cut-off tower growth can now be foretold in part, at least, from the model. The less favorable or unfavorable Figure 15. — Model cloud 9 for Barbados, Aug. 22, 1963. Model used was EMB 68K, with Berry marine (solid) and Berry land (dashed) autoconversion. Radius data, observed radar echo, and top heights obtained from original records of Saunders (1965). The Barbados radiosonde for 1823 omt was used. The tower was followed by Saunders between 1802-1817 omt. UNMODIFIED MARINE CLOUD MODIFIED MARINE CLOUO. N6 = 2000 c FALLOUT UNMODIFIED'! 48qm/m' MOOIFIED-0 42gi SALT-SEEDING EXP I MARINE CLOUD I BARBADOS CLO 9) SEEOED WITH SMALL PARTICLES (KMI 40 2 0 1 0 20 40 -1 0 1 0 2 4 6 WATER CONTENT RADAR ECHO Tc-T4 ASCENT RATE (gmp.rm'l IOLOG Z (mm'/m'l CCI W (m/i.ci Figure 16. — Hypothetical salt seeding experiment 1. Solid lines denote unmodified cloud. Dashed lines denote modified cloud. Attempt to convert maritime toward continental cloud by addition of small particles to make jV6=2000 per cm3. Relative dispersion unchanged from 0.366. Note reduced precipitation production and fallout. situations for seeding are those with high natural cloud growth and small seedability. Hygroscopic seeding of warm clouds appears to be an interesting and promising experimental series to test in the field on individual clouds. Several groups, particularly Howell and Lopez (1968), have such experiments under- way. However, front both the cloud study and large-scale viewpoint, silver-iodide experiments on supercooled clouds probably have more to offer, in that the dynamics of single clouds and probably of whole cloud groups can be 152-IF2 O - 09 488 MONTHLY WEATHER REVIEW Vol. 97, No. 7 UNMODIFIED LAND CLOUD ■ MODIFIED LAND CLOUD, D,"0 488 FALLOUT UNMODIFIED OI9gm/m' MODIFIED 0 46gm/m' T SALT-SEEDING EXP 2 LAND CLOUD (BARBADOS CLD 9) SEEDED WITH LARGE PARTICLES WATER CONTENT (gm per m') ASCENT RATE W (m/sec) Figure 17. — Hypothetical salt seeding experiment 2. Attempt to convert continental toward maritime cloud by addition of large particles. Relative dispersion is increased from 0.146 to 0.488, while N ;, remains 2000 per cm3. Note small but percentually significant increase in precipitation production and fallout. drastically altered; this quite possibly can trigger per- sistent alterations in the physical cloud processes, such as precipitation structure and fallout. Note added in proof — Some observational evidence on the hydrometeor spectrum in the ice phase has become available since completion of this paper. During a Florida cumulus seeding experi- ment in May 1968, it was found that while the slope of the ice particle spectrum did not differ much from the Marshall-Palmer relation used herein, the intercept n0 (Takeuchi, 1969) was about one order of magnitude higher than that given in table 2. In our model, n„ appears to the 0.125 power in the collection equation (11) and the terminal velocity equation (12). An order of magnitude increase in n0 would, therefore, lead to a collection rate multiplied by a factor of 1.33 and a particle terminal velocity divided by this factor, other parameters and variables being equal. Let us consider the effect of the higher n0 on model EMB 68K, which gave the best fit with observations. In this version of the model, the ice collection efficiency E was one, while the ice terminal velocity was reduced to 20 percent of the corresponding values for water. With ra0 increased by the 10 factor, we would obtain the same results as in 68K if we reduce the ice collection efficiency to two-thirds the water value and take the terminal velocities for ice to be 30 percent of those for water particles the same size. These changes appear quite reasonable. Unfortunately, no adequate measurements of cither ice collection efficiencies or terminal velocities yet exist to test these inferences. ACKNOWLEDGMENTS The authors gratefully acknowledge the valuable help of their colleagues Roscoe Braham, Robert Ruskin, and Helmut Weick- mann. They are particularly grateful to Edwin Kessler, upon whose fine work much of this approach is based and to Edwin X. Berry who worked closely with us on autoconversion. Mr. Robert Powell ably drafted the figures, and Mrs. Peggy Lewis prepared the numerous versions of the manuscript. The work on warm cloud experiments has been kindly supported by the Bureau of Reclamation, U.S. Department of the Interior. REFERENCES Andrews, D. A., "Some Effects of Cloud Seeding in Cumulus Dynamics," M. A. thesis, Department of Meteorology, University of California, Los Angeles, 1964, 139 pp. Arnason, G., Greenfield, R. S., and Newburg, E. A., "A Numerical Experiment in Dry and Moist Convection Including the Rain Stage," Journal of the Atmospheric Sciences, Vol. 25, No. 3, May 1968, pp. 404-415. Austin, P. 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E., and Lopez, M., "Project Rainstart," Interim Report, Contract No. NSF-C453, E. Bollay Assoc, Inc., Goleta, Calif., July 1968, 66 pp. Kessler, E., Ill, "Kinematic Relations Between Wind and Precipita- tion Distributions, I," Journal of Meteorology, Vol, 16, No. 6, Dec. 1959, pp. 630-637. Kessler, E., Ill ."Kinematic Relations Between Wind and Precipita- tion Distributions, II" Journal of Meteorology, Vol. 18, No. 4, Aug. 1961, pp. 510-525. Kessler, E., Ill, "Elementary Theory of Associations Between Atmospheric Motions and Distributions of Water Content," Monthly W.alher Review, Vol. 91, No. 1, Jan. 1963, pp. 13-27. July 1969 Joanne Simpson and Victor Wiggert 489 Kessler, E., Ill, "Microphysical Parameters in Relation to Tropical Cloud and Precipitation Distributions and Their Modification," Geofisica International, Vol. 5, No. 3, July 1965, pp. 79-88. KesSler, E., Ill, "On the Continuity of Water Substance," ESSA Technical Mimorandum IERTM-NSSL 33, U.S. Department of Commerce, Washington, D.C., 1967, 125 pp. Levine, J., "Spherical Vortex Theory of Bubble-Like Motion in Cumulus Clouds," Journal of Meteorology, Vol. 16, No. 6, Dec. 1959, pp. 653-662. Levine, J., "The Dynamics of Cumulus Convection in the Trades: A Combined Observational and Theoretical Study," Ref. No. 65-43, Woods Hole Oceanographjc Institution, Mass., 1965, 129 pp. List, R. J., "Smithsonian Meteorological Tables," Publication 4014, Smithsonian Institution, Washington, D.C., 6th Rev. Ed., 1951, 527 pp. MacCready, P. B., Jr., and Takeuchi, D. M., "Precipitation Mechanisms and Droplet Spectra of Some Convective Clouds," Analysis of Flagstaff Data, Report No. 2, Contract No. DA 28-043~AMC-00406(E), Meteorology Research, Inc., Altadena, Calif., 1966, pp. 3-33. MacCready, P. B., Jr., and Takeuchi, D. 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M., "Natural Glaciation and Particle Size Distribution in Marine Tropical Cumuli," Final Report Contract No. E22-30-68(N), Meteorological Research, Inc., Altadena, Calif., Aug. 1968, 71 pp. Murray, F. W., and Hollinden, A. B., "The Evolution of Cumulus Clouds: A Numerical Simulation and Its Comparison Against Observations," Final Report, Contract Nonr-4715(00), Douglas Aircraft Co., Inc., Santa Monica, Calif., Mar. 1966, 149 pp. Ogura, Y., "The Evolution of a Moist Convective Element in a Shallow, Conditionally Unstable Atomsphere: A Numerical Calculation," Journal of Atmospheric Sciences, Vol. 20, No. 5, Sept. 1963, pp. 407-424. RuskLn, R. E., "Measurements of Water-ice Budget Changes at — 5C in Agl-Seeded Tropical Cumulus," Journal of Applied Meteorology, Vol. 6, No. 1, Feb. 1967, pp. 72-81. Saunders, P. M., "The Thermodynamics of Saturated Air: A Con- tribution to the Classical Theory," Quarterly Journal of the Royal Meteorological Society, Vol. 83, No. 357, July 1957, pp. 342-350. Saunders, P. M., "Some Characteristics of Tropical Marine Showers," Journal of Atmospheric Sciences, Vol. 22, No. 2, Mar. 1965, pp. 167-175. Sax, R. I., "The Importance of Natural Glaciation on the Modifi- cation of Tropical Maritime Cumuli by Silver Iodide Seeding," Journal of Applied Meteorology, Vol. 8, No. 1, Feb. 1969, pp. 92-104. Shafrir, U., and Neiburger, M., "Collision Efficiencies of Two Spheres Falling in a Viscous Medium," Journal of Geophysical Research, Vol. 68, No. 13, July 1, 1963, pp. 4141-4148. Simpson, J., "Photographic and Radar Study of the Stormfury 5 August 1965 Seeded Cloud," Journal of Applied Meteorology, Vol. 6, No. 1, Feb. 1967, pp. 82-87. Simpson, J., Brier, G. W., and Simpson, R. H., "Stormfury Cumulus Seeding Experiment 1965: Statistical Analysis and Main Results," Journal of Atmospheric Sciences, Vol. 24, No. 5, Sept. 1967, pp. 508-521. Simpson, J., Simpson, R. H., Andrews, D. A., and Eaton, M .A., "Experimental Cumulus Dynamics," Reviews of Geophysics, Vol. 3, No. 3, Aug. 1966, pp. 387-431. Simpson, J., Simpson, R. H., Stinson, J. R., and Kidd, J. W., "Stormfury Cumulus Experiments: Preliminary Results 1965," Journal of Applied Meteorology, Vol. 5, No. 4, Aug. 1966, pp. 521-525. Simpson, J., Wiggert, V., and Mee, T. R., "Models of Seeding Experiments on Supercooled and Warm Cumulus Clouds," Proceedings of the First National Conference on Weather Modifica- tion, Albany, New York, April £8- May 1, 1968, American Meteorological Society, State University, Albany, 1968, pp. 251-269. SIoss, P. W., "An Empirical Examination of Cumulus Entrain- ment," Journal of Applied Meteorology, Vol. 6, No. 5, Oct. 1967, pp. 878-881. Squires, P., "The Microstructure and Colloidal Stability of Warm Clouds: Pt. 1. The Relation Between Structure and Stability, Pt. 2. The Causes of the Variations in Microstructure," Tellus, Vol. 10, No. 2, May 1958, pp. 256-271. Stommel, H., "Entrainment of Air Into a Cumulus Cloud," Journal of Meteorology, Vol. 4, No. 3, June 1947, pp. 91-94. Takeuchi, D. M., "Analyses of Hydrometeor Sampler Data for ESSA Cumulus Experiments, Miami, Florida, May 1968," Final Report, Contract E22-28-69(N), Meteorology Research, Inc., Altadena, Calif., 1969. Telford, J. W., "A New Aspect of Coalescence Theory," Journal of Meteorology, Vol. 12, No. 5, Oct. 1955, pp. 436-444. Todd, C. J., "Ice Crystal Development in a Seeded Cumulus Cloud," Journal of Atmospheric Sciences, Vol. 22, No. 1, Jan. 1965, pp. 70-78. Turner, J. S., "The 'Starting Plume' in Neutral Surroundings," Journal of Fluid Mechanics, Vol. 13, No. 3, July 1962, pp. 356-368. Turner, J. S., "The Motion of Buoyant Elements in Turbulent Surroundings," Journal of Fluid Mechanics, Vol. 16, No. 1, May 1963, pp. 1-16. Turner, J. S., Department of Applied Mathematics and Theoretical Physics, Kings College, Cambridge, England, 1964, (personal conversation) . Twomey, S., "The Nuclei of Natural Cloud Formation: Pt. 2. The Supersaturation in Natural Clouds and the Variation of Cloud Droplet Concentration, " Geofisica Pura e Applicata, Vol. 43, May/ Aug. 1959, pp. 243-249. Twomey, S., "Statistical Effects in the Evolution of a Distribution of Cloud Droplets by Coalescence," Journal of Atmospheric Sciences, Vol. 21, No. 5, Sept. 1964, pp. 553-557. Weickmann, H. K., "A Nomogram for the Calculation of Collision Efficiencies," Artificial Stimulation of Rain, Proceedings of the First Conference on the Physics of Cloud and Precipitation Particles, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts. September 7-10, 1966, Pergamon Press, New York, 1957, pp, 161-166. Weinstein, A. I., and Davis, L. G., "A Parameterized Numerical Model of Cumulus Convection," Report No. 11, Contract No. NSF GA-777, The Pennsylvania State University, University Park, May 1968, 44 pp. Wexler, R., "Radar Detection of a Frontal Storm 18 June 1946," Journal of Meteorology, Vol. 4, No. 1, Feb. 1947, pp. 38—44. Woodley, W. L., "Computations on Cloud Growth Related to the Seeding of Tropical Cumuli," Bulletin of the American Meteoro- logical Society, Vol. 47, No. 5, May 1966, pp. 384-392. Received October SI, 1968; revised January 6, 1969] 60 U.S. DEPARTMENT OF COMMERCE Environmental Science Services Administration Research Laboratories ESSA Technical Memorandum ERLTM-APCL 8 INTENSIVE STUDY OF THREE SEEDED CLOUDS ON MAY 16, 1968 Joanne Simpson William L. Woodley Experimental Meteorology Branch Coral Gables, Florida Atmospheric Physics and Chemistry Laboratory Boulder, Colorado May 1969 TABLE OF CONTENTS ABSTRACT Page 1. INTRODUCTION 2. RADAR AND PHOTOGRAPHIC OBSERVATIONS OF THE SEEDED CLOUDS 2 . 1 CLOUD 5 2.2 CLOUDS 6 AND 8 3. DETAILED CLOUD PASS OBSERVATIONS 4. NUMERICAL MODEL STUDIES OF THE MAY IS, 1968, CLOUDS 5. CONCLUDING REMARKS 6. ACKNOWLEDGEMENTS 7. REFERENCES 3 3 8 15 25 39 40 41 in ABSTRACT Three cumulus clouds were seeded over the south Florida pen- insula on a day ideally suited for a cloud modification experi- ment. Following seeding, one of these clouds dissipated without growth, while the other two grew explosively. Of these two, the first exhibited rapid growth of the tower that was tallest at the seeding time, the second underwent "hesitation" growth of a later tower, with dissipation of the tower that was tallest at seeding time. This paper analyzes the history of each cloud with aircraft and ground radar observations and with a parameter- ized numerical model. Cloud measurements were made by four aircraft. Observations from the ESSA DC-6 and B-57 are described here. These consisted of quantitative photography and of in-cloud records of tempera- ture, humidity, and water content. Pho togr amme t r y with the air- borne cameras was performed to obtain the heights and sizes of the clouds as a function of time. The numerical model predicts the rise rate, cloud and pre- cipitation water contents, and radar echo intensity of a rising cloud tower. The calibrated ground radars were used in con- junction with the aircraft penetrations to test the model pre- dictions. The model was found to predict all parameters effec- tively in the case of liquid clouds. Complete data for a simi- lar test for frozen clouds are still lacking. The model results showed that the first cloud that failed to grow had (due to narrow width) zero seedability or growth potential. The second cloud was shown able to grow with little tower expansion, while the third cloud required significant tower expansion to reach observed heights, thus explaining the "hesitation" growth. ' IV INTENSIVE STUDY OF THREE SEEDED CLOUDS ON MAY 16, 1968 Joanne Simpson and William L. Woodley INTRODUCTION During the period May 15 to June 1, 1968, the Experimental Meteorology Branch (EMB) and Research Flight Facility (RFF) of ESSA and the Naval Research Laboratory (NRL) conducted a super- cooled cloud seeding project in south Florida. A description of the seeding system, experimental procedures , and a summary of results to date are reported elsewhere (Simpson et al. , 1969) . The results of the May 1968 Florida program left little doubt that seeding was effective in inducing explosive cloud growth. These results are consistent with past experimentation on tropi- cal cumuli conducted in the Caribbean (Malkus and Simpson, 1964; Simpson et al. , 1967) . The summary figures of the effect of silver iodide seeding on tropical cumuli are certainly of inter- est. However, it is the case study that provides the best in- sight into the response of clouds to airborne silver iodide seed- ing. This paper is such a study. Three clouds were selected for experimentation on May 16, 1968, with the randomized seeding instructions dictating that all clouds be seeded. The first experimental cloud on May 16 collapsed completely following seeding, while the second and third experimental clouds grew explosively following seeding. These clouds received careful scrutiny based on aerial time- lapse photography, detailed cloud pass observations, iso-echo radar data, and EMB numerical model predictions. Radar and photo- graphic documentation of general convective developments over south Florida on May 16, 1968, have already been provided by Woodley and Partagas (1969). Photogramme t ri c documentation of seeded cloud behavior was provided by 16 and 35 mm aerial time-lapse photography. The 3 5 mm cameras were mounted on the left and right sides of the RFF DC-6 , while the 16 mm cameras were mounted on the noses of the RFF DC-6 and B-57 aircraft. The pho togr amme t r i c calculations of cloud tower diameter and rise rate were made from the time- lapse photography based on a system described in a report by Herrer a-Cant i 1 o (1969). Briefly, the values of aircraft pitch and roll provided by the APN-81 Doppler on the DC-6 were used, along with a scaled plot of the aircraft track and a series of grid overlays to read horizontal and vertical angles to prominent cloud features at various points along the flight track. The azimuths to im- portant cloud features read from the pictures were then plotted on the scaled flight track. The common intersection (generally only approximate to within a mile or so) of the azimuthal lines provided range of the aircraft to a particular cloud feature. The range values plus the readings of vertical and horizontal angles permitted a calculation of cloud tower height and di ameter . The radar measurements were obtained from the ground-based UM/10 cm radar of the Radar Meteorological Laboratory of the University of Miami operated with the iso-echo system described by Senn and Andrews (1968) . This system provided four contours of echo return corresponding to — -iyu , -86, -76, and -64 dbm as verified by the calibration scheme of Senn and Courtright (1968). The detailed cloud pass measurements included temperature, relative humidity, liquid water, and inferences of cloud draft structure. In addition, samples of cloud and precipitation size particles were obtained with a continuous cloud particle sampler (MacCready and Todd, 1964) . The final phase of this study is a comparison of cloud behavior with that predicted by the latest version of the EMB cumulus model (Simpson and Wiggert, 1969). Maximum cloud top heights and cloud rainfalls computed with the radar data are compared with model predictions. 2 2. RADAR AND PHOTOGRAPHIC OBSERVATIONS OF THE SEEDED CLOUDS The behavior of experimental clouds 5, 6, and 8 on May 16 is documented in figures 1 through 4. The time of each photo- graph and the aircraft from which it was taken are indicated under each picture. Important cloud features are lettered for easy identification and to facilitate discussion. Aircraft position and heading at the time of each photograph are indicated on the contoured 10 cm radar depiction of the subject cloud. The time of the radar depiction appears below each panel. The radar beam was centered at the flight level of the DC-6 ("V 20,000 ft) in all radar depictions. True north is at the top of each panel. 2.1 Cloud 5 The first view of cloud 5 is found in the right foreground of picture 1 in figure 1, 2 min after the RFF DC-6 had flown just over the cloud at A. The towering cloud in the background was the first to reach cumulonimbus stature over south Florida on this day. Cloud 5 had a double structure on radar at 1750Z. This cloud reached its reflectivity maximum at this time. The view of the cloud from the nose camera of the B-57 dur- ing the first seeding run is shown in picture 2 (fig. 1) . The cloud had dissipated considerably both visually and on radar since the first DC-6 cloud pass. Cloud 5 collapsed completely 6 min after commencement of the first seeding run (picture 3, fig. 1) . It was the only cloud during the May program that failed to respond to seeding. No detailed photogr amme tr i c calculations were made on this cloud because it did not grow following seeding. Cloud 5 had a maximum top of 20,000 ft}which coincided with the time of the first DC-6 pass. No detailed cloud pass information was obtained by the RFF DC-6 because the cloud was below the aircraft flight altitude at all times. o Q 2 UJ O UJ < < o o < UJ X 2 h- O u. 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Because these clouds reacted so spectacularly to seeding, scale outlines (fig. 5) and pho togramme t ri c calculations Were made for those clouds. Cloud top heights and tower radii calculated for clouds 6 and 8 appear in figures 6 and 7. The numbers appearing along the curves correspond to the numbers of the photographs in figures 2 through 4. Cloud top height and tower radius at the time of any picture is easily read from these curves. Prominent cloud towers are lettered, while the subscripts refer to short- lived turrets or bubbles on the towers. In figure 6, we see that the air craft- measured maximum top of tower AB is nearly 6000 ft higher than the highest top seen photogr ammetr ical ly . This recurring discrepancy has been explained by Woodley (1969) , and the explanation is illustrated in figure 8. The aircraft was flying at a distance of only 9 mi from cloud 6. Simple trigonometry shows that a tower 3 mi farther (the distance of the strongest echo) and 7000 ft higher than that measured would not have been visible on the photograph. Rather small distances from aircraft to cloud were necessary in order to obtain pene- trations every 10 to 15 min. Cloud 6 was photographed at 1822Z by the nose camera of the B-57 seeder aircraft while in formation to the right of the RFF DC-6 (picture 1, fig. 1) . At this time, cloud 6 had several o towers, none with special prominence. The B-57 then made a 90 right turn and a 180 left turn to position itself for the first seeding run, while the DC-6 continued on the same heading for its first penetration of cloud 6. The photograph from the B-57 at 1824Z (picture 2, fig. 2) shows cloud 6 seconds before 10 silver iodide flares were ejected into tower A, which was the most prominent cloud feature. The photogrammetric calculations for this cloud (fig. 6) revealed TIME JGCJj. LEGENO DIRECTION Of COMPOSITE 182900 Z 183230 Z 183845 Z 194825 Z — > N SEEDED CLOUD 6 MAY 16, 1968 K2KM-H SHEAR TIME (OCT) LEGENO DIRECTION OF COMPOSITE 194405 Z 195555 Z 200210 Z 201230 Z 202045 Z SE — x — • e ENE SEEDED CLOUD 8 MAY 16, 1968 -2KM-H 1. N ^_y / r> ANVIL S "■^1 / P ANVIL •J C ^ 0 \ \ SHEAR I9.0O0 FT at selected ti mej 5 2 9 <» * * V 10 (* * CM O IO CM CM C\J CO 1 t ' ' 1 ' I1 1 1 1 I'M 1 I 1 '1 ' - * * * 0 1- &> O O K 1 — 5 1 1 . > 1 < 1 1 / 2 — if) (0 1 1 1 - Z> ~— — _ u> . Q < CC " f tr. m - LU < cr s a s « 2 * 1 1 1 1 1 I O £ H 0 - Q » £» 2: / 1/ < - h- X " CO LU X - LL CD O < h~ ■°\ A CD CC 1 . V . CC •v $ O • \ LU X. O "J \ i_ u. as 3 O X o< "" O r- X k <« \ uj a: _J \ ^S \ wo " - •*> \ !►■ >-~-' Ll 1 "■■ O \ >v CD \ cc LU *\ w^ \ * \LU ~ O \. / P ~7 < ir\ \ lio X "• I O M LU < N. *\ ^ CC X LU X g \ - h- CO O 1- 1 1 1 1 1 1 - 0 0 o> <*> 1! 1 ll . 1 . 1 1 li .ll ii 1 10 •w 0 CO O *-> •H T> •H C -o 0 •* (0 Cm CO V) to OJ Wi u (V M > O <* 0 O ao ■p (A TJ OJ C 5- t& ^ 0 3 ■ Si w O <"> -j ,d <1> T5 &» -C Z ■H ■P <0 OJ x! Cn 10 -ri ro CD 0) to iw X iM •SJ ro u x: » +j U CO •H rH 1 CM OJ «? CO ao g S n 6 OJ A) - XJ M cd e ■:0 tn 3 CM O T3 C CO +J 3 O 0 OJ rd H X CC O -P 8 CD 0> M 3 tr> -r4 Lv V CM O CO (0 * CM O CD <0 * V «■ V ro ro fO IO IO CM CM CM (t0|xlJ)iH9l3H dOl OnOlO 10 CLOUD 8 TIME CHANGE OF CLOUD TOP HEIGHT AND TOWER RADIUS 16 MAY, 1968 i < r 1 1 r -i 1 1 r -i 1 1 1 1 1 1 1 1 1 1 1 1 r cloud top height cloud radius -extrapolated curve 42 ■ 40 S 38 N l- t »• I 54 (9 Hi X 32 a. o 50 3 28- o TOWER A - ** J 44 I 4" -40 - 58 - 56 - 34 - 32 - 30 - 28 - 2« - 24 ~ 22 - 2C - IS 2'J'8 TIME (MINUTES) 44 - 42 -13 40- -12 „~ 38- O i 36- t -" i34" I % 30- K - 9 24- 22-' 20- - i 18 - URCRAFT WCASUREO MAXIMUM TOP OF TOWER 8 TOWER C, (EAST) TOWER C, _L _1_ _L_ J_ J_ - 44 -44 -42 -40 -38 -36 - 34 -32 - 30 - £8 - 26 - 2* - 22 - 20 - IS J_ 2020 2022 2024 2026 2028 2030 2052 2054 2056 2038 2040 2042 TIME (MINUTES) Figure 7. Photogrammetr i c calculations of the top heights and tower radii of cloud 8, May 16, 1968. The numbers along the curves correspond to the numbers of the photographs in f igs . 3 and 4 . 11 / c o •H P ■H W O ft s o c 0) CO (0 P Cn •H a> ft o p £ e -H X (0 e (0 o •H P •H P o •r-! Em C o •H P •H CO O a. e o n c a> 0 3, «.T00 £ •9.SOO >-w II §5 rl Uig s UJ (T I . > > 5 T i| il i i TTu n ii il i I ! . IV I, II Ml t ini i vti il 4 t till III II j VERTICAL MOTION TJTT LATITUOC 25.TH LONGITUDE 80»*W J L BztoO «2CK> M2E20 MO «2t40 «2tS0 B22O0 1822 10 162220 B2230 022.40 022.-90 162300 02110 182320 TIME Figure 9. Internal measurements at 19,000 ft (pressure" altitude) in cloud 6, pasc 1, on May 16, 1968, made by instrumentation in the RFF DC-6 . The temperature and humidity measurements were made with an infrared hygrometer and a vortex thermo- meter, respectively. Total liquid water (dashed curve) was measured with Levine instrumentation, while cloud water (in drops with diameter <^ 40u) was measured with a Johnson- Williams hot wire instrument. Cloud drafts were inferred from the output of an integrating accelerometer . The wind observations were made with the Doppler navigation system. The true aircraft heading on this pass was 250 . 16 ^rrrf rffff rf\^^ \ f tfffffffffn ™f oyr y oy- °f oy- °y to 10 UJ 18.500 or a. 18.300 if < u. 100 60 0 — UJ CE r> i- Si 0. It _i -8.0 > > -9.0 -10.0 I i. I Q O 3.0 2.0 1.0 0 — VERTICAL MOTION t±i TT LATITUDE 25.6,N LONGITUDE 8Q9*W -IN CLOUD- J L J L 1 O9490 1834:40 O9450 O3S00 O9KI0 099:20 183530 B9540 1835:50 1836:00 183610 «36:20 1836 30 1836:40 1836 50 TIME Figure 10. Cloud 6, pass 2, May 16, 1968. True heading 260' Records same as fig. 9. 17 iMOO n.ioo o c *»oo g (•.700 3 to S «MO0 a. if >£ UJ nfrffn{{ ( (f(ff(t\\\ rrffffffff Y^7'TTT'T^'TiTT^Twis'T'TTT'T(T't1t'TT0T .«T'Q1T.orr'n.,.o.T- a: (- 1 20 — 0 — -feVJt-" -8.0 UJ' t- -10.0 1 3i> ■v. I ~ 2-0 i.0 VERTICAL MOTION LATITUDE 25.5*N LONGITUDE 809*W J L •0040 «50:50 I8SO0 I85CI0 185)20 I85C30 1851:40 1851:50 I85Z00 I85ZI0 I85Z20 1852:30 185240 1852:50 189X00 TIME Figure 11. Cloud 6, pass 3, May 16, 1968. True heading 251° Records same as fig. 9. 18 WIND 19,500 19.300 < 19.100 UJ _» (n e.900 UJ LL 18,700 100 a* 1§ ii ujg > K > 10 0 £ 5 a — < < u. _l ? 40 20 -8.0 — UJ or 3 1 -9.0 1— K < «-> e 2 « -^-ioor- MO i — TO — I Q O O 30 10 L I H i I 0IJ*no..002'oo,.0CMI-0(.. <»•• o... (MS OO**"",' 001 „.. <»•• <„. O^^OW- <„«. «•• VERTICAL MOTION LATITUDE 259*N LONGITUOE 8I.9*W I I 1946 00 1946.10 194620 194630 194640 194650 1947 00 1947 10 194720 194730 194740 194750 194*00 194810 194820 TIME ( Figure 13. Cloud 8, pass 2, May 16, 1968. True heading 087 Records same as fig. 9. 20 virtual temperature excesses (T - T ) were small in both vc ve passes (0.3 C) , but the average water contents were 3 and 3.5 g m in passes 1 and 2 respectively. Pass 2 through cloud 8 is further evidence that the 10 cm radar underestimated the water in cloud 8 because of the obstructions on the Univ- ersity of Miami campus. Cloud 8 had more average liquid water than cloud 6 during the preseeding pass, yet the radar return is considerably greater for cloud 6 (fig. 2, panel 3 vs. fig. 3, panel 5) . (For further detail, see sec> 4.) Pass 3, the first postseeding pass through tower A of cloud 8, corroborates the dissipation evident in the photographs (fig. 14) . There was still a temperature excess of 0.3 C, with a wet bulb cooling upon exit from the cloud, but the average -3 liquid water had decreased to 1 g m The first pass (pass 4) through the growing seeded tower (tower B) of cloud 8 indicated that it was a very vigorous tower (fig. 15) . The cloud virtual temperature excess was 2.3 C, with a strong wet bulb cooling upon exit from the cloud. Total liquid water values were not available for this pass, but the Johnson-Williams readings which are indicative of cloud -3 drops (diameter <40 y) exceeded 2 g m at two points in the cloud. The relative humidity values exceeding 100 percent are not errors, but are the result of evaporation of precipitation water . Pass 5 (fig. 16) through cloud 8 includes observations ob- tained in towers C and B (see picture 10, fig. 4) . The first group of water values are those of tower C, with average total The water values -3 -3 water of 3 g m and a peak value of 5.8 g m beginning at about 2019:15Z are those of tower B. The average -3 total water in this tower was 2.5 g m . The virtual tempera- ture rise commencing in the active portion of tower B and ex- tending downwind reached a peak exceeding 6 C. The first im- pulse was to ascribe this warming to fusion heat release 21 ra.7oo o 19,500 < I9.5O0 V _> in to UJ or a 1*100 I6£00 !00 eo 60 Si If Xi l"w 40 < u. -7 0 -8.0 -9.0 orS« w 1 2 -».o -no -BO £ 30 i 20 1 s o iO 1 11 1 1 1 H T H ilTT 1 1 1 1 1 1 1 T m 1 n T .V VERTICAL MOTION LATITUDE 25.9*N LONOITUOE 8I.0*W r HN CLOUDH 1 I I 19*810 1958:20 199830 1958:40 195850 195900 195910 1959.20 195930 195940 1959:50200000 2000:10200020200030 TIME ( Figure 14. Cloud 8, pass 3, May 16, 1968. True heading 101 Records same as fig. 9. 22 1*800 Ld a t rMOO 4 «*J 9.400 in to uj 19,200 Q. ( 140 120 100 Ix 80 K« 60 < u. -II UJ or 40 -7.0 -9.0 t ».0 Q O 1.0 TrTrTTTTTrfrH I i TtTtTtTtTtI^F LCVINC tMXHO WRTCR > «0 fmm'*(0FF SCALE) VERTICAL MOTION LATITUDE 29**N Lomrruoc •as-w IN CLOUO- 0T2O! J L J L 200T20 2OOT30 2007:40 200730 200*00 200810 20OS20 200830 200840 200890 2009O0 200910 200*20 2009^0 200940 TIME Figure 15. Cloud 8, pass 4, May 16, 1968. True heading 222' Records same as fig. 9. 23 WIN^. ..•»• °* l*4»"**0»*,,,**0»8' C '*** ■W. I9.4O0 UJ o 3 19200 < UJ I9.0O0 in UJ a IMOO X I 100 eo >5 -I? UJ 40 20 o t- I uj)-; UJ -7.0 I Q a 50 4.0 — 1.0 — Km f | i | i i i 1 i mivi I i I i P» I i I i I VERTICAL MOTION J L J L 201630 2018.40 20)890 201900 201910 2019:20 201930 201940 201990 202000 2020:10 202020 2020302020:40 202030 TIME Figure 16. Cloud 8, pass 5, May 16, 1968. True heading 177 Records same as fig. 9. 24 provided by icing of the temperature probe. However, this rise was substantiated by a Rosemount probe and a thermocouple vortex thermometer at other locations on the aircraft and by the tem- perature observations made during pass 6. Pass 6 (fig. 17) was made at approximately the same altitude as the previous passes, yet the temperatures in the cloud and the environment averaged 3 C warmer than before. It is very unlikely that any ice obtained during pass 5 could have persisted until pass 6, especially in an environment with an average relative humidity of 30 percent. An examination of the Miami soundings showed that the temperatures at the flight altitude of the DC-6 were -9.5 C at 1800Z and -10.5 C at 0000Z on May 17, 1968. One is led to the tentative conclusion that this large cumulonimbus complex had warmed its immediate environment. The average total -3 liquid water measured in tower C exceeded 6 g m , while the average total liquid water averaged approximately 1.7 g m in the first half of tower B. It is not known why only 65 percent relative humidity was measured in tower C in spite of the high liquid water content. 4. NUMERICAL MODEL STUDIES OF THE. MAY 16, 1968, CLOUDS The EMB numerical cumulus model was used in two distinct ways in the 1968 experiment. The first way was the real time usage to predict seedability in advance of each day's operation. For this purpose the 0800 LDT (1200Z) Miami radiosonde was run with the model, with the use of a hierarchy of cloud radii. The results for May 16, 1968, have been discussed by Woodley and Partagas (1969). Good seedability, or vertical growth due to seeding, was predicted for initial radii in the range of 750 to 1250 m. Clouds with radii smaller than 750 m were pre- dicted not to grow when seeded, while those with radii much above 1250 m were predicted to grow naturally almost as well as seeded clouds, provided the available fusion heat were released linearly between the -15 C and -40 C level. 25 113* kM* 0*0* ' IOt**" »00* t%4O0 Q 3 BUOO -J < w •,000 3 CO CO Id Q. l«800 100 80 60 40 20 — -5.0 — -ro 7.0 6.0 1 1 i Q O S.0 4X> 3.0 2.0 1.0 \f\ !! LATITUOE LONGITUDE J L VERTICAL MOTION \-IH CLOIKH I- 25S*N 80l9*W -IN CLOUD- J L 203520 2033.30 2035:40 203530 203600 203610 2036:20 203630 203640 203650 2037:00 2037K> 203720 2037:30 2037:40 TIME ( Figure 17. Cloud 8, pass 6, May 16, 1968. True heading 185 Records same as fig. 9. 26 The second and most intensive use of the model lay in the data analysis, with the actually measured cloud radii and the sounding nearest the clouds in space and time constituting the input information for the model. It is this use of the model that will be described here. In the pos tanalysis, a slightly improved version of the model was used. The real time version of the model was called EMB 68A . In this model, Kessler's (1965) autoconver sion equation was used, 100 percent of the liquid water present in the cloud at -4 C was frozen, the collection efficiency of ice for ice was 0.1, and the ice terminal velocity was 20 percent of that for droplets of equivalent mass. The postanalysis version of the model is called EMB 68K . In this version, Berry's (1968) autoconversion equation is used, 80 percent of the liquid water present in the cloud at -4 C is frozen, the collection efficiency of ice for ice is 100 percent, and the ice terminal velocity is the same as in EMB 68 A . A K hierarchy of EMB models with precipitation growth and different seeding subroutines have been discussed by Simpson and Wiggert (1969) . Each model is used to predict heights of the seeded and control clouds of the Stormfury 1965 cumulus program, and the results are compared with each other and with the field observations. Model K gave very slightly better height pre- dictions than model A and hence is used here. Berry's autocon- version formula generally gave slightly better results than Kessler's and permits introduction of the droplet number and relative spectral dispersion at cloud base. In the calculations to be discussed here we took a cloud base particle concentration 3 of 500 per cm f which was a good average of the measured nuclei counts in the operational area. The relative spectral disper- sion was assumed to be 0.146, an average figure for continental clouds . 27 Clouds 5, 6 and 8 were seeded on May 16. Woodley and Partagas (1969) give the locations of these clouds. All were over land about 40 n mi from Coral Gables, in directions rang- ing from due west to west-southwest. Cloud 5 was seeded at 1800Z , cloud 6 at 1824Z, and cloud 8 at 1849Z. Since no drop- sondes were available on May 16, the 1800Z Miami radiosonde is the closest sounding in space and time. This sounding, in comparison with the morning sounding (1200Z) , is shown in figure 18. Aircraft also measured temperatures and humidities in the immediate vicinity of the experimental clouds, and some of their measurements are indicated on the tephigram. With the exception of a more moist layer between 800 to 900 mb , the aircraft values are close to, and mostly lie between, the two radiosondes. Model calculations with both radiosonde obser- vations were made, and, since the results were quite similar, only those obtained with the closest (1800Z) sounding will be discussed. The cloud base heights were measured by the Navy S-2D, and the measured values were used in the calculations. The radius of each tower was measured by photogrammetry , as discussed, and the results have been shown in figures 6 and 7. The main results of the model calculations for May 16 are shown in figures 19 and 20. In comparing heights in figures 6 and 7 with figures 19 and 20, it should be recalled that figures 19 and 20 give height of tower center above cloud base. Hence to go from this number to absolute height of cloud top it is necessary to add cloud radius and cloud base. Two points are immediately clear. First, cloud 5 had virtually no seed- ability, being too narrow a tower for growth. The measured tower radius was about 650 m. Thus its dissipation following seeding is explained. Second, the great vertical growth of cloud 6 and especially that of tower B of cloud 8 is not well predicted unless the measured tower expansion is included in the model calculation. In the case of cloud 6, the expansion was only about 30 percent, and the unexpanded tower would have 28 b * P P 73 ■P 3 < O rH U o O E -H p +J !X C •P 0/ 4= e o ft -h o cu P on a t e expe b -O -P &1 3 .H C b -P V0 H C\J .H

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& 0 o H 0 •-i 0 ai M (0 ?: I'- C) H r_i 4J H ,a 3 Ul H < • _ £ en ro CD CM P .0 X I- OJ030 m uJ u-1030 ffl z Ul -> o o 3 < O Q b QC O < E -1 u. E O >- or or ui m ro CO GO H or CO < o 00 1 UJ 3 o O) 1 co J g> * < CD o CD CO <0 O 3 > CO Ul O -1 o < 2 _l UJ o o 2 z o CO z 2 X Ul r- o X E O 5> CM 1 o 00 z o CO z 2 X UJ X 1- o $ * UJ a a Q Ul Ul UJ Ul a a CO UJ w z UJ UJ' 3 CO CO /' h— i — h h — I — i — l — i — i — i — I — I t—+ IS o o b o 00 — e> x t- <£ CM S O • — or • m e •^ £E IT) z— » 00 UJ^ m o* 00 CO < •u * «J a) o « (0* i0 ro TD 3 0 u oo en UJ S co 00 TS & 3 ■A 0 m H O gg « M 0 0) M 3 0^ ■A fc attained a level only 350 m short of the expanded tower. But in the case of cloud 8, tower A, which did not expand, terminated about 5 km lower than tower B, which was measured to expand by from 850 to about 3000 m following seeding. This result points up a long-known weakness in the current EMB models, but also teaches us something about seeding effects. Our new method of seeding with many pyrotechnics on two mutually perpendicular passes (Simpson et al . , 1969) permits such a good distribution of silver iodide smoke through a cloud body that not only an originally protuberant tower is seeded, but also fresh towers forming within or at the edge of the cloud at lower levels receive silver iodide. The fresher, lower towers can apparently draw upon their saturated cloudy environment to ex- pand and attain greater heights than they could have without expansion. We hypothesize that this fresh tower seeding may be, a main reason for the higher proportion of explosive growths in the 1968 experiment compared with that in 1965. This phenomenon is well illustrated by comparing towers A and B of cloud 8. Tower A was exposed to a dry environment (fig. 3) at seeding time, while, when tower B received silver iodide it was a recognizable part of the moist cloud body and thus able to expand in size. We plan later to try to model this type of growth with a "field of motion" type model developed by Murray (1968). When the measured expansions are included, the observed top heights of all seeded towers are predicted fairly well. The rates of rise for cloud 6 check well against the values found from photogr amme t ry , as illustrated in table 1. 32 Table 1. Rise Rates of Tower Top Height Interval (abs. altitude km) Model Ca lc. Measured Rise Rate m/sec m/sec 8.0 6 .1 9.0 12.0 8. 8 9 .7 8.5 6.0 7-8 8-9 9-10 10-11 Average 8.6 8.5 In the case of cloud 8, tower A was modelled as an 850 m tower that rose without expansion, as observed. Its predicted top height agrees well with measurements, as illustrated by the dotted curves in figure 20. In the case of tower B, the ob- served expansion curve was approximated in the model by two linear segments. Even so, model results are only fair. The extreme growth is underpredicted by 400 m, and the rise rates are more seriously underpredicted. The average measured rise rate from seeding to maximum top is 6.8 m sec , while the value given by the model is about 4.4 m sec . At 6 to 7 km above cloud base, the measured rise rate was 4.5 m sec , in good agree- ment with a model value of 4.2 m sec , but at higher altitude the departures are worse. At 9 to 10 km above cloud base, the measured rise rate is 7.5 m sec , while the model gives only 3.4 m sec . This problem and the underpredicted top could have arisen from an environment sounding less stable in the upper troposphere than the Miami sounding. This hypothesis is supported by the fact that .the local B-57 temperature at 200 mb is about o 1.5 C colder than that of the radiosonde (fig. 18) . Tower C, which began growing on the northwest flank of cloud 8 about 11 min after tower B had achieved maximum height, 33 was 6 mi away from the seeded region (see figs. 4 and 5) . Since it was located upshear of tower B, it is virtually impossible that C was seeded by silver iodide and not likely that it was seeded by ice particles falling from tower B's anvil. Model calculations were undertaken on tower C to determine whether the very high rise rate could be explained. With the observed expansion, top height was well predicted when the fusion heat was released linearly between temperatures of -15° and -40°C -1 However, the maximum predicted rise rate was only about 7 m sec above 8 km. It seems that the high measured rise rate could only be explained by a marked steepening of the ambient lapse rate or by some dynamic effect of the large nearby cumulonimbus. Suc- cessive B-57 ascents between the time of tower B and tower C showed about a 6 percent steeper lapse rate at the appropriate levels, not enough to account for the increased ascent speed. The removal of all drag from expanding tower C gave a maxi- mum rise rate of only 8 m sec - still far smaller than measured. In fact, only if tower C were seeded between -4 C to -8 C do we obtain rise rates approaching those observed near 10 km, and un- der these conditions the predicted top height is more than 2 km higher than that measured. Hence we must deduce that some dy- namic interact ions , such as a strong convergent flow, for ex- ample, took place with the nearby cumulonimbus (tower B) which cannot be incorporated in this model. It is noteworthy that several other cases were observed during the program of spec- tacular growth of a tower quite far on the upshear flank of a seeded cloud. These growths of outlying towers are very impor- tant to examine when we wish to extend our study from seeding effects on single clouds to the effects of this type of seeding on the cloud and rainfall patterns over a whole area. This latter type of study will be an essential prerequisite to any operational program undertaken with the purpose of altering rainfall . 34 A comparison that is possible for the EMB 68 model, but was not possible for earlier EMB models, is radar echo intensity. The model follows the rising active tower, and hence the most meaningful comparison is the computed maximum radar echo of the unseeded cloud versus the observed radar echo at a comparable level and time. In figure 19 we see that for cloud 6 the maxi- mum echo intensity is about 47 db at a model height of 5 km, or an absolute height of about 19,000 ft. Figure 21 shows the radar echo distribution in cloud 6 at seeding time. Note that the maximum echo observed was 53 db at 16,000 ft. Hamilton (1966) has presented a graph relating the height of maximum radar echo to the mean updraft in a thunderstorm. He found that these properties are inversely related. Using his graph, we find that a maximum echo at 16,000 ft corresponds to an average updraft of 5 m sec in our cloud body at this time. The inset graph in figure 21 shows the 20,000 ft scan of the University of Miami 10 cm radar. At the 40 mi range, this scan covers a cloud depth between 16,000 ft and 25,000 ft. The dark central region is surrounded by the 50 db contour. An average value for the cloud of 47 db seems about right. Another check is provided by the DC-6 before seeding pene- tration shown in figure 9. Photogrammetry shows that the DC-6 at 19,000 ft (pressure altitude) penetrated the cloud tower about 700 m below its top. This and the penetration width of 1900 m demonstrates that the aircraft probed the heart of the active tower. We assume, for a rough computation, that the difference between the total liquid water and that measured by the Johnson- Williams hot wire is the precipitation content. The average -3 precipitation content is then about 1.9 g m . Using the Z, M relation derived by Kessler (1967) from theory, namely, Z = 1. 8 x 10 (M) 1.75 6 -3 mm m (1) 35 CLOUD 6 MAY 16, 1968 I824Z SEEDING TIME RADAR ECHO DISTRIBUTION rr^LOUD TOP 10 20 30 AREA (N Ml2) 40 50 Figure 2 1 Area covered hy radar echoes of given intensity at seeding time for cloud 6 C1824Z) . The maximum intensity was 53 db at 16,000 ft. Inset diagram shows tracing of radar scope (20,000 ft scan) with same contours. DC-6 track indicated, Echo is wider than aircraft penetration because radar is integrating layer from 16,000 to 25,000 ft. 36 -3 when M is in g m , we get a Z of 47 db , in too good agreement with the model prediction*. A further test compares the total liquid water prediction of the model with that observed. The peak total water in the -3 cloud from the DC-6 at 19,000 ft is 4.5 g m , while the average -3 -3 value is about 2.5 g m . The model value is 3.3 g m , some- where between the peak and mean value. For cloud 8, a satisfactory comparison of model, aircraft pass, and radar observation is not feasible. First, the radar beam was obscured by the University library building. The maxi- mum contour appearing on the 20,000 ft scan was only 30 db at seeding time (fig. 3) . Using the liquid water contents in -3 figure 12 with (1) , we find an average difference of 3.0 g m between total water and cloud water measured by the Johnson- Williams hot wire. This value gives a radar echo intensity of 51 db . Even if only half this liquid water were in true pre- cipitation sizes, an echo of 46 db should have been measured as a minimum. In addition, the penetration measurements in figure 13 cannot be. used as a good test of the model prediction for cloud 8 The middle left photograph in figure 3 shows that the aircraft entered the cloud well below the central portion of the rounded tower, as is confirmed by the great length of the penetration -3 (about 3500 m) . The peak total water content was 6.2 g m , while the average value was 3.5 g m . The model value of 2.0 g m should have been more characteristic of the cloud tower above the aircraft. Finally, the model makes a prediction about the precipi- tation fallout from a single tower, seeded and unseeded. For -3 a cloud 6 tower, the seeded fallout is predicted at 3.70 g m , -3 while the unseeded value is 3.38 g m , an increase of less than 10 percent. For comparison with the radar results, we multiply -3 3.70 g m by the volume of the cloud tower and convert to acre- 37 feet. A single seeded tower, in the model, would have a fall- out of about 26.5 acre-feet of water. The radar observations showed that cloud 6 produced about 185 acre-feet of rainfall in the first 10 min following seeding. This is more rainfall by a factor of seven than has fallen from the model tower when it reaches its maximum height. The real exploded cloud differs from the model in two main respects: (1) The real exploded cloud is a succession of towers, but the model is not, and (2) the fallout from each descends mainly through cloud body where it can collect smaller drop- lets and thus augment itself on the descent. If, in fact, two or three towers contributed to the measured 10 min precipitation and if the rain falling from each augmented itself by a factor of 2 to 3 by accretion during descent, the 185 acre-feet in 10 min is readily accounted for. Figure 2 shows that cloud 6 at 10 min after seeding consisted of at least two amalgamated towers (A and B) . A rough calculation shows that the falling precipitation from the tower can easily be doubled or tripled during descent. For this, we use an equation for drop growth by coalescence from Johnson (1954) , namely, j j Em i \ d„ - d, = - — (z„ - z,) 2 1 2p 2 1 (2) where d is the final raindrop diameter in cm, d is the ini- tial raindrop diameter in cm, E is the average collection effi- ciency of raindrops for cloud drops, assumed unity, m is the average cloud water content in grams per gram, p is the density of water, and z z is the height fallen in cm. The model gives the values of d as about 1.75 mm when we define d as the median volume diameter at the tower center when it has reached its maximum height. If this particle falls through a cloud water content of 0.5 g m for 2 km, (2) shows it will 38 double its mass, while the mass will increase by five times if the fall distance in cloud is 5 km. This result indicates that our accretion hypothesis is conservative. Because of the large expected accretion, the current model can probably not predict the final precipitation to a useful approximation. Since the distances required for doubling are so short, it should not affect this argument that the collecting particles are ice for the first few kilometers of fall. The accretion hypothesis is further supported by the fact that the aircraft at 19,000 and 17,000 ft often measured higher than adiabatic water contents after seeding. An example is cloud 8, in which a peak total water content exceeding 7.0 g m was recorded on pass 6 (fig. 17) . Since the Johnson-Williams -3 recorded only a little more than 1.0 g m on this pass, most of the water must have been in precipitation. -3 5. CONCLUDING REMARKS May 16 offered a rather complete study of three seeded clouds by means of photogrammetry , aircraft penetrations, cali- brated radar, and a numerical model. These components fit rather beautifully together to document the behavior and struc- ture of the clouds. One cloud (5) showed no computed seedability and failed to grow. The two other clouds (6 and 8) grew ex- plosively following seeding. The model calculations suggest that cloud 6 would have grown without tower expansion, but cloud 8 required the tower size to more than double in order to account for the observed explosion. A main factor in this growth is believed to be the repetitive seeding with many small pyrotechnics, which seeds fresh towers growing within the main cloud body. A weakness of the EMB 68 model is that it does not predict expansion, which must be entered as input from observa- tion. A more sophisticated model is being adapted for use with these experiments, which hopefully may predict expansion. 39 An excellent comparison was obtained for cloud 6 for the model's predicted (unseeded) radar echo with the echo observed on the University of Miami radar and with that computed from the water measurements made during the DC-6 penetration. This indicates that the model is handling the growth of precipita- tion in liquid clouds effectively. From comparing model-predicted precipitation fallout with measured radar rainfall at cloud base, a hypothesis relating the dynamics and precipitation from an exploded cloud was ad- vanced. This involves several towers contributing precipita- tion, which is augmented within cloud on descent. This hypo- thesis will be tested in further case studies from 1968, based on the airborne foil and Formvar particle samplers together with the measurement tools discussed here. Unfortunately, the DC-6 foil sampler was inoperative on May 16, although a simi- lar sampler operated at cloud base. Results from the other two penetrating aircraft will be incorporated in this case study later. We conclude that the focusing of these four tools (air- craft, radar, photography, and model) provide a uniquely produc- tive method of analyzing both cloud physics and dynamics in general and seeding effects in particular. 6. ACKNOWLEDGEMENTS The writers dedicate this effort to Dr. Helmut K. Weickmann, Director of the ESSA Atmospheric Physics and Chemistry Labora- tory, for his persistent support of this program and for val- uable discussions of every phase of the work. We are much indebted to the personnel of the University of Miami Radar Laboratory for their valuable contribution of talent and f aci li t ies, whi ch were key parts of this research. Sincere appreciation is also due the Southern Region, U.S. Weather Bureau; the Director and staff of the National Hurricane Center, Miami, Florida, for making the extra radio- 40 sonde observation at 1800Z that was indispensable to the cloud modelling; Dr. Gerald Conrad and Mr. Lloyd Devol of RFF , ESSA, for providing and analyzing the Levine water content measure- ments; 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 . 7. REFERENCES Be^ry, 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. Byers, H.R. (1968) , Cumulus cloud structure and dynamics from aircraft observations, Proc. Intern. Conf. on Cloud Physics, Toronto, Canada, August 26-30, 1968, 544-548. Hamilton, P.M. (1966) , Vertical profiles of total precipitation in shower situations, Quart. J. Roy. Meteorol. Soc. 9 2 , 346-362. Herrera-Cantilo , L. M. (1969) , Cloud aerial photogr ammetry based on Doppler navigation, Report on work performed under Contract No. 22-2-68(N) between ESSA and the Univ. of Miami . Johnson, J.C. (1954), Physical Meteorology, 229-231 (Wiley Technology Press, New York, N.Y.) . Kessler, E. (1965) , Microphysical parameters in relation to tropical clouds and precipitation distributions and their modification, Geofisica Intern. 5_, No. 3, 79-86. Kessler, E. (1967), On the continuity of water substance, ESSA Tech. Memo. IERTM-NSSL 33 (in press as Meteorological Monograph ) . MacCready, P.B., Jr., and C.J. Todd (1964), Continuous particle sampler, J. Appl. Meteorol. 3_, 450-460. Malkus , J.S., and R.H. Simpson (1964), Modification experiments on tropical cumulus clouds, Science 14 5 (3632) , 541-548. 41 Murray, F.W. (1968) , Numerical models of a tropical cumulus cloud with bilateral and axial symmetry, Rand Memo. RM-5870-ESSA , The Rand Corporation, Santa Monica, Calif., 31 pp. Senn, H.V., and C. L. Courtright (1968), Radar hurricane research, Inst, of Marine Sciences, Univ. of Miami, Miami, Fla., Final Rept. Contract No. E22-6 2-68 (N) , 31 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. 7_3_, 1201-1207. Simpson, J., and V. Wiggert (1969), Models of precipitating cumulus towers, Monthly Weather Rev. (in press). Simpson, J., G.W. Brier, and R. H. Simpson (1967), Stormfury cumulus seeding experiment 1965: Statistical analysis and main results, J. Atmospheric Sci. 2_4, 508-521. Simpson, J., W. L. Woodley, H. A. Friedman, T. W. Slusher, R. S. Scheffee, and R. L. Steele (1969) , An airborne pyrotechnic cloud seeding system and its use, ESSA Tech. Memo. ERLTM-APCL 5, 44 pp. Wcodley, W . L. (1969) , The effect of airborne silver iodide pyrotechnic seeding on the dynamics and precipitation of •supercooled tropical cumulus clouds, A dissertation sub- mitted to the Graduate School of Florida State Univ. in partial fulfillment of the requirements for the degree of Doctor of Philosophy, 139 pp. Woodley, W. L. , and J. F. Partagas (1969) , Radar and photo- graphic documentation of convective developments on May 16, 1968, ESSA Tech. Memo. ERLTM-APCL 7, 16 pp. 42 61 U.S. DEPARTMENT OF COMMERCE Environmental Science Services Administration Research Laboratories ESSA Technical Memorandum ERLTM-APCL 5 AN AIRBORNE PYROTECHNIC CLOUD SEEDING SYSTEM AND ITS USE Joanne Simpson and William L. Woodley Experimental Meteorology Branch, ESSA Howard A. Friedman Research Flight Facility, ESSA Thomas W. Slusher Olin Mathieson Corporation R. S. Scheffee Atlantic Research Corporation Roger Li. Steele Colorado State University Atmospheric Physics and Chemistry Laboratory Boulder, Colorado February 1969 TABLF OF CONTENTS ABSTRACT 1. INTRODUCTION 2. THE PYROTECHNICS 3. LABORATORY TESTS 4. FLARE CONFIGURATIONS AND DELIVERY SYSTEM 5. FLIGHT TESTS 6. DESIGN OF THE 1968 FLORIDA EXPERIMENT 7. FIRST RESULTS OF THE FLORIDA 1968 SEEDING PROGRAM 8. CONCLUSIONS AND FUTURE WORK 9 . ACKNOWLEDGMENTS 10. REFERENCES Page iv 1 2 14 18 26 33 36 37 41 43 in ABSTRACT The development, testing, and use of an airborne pyrotechnic cloud seeding system is described. Pyrotechnic flares producing 50 g of silver iodide smoke each were developed by two industrial corporations and labora- tory 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 aircraft. 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, Incorporated. 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 10,900 ft higher than the controls, with the difference significant at better than the 1/2 percent level. Rainfall from seeded and control clouds was compared by means of calibrated ground radars. Large in- creases in rainfall were found from seeded clouds, but unfortunately not at a satisfactory significance level. A single successful repeat of the experi- ment could result in rainfall differences significant at the 3 percent level. IV AN AIRBORNE PYROTECHNIC CLOUD SEEDING SYSTEM AND ITS USE Joanne Simpson and William L. Woodley Experimental Meteorology Branch, ESSA Howard A. Friedman Research Flight Facility, ESSA Thomas W. S lusher Olin Mathieson Corporation R.S. Scheffee Atlantic Research Corporation Roger L. Steele Colorado State University 1. INTRODUCTION A silver iodide cloud seeding system was desired for a modification experiment upon individual cumulus clouds growing over and near the Florida peninsula in May 1968. This experiment, 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, Incorpo- rated, was the sequel to the Stormfury cumulus seeding experiment conducted in the Caribbean in 1965 (Simpson et al. 1966, 1967; Simpson, 1967; Ruskin, 1967). The seeding was intended to release as rapidly as possible all the latent heat of fusion in selected supercooled cumuli. The size of the subject clouds was about 1.5 to 3.0 km in tower diameter and 6 to 8 km in height, cloud base was at about 500 to 1000 m, and the freezing level was at roughly 4 km at this location and season. The purpose of the experiment was to study with aircraft and cali- brated ground radars the induced dynamic and physical changes in the seeded clouds and to compare these with unseeded control clouds, both chosen on a statistically randomized basis. Some previous randomized seeding experiments are summarized in table 1, including the first results of the May 1968 Florida experimentation. The amount of silver iodide introduced per cloud is seen to vary widely, the only very high concentrations being achieved with pyrotechnics. Since complete and rapid latent heat release was desired, the aim was to introduce not less than about 100 nuclei per liter into the supercooled portion of the clouds. This figure is based on a calculation by MacCready (1959). To achieve this concentration in clouds of the size mentioned requires that about 10 " nuclei be introduced and distributed through the cloud in a few minutes. This could be done with 1000 g of silver iodide smoke if the 12 nucleation efficiency is 10 active particles per gram, which is within the capacity of pyrotechnics (Davis and Steele, 1968). Most airborne generators would require about 1 hour to produce the necessary quantity of silver iodide particles at these warm temperatures. This and the distribution problem precluded their use in our experiments. 2. THE PYROTECHNICS Pyrotechnic flares were desired that could be dropped from the ESSA Research Flight Facility B-57 jet aircraft. For optimum distribution, it was planned to drop twenty (20) 50 g flares into each cloud top at approxi- mately 100 m horizontal intervals. The flares were to be ejected on two successive seeding passes, made at right angles to each other about 3 min 00 T5 18 3 T) o- -a • 3 4J 60 • o nx I B o -o C N co h hi M o O c V a) •H ' B i) emu L, u e ai O O rH O O -H I- CO ji i-i a jz u a. 1 m 1-1-3 6 u -a e -o 6C •h >, co •H >s CO ID CO < -C CO <: j= co a. 01 s -a 0) ft! c 4-* M u <0 U-4 CO ao CO 00 O >s 1-4 xj 1- o 0 u M ■H .r OJ ■H CO c_ g CO OS CJ a. •h a co o OJ o co o •a C C M 4J 3 4J CO -H a ■-> i-t ,-v M X) C_) uuu CO 1) a • 3 o C 3 o 31 00 ■H S- 0 o O O O l-i O C CJ O r-1 ,-H O H H o x: co 0) C O 1 a o i c o x: 14 1—1 *w V W s—' V ►— c OJ CJ a H-1 00 1-1 -^ co 4-1 T3 4-4 T3 h T> u U "O 0 3 O 3 0 3 o C 3 4J O 4J O u o u 4-1 ^ CO —1 (0 r-l CO ^ CO ^ CO -i u a U O 4-1 CO 1 CJ U CO »- CJ - M O OJ C >- C I) a; .-i 1l *H 11 CO >, 1-1 .H 11 co OJ -4 00 00 oo oo oo v^ a. c or c£^ oo or C c j= C c f-H -H 1-4 «H 1— 1 H O tI 1—1 *rl O CO O CO CJ CJ OJ CO O CJ 10 < w < ^ <: <: 4-i w < < -— 4-1 CJ -^ >, -H CO Cl C 0) . co --, CO CO ^y c c • O Jl^ B <— i ^-^ H Cj \D 3 r-l 1-4 -x> CO o ^O CO J3 I-n CO 11 r» CO 4-1 VO jt CO 4J vO N >£l a -h vo e CO vO CO on 4J C5 0"\ 4-4 ■H o> S >-i o 3 i-i a- 4-1 3 -H 11 4-1 3 Rt M ■rH CO r-4 01 CO »-4 11 *£ OS 01 < N- OQ < "^-^ t« u s— y. 4-4 N^ 11 CO C ^ CO O CD •H !S) \£> > -H CJ 11 •H J IA M-l 0) -* »« >- C lA 60 i-l o c oi oj 00 -H < C 3 4-1 O CO 00 ■h w *: 01 0) O T3 3 C P. • O i-l § O .-I 3 Z c_> cn I a o -o ■O OJ C N ■o 1 3 00 11 O c u i-l o o u 4J CO u 1 u-1 n o a B ~< m j<: X J u c ■H s ^ o 4J 00 u-> u-i o c — 1 1 -J Ij tH 1 41 H T3 o U 5^ i-l OJ o U 03 U-l 11 I-t « -^ CD 0) < S o u 3 o o C »-i H OC -a Tl 3 3 O O i-H i-( -o O 1 o o o tn x: CU OJ h U 11 V O i-l >>-H iH U •H OO a c oo X a £ S >>-H i-l 0) M O i-t CJ 0J U) Q ^ < u ^ -^ c CO * c • CO ^-^ o T3 S-\ 11 H CO (0 1-4 o-. •H CO OJ tO a. >J MO U en Ol E a at 0 tJ 3 ■H i-H i-l ^ 01 a: ^ Cfl b, *— ' >-. X 01 •H OJ M-l I-l i-H OJ o XI I-l 10 CO OJ i-H CO ■o i-t •H (0 0) w > OJ c CO X! 01 u B 4-1 c i-l o OJ U c M OJ CO a c o. X o OJ 1-1 c u •H CO <0 T3 6 en •H 1* 01 l-i o i-i O U-l CO •H c a Pti apart. The flares were to burn at ambient pressure for about 60 sec and to fall about 3 km vertically before burning out. Complete burnout was re- quired for safety in use over land areas. Design goals were established in terms of laboratory tests of the efficiency and flight tests of the ignition reliability. The efficiency goal was 10 active nuclei per gram at -5°C 12 and 10 active nuclei per gram at -10°C, with equal or better efficiency at lower temperatures. 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 percent of the flares should ignite and remain ignited until burnout when dropped from 20,000 ft. The Olin Mathieson Company 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 proper- ties as safety, shelf life and burn characteristics, and the most promising mixes were then sent to Colorado 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 Scheffee 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 AgI0_ 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 KCIO, and thiourea as the oxidizer and fuel, respec- tively, while those containing AgI0„ were composed of KCIO, , magnesium and nitrocellulose plastecized with triacetin. These compositions were found to be safe to manufacture and use and to have acceptable physical properties and shelf life. Better combustion characteristics were found for composi- tions containing AglO- and magnesium than for Agl-KCIO, -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 -5° to -15°C temperature range had two properties in common. The first was high percentages of metallic condensed species in the output, and the second was a high flame temperature (^ 2000°K or more). With the high flame temperature, the silver iodate is reduced, and the products are vaporized and react to form condensed silver iodide during the quenching process. The high burn temperatures should favor nucleation 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 -6.5°C and -9.3°C, 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 that in the warm range of supercooled cloud temperatures nucleation may take place predominantly by contact and condensation, rather than by sublimation and diffusion as at lower temperatures. With only pure Agl, it is unlikely that condensation will occur at all in the regimes of saturation pressures found in nature, and particles greater than 1 \i are required. With supersaturations of about 3 percent, particles as small as 0.01 u become effective as condensation nuclei. St. Amand et al. (1969) 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 percent 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 formulation X1055 chosen for the field experiment are given in tables 2 and 3. Table 2. Composition, Atlantic Research Corporation Formulation 1-20M-45A Material Percent by Weight Silver iodate Potassium perchlorate Magnesium Nitrocellulose Triacetin 45.0 27.0 20.0 4.0 4.0 Table 3. Composition, Qlin Mathieson Company Formulation X1055 Material Percent by Weight Silver iodate Potassium iodate Magnesium Aluminum Strontium nitrate Polyester binder 53.0 8.0 5.6 12.9 10.5 10.0 The reaction of Agl with likely combustion products is an important consideration in the design of pyrotechnic compositions. Since the compu- tation of equilibrium mixtures is arithmetically complex and laborious, equilibrium calculations of mixtures of compounds at an assigned temperature and pressure were carried out at both the Atlantic Research Corporation and the Olin Mathieson Company by means of digital computer programs. These 8 programs are used on a routine basis primarily for the computation of rocket propellent specific impulse and associated interior ballistics parameters in which it is assumed that combustion at an assigned pressure is adiabatic, that 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 vari- ations of this program, equilibrium values of the flame temperature and combustion product composition of ARC formulation 1-20M-45A and Olin formu- lation X1055 were computed and are given in tables 4 and 5. These results may or may not be representative of the actual species in the products but plume sampling by ARC does verify some of the predicted outputs. Table 4. Equilibrium Composition of the Combustion Products of Composition 1-20M-45A for Adiabatic Combustion at 1 Atmosphere Flame Temperature = 3082°K Total Mols of Gas = 1.4208 g mol/100 g Combustion Product Composition g mol/100 g Specie Amount Specie Amount Ag(g) 0.1466 K(g) 0.0359 Agd) 0 KCl(g) 0.1315 AgCl(g) 0.0020 KC1(1) 0 AgH(g) 0.0002 KCl(s) 0 AgKg) 0.0100 KKg) 0.0216 Agl(l) 0 Kl(l) 0 AgO(g) 0 K?I?(g) K0(g) 0 Ag2(g) 0.0002 0.0011 KOH(g) 0.0048 C(g) 0 K0H(1) 0 C(s) 0 C0(g) 0.1548 Mg(g) 0.0865 co2(g) 0.0983 MgCl(g) 0.0071 MgCl (g) 0.0024 ci(g) 0.0266 MgCl (1) MgKg) 0 Clo(g) ci6(g) 0 0.0054 0.0001 Mgl2(g) MgOfg) 0 0.1278 Kg) 0.1207 MgO(l) 0 i2(g) ICl(g) 0 MgO(s) 0.5721 0 MgOH(g) 0.0201 Mg(0H) (g) 0.0011 N0(g) 0.0054 £, NOI(g) 0 o(g) 0.0584 N2(g) 0.0153 o2(g) Ofl(g) 0.1098 0.0564 H(g) 0.0337 H20(g) 0.09 30 HCl(g) 0.0230 HKg) 0.0014 H2(g) 0.0199 10 Table 5. Equilibrium Composition of the Combustion Products of Composition X1055 for Adiabatic Combustion nt 1 Atmosphere Flame Temperature = 2296°K Total Mols of Gas = 1.5589 g mol/100 g Combustion Product Composition, g mol/100 g Specie Amount Specie Amount Ag(g) 0.1011 AgH(g) 0.0007 AgKg) 0.0841 Agl(l) 0 Ag2(g) 0.0008 Al(g) 0.0350 Al(l) 0 AlH(g) 0.0021 A10H(g) 0.0002 Al 0(g) AlN(g) 0.0429 0 AlN(s) 0.0357 Al 0 (s) Al^Cl) 0.1597 0 C(g) 0 C(s) 0 C0(g) 0.5905 co9(g) 0 CK(g) CH7(g) C2H(g) 0 0 0 C,H (g) Cfl(g) 0.0001 0 H(g) 0.0066 HCN(g) 0.0010 HI(g) 0.0044 H2(g) H20(g) 0.3101 0 Kg) K(g) KCN(g) KCN(l) KI(g) KI(1) KH(g) Ms) K2I2(g) Mg(g) MgH(g) MgKg) Mgl2(g) MgOTg) MgO(s) MgN(g) N2(g) Nfl(g) NH (g) NH3(g) Sr(g) SrH(g) SrO(g) SrO(s) SrOH(g) 0.0311 0.0030 U.0001 0 0.0343 0 0 0 0 0.1584 0.0013 0.0700 0.0005 0 0 0 0.03122 0 0 0 0.0495 0.0001 0 0 0 11 Tables 4 and 5 show a considerable degree of dissociation 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 con- taining potassium perchlorate, potassium chloride and silver iodide are the major stable products rather than potassium iodide and silver chloride. This was confirmed by X-ray analysis of samples collected in the smoke plume, where the latter products could not be detected at the 5 percent 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. 12 Table 6. Expected Exhaust Products at Ambient Temperature Formulation 1-20M-45A Compound Grams per 100 g mix Silver iodide 37.4 Potassium chloride 14.5 Magnesium oxide 33.2 Carbon dioxide 11.1 Water 3.3 Nitrogen 0.5 Table 7. Expected Exhaust Products at Ambient Temperature Formulation X1055 Compound Grams per 100 g mix* 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 atmos- phere. The flame temperatures (estimated by calculation) were 3082°K for the 1-20M-45A mix and 2296°K for the X1055 mix. Attempts are currently underway to measure the flame temperatures. 13 3. LABORATORY TESTS A facility has been constructed at Colorado State University (CSU) for testing and comparing silver iodide generators and other devices 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 intro- ducing the dilute smoke into a temperature-controlled chamber in which a supercooled cloud is maintained. The number of ice crystals in a fixed portion of the chamber are counted and related 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. The results reported here and the inferences drawn from them are only preliminary because of limita- tions in simulating a pyrotechnic in free fall and in simulating real clouds, The wind runnel used to produce the results reported here had a test section 3 -1 approximately 0.5 m in diameter and produced a flow of only 130 m min The small diameter produced adverse wall effects. It was also far from representative of the ventilation past the unit at its normal fall soeed. Free fall is currently being simulated in a new vertical wind tunnel in which actual free fall velocities can be simulated by La Grangian tech- niques. Wall effects are minimized, since the new tunnel has a test section 1.15 m, which results in an area 6.25 times greater than the old tunnel. 14 3 -1 -1 Flows of 3100 m rain are possible at velocities up to 62 m sec . Recent results show that the measured nucleation efficiency depends strongly on ventilation past the pyrotechnic. In the cloud chamber, ice crystal counts have been made so far with a -3 cloud liquid water content of about 0.8 g m . Recent addition of improved cloud chamber instrumentation shows that measured nucleation efficiencies depend markedly upon the cloud liquid water content, as described below. With these reservations, test results from the old CSU facility are shown for the two mixes in figure 1. Note that the apparent greater effi- ciency of the 1-20M-45A flares is due to sample size and is not representa- tive. The full X-1055 flare was burned in the tunnel with a burn rate of 45 g min, while only a 2 g sample of the 1-20M-45A mix was burned, with a burn rate of 4.5 g min . As shown by Davis and Steele (1968) and by Scheffee and Steele (1968), coagulation of the smoke particles was a major problem in the old slow-speed wind tunnel. In their study of effectiveness as a function of burn rate Davis and Steele (1968) showed that increasing the sample size of the 1-20M-45A mix to that of the full flare would reduce its measured effectiveness (in the old tunnel) to values very close to that of the X-1055 flares. Since these preliminary tests, others have begun with the new vertical wind tunnel described above. Results for a very similar Navy flare are 3 -1 shown in figure 2. A tunnel flow of 3100 m min "" corresponds to about 62 m sec , or about 200 ft sec . At most temperatures, about one order of magnitude greater effectiveness is measured at these more realistic air flow Naval Weapons Center (China Lake, California), Pyrotechnic LW-83, Information kindly furnished the authors by Dr. Pierre St. Amand , 15 NUCLEATION EFFECTIVENESS OF PYROTECHNIC COMPOSITIONS -10 -12 -14 -16 TEMPERATURE °C OLIN X-1055 ARC I-20M-45A 22 □ OLIN DATA ® CSU DATA • CSU DATA PROGRAM GOALS Figure 1. Nucleation effectiveness of the two pyrotechnic compositions used in 1968 Florida experiment. Higher solid line (with heavy circles) shows effectiveness as function of temperature for mix 1-20M-45A, with the burn rate of 4.5 g minT1 Lower solid line (with squares and double circles) shows effective- ness as function_of temperature of mix X-1055 with the burn Dashed line denotes desired program goal. 16 rate of 45 g min, 10 16 15 10 6 u 3 C o 14 !0 £ 13 S3 10 10 10 Effectiveness vs. Tunnel Flow for Navy Pyrotechnic LW-83 1000/1 Dilution o - 20 °C A - 15 °C D - 10 °C O - 8 °C J— L Velocity for Air Stream -ft/sec 95 203 i i i i i i j I i ■ i i i 0; I04 Tunnel Flow - cfm 10 ! 10' Figure 2, Nucleation effectiveness vs. tunnel flow for Navy Pyrotechnic LW-83 (a mix similar to X-1055) . A flow rate of 10* cfm corresponds roughly to 150 ft sec" , the fall speed of the pyrotechnics. . 7 speeds than was measured in the old tunnel. Applying a corresponding correction to the lower curve in figure 1, we have easily an effectiveness 12 of 10 particles per gram at -10°C. It is also significant that the new facility will permit effectiveness measurements at -5°C, which were awkward if not impossible with the old facility. Finally, the effect of varying cloud liquid water content upon the measured effectiveness was evaluated, and figure 3 shows a typical result for a low output, steady state, silver iodide generator. In the range just -3 above 1 g m , increasing the cloud water content by only 50 percent in- creases measured nucleation efficiency by a factor of 100 at temperatures in the range of -12°C (Steele and Davis, 1969). Since our experimental clouds -3 rarely exhibited water contents of less than 1 g m and often had water -3 12 contents of 2-3 g m at seeding times and levels, we conclude that 10 nuclei per gram of silver iodide smoke at -10°C is probably a very conserva- tive figure. Detailed measurements in the new CSU facility are now being performed with both Olin and ARC pyrotechnic flare mixes, at varying flow speeds (fall velocities) and with liquid water contents in the range simulating natural cloud conditions. Until these results are available, we conclude tentatively that at -5°C and -10°C respectively, 10 and 10 active nuclei per gram of silver iodide are reasonable but probably considerable underestimates for the flares used in our May 1968 Florida cumulus experiments. 4. FLARE CONFIGURATIONS AND DELIVERY SYSTEM The standard aircraft signal flare case was found to be of sufficient size to meet the 50 g Agl output requirement. The unique feature of the 18 IO,5L_ 14 10 h- < e 0) o z o «♦- 10 h 2x1 o'3. Preliminary Liquid Water Content Data for a Steady State Flame Type Agl Generator Burning Solution of Agl and Isopropylamme 0 -12 -L • L.W.C. > I.I gm/m3 but < 1. 65 gm/m3 O L. W.C > S.OOgm/m3 but <6.75gm/m3 Note: A 2% Agl- Isopropylamine Solution was Used for this Series of Tests j. -14 -16 Temperature °C -18 ■20 -22 Figure 3. Silver iodide generator effectiveness as a function of cold chamber liquid water contents and temperature. 19 signal flare cartridge as adapted to this application was an electric squib for initiation. A sketch of this 40 nun outside diameter by 96 mm long device is shown in figure 4 and a photograph in figure 5. The flare cartridge was designed to use the exhaust gas pressure to expel the candle to assure posi- tive ignition while providing mild fail-safe expulsion. The flares weigh a total of 120 g and cost about $14.00 each. The firing control for the dispensing system is provided by an AN/ALE-20 flare ejector set. The ESSA Research Flight Facility (RFF) in- stallation 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. 6), (2) junction box, (3) stepping switch assembly, and (4) in the present RFF configuration, flare mounting racks. Figure 7 is a functional 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 Company designed and manufactured the rack, and the RFF de- signed 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 in. long (parallel to the longitudinal axis of the aircraft), 16 in. wide, 4 1/2 in. deep, and weigh approximately 50 lb each unloaded. Each rack contains 56 steel cylinders, which house the flare canisters arranged in an 8 x 7 matrix, which are fired in a fixed sequence. The racks are installed on the left and right undersides of the 20 5 00 41 O** (9 o C V *«■■* Ll o 5 LU O Q tr o a) -^ j: 1 4J X X <0 ■H £. B ■J) JZ lu q: < tridge used v OM-45A cartri construction < LU LU < f flare car rogram; 1-2 similar in o Ll. gram o rida p were cr 4-1 O CO V) •H . n c 4J 4J •1-1 U-l U-| a> CO o r— 1 U 4J CJ c M ^^ o •i-l 4-1 CO U-l CO CO •■-I [^ i-l un CJ 4J i i-l <4-( pq •1-1 CO CO u < o w CD ^ CO T3 •1-1 w •i-l CO CO c c 14-1 o •1-1 o ^ CD CJ 4= co CO CJ O !-i 4J S3 Q) •H U CO CO co t-l 00 a U-l C •i-i •i-l u bO a 4J C ex CO •i-i , 0) U J«5 •r-l 4J CJ > •H CO 3 M (D CJ TD U CD •H •i-4 4= co CJ 4-1 00 0) I-l 3 bC 27 Figure 9. Front view of flare rack (in "down" position) on FSSA B-57 aircraft, looking toward tail of aircraft Numbers on flares indicate firing sequence. 28 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 reliability, burn time, and trajectory. Representative photographs of an ARC and Olin flare test are -1 shown in figures 10 and 11, respectively. The aircraft was flown at 400 ft sec, 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 fall speed of about 150 ft sec The Olin flares were tested with units having both 10 g and 20 g of first fire material. Twenty-five of 25 units with 20 g first fire burned completely. Only 9 of 25 units with 10 g of first fire burned completely. The other units went out after the first fire was consumed because of the high velocity and tumbling 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. 29 Figure 10. Time exposure photograph of nighttime release of two flares ejected at 20,000 ft. 30 Figure 11. Time exposure photograph of nighttime release of five 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 31 A breakdown of the tests with 20 g of first fire is as follows: Altitude (ft) Successful Tests 20,000 15 of 15 15,000 2 of 2 12,000 2 of 2 11,000 3 of 3 10,000 3 of 3 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 percent 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 percent of the 30 flares tested ejected, and of these only 76 percent burned com- pletely. A slightly better ejection record was obtained in the field. On the first 2 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 X-1055 flares. Unfortunately, some with the 10 g first fire mix were inadvertently used on the last 5 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 g of silver iodide, while the remaining ones almost surely received 650 g or more. 32 6. DESIGN OF THE 1968 FLORIDA EXPERIMENT The field phase of the 1968 Florida cumulus seeding program en- compassed the period May 15 through June 1, during which time there were 13 days of successful flight operation. Participating in the program were the Experimental Meteorology Branch (EMB) and the Research Flight Facility (RFF) of the Environmental Science Services Administration (ESSA) , the Naval Research Laboratory (NRL) , the Radar Meteorology Laboratory of the University of Miami, the U. S. Air Force, and Meteorology Research, Inc. (MRI) of Altadena, California. Aircraft altitudes and tracks flown are shown in figure 12. The RFF supplied two aircraft, a DC-6 for command control, cloud physics measurements, and photogrammetry at 19,000 ft (^ -9°C), and a B-57 for seeding and moni- toring cloud top. The NRL supplied two aircraft, a WC-121 Super Constellation for cloud physics measurements at 17,000 ft (^ -5°C) and a S-2D for measure- ment of rainfall and other parameters at cloud base. The Air Force provided a C-130 for dropsondes 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 conden- sation nucleus counter, a continuous 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 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. 33 FLIGHT TRACKS OF EXPERIMENTAL AIRCRAFT -87 M0NIT0RIN8 TRACK OC-* FLIQHT ALTiTUDES (FEET) 20,000 19,000 17,000 DC-6 ; WC-I2I , S-20 B-57 (SEEDER) POSITIONS OF FLARE DROPS PLAN VIEW 2000-3000 AIRCRAFT WC-I2I <—SZ-0 PROFILE Figure 12. Plan view (left) and profile view (right) of air- craft tracks in Florida 1968 cumulus experiment. 34 If it predicted good seedability 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 ft range. If suitable clouds were found, or expected within an hour, the shorter range seeder and cloud base aircraft were launched. When all project air- craft 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. 12) . 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 randomized 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 approximately 2-3 min later. If he had received a seed instruction, 10 silver iodide flares were dropped at about 100 m intervals on each pass. Following the seeding run, the B-57 aircraft monitored the cloud top, fol- lowing 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. When 1-20M-45A flares were used, 15 per pass were drooped to compensate for unreliable ignition. 35 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 selection, the scien- tists 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 practi- cable (sometimes 1 hour) after the seeding pass. The NRL aircraft made repeated penetrations of the cloud, while the DC-6 flew a compromise pattern, a rectangle with the cloud centered on one of the long sides of the rectangle (fig. 12). 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 Stormfury experiments (Simpson et al., 1967). Two hundred envelopes in sets of 10 were prepared by Mr. J. Cotton of the Meteor- ological Statistics Group of ESSA. The instructions were weighted 0.65 versus 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. 36 The dates and locations of all experimental clouds are shown in figure 13. 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 12,000 ft for the 14 seeded clouds and 1,100 ft for the five control clouds. The difference is 10,900 ft, which is signficant to better than 1/2 percent based on a two- sided "t" test. The average maximum top of the seeded clouds was 35,300 ft (pressure altitude) , 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 occurred 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. 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 seeding, and the average seeded cloud grew more than twice as much (10,900 ft vs. 5,200 ft). The main reason was the use of the computer 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 37 38 00 0) .-I £> H z X 3 » o K ui H z o o o o 8 in o o o_ o o o O o o o o o o o o o O o o. o o o o o CD o o n o o o o o *) 8 O O 19 u. o Ui ■n CO CM CM CO r~ o" CM — to to ctv 00 K o a. 4 CM - — "~ ~ ~ o ►- Ul to O X a o o Ui * o o o o o o o o o o o O o o o o o o o Ul *■* o o o o o o o o o o o o o o o O o o o CO ►- UJ o o «■> o o If) o o o o o r. o in a o o o o 4 fit 1— UJ m en o If) * _ to CO o — CO „ f- CM CM to K CO _ * IO * * to CM CM to * CM to to IO to IO to »o K) IO s 4 (9 s. o o o o o O O o o O o O o o o o o O o Z p o o o o o o O o o o 8 O o o o o o O o o Ui o o o o o If) O o o o if) o » m o in o o a o UJ Ul CO Ui u. o 9> CM IO CM _ to o to _ CO 9> CO 9> CO n so _ _ —" to CM CM CM CM CM CM CM CM CM CM CM M CM CM CM CM © — a. 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"s >x ^ V. m CD CO u> 0) 9) o o — CO •o l>- N CO o 8 o o CM CM CM CM CM CM CM CM IO to to *>» \ N, V \ ■v. ^v ^ ^s ^ \ >S ^ •V X V »v \ \ >- >- >- >- >- >■ )- >- >- >- >- V >- >- V V > >- Ui < < < < < < < < < < 4 < < < < 4 4 4 z z I Z z 5 z s s s S S Z z Z z Z Z z 3 -> 39 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 generation in or near the same spot. Additional effects of continentality, such as higher water contents distributed in more, smaller drops, are also being investi- gated. 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 rain gage 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. 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. 40 Preliminary results of the radar rainfall study indicate 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 to 150 acre-feet per cloud, which could be important. Unfor- tunately, the small sample and large cloud-to-cloud variability in precipi- tation reduces the statistical significance of the rainfall results to the 25 percent level when a two-sided "t" test is used. Calculations show that if the experiment was repeated one more time with identical outcome, and the results of both experiments combined, the rainfall increases would be significant to better than 3 percent. Hence it is imperative to repeat this experiment at least once. 9 . 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 program 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 Marshall 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 delivery system. Richard Decker and Frank Norimoto capably carried out the photography. 41 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, California, for many useful discussions on the physics, design and use of pyrotechnics in relation to cloud seeding; and the Naval Air Systems Command, who, through Mr. Robert Ruskin of the Naval Research Laboratory, purchased and provided the X-1055 flares used in the experiment. 42 10. REFERENCES Battan, L. J., (1966), Silver-iodide seeding and rainfall from convective clouds, J. Appl . Meteorol. _5, 669-683. See table 1. Battan, L. J., (1967), Silver-iodide seeding and precipitation initiation in convective clouds, J. Appl. Meteorol. 6^, 317-322. See table 1. Bethwaite, F. D. , E. J. Smith, J. A. Warburton and K. J. Heffernan (1966), Effects of seeding isolated cumulus clouds with silver-iodide, J. Appl. Meteorol. 5_, 513-520. See table 1. Braham, R. R. , Jr., L. J. Battan and H. R. Byers, (1957), Artificial nucleation of cumulus clouds, Meteorol. Mongraphs _2, 47-85 (Am. Meteorol. Soc, Boston, Mass.). See table 1. Davis, C. I. and R. L. Steele (1968), Performance characteristics of various artificial ice nuclei sources, J. Appl. Meteorol. _7, 667-673. Davis, L. G., Kelley, J. I., Weinstein, A., and Nicholson, H. , (1968), NSF Report #12A. Final Report NSF GA-777, The Pennsylvania State Univer- sity, University Park, Pennsylvania, 128 pp. See table 1. Flueck, J. A., (1968), A statistical analyses of Project Whitetop's precipi- tation data. Proc . First Natl. Conf . on Weather Modification, Albany, New York, 26-35. See table 1. Friedman, H. A., G. Conrad, and P. Connor (1969), Research Flight Facility. Description of instrument systems. Part 3. ESSA Tech. Rept. (to be published) . Fukuta, N., 1958, Experimental investigations on the ice-forming ability of various chemical substances, J. Meteorol. 1_5, 17-26. Jiusto, J. and W. C. Kochmond (1968), Condensation on non-hygroscopic particles, Journal de Recherches Atmosph£riques J3, 19-24. Korienko, E. E., B. N. Leskow and I. P. Polvina (1968), Results of seeding clouds with solid CO- aimed at the stimulation of precipitation over the Ukraine. Proc. Intern. Conf. on Cloud Physics, Toronto, Canada, 724-729. See table 1. MacCready, P. B. (1959), The lightning mechanism and its relation to natural and artificial freezing nuclei, Recent Advances in Atmospheric Electricity, 369-381 (Pergamon Press, London). Mossop, S. C. (1968), Silver iodide as nucleus for water condensation and crystallization, Journal de Recherches Atmospheriques 3,, 185-190. 43 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. See table 1. Ruskin, R. E. , 1967, Measurement of water-ice budget changes at -5°C in Agl- seeded tropical cumulus, J. Appl. Meteorol. 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 stimulation of rainfall, Naval Weapons Center, China Lake, Calif, (to be published). Scheffee, R. S., R. W. Evans, and C. Huggett (1967), Development of a pyrotechnic cloud seeding system. Part 1: Development of pyro- technic compositions, Report by Atlantic Research Corporation to ESSA under Contract Cwb-11346, 42 pp. Scheffee, R. S. and R. L. Steele (1968), Production of silver iodide smokes by pyrotechnics. Proc. First Natl. Conf . on Weather Modification Albany, New York. Simpson, J. (1967), Photographic and radar study of the Stormfury 5 August 1965 seeded cloud, J. Appl. Meteorol. 6_, 82-87. Simpson, J., R. H. Simpson, J. R. Stinson, and J. W. Kidd (1966), Stormfury cumulus experiments: Preliminary results 1965, J. Appl. Meteorol. 5, 521-525. Simpson, J., G. W. Brier, and R. H. Simpson (1967), Stormfury cumulus seeding experiment 1965: Statistical and main results, J. Atmospheric Sci. 24, 508-521. Simpson, J. and V. Wiggert (1969), Models of precipitating cumulus towers, Monthly Weather Rev. (in press) . Steele, R. L. (1968), Evaluation of ice nuclei sources and their development, Production and Delivery of Cloud Nucleating Materials, Project Sky- water Proceedings, Skywater Conference III, Office of Atmospheric Resources, Bureau of Reclamation, U. S. Dept. of Interior, Denver, Colorado, 51-92. Steele, R. L. and C. I. Davis (1969), Variation of ice nuclei effectiveness with liquid water, J. Atmospheric Sci. 26_ (in press). 44 62 U.S. DEPARTMENT OF COMMERCE Environmental Science Services Administration Research Laboratories ESSA Technical Memorandum ERLTM-AOML 2 PRECIPITATION RESULTS FROM A PYROTECHNIC CUMULUS SEEDING EXPERIMENT William L. Woodley Experimental Meteorology Laboratory Atlantic Oceanographic and Meteorological Laboratories Miami, Florida Augus 1969 TABLE OF CONTENTS Page ABSTRACT iv 1 . INTRODUCTION 1 2. BACKGROUND OF FLORIDA PROGRAM 5 3. RADAR SYSTEMS FOR STUDY OF PRECIPITATION 7 4. RADAR PROCEDURES 10 5. ANALYSIS 13 6. RESULTS OF RADAR RAINFALL ANALYSES 20 7. STATISTICAL TEST OF RAINFALL RESULTS 27 8. UNCERTAINTIES IN THE RAINFALL ANALYSIS 33 9. REPRESENTATIVENESS OF Z-R RELATION 36 10. VALIDITY OF Z-R RELATION FOR THE SEEDED CLOUDS 37 11. NATURAL GLACIATING BEHAVIOR OF FLORIDA CUMULI 41 12. DISCUSSION 43 13. SUMMARY AND CONCLUSIONS 44 14 . ACKNOWLEDGMENTS 46 15. REFERENCES 47 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 Florida 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 silver iodide smoke. Seeding was found to be effective in promoting increased cloud growth; the average growth difference between the seeded and control clouds was 11,400 ft, sig- nificant at the 1 percent 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 to 150 acre-feet 40 min after the seeding pass, an increase of over 100 percent. The result is changed little by using an alternate analysis scheme or by including 5 additional control clouds selected after the program. The rainfall increases would probably have been greater if calculations had been possible for entire cloud lifetimes. Because of heavy natural rains during the program, the rainfall computations must be viewed with reservation. The significance of the rainfall results ranged between 5 and 20 percent based on two-sided statistical tests. Comparison between radar and rain gage rainfall demonstrates that the rainfall calculations are probably underestimates by no more than 30 percent. 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; there is no evidence that they were produced by improved efficiency of natural pre- cipitation processes through disturbance of stability of supercooled drops. The natural glaciating behavior of the experimental clouds would appear to preclude the "colloidal stability" approach to rainfall augmentation from Florida cumuli. . IV PRECIPITATION RESULTS FROM A PYROTECHNIC CUMULUS SEEDING EXPERIMENT William L. Woodley 1. INTRODUCTION Since laboratory discoveries of the ice nucleating properties of dry ice (Schaefer, 19^6) and silver iodide (Vonnegut, 19^7) > there have been numerous attempts to increase precipitation by seeding supercooled cumulus clouds with these materials. Most efforts have been predicated on the pro- duction of "colloidal instability" in a cloud containing supercooled drops. The theoretical principles for this type of seeding have been formulated for many years. Seeding with silver iodide or dry ice induces ice particle formation in a supercooled cloud that has little ice because natural ice nuclei are lacking. The stability of such a cloud is disturbed by the ice parti- cles, because the equilibrium vapor pressure for ice particles is lower than that for water drops at temperatures below 0° C. Because of this vapor pressure difference, the ice particles grow by diffusion at the expense of the cloud vapor and water drops. When they are large enough to fall relative to the cloud updrafi^ they grow further by accretion of other cloud hydrometeors . If conditions are right, the falling particles grow large enough to reach the ground before evaporating. Between one (McDonald, 1958) and 10 (Fletcher, 1962; Mason, 1962) artificial ice nuclei per 10 liters of cloud air are considered optimum for promoting precipitation growth. Massive seeding of cumulus clouds, producing many 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 during seeding. The active approach would be the mod- ification of the buoyancy forces and circulations that sustain the clouds, referred to here as dynamic modification. If it were possible to artifici- ally 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 con- version of the vapor excess over ice saturation following seeding might produce a warming of 0.5 to 1.0° C, even if only a fraction of the liquid water is artificially glaciated. Because clouds are rarely more than 1° C warmer than their environments, seeding might, under ideal circumstances, effectively double cloud buoyancy and lead to increased growth. One hun- dred ice nuclei per liter of cloud air is thought to be the minimum number for sudden and complete glaciation (McCready, 1959) --a number that, interestingly enough, in the "colloidal instability" approach to rainfall enhancement is thought to represent overseeding. Although there is a theoretical basis for dynamic modification, as late as I960 serious doubts existed that man could significantly affect cloud dynamics (McDonald, 195&). Except for isolated cases (Kraus and Squires, 19^7; Orr, Fraser, and Pettit, 19^9; Vonnegut and Maynard, 1952), dynamic modification was not observed during seeding experiments before 19 60. There are several reasons for this circumstance. The objective of most of the early experiments was to alter cloud precipitation processes directly, not cloud dynamics. 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 I960, more attention has been given to the possibility of modi- fying 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 cum- ulus experiments over the Caribbean south of Puerto Rico in 1963 (Malkus and Simpson, 1964) and in 1965 (Simpson et al., 1967), in which impressive cloud growth after seeding occurred. In the 1965 experiment, 23 clouds were studied; lk were seeded and 9 were controls as dictated by the randomized seeding instructions. Individual seeded clouds received up to 3^ kg of silver iodide smoke. The average vertical growth difference between the seeded and control clouds was 1.6 km, which is significant at the 1 percent level. The top heights of unseeded and seeded clouds predicted by the Stormfury dynamic cumulus model agreed very well (correlation of 0.97* significant at the 1 percent level) with the observed top heights. The behavior of the seeded clouds could only be explained by incorporating the postulated effects of seeding (fusion heat release and establishment of sa1> uration with respect to ice). This result demonstrated that the physical hypothesis behind dynamic modification has basis in fact and that man can alter cloud dynamics under specifiable conditions. No specification of the effects of dynamic invigoration on precipitation was obtained in these experiments . Following the Stormfury experiments, seeding in Pennsylvania (Davis and Hosier, 1967) and Arizona (Davis et al., 1968) resulted in impressive cloud growth. In the Arizona experiments, nine pairs of clouds were the subject of randomized seeding and received up to k-OQ g of silver iodide, considerably less than the amount used in Project Stormfury. The average tops of the seeded clouds were 5900 ft higher than the corresponding con- trols, a difference that is significant at the 1 percent level. Seeded cloud behavior predicted by a dynamic cumulus model developed at Pennsylva - nia State University (Weinstein, 1969) agreed very well with the observa- tions. A 10-cm radar, calibrated twice daily, was used to infer changes in precipitation following seeding. The average rainfall measured at cloud base from the "core" of the cloud was U.52 mm for the seeded clouds compared with the 1.52 mm for the control clouds, an increase of 186 percent, which is significant at slightly less than 5 percent. Because of the high cloud bases and dry environment, it is questionable how much of the rainfall increase produced by seeding actually reached the ground. There has been little study of the effect of dynamic changes on pre- cipitation. Where attempts were made to measure the effect of dynamic modification on precipitation, no evidence was found of real precipitation increases on the ground. h 2. BACKGROUND OF THE FLORIDA PROGRAM Individual cumulus clouds growing over and near the Florida penin- sula were seeded with silver iodide in May 1968. The experiment was con- ducted 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. (MRl) to study with aircraft and calibrated ground radars the induced dynamic and preci- pitation changes in the seeded clouds and to compare these with the un- seeded control clouds, both chosen on a statistically randomized basis. Simpson et al. (1969) discuss the experiment, the pyrotechnic seeding system, and the first results. The seeding was designed to glaciate the supercooled portions of the clouds suddenly and completely to provide the impulsive fusion heat release necessary for dynamic invigoration and increas- ed cloud growth. Precipitation changes were expected as the by-product of the dynamic alteration. The selection criteria for the experimental clouds were: (l) hard, cauliflower appearance with top between 19,000 and 26,000 ft, indicating a vigorous cloud with its top cooled below the activa- tion threshold of silver iodide (-k° C) but not cold enough for complete _o natural glaciation, (2) minimum supercooled water content of 1 g m as measured by Johnson-Williams instrumentation during cloud penetration, indi- cating the fusion heat potential necessary for dynamic changes, (3) cloud still vigorous after first penetration by the three monitoring aircraft, and (k) isolation from other convective activity, especially cumulonimbus where the risk of natural seeding is especially great. If a cloud was accepted for experimentation, the final go-ahead was given to the seeder aircraft pilot, who then opened a sealed envelope for his instructions. No matter what the decision, his flight pattern was exactly the same: one penetration near top of the cloud, followed by a second penetration perpendicular to the first. If the pilot obtained a seed instruction, 10 silver iodide flares were dropped at about 100-m intervals during each penetration. The multiple pass technique was used to insure better distribution of the silver iodide. Following the seeding run, all aircraft flew patterns to monitor the cloud (fig. l). B- 57 MONITORING FLIGHT ALTITUDES (FEET) 20,000 19,000 17,000 DC-6 ; WC-I2I , S-2D B-57 (SEEDER) POSITIONS OF FLARE DROPS PLAN VIEW 2000-3000- AIRCRAFT S2-D PROFILE Figure 1. Flight tracks of experimental aircraft There were 19 experimental clouds during the Florida program; l4 were seeded and 5 were controls as dictated by the randomized seeding instructions. The seeded clouds grew an average of 11, MX) ft more than the controls, a difference significant at the 1 percent level. This result is consistent with post-1960 experimentation over the Caribbean, Arizona, and Pennsylvania that demonstrated the feasibility of seeding to alter cloud dynamics. Woodley (1969) and Simpson and Woodley (1969) treat instances of dynamic alteration in some detail. Because cloud dynamics and precipitation physics are intimately connected in cumulus cloud, alteration of one must affect the other. This effect is treated extensively in the next section. 3. RADAR SYSTEMS FOR STUDY OF PRECIPITATION The modified UM/lO-cm radar of the Radar Meteorological Laboratory, Institute of Marine Science, 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/lO-cm radar has a 2° conical beam, a transmitter power of 5*5 x 10^ W, a minimum detectable signal of 10"1 W, a pulse length of 2 u s, and a pulse repetition rate of 300 pulses/sec. Important features include special logarithmic and linear radar receiver systems and an RF range attenuation corrector (Riser and Andrews, 1966). The UM/lO-cm radar has an iso-echo contour (LEC) unit developed by Senn and Andrews (1968). Another "level" has been added to the unit by inverting signals again at a given level higher than the highest used in the basic device. The effective antenna gain of the 12 -ft reflector and radome of the UM/lO-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/lO-cm radar system simultaneously. Briefly, it puts known signal levels on all scopes including those used for photography, so that the range attenuation correction, IEC, and all signal handling including degradations due to the photographic process are simultaneously calibrated on the final filmed data used by the analyst. This was done twice daily during the experiment. Table 1 presents the signal levels used and the radar reflectivities and approximate precipitation rates, all nor- malized to 100-n mi range. The IEC values are somewhat different from those requested because of the differences between the methods and video paths used in setting up values and those used in the data-gathering process, The Z-R relationship used to obtain the values in table 1 is based on the work by Sims et al. (1963), who obtained the relation 1 kl Z = 286 R ' D (1) by independently calculating reflectivity Z and rainfall rate R from rain- drop photographs taken during showers in Miami, Florida. Equation (l) has been modified slightly to 1 h Z = 300 R (2) by Gerrish and Hiser (l9o5), who averaged 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, Florida. The overall accuracy of any radar system is difficult to estimate. Senn and Courtright (1968) estimate the relative accuracy of the UM/lO-cm 6 OS w i—i CO > •H 3 cr w 6 CO xt U a 60 CO O *s. M CO Ph a) 3 CO ■—( 13 CO •H > M o N .—1 Pn *% •~V 00 !-) o Pm cr> v 1—1 co >» r— 1 CO 01 £ CO a oo •i-i go 6 x> CO H ce i v. z ac m IO m IO in fO m IO o o O o o IO CM ?■ E N m O X en m o X 0> m o X en in o X en m O X CM m o X CM m o X CM m o X CM in o X en 1 a.1" (0 i CO 1 (O I CO I IO CO 1 IO CO 1 IO (0 1 IO CO CO i K O t- Z O o * «■ * * * * * * «■ X z oc in o m o CO o CO o co o in m in rO 1 E "e E N X o X en o X o X CO o X IO o X CO o X en o X o X CM "e a.1" CO I 1 (O 1 l>- 1 CM 1 1 t«- r- i in r- i IO i K O 1- z o o IO IO IO IO IO IO IO IO IO 2 X z oc en o en o en O o O 0> o en o en o o ?E <°E E o X IO o X IO o X IO o X m IO o X m IO o X IO o X IO o X IO o X 1 a.1" CO CO 1 (0 CO i (O CO i m CO i m CO CO CO 1 CO CO 1 (O co 1 m CO i ac O H Z O o CM CM CM CM CM CM CM CM CM X \ z ac CM O O CM O O CM o o CM o o CM o o IO o o CO o o en o o 1 ro 1 E E N m m m m m - CM o * 1 1 ■o cr> o en o i en O i en O I en O i CO o 1 CM O 1 o o 1 1 oc o z o o 111 < a o CM 1 IO < CM ro CM m CM (0 CM CM CO CM o IO Q a. radar at 1 to 2 db. Antenna elevation angles are probably accurate to * 0.1°. Azimuth checks of known targets were made several times daily to determine error between the printed azimuth and PPI scan azimuth. k. RADAR PROCEDURES The meteorologists in the Radar Meteorological laboratory were in continuous VHF radio contact with the scientists on the project aircraft, who were informed of their azimuth and range from an experimental cloud by the navigator on the command DC-6 aircraft. Positive identification of the experimental cloud by the ground radar was possible if it had a 10-cm radar echo (the usual case); if not, the azimuth and range of the cloud were monitored on the scope for appearance of an echo. It was often pos sible to see the experimental aircraft on radar and follow their patterns around the cloud echoes. The UM/lO-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 lU,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, bright-band middle, and slightly higher levels. The locations of the experimental clouds with respect to the UM/lO- cm radar an shown in figure 2, summary information on the experiment is given in tabl^ 2, and the distances of the experimental clouds from the 10 > >• V < < < 5 5 5 o o o to ro ro I750Z I842Z I942Z id r^ cb >- v >- ! < < < 5 5 5 N CO O ! c\j cm to 1 6 1 8Z I640Z 1 659Z to •cr in > V >- < < < 5 5 5 to to r- CM CM CM M M N CO ro CD ro CM CM r- co m < < < o o - CM CM CM M Nl N CO 00 f >->•>- < < < 5 5 5 CO CD 0> N N N S in to to in o oi s o CM ^ iri to >->->■ < < < 5 5 5 m to to M M M O IO CM to in CM N 00 — — — — CM IO 11 z ?: => ROW! TER NG R o O IO_ o O O m o o o_ o o o_ o o O O o o o o O o o q O O q. O o o_ O O o_ O O o o o O o m 8 q o o o_ o u. ~ CM oo CM CM CO r- o* CM — ro ro CD CO r-* o Q. < ui CM — ■" ~™ "" "~ — O UJ e> z X TOP ER SEEDI EET) * o o o O o o o o O O o O o O O O o o o o o o O o o o o o o o O o O O o o o o m o m O o m o o o o o m o m O o o o o CM en o in * _ ro (0 o — CO _ r^ CM CM ro r- 00 _ < H "" t *■ *■ ro CM CM IO «• CM ro ro ro to IO ro ro to ro 2 u. — < O o o o O O O o o o O O O o o O O o O O o o o O o O o o o O O O o o O O o o o H o o o o O m O o o o O in O tf> in O in o o 0- UJ ^ O UJ u- o 9> CM ro CM — ro o ro — CO en CO en 00 m eo — — r- CO w IO — CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM O "• °- -n o — ro * CM to CM * O in m ro ro U. « CO oo en r- O CO en O r- CO m co CO K r~ CD en ao O o C uj Z s 1 m 00 IO en 1 o o> 1 m 1 O 1 IT 1 r- 1 m en I m l CO i m I o i O I O 1 r- 1 i in i o i 2 <=> O — UJ • m o o m ao CM m ro O m r^ m m ro m ro CM o CO in ao ro * ao in CO CD 1- UJ co o CM * m m o ro f CM ro CM ro o m * to CM 00 00 en r- O r- en O S CO m CO CO r^ r«- ao en ao UNO) SSVd 9-oa isaid o ro ro m CM CM CO r- ro CD m m ID O O 00 r- 00 o en ro O oo ro r^ to CM CO en CM m CO co m ro CO en CO O m r- CM ao CM en CM CD JO 3WI1 M38WnN in m co 00 * m CM en = _ CM m CO r^ CO O 00 anoio xniva d38Wf1N anoio - CM PO * m CO r^ co en O - CM to * in (O r^ 00 en ~IVlN3WIH3dX3 00 00 00 00 00 00 ao 00 ao ao CO CO 00 00 eo CD 00 eo ao UJ CD co co CO CO id * \ V. "S, >N \ V >. "V >. \ \ r- < m CO CO (0 0> 0> o CM o CM CM CO CM CO CM r- CM r- CM 00 CM o ro s o ro o ro - o v. \ -^ "V V, V V, V. \ N. \ \ V v. \ \ \ *N. N. > >- > >- > > > >- >- > >- > >- >- V V V >- UJ z < < < 5 < < < < < < < < < < < < < < z 5 2 2 5 '£. 5 z 2 2 5 5 5 2 I 5 5 s _ © 12 radar are summarized in table 3« All but one of the 19 experimental clouds were within 100 n mi of the UM/10-cm radar. The radar control clouds are discussed later. 5- ANALYSIS The PPI radar return at the bases (0.5° tilt) of all but one of the experimental clouds was converted to rainfall. Seeded and control clouds were compared in terms of the radar-derived precipitation. The size of the cloud sample could be increased artificially by selecting control clouds from the aerial time-lapse photography. These clouds were not se- lected randomly and, in this sense, are not true controls. In an attempt to avoid bias in the cloud selection, an individual experienced in the study of cumulus clouds but unconnected with the project viewed the nose camera films taken by the seeder aircraft and selected clouds from the films that fulfilled the visual eligibility criteria for experimental clouds. These clouds were then located on the radar film. The time of selection was taken as the time of a simulated seeding pass, and the rest of the analysis was done in the same way as for the actual experimental clouds (described below). Five additional control clouds were selected toy this procedure. These were clouds we might have selected for experimentation but did not, either because we were busy studying another cloud or because we found that they formed in air space restricted to our use. The analysis procedure included (a) location of the experimental clouds on the photographs of the UM/lO-cm radar scope, (b) tracings of the iso-echo contours as long as a cloud remained eligible for analysis, and (c) planimeter measurement of the areal coverage of the contours by 13 Table 3* Distance of Experimental Clouds prom Radar Seeded Control Date Time Distance Date Time Distance May 15 1930 Z May 16 1735 z May 16 1822 Z May 16 1937 z May 19 1755 z May 20 1908 z May 21 2034 z May 26 1823 z May 27 1618 z May 28 1640 Z May 30 1750 z May 30 1842 Z May 30 1942 Z 52 n 45 n 38 n 36 n 43 n 55 n 37 n 83 n 85 n 71 n 60 n 50 n 58 n mi mi mi mi mi mi mi mi mi mi mi mi mi May 19 May 20 May 26 May 27 May 30 May 15 May 16 May 20 May 28 May 28 2006 Z 1748 Z 1738 z 1529 Z 1659 z MEM: MEDIAN: 1916 Z 1738 z 1553 z 1608 Z 1637 Z" 35 n mi 50 n mi 36 n mi 65 n mi 33 n mi 44 n mi 36 n mi 43 n mi 30 n mi 52 n mi 62 n mi 72 n mi All Seeded Mean : 55 n mi Mean : 52 n mi Clouds . Median: 52 n mi All Median: 52 n mi Control Mean : 48 n mi Clouds Median: 46 n mi 14 a person who did not know whether an echo was that of a seeded or unseeded (control) cloud. An example of the iso-echo contour tracings is shown in figure 3 for part of the life history of cloud 6 on May l6, 1968. To be eligible for analysis, the echoes of the experimental clouds had to be separate from the echoes of neighboring clouds. When the echo of an experimental cloud expanded and merged with its neighbors, the analysis was discontinued. This criterion, while necessary for an objective anal- ysis t led to a nonhomogeneous data sample. The number of clouds dropped from consideration increased with elapsed time after seeding. The areal extent of the cloud base iso-echo contours were measured for all experimental clouds before and for as long as possible after the seeding pass. These area magnitudes were plotted on a time-area diagram with the time of the first seeding pass used as a reference as shown in figure k. The ordinate of the diagram is area in (n mi) , the abscissa is in minutes after the first seeding pass, and the three curves represent the time change of the areas contained within the specified contours. If the radar rainfall at cloud base had exceeded 3.50 in. hr -*-, the threshold for the next contour, a fourth curve would be shown in the graph. The problem now is to calculate total rainfall from the cloud. The area covered by rainfall rates between 09 in. hr" and .^5 in. hr" in the 10-min period after seeding is shown as the hatched region B. The rain- fall contribution from this region is the area of region B having units (n mi)2 min, multiplied by a mean rainfall rate having units in.min_1. By inserting an appropriate constant, the result is converted to acre-feet of water, which is merely a volumetric measurement and does not represent the 15 I8I0Z I8I7Z SEEDING BEGINS I824Z SEEDING ENDS I828Z I835Z I84IZ I847Z I9I8Z I855Z I930Z H H 5N.MI. I904Z I945Z Greater Than .002 in.hr Greater Than .09 in./hr. Greater Than .45 in./hr. Figure 3. Example of cloud base iso-echo contouring for cloud 6, May 16, 1968 16 60 50 c^40 'i c w 30 < UJ tr. < 20 - 10 MAY 16, 1968 C LOU D 6 TIME RELATIVE TO SEEDING PASS (min.) Figure 4. Graph of iso-echo area relative to time of seeding pass, true distribution of water on the ground. When this procedure is extended to all contours for the lifetime of the cloud, an estimate of total rainfall is possible. The selection of a mean rainfall rate for an area bounded by two known rates was an arbitrary one. The mean value selected was one-third the difference between the known rates plus the lower value. This decision was based on rainfall analyses, which often show that the isoheyts are 17 concentrated near the higher values, implying that the increase in rainfall rate from the edge of a shower to the core is nonlinear. The mean rainfall rate for an area bounded by only one rainfall rate was obtained by taking one -third the difference between the boundary value and the next iso-echo contour permitted by the system plus the boundary value. The mean rainfall rate assigned to the area inside the last contour permitted by the system was one-tenth the boundary value plus the boundary value. Since rainfall rate at cloud base rarely approached the value corresponding to the fourth contour, this last mean was seldom used. Other more elaborate schemes could be devised to arrive at mean rain- fall rates, but they are not warranted because of the many other uncer- tainties. The same analysis was applied to seeded and control clouds, and the relative differences, seeded cloud rainfall minus control cloud rain- fall, should still be valid. The accuracy of the rainfall calculations is discussed in section 8. All rainfall derived was assumed equal to rainfall reaching the ground. However, at a constant antenna tilt the height of the scan is range dependent; as range increases the height of the scan increases. Therefore, the radar measurements at 0.5° elevation are not at the same heights in the experimental clouds. For clouds at ranges between 25 and 50 n mi, the center of the beam is within 1000 ft of cloud base, which averages approximately 2500 ft at this time of year (fig. 5) • Evaporation of the rainfall in falling from the level of measurement has been assumed insignificant, especially in view of the other uncertainties in this pro- cedure. A radar-rain gage comparison (sec. 9) shows that this is not a bad assumption. IB BEAM WIDTHS TO HALF-POWER POINTS ELEVATION ANGLES SET TO STUDY CLOUD AT 40 n. ml 30 40 50 60 RANGE (n.mi. ) Figure 5. Beam dimensions for the UM/10-cm radar for the tilts that were used to study an echo at 40 n mi (after Senn and Courtright, 1968) Two comparisons were made between seeded and control rainfalls. First, total radar rainfall from the seeded clouds in 10-min intervals (relative to the time of the first seeding pass) was compared with that from the controls. Second, the seeded and control clouds were compared among themselves and then with each other. The radar rainfall from a given cloud in the 10-min period before the seeding pass was taken as a standard, which was then subtracted from the radar rainfall produced by the cloud in the 10-min intervals after the seeding pass. If a cloud produced 10 acre- feet of water in the 10-min period before the seeding pass and 30 acre- feet afterward, the difference is 20 acre -feet. The cloud produced 20 acre- feet more water in the 10-min period after the seeding pass than it would 19 have had the rainfall rate in the 10-rain period prior to the seeding pass persisted through the 10 min after the seeding pass. Similar calculations were made in 10-min increments for the entire lifetime of the cloud. The second comparison should be better than the first as a measure of the effects of seeding on rainfall. The first comparison of total, post-seeding pass rainfall weights the result toward the clouds with a head start, that is, those that already have a large echo at the time of seeding. The second scheme should be insensitive to the initial size of the echo. It was not possible to calculate percentage changes in rainfall or to normalize the rainfall to that falling before seeding for all the experimental clouds. To have done so would have meant an infinite increase in rainfall for the five clouds that had no pre -seeding echoes on the 0.5° scan. 6. RESULTS OF RADAR RAINFALL ANALYSES The most striking feature of the analysis was the high variability in rainfall from the experimental clouds, which occurred in rainfall from cloud-to-cloud and day-to-day, as shown by the rainfall figures in table k and by the bar graph plot of these values in figure 6. The solid portion of the bar in figure 6 indicates water relative to that produced by the cloud in the 10-min period before the seeding pass (see sec. 5). The entire bar represents the total water produced by the cloud in the interval specified; the cloud number and date corresponding to the numbers over the bars are shown. The number of experimental clouds in the sample decreased with elapsed time after the seeding pass because many of them merged with their neighbors. As seen in this figure, ^0 min after the seeding pass, the rainfall observations represent a bias in favor of the smaller drier clouds. 20 00 CU c >-> I cO a CO CO co Pm bfl •H CU CU C/} CU e •H H CU CO Pi u CO 'O CO cu i-H •3 io ■H o JJ N CO .H * CU < Pd CU CU 1 * 1 CU O to CM o i O to v_^ * CO < 4J cO Q o o * a o2 q | I I I d | | K) <0 O I * I d | | I I I o | o | | I I I I I I m co * o q I — cri cm d d io q cm q is q *>' c! — d cm d — IO q cm to q * q q O | CO — — CM CM O cr. <£ CM CM ">■ i i °J <£> *! 1 h N o rO en * 1 1 * o * 1 IO IO IO io o m O (0 h- IO IO CO CO IO IO IO 01 IO CM CM — IO 10 r-- co *» o q * CO IO 10 1 IO cri — I — io * CO cm r- cm h- q O m tf> i* f- CM • CM CM o » o s « o o <0 — CO — CM * IO — CO — (0 Cft f- io r» co r- co 10 10 — IO (0 0> _ K — V 1- CO CM CM (0 <0 qq— q— qr^q I ddmdtONO IO co o^qqq^^q d*-" — — cm cm d • - • 10 ■ * ocMioqqq — — cri I diocMCMiodto'd cm en o q q e » i 10 diodn-'iodr^V — 10 — r- r- cm — — q — q q r>-_ I r--' f-' d co -a q — cndio'iocMio — ' — 4;«»qsio- — q«o cbiodcMio — 10— oi * * — 0 — 'CD K 0) * — (0 CM — k co 1 q q q * q q K » cm d d en - ' — co — — 10 — IOHJOOHNN* uj 1 10 en id n ' — ' — 'CM 10 — — — q n- q cm d d cm id 10 en °°. - 9 °. » N O $ o UI o *f Si -1 < o < K cc co a < 3 a -1 o 3 < CC O > 0= -I < 3 O CO CO -I Z U. OOO H- 5 Ul 5 $ 4 cc 21 z o en co z z C/l (/) (/> ..ooO-uJiar-i^oococoOooO -NlOVOll)SCO(D9:^l25£i5t2!!(MNNN — cu in o o So O uJ s# htSH h-^rH 1 ! Z I 1 1 ! 5 . ■ s[Z 1 • o «■ =1 • o ro i • =1 ■ M 01 •H ■--i > 4J 4-J CU •fl CO e rC 4-1 •— 1 cu H CO r-l CU u cu cu rC M U cu H X cu (0 4J ■r-l 4J CO ci-l a 3 CO •r-l ai [fl 'J fi 'X, ro 11 a; CU a a. M 4-1 CO CJ to 00 c CJ c r-l ■H •l-l •H ro T3 T3 > c c cu r4 •i-l • -I CU CJ R CO 4-1 i u C X o ro cu ■H C ■—) -2 rC 01 -J CU 00 c HI r cu ■1-1 X! 4-1 cu -4 j-j 1—1 co o c cu T3 '-4-1 14-1 ■l-l rC => o CU 4J O Zl x> i — I c 3 c o o "O O •H ■r-l o i—i r— 1 4-) ■r-l CJ co ro S-I 1-4 r4 4-J o a> CU CU c CL a. rC -3 0) 4-1 e 6 XI c 3 ■H • r-i •H J*. c M i—l e J3 cu 0 i cu a CO o X) rfl X 1—1 CU 4-1 a) CU u 43 CU 2 o a) H — X 4-1 X! 4J o 4-1 r4 X c a. c M co •H 0 o to u a. '-'-1 ro XI cu CO a 3 4J CU 1 — 1 O to u 1—1 00 r-l 3 u ro c 'J o 4-1 ■r-l i— < CJ c -a CU to ■H CU rC 4J r4 [fl CU 4-1 o CO r4 co >. 4-1 jQ J-i CU XI CU -C ro J3 -C CJ XI 4-J X) 4J CO crj cu CU S-i C4-I CJ a o 3 4-1 CU 14-1 X) ^ > O cu o CU o F u CO -•J c ■H a HI to EX 4-1 u to 4-1 a CO M H) CO cu r-l 60 -C _n j-i CU 4J j ,C u J-l e CO o o ro 3 CQ ±-> 4-J o C CU r4 3 O ••-I (133d 3dDV) U31VM 22 The bar graph of rainfall (fig. 6) reveals tnat the sample is domi- nated by the few wet clouds, especially cloud 6 on May 16, 1966. Seeded cloud 8 on May 16, 1968, probably produced more rain than any in the sample, but because of its azimuth from the radar the rainfall estimates are gross- ly too low. Cloud 8 was at the azimuth of the partially blind cone, 267° and 273°, of the UM/10-cm radar which is due to interference by the Uni- versity 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 underesti- mate is supported by Simpson and Woodley (1969), who compare measured reflectivities with those computed theoretically. Woodley (1969) calcu- lates that the actual rainfall from this cloud is probably twice that computed. Seeded clouds 1 on May 19 and 10 on May 30, and control cloud k on May 19 were also within the partially blind region at some time during their life histories. The estimates of rainfall from these clouds are prob- ably also too low. The amount of rain from the seeded clouds was positively correlated with the maximum top growth following seeding. Table 5 shows the corre- lations 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 to ^0 min following seeding. This finding implies that the more a cloud grows following seeding, 23 Table 5. Correlation Between Maximum Growth and Total Water in 10-min Intervals After First Seeding Pass TIME INTERVAL (MIN.) 0-10 10-20 20-30 30-40 40-50 NO. OF CLOUDS 13 1 2 II 8 6 CORRELATION COEFFICIENT .20 .18 .54 .9 1 79 SIGNIFICANCE > 50 % > 50 % 10% < 1 % ■ < 5 % 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 xn 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 indicate that precipitation decreases accompany the collapse or the cutoff tower growth of seeded clouds con- sisting of one primary tower. This is consistent with the conclusions reached above and is supported by the analysis of cloud 5 on May 16 and cloud 8 on May 30, 1968. The seeded tower of cloud 5 on May lb collapsed complete- ly following the seeding, and no new tower appeared. In successive 10-min 2k intervals after seeding, this cloud produced increasingly less rainfall than it had in the 10-min period before seeding (fig. 6). There is no way of knowing whether these decreases would have been even larger had the cloud not been seeded. In seeded cloud 8 on May 30, discussed by Woodley (1969), a cutoff tower growth was followed "by collapse and then regeneration of the cloud body and explosive growth. The rainfall calcu- lations are consistent with this behavior. During the cutoff tower regime 0-10 and 10-20 min period after seeding, this cloud produced 22.8 and 8.0 acre -feet less w^ter respectively than it had in the 10-min before seed- ing. During the 20-30 min after seeding, regeneration and intense growth began, with the cloud producing 26.7 acre-feet more water than it had in the 10-min before seeding. Subsequently, this cloud merged with its neigh- bors and was dropped from the sample. The average rainfall statistics are of interest, provided 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 figure 7a. The number in parenthesis near each data point refers to the number of clouds contributing to the average. Rainfall values are presented only to kO min after the seeding pass, because the sample is very small after this. Inclusion of the radar control clouds in the sam- ple 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 two 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 25 70 1 1 1 1 1 (12) 1 | 1 1 1 (12) 60 03)/ 60 / r X(8i / / / / / 50 / / / 50 P / LlI 40 " / - £40 _ / / - / (51 / Ul O / (10) ^.«— •""" / / / \m 30 °n-l, .975 otherwise do not reject H, . For the problem at hand, t* = 2.35 and t-jp .975 2.179 so reject H-, . 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 percent level. This says, in effect, that the seeded and control cloud rainfalls constitute distinctly different populations, which is the same conclusion reached earlier. 8. UNCERTAINTIES IN THE RAINFALL ANALYSIS 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 representation of rainfall, the comparison of seeded and control cloud rainfalls should still be valid. 'She sources of uncertainty in the radar rainfall study are analyzed in table 9- They are not listed in order of importance, because the author 33 * 00 CO a bO C •H U Q w TJ 3 O O S-i 4J g o CO (U co UJ o z < 2 CO UJ or UJ > o UJ Si 2E »- CO UJ (T UJ o w ,« r- UJ w CO 3 Ul UJ ^ X truto o co < CD < LU tr <* o o 3 1- o o CO _i < > UJ Ul CJ UJ tr w cj z z — < Ul > ID 5 CO tr* Q *-& => ui 2 -J 0.OO coro u. " ° \± M UJ -= >- UJd CO < o° -I Ul 3 cj Si CO I- cj tr 3t K > - _i §2 o z z 3 O z z 3 C\J I + 1 O UJ CO Ul Q z < CO o 3 o _l o < to LT Z OO U. > ^ to Id a. o UJ tr o_ UJ I- < CO UJ tr UJ o z 3 O >- Ul CD to a 3 O _J CJ tr o u. z §* £ to o Ul tr a. ui < 2 h- to ui tr ui > o a »- Ul o UJ Ul . to5 Z 3 Otr C3»- z° ± UJ Q 0. Ul CO 2 Ul h- co > CO tr < . Q >- < < tr < < tr u_ o >- o < tr 3 CJ o >- z -1 o Ig OP Ul Oq. Ul tr i- to _i < X K- 3 s N UJ tr o x < (O Q. U.O z w 5 1- — X to»- < 3i Q Z < CJ Q % 2 < UJ tr uj UJ UJ 3 z _ tr i- < _i o U. O < tr Ul to 2d Z U. _l X 3 > > i- o< cd a UJ UJ X CJ to z o o Q- tr < h- co Ul tr ui a o z 3 O tr CJ tr UJ tr < < tr to to o o < ui l- to >- to < z CO Ul tr ui > o z o z o ii tr o o. < > Ul u. o i- o Ul _l o Ul z ts < m o tr a. 3 to i- z Ul tr 3 CO < UJ cr S UJ — h- m UJ 5 Z z 5 < 2 _l 3 Q. X LU O l80u) in the experimental 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. A preliminary analysis of the MRI continuous particle sampler (MacCready and Todd, 1964) observations (particle diameters < l80y) made from the same aircraft in the same clouds (Takeuchi, 1969) indicate substan- tial amounts of liquid water in cloud droplets before the seeding pass concurrent with the predominance of ice in precipitation size particles. There was still enough fusion heat potential in the smaller supercooled drops to provide the impetus for dynamic changes induced by seeding. This 1+1 RAINFALL RATE (mm hr" ) Figure 9. Z-R regression lines for Miami, Florida. The solid line is based on measurements of droplet spectra by Sims et al. (1963) with a droplet camera on the ground. The dash and dot-dash lines were obtained from droplet measurements at the bases and at 20,000 ft in selected experi- mental clouds. A continuous hydrometeor sampler was used to obtain the in-cloud measurements. k2 agrees with Sax (1969)., who found that portions of the cumuli studied during the 1965 Stormfury cumulus experiments were partially glaciated at -5° C. However, he could explain the dynamical behavior of the clouds following seeding only if their updraft cores remained largely supercooled to -10° C or colder. The presence of one ice particle per liter of cloud air in the experi- mental clouds before the seeding pass has several important implications. The "colloidal stability" 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, the "colloidal staoili^y" approach to increase rainfall does not seem to be applicable here. Braham (1964) has found natural concentrations of ice as high as 10 per liter in Missouri cumuli with top temperatures of -10° C and warmer. A partial explanation for the failure of the "colloidal stability" approach to produce rainfall increases from seeded Missouri cumuli (Fluecii, 1968; Neyman et al., 1969) may be related to the natural ice concentrations in these clouds. 12. DISCUSSION The increases in precipitation noted during May 1968 Florida pro- gram were the result of dynamical invigoration 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 have been noted between the seeded and control clouds. ^3 The seeded clouds were larger and more lasting and processed more moisture than their unseeded counterparts, which accounted for the increases in precipitation. Because dynamics and not microphysical processes control rain from cumuli in Florida, Missouri (Braham, 1964), and Arizona (Battan, 19o3)> the dynamic approach to rainfall enhancement from these clouds seems to be the most promising. 13. 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 supercooled Florida cumuli induced cloud growth. This phase of the research strongly suggests that seeding increased rainfall and that these increases were positively correlated with increased cloud growth. Precipitation increases 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 (especially in sec- ondary 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 significant between the 5 and 20 percent 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 kk to provide the fusion heat necessary for dynamic alteration. This is an important finding, considering the natural glaciating behavior of cumulus clouds in Missouri, Florida, and elsewhere. The presence of pockets of ice at relatively warm temperatures (-5° C to -10° C) need not preclude sil- ver iodide seeding to alter cloud dynamics and increase rainfall. However, the "colloidal stability" approach to rainfall enhancement is apparently not applicable to Florida cumuli -- whether it is to clouds of other sea- sons and locations must still be determined. The calibrated 10-cm radar of the Radar Meteorological Laboratory was particularly effective in evaluating precipitation changes following seeding, not only relative precipitation differences between seeded and control clouds but, as indicated by the radar rainfall-rain gage rainfall comparison, the magnitude of the volume rainfall within 30 percent 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 dy- namic changes and new growth had not been evaluated here. However, their effectiveness will probably depend on where and at what rate the silver io- dide is released in the cloud. (A critical amount of silver iodide is un- doubtedly necessary to affect cloud dynamics, but its distribution is prob- ably of greater importance.) As this research indicates, as little as 500 g of silver iodide can induce growth if it is strategically placed in the active supercooled portion of a cloud. To recommend routine use of pyrotechnic seeding of individual clouds for augmenting rainfall would be premature. Cloud and environmental conditions favoring large increases in rainfall must be better specified. *5 Model predictions, which indicate that large precipitation increases can be expected from clouds with large 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 repre- sent 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 of areas of clouds with subsequent precipitation increases, this would be an important finding indeed. Ik . ACKNOWLEDGMENTS I am greatly indebted to Dr. Joanne Simpson, Chief of the Experi- mental Meteorology Laboratory, for her help throughout all phases of this research. Without her efforts, the seeding experiment would never have been possible and her advice and suggestions were invaluable in planning and in seeing this research to its completion. I am also indebted to the following groups and individuals for their outstanding assistance: the Research Flight Facility (RfT) 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 partic- ularly helpful in discussions and in helping reduce the liquid water data; the Radar Meteorological Laboratory, University of Miami, which pro- vided radar observations of high quality; Professor Harry Senn whose discus- sion of the radar systems were most helpful; the Naval Research Laboratory k6 and particularly Mr. Robert Ruskin of NRL, who made his observations 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 suffered with me through the many tedious calculations; Mr. Don Takeuchi of Meteoro- logy Research, Inc., for helpful discussions and for his work with the hydrometeor observations; Mr. Glen Brier, Director of the Meteorological Statistics Group, Washington, D, C, and his associate Mr. Gerald Cotton provided guidance on the statistical analysis and compiled the randomized seeding instructions; Mr. John Brown for selecting the radar controls. 15. 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Conf . Conservation and Utilization of Resources, Water Resources 4 Sax, R. I. (1969), The importance of natural glaciation on the modification of tropical maritime cumuli by silver iodide seeding, J. Appl. Meteorol. _8, 92-104. Schaefer, V. J. (1946), The production of ice crystals in a cloud of super- cooled water droplets, Science 104, 457-459. Senn, H. V., and G. F. Andrews (1968), A new, low-cost multi-level iso-echo contour for weather-radar use, J. Geophys. Res. _7_3, 1201-1207. Senn, H. V., and C. L. Courtright (1968), Radar hurricane research, Final Rept. by Institute of Marine Sciences, Univ. of Miami, Radar Meteor- ology Section to U. S. Weather Bureau, Contract No. E22-62-68(N) , 31 pp. Simpson, J., G. W. Brier, and R. H. Simpson (1967), Stormfury cumulus seeding experiment 1965: Statistical analysis and main results, J. Atmospheric Sci. 24, 508-521. Simpson, J., and V. Wiggert (1969), Models of precipitating cumulus towers, Mon. Wea. Rev. 91_(1) , 471-489. Simpson, J., and W. L. Woodley (1969), Intensive study of three seeded clouds on May 16, 1968, ESSA Tech. Memo. ERLTM-APCL 8. Simpson, J., W. L. Woodley, 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. Sims, A. L. , E. A. Mueller, and G. E. Stout (1963), Investigation of quanti- tative determination of point and areal precipitation by radar echo measurements, 8th Quart. Tech. Rept., 1 July 1963-30 September 1963, Meteorological Laboratory, Illinois State Water Survey, University of Illinois, Urbana, 111., 27 pp. Takeuchi, D. M. (1969), Analysis of hydrometeor sampler data for ESSA cumulus experiments, Miami, Florida, May 1968, Final Rept. by Meteorology Research, Inc. to Experimental Meteorology Branch, APCL, ESSA, Contract No. E22-28-69(N), 44 pp. Vonnegut, B. (1947), The nucleation of ice formation by silver iodide, J. Appl. Phys. 18, 593-595. Vonnegut, B., and K. Maynard (1952), Spray-nozzle type silver iodide smoke generator for airplane use, Bull. Am. Meteorol. Soc. 3J3, 420-428. Weickmann, H. (1953), Observational data on the formation of precipitation in cumulonimbus clouds, Thunderstorm Electricity, 66-138 (University of Chicago Press, Chicago, 111.). Weinstein, A. I. (1969), A numerical model of cumulus dynamics and micro- physics, Dept. Meteorol., Pennsylvania State University, State College, Penn., 75 pp. Woodley, W. L. (1969), The effect of airborne silver iodide pyrotechnic seeding on the dynamics and precipitation of supercooled tropical cumulus clouds, A dissertation submitted to the Graduate School of Florida State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy. 187 pp. Woodley, W. L. , and A. Herndon (1969), A rain gage evaluation of the Miami Z-R relation (to be published) . 50 GPO 853 -653 63 U.S. DEPARTMENT OF COMMERCE Environmental Science Services Administration Research Laboratories ESSA Technical Memorandum ERLTM-AOML 3 A RAIN GAGE EVALUATION OF THE MIAMI REFLECTIVITY-RAINFALL RATE RELATION William Woodley Alan Herndon Experimental Meteorology Laboratory Atlantic Oceanographic and Meteorological Laboratories Miami, Florida September 1969 TABLE OF CONTENTS Page ABSTRACT iv 1. INTRODUCTION 1 2. RADAR SYSTEMS 2 3 . METHOD 3 k. ANALYSIS PROBLEMS 6 5 . RESULTS 7 6. CONCLUSIONS 13 7- ACKNOWLEDGEMENTS 1^ 8. REFERENCES !5 in ABSTRACT To provide a foundation for other radar studies in the Miami area, fifty comparisons were made between shower rainfall recorded by rain gages and observed with radar to evaluate the reflectivity (Z) -- rainfall rate l.k (R) relation, Z = 300R * , referred to here as the Miami Z-R relation. Total shower rainfall measured by recording rain gages was compared witn estimates derived from the Miami Z-R relation in conjunction with radar reflectivity measurements with iso-echo contouring and the analysis scheme described. The radar and rain gages estimates of shower rainfall were highly correlated (+0.93, significant at the 1 percent level) and dif- fered an average between 8 and 30 percent. Stratification by shower amount revealed that radar estimate of gage-recorded rainfall was too high for small shower amounts (<0.25 in.) 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 radar made a small (3 percent) but statistically signi- ficant (< 1 percent level) reduction in the variance and improved the cor- relation (0.93 to 0.9^+*0 between the gage and radar estimates of precipi- tation. It is concluded that the Miami Z-R relation, when used with the radar system described, is an effective tool in representing point and areal rainfall from South Florida convective showers. iv A RAIN GAGE EVALUATION OF THE MIAMI REFLECTIVITY-RAINFALL RATE RELATION William Woodley and Alan Herndon 1. INTRODUCTION Over the last two decades radar has been used for quantitative measurements of rainfall, based on investigations relating rainfall rate, R, to reflectivity, Z. The Z-R relations computed directly by measuring radar reflectivity and rainfall amount or indirectly by measuring raindrop size spectra, have been derived for various locations, seasons, and storm types. Stout and Mueller (1968) give an excellent survey of these relations and a discussion of their accuracy 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 experi- ments in Arizona (Davis et al. , 1968) and in Florida (Woodley, 1969) are but two recent examples. The Florida study showed that seeding increased rainfall an average of 100 to 150 acre -feet per cloud by k-0 min after the seeding pass, representing an increase of over 100 percent. If these radar-derived precipitation results are to have credibility, it is impor- tant to demonstrate that the Z-R relation and 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 = 286R1'43 (1) by independently calculating reflectivity (Z ram m J) and rainfall rate (R, mm hr ) from raindrop photographs taken during showers in Miami, Florida. Equation (l) has been modified slightly to Z = 300R1' (2) by Gerrish and Hiser (1965), who averaged the coefficients 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, Florida. Equation (2), referred to here as the Miami Z-R relation, is evaluated in this paper by comparing recording rain gage 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 rain gage trace was too compressed to permit rainfall rate com- parisons. Gage-measured rainfall was the standard of comparison, although the accuracy might be questionable since no attempt was made to evaluate the condition and exposure of the rain gages used. 2. RADAR SYSTEMS The modified UM/lO-cm radar of the Radar Meteorological Laboratory, Institute of Marine Science, University of Miami, was used in the compari- son. It has a 2° conical beam, a transmitter power of 5»5 x 10 W, a mini - -Ik mum detectable signal of 10 W, a pulse length of 2 ps, and a pulse repeti- tion rate of 300 pulses/sec. Included are special logarithmic and linear radar receivers, an RF range attenuation corrector, and an iso-echo contour unit. The UM/lO-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 Courtright (1968) and Woodley (1969)- The comparisons between radar and rain gage rainfall observations were made in the annulus 20 to 50 n mi from the UM/lO-cm 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 cloud echoes were contoured with the IEC unit built at the radar laboratory (Senn and Andrews, 1968). The Z values and equivalent precipitation rate for various contours are shown in table 1. 3 . METHOD The photographs of the UM/lO-cm radarscope were projected frame by frame onto the rain gage map as shown in figure 1. The map projection repre- sents 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 rain gage map. Each contour corresponds to a reflectivity threshold and rainfall rate; the former was obtained with the calibration systems described by Andrews and Senn (1968), the latter from the Miami Z-R relation in (2). Readings were made from the radar photographs taken at 1- to 2-min intervals at the location of a recording rain gage, plotted versus time, integrated with a planimeter to provide total shower rainfall, and then compared with the shower rainfall recorded by the rain gage. Evap- oration of the rain drops in falling from the level of scan to the i u bO o u fin •H H F-4 CO VD ON I to OJ H > IN) -d Pi 0J PM CO. > •H 8 I O 0) H ■3 EH ! z in IO m m K> ro O o o O O IO CM •s E IM O X 0) in O X m o X in O X en in o X cvi m o X CM m o X CM m O X cm in O X 1 10 1 CO i u> I CO 1 IO CO i ro CO 1 ro CO 1 IO CO i p- co 1 c z> o p- z o o <■ «■ <■ * «■ * «■ <• «• X z tr o o CO o 00 o CO O m m p- ro 1 E E n X o X o X o X 09 o X IO Q X CD o X CD O X o X CM <0 p- 1 P- P- 1 co r- 1 p- CM P- 1 p- i P- P- 1 m p- l IO P- 1 O H Z O o IO IO IO ro ro IO IO ro ro CC I z oe on O o o O o o o O o E PJ o X IO o X IO o X IO o X in IO o X m ro O X IO o X IO O X ro O X "e a.1" CO oo 1 CD 00 1 CO 00 1 m 00 i in oo 1 CO 00 1 (0 oo 1 CO oo 1 in 00 i o H Z o o CM CM CM CM CM CM CM CM CM or X Z oc cm o o C\J O O 04 O o CM O O CM O O ro O O CO O O o o 1 ro IE "g E PJ IO m m m m = CM o 1 1 .a a.*" o O 1 O i O 1 o CO o 1 CM O 1 o o 1 1 or o r- Z o o UJ r- < o CM in >- < 2 CVJ IO CM m CM CO CM CM 00 CM o ro a Uic/> £S s> Figure 1. Example of contoured echoes superimposed on the South Florida rain gage network (network based on the work by Mr. Garold Gerrish, Radar Meteor- ological Laboratory, University of Miami). The first (boundary) contour corresponds to .006 in. hr"1, the second to .09 in. hr"l. Inside the white area the rainfall rate exceeds 0.4U in. hr~l. 5 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 rain- fall 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 contained by A. The rainfall rate for a point within the high- est contour permitted by the system was linearly interpolated between the boundary value and rainfall rate of 6.00 in. hr , which was assumed to exist as a point value at the center of the contoured area. k. ANALYSIS PROBLEMS Comparing a radar estimate of shower rainfall with a rain gage esti- mate is difficult. The vertical separation (1000 to 4000 ft) between the rain gage and the level of the radar scan and the drift of the precipitation while falling this distance are decided problems. Also degrading the com- parison are the tremendous difference between the size of the radar and rain gage samples and the likelihood that the radar beam is not always uni- formly filled with precipitation, but the most serious obstacles are the convective rains in Florida; the observation that it often rains heavily on one side of the street and not on the other is certainly true here. Unfor- tunately, the 10-cm radar does not have resolution to this distance scale, and even if it did the l/2 n mi diameter of the dot representing the rain gage 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 l/k 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 rain gage locations on the map are perfect. However, the resulting error in estimating point rainfall should not be systematic. 5 . RESULTS The rain gage (G) and radar observations (Ra) permitted 50 compari- sons, none of which involved seeded clouds. These comparisons are tabu- lated in table 2 and summarized in table 3» Using the rain gage results as the standard, the average error is an 8 percent underestimate by the radar when the differences are summed algebraically and about 30 percent if their values are summed. The average percentage difference is defined here as the average difference divided by the average gage -recorded rain- fall, rather than the mean of the individual percentage differences, in order not to give undue weight to the few comparisons with the small absolute differences but large percentage differences. The correlation coefficient between G and R was found to be 0.93> significant at better than the 1 percent level. A more meaningful analysis of the comparison between G and Ra is stratification of the observations by shower amount, as shown in table k. The mean difference (G - Ra) suggests that the radar overestimated the gage-recorded rainfall for shower amounts less than 0*25 in. and underestimated it for larger amounts. The radar did best for the heavy showers, as suggested by the ratio of the mean difference to the mean gage- recorded rainfall and the ratio of the standard error to the mean Table 2. Comparison of Rainfall Recorded hy Rain Gages and Rainfall Observed With the UM/10-cm Radar, May 1968. DATE STN. NO. RAIN GAGE MEASUREMENTS RADAR MEASUREMENTS G"Ra (IN.) G-Gp Gp= -0.1488 + 1. I428R DIST. OF GAGE (MAY) MAX RAINFALL SHOWER RAINFALL (R„) , FROM RADAR RAINFALL (G) RATE (IN HR-') DURATION (IN.) + .OOOI53d* (N. Ml.) (IN.) (MIN.) 1 6 433 .00 .20 1 1 .01 -.01 -.03 33.3 1 6 423 .07 .45 37 .10 -.03 -.09 35.8 1 6 415 .05 .10 35 .03 .02 .0 5 2 7.5 19 422 1.22 3.40 52 .71 .31 .2 2 47.0 19 423 .22 2.00 44 .29 -.07 -.16 35.8 1 9 425 .1 5 .80 70 .22 -.07 -.07 27.4 19 430 .1 8 1.50 56 .37 -.19 -.18 23.0 19 415 .05 1.50 62 .18 -.13 -.12 27.5 19 425 .08 .60 30 .10 -.02 .00 2 7.4 19 424 .03 .20 29 .02 .01 .08 2 1.6 1 9 424 .20 1.00 34 .13 .07 .13 2 1.6 20 8 1 2 .78 1.50 62 .41 .37 .3 5 2 7.0 20 426 1.41 3.60 56 1.19 .22 .08 28.1 20 428 .10 .40 15 .03 .07 -.0 1 38.2 20 604 .21 4.00 35 .46 -.25 -.23 20.4 20 605 .19 2.00 22 .21 -.02 -.0 1 2 6.5 20 423 .1 1 .50 2 1 .09 .02 -.04 35.8 20 435 .39 3.50 28 .40 -.01 .00 23.5 20 807 .99 3.50 65 .92 .07 .0 1 22.5 20 61 3 .18 .60 48 .1 1 .07 .12 2 3.5 2 1 435 .10 1.00 35 .13 -.03 .02 23.5 2 1 605 .01 .50 16 .02 -.0 1 .03 26.5 25 807 .48 .65 88 .39 .09 .1 1 22.5 26 702 .20 1.50 32 13 .07 -.03 38.7 26 433 1.06 3.00 35 .77 .29 .16 33.3 27 426 .1 1 1.50 18 .14 -.03 -.02 28.1 28 428 .30 .53 35 .18 .12 .02 38.2 26 61 2 .17 .50 50 .16 .01 .02 2 7.0 28 81 2 .47 .90 55 .33 .14 .13 2 7.0 28 81 1 .15 .50 48 .16 -.0 1 .14 22.1 28 432 .02 .40 22 .05 -.03 -.2 1 45.6 28 422 .43 .45 1 7 .06 .37 .17 47.0 28 807 .13 .45 50 .1 1 .02 .08 22.5 28 807 .03 .60 20 .06 -.03 .03 22.5 28 804 .15 .60 22 .07 .08 .02 36.1 30 613 .00 .40 14 .04 -.04 .02 23.5 30 423 .06 .60 28 .10 -.04 -.10 33.8 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 .18 1.00 21 .17 .01 .01 28.1 30 807 .22 2.45 2 1 .30 -.08 -.05 22.5 30 807 .60 2.00 38 .46 .14 -.15 22.5 30 8 1 1 .04 .55 26 .07 -.03 .03 22.1 30 81 2 .05 .60 20 .09 -.04 -.02 2 7.0 30 81 1 .48 3.55 30 .38 .10 .12 22.1 30 702 1.40 4.00 1 13 1.05 .35 .12 38.7 30 435 1.59 5.00 75 1.30 .29 .17 2 3.5 « 3 03 CO 03 CO 03 • oo rH -s EH e? u o o H >£. i o Itf i O o o >£- f o lo I 1 03 u Ic3 CO • m a • ■H VO r4 • VO d m rH • VO o o CO on ON o oo CO o on m H in H QJ 0) Sh rH ft U U o p o H cl o CO •H 03 C3 a3 03 difference. The better radar-rain gage agreement with increasing shower amount is a fortunate circumstance, because the heavy rainfall is the one of most concern. Table 4. Stratification by Shower Amount of G and Ra Comparison. Rainfall n G (in.) a a Category G - R a (in.) G-Ra 5 G - Ra 0 G .10 15 .046 -.023 -.49 .04 -1.74 .11 G .25 17 .175 -.046 -.27 .13 -2.83 .26 G .50 7 .418 .091 .22 .18 1.98 G .50 11 1.055 .200 .20 .20 1.00 0 = S.(G-Ba)! - ^TTrJ n- 2 1/2 In figure 2, G and R are plotted on a scatter diagram, where the a solid line is a theoretical line of perfect agreement (slope 1, intercept 0) between the two measures of shower rainfall and the dashed line is the least squares best fit line (Guttman and WilJcs, 1965) for the plotted points. Gage-recorded rainfall (G) was the independent variable in this analysis. The values of the slope and the R_ intercept of the best fit line are given in table 3« The scatter of points about the best fit line (fig. 2) is probably the result of the nonsystematic, inexact placement of the rain gages with respect to the echoes, especially in regions of intense rainfall rate 10 X o o g < U. S. Army Electronics Laboratories, Fort Monmouth, New Jersey, 63 pp. Guttman, J., and S. S. Wilks (1965), Introductory Engineering Statistics (John Wiley and Sons, Lnc, New York), 3*4-0 pp. Senn, H. V.jand 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 hurrricane research, Final Rept. by Institute of Marine Sciences, Univ. of Miami, Radar Meteorology Section to U. S. Weather Bureau, Contract # E22-o2-68(N), 31 PP. Sims, A. L., E. A. Mueller, and G. E. Stout (1963), Investigation of quanti- tative determination of point and areal precipitation by radar echo measurements, 8th Quart. Tech. Rept., 1 July 1963 -- 30 September 15 1963 , Meteorological Laboratory, Illinois Water Survey, Universi- ty of Illinois, Urbana, 111., 27 pp. Stout, G. S.; and E. A. Mueller (1968), Survey of relationships between rainfall rate and radar reflectivity in the measurement of preci- pitation. J. Appl. Meteorol. J, ^65-^73 • Woodley, W. L. (1969), Precipitation results from a pyrotechnic cumulus seeding experiment, ESSA Tech. Memo (to be published). GPO 854 - 004 16 U.S. DEPARTMENT OF COMMERCE Environmental Science Services Administration Research Laboratories ESSA Technical Memorandum ERLTM-AOML 5 LARGE-SCALE PRECIPITATION EFFECTS OF SINGLE CLOUD PYROTECHNIC SEEDING W. L. Woodley A. Herndon R. Schwartz Experimental Meteorology Laboratory 64 Atlantic Oceanographic and Meteorological Laboratories Miami, Florida November 1969 TABLE OF CONTENTS ABSTRACT 1. INTRODUCTION 2. APPROACH TO THE PROBLEM 3. MICROPHYSICAL EFFECTS OF SINGLE CLOUD SEEDING ON AREAL PRECIPITATION 3.1 Superposition of Silver Iodide Plume on Rai nf al 1 Anal yses 3.2 Method 3.3 Problems and Uncertainties 3.4 Results 3.5 D i scuss ion 4. DYNAMIC EFFECTS OF SINGLE CLOUD SEEDING ON AREAL PRECIPITATION 4.1 Tools 4.2 Method 4.3 Results 5. SUMMARY AND CONCLUSIONS 6. ACKNOWLEDGEMENTS 7. REFERENCES Page i v 1 3 3 4 4 11 15 15 16 17 20 24 25 25 1 1 1 ABSTRACT The large-scale precipitation effects of single cloud pyrotechnic seeding in South Florida during May 1 968 are investigated with a twofold approach : (1) Rainfall over areas traversed by the silver iodide plume is compared with that over areas not affected by the plume, and (2) "radar rainfall" over a circular grid centered on the core of the seeded clouds is compared with grid rainfall centered on the non-seeded experimental clouds. Analysis techniques are described with their limitations and un- certainties. The results are not conclusive. In the plume analysis, the precipitation maxima on four of the nine experimental days might be explain- ed by the passage of the seeded plume. In the grid analysis there was higher average grid rainfall within a 20-n mi radius of the seeded clouds than there was for the controls, but this result is not significant, even at the 20% level using a W i 1 coxon-Mann-Wh i tney non-parametric test. Data limitations preclude a meaningful statement about the grid rainfall at greater radii from the experimental clouds. Although single cloud silver iodide pyrotechnic seeding caused in- creased growth and precipitation from the seeded clouds during May 1 968 , the large scale precipitation effects during this period, while positive, were apparently too small to be significant. A more definitive statement must await a longer experimental period with a much larger sample of clouds. 1 v LARGE-SCALE PRECIPITATION EFFECTS OF SINGLE CLOUD PYROTECHNIC SEEDING W. L. Woodley, A. Herndon, and R. Schwartz 1. INTRODUCTION Silver iodide pyrotechnic seeding of individual supercooled cumulus clouds in South Florida is an effective technique in promoting growth, longer lifetime, and, as a consequence, increased precipitation from these clouds (Woodley, 1969)- The effect of this seeding on clouds and precipi- tation on a scale one to two orders of magnitude larger than that of an individual cloud is not known. The precipitation increases produced by single cloud seeding could represent a net increase, a decrease, or simply a redistribution of the precipitation over a large area encompassing the seeded cloud. Analysis of two other seeding experiments in which silver iodide was dispersed from airborne silver iodide generators into clear air upwind of the target clouds has revealed apparent decreases (not significant at 5% level) of the large- scale precipitation (Battan, 1966; Flueck, 1968; Neyman et al., 1969). Be- cause the seeding technique and physical hypothesis behind these experiments differ considerably from that behind the Florida experimentation, it is not wise to extrapolate their results to cloud seeding studies in Florida. For this reason, we have embarked on a study of the large-scale precipitation effects of single cloud seeding in Florida. The response of the South Florida supercooled cumulus clouds to pyrotechnic seeding during May 1 968 was dramatic in almost all instances. Thirteen of the fourteen seeded clouds attained cumulonimbus stature with an attendant increase in precipitation, while none of the five controls grew significantly. In some instances the seeding may have hastened natu- ral cumulonimbus development; in others it may have induced cumulonimbus development when none would have occurred naturally. In either instance the seeded cumulonimbus clouds probably had some effect on cloud develop- ments and precipitation in their environments. A seeded cumulonimbus cloud might affect environmental cloud develop- ments and precipitation in a number of ways. The silver iodide introduced into one cloud might remain active in a plume an order of magnitude longer than the lifetime of the seeded cloud, entering other clouds and affecting their precipitation processes (mi crophys i cs) in an unknown way. Dynamic effects of the seeded cumulonimbus cloud might be a preci pi tat ion - i nduced downdraft that might act as a meso-front, radiating away from the parent cloud, lifting sub-cloud moist air, resulting in other clouds and precipi- tation. Cloud developments tens of miles from a seeded cumulonimbus might be inhibited due to either the anvil cirrus canopy that cuts off insolation or to compensating subsidence around the vigorous seeded cloud. Natural cumulonimbus clouds over South Florida undoubtedly have a profound effect on other cloud developments and precipitation in their environments, but few are concerned because little can be done about it. However, when man can induce cumulonimbus clouds that may act to reorganize and redistribute the rainfall or to increase or decrease it over large areas, everyone is concerned because any adverse effects can be eliminated by simply terminating the seeding. 2. APPROACH TO THE PROBLEM There are many approaches one might take in the investigation of the large-scale effects of silver iodide seeding of individual cumulus clouds. Two are adopted here: (1) investigation of mi crophys i cal (i.e., on the scale of the individual cloud particles) effects and (2) investigation of any dynamic effects. With the mi crophys i ca 1 approach, rainfall over areas traversed by the seeded plume is compared with the rainfall over areas un- affected by the seeded plume. With the dynamic approach "radar rainfall" is calculated over a circular grid of 120-n mi diameter, centered on the experimental clouds. 3. MICROPHYSICAL EFFECTS OF SINGLE CLOUD SEEDING ON AREAL PRECIPITATION 3.1 Superposition of Silver Iodide Plume on Rainfall Analyses The silver iodide introduced into one cloud may have entered other clouds at a later time, affecting their precipitation processes. Our cal- culations indicate that the concentration of silver iodide active at -10°C 2 3 decreased from 10 to 10^ nuclei per liter in a typical seeded cloud with a 1-km radius and supercooled depth of 2 km to about one nucleus per liter in a triangular plume volume 37 km on a side and 2 km deep. Because about 100 nuclei per liter in the supercooled portion of a cloud is apparently necessary for important dynamic effects through fusion heat release (MacCready, 1959), the silver iodide concentration in a typical seeded plume was too low to induce dynamic changes. However, one ice nucleus per liter of cloud air has been considered optimum for inducing increased precipitation through alteration of cloud microphysics (McDonald, 1958; Fletcher, 1962; Mason, 1962). This phase of the research is approached with this in mind. Silver iodide plumes subsequent to seeding are constructed^and rainfall over areas traversed by the plume is compared with that over areas not affected by it. 3.2 Method Horizontal projections of air trajectories at 8,000 and 20,000 ft were estimated from streamline analyses for an air parcel originating at the location of each of the experimental clouds at the time of the first seeding pass. The altitudes of the trajectories were chosen for two reasons: (1) the pyrotechnics were dropped at 20,000 ft MSL,and (2) tests have indicated (Simpson et al., 1969) that the pyrotechnics, when dropped from 20,000 ft, probably burn out before reaching 8,000 ft. Connection of the terminus of each trajectory after any time interval defines the largest possible volume in which the silver iodide might be distributed. After construction, each seeded plume was superimposed on the rain- fall analysis closest to it in time. Two different individuals did the plume and rainfall analyses, neither seeing the work of the other until it was completed. Comparisons were made between rainfall beneath the seeded plume with that over areas not traversed by the plume, with care taken to determine whether the rainfall fell before or after plume passage. 3.3 Problems and Uncertainties The most serious problem with this phase of the study was obtaining a representative rainfall analysis. The South Florida rain gage network (fig. 1) is least dense at ranges exceeding 20 n mi west and northwest of Miami where most of the experimental clouds were located. Because inter- polation of the rainfall between gages is of questionable value in instances of showery precipitation, a true representation of the rainfall was diffi- cult to obtain. This problem could have been circumvented had there been continuous UM/10-cm radar observations. This radar with its iso-echo con- touring unit, discussed later, has been shown to be an effective tool in accurately (within 30%) representing rain reaching the ground (Woodley and Herndon, 1969). If the radar observations had been available for extended periods, it would have been a simple matter to project the filmed radar observations on a gridded map of South Florida and then make radar rainfall readings at selected time intervals at the points on the grid. The rain- fall rate readings could then have been t ime- i ntegrated to provide total rainfall at each grid point. The isohyetal analyses resulting from this procedure certainly would have been more accurate than those used in this study . With the observations made during the seeding program, there is no way of knowing exactly where the silver iodide went or how long it remain- ed active after it was dropped into a single cumulus cloud. It is likely that much of it was either washed out with the precipitation or was carried away in ice crystals in the anvils of the large cumulonimbi that formed subsequent to seeding. The scheme used to define the volume containing silver iodide, described earlier, is an approximation that probably maximizes the true plume volume, if anything. In instances where the wind did not change linearly between 8,000 and 20,000 ft, the true shape of the seeded plume differed from that provided by the analysis scheme. 27*00 26*45' 26° 30' 26° I 5' — j 26°00' 2545 25*30' 25*15' -w 27*00* 26*45 26*30' 26* I 5' 26*00" — 25*45* — 25*30* — 25' I 5 81*30' 81*15' 81*00' Figure 1. South Florida rain gage ne Radar Meteorological Labor tions of the experimental off map. 80*45' 80*30' 80* 1 5' twork(after Mr. Harold P. Gerris atory ,Un i vers i ty of Miami) with clouds denoted by A. Four cloud h of pos i - s are '30' Bl" 15' *00' 60*45' 80*30' 80*13' 25* I 5' - + LOCATION OF RAOAR MAY 16, 1968 <-yr\ 25*30 81*13' 81*00' 80*43' 80*30' 80*13' Figure 2. Superposition of silver iodide plume on obser rainfall pattern. May 15 and 16, 1968. ved '50' 81*15' 81*00' 60*45' 80*30' 80*15' ■4- LOCATION OF RADAR MAY 19, 1968 80*45' 80*50' 80*15' 26*00 1 ^, -"" 1 " ±-~£ 1 / — .50 / -i.sX V 1 — gnNT*^ \l i SEEDING ^- _^~» /- "7 6D*| ^l-Sx L-50 ^10 -I308EDT ^ / l0"~~~----^ ^•^^ONMI n\ ^&-v / 20 N V) ^ ^m ufKvZ l5-v/ ' 4QM /^ y-2or\ ♦Y' 7 \ *§ Yjh^oll j> i \ ^^s^^^ I Ns-yT? "^ + LOCATION \ f^i' S^ OF RAOAR \ ( \*r \ 1 ^^ MAY 20, 1968 \ p*f /L..3£ l0 — ** .^ i 81*30' 81*15' 81*00' 80*45' 80*50' Figure 3. Superposition of silver iodide plume on observed rainfall pattern. May 19 and 20, 1 968 . 81*30' 81* 15' 61*00' 80*45' 80*30' 80* 1 3' 1 1 \S 1 II 0 / io \ N /'0\f 26" 15' 60NMI y^ \ 360° /j 26*15' / 40NMI 1 50 J] 26*00' ^tfrVk. / / 20NMI y/ 26*00' j^S f /^//O X 25*45' \jo£k w — (— 270* 1 jA^JPSoX \ 25*43' 25*30' \ '^x^\ W^^ \ f \ ' \-> 23*30' 25" 15' \ SEEDINGf^~ lCy V - ^^ \ \ "^a \ TIME - *&■ "><\ \ ^^5"*n\ -4- location \ rsi'A>>\r ^V^-— **""^T ^Q^v/ OF RADAR \ ( \TJT , Ya-J****^"^ \S0"Z/ , MAY 21, 1968 \ %iel^-^rr«Y7^v • ^kJ 25' 15' 7J 81*30' 81*13' 81*00' 80*45' 80*30' 80* 1 5' 26" 15' 1 1 '/" / ' ' / X __ 50 _ 0 / io /^^— -.io-C^\ / / / ( ^"-*"V"^--I.*K ' / I \ ^>r / /2-0\ SON Ml 1 \ \ /^ V ( n\ \ I 26*15' \36o* yy^ \\_yx /ftzx> / 40NMI \v. ^ ^~~^ %@T" 2S"00' yTJifx" 26*00' 25"4S' ^nviiao 25*45' 5M *4r\\\ l_L / V \ 1\\ x^wSx 25*30' - \ PSV^^W /,i.o «f a 25*30' MAY 26, 1968 V^vA ^\ I jS< A so — *r V/ 25" 15' + LOCATION \ f^A^lf \x ^-*1\^ /^ V OF RADAR \ / \»f , \rf ***^ \\ / } SEEDING \ >• .jj?*5n( i^ak. Vs^^^^J^ TIME \ kxvX?' df ^^-^0-£.'Sh^ir% ' / l 1423 E0T V?^ie_ -\J ^eY'vtO'' ' Kr£i 7/ \ 23*15' 81*30 81*13' 81*00' 60*45' 60*30' 80* 1 5' Figure k. Superposition of silver iodide plume on observed rainfall pattern. May 21 and 26, 1 968 . 81*15' 81*00' 80*45' 80*J0' 80*15' 25*45 81*15' 81*00' 80*45' 80*50' 80*15' Figure 5. Superposition of silver iodide plume on observed rainfall pattern. May 27 and 28, 1969 10 MAY 30, 1968 Figure 6. Superposition of silver iodide plume on observed rainfall pattern. May 30, 19&8, 3.4 Results The results of the superposition of the seeded plumes on the rain- fall analyses are presented in figures 2 through 6. The important points to be gleaned from the individual analyses are summarized below: May 1 5 - The seeded plume moved over the Gulf of Mexico and did not pass over the region of heavy rainfall centered 20 n mi west-southwest of Miami. However, the rainfall beneath the plume along the Florida west coast is a gross underestimate because of lack of rain gage observations. An examination of the available radar observations suggests that over 1 in. of rain may have fallen in this region associated with the seeded cloud. There is no way of knowing whether the plume affected the pre- cipitation processes of other clouds in its path. May 16 - There is strong evidence that the rainfall maximum was directly associated with the three clouds that were seeded, especially the last two. There is no evidence that a significant portion of the rainfall fell from secondary c'ouds that may have entrained silver iodide from the plume. May 1 9 - On this day the seeded cloud entered a squall line moving southeastward over South Florida and the squall system produced the heavy precipitation. It is not known whether the intensity of the pre- cipitation was increased because of the presence of the silver iodide. The rainfall at the origin of the plume to within 20 n mi of Miami is an underestimate due to a lack of rain gage observations. May 20 - The silver iodide plume passed over the regions of heavy rainfall after the rain had fallen. There is no evidence that the plume affected the rainfall on this day. May 21 - The silver iodide plume passed over the regions of heavy rainfall at the time the rain was occurring and could have affected the precipitation in some way. The heaviest rainfall over South Florida fell near the path of the plume. May 26 - The silver iodide plume originated over the Gulf of Mexico, 80 n mi south-southwest of Miami, and moved northeast, crossing the extreme southern portion of the Florida peninsula. The plume did not cross the regions of maximum rainfall. 12 May 27 - The silver iodide plume originated over the Gulf of Mexico, 85 n mi west-southwest of Miami and moved eastward over the Florida pen- insula. It passed over the area of heaviest rainfall at least 6 hours after the rain had fallen. May 28 - The silver iodide plume passed over a region of heavy rain- fall at the time of the heavy precipitation. The radar observations indicate that the seeded cloud and plume were amalgamated into the group of clouds that produced the heavy precipitation. It is not known whether the rain was heavier because of the silver iodide. May 30 - There were three seeded clouds on this day with very dis- torted plumes caused by highly diverging winds between 8,000 and 20,000 ft Heavy precipitation was noted over most of South Florida, and there is no evidence that it was either increased or decreased because of the silver iodide plumes. A summary of the results of the superposition of the seeded plumes on the rainfall analyses is presented in table 1; four of the nine calcula- tions indicate that the seeded plume traversed a region of heavy rainfall at approximately the time the heavy precipitation was occurring, although the time and space superposition of the seeded plume and the heavy rainfall may have been merely fortuitous. In one instance (May 16) the rainfall max- imum was produced by the seeded clouds and not by any others that may have ingested the silver iodide at a later time. In another (May 19) the seeded cloud entered a squall line moving southeastward over South Florida and the squall system produced the very heavy precipitation. It is not known whether the intensity of the precipitation was increased because of the 13 Table 1. Seeded Plume Rainfall Summary Rainf al 1 Poss ible Number Rainfall Maximum That Plume Seeded Maximum Under Increased Date Clouds on Map (in.) PI ume (in.) Comments Ra i nf a 1 1 ? May 15 1 2.00 ? Plume moved over the No the Gulf of Mexico May 16 3 2.00 2.00 Maximum rainfall trav- Yes versed by plume May 19 1 8.00 4.00 Maximum rainfall Yes 10 n mi south of pi ume . Squal 1 1 i ne crossed region May 20 1 2.00 2.00 Rain fell 2-3 hrs No before passage of the plume May 21 1 1.00 1.00 Plume traversed Yes area of heaviest rainfal 1 May 26 1 3.00 ? Much of plume No over water May 27 1 2.00 2.00 Rain fell 6 hrs No prior to passage of plume May 28 1 2.00 1.50 Maximum rainfall Yes south of plume May 30 3 3.00 2.50 Distorted and No elongated pi umes . Chaot i c ra i nf al 1 pattern silver iodide. In five of the nine cases the heavy rainfall over the pen- insula could not be explained by the passage of the seeded plume because either the plumes remained mainly over water or the rainfall occurred be- fore the passage of the plume. 14 The results of this phase of the study are hardly conclusive; there is no evidence that the seeded plume either increased or decreased the precipitation over areas not traversed by the originally seeded clouds. 3.5 D i scuss ion For the silver iodide plume to alter the precipitation processes of clouds in its path, some of it would have to be entrained through the sides of these clouds. Further, to produce precipitation increases these clouds would also have to be deficient in natural ice nuclei. Cloud seeding studies in Arizona (Battan, 1 966) cast doubt on the efficacy of entrainment as an efficient mechanism for drawing silver iodide into the sides of a cloud, while study in Florida (Woodley, 19&9) has indicated that from a micro- physical standpoint, the clouds here are not deficient in natural ice nuclei. In view of these findings it is not surprising that superposition of the seeded plume on rainfall analyses produced inconclusive results. The results of the first phase of this study imply that the seeding of a single cloud has no detectable effect on the mi crophys i cal processes of other clouds in its environment; the dynamics of the problem are yet to be examined. Changes in the wind field and patterns of insolation associ- ated with the vigorous seeded cloud may well affect precipitation develop- ment in its environment. The next phase of this study is concerned with this problem. k. DYNAMIC EFFECTS OF SINGLE CLOUD SEEDING ON AREAL PRECIPITATION A second approach is adopted in the investigation of the large scale precipitation effects of silver iodide pyrotechnic seeding of individual cumulus clouds. Radar rainfall at selected time intervals is calculated 15 over a circular grid, 120 n mi diameter, which is orientated along the k, 000 to 20,000 ft shear vector and centered on the core of each experi- mental cloud. Comparisons are made between seeded and non-seeded grid rainfall and, with the shear vector as a reference, the grid rainfall is examined for preferred regions of development. 4.1 Too 1 s The modified UM/10-cm radar of the Radar Meteorological Laboratory at the University of Miami was the main tool in this phase of the research. This radar has a 2 conical beam, a transmitter power of 5-5 x 1 O-'W , a -14 minimum detectable signal of 10 W, a pulse length of 2/is , and a pulse repetition rate of 300 pulses per second. Important features of this system include special logarithmic and linear receivers, an RF range attenuation corrector (Hiser and Andrews, 1 966) and an i so-echo-contour (IEC) unit developed by Senn and Andrews ( 1 968) . This 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 the report by Senn and Courtright (1969). All radar echoes within range during the period of study were con- toured using the IEC unit. The reflectivity (Z) values and equivalent rainfall rates (R) for the various contours are shown in table 2. The Z values in this table were obtained using the calibration systems of Andrews and Senn (1968). The R values were then computed from the Miami Z-R relation, Z=300R , which has been shown by Woodley and Herndon ( 1 969) to accurately represent South Florida showery precipitation when it is used with the modified UM/10-cm radar and a linear interpolation scheme. 16 Table 2. UM/10-cm Signal Levels (Pr) , Z Values and Equivalent Precipitation Rates (R) May 1968 Florida Program DATE • CONTOUR Pr (dbm) _ 6-3 zmm m R(IN/HR) CONTOUR R, (dbm) Zmm6m3 R(IN/HR MAY 15-20 -109 5 .002 2 -86 I.IXIO3 .09 21 -109 5 .002 2 -86 I.IXIO1 .09 23 -109 5 .002 2 -86 I.IXIO3 .09 25 -109 5 .002 2 -85 I.5XI03 .10 26 -109 5 . 002 2 -85 L5XI03 ( .10 27 -106 II . 003 2 -86 I.IXIO3 1 .09 28 -102 24 . 006 2 -86 I.IXIO3 . 09 30 -100 40 .009 2 -86 i.ixio- 1 .09 REQUESTED VALUES - - - 2 -85 1.1 XIO3 .10 DATE CONTOUR Pr (dbm) _ 6-3 Zmm m RON/HR) CONTOUR Pr(dbm) 6-3, Zmm m 1 *(IN/HR) MAY 15-20 3 -76 I.I X 10* .45 4 -64 I.9XI05 3.5 21 3 -77 .9XI04 .40 4 -64 1.9 XIO5 3.5 23 3 -76 I.IXIO4 .45 4 - 64 I9XI05 3.5 25 3 - 74 I.8XI04 . 60 4 - 64 I.9XI05 3.5 26 3 - 72 3X I04 . 80 4 - 63 2.IXI05 4.0 27 3 -74 I.8XI04 . 60 4 - 63 i MXIO5 4.0 28 3 - 77 .9XI04 .40 4 - 63 i MXIO5 4.0 30 3 -75 I.4XI04 . 55 4 - 63 i MXIO5 4.0 REQUESTED VALUES 3 -73 2 X I04 . 75 4 - 67 .9XI05 2.30 4.2 Method The experimental cloud echo and all surrounding echoes were traced onto a circular grid at 20-min intervals for as long as possible after the seeding pass . At all times the grid was centered on the central core of the experimental cloud and orientated along the 4,000 to 20,000 ft shear 1 This refers to the first pass of the seeder aircraft through the experi- mental cloud. There was no seeding during its pass through the control cloud 17 vector, as shown in figure 5- The shear vectors for the days with experi- mental clouds are tabulated in table 3. The grid is composed of twelve annular sections each with a width of 20 n mi ; the downshear sections are numbered 1-6 and the upshear sections are numbered 7-12. The method of obtaining radar rainfall is analogous to that used by Woodley (19&9) for a similar problem. All of the echoes in a section were integrated with a planimeter to provide the total area (in n mi ) contain- ed between the contours - each contour corresponding to a discrete rainfall rate. The areas contained between the contours were then multiplied by the SHEAR VECTOR (4,000-20,000 ft.) Figure 5. Analysis of grid superimposed on contoured cloud echoes. Each contour of an echo corresponds to a discrete rainfall rate. 18 appropriate mean rainfall rate and a constant to convert the result to acre-feet of water. Each echo was assumed to remain unchanged for 10 min so the final rainfall values represent 10-min contributions. Total water values were not used in this study; rather the change in water ( ^W) relative to that at seeding was computed. The change of water in a section was defined as the total water in the section in a 10- min period after seeding minus the total water in the section in the 10- min period immediately before the seeding pass. The use of water change was desirable to eliminate the "head start" enjoyed by a section with strong echo development at seeding time. The original intention was to include cloud conditions up to a 60- n mi radius from the experimental cloud for 2 hours after the seeding pass, but this was impossible. A sample large enough for statistical testing was obtained only for the annulus 20 n mi from the core of the experimental Table 3. Vertical Shears (Degrees S- Knots) on the Experimental Days During May 1 968 Al t i tude (ft x 103) 4-8 8-12 12-16 16-20 4-20 Date SHEARS May 15 070/08 325/05 230/04 0 010/05 May 16 345/08 085/05 325/03 255/05 330/10 May 19 130/04 265/13 305/04 070/02 270/11 May 20 245/03 230/03 280/12 020/05 255/21 May 21 0 0 250/05 255/18 255/23 May 26 230/04 325/03 320/03 070/01 290/06 May 27 325/02 310/04 300/04 320/04 315/14 May 28 315/03 0 0 335/07 330/10 May 30 155/11 295/08 005/08 245/03 270/05 19 cloud for a period of 1 hour. The sample could not be extended to the desired limits for the following reasons: early shutdown of the radar, ground clutter and anomolous propagation, the limited range of the scope used for analysis (100 n mi), and the overlap in time and space of the seeded and control clouds. 4.3 Results The water calculations for the 12 sections of the grid with means for sections 1, h, 7, and 10 are found in table 4. The calculations are segregated depending on whether the cloud at the center of the grid was seeded or unseeded. The first block of values are the total water values in the 10 min before the seeding pass. The values in all subsequent blocks represent the change in section rainfall in the specified 10-min interval over the section rainfall in the 10 min immediately before the seeding pass The radar control clouds are control clouds selected after the seeding pro- gram from airborne, 16-mm time-lapse photography (see Woodley, 1969). There are severe gaps in the data. Even the averages presented for section 1, k, 7, and 10 can be misleading because of the great range of values and the small sample size. There are certain points of interest, however. In the 40-n mi diameter circle surrounding the experimental clouds, there were no important differences between the water values for the seeded and control clouds, with the exception of downshear section 1. In this section the seeded rainfall averaged 2 to k times that of the controls. This may be a real effect due to either new cloud development downshear to the left of the seeded cloud or to the seeded cloud itself streaming off downshear. It is not known why downshear section k (to the 20 right of the shear vector) did not show a corresponding increase in rain- fall. Section k is a section of minimum rainfall in most time intervals regardless of whether the cloud at the center of the grid is seeded or non-seeded . The seeded grid rainfall for sections I, h, 1, and 10 was tested for significant differences against the non-seeded grid rainfall in the corresponding sections using the W i 1 coxon-Mann-Wh i tney test (Guttman and Wilks, 1965), a test which is non-parametric and two-sided. No significant differences were found in the ^W values between the seeded and unseeded sections at any time, not even at the 20 percent level. This is not sur- prising in view of the small rainfall differences and small sample size. The seeded rainfall in sections 1 and k were pooled and tested for dif- ferences against the pooled non-seeded rainfall in the corresponding sec- tions (pooling has the effect of doubling the size of the seeded and non- seeded samples). Again, no significant differences were found at the 20-percent level . Several other comparisons were made between seeded and non-seeded section rainfall. Seeded section rainfall differences along the shear vec- tor (^WS| -/Iw^jQ and ^Wc^ - A^r-i) ; perpendicular to the shear vector ( ^W . - ZIw^k) ; and diagonally across the shear vector ( 4w<-^ - ^W_7 and ^W^i -^Wc-iq) were tested for significant differences against the corre- sponding non-seeded section rainfall differences (first subscript refers to seeding action and the second to the section number). Again, no signifi- cant differences were found at the 20-percent level. 21 fa U < o fO M- C fD K -o ^_ .O o t o I ♦ I «3 ax ■> « « o 9 co 0> I O III || I O ' O - i ** I I I I I »> I • K * io i o | a ' 7 i O K CO *- », CM O CO Cff N — t' N * « t m ro i i O t g O o — UJ I CO £1 CM O I | I O g | 2" **• co col » — • m « * o n XI ♦ = I I I = o o , 6 oi « — ^1 10 — o o ■J o> i i i i i i i ! 00 J I o o ~ I m co ♦ m o o ' r- 2 " 8 ij m i o | 10 I i I I I I CM o | | I O - TT"S"«r O O N — "2 n * a o • O » i- ■ o ♦ IIOI I I o I * o o K • K o> O 1^ — *» en CO * * CM -.♦•••Tt""*1" •> :~-+N*>','~-- 0) I O O I III IIOI O O O O | | | — CM o • B KO iM^ n O CO CM M- -«-*-£; '^COOCOiO * fu i Z. « * • i I n CM O I I I Si i °° i i a , N f • so ad o 7 5 » £ 2 * ^ • i i i i i i i i ° i i i i I I II I »- ° u> m co 7 » o - o O f- A 1 1 I o i I t* i S i i N 1 IO 1 1 O | . ° o 1 lO I - o o CM — CO Ch O * 10 0-*»2-»0,° «> CM N «> ♦ •» £ - cm |OO0| I I I ||0| 0 0 0 0,0, , O " O COOcococo* — K ♦"" w - * o "> O ™ N * CM CM ° I - I I I I ° ° I !f i o i o o i i ooo-pnnct cm « ml to I I I I I I I O | | | | n 61 «; co o o 0 Si „ • 2 S « I I I I I J0 «""» * co ^ o» M ♦ • — OI CC» — CO Of f* 0 ,o IO X*«i4 n « CM - • CO CMn»CM» ♦ O h. — — boio-on;non«_ w c sanono aaaaas NO a3H3lN3D aid? 22 o ! o i o t o IP < o t o 1 1 o n f o < z o t- o UJ CO z o 1- o UJ CO ~ 1 o i i i 9) i i • I' • 3 00 si «» " <• «. OJ tO oj « | 1 i « - • I 1200 2 6496 10919 809 7 21094 -39.4 717 3 3140 nil II II II 9 9 9 9 A 1 en •4 m CM <0 p OJ at at m n 01 o z < w 1- UJ UJ u. UJ or o < z or UJ 1- < * H * UJ _i CO CO CO o 0. z o o 3 1- 3 < -J 3 o | 10 O * | - N * ■ fOflboio<0— =— 5 O i - n n i ,«-/▼- II 1 III 1 1 • N O 1 I | I t 1 O 1 CO 1 5 3 1 O II 1 1 *> ■«■ CD O O | | , | • JJO 1*- 1 ~ ~ - 2 " 1 O O ^ OJ oj 10 b CM . (DN(DI)tlit«0O CD fM m « - ij^rt- cfl | O 1 OJ II 1 1 ~ 1 1 1 1 1 1 1 1 1 ° 1 II in | CO » — iiS 'i CVJ ° i S i i i ° ° i i CM o oj en co i go cnj rt K) Two ' T II 1 III CO oi . CitONIOiOCOtfliDt ^" * r 6 jf i* "* " • «• a» * ' i k> rt o ro I 1 1 CD 1 1 1 1 1 1 1 1 1 C\J o in ii i °i i to CM cm en Of • Ri BV _ ffl O) t O I I I i * ° JS w ?! 9 CO « *. * •> p! t*l O ♦ 1"* u> 1 9* * (vj - m CM 1 - CNJ FO CM | 1 v^csintD-rNK — ; -j* = CD«0*»O 1 C0CNJ *» g v>«« » m 2 * 7 10 i oj " §£ 2"g U s- • -s- m m C0 — «> CM = CM *> K • 2 uj - iC O VD N CO O — CM CM N N K) i E ¥ waO-cok«ooo - -NNN NN« lOfl < $ a sonono NO Q3H3 "I0H1N00 1N30 QIW9 SanOHD 03033S NO Q3M31N33 QIH9 23 Considering the results of this portion of the study, there is reasonable statistical justification for stating that the seeded clouds did not have a significant effect on the rainfall in a 40-n mi diameter circle centered on them up to 1 hour after the seeding pass. Because of the problems mentioned earlier, no statement can be made about the rain- fall at ranges exceeding 20 n mi from the experimental clouds. 5. SUMMARY AND CONCLUSIONS Although seeding had a profound effect on the growth and precipi- tation of the seeded clouds, it apparently did not significantly affect cloud developments in their environments. Neither plume nor grid rainfall comparisons detected significant differences between precipitation develop- ments in the vicinity of the seeded and control clouds. Although both approaches suggested that the large scale effects of single cloud seeding were precipitation increases, these increases were small and not significant at the 20-percent level. The analysis schemes used in this study are potentially very power- ful techniques for detecting large scale precipitation changes near experi- mental clouds. There are several requirements if these techniques are to be of any use in future analyses: (1) A larger cloud sample with a more complete time and space history is mandatory. (2) Twenty-four hour operation of the UM/10-cm radar with the systems described is an absolute necessity. (3) Overlap of the experimental clouds in time and space should be avoided by the scientists selecting them during future experiments. 2k (4) Finally, it is desirable to study clouds during a period with less developed natural convective activity. The heavy natural rainfall during May 1968 was an annoying source of noise throughout all phases of this anal ys i s . 6. ACKNOWLEDGEMENTS We are especially indebted to Mr. Jose Fernandez Partagas for making the silver iodide plume and shear calculations that were used in this paper, We also appreciate the following contributions: the radar observations from the Radar Meteorological Laboratory of the Institute of Marine and Atmos- pheric Sciences at the University of Miami and the map of the South Florida rain gage network from Mr. Harold Gerrish of the same organization; the rain gage measurements provided by many agencies in South Florida; and the advice and assistance afforded us by the staff of the Experimental Meteorol- ogy Laboratory. 7. 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. 6, 317-322. Fletcher, N. H. (1962), The Physics of Rainclouds (Cambridge University Press, Cambridge, England), 386 pp. Flueck, J. A. (1968), A statistical analysis of Project Whitetop's precipitation data, Proc. First Natl. Conf. Weather Modification, Albany, New York, 26-35- Guttman, J., and S. S. W i 1 ks (1965), Introductory Engineering Statistics (John Wiley and Sons, Inc., New York), 3^0 pp. 25 Hiser, H. W.,and G. F. Andrews (1966), A new approach to range normaliza- tion and stepped attenuation for weather radars, Proc. 12th Radar Meteorol . Conf., Norman, Oklahoma, 62-66. MacCready, P. B. (1959), The lightning mechanism and its relation to natural and artificial freezing nuclei, Recent Advances in Atmos- pheric Electricity (Pergamon Press, London, England), 369-381. McDonald, J. E. (1958), The physics of cloud modification, Advances in Geophysics 5, (Academic Press, Inc., New York, N.Y.). Mason, B. J. (1962), Clouds, Rain and Rainmaking (Cambridge University Press, Cambridge, England), 145 pp. Neyman, J., E. Scotland J. A. Smith (1969), Areal spread of the effect of cloud seeding at the Whitetop experiment, Science 163 , ]kk$-]Uk3 Senn, H. V., and G. F. Andrews ( 1 968) , A new, low-cost multi-level iso-echo contour for weather-radar use, J. Geophys . Res. _7_3, 1201-1207. Senn, H. V., and C. L. Courtright (1968), Radar hurricane research, Final Rept. by Institute of Marine Sciences, Univ. of Miami, Radar Meteorology Section to U.S. Weather Bureau, Contract No. E22-62- 68(N), 31 pp. Simpson, J., W. L. Woodley, H.A. Friedman, G. W. Slusher, R.S. Schef^ee, and R. L. Steele (1969), A pyrotechnic cloud seeding system and its use, ESSA Tech. Memo ERLTM-APCL 5. Woodley, W. L. (1969), Precipitation results from a pyrotechnic cumulus seeding experiment, ESSA Tech. Memo ERLTM-AOML 2. Woodley, W. L.yand A. Herndon (1969) A rain gage evaluation of the Miami Reflectivity-Rainfall Rate Relation. ESSA Tech. Memo ERLTM-AOML 3. 26 65 U.S. DEPARTMENT OF COMMERCE Environmental Science Services Administration Research Laboratories ESSA Technical Memorandum ERLTM-APCL 7 RADAR AND PHOTOGRAPHIC DOCUMENTATION OF CONVECTIVE DEVELOPMENTS ON MAY 16, 1968 William Lee Woodley Jose Fernandez Partagas Experimental Meteorology Branch Coral Gables, Florida Atmospheric Physics and Chemistry Laboratory Boulder, Colorado April 1969 TABLE OF CONTENTS Page ABSTRACT iv 1. INTRODUCTION 1 2. SYNOPTIC SITUATION 2 3. MORNING FORECAST 2 4. LARGE-SCALE CLOUD COVER 5 5. RADAR AND PHOTOGRAPHIC OBSERVATIONS 5 6. SUMMARY AND CONCLUSIONS 14 7. ACKNOWLEDGEMENTS 16 8. REFERENCES 17 in ABSTRACT The convective developments over South Florida on May 16, 1968^are documented to provide a basis for comparison for seeded cloud behavior on this day. Ground-based 10-cm radar observations, concurrent aerial time lapse photography, and an ESSA VI satellite picture are used in the docu- mentation. Large convective clouds developed in a band near a preexisting cloud line that stretched from the Gulf of Mexico to Miami. Four cumulo- nimbus clouds formed in this band; two were natural and the other two were apparently artificially induced. By late afternoon several other small cumulonimbus clouds were scattered over the southern portion of the peninsula. Seeding probably induced two of the cumulonimbi studied, which, once formed, behaved like their natural counterparts. The natural and artificially induced cumulonimbi were similar in appearance and had comparable lifetimes and radar echoes. Detailed study based on the cumulus model developed by ESSA's Experimental Meteorology Branch is needed to clarify the effect of seeding on May 16, 1968. IV RADAR AND PHOTOGRAPHIC DOCUMENTATION OF CONVECTIVE DEVELOPMENTS ON MAY 16, 1968 William Lee Woodley and Jose Fernandez Partagas 1. INTRODUCTION From May 15 to June 1, 1968, a joint cloud seeding project was con- ducted over the South Florida peninsula. Participating in the program were the Experimental Meteorology Branch (EMB) and the Research Flight Facility (RFF) of ESSA, the Naval Research Laboratory, U. S. Air Force, and the Radar Meteorological Laboratory of the University of Miami. Nineteen clouds were selected randomly by a sealed envelope procedure; 14 were seeded and five were used as controls. The analysis to date indicates that silver iodide seeding was effective in inducing increased growth and precipitation from the seeded clouds. Details of the analysis will appear in a sequel to this report . To correctly interpret seeded cloud behavior, it is important to study the behavior of unmodified convection close in space and time to the seeded clouds. Such a study was made for May 16, 1968, a day on which there were three seeded clouds, one that collapsed and two that showed explosive growth . The important convective developments over South Florida were studied on the basis of radar data and aerial time lapse photography. The radar data were obtained by the AN/CPS-6B 10-cm radar of the Radar Meteorological Laboratory of the University of Miami operating with the iso-echo system described by Senn and Andrews (1968) . The photographic data were obtained by the 35-mm side cameras installed on the Research Flight Facility (RFF) DC-6. 2. SYNOPTIC SITUATION The surface pressure pattern was very weak over the Gulf of Mexico, Florida and the western Bahamas at 1200Z on May 16, 1968 (fig. la). Just above the surface, the main feature of interest is a small high-pressure area west of Tampa producing a light north-northwest flow over the southern portion of the peninsula. The situation at 500 mb is just as indeterminate (fig. lb), with a weak pressure field and light winds. The center of highest pressure is displaced westward into the central Gulf of Mexico with a large col region over central Cuba. The Miami 1200Z sounding (fig. lc) shows moderately moist conditions up to 600 mb , with drying above this level. 3. MORNING FORECAST The EMB cumulus model developed by Simpson and Wiggert (1969) of ESSA's Experimental Meteorology Branch was used for the first time in real time as a tool in forecasting seeding conditions. Based on the 1200Z Miami sounding and a spectrum of cloud radii as input, the model was used to pre- dict the maximum top growth for seeded and unseeded clouds. The major unknown is the characteristic tower diameter that atmospheric conditions will produce on any given day. The May 16 predictions could be expected to be valid if cumulus clouds with tower radii comparable to those assumed developed during the day. 35 SURFACE MAP 1200 Z 16 MAY, 1968 |0|2 -^ — r 1012 Figure la. Surface map for Florida and surround- ing region, 1200Z, May 16, 1968. Figure lb 500-mb map for Florida and surround ing region, 1200Z, May 16, 1968. MIAMI RADIOSONDE 1200 2 MAY 16 ,1968 TEMPERATURE POINT -70* -60 -40' -SO' -20* -10* TEMPERATURE CO Figure lc. Miami radiosonde, 1200Z, May 16, 1968 -175 O X 40,000 ft) without seeding. Seeding was predicted to induce very little additional growth in such clouds . The model predictions indicated that there would be cumulus clouds that would be responsive to seeding and also some that would grow to cumulonimbus naturally. 4. LARGE-SCALE CLOUD COVER The convective conditions during late morning over and near the Florida peninsula are shown on the 1521Z ESSA VI satellite picture, on which a 1200Z-ft streamline analysis has been superimposed (fig. 2). There is little convection anywhere except for a cloud line that extends from the Gulf of Mexico across the southwest Florida coast. This line of clouds is still evident on the aerial time lapse photographs during the afternoon. Note that it lies close to the line of confluence in the streamline analysis, which was made independently of the satellite picture and then superimposed. The analysis to follow shows that this line consists of small cumulus with the portion extending across the peninsula marking a preferred region of cloud development. 5. RADAR AND PHOTOGRAPHIC OBSERVATIONS The radar and visual appearances of the subject clouds are compared in the analysis that follows. All clouds are lettered alphabetically ESSA 3ZT SATELITE PICTURE WITH 2000 FOOT STREAMLINE ANALYSIS SATELLITE PICTURE: 1 52 1 z STREAMLINE ANALYSIS: 1200 2 •rmw m>**i>m Figure 2. ESSA VI satellite picture at 1521Z with 1200Z 2,000-ft streamline analysis superimposed; May 16, 1968. (except the unnamed cloud) by order of appearance on the radar. The radar antenna is at 0.5° elevation angle in all the radar pictures. This means that the radar is depicting increasingly higher portions of the clouds as range increases. The echoes were contoured, but the contouring is not shown here because of difficulty in presenting it in the small diagrams. Only the outer boundary and cores are delineated. The position of the DC-6 aircraft, its heading, and the camera direction when the picture was taken are also shown on the radar plot . The camera data chamber has been included for easy reference . Cumulus cloud development began over South Florida by midmorning, with the preferred region of convective activity lying in a band extending 10 mi on both sides of the cloud line southwest of the col point shown in fig. 2. Cloud bases were generally at 2,000 ft. The positions of the major cloud developments, including times of appearance and disappearance of their echoes from the 10-cm radar scope, appear in figure 3. The initial clouds of interest are experimental cloud 5 and the Homestead cloud, having first echo times of 1647 and 1727Z respectively (fig. 4a). Cloud 5 attained its peak reflectivity at 1750Z and then decayed, although it was seeded at 1800Z. Seeding did not appear to interrupt the decay. The Homestead cloud, which was not seeded, attained cumulonimbus stature (characteristic anvil appearance) at about 1800Z, 33 min after its initial appearance on radar. Note the linear organization of the three echoes and the interesting line of small cumulus that extends well out into the Gulf of Mexico (picture from left-side camera) . This is the same line of cumulus that appears in the satellite picture discussed earlier. This NITIAL TIME AND POSITION OF IMPORTANT CONVECTIVE DEVELOPMENTS MAY 16, 1968 • POSITION OF INITIAL APPEARANCE OF CLOUD ON 10cm RADAR DESCRIPTION CLOUD 5 HOMESTEAD CLOUD UNNAMED CLOUD CLOUD 6 MIAMI CLOUD NAPLES CLOU D CLOUD 8 DESIGNATION TIME OF FIRST APPEARANCE ON 10 cm. RADAR (GMT) 1647 1727 1733 1804 GROUND CLUTTER 1843 1948 TIME OF DISAPPEARANCE FROM 10cm RADAR (GMT) 1837 >2I00 1806 ^ 2100 GROUND CLUTTER > 2100 >2I00 Figure 3. Inital time and position of important convective developments as indicated by 10-cm radar. Figure 4a. Radar and photographic documentation of convective developments, 1756Z, 1830 Z/ X^ Figure 4b. Radar and photographic documentation of convective developments, 1830Z, 9 cloud line crosses the coast line, passes under the aircraft and then up into cloud region C, just north of cloud 5 (right-side camera) . The cloud tower marked B is the Homestead cloud that attains cumulonimbus form 6 min later; it too lies in this convective zone. Cloud 6, seeded at 1824Z, will come from region C. The mechanism that accounts for the convective line stretching from the Gulf of Mexico across the Florida peninsula is not fully understood, although the streamline analysis suggests that weak convergence is the primary factor. The portion of the line over the water consists of very small cumulus, but the portion over land has large cumulus that were un- doubtedly influenced by solar heating of the ground. The situation at 1830Z is shown in figure 4b. All echoes have drifted slowly west-southwest. The northern portion of experimental cloud 6 (marked C) , seeded 6 min earlier, is shown on the picture of the right-side camera, while the Homestead (B) and Miami (D) clouds appear on the left. It is difficult to get an accurate position and tracing for the echo of the Miami cloud because it is well within the Miami ground clutter. At 1900Z there are new echo developments 15 mi southeast of Lake Okeechobee, 10 mi east of Naples (the Naples cloud marked E) and a new echo just northwest of the Homestead cloud (fig. 5a). The picture of the right- side camera shows the cloud line crossing the coast and extending into cloud 6 (C) , which has grown tremendously. The situation is little changed at 1930Z, as shown by figure 5b. Here the nose camera of the DC-6 shows the Naples cloud at approximately the time it was rejected as an experimental cloud because it had grown too 10 RADAR AND PHOTOGRAPHIC DOCUMENTATION OF CONVECTIVE DEVELOPMENTS MAY 16, 1968 -^key" west •-;-.' Bie«0 TIMd I feu |ft \/£.WOO \ c fa— 20 2/ * r ^hp pP"" VU* »y!> --"*---- ■'■ UEM S/M I036ISI * '", *» 1 D L. 7 0 * toAl ELAPSED Illf (SECOlks: RIGHT VIEW Figure 5a. Radar and photographic documentation of convective developments, 1930Z. o ^-^KEY WEST Figure 5b. Radar and photographic documentation of convective developments, 1900Z 11 large. This picture is the only one in the series taken with this camera. The protrusions on the boom are the probes for the hot wire liquid water ins t rumen tat ion . There are several developments over the southern portion of the Florida peninsula at 2000Z (fig. 6a). The echo of cloud 8 (marked F) now appears on the scope, 6 min after seeding. The pictures of the side cameras show the cloud developments of interest very well. The growing tower of cloud 8 (F) can be seen with cloud 6 (C) , the Homestead (B) and the Miami clouds (D) arrayed behind it. The picture 7 min later, again from the left side, shows the Naples cloud (E) , now a cumulonimbus, 57 min after initial appearance on radar, and the growing tower of seeded cloud 8 (F) . There are also two other small cumulonimbus developments between Miami and Lake Okeechobee . Cloud 8 has grown significantly between 2000Z and 2030Z (fig. 6b) attaining cumulonimbus form 22 min after initial appearance on radar . At 2030Z this cloud has two cores marked on the radar display and on the side- camera photo. lower F„ is growing very rapidly as the picture is taken. Cloud 8 and the Homestead clouds merge shortly afterwards. Cloud 6 and the Miami cloud have diminished significantly. The picture from the left side at about 2040Z shows decaying cloud 6, the anvil overhang from cloud 8 (top of picture) and the persistent cumulus line in the Gulf that crosses the coast and feeds into the northern portion of Cloud 6. Top-height information is available for several of the clouds examined here. Cumulonimbus tops were generally around 40,000 ft, with clouds 6 and 8 having aircraft-measured, maximum tops of 40,500 and 45,000 12 RADAR AND PHOTOGRAPHIC DOCUMENTATION OF CONVECTIVE DEVELOPMENTS MAY 16, 1968 KEY WEST L E F T V I E W L E F T V I E W 'igure 6a. Radar and photographic documentation of convective developments, 2030Z. 2030 Z PALM BEAO /&80NM (Q or ^-^KEY WEST R I G H T V I E W E W Figure 6b. Radar and photographic documentation of convective developments, 2000Z. 13 ft respectively, which is at or slightly above tfhe tropopause height of 39,000-40,000 ft (196 mb) . The Homestead cloud had a maximum radar top of at least 47,000 ft, while experimental cloud 5 had a maximum top of approxi- mately 20,000 ft. The pictures from the side cameras indicate that the shear was from the north, with new convective towers growing upshear. This is not unexpected and is qualitatively consistent with the shear diagram (fig. 7), which was estimated for the locations of clouds 5, 6, and 8 from the three-dimensional streamline analyses for 1200Z May 16 and 0000Z May 17. Since flights ended after 2045Z, there are no photographs of develop- ments after this time. However, examination of the radar film indicates that the basic pattern persisted into the early evening, with the Homestead- cloud 8 amalgamation and the Naples cloud disappearing from the scope between 2200 and 2300Z. 6. SUMMARY AND CONCLUSIONS Cumulus cloud development occurred over all of the southern portion of the Florida peninsula on May 16, 1968, with the region of preferred development near a preexisting cloud line extending from the Gulf of Mexico across the peninsula to Miami. In the region 10 mi to either side of this line at a range exceeding 20 mi from Miami, there were six distinct separate echoes, three of which were those of clouds that eventually reached cumulo- nimbus proportions. One of the cumulonimbus was natural; the other two were apparently the result of seeding. There were also radar echoes one of which was that of a cumulonimbus within 20 mi of Miami, but little can be said of them because of ground clutter. Several smaller cumulonimbus developments 14 WIND HODOGRAPH IN VICINITY OF CLOUDS 6 AND 8 — MAY 16, 1968 4-20 WIND VECTOR SHEAR VECTOR ESTIMATED WINDS (I800Z) HEIGHT WIND WIND SHEAR (FT) OIR SPEED (KTS) HT(FTXI05) DIR. SPEED (KTS) 4.000 320 02 4-8 345 8 8,000 340 10 8-12 085 5 12,000 010 10 12- 16 325 3 16,000 360 12 16-20 255 6 20,000 330 12 20-25 015 4 25,000 340 15 25-30 015 6 30,000 350 20 30-35 085 4 35,000 360 20 4-20 330 10 20-35 030 1 1 4-35 005 18 25-30 20-35 30-35 Figure 7. Shear diagram estimated for the times and locations of clouds 6 and 8. 15 also appeared by late afternoon between Miami and the vicinity of Lake Okeechobee . The visual and radar appearance of the seeded clouds did not differ noticeably from that of unseeded clouds of comparable size. Cloud lifetimes were also comparable. However, the average time from first appearance on radar to cumulonimbus form was less for the seeded clouds. This suggests that seeding is either inducing cumulonimbus stature that could not have developed naturally or inducing it prematurely. The possibility also exists that the dissipation of cloud 5 was hastened by seeding and the disruptive effects of the monitoring aircraft. Detailed study of individual clouds, including predictions of the EMB cumulus model, is necessary before a definite statement can be made about the effects of seeding on this day. The occurrence of natural cumulonimbus during the seeding program emphasizes the importance of randomization in determining the seeding de- cision to avoid criticism that cloud developments attributed to seeding would have occurred naturally. Randomization does not eliminate this possibility, but it makes it much less likely. 7 . ACKNOWLEDGEMENTS The authors are especially indebted to the Research Flight Facility for the excellent photographic data and the superb way in which it carried out all phases of the seeding operation. The Radar Meteorological Laboratory of the University of Miami also receives our special thanks for the excellent quality of the radar data. Thanks are also due the members of EMB, particu- larly Dr. Joanne Simpson and Mr. Ronald Holle for helpful discussions, Messrs. Jorge Posada and Robert Powell for the drafting of the figures, and Mrs. Peggy M. Lewis who capably typed the manuscript. 8. REFERENCES Senn, H. V., and G. F. Andrews (1968), A new low cost multi-level iso-echo- contour for weather-radar use, J. Geophys. Res. TJ>_, 1201-1207. Simpson, J., and V. Wiggert (1969), Models of precipitating cumulus towers, Monthly Weather Rev. 9_7 (to be published). 16 66 IT) ITI O O H Z OS Qu W OS W CO ft < w w ai o pq Pi l-H < o h H W < o o Eh O K Oh P D O u ex c O fa a .2 a ■ 2 ^ a* u » <•> ■S 3 .5 « M g-s-s n 3 o „ '5 c o 'E 5 a * «> o ft >. » Z JC o H o w • J3 £ c "i O z ui a: Z o- O - O 1A -1 N < d ° i ** S s »u 3 ? tt © 5= a. — < H 3 s s J 2 c — E 8-0 • a ! u • •£ c u .2 > 2 3 l-» «o « u ?! 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CD CC cc Q LlJ \ o >v O m 3 - \ 1— u- <0 \ o< - CO O \ i- \ cr (A \ uj (r _l \ £ * o \ w o \ 3 *" o u_ \/ - CD o CD LU *\ ^x ♦ .>! - CD -z. ./g - CO CNJ CD < k\ * X (jOixw) sniavu _ ^J !\J x< o _l o ^5 ^ 5: 5 °> * * 1 ill .1 1 . 1 . ll 1 h ill H i o N 5 Z> (toixid)iH9i3H doi anono 00 CD •X-,;.**'** *%>, .•;•;**><> V N 00 UJ oooo b^^"" n ,■ ooo z2 I ft L5%* UJ \*t UJ .00 Br ^» N r< * ^* CVJ< ii v< oo o: — UJ H CVJ< Ri ' o CD i o N 0> CVJ GO 67 Reprinted from Journal of Geophysical Research, Vol. 74, No. 10, 2590-2596. Field Occurrences of Induced Multiple Gravity Waves1 Robert J. Byrne ESSA Research Laboratories, Norfolk, Virginia 2S510 Field evidence is presented for the occurrence of additional waves arising from an interaction between incident shallow-water waves and submerged shoals. A given additional wave is induced by the passage of an incident wave crest over the crown and downwave flank of a bar. Induced waves were observed under conditions that commonly occur on beaches with wave- built bars. Such waves may significantly influence nearshore processes. Previous discussion or documentation of this interaction is unknown to the author. Introduction. This report presents field evi- dence of the occurrence of a particular mode of wave transformation arising, apparently, through the interaction of shallow-water waves and irregular bottom topography, such as submerged bars. This interaction is characterized by the formation of an additional wave that is induced by the passage of the incident wave crest over the crown and downwave flank of the bar. A number of reports have dealt with other conditions under which multiple wave crests have been observed and studied in the labora- tory. These occurrences are limited to conditions of small relative depth (d/L < 0.1) wherein multiple crests arise as incident waves: (1) abruptly enter shallow water from deep water [Mason and Keulegan, 1944; Horikawa and Wiegel, 1959; Wiegel and Arnold, 1957]; (2) shoal on a plane beach [Galvin, 1967] ; (3) travel over a horizontal bottom [Horikawa and Wiegel, 1959; Goda, 1962; Galvin, 1968]. It now appears that these occurrences fit the be- havior of some numerical solutions of the Korteweg and de Vries equation for finite- amplitude shallow-water waves [Zabusky and Kruskal, 1965; Zabusky and Galvin, 1968]. In these solutions and in the experiments, the initial wave decomposes into two or more waves of differing amplitude (called solitons) that initially appear on the upwave flank of the crest. The wave speeds are dependent on their 1 Contribution 14 of the Land and Sea Interac- tion Laboratory (LASIL) Atlantic Oceanographic Laboratories, ESSA, Norfolk, Virginia 23510. Copyright © 1969 by the American Geophysical Union. amplitudes. A particularly interesting facet of their nonlinear behavior is that, when the sepa- rate waves become 'superimposed,' the net crest elevation is less than the elevation when the waves are isolated. A case more closely related to the present discussion is that of waves observed in the lee of a submerged finite dock. Williams [1964], for example, examined the occurrence of waves incident to a thin rigid barrier, parallel to and below the plane of the free surface. The waves on both sides of the plate were 'deep-water' waves (d/L > 0.5) and the plate submergence was less than 20% of the total depth. Among other interesting results, it was demonstrated that the submerged barrier generates, in the downstream region, a system of linear harmonic waves, the fundamental of which is the same frequency as the incident waves. Furthermore, it was found that the amplitude of a given harmonic in the downstream region was propor- tional to the harmonic content of the same order in the incident wave just before leaving the dock section. It is, at present, uncertain whether the occur- rence discussed by Williams and that presented here arise from the same physical mechanism. The documentation of the 'multiple' wave phenomenon in the field has, apparently, been rare. Wiegel [1964] notes that multiple waves have been observed over reefs and in wave re- flections from beaches. Photographs of the proc- ess over reefs are shown by Johnson et al. [1951, Figure 1] and Munk and Traylor [1947, Plate 3]. In both these cases, however, waves are breaking at the reef face and the higher fre- 2590 TOPOGRAPHICALLY INDUCED GRAVITY WAVES 2591 quencies may be generated in the breaking process. It is this paucity of description that motivates the author to publish his observations at this time. It is hoped the description will lead to further field documentation as well as to theo- retical and experimental study. Field site. All observations discussed in this report were obtained on the Outer Beach of Cape Cod, in the immediate vicinity of Cape Cod Lighthouse. An aerial view of the region is shown in Figure 1. The photograph, taken on August 25, 1966, illustrates very clearly the sinuous offshore bar paralleling the beach at a distance between 450 and 600 meters. Also shown is the complex nearshore bar system that during the summer is a quasi-periodic sequence of curved bars. A bathymetric profile is shown in Figure 2. The offshore bar is a dominant feature that essentially maintains its position throughout the year. Seaward of the offshore bar, the bottom slope is approximately 1 : 100. Observations. The material presented below is a consequence of two sets of observations, one on September 2, 1966, and the other from early August 1967. Because the August 1967 set offers an explanation of the process, the pres- entation is given in reverse chronological order. In August 1967 the author observed waves passing over a curved bar in the nearshore bar complex. The topographic situation is shown schematically in Figure 3. The bar complex, at midtide, was submerged with a uniform swell of approximately 7-second period approaching parallel to the bar axis. The water depth was approximately 1 meter over the bar and was 1.7 meters deep in the trough. It was apparent from casual observations that there were more breakers at area 2 of the foreshore as compared to area 1 (Figure 3). Sighting along the axis of the bar, I counted the number of waves that Fig. 1. Aerial view of the study area. Photographed August 25, 1966. 2592 + 3 — ROBERT J. BYRNE INSTRUMENT INSTALLATION -9- -12- + 2 5m 1400 hours HIGH TIDE " )300 1200 -1100 -1000 -0900 -0800 hour! LOW TIDE - SEAWARD DISTANCE FROM BEACH x (m 160 320 480 640 800 Fig. 2. Bathymetric profile of study area. Sounding in July 1965. 960 v& mmm^^i^&^mK **** AREA 2 AREA 1 -> Fig. 3. Schematic (plan view) of nearshore bar. TOPOGRAPHICALLY INDUCED GRAVITY WAVES 2593 peaked up on approaching the bar while another observer counted the number of breakers at area 2. The same procedure was used with a second observer at area 1. It was found that the number of breakers at area 1 was the same as the number of waves peaking at the bar, but the number of area 2 was double this number. The wave heights at the crown of the bar were approximately 0.5 meter. During these observations, an essentially cross-sectional view of the deformation process could be obtained by sighting along the axis of the bar. The various stages are shown diagram- matically in Figure 4. The incident wave (1) peaks up as it approaches the crown of the bar (Figure 4a). After the crest passes over the bar, the water surface associated with the trough becomes nearly parallel to the nearshore flank of the bar (Figure 46), and for an instant the seaward flow, associated with the trough, ap- pears to cease. At this point, another wave crest (la) becomes dissociated from the crown and upper nearshore flank of the bar and propagates shoreward (Figure 4c). This separation occurred between 0.3 and 0.5 of a wave period after the incident crest (1) passed the bar. Similar conditions existed during the observa- tions of September 2, 1966. Then, however, the interaction was between the offshore bar (Fig- ure 2) and the large long-period swell from Hurricane Faith. On that day, a time-lapse motion picture camera and a nearshore wave monitor were operative. The time-lapse camera (16 mm at 26.5 frames per minute) was situated on a bluff behind the beach at an elevation of 40 meters. At the nearshore instrument installa- tion (position shown in Figure 2) the following parameters were measured: surface time history, tide level, and the horizontal component of fluid velocity 0.64 meter above the bottom. In- cluded in Figure 2 is the water depth during a partial tidal cycle for September 2, 1966. In viewing the time-lapse film it was apparent that the bar was acting as a source area of 0) Fig. 4. Schematic representation of induced wave generation over a submerged bar. Figures not to scale. 2594 ROBERT J. BYRNE additional waves. This effect was particularly striking when the film Was viewed in reverse motion as the complex inshore waves could be seen to be screened by the bar. The time-lapse film was run from 0800 hours (low tide) to 1630 hours, encompassing the arrival and passage of high tide. Inspection of the film indicated the waves incident on the bar maintained a rather constant period (T = 15 seconds), but, as high tide approached, the number of additional waves, shoreward of the bar, decreased. Under these conditions, only the largest incident waves generated addi- tional waves. To examine the occurrence in greater detail, sixty-six consecutive frames (149 seconds real time) were enlarged and the number of waves passing at the bar and the number of corre- sponding waves at the nearshore installation were counted. Eleven waves were observed at the bar, whereas twenty-one waves were in evi- dence at the tower. An example from the film enlargement is shown in Figure 5. Inspection of the sixty-six enlarged photographs show that by the time an incident crest is one wavelength shoreward of the bar, a smaller crest is apparent in its following trough. A segment of the surface wave record, corre- sponding within minutes to the 2-minute film sampling, is shown in Figure 6. At this time, the water depth at the offshore bar was 5 meters and the mean water level at the sensor was 2 meters. Comparison of the relative direction of pen deflection between the wave sensor (upper trace, Figure 6) and the current meter (lower trace, Figure 6) indicates that a considerable amount of wave energy is reflected from the beach. At the time these recordings were made, LOCATION OF OFFSHORE BAR ^f^f*mimj^*^^<< WAVE MON4T0R TOWER 100 _1 SCALE (It ! Fig. 5. Photo of incident and induced waves, September 2, 1966. Enlarged from 16-mm color motion picture film. TOPOGRAPHICALLY INDUCED GRAVITY WAVES m 2595 MEAN WATER LEVEL TROUGH, -5ft- (1.5m) FLOW TOWARD SHORE, 4-7ft/MC- -JL.l 12.1). It was previously mentioned that at the higher tidal levels (September 2, 1966) only the largest waves of the groups produced a pro- nounced induced wave. If the wave periods within the incident wave group are assumed constant, then, to a first approximation, the d/L ratio is likewise constant. This implies that the ratio H/d exerts a strong influence in the formation of the induced waves. From the same estimated values of wave height for low and high tide, the respective H/d ratios are 0.4 to 0.5 and 0.26 to 0.32. Certainly the observations discussed here are not extensive enough to define the physical mechanism responsible for the induced waves. However, a possible explanation is suggested. After the incident crest passes over the crown of the bar, it accelerates in passing over the steep flank of the bar. As observed, the water surface following the crest becomes nearly parallel to the bar flank. The seaward flow associated with the trough, is thus directed parallel to the upward sloping flank of the bar. This flow is brought to rest by the gravitational component parallel to the bed and the water 2596 ROBERT J. BYRNE mass, no longer dynamically supported, then surges forward as the leading face of the new crest. If this is the mechanism, the generation process is, in a sense, impulsive. It should also be recalled, however, that the soliton interaction noted by Galvin [1968] occurred when the depth-to-wavelength ratio d/L was less than 0.1. Since the ratios for the cases discussed here are smaller than this limit, it is possible that the interaction of the incident wave with the bar simply amplifies a weak soliton interaction. The induced wave occurrences discussed in this report were observed under conditions that commonly occur on beaches with wave-built bars. Shepard [1950], for example, gives data on wave-built bars for the east and west coast beaches of the United States, the bulk of the information having been acquired from daily measurements of the nearshore profile and waves at Scripps Pier, La Jolla, California. He found an average value of 0.66 for the ratio of bar depth to trough depth. Furthermore, the range of associated wave heights, relative to the bar depth, encompasses the values for the cases re- ported here. This suggests that the interaction may occur quite frequently. Further study, ex- perimental and theoretical, is needed to define the range of conditions under which an induced wave is to be expected. The interaction may exert a significant influence on nearshore pro- cesses as the induced waves redistribute, in time, the energy input to the coastline. Acknowledgments. The field observations were made while I was affiliated with the Woods Hole Oceanographic Institution. I am indebted to the entire Coastal Studies Group, then under the di- rection of Dr. John M. Zrigler. Special thanks are due Herman Tasha and William Athearn for their assistance. I thank Drs. G. S. Giese and L. F. McGoldrick for critically reading the manuscript. References Galvin, C. J., Classification of breaking waves on three laboratory beaches, unpublished paper available from U.S. Army Coastal Engineering Research Center, 24 pp., Aug. 1967. Galvin, C. J., Shapes of unbroken periodic gravity waves (abstract) Trans. Am. Geophys. Union, 49(1), 206, 1968. Goda, Yoshimi, A travelling secondary wave crest in a wave channel, Memorandum for seminar at Hydrodynamics Laboratory of Massachusetts Institute of Technology, Cambridge, Mass., 1962. Horikawa, Kiyoshi, and R. L. Wiegel, Secondary wave crest formation, Univ. Calif. Wave Res. Lab., Ser. 89, Issue 4, 23 pp., 1959. Johnson, J. W., R. A. Fuchs, and J. R. Morison, The damping action of submerged breakwaters, Trans. Am. Geophys. Union, 32(5), 704-718, 1951. Le Mehaute, B. J., G. F. Snow, and L. M. Webb, Gravity waves on bottom slopes, Natl. Eng. Sci. Co. Rept. S245-A, Pasadena, Calif., 1966. Mason, M. A., and C. H. Keulegan, A wave method for determining depths over bottom discontinuities, U.S. Army Beach Erosion Board Tech. Memo. 5, 29 pp., 1944. Munk, W. H., and M. A. Traylor, Refraction of ocean waves: A process linking underwater topography to beach erosion, J. Geol., 4(1), 1-26, 1947. Shepard, F. P., Longshore bars and longshore troughs, UJS. Army Beach Erosion Board Tech. Memo. 15, 30 pp., 1950. Wiegel, R. L., and A. L. Arnold, Model study of wave refractions, U.S. Army Beach Erosion Board Tech. Memo. 108, Dec. 1957. Wiegel, R. L., Oceanographic Engineering, 532 pp., Prentice-Hall, Englewood Cliffs, N. J., 1964. Williams, J. A., A nonlinear problem in surface water waves, Univ. Calif. Inst. Eng. Res. Tech. Rept. HEL-1-5, 246 pp., Oct. 1964. Zabusky, N. J., and M. D. Kruskal, Interaction of 'solitons' in a collisionless plasma and the recurrence of initial states, Phys. Rev. Letters, 15(6), 240-243, 1965. Zabusky, N. J., and C. J. Galvin, Secondary waves as solitons (abstract), Trans. Am. Geophys. Union, 49(1), 209, 1968. (Received August 15, 1968.) 68 Reprinted from E9S, Transactions, American Geophysical Union, Vol. 50, No. 7, 472-477 Pelagic Tidal Measurements A suggested Procedure for Analysis David Cartwright, Walter Munk, and Bernard Zetler There has long existed a need for pelagic tide and current measurements, but the technology for making such observa- tions has been developed only recently. In 1965, an inter- national working group on deep-sea tides was formed (now sponsored by IAPSO, SCOR, and Unesco) that would concern itself with the exchange of information on instrumentation and analysis and with the formulation of a worldwide data acquisition program. Some pelagic tide observations have now been obtained by pressure sensors on the sea bottom connected by cable to the surface [Eyries, 1968] or to shore [Nowroozi et al, 1968] and by self-contained bottom instruments that record inter- nally and are recalled to the surface by an acoustic signal [Snodgrass, 1968] and time-release device [Filloux, 1968, and Hicks et al, 1965]. The equipment described by Snodgrass and by Nowroozi include current meters measuring speed and direction. The over-all objectives of the deep-sea tide program are described by Munk and Zetler [1967] and Cartwright [1969]. The working group has recommended records of at least a month's duration. It is quite clear that this requirement en- tails considerable effort, logistics, and expense (quite aside from many failures), and accordingly it is most important that the analysis of each set of good data be as comprehensive and meaningful as possible. The authors of this article have been concerned for some time with this very problem. They met in La Jolla, California, in March 1969 to design an analysis program for the pelagic observations. (We are indebted to SCOR for providing travel funds for Cartwright.) This paper describes the method that is recommended and the rationale for some of the steps. The method is suitable for the analysis of tidal disturbances in any 472 geophysical measurements in exposed areas where it is possible to take advantage of data from related, long-established reference stations. Transfer Functions The proposed program leans heavily on the 'response method' of tidal analysis; we refer to Munk and Cartwright [1966] for a discussion of this method. Here we sketch only the underlying principles. For any linear system, an input function x,-(f) and an output function x0(t) can be related according to1 xo([) ~ ioxi(t ~ T)w(r)dr + noise(r) where w(t) is the 'impulse response' of the system, and its Fourier transform Z(f) = %w(T)e-2"ifTdT = R[f)j*f) is the system's admittance (coherent output/input) at fre- quency / . In practice, the integrals are replaced by summa- tions; Xj, w, and Z are generally complex. The discrete set of w values are termed response weights. The basic motive under- lying the response method for analyzing and predicting tides is to evaluate the station transfer function (w or Z) between a suitable input series and the observed tide. The classical meth- od consists of evaluating amplitudes and phases of the princi- •The formalism can be extended to weakly nonlinear sys- tems, but here we shall not be concerned with this generaliza- tion. pal constituents of the observed tide at the station. If input and output are alike, then evidently Zif)-\, or w(t) = 5(t) and this is called a 'unit transfer function.' In general, \Z\ = R(f) and Arg(z) = 6(f) measure the relative magnification and phase lead of the station at frequency / . If R and 8 vary sensibly across the frequency band of a tidal species, then w(t) has to be defined at nonzero values of r . In the physical interpretation of the pelagic measurements we find it instructive if the analysis is broken into three steps: Flow Diagram The flow diagram (Figure 1) describes five stages of cal- culation for dealing with pelagic tide and current observations obtained at or near the same location. Stages A, B, and C are response analyses of the tide at a coastal reference station at time tt , pelagic tides at time t2, and pelagic currents at time t3, respectively. Stage B ' is a cross-spectral analysis of pre- dicted coastal tide with observed pelagic tide pressure, and C'is predicted pelagic pressure with observed pelagic velocity. Stages B ' and C ' are only for decision-making in B and C rather than part of the basic computations. Tide Potential Coastal Reference Tide Elevation Pelagic Station Tide Elevation Pelagic Station Tidal Current Arrow A represents the transfer function between the tide- producing forces and a coastal tide elevation so chosen as (1) to be in the vicinity of the pelagic station, (2) to be not subject to undue local transformation, and (3) to have avail- able a good record of long duration f> 1 year), enabling one to determine the first transfer function with precision. Arrow B represents the transfer function between coastal and pelagic tidal elevations; if (1) and (2) above are favorable, this will be nearly proportional to a unit transfer function. Arrow C relates the pelagic tidal elevation to the local tidal current, which is an important diagnostic element in deter- mining the wave dynamics. Under favorable circumstances we can also separate the locally coherent tidal currents (associated with the surface, or barotropic tide) from the incoherent cur- rents (associated with the internal, or baroclinic tides). The pelagic velocity data refer to a time series of a vector in a given azimuth. Ordinarily, northward and eastward orthogonal vectors will be used; the example shown is the northward component. The sequence of steps following the flow diagram and re- lated discussions are as follows: A. Response Analysis of Coastal Reference Station 1. Prepare time series of observed tides along the coast in the general vicinity of the pelagic pressure observations. The coastal series should be for at least one year. 2. Compute gravitational and 'radiational' tide potentials (merged) for the same period as the coastal observations. We shall refer to such a series as a 'TIDPOT' series after the name COASTAL REFERENCE STATION PELAGIC PRESSURE PELAGIC VELOCITY A- RESPONSE ANALYSIS h B-CROSS-SPECTRUM »2 3- RESPONSE ANALYSIS C -CROSS-SPECTRUM 3 RESPONSE ANALYSIS Coostol Press Obs Pelogic Press Obs Pelogic Velocity Obs h.»2.»3 UJt «Z.«3 t3 »3 Grav and Rod. Potential (merged) Pred. Coostol Press (merged) Pred Pelagic Press(merged) f$0- 1 1 s > \ V Sum Variance Fig. 1. Flow diagram. 473 of the BOMM routine used to compute it. 3. Compute 'coastal response weights' for optimum re- sponse prediction of the coastal tide. 4. Compute admittances from weights at a resolution of 1 cycle per month (cpm) and at the principal tidal lines. 5. Use coastal response weights and TIDPOT series to pre- dict coastal pressure. 6. Plot sample (15 or 30 days) of observations and pre- dictions. 7. Compute residuals for entire series. 8. Fourier-analyze observations and residuals at record harmonics and cpm resolution. 9. Sum observed and residual variances in the harmonics spanning (1 cpSd - 4M cpm) to (1 cp$d + 4V£ cpm) and similarly for species 2 centered at 2 cycles per lunar day. B '.Cross-spectral Analysis of Predicted Coastal Tide with Observed Pelagic Pressure The coastal record may not be available for the duration t2 of the pelagic pressure observations. It can, however, be predicted on the basis of previous observations (time tt), as in stage A. But even if the coastal observations are available, there is some advantage in using the noise-free predicted tide in the cross-spectral analysis. Any noise residuals are then associated with the pelagic pressure observations. The same consideration holds in subsequent stages; noise-free input functions are particularly attractive in the response method. 1 . Predict coastal pressure for time t2 using the coastal weights and an appropriate TIDPOT series. 2. Compute at cpm resolution the cross spectrum of the predicted ocean tide with observed pelagic pressure. Select a series length that minimizes sidebands (such as 29 solar days). This analysis yields the amplitude ratio and relative phase be- tween observed pelagic pressure and predicted coastal tide for each frequency band. The results will determine (1) whether the radiational terms should be used for predicting the coastal pressure and (2) how many weights should be used in fitting the pelagic pressure to the coastal pressure predictions. Radiational potentials were included to allow for non- gravitational changes in coastal sea level (such as winds, tidal atmospheric pressure, or thermal effects). A strong discrep- ancy between M2 and S2 admittances would suggest that the radiational effects were not comparable at the coastal and pelagic stations. In that event it would be better to exclude the radiational terms from the predicted pelagic pressure (B2). The radiational terms are included in the examples given here. The number of pelagic pressure weights for stage B are selected (with due allowance to noise level) on the basis of the variability of the amplitude ratios and relative phases in the tidal bands. Significant variations in admittances call for multiple weights. B. Response Analysis of Observed Pelagic Pressure 1 . Prepare time series of the observed pelagic pressure using the complete length of good data. 2. Use appropriate TIDPOT series and coastal weights to prepare predictions for time t2 . 3. Compute response weights for the pelagic pressure. 4. Compute admittances from weights (as in step 4 of stage A). 5. Use pelagic pressure weights and predicted coastal tide to predict pelagic pressure. 6—9. Same as steps 6—9 of stage A. C' .Cross-Spectral Analysis of Predicted Pelagic Pressure with Observed Pelagic Velocity (Vector in a Fixed Azimuth) As before, it is desirable to use noise-free predictions for the pelagic pressure. 1. Predict pelagic pressure from pelagic pressure weights and coastal pressure predictions. [If t2 and t3 are the same, this has already been done in step 5 of stage B. In this case, the predictions are truncated to an appropriate length (see step 2 of stage B')] . 2. Compute the cross-spectrum of predicted pelagic pres- sure and observed pelagic velocity as in step 2 of stage B'. The decision on use of radiational potential was made after stage B, and it is not reviewed again at this point. We found large and erratic variations in the amplitude ratios and phase relations across the tidal bands, and we attribute these to baroclinic 'noise.' (This hypothesis was supported by large differences in the cross-spectral analyses of the first and last 29 days of a 37-day series.) We therefore limited the number of weights to one unlagged pair for each species, thus imposing a constant amplitude ratio and a constant phase difference across each of the two tidal bands. We could, of course, improve the current prediction (curve fitting would be a better term) for time t3 at will by allowing additional weights; but if our hypothesis regarding the large noise content is correct then these additional weights could actually lead to a deterioration of a future prediction. C. Response Analysis of Observed Pelagic Velocity 1. Prepare a time series of the observed pelagic velocity using the complete length of good data. 2. Use appropriate coastal pressure predictions and pelagic pressure weights to prepare pelagic pressure predictions for time t3 . 3. Compute response weights for pelagic velocity. 4. Compute admittances from weights (as in step 4 of stage A). 5. Use pelagic velocity weights and pelagic pressure pre- dictions to prepare velocity predictions. 6—9. Same as steps 6-9 of stage A. Presentation Our standard presentation of the final results of the analysis as described above aims to satisfy both those who like to think in terms of 'admittances' and those who require only 'amplitudes' and 'phase lags' of major harmonic constituents. Admittances are detailed on the left-hand side of the output list, harmonic constituents on the right. For each tidal species, the elements of admittance are given at five evenly spaced frequencies, namely m cycles per lunar day + k cycles per month = (0.9661368m + 0.036601 lfc)cpd where m is the species number and A: takes the values -2,-1, 474 0, 1, 2 . These frequencies, listed in cpd units (cycles per solar day), approximate to the centers of the principal tidal 'groups' although they do not all belong to major 'constitu- ents.' The admittance function at intermediate frequencies can be assumed to vary smoothly between the given values. Exper- ience has shown that the admittance function is more directly meaningful than corresponding set of 'response weights' since it maintains greater constancy on repeated analysis. We there- fore do not list response weights in this presentation. Below the species admittance is shown the variance of the station series within a band of frequencies from k = -4.5 to k = +4.5 . This variance is derived from a Fourier analysis of the entire series. Below it again is shown the corresponding variance of the residual series when the response convolution ('prediction') is subtracted from the recorded series. These two figures indicate the reliability of the admittance figures. Assuming that the local noise in each tidal group is propor- tional to the tidal variance of the group (which is approxi- mately true for the major groups), then the relative sampling variance of the real and imaginary parts of the admittance is 2 residual variance 0 =: 2 X recorded variance The relative sampling variance of the admittance amplitudes R and the sampling variance in radians2 of their phase leads 0 are both approximately o2=a'2/R2 The harmonic constituent amplitudes for the station are obtained by multiplying the amplitudes for the reference sta- tion by the value of R at the appropriate frequency. The Greenwich phase lags G (not g) are similarly obtained by sub- tracting the leads 6 from the reference G values. All relevant quantities are listed on the right-hand side of the output list. The unbracketed constituents 01, K\, Ml, Kl are derived directly from the figures on the left and from the 'reference' constituents. For the bracketed constituents Ql, PI, Nl, and 52, the admittance was re-evaluated from the response weights at the exact frequencies of the constituents. In the special case when 'reference' is a set of gravitational and radiational potentials, and 'station' is the long-term tide record to be used later as a reference for shorter pressure records, the listed figures have special meanings. The listed admittances relate to the gravitational components a\ and a\ only (see Munk and Cartwright [1966]) although the full set of response weights will in general refer to other potentials also. The station harmonic constituents are derived from the complete set of weights and potentials, and reference con- stituents are not given. TABLE 1 STATION: Bottom Pressure (La Jolla, 600 m from shore off Scripps Pier), water depth 1 8 m; sensor buried 3 m below bottom; 418 days; 1961 Dec. 10 to 1963 Feb. 1 (542953.9583 to 552985.9583 Greenwich hours since 1900 Jan. l,0h). REFERENCE: Gravitational and radiational potentials c}(0, ±1 , ±2), c'3, xi , xi . c|(0, ±1 , ±2), c| , xl • Admittances (Station / Reference) Principal Harmonic Constituents Intervals 1 cpm (0.036601 1 cpd) CPD Station CPD Real Imag. R * deg H,cm C,« deg 0.8929346 0.8454 -0.0986 0.8512 -186.66 (QD 0.8932441 4.18 186.63 0.9295357 0.8218 -0.1737 0.8399 -191.94 OX 0.9295357 21.81 192.02 0.9661368 0.6689 -0.2492 0.7138 -200.43 (PI) 0.9972621 10.85 206.25 1 .0027379 0.8332 -0.4205 0.9333 -206.78 K\ 1 .0027379 34.40 206.80 1 .0393390 0.8691 -0.5609 1 .0343 -212.84 Recorded variance: 814.04 cm2 Residual variance: 0.97 cm2 Ratio: 0.0012 1.8590714 -0.0322 -0.9968 0.9973 - 91.85 1.8956725 -0.5233 -0.8650 1.0110 -121.17 W2) 1 .8959820 12.21 122.92 1.9322736 -0.6433 -0.4903 0.8088 -142.69 Ml 1 .9322736 51.02 142.66 1 .9688747 -0.5416 -0.2001 0.5774 -159.72 (S2) 20000000 21.33 137.58 2.0054758 -0.4881 -0.5483 0.7341 -131.68 Kl 2.0054758 6.08 131.31 Recorded variance: 1682.76cm2 Residual variance: 0.66cm2 Ratio: 0.0004 *G is Greenwich epoch, 0 is station lead. 475 TABLE 2 STATION: Bottom Pressure (Josie 175 SW), 31° 01.7' N, 1 19° 47.9' W, Depth 3.64 km, 37 days, 1968 Aug. 1 to Sept. 7 (601201.0833 to 602078.0833 Greenwich hours since 1900 Jan. 1,0»>). REFERENCE: 'Predicted' Bottom Pressure at La Jolla, 600 M from Shore off Scripps Pier. Admittances (Station / Reference) Principal Harmonic Constituents Intervals 1 cpm (0.036601 1 cpd) Station Reference CPD Real Imag. R, * deg CPD H, cm G, deg H, cm G, 0.8929346 0.8733 0.1044 0.9295357 1 .0286 -0.0534 0.9661368 1 .0997 -0.1036 1.0027379 1.0720 -0.0360 1 .0393390 0.9511 0.1356 Recorded variance: 1202.65 cm2 Residual variance: 2.35 cm2 Ratio: 0.0020 1.8590714 0.9212 0.1111 1 .8956725 0.9323 0.0554 1.9322736 0.9419 0.0239 1 .9688747 0.9481 0.0232 2.0054758 0.9497 0.0535 0.8795 1.0299 1.1046 1.0726 0.9607 6.82 -2.97 -5.38 -1.92 8.11 (01) 0.8932441 3.68 01 0.9295357 22.46 179.81 4.18 194.99 21.81 (PI) 0.9972621 11.76 209.07 10.85 K\ 1.0027379 36.90 208.72 34.40 186.63 192.02 206.25 206.80 0.9279 6.88 0.9339 3.40 W) 1.8959820 11.40 119.52 12.21 122.92 0.9422 1.45 Ml 1.9322736 48.07 141.21 51.02 142.66 0.9484 1.40 (S2) 2.0000000 20.28 134.74 21.33 137.58 0.9512 3.22 Kl 2.0054758 5.78 128.09 6.08 131.31 Recorded variance: 1483.81 cm2 Residual variance: 0.73 cm2 Ratio: 0.0005 *G is Greenwich epoch, is station lead. TABLE 3 STATION: Bottom Velocity, Northward Component (Josie 175 SW), 31° 01 .7' N, 1 10° 47.9' W, Depth, 3.64 km, Sensor 1.70 m above Bottom, 37 Days, 1968 Aug. 1 to Sept. 7 (601201.0833 to 602078.0833 Greenwich hours since 1900 Jan. l,0h). REFERENCE: 'Predicted' Bottom Pressure at Same Position and Time. Admittances (Station / Reference) Princip al Harmonic Constituents Intervals 1 cpm (0.0366011 cpd) CPD Sta ion Reference CPD Real, sec Imag., sec R, sec"1 * deg H, cm/sec G, deg H, cm G* deg 0.8929346 0.0165 0.0022 0.0167 7.69 (00 0.8932441 0.062 172.12 3.68 179.81 0.9295357 0.0165 0.0022 0.0167 7.69 01 0.9295357 0.375 187.30 22.46 194.99 0.9661368 0.0165 0.0022 0.0167 7.69 (PI) 0.9972621 0.196 201.38 11.76 209.07 1.0027379 0.0165 0.0022 0.0167 7.69 Kl 1 .0027379 0.616 201.03 36.90 208.72 1 .0393390 0.0165 0.0022 0.0167 7.69 Recorded variance: 0.580 (cm/sec)2 Residual variance: 0.206 (cm/sec)2 Ratio: 0.355 1.8590714 0.0477 -0.0063 0.0481 -7.49 1.8956725 0.0477 -0.0063 0.0481 -7.49 m) 1.8959820 0.548 127.01 11.40 119.52 1 .9322736 0.0477 -0.0063 0.0481 -7.49 Ml 1.9322736 2.312 148.70 48.07 141.21 1 .9688747 0.0477 -0.0063 0.0481 -7.49 (S2) 2.0000000 0.975 142.23 20.28 134.74 2.0054758 0.0477 -0.0063 0.0481 -7.49 Kl 2.0054758 0.278 135.58 5.78 128.09 Recorded variance: 3.961 (cm /sec)2 Residual variance: 0.641 (cm/sec)2 Ratio: 0.162 *G is Greenwich epoch, 0 is station lead. 476 We have included three examples of lists (Tables 1 -3) as de- scribed above, giving the results of analysis of records recently made by IGPP, La Jolla. The 'reference station' is a high qual- ity pressure record of 14 months' duration taken near Scripps pier. It is applied to a 37-day record of pelagic pressure and velocity from a Snodgrass capsule [Snodgrass, 1968] some 325 Jem southwest of La Jolla at a depth of 3.64 km. Note that in the third analysis, velocity versus pressure, no time lags were allowed for reasons explained in stage C' of section 3. The resulting admittance figures for each species are therefore constant. REFERENCES Cartwright, D., Deep-sea tides, Sci. J., 5(1), 60-67, January 1969. Eyries, M., Maregraphes de grandes profondeurs, Cahiers Oceanogr., 20(5), 1968. FU16ux, J. H., Deep-sea tide record from the northeastern Pacific, (abstract), Trans. Amer. Geophys. Union, 49, 211, 1968. Hicks, S. D., A. J. Goodheart, and C. W. Iseley, Observations of the tide on the Atlantic continental shelf, J, Geophys. Res., 70(8), 1827-1830, 1965. Munk, W., and D. Cartwright, Tidal spectroscopy and prediction, Phil. Trans. Roy. Soc. London, A, 259, 533-581, 1966. Munk, W., and B. Zetler, Deep-sea tides: a program, Science, 158, 884-886, 1967. Nowroozi, A. A., M. Ewing, J. E. Nafe, and M. Fleigel, Deep ocean current and its correlation with the ocean tide off the coast of northern California,/ Geophys. Res., 73, 1921-1932, 1968. Snodgrass, F., Deep-sea instrument capsule, Science, 162, 78-87, 1968. David Cartwright is with the National Institute of Oceanography, U. K. Walter Munk is Director of the In- stitute of Geophysics and Planetary Physics at Scripps In- stitution of Oceanography , University of California, La Jolla. Bernard Zetler is Director of the Physical Oceanog- raphy Laboratory, Atlantic Oceanographic Laboratories, Miami, Florida. 477 69 Reprinted from Solar Physics Vol. 7, 417-433. BRIGHTNESS VARIATIONS OF THE WHITE LIGHT CORONA DURING THE YEARS 1964-67 RICHARD T.HANSEN, CHARLES J. G A RCI A, SHIRLEY F.HANSEN High Altitude Observatory, National Center for Atmospheric Research, Kamtiela, Hawaii, U.S.A. and HAROLD G. LOOMIS* Environmental Science Services Administration, Honolulu, Hawaii, U.S.A. (Received 4 November, 1968) Abstract. Observations of the white light corona were made on over 900 days during the years 1964-67 at heights between 1.125 and 2.0 Rq with the K-coronameter at Mount Haleakala and Mauna Loa, Hawaii. The brightness distribution of the minimum corona was elliptical with average equatorial intensities three times the polar. Coronal features of the new cycle at 1.125 RQ occurred predominantly in the sunspot zones at 25-30° latitude and in a high latitude zone which migrated toward the North pole before solar maximum. The brightness of the inner corona doubled over this period and a close association is found between the average corona and 10.7-cm solar radio flux. Electron densities in the equatorial regions were nearly twice those of Van de Hulst's model corona, in agreement with the results of recent eclipse observations. 1- Introduction Systematic observations of the sun's corona have been made at total eclipses for over a century and have well established that the corona changes, possibly in periodic ways, with the solar cycle. Basically, near maximum, it appears relatively circular with streamers extending outward radially from all latitudes but then at sunspot minimum becomes more concentrated along the equatorial plane. Lockyer (1931) classified the shapes according to latitude distributions of the streamers and showed that three basic structural forms - polar, intermediate and equatorial - are related in a general way to phase of the solar cycle, although even more directly tied to the changing latitude of the prominence zones. Ludendorff (1928) introduced the index of ellipticity as a numerical measure of the tendency for coronal isophotes to flatten at sunspot minimum as rifts develop in the polar corona and the equatorial streamers become more pronounced. This trend has been substantiated by observations of a dozen or so eclipses during the past several decades. However, the extent of changes in total brightness of the corona with the solar cycle has not been clearly established from eclipse observations (summarized by Hata and Saito, 1966, especially their Figures 6 and 8). This is inherently a difficult study because of differences in size of the moon projected on the sun causing variations in the obscuration of the brighter inner corona, uncertainties as to atmospheric transparency at the time of the eclipse, and, more basically, the fact that the corona * At Hawaii Institute of Geophysics. Solar Physics 7 (1969) 417-433; © D. Reidel Publishing Company, Dordrecht -Holland 418 RICHARD T.HANSEN ETAL. on a specific day is not necessarily truly representative of its place in the solar cycle. One series of visual and photographic observations reported by Sytinskaya and Sharonov (1963) for six eclipses 1936-61 "did not reveal any correlation at all between the integrated coronal brightness and sunspot number or any factor". On the other hand, some convincing evidence for such changes is provided by other observers including the University of Minnesota group whose measurements of the eclipses of 1959 and 1963 with identically the same photoelectric instruments showed a decrease in total intensity in the equatorial direction by 30% between the two dates, which occurred during high and relatively low phases, respectively, of sunspot activity (Gillett et ai, 1964). Also, at the distance of 1.5 RQ they found the 1959 corona to be 1.5 times brighter at the equator and 2.4 times brighter at the polar regions than the 1963 eclipse. With Lyot's development of the coronagraph, it has become possible to study coronal variations with a more plentiful supply of data, freed from the coarse sampling procedure imposed by the infrequency of natural eclipses. From his own observations Lyot reached the important conclusion that "the continuous spectrum of the corona (polarized light) has increased between the minimum of 1944 and the maximum in 1947 by a factor of about 2.3 in the polar regions and 2 in the equatorial regions" (from Van de Hulst, 1953). Presumably this result is for the innermost corona at 1.1 to 1.2 RQ. Reported here is a new study of the changes in brightness distribution of the inner corona, based upon a highly concentrated series of K-coronameter (Wlerick and Axtell, 1957) observations from February 1964-December 1967, corresponding to solar minimum and the ascending phase of cycle 20. In late 1963, as a cooperative program with the University of Hawaii for the International Quiet Sun Year (IQSY), the High Altitude Observatory's K-coronameter was installed in the Mees Solar Laboratory of the Hawaii Institute of Geophysics on Mount Haleakala, Maui, Hawaii. In November 1965 the instrument was moved to its present location at the Environmental Science Services Administration's Mauna Loa Observatory, 1 1 150 feet elevation on the Island of Hawaii (Hansen et a!., 1965). Extremely favorable condi- tions at both sites permitted observations on more than 200 days per year. Earlier studies with the K-coronameter, then operated at Climax, Colorado, are described by Newkirk et al. (1958). The basic instrument and reduction procedures remain the same. The measurements are of the quantity pB as the instrument scans around the sun at a selected height above the solar limb, where p is the polarization tangential to the limb and B the radiance of the corona in units of 10" 8 the radiance of the center of the solar disk. These observations have two principal limitations as contrasted to those possible at natural eclipse. First, spatial resolution is compromised by the significant size of the scanning aperture used in the telescope. Its diameter is 1.3 min of arc and thus any smaller coronal details are blurred together. Second, even during cloud-free days, reliable measurements are restricted to the inner corona of R < 2 RQ but more generally to R< 1.75 RQ, because of the brightness of the non-eclipse sky and also because of BRIGHTNESS VARIATIONS OF THE WHITE LIGHT CORONA DURING THE YEARS 1964-67 419 random fluctuations in polarized signal due to atmospheric contaminants which produce a background noise level of at least 1 x 10" 8 pB. 2. Representative Daily Observations Examples of the original K-coronameter measurement at 1.125 RQ are shown in Figure 1, superposed for the months of July for each year 1964-67. From these it is possible to describe qualitatively the evolution of the corona over this part of the solar cycle. During the solar minimum of 1964, the general level of brightness was Fig. 1 . Superposed polar plots of representative daily observations of the K-corona for successive months of July, 1964-67. The quantity pB is plotted radially as a function of heliographic position angle. - 1.125 RQ. low with only slight day-to-day changes and the distribution was symmetric about the equator; there was no North-South asymmetry. Recalling that these are polar plots with intensity proportional to radial distance rather than the usually presented iso- photes, it is still apparent that the distribution was highly elliptical with equatorial brightness some 3 times greater than polar at the same height. By the next July (1965), K-coronal activity increased slightly as shown by successive East- and West-limb passages of a single distinct feature in the South, but similar features at 20-30° latitude were more numerous in the North. Another zone of activity developed at higher Northern latitudes around 60° which sometimes created the appearance of a polar rift or a deficiency of corona at the pole. In 1966 there was a comparable rift over the South pole, but meanwhile the general level of activity in the North was more advanced. K-coronal features 2 to 3 times brighter than the quiet or minimum 420 RICHARD T.HANSEN ET AL. phase corona were frequent.* By July 1967, activity in the Southern hemisphere was well-developed at 30c latitude, similar to that in the North, but with a relative void remaining over the South pole. Comparable daily measurements at the greater height of 1.5 RQ are shown in Figure 2 for three years, 1965-67, again for the representative months of July. The Fig. 2. Same as Figure I but for 1.5 RQ. Observations during 1965-67 only. general appearance is considerably more chaotic than at 1.125 RQ because the do- minance of activity at sunspot latitudes did not extend to this height as distinct coronal features occurred at high as well as low latitudes. Features also appeared over the equator at this greater height of 1.5 RQ, consistent with eclipse photographs which sometimes show coronal arches spanning between the two hemispheres. The large brightness fluctuations in the vicinity of the North pole are due to projection of high latitude features seen near central meridian passage over the pole. The changing appearance which may be expected from a simple idealized coronal feature is illustrated in Figure 3 and 4 (from Perry, 1967) where radial streamers are assumed to be based on 0°, 30°, 60° North latitude and successive days' observa- tions with the K-coronameter made at a fixed scanning distance. The zero date denotes the observation just at limb passage with minus and plus dates showing the apparent latitude on the days before and after. Relative intensities for each date are represented by the radial distance from the circle. In Figure 3 the sun's axial tilt (BQ) is zero. A feature based at the equator appears to remain at that latitude and is visible for just 4 days on each side of its limb passage. A high latitude (60 ) feature however is * The very bright coronal feature in the Northwest quadrant was associated with a proton flare region for which electron density models have been constructed (Newkirk et «/., 1967). BRIGHTNESS VARIATIONS OF THE WHITE LIGHT CORONA DURING THE YEARS 1964-67 421 observable continuously and even when projected over the pole from in front of or behind the visible disk,' it remains at about £ of its true (limb passage) brightness. The extreme situation is shown in Figure 4 with the sun's axial tilt at the maximum of +7.2° (toward or away from the earth) corresponding to the orientation during the months of September and March. At polar passage, the high latitude streamer appears to fluctuate between a low of less than 10% to a maximum of 40% of the brightness observed at limb passage. Thus, while a high latitude radial coronal feature is based at a specific longitude Fig. 3. Variation in apparent latitude and brightness of idealized narrow coronal features based at 0°, 30° and 60' North latitude as they are subjected to the sun's rotation. At zero day, the feature is in the plane of the sky; other numbers indicate the observed latitude on days before and after limb passage with relative intensities represented by the radial distance from the edge of the circle. The sun"s axial tilt (BQ) is assumed to be zero. Fig. 4. Same as Figure 3 except that the sun's axial tilt is assumed to be at the maximum of 7.2C 422 RICHARD T.HANSEN ET AL. and latitude, by projection it could appear on the limb at any higher latitude. This effect has surely contributed to the difficulty and ambiguity of using eclipse photo- graphs to relate white light coronal features to underlying chromospheric phenomena. 3. Distributions of Average Radiance The entire 4 years of K-coronal measurements are divided into half-year groupings as listed in Table I with numbers 1-8 designating successive periods. The distribution of average radiance, at 5° increments of latitude, is shown at each height 1.125, 1.25, TABLE I Number of daily observations of K-corona at selected heights during successive six-month periods Dates 1.125 1.25 1.50 1.75 RQ 1. Feb.-Jun. 1964 75 66 _ _ 2. Jul.-Dec. 1964 107 92 - - 3. Jan.-Jun. 1965 114 88 - - 4. Jul.-Dec. 1965 117 99 78 - 5. Jan.-Jun. 1966 116 107 109 79 6. Jul.-Dec. 1966 132 114 111 86 7. Jan.-Jun. 1967 113 96 85 80 8. Jul.-Dec. 1967 130 124 115 108 1.5 and 1.75 RQ in Figures 5 to 8. During the solar minimum of 1964, the white light corona nearest to the limb of the sun (Figure 5) was nearly symmetric around the equator with uniform brightness of 30-35 x 10~8 pB between ±40°. The first response BRIGHTNESS VARIATIONS OF THE WHITE LIGHT CORONA DURING THE YEARS 1964-67 423 to the new solar cycle was the increase in brightness in the sunspot zone at 25-30° North latitude in 1965 Which steadily progressed until by the end of 1966 (period 6) the average in this zone was more than double that at solar minimum. A similar brightness increase occurred in the Southern hemisphere about a year later, corre- sponding to the general lag in development of sunspots and other aspects of activity in the South during the early phase of cycle 20. The polar corona in the North also steadily brightened during this time, reaching an average of 4 times that at minimum. Fig. 7. 424 RICHARD T.HANSEN ET AL. By the end of 1967 the North polar corona was brighter than any position around the sun had been during minimum, but the corona over the South pole changed very little during the entire four years. Meanwhile the behavior at 1.25 RQ (Figure 6) was essentially parallel to that at 1.125 RQ except that the intensities were lower by a factor of 2. Figs. 5-8. Average brightness distributions of the K-corona at 1.125, 1.25, 1.5 and 1.75 RQ vs. latitude for each six-month interval from 1964-67 (denoted by numbers 1 to 8). Observations were not made at 1.5 and 1.75 RQ during the earlier periods. At 1.5 RQ (Figure 7) and 1.75 RQ (Figure 8), K-coronameter measurements were made regularly only from the latter half of 1965 and the beginning of 1966, respective- ly; thus documentation on the evolution of brightness at these heights is not as complete. Nonetheless, certain patterns are apparent including again the monotonic increase over low latitudes and the North pole but almost complete lack of response to the new cycle at the South pole. However, the marked zonal form of the corona as seen at 1.125 RQ did not extend to these heights of half and three quarters radius above the limb. Instead the average increased more uniformly over a wide range of latitude. In fact, by the end of 1967 the average brightness distribution at heights above 1.5 RQ was essentially uniform and thereby had achieved the circular form which is considered to be typical of solar maximum - except in the sector 40 to 90 South. 4. Total Radiance at Each Height We now consider the increase in total light radiated by the electron corona at each of the several standard observing heights. This is based upon simple comparison of BRIGHTNESS VARIATIONS OF THE WHITE LIGHT CORONA DURING THE YEARS 1964-67 425 the areas under each of the brightness distribution curves of Figures 5 to 8. The totals at 1.125 and 1.25 ^?0 are normalized in terms of 1964, and those for 1.5 and 1.75 R0 to the levels during the beginning of 1966 (period 5), and their development is shown in Figure 9. The corona remained practically constant through mid-1965 and then steadily increased in brightness at all heights to twice the minimum level. Less com- plete and less reliable observations at 2.0 RQ indicate that the brightness increased by only 1.5 higher in the corona, but our degree of confidence in this data does not warrant inclusion with the other points of Figure 9. Fig. 9. Variation in total normalized radiance of the K-corona at several heights during the as- cending phase of cycle 20. Six-month averages of 10.7-cm radio flux are shown as solid points through which a smooth curve has been drawn. In order to relate the total radiance to phase of the solar cycle, comparison is made with the half-year averages of 10.7-cm (Ottawa) solar radio flux, known to be closely associated with sunspot and plage areas (Kundu, 1965). This is shown in Figure 9 by solid circles through which a smooth curve has been passed. It is obvious that the K-coronal brightness, out to a height of 1.75 RQ, is highly correlated with the slowly varying component of 10.7 solar radio flux. As the radio component increased by 2.0 from 1964 to 1967 the coronal brightness increased by factors 1.9 426 RICHARD T. HANSEN ET AL. to 2.1. By extrapolating the radio index to the level at the maximum of cycle 19 in 1958 it appears that the K-corona at great solar activity would have been 3 times brighter than its quiet level as represented by the minimum years of 1964-65. TABLE II Determinations of the maximum-minimum ratio in brightness of the K-corona Source Period Height Ratio Van de Hulst max/min (6 eclipses, 1918-45) Hata and Saito max/min (8 eclipses, 1952-63) Lyot 1947/1944 (Synoptic coronagraph observations) Hansen, Garcia, Hansen, 1967/1964 and Loomis (Synoptic coronagraph observations, six-month averages) 1.03-6.00 RQ 1.8 1.2 RQ 2.5 1.03-4.00 RQ 2.5 1.1-1.2 RQ 2.1 IA25RQ 1.9 1.25 RQ 2.0 1.50 RG 2.1 1.75 Re 1.9 Several previous determinations of brightness changes in the white light corona during a solar cycle are summarized in Table II. The entry identified with Van de Hulst was actually based largely upon Nikonov's analysis of six eclipses between 1918-45 in which he found an increase of 1.8 from minimum to maximum in the coronal ring bounded by 1.03-6.00 RQ. Hata and Saito later concluded from their more comprehensive review of all available eclipses (1898-1963) that only observa- tions having absolute photometry, essentially those made since 1952, were useful for demonstrating possible solar cycle variations. And from the 8 eclipses 1952 through 1963 they concluded that at 1.2 RQ and also within the ring bounded by 1.03 and 4.00 RQ the corona increased in brightness by 2.5. Inspection of Hata and Saito's Figure 8 suggests that their result is derived almost exclusively from the observed variations at 1.2 and 1.5 RQ between the maximum eclipses of 1958 and 1959 compared with the minimum of 1954. At the height of 2.0 RQ and beyond, the corona is so much fainter (by nearly 2 orders of magnitude) that any cyclic variation would have no significant influence on the total integrated brightness. Thus K-coronameter measurements, even though presently limited to the inner corona of R<2 /?0, are intrinsically as well-suited to answering this question as are measurements at natural eclipse. 5. Zones of Activity and Poleward Migration The arithmetic averages of the previous section tend to obscure the fact that the K-coronal features occur in discrete latitude zones. The zonal character is rather obvious from inspection of even the small sample of observations of Figure 1 and 2, but is better represented by the statistical standard deviation of intensity from the BRIGHTNESS VARIATIONS OF THE WHITE LIGHT CORONA DURING THE YEARS 1964-67 427 six-month mean. As an example both parameters, average and standard deviation, are shown together in Figure 10. Clearly the principal zone of 'activity' (in the sense of day-to-day changedness) as well as enhanced brightness for the period occurred in the Northern hemisphere at about 25° latitude. And a similar but considerably Fig. 10. Comparison of the latitude distribution of average K-coronal brightness and standard deviation from this mean for the period July-December 1966. - 1.125 RQ. weaker zone, also associated with sunspot and plage regions, occurred at 25° South. However only the standard deviation curve reveals the high latitude or polar zones at 70° North and 60° South. Because individual coronal features continue to be observed for at least several days as they are carried by solar rotation into and away from the plane of the sky, their apparent position is systematically smeared to higher latitudes. This effect is necessarily greater for the polar zone and the extent is also influenced by the shape and gradient of particular coronal features. Nonetheless, peaks of the standard deviation curve do indicate the approximate latitude of the polar activity zones. The complete set of standard deviation curves for the entire interval 1964-67 at the observing height 1.125 RQ is shown in Figure 1 1. The general pattern is similar to that found from the averages (Figure 5) with the principal activity developing in the zone at 25° North latitude after 1965. Activity in the Southern hemisphere is again seen to lag by about a year and changes over the poles were slight. By enlargement of the right hand part of Figure 1 1 into Figure 12, it is found that the high latitude zone steadily migrated to the pole, beginning at 55° North during 428 RICHARD T. HANSEN ET AL. Latitude Fig. 11. Latitude distributions of standard deviation from mean brightness for each six-month period 1964-67 (numbered 1 to 8). - 1.125 RQ. Latitude Fig. 12. Enlargement of the right hand portion of Figure 1 1 showing the poleward migration of the high latitude zone of coronal activity. BRIGHTNESS VARIATIONS OF TUL WHITE LIGHT CORONA DURING THE YEARS 1964-67 429 the latter half of 1965 and reaching 80° by the first half of 1967. Similar migratory movements of prominences and filaments, culminating in a 'rush to the poles' at the time of solar maximum, have been well established for many years (Anantha- krishnan, 1954, and references therein). Waldmeier (1960) further suggested that during the solar maximum of the late 1950's reversal of the sun's polar magnetic fields occurred at the same time that the green corona's high latitude zone reached the poles and prominences reached 68°. Hyder (1965) reported a corresponding synchro- nism in the rush to the poles of filaments and reversal of the polar magnetic fields for the same cycle. Based on these observations of migration of the white light corona from 1965 to 1967, activity will reach the North and South poles in 1968 and 1969 respectively. Thus one might predict a reversal of the North and South polar fields during these years. 6. Electron Densities The gradients of coronal brightness with increasing distance from the solar limb in the equatorial regions for the minimum year 1964 and the near-maximum year 1967 200 r/Ro Fig. 13. Gradient of brightness with height for 1964 and 1967 equatorial regions compared with Van de Hulst's models and the exceptional feature of 10 July 1966. Vertical bars on the 1967 points denote one standard deviation above and below the mean. Points for 1964, shown as x 's, fall almost exactly on the curve for Van de Hulst's maximum. 430 RICHARD T. HANSEN ET AL. are shown in Figure 13. We follow the convention of considering the equatorial regions to be between plus and minus 50° latitude. By Figure 5 it is seen that this assumption is reasonable for 1964 in that the average brightness is uniform over a wide range of latitudes, although the somewhat smaller range of +40° might have been more appropriate. During active phase (such as periods 7 and 8) the brighter features of the inner corona are concentrated in zones above the sunspot regions, leaving a trough in the equatorial direction as seen in Figure 5. But this procedure of averaging over +50° to describe the 'equatorial corona' does assure inclusion of most of the bright features of the inner corona. Period 4 is used to represent the minimum corona at 1.5 RQ for the brightness decrement plot of Figure 13. Our brightness gradients are compared in this figure with those assumed by Van de Hulst for his classic development of coronal electron models. Van de Hulst's maximum was 1.78 times brighter than his minimum; we find a similar increase (1.9) for the near-maximum year 1967 compared to the minimum year 1964. However our minimum brightnesses are essentially identical to those assumed by Van de Hulst for his maximum model corona, and the two curves coincide in Figure 13. This is con- sistent with other recent measurements of the eclipse corona, including those of 1958 (Saito and Yamashita, 1962) and 1959 (Ney et al., 1961) which similarly showed that it is necessary to increase Van de Hulst's model for the equatorial maximum corona by a factor of 2. Vertical bars on the 1967 brightness decrement points denote one standard deviation above and below the means as an indication of the differences one may realistically expect from particular eclipse observations during this phase of the solar cycle. During minimum the expected variations are of course much smaller. Also shown for comparison is the gradient of the exceptionally bright feature of 10 July 1966 that was associated with a center of activity producing proton flares (Newkirk et al., 1967). TABLE III Comparison of average equatorial electron densities of 1964 and 1967 with other models (units 106/cm3) Hansen, Garcia Van de Hulst Newkirk Proton region Hansen and Loomis models 1956-58 10 July 1966 1964 1967 rlR0 Min Max Mm Max Quiet Active 1.1 90 160 1.125 120 230 70 125 290 570 820 1.2 71 137 39.8 70.8 160 340 410 1.3 38 72 21.2 37.6 86 176 195 1.4 22 41 12.8 22.5 51 99 105 1.5 14 26.9 8.3 14.8 33 61 63 1.6 - 18.6 5.7 10.0 22 39 40 1.7 - 13.2 4.0 7.1 15 26 27 1.8 - 9.7 2.9 5.0 11 17 19 2.0 — 5.7 1.6 2.8 6 9 11 BRIGHTNESS VARIATIONS OF THE WHITE LIGHT CORONA DURING THE YEARS 1964-67 431 The derivation of electron densities is standard following Van de Hulst's technique with the assumption that the corona is azimuthally symmetric, an assumption which is well-recognized to be quite good for the minimum corona in the equatorial regions but obviously only a crude approximation to the real corona near solar maximum. Electron densities for 1964 and 1967 are shown in Figure 14 and Table III, again Fig. 14. Electron densities derived from Figure 13 with x 's again denoting our equatorial minimum of 1964. compared with those of Van de Hulst and the exceptional isolated feature of July 1966. Also included in the table are Newkirk's models for the quiet corona and the electron density above an active region, based upon some 20 days K-coronameter observations at Climax during the period September 1956 to January 1958 (New- kirk, 1959). This interval covered a pre-maximum phase of the solar cycle similar to 1967. However, the observational data were treated in a somewhat different manner so that the results are not exactly comparable. Ours are based on average K-coronal brightness for every day over the latitude range +50° while Newkirk extracted the contributions of the 10 most active regions (which formed the basis of his active region model) and then averaged all remaining data to within 15° of the poles. Both 432 RICHARD T.HANSEN ET AL. of these differences work in the direction of depressing his model for the quiet corona of 1956-58 as compared to our average for 1967. 7. Conclusions There was a systematic change in brightness of the corona from the solar minimum of 1964 through the pre-maximum year of 1967, as clearly demonstrated by: Ap- pearance of typical daily observations from year to year; average intensities at all latitudes except over the South pole; and total radiation at several concentric heights in the lower corona. The corona brightened uniformly at all heights in the range 1.125-1.75 ^?0 by a factor of 2. A close correlation is found between six-month averages of white light coronal intensity and 10.7-cm solar radio flux. Extrapolation to the radio flux level of the great maximum of cycle 19 in 1958 suggests that the integrated brightness of the corona may have increased by a factor of three at that time. The brightness variations were due to discrete coronal features in preferred zones, in the sunspot activity belts at 25-30° and in a North polar zone which was observed to migrate from 55° to 80° during the period. Presumably this migration was the coronal manifestation of the 'rush to the poles' that has been well-established for filaments and prominences. Typical coronal features as observed through an aperture giving 1.3 min resolution are 20° to 40° wide in position angle and may appear 4 times brighter than the quiet, minimum-level corona. Their association with other solar phenomena will be discussed in a later paper. Following the usual assumption of spherical symmetry, our average equatorial coronas for 1964 and 1967 had electron densities nearly twice Van de Hulst's models for the minimum and maximum corona, respectively. Acknowledgements This work would not have been possible without the generous cooperation of many staff members at the University of Hawaii's Haleakala Observatory and the En- vironmental Science Services Administration's Mauna Loa Observatory. We wish to particularly thank Walter Steiger, John Jefferies, Howard Ellis and Lothar Ruhnke. References Ananthakrishnan, R.: 1954, Proc. Indian Acad. Sci. 40, 72. Gillett, F. C, Stein, W. A., and Ney, E. P.: 1964, Astwphys. J. 140, 292. Hansen, R. T.„ Hansen, S. F., and Price, S.: 1965, Publ. Astron. Soc. Pacific 78, 14. Hata, S. and Saito, K.: 1966, Ann. Tokyo Astron. Obscrw, 2nd Scries 10, 16. Hyder, C: 1965, Astwphys. J. 141, 272. Kundu, M. P.: 1965, Solar Radio Astronomy, lntcrscience. Now York. Lockyer, W. J. S.: 1931, Monthly Notices Roy. Astron. Soc. 91, 797. Ludendorff, H.: 1928, Sitz.-Ber. Preitss. Akad. Hiss. 16, 185. Newkirk, G. A.: 1959, Paris Symposium on Radio Astronomy (ed. by R. N. Braecwell). p. 149. BRIGHTNESS VARIATIONS OF THE WHITE LIGHT CORONA DURING THE YEARS 1964-67 433 Newkirk, G. A., Curtis, G. Wm., and Watson, D. K.: 1958, IGY Solar Activity Report Series No. 4, High Altitude Observatory, Boulder. Newkirk, G. A., Hansen, R. T., and Hansen, S. F.: 1967, Annals of the IQSY, Vol. 3, Paper 8. Ney, E. P., Huch, W. F., Kellogg, P. J., Stein, W„ and Gillett, F.: 1961, Astrophys. J. 133, 616. Perry, R. N.: 1967, Astro-Geophysical Memorandum No. 175, High Altitude Observatory, Boulder. Saito, K. and Yamashita, Y.: 1962, Ann. Tokyo Astron. Observ. 7, No. 4, 163. Sytinskaya, N. N. and Sharonov, V. V. : 1963, in The Solar Corona (ed. by J. W. Evans), Academic Press, New York, p. 301. Van de Hulst, H. C.: 1950, Bull. Astron. Inst. Neth. 11, 135. Van de Hulst, H. C.: 1953, in The Sun, 261 (ed. by G. P. Kuiper), Univ. of Chicago Press, Chicago, p. 261. Waldmeier, M.: 1960, Z. Astrophys. 49, 176. Wlerick, G. and Axtell, J.: 1957, Astrophys. J. 126, 253. 70 Reprinted from Solar Physics Vol. 10, 135-149. DIFFERENTIAL ROTATION OF THE SOLAR ELECTRON CORONA RICHARDT. HANSEN and SHIRLEY F. HANSEN, High Altitude Observatory, National Center for Atmospheric Research, Kamuela, Hawaii, U.S.A. and HAROLD G. LOOMIS* Environmental Science Services Administration, Honolulu, Hawaii, U.S.A. (Received 20 May, 1969) Abstract. Autocorrelation analyses of K-coronameter observations made at Haleakala and Mauna Loa, Hawaii, during 1964-1967 have established average yearly rotation rates of coronal features as a function of latitude and height above the limb. At low latitudes the corona was found to rotate at the same rate as sunspots but at higher latitudes was consistently faster than the underlying photosphere. There were differences as large as 3-4% in the rate at specific latitudes from year to year and between the two hemispheres. In 1967 a nearly constant rotation was found for heights ranging from 1.125 to 2.0 Ra. For 1966 there was a more complicated pattern of height dependence, with the rate generally decreasing with height at low latitudes and increasing at high latitudes. 1. Introduction More than a hundred years ago on the basis of his observations of the latitude- dependence of the westward drift of sunspots, Carrington demonstrated that the sun does not rotate as a rigid sphere. Sunspots at high latitudes have a longer rotation period than those nearer the equator. His basic result on differential rotation of the photosphere has since been confirmed by many later studies (including Newton and Nunn, 1951 ; Ward, 1966) and also has been extended to greater heights in the solar atmosphere by investigations of the day-to-day displacements of filaments (D'Azam- buja and D'Azambuja, 1948; Bruzek, 1961) and bright coronal regions (Waldmeier, 1955; Trellis, 1957; Cooper and Billings, 1962). Meanwhile, spectroscopic analysis of the Doppler shifts of spectral lines originating in identifiable features and in specific levels of the solar atmosphere has provided independent verification of the differential rotation effect (reviewed by Goldberg, 1953). Each of these two methods - displacement and spectroscopic - for deriving rotation rates has its own limitations although fortunately few of the limitations are common to both (Delury, 1939; Ward, 1966). Individual sunspots, filaments, and presumably the photosphericfaculae undergo proper motion and are not truly tracers for the medium in which they are embedded. Similarly these solar phenomena may display an asym- metric growth which is superimposed on apparent rotational displacements. A further limitation of this method is that features tend to occur in a limited range of latitudes; * At Hawaii Institute of Geophysics. Solar Physics 10 (1969) 135-149; © D. Reidel Publishing Company. Dordrecht -Holland 1 36 RICHARD T. HANSEN ET AL. sunspots for example are confined to essentially 5-35°. And since there are practically no spots during solar minimum, it has been necessary to assume that the rotation rate is constant throughout the solar cycle although there is some evidence to the contrary (Evershed, 1945; Livingston, 1969). By the spectroscopic method, rotation rates can be found over a wider range of latitude and throughout the solar cycle. In actual practice however the accuracy is limited by the presence of inhomogeneities of the photospheric velocity field and also by macroscopic motions within coronal and prominence features so that the scatter between repeated measurements is large (Hart, 1954, 1956; De Jager, 1959). Nonetheless the two methods concur on an average equatorial rotation rate of 1 4.4 + 0.2°/day. The purpose of this paper is to describe the latitude-dependent rotation rate of the electron corona, based on analysis of over 900 daily observations made with the K-coronameter (Wlerick and Axtell, 1958) at Haleakala and Mauna Loa, Hawaii during 1964-1967. The height range of our data extends from 1.125 to 2 R0 so that it is possible to search for changes in rotation rate at increasing distances from the solar limb. Some of the characteristics of the K-corona over this period have been discussed earlier (Newkirk et aL, 1967; Bohlin 1968; Hansen et aL, 1969). Determination of rotation rates is possible because of the occurrence of localized coronal features, as much as two or three times brighter than the quiet corona, and with sufficient stability to reappear at the limb for several rotations. These features thus act as our tracers for the corona's rotation. 2. Methodology Representative examples of the day-to-day brightness variations of the K-corona are shown in Figure 1. Successive observations are joined by line segments wherever the 40/ 30- 20- 1967 40° NORTH 1965 NORTH POLE ;/a ^w/v. .^.r. --ftA^^WW^^v* /,- -^ 1965 EQUATOR ■r /^v -. .kt. v^/v-^^-^^^ ^ •' ^ TIME (DAYS! JO 60 90 120 150 (80 ?I0 240 270 300 330 360 Fig. 1 . Representative time sequences of the brightness of the K-corona. DIFFERENTIAL ROTATION OF THE SOLAR ELECTRON CORONA 137 data gaps do not exceed two days. The upper curve (1967, 40° North) is at a latitude where strong and persistent coronal regions reappeared many times during the year, so that a good estimate of the rotation rate is readily found. The autocorrelation for this sequence is shown at the top of Figure 2. The time delay for reappearance of these features after one, two and three rotations is obviously about 30, 60 and 90 days. The strength of the third peak demonstrates the longevity of some coronal features. \ \ \ \- \ z-2 o 1 6 Q * J 2 s a -2 4 2 0 \ /" \ / "\ / / \ /' \ / \ / \ /' \ / "\ / \ J \ \ \ \ r. \ / "■- / \ / 1965 Norih Pole . A. / n r\ '"-- \, / \ j I V v. 1965 Equotor f\ A V j V-v i i \± i I I ! 10 20 40 50 60 TIME LAG (DAYS) 70 80 90 100 Fig. 2. Autocorrelations of the K-coronal data of Figure 1. The top curve shows the delay times for successive limb passages of strong coronal features at 40 North latitude to be about 30, 60 and 90 days. The maxima at intervals of about 1 5 days in the middle curve are due to high latitude features that were visible in projection over the North pole twice per rotation. The lower curve confirms that there were no dominant recurring K-coronal features at the equatorial latitude during the year 1965, and without such tracers, no rotation period could be found. The middle curves of Figures 1 and 2 are for the North pole in 1965. Around midyear there was a high-latitude feature that was continuously visible during complete solar rotations as it appeared to oscillate east and west over polar latitudes. Thus at the polar position it was observed twice per rotation, projected alternately from the visible and invisible disk, and the resulting autocorrelation shows distinct maxima at intervals of about fifteen days. The lower curves are for the Equator in 1965. There appear to be no pronounced recurring coronal features (Figure 1) and accordingly no strongly preferred periodi- cities in the autocorrelation (Figure 2). Therefore a rotation period is not found for this position for this year. The detailed procedure that was systematically applied for determining rotation periods from the autocorrelation and for assigning confidence limits is described in Appendix A. 138 RICHARD T. HANSEN ET AL . 1 1 — 1 1 1 - D o \ \ o \ xs'- ' K •* - I y'\ »' — o ■ / 7 o / ^ / s i 9 iOIOOSj n -=i=z=r L^_ <^- — _=S^ ~ —=*^— ° '=3=- . s ? 1 » i i i ? i- o 03 •- ■° .2 — *n K) -O c < > -S o cd jr 4) X 0 J= u X! 5 "J u a "5 !d o. n E B) i/i •p U C ^ n u .C u >> > VU u ■~r; 01 £5 On U 03 c r- 43 Id &d <°p/0 3iva NOUBiou *»P/. 3i7d NOIlViOd >» \£> o a_o' is u ■a 3 c '— c _ra "3 0 A J= o (8 IT, s 1< u 0 >> e tl-l o 0 O o 1) 43 > o .2, ■8 2 2 «s .E *op/. 317d NOUffiOU *»P/. 31Vd NOllViOH •n ■*- 3 u-i ♦^ 3 O McARTHUR 1967 » VEMA 1958 • REHOBOTH 1960 X DANA 1928 □ GALATHEA 1952 ■ CARNEGIE 1928 4 ALAMINOS 1967 Figure i. Potential temperature distribution at depths greater than 3000 m and within 200 m of the bottom. Bottom topography is after Chase (1968); shaded areas are less than 2500 m. 1969] 1.00°C 120 2000m 2200- Laird: Temperature in the Panama Basin 1.40 1.60 1.80 2.00 220 357 2400 2600- 2800- 3000- 3200- 3400- 3600 3800- 4000 I I 1 1 1 4 ? L icP sill depth of Panama Basin — g*i - XXD xV X - " D X A *4 - 0 X A 1 3# do - □ X A |+ + 0 D - D 1* T 0 Oo a D \ + 0 - a A* * Q Pacific deepwater X' Penj Basin Q X A Guatemala Basin + Panama Basin (east) D O Panama Basin (west) □ + 1 ' 1 1 1 1 Figure 2. Observed potential temperature in the Panama Basin and adjacent waters. REFERENCES Chase, T. E. 1968. Sea floor topography of the central Pacific Ocean. U. S. Bur. Com. Fish., Cir. 291; 33 PP- Wyrtki, Klaus 1961a. Physical oceanography of the southeast Asian waters. NAGA Report, Vol. 2, University of California, La Jolla; 195 pp. 1 96 1 b. The flow of water into deep-sea basins of the western South Pacific Ocean. Aust. J. mar. freshw. Res., 12: 1-16. Printed in Denmark for the Sears Foundation for Marine Research, Yale University, New Haven, Connecticut, U.S.A. Bianco Lunos Bogtrykkeri A/S, Copenhagen, Denmark Reprinted from Journal of Geophysical Research, Vol. 74, No. 23, 5433-5438. Bottom Current Measurements in the Tasman Sea N. P. Laird and T. V. Ryan Pacific Oceanographic Research Laboratory, ESSA Seattle, Washington 98102 Bottom current velocities of 1 to 9 cm/sec were measured for periods of 0.5 to 1.2 hours at five sites in the Tasman Sea. At four sites a northerly component was present. Bottom photographs indicate stronger currents have occurred at several sites. The results in most cases support previous ideas on flow inferred from water properties. 72 Introduction. Bottom cunent observations have been reported by numerous authors and are summarized by Heezen and Hollister [1964] and Knauss [1965]. No observations have been reported, however, for the Tasman Sea and adjacent areas, although Rochford [1960] and Wyrtki [1961] have inferred flow in this area from water mass analysis and geostrophic cal- culations. In September 1967, five current stations of short duration were occupied between Australia and New Zealand (Figure 1) from the TJSC& GSS Oceanographer. A Geodyne current meter [Richardson et al., 1963], and an EG&G camera were mounted on a frame and lowered to the bottom from the drifting ship [Pratt, 1963]. A pinger with a tilt switch was used to indicate bottom contact and system posture. The cur- rent meter's sensors were approximately 1 meter above the bottom. Treatment of data. Current data from periods during which the system was stationary on the bottom for 5 minutes or longer are sum- marized in Table 1. Directions from the EG&G compass vane were averaged (nearest 5°) from photographs obtained at 8-second intervals. Current direction and speed were calculated from current meter readings and averaged for each series. All tabulated directional data were corrected for magnetic deviation (11° to 15°E). There is generally good agreement between the compass vane and current meter directions except at station 2, series A, where we suspect 'sticking' of the current meter compass. Nu- merous small-scale fluctuations in both speed and direction were evident in the data, but they Copyright © 1969 by the American Geophysical Union. were of smaller magnitude than the changes discussed in the following section. Discussion. Station 1 was located in the Tasman basin, where Wyrtki [1961] postulated that bottom water and deep water spread northward with deep water at the 3000-meter level eventually entering the Coral Sea to the north. The observed current direction changed 15° clockwise and speed increased 1 cm/sec over the period of the record (70 minutes). Bottom photographs at this station revealed ripple marks with a wavelength of about 50 cm, which were nearly parallel to the measured current (Figure 2). These may be longitudinal ripples because some current lineations are pres- ent that appear to parallel the ripples. At station 2, an appreciable difference in speed (4 cm/sec) was found between the two series, but the direction and speed of each series were fairly stable. This difference may be due to a slight change in the location of the system after series A. A photograph at this site (Fig- ure 3) shows coarse sediments, which are indi- cative of active currents. Tidal currents may be strong at this depth, and it is probable that the East Australian current is occasionally present at this site. At station 3 the current direction rotated 45° counterclockwise, and the speed increased from 1 to 4 cm/sec at a fairly constant rate over the period of the record. The speed ap- pears to increase as the direction becomes more parallel to the major trend of the Lord Howe rise. At depths of this observation, and between latitudes 30° and 40°S, is an area in which two branches of antarctic intermediate water mix, and there is no clearly developed circulation [Wyrtki, 1962]. A photograph at this site (Fig- 5433 LAIRD AND RYAN 160° 165° 170° 175" 180° 25°S V5 FT '' j I \ • ■ s o c / / s \ ■ ; , i i ] /' /' / £ ! 8 1 8 ', / .-, 30° 150°E 155" 160° 165° 170" 175° 180° Fig. 1. Bathymetry of the Tasman Sea with station positions. Arrows represent average current direction ; the length of the arrow is proportioned to the speed. ure 4) shows the bottom was disturbed by numerous animal tracks, which indicates sluggish bottom currents. Station 4 was located in the New Caledonia trough. Wyrtki [1961] proposes that water at 3000 meters enters the trough at the northern end and spreads southward, whereas Rochford [1960] suggested that it is filled from the southern end. Our records favor neither con- clusion as we found a constant westerly direc- tion (290°) with speed increasing from near 0 to 1 cm/sec, which suggests that any flow is very sluggish. The sea floor at this station (Figure 5) seems devoid of any active currents. TABLE 1. Summary of Current Measurements in the Tasman Sea Current Direction, °T Depth, Start Duration, Speed, Station Location meters Series (GMT) min cm/sec Geodyne EG&G vane 1 30°57 ,9'S, 155°00 8'E 4572 A Sept. 24, 1967, 0001 GMT 16 5 315 310 B Sept. 24, 1967, 0058 GMT 13 6 330 320 2 31°00'S, 153°18 O'E 336 A Sept. 24, 1967, 1140 GMT 6 8 90 120 B Sept. 24, 1967, 1128 GMT "'.3 4 150 130 :s 33°20 2'S, 163°07.5'E 838 A Sept. 28, 1967, 0202 GMT 32 3 10 360 4 33°29 9'S, 165°03.5'E 2974 A Sept. 28, 1967, 1649 GMT 27 1 290 295 5 33°44 ,7'S, 167°33.6'E 770 A Sept. 29, 1967, 1012 GMT 18 9 5 355 B Sept. 29, 1967. 1044 GMT 10 8 365 365 C Sept. 29, 1967, 1058 GMT 13 9 355 345 Fig. 2. Station 1, rippled muddy bottom in the Tasman basin. Fig. 3. Station 2, coarse sediments on the Australian continental shelf. Fig. 4. Station 3, photograph on Lord Howe rise. Note animal track and worm holes. Fig. 5. Station 4, in New Caledonia trough, abundant animal life. BOTTOM CURRENT IN T ASM AN SEA 543< Fig. 6. Station 5, on Norfolk rise, prominent ripple marks in globigerina sand and possibly an animal burrowed in the sand. At station 5, along the western slope of the Norfolk ridge, the current direction and speed remained fairly constant over 59 minutes. Be- cause this station was also at the level of ant- arctic intermediate water, the fact that speeds here were much higher than at station 3 sug- gests that the topography of the Norfolk ridge has a significant effect on flow. Ripple marks photographed in globigerina sand (Figure 6) were oriented normal to the measured current. The recorded velocities (8-9 cm/sec) do not appear to be competent, however, to produce ripples in this type of sediment [Heezen and Hollister, 1964], and it is suspected that faster currents must exist at times. Conclusion. The Tasman Sea is an area of complex topography, with continental slopes, ridges, basins, and troughs occurring in close proximity. These features probably exert a no- table influence on the circulation pattern. Al- though the duration of these measurements does not allow for the isolation of the tidal effect from the net flow, it may be significant that a north to northwesterly component, paralleling the trend of the topographic features, was ob- served at four of the five stations. A similar correlation between current direction and trend of bathymetric contours has been noted in the western North Atlantic [Heezen et al., 1966]. Acknowledgments. The cooperation of the offi- cers and crew of the USC&GSS Oceanographer is gratefully acknowledged. We are indebted to Ronald Reed and James Stephens for assistance and helpful suggestions in the analysis of the data. References Heezen, B. C, and C. Hollister, Deep sea current evidence from abyssal sediment, Mar. Geoi. 1(2), 141, 1964. Heezen, B. C, C. D. Hollister, and W. F. Ruddi- man, Shaping of the continental rise by deep geostrophic contour currents, Science, 152(3T21). 502, 1966. Knauss, J. A., A technique for measuring deep ocean currents close to the bottom with un- 5438 LAIRD AND RYAN attached current meter, and some preliminary results, /. Mar. Res., 23(3), 237, 1965. Pratt, R. M., Bottom currents on the Blake plateau, Deep-Sea Res., 10, 245, 1963. Richardson, W. S., P. B. Stimson, and C. H. Wilkins, Current measurements from moored buoys, Deep-Sea Res., 10, 369, 1963. Rochford, D. J., Some aspects of the deep circula- tion of the Tasman and Coral seas, Aust. J. Mar. Freshwater Res., 11, 166, 1960. Wyrtki, K., The flow of water into the deep sea basins of the western South Pacific Ocean, Aust. J. Mar. Freshwater Res., 12, 1961. Wyrtki, K., The subsurface water masses in the western South Pacific Ocean, Aust. J. Mar. Freshwater Res., 13, 18, 1962. (Received February 27, 1969; revised May 22, 1969.) 73 Reprinted from Journal of Marine Research, Vol. 27, No. 1, 1-6. SEARS FOUNDATION FOR MARINE RESEARCH Yale University journal of Marine Research Volume 27, Number 1 Long Waves along a Single-step Topography in a Semi-infinite Uniformly Rotating Ocean J. C. Larsen jfoint Tsunami Research kjfort Environmental Science Ser-vices Administration Uni-vcrsity of Hawaii Honolulu, Haivaii ABSTRACT The dispersion equation for Kelvin-type waves tor a single-step topography is derived. Solutions for this equation indicate that, in addition to the Kelvin-type waves, there also exist quasigeostrophic waves that are related to the topography structure. The lunar semidiurnal tide (12.4206 hour period) along the California coast appears to approximate a Kelvin wave since its amplitude is nearly con- stant (0.5 ±O.Oi m) while its phase speed (about 200 m/sec) and direction (north) are consistent with the Kelvin-wave solution (Larsen, 1968). In the present paper it is shown how a single-step topography (corresponding to the shelf off California) influences the modification of the Kelvin-wave solution. Other types of waves are also possible, and these are described. Choose a rectangular coordinate system (#, y, z) such that x is north, y is I. Accepted for publication and submitted to press 8 July 1968. I 'Journal of Marine Research [27,1 west, and z is up, and let the ocean be confined to the space (— co <#< oo, 0 <_y< °°). The linearized equations of motion for long free waves of small amplitude are du . 8C dv , dC (0 and the continuity equation is dt r„M-r,M-- w here £ is the wave height, u and v arc the horizontal particle velocities in the x and y direction, and / is the Coriolis frequency, assumed to be constant. Let the bottom topography consist of a shelf region (o < y < A) of depth hi and of an open-ocean region (A ) of depth hi, and seek solutions of the form C = Z(y)exp[i(kx-wt)] u - U(y) exp p (kx -wt)1 \ (3) v = V{y) exp p {kx - wt)] , where k is the longshore wave number and w is the radian frequency, which is assumed to be always positive. Then, if £v>o Z = a sin (sy) + b cos (sy) for s1 = — v, v < 0 . The boundary conditions require that V vanish at the coast, that Z and hV be continuous at the step, and that the solutions remain finite at infinity (Munlc et al. 1964). Letting the solutions be Zi for the shelf region and Za for the open-ocean region, the boundary conditions require: (i) ilZijdy + (//•/&>) Zi = o for y = o; (ii) Z, = Z2 and hi[d2.lldy + a-/W*)],/a>°. The dispersion relationship is found to be [* - {fklco)] [sr coth (Sl A) - (fklo)-] + (hjh) ft - (/*/a>>] = o, (5) where s\ = k1 - (a>2 ~f2)l(ghi) may be either positive or negative. The roots were found, numerically, for the three following topographies: (i) A = o, /;: = 4.4 km, (ii) A = 80 km, hi = 0.6 km, h2 = 4.4 km, (iii) A = 250 km, /ji = 0.6 km, h2 = 4.4 km. Topography (i) corresponds to a flat ocean depth, topography (ii) corresponds approximately to the shelf and ocean off central California, and topography (iii) corresponds to the ocean ofF southern Cali- fornia with its broad borderland region. The results are presented in Fig. 1, computed for 35°N. For topographies (ii) and (iii), Fig. 1 shows two types of trapped-mode solutions; one solution (K) corresponds closely to the Kelvin- wave solution, the other (G) corresponds to the quasigeostrophic solution (Reid 1958). [The leaky-mode solutions (R), which correspond to reflected- wave solutions, lie above the hyperbola whose right wing is shown as the dotted line in Fig. 1 ; see Leaky Modes below.] The Kelvin-type wave for shelf topography (hi hz) propagate only in the positive x directior in the northern hemisphere. For kA << 1 and fAKghi)11* « 1 , the solutions for topographies (ii) and (iii) approach the Kelvin-wave solution for topography (i), with the dispersion relationship oi\k = (gh2yl2; for fAKghi)'1'}} 1 , the solutions ap- proach the Kelvin-wave solution for an ocean of uniform depth, hi, with the dispersion relationship (ojk = (ghj*12. The quasigeostrophic waves have relatively lower frequencies and higher wave numbers. Thus an approximate expression for the dispersion relationship for these waves can be obtained by letting P » (a>2 -f2)l(ghi) , with the result thai Si*sk and jz^U|. Then the dispersion relationship becomes coth (kA) = (flat) [1 - A./AJ - (|*|/*) fa/Aa). This puts an upper limit on the frequency, co < f\hz — hi\j(hz + hi), a result that depends only on the absolute sum and the difference of the step. For kA « 1 and hi<=xhz, the longshore pnase velocity is approximately co/k = /A (1 —hijhx). The waves are then nondispersive and have speeds that are de- Journal of Marine Research IW .0005 CYCLES -| i i p i | .0010 .0015 PER KILOMETER Fitrure i. Diagnostic diagram for single-step topography. Plotted is frequency versus longshore wave number in the positive x direction. Reflected-wave solutions, R, lie above the dotted line. The Kelvin-type solutions are AT and the quasigeostrophic solutions are G. The width of the shelf is noted; the depth of the shelf is 0.6 km while the offshore depth is 4.4 km. The Coriolis frequency, f, is noted with a value appropriate to 35°N. pendent on the width of the shelf as well as on the magnitude of the step. For a shelf topography (hi h2), the waves propagate in the negative * direction. For a flat topography (hi = A2), these waves do not exist. For an infinitely wide shelf (A = °o), coth (kA) = I . Then the dispersion relationship becomes co =/| hz - hi \l(ht +hi). This equation has been derived by Longuet- Higgins (1968), who studied in detail the trapping of waves along a discon- tinuity of depth in an unbounded ocean. (The waves labeled in his paper as the "double Kelvin wave" or "seascarp" wave appear to correspond, in the limit A = 00, to what is labeled here as the quasigeostrophic wave.) The ratio of the components of the water motion for both types of waves in the open ocean (y~> A) is VJU = -i((DSi- kf)l(fsz - k co) . For shelf topography, kfjcoo. This mode corre- sponds closely to the re fleeted- wave solution for an ocean of uniform depth. The dispersion relationship is found to be [xs tan (Si A + 6) - (Pico)] [x, coth (xx A) - (/*/»)] + (ht/ht) ft - - C/WJ = 0, U where s* = k2 - (or —f^Kghi) may be either positive or negative. Discrete solutions, in terms of the longshore wave number i, do not occur, but the ratio of coastal amplitude over incident amplitude could be contoured (Munk et al. 1964); this has not been attempted here. The low-frequency cut-off is a>* = f1+ghiP-> which, in Fig. 1, is the dotted hyperbola above which the leakv modes lie. REFERENCES Isaacs, John, Joseph Reid, George Schick, and Richard Schwartzlose 1966. Near-bottom currents measured in 4 kilometers depth off the Baja California coast. J. geophys. Res., 71: 4297-4303. Larsen, J. C. 1968. Electric and magnetic fields induced by deep sea tides. Geophys. J. R. astr. Soc, 16: 47-70. 74 Reprinted from Journal of Geophysical Research, Vol. 74, No. 13, 3408-3414. Heat Transfer in the Top Millimeter of the Ocean E. D. McAlister and William McLeish1 Scripps Institution of Oceanography, University oj California, San Diego La Jolla, California 92037 Different mechanisms of heat transfer to the ocean surface dominate within different depth regions. Under suitable weather conditions, radiation dominates within the upper micron of depth. Turbulence is dominant at greater depths, but the evidence indicates that, with wind speeds less than 10 m/sec, it dominates only at depths greater than 0.5 mm. A region in which heat is transferred almost entirely by conduction lies between. Radiometric measurements of the total heat flow to the ocean surface may be made in this region. Introduction The mechanisms of heat transfer in the top millimeter of the ocean are not well known, partly because of the experimental difficulties in obtaining temperature measurements in this region and partly because of the theoretical problems in predicting properties of the water near a wind-disturbed wavy surface. Neumann and Pierson [1966] emphasize that this region has not been studied adequately. However, the temperature profile through this region is criti- cal to important areas of current research. It introduces a significant difference between the bulk water temperature and the airborne or satellite infrared radiometric readings of sea surface temperature [Saunders, 1967]. Further- more, a knowledge of the mechanisms of heat transfer is necessary for interpretation of the readings of an infrared radiometer developed in this laboratory to measure the heat flow to the ocean surface through measurement of water temperature at two different depths [McAlister, 1964, 1967]. The present paper is a compila- tion of results of various studies that examine the different mechanisms. Through these re- sults rough quantitative estimates of the tem- perature profile and of its influence on the ra- diation emitted from the ocean are found. Thus, a basis for the calculation of heat flow from radiation measurements is provided. 1 Now at ESSA Atlantic Oceanographic Labora- tories, Sea-Air Interaction Laboratory, Miami, Florida 33130. Copyright © 1969 by the American Geophysical Union. Heat within the ocean is transferred to the surface through turbulence, conduction, and radiation. Turbulence tends to produce an ap- proximately logarithmic temperature profile, and conduction gives a linear one, whereas ra- diation from the ocean gives a decrease in tem- perature gradient (Figure 1). Direct laboratory measurements of the mean temperatures in the upper few millimeters beneath smooth water surfaces have shown a region of linear profiles such as given by conduction [Haussler, 1956]. However, these experiments apparently had not allowed the formation of wind-induced turbu- lence in the water, and Timofeev [1966] sug- gested that the conduction region does not ex- ist in the ocean with appreciable wind speeds. KanwisJier [1963] in laboratory experiments on gas exchange rates between air and water showed the existence of a lamellar diffusion layer at the water surface under moderate wind speeds (his Figure 4, p. 202). Several investi- gators have hypothesized the existence of this region [e.g., Saunders, 1967], and McAlister [1964] showed it to be present with light winds. We know of no observation demonstrating its existence in the ocean under a moderate wind. Without the present calculations it is conceiv- able that the regions with significant radiation and turbulent transfer could merge. The pres- ent studies provide additional evidence that the conduction region exists and give estimates of its minimum thickness. Radiation The influence on the temperature profile of the nighttime exchange of infrared radiation be- 3408 HEAT TRANSFER IN THE OCEAN 3409 RADIATION TURBULENCE Fig. 1. Schematic representation of temperature profile near the sea surface. tween the sky and the water beneath the ocean surface is estimated through sample numerical calculations. In these calculations, the sky is assumed to be a blackbody having a constant temperature, so that the influence of the at- mosphere in modifying radiation intensities at different wavelengths and from different direc- tions is ignored. The effect of waves in changing the field of view of a surface element is con- sidered to have a negligible effect on the mean temperature profile, and the influence on this profile of the alternate surface convergence and divergence induced by waves is also small [O'Brien, 1967]. In an investigation begun in this laboratory, Lick [1965] examined transient effects on the temperature profile of a radiating and conducting medium. Such effects can be neglected in the present problem. Calculations in the next section indicate that turbulence is not significant in this region. The radiational transfer of heat from one level to another within the water is negligible in comparison with the transfer by conduction and the radia- tional exchange with the sky. Also, the varia- tion in temperature of the water within the radiation exchange region is small when com- pared with the temperature difference between the water and the sky. With these conditions, the radiational heat exchange with the sky through any level is just that for the transfer between two parallel plates, attenuated by the intervening water: ?„..(*) = 2tt f [B,(T„) - Bt(T.)]E3(k,z) dv (1) where BV{T) is Planck's function and the ex- ponential integral E3(kyz) represents the at- tenuation of diffuse radiation by the water above the level [Goulard and Goulard, I960]. The temperature gradient is given by the con- ductive heat flow Hc(z) = 5 dT/dz (2) and, since the total heat flow is constant with depth, A ~ 8{Ht ?net(z)) (3) Substituting (1) into (3) and integrating, we have the temperature profile T(z) = T0 + HTz 2tt o Jo •> 0 [B,(TW) - B,(T.)]E3(k,z) dv dz (4) For convenience of introduction into a com- puter, the kernel % exp (—3krz/2) was sub- stituted for Es(k„z) [see Lick, 1965]. Values of k, were derived from Plyler and Acquista [1954]. Observations at sea with a total-wave- length net radiometer and a 7- to 12-ju, radiation thermometer indicated that, with a clear sky, T, was at times as low as 0°C. Calculations of T{z) using values of T, near this value and T(0) =: 15°C showed little influence of radia- tion on the temperature profile. An extremely low value of T. of — 20° C led to a departure of the temperature profile from a linear one of only 0.0015°C at the surface. Thus the over-all temperature changes resulting directly from emitted radiation are small. The distribution with depth of radiation and conductive heat flow was examined in further calculations by using (1). A value of 0.34 cal/cm'/min was taken for HT, in accord with the maximum value reported by McAUster 3410 McALISTER AND McLEISH TURBULENCE J — I — I I I I I L_L 500/j 0 0.5 i.o Fraction of heat transport Fig. 2. Mechanisms of heat transport to the sea surface at different depths. [1964], and T, = -20°C, so that the radia- tional heat transfer at the surface was 63% of the total. Figure 2 shows the fraction of trans- port by radiation as a function of depth. Ra- diation may be negligible at any depth, but even with an extremely cold sky it would gen- erally constitute less than 10% of the total heat flow at depths greater than 10 p.. The above calculations were completed in 1964; since then the compilation of optical properties of water by Irvine and Pollack [1968] has become available. They presented absorption coefficients that are significantly smaller in the 12- to 20-/x region than were used above. An approximate recalculation of the radiation curve in Figure 2 has been performed with these data and an infrared slide rule. The sky temperature for wavelengths shorter than 15 p. was taken to be — 20 °C, as before, but for longer wavelengths a sky temperature of 10°C was assumed in order partially to repre- sent atmospheric emission. Sky radiation in these longer wavelengths is largely emitted from the lower atmosphere, where the tempera- ture is seldom much below the water tempera- ture. The recalculated values, shown by solid dots in Figure 2, show a profile similar in shape to the previous one. Changes in the wave- length distribution of sky radiation appear to have only a limited effect on the shape of the heat transfer profile. Although the total solar radiation reaching the sea surface is at times much greater than the total heat loss, calculations based on the values of Irvine and Pollack indicate that only about 10% of it is absorbed within the upper 1 mm. Thus, even when the insolation is 2-3 times as great as the heat loss, there is only a small departure from a linear temperature pro- file. Tt/kbtjlence The water near the ocean surface is com- monly in turbulent motion induced either by .vind (forced turDulence) or by gravitatioual instability resulting from evaporation and sur- face cooling (free turbulence,). Haussler [1956] measured the mean temperature profile beneath a laboratory water surface where gravitational instability appeared to be responsible for the turbulence. The mean profile with rates of heat loss comparable with the values at sea was linear to depths of 1-2 mm. A theoretical cal culation by J. Pierce (1962, unpublished report in this laboratory) is in accord with Haussler's profile. These measurements indicate that at sufficiently low wind speeds and rates )i heat loss turbulence is not dominant in the heat transfer in the upper 1 mm. At higher wind speeds, however, forced turbulent transfer can become dominant within some of this region, and the present effort is directed to estimating extent. This estimate is made through an ex- amination of the temperature profile and eola- tion 2. It was observed by McLeish [1967] that the initiation of wind-driven turbulence in the water near the surface was always accom- panied by the formation of steep capillary waves, and a direct measurement of the tem- perature profile near the surface under these conditions would appear to be difficult. A lim- iting form of the temperature profile may, how- ever, be estimated by an indirect method, in which the temperature profile at a solid bound- ary expected for a given surface stress is de- termined. There is evidence that the linear re- gion extends at least as deep into the fluid at a free surface as at a solid boundary on which the surface stress is equal to the wind stress on HEAT TRANSFER IN THE OCEAN 3411 the water. The disruption of the surface by whitecaps is not considered here. Stresses on the water at wind speeds of 2- 10 m/sec have been estimated from empirical relationships. The temperature profiles corre- sponding to these stresses for a given rate of heat flow at a solid boundary were calculated from the 'universal' temperature profile of Deissler [1955]. The profile for 2 m/sec is similar to the profile derived by Pierce, but the profile for 10 m/sec remains linear only to about 0.4 mm. The no wind (Pierce) and 10- m/sec temperature profiles were transformed into heat transfer profiles with equation 2 and are presented in Figure 2. The evidence that the conductive region ex- tends deeper at a free boundary than at a solid one with the same totai stress is derived from measurements of the velocity profile near the water surface. Techniques given by Schraub et al. [1964] were used to produce lines of small hydrogen bubbles in the water by intermittent electrolysis along a thin vertical wire extending through the surface of the water in a laboratory wind-water tunnel. The lines of bubbles were carried downstream by the current, and side- view cine photographs recorded their positions to indicate watei speeds. The mean current near the surface increased with the length of time that the air had been flowing, but the mean shear at any level within the upper cen- timeter soon attained a nearly steady state. Figure 3 shows the average of twenty-five sets of velocity readings at different fixed dis- tances beneath the mean water level, denoted by open circles. The air speed was 6 m/sec and the fetch was 1 meter. This fetch was sufficient for the development of small-scale waves and turbulence that appeared to be similar to the conditions in the ocean. The velocities at fixed distances near the surface could not be de- termined because of the waves, and a second series of measurements near the surface was obtained in which the depths were measured from the instantaneous position of the water surface in each photograph. The two methods of measurement were somewhat different; the deeper measurements were made of the dis- tances between bubble lines, whereas the near- surface measurements had to be made of the distance from the wire that a bubble line crav- eled in a known number of cine frames. The latter values were about 20% less in the region of overlap, presumably because of the slower flow in the wake of the wire [Schraub et al., 1964]. These values were corrected by this amount and are denoted by solid dots in the figure. The wind stress for the measured air speed in that experiment was estimated as 0.4 dyne/cm2. A velocity profile for a solid bound- ary at this stress was derived from Deissler's profile and fitted to the measurements in tne lower portion of the region (the solid line in Figure 3). This curve differs markedly from the measurements nearer to the surface. A velocity profile for a stress of 0.1 dyne/cm* (dashed line) fits the measurements more closely. Possibly much of the momentum trans- ported vertically from the air to the water, representing the stress of 0.4 dyne/cm2, passes into the waves through pressure variations in- stead of into surface currents through viscosity [Stewart, 1961, and personal communication, 1968]. If so, a given wind speed produces less shear stress in the water at the surface than assumed in these calculations. Since the thick- nesses of both the viscous and the conduction regions are expected to vary in an inverse man- ner with the shear stress, the conduction region 0.4 £ u HI u (cm/sec) Fig. 3. Velocity profile in the top centimeter of water under a 6-m/sec wind. 3412 McALISTER AND McLEISH at a wind speed of 10 m/sec should extend deeper than shown in Figure 2. The diffusion to the surface of dissolved gases and other materials would also be in- hibited by this factor. Conduction The depth region in which conduction is dominant has an especial significance to infra- red radiometric measurements of the ocean since this region is largely responsible for the temperature difference between the surface and the bulk water and since it forms the basis for radiometric heat flow measurements. Con- versely, it is also a region that can be studied with infrared radiometers. In particular, a heat flow radiometer has demonstrated the existence of this layer under some conditions found in the ocean. A radiometer measuring tempera- tures at effective depths of 75 and 500 /i. ob- tained values of heat flow to the ocean surface with 2- to 3-m/sec winds that averaged within 20% of the value obtained from empirical formulas [McAlister, 1964]. The turbulence near the ocean surface dur- ing the radiometric measurement might have been produced by gravitational instability rather than by the wind at these low speeds. A series of laboratory experiments has shown, however, that a conductive layer exists at higher wind speeds with wind-driven turbulence similar to that at sea. An air flow of 4.5 m/sec was passed over a 70 X 220 X 4 cm labora- tory water surface. Three distinct regions of the water surface could be distinguished: a smooth upwind region containing small-ampli- tude regular waves; a rough central region containing steep, irregular capillary and grav- ity waves; and a slick at the downwind end. Wind-driven turbulence began at the upwind end of the rough region and continued into the slick. The water container was insulated from heat loss, and the water was maintamea at an approximately constant temperature with electrical heaters. The electrical power input, corrected for small rates of change of the water temperature, represented the total heat flow through the water surface. A different infrared radiometer than mentioned above, measuring temperatures at 25- and 75-fi effective depths, recorded the heat flow through the three dis- tinct regions of the surface in separate experi- ments. A description of this instrument will ap- pear in a separate publication. Table 1 shows the experimental conditions and the results of these measurements. The de- crease in the heat flow with increasing fetch is attributed to the development of a warm, moist boundary layer in the air. An abrupt change in the temperature near the surface at the be- ginning of the slick is illustrated by the in- creased difference between the temperature of the bulk water and that at 25-/z depth. This increase is attributed to a reduction in the turbulence beneath the slick resulting from the rigidity of the slick. The heat flow to the entire surface was obtained from the radiometric measurements with the assumption that the heat flow was constant within each region. The radiometric measurement of heat flow was 93% of the input heat flow. The difference could be ascribed to errors in the experiments. Thus, in TABLE 1. Measurement of Heat Flow through Different Regions of a Water Surface Smooth Rough Slick Fetch distance, cm Air temperature, °C Wet-bulb temperature, °C Bulk water temperature, °C Radiometer distance, cm Temperature at 75-ft depth, °C Temperature at 25-fi depth, °C Temperature difference, bulk water — 25-jt depth, °C Radiometric heat flow, cal/cm'/min Total heat flow, cal/cm'/min Ratio 0-70 70-160 160-220 17.4 17.1 16.8 11.1 11.0 10.7 31.4 31.3 32.7 20 110 180 30.48(3) 30.21(8) 30.44(9) 30.35(4) 30.11(4) 30.36(4) 1.0 1.2 2.3 2.27 1.83 1.50 1.96 1.96 2.28 1.16 0.93 0.66 HEAT TRANSFER IN THE OCEAN 3413 h T ok •05 .11 11 1 .11 .1 .06 04 :: : — V ill : • ■ " i A ; : t 1 III -r ! £ ":':•' * : 1 1 30.5 './ j ' — *. ! - !' .1 Depth 25 M ■ i lit ' : \ 1 — ? — ft" • i / "" .i ■— 1 — - — \ 1 / j "- ■ K1 ; -;- 1 _ i ■ : ! ' - rHT i • : =1 0.0 - "I 1 . ~ ££l 1 . 1 No ft "t r 1 S m/spr — — ■ — i H h_l— •» — rfrr — jw— 1 1 .... No air flow j '■■::- :•::: ~-r .. -1 ! ! Mi - i ■ )--- j : . : - I * |:'i""|Nl/f '■■ \ — f— ~1" T .] 5A C \W* *?s ■ i |: j I j . | - : ' A. l : l r L Li ;\ .'::'■ | 4 Depth 75 M ! 1 ■' P:l M : \ . :::■ -\ L, , , -, .,- , ■ r : -,V. I ^0.0 ± .1 . :■.:: M± ifeli .I — i— j ^3E_, ... ... ...... j I 1 , ..,.».... ' I: lp :.: i , — ^fm — — | — 1 — t™ ; 1 1 i J . . . ! . i . 'T . i j i jty . r Time Fig. 4. (sec) 0 60 120 Two-wavelength radiometer measurements from a laboratory water surface when an air flow is started and stopped. The heat flow is proportional to AT. spite of the wind-driven turbulence and a heat flow several times larger than that commonly occurring in the ocean, the conductive layer was adequately thick for the radiometric measure- ment of heat flow. Some relationships between the conductive and the turbulent mechanisms of heat transport are illustrated by radiometric measurements of heat flow in laboratory experiments in which the air flow is started and stopped (Figure 4). The results are interpreted in terms of the structure of the flow near the surface. In these experiments, the air temperature was lower than the water temperature, so that heat was being transferred from the water. The radiom- eter viewed the 'rough' portion of the surface. The surface temperature decreased rapidly when the air flow was started. This cooling was associated with the development of a nearly laminar flow near the surface. However, the surface temperature rose rapidly when the steep waves and wind-driven turbulence ap- peared, then remained nearly constant. (Kan- wisher [1963] observed a decrease in the thick- ness of the lamellar layer occurring at the onset of capillary waves.) The heat flow was small without air flow and larger during the steady air flow. When the air flow was stopped, the heat removal from the water was seen to be decreased, and the surface temperature rose slightly. With the decay of the wind-driven turbulence in the water, however, the surface again became cooler and the heat flow decreased further. Later, the electrical heaters caused the surface water temperature to rise again. Thus the heat flow and the surface temperature show a close relationship to the air flow and to the state of turbulence in the water near the sur- face. Limiting temperature profiles derived from the previous sections may be used to predict some ranges of conditions under which an in- frared radiometer can measure the heat flow to a water surface. Radiation with wavelengths 3414 McALISTER AND McLEISH near 2.2, 3.8, and 4.S /x with effective depths near 500, 75, and 25 /x has been used in such measurements. Clearly the transfer of heat by radiation from near the surface will have negli- gible influence on the measurement, but the turbulent transfer of heat may be significant. Calculations of the errors in heat flow measure- ments with wavelengths giving 75- and 500-/x effective depths have been made for different intensities of turbulence near the surface. With the approximation of a linear relationship be- tween intensity of radiation and temperature over the small range of temperature near the surface, BV{T) - BV{T0) = a{T - T0) (5) the intensity of radiation within a narrow band- width received by a radiometer is I, = akv I T(z) exp ( — kvz) dz Jo - aT0 + B,(T0) (6) and the temperature read by the radiometer is TT = k, f T(z) exp(-£,z) dz (7) The expected reading for each of the two wave- lengths with a given temperature profile was calculated by a computer summation, and the expected error in a heat flow measurement was determined. Temperature profiles taken from Deissler [1955] with stresses expected for wind speeds of 2, 3.5, 5, and 10 m/sec gave predicted errors of 0, 0, 14, and 35%, respectively, with the 75- and 500-//. effective depths. If the con- duction layer were no thicker than that at a solid boundary with the same total stress, these results would indicate that either the 500-;u ef- fective depth infrared region should not be used with wind speeds of 5 m/sec or more, or else a correction factor based on the wind speed should be applied. No significant error from turbulence would be expected at these wind speeds with a radiometer using effective depths of 25 and 75 /x. Acknowledgments. We are indebted to R. W. Stewart for advice in the interpretation of the velocity profile. R. C. Steinbach wrote the com- puter programs, and J. Cook assisted in the measurement of the velocity profile. This research was supported by the Office of Naval Research, codes 461 and 481 ; Naval Oceanographic Office, code 7007; and National Science Foundation, Atmospheric Sciences Sec- tion, grants GA-854 and GA-1491. References Deissler, R. G., Analysis of turbulent heat trans- fer, mass transfer, and friction in smooth tubes at high Prandtl and Schmidt numbers, NACA Rept. 1210, 14 pp., 1955. Goulard, R., and M. Goulard, One-dimensional energy transfer in radiant media, Intern. J. Heat Mass Transfer, 1, 81-91, 1960. Haussler, I. W., tjber die temperaturprofile beid- erseits einer verdunstenden wasseroberflache, Wiss. Z. Tech. Hochsch. Dresden, 5, 435-450, 1956. Irvine, W. M., and J. B. Pollack.. Infrared optical properties of water and ice spheres, Icarus, 8(2), 324-360, 1968. Kanwisher, J., On the exchange of gases between the atmosphere and the sea, Deep-Sea Res., 10, 195-207, 1963. Lick, W., Transient energy transfer by radiation and conduction, Intern. J. Heat Mass Transfer, 8, 119-127, 1965. McAlister, E. D., Infrared optical techniques ap- plied to oceanography, 1, Measurement of total heat flow from the sea surface, Appl. Optics, 8(5), 609-612, 1964. McAlister, E. D., Using infrared to measure heat flow from the sea, Ocean Ind., 2(5), 35-39, 1967. McLeish, W. L., On the mechanism of wind-slick generation, Ph.D. thesis, University of Washing- ton, Seattle, 1967. Neumann, G., and W. J. Pierson, Principles of Physical Oceanography, pp. 255 and 421, Pren- tice-Hall, Englewood Cliffs, N. J., 1966. O'Brien, E., On the flux of heat through laminar wavy liquid layers, J. Fluid Mech., 28, 295-303, 1967. Plyler, E. K., and N. Acquista, Infrared absorp- tion of liquid water from 2 to 42 microns, J. Opt. Soc. Am., 44(6), 505, 1954. Saunders, P. M., The temperature at the ocean- air interface, J. Atmospheric Sci., 24, 269-273, 1967. Schraub, F. A., S. J. Kline, J. Henry, P. W. Run- stadler, Jr., and A. Littel, Use of hydrogen bubbles for quantitative determination of time dependent velocity fields in low speed water flows, Thermosciences Division, Department of Mech. Engineering, Stanford University, 1964. Stewart, R. W., The wave drag of wind over water, J. Fluid Mech., 10, 189-194, 1961. Timofeev, Yu. M., Thermal sounding of surface water layers by means of thermal radiation, Izv. Atmospheric Oceanic Phys., 2(7), 772-774 (translated by F. Goodspeed), 1966. (Received August 5, 1968; revised January 27, 1969.) Reprinted from "Oceans from Space," 75 Gulf Publishing Co., Houston, Texas, 38-45. 3. The potential application of remote sensing to selected ocean circulation problems Raymond M. Nelson, General Physical Scientist, Institute for Ocean- ography, Environmental Science Services Administration. Introduction As part of its mission, Environmental Science Services Administration (ESSA) has the long-term problem of monitoring the ocean and the related physical environment. Its purpose is to understand the physical processes and improve prediction techniques so that it can enhance its existing scientific services and anticipate new ones, emphasizing the prob- lem of environmental hazards. It is obvious that to do this job, all facets of oceanography will have to advance on a broad front, such as the development of new tools, the inception of new ideas, the refinement and broadening of the various theories, and a worldwide continuous measure- ment program. We believe in an integrated program of coordinated data collection, using each tool where it can perform best, applying as many parameters and dimensions as appropriate. A major part of this problem is ocean circulation, and we look forward to the prospect of using air/space as a surveillance and data collection medium. Therefore, ESSA is experimenting with remote sensing (in addition to many other techniques) as an additional method to apply to the various problems. Stommel,9 McAlister,4 Gifford Ewing3 and others have pio- neered in applying aerial photography and airborne infrared radiation devices to oceanography. This work has been continued by many, both in and out of government. We are interested in aircraft and spacecraft capa- bility, but at present we are in the experimentation and problem defining stage, exploring potential usage. 38 Another phase of remote data collection is the interrogation of buoys from air or space, where the buoys are either stationary, or free floating, such as surface and subsurface types. Although ESSA is interested in all phases of such instrument application, this chapter is confined to poten- tial usage of remote sensing to certain aspects of ocean currents and circulation problems. An examination of Nimbus 2 high resolution infrared (HRIR) line scan Nimbus 2 imagery imagery shows that high thermal contrasts on the water surface are dis- cernible. Nimbus 2 was designed to be a meteorological satellite, and since the ground spot size is approximately 23 miles,6 any data about the water surface is a distinct bonus. Allison, Foshee, and Warnecke at NASA, Goddard, and Wilkerson at the Naval Oceanographic Office1 collaborated on determining water surface temperatures from such data. Although the problems of clouds and radiation transmission losses are obvious, the Nimbus 2 HRIR imagery as compared with correlated ESSA satellite photography shows periods of cloudless skies off the east coast of the United States where the high contrast, thermal surface and boundary of the Gulf Stream can be detected, and point temperature distributions could be measured between clouds. Time-sequence analyses of such quasi- synoptic coverage over large areas of the ocean could show surface thermal drift, possibly boundary regions for currents, and may reveal previously undisclosed surface circulation effects. For example. Figure 3-1 A is an ESSA-1 television picture of the east coast of the United States and was exposed at 17:38Z (Z represents Greenwich Civil Time) on June 2, 1966. Figure 3- IB, a Nimbus 2 HRIR photograph, was exposed at 04:26Z (night), June 3, 1966, 1 1 hours after the ESSA-1 photograph. The front line appears to have moved farther east on the infrared photograph, and some cloud patterns, imaged near the coast on the ESSA-1 photograph, are not discernible on the Nimbus exposure. Aircraft coverage at the time of this Nimbus orbit proved that the local sky was free of clouds. The surface effects of another western boundary current are also dis- cernible. Figures 3-2A and B are two Nimbus 2 HRIR images of the extension of the Agulhas Current (see arrows) south of the Cape of Good Hope, Africa. Figure 3-2A was exposed September 18, 1966 at night, and Figure 3-2B the next night. An example of Nimbus 2 HRIR daylight effects are provided in the next series of illustrations. Figure 3-3A, B, and C are ESSA-1 television pictures exposed May 24, 1966. Figure 3-3A and B at approximately 17-55Z, Figure 3-3C at 16:17Z (day). Figure 3D is a Nimbus 2 HRIR photograph collected on the same date at approximately 14:57Z (day). An imagery comparison shows similar cloud patterns. If the boundary lines and the possible warm cell (arrows on Figure 3-3D) are really water surface effects (the ESSA-1 photographs are remarkably free of clouds in 39 Figure 3-1 A: t'SSA-1 television photo of U.S. east coast and adjacent waters of Atlantic Ocean. these areas), we would like to have ships and buoys out there monitoring such effects in depth. However, this kind of comparison when no ground check is available, indicates a need for multiple simultaneous sensors to re- duce the problem of ambiguity. Meteorological thermal discontinuities have been collected in a vis- ually transparent atmosphere with airborne infrared systems, causing an ambiguity in attempts to analyze the water surface. Oshiver, et al,7 in an aircraft/ship experiment with infrared radiometers and meteorological data collectors over continental shelf water southeast of New York City, discovered a low altitude visually transparent atmospheric lens that cre- ated a sharp discontinuity in the data from the airborne radiometer. This discontinuity was not observed with a similar radiometer mounted over the bow of the ship. The discontinuity was identified as a lens from infor- mation supplied by meteorological instruments attached to a captive balloon as it was raised and lowered from the ship. Similarly. Clark2 at the U. S. Naval Research Laboratory used airborne infrared radiometers to re- cord and assemble a statistical history of low altitude visually transparent convection cells over north Atlantic and Gulf Stream water. The apparent temperature discontinuities of such cells are no more than approximately 1° C, and the horizontal dimensions range from 1-10 miles. In addition to such low altitude phenomena, there are other effects, such as small cloud patches, haze, and thin stratus and cirrus cloud pat- terns, within the noise level of existing ESSA and Nimbus satellite television camera systems. Such phenomena cannot be resolved on Nimbus 2 HRIR data, on either day or night exposures. Many theories of the Gulf Stream hold that meanders can be expected almost anywhere. Therefore, high spatial resolution, multi-sensor surveil- 40 Figure 3-1B: Nimbus 2 high resolution infrared photo of U.S. east coast and gulf stream. Figure 3-2 A: Nimbus 2 photo off the southern tip of the Cape of Good Hope, Africa. Arrows show extension of Agulhas Current. Figure 3-2B: Nimbus 2 photo off the southern tip of the Cape of Good Hope, Africa. Exposure about 24 hours after Figure 3-2 A. 41 Figure 3-3 A (left): ESS A- 1 television photo of area off the U.S. east coast. Figure 3-3 B (right): ESSA-1 television photo of area south of Nova Scotia. lance systems, including microwave with a cloud penetration capability, are necessary to detect meanders, at which time ships and aircraft could be sent to monitor them in greater detail. Information from both satellite and aircraft may contribute to reducing the ambiguity of interpretation of both remote sensing and ship recorded data. A time-sequence analysis of the evolutionary pattern could show the rate and size of growth, and the pinching off into an eddy, and decay. In time, we would like to predict the development, location, and size of meanders, as well as their like- lihood of invading the banks and the fishing grounds. We would also like to know if meander dynamics are the same for the right as for the left side of the Gulf Stream. Time-sequence charting of surface currents boundaries, as to shape, size, and location, will be another element toward understanding the total dynamics, in addition to providing data for the shipping industry. The interface of the Gulf Stream with the Labrador current and the trans- mission into the North Atlantic current are particularly interesting. The capability of an aircraft infrared line scan system to detect an ocean eddy is illustrated in Figure 3-4. After detecting an eddy, a ship can make surface and subsurface profile passes at the same time an aircraft collects such imagery. Thermal profiles generated from microdensitometer cans across the image can be correlated with a ship-towed surface ther- mistor for calibration and comparison. Time-sequencing by the aircraft. such as at 15-20 minute intervals, could reveal the motion within the eddy, assuming the eddy shape effects are maintained and move during the time period. From short-time-sequence data collection by both ship and aircraft, information on eddy motion and its three dimensional size and shape could be obtained, and probably reduce ambiguity of data in- terpretation. Longer time-sequencing could show changes in position, si/e. and shape. Figure 3-3C (left): ESSA-1 television photo south and east of Newfoundland. Figure 3-3D (right): Nimbus 2 photo of north Atlantic south of New England, Nova Scotia and Newfoundland. Figure 3-4: Taken 200 miles east of Cape Cod, this photo clearly illustrates the capability of an aircraft infrared line scan system to detect an ocean eddy. Figure 3-5, is an aircraft color photo of an eddy in the Caribbean, north of St. John, Virgin Islands. Again a time sequencing of 10-15 min- utes between photographs may reveal eddy motion. An additional goal with aircraft sensors is to examine the complex structure of eddy mixing, as well as boundary current interfaces with other water masses. In some areas, such effects as eddies, meanders, and major changes in current direction will require a continuous surveillance capability just to 43 Figure 3-5: Aircraft photo of an eddy in the Caribbean, north of St. John, Virgin Islands. find them. Space sensors will do yeoman's work in this regard, but aircraft systems will also have their place. Plans for What are ESSA's plans for the near future? First, aircraft/ship experimen- the future tation programs will continue. Then in 1969, the ESSA Barbados Oceanographic and Meteorological Experiment will take place during the summer, covering a part of the eastern Caribbean and a small section of the Atlantic due east of the Antilles arc. Present plans are to use sensors ranging in heights from satellite altitudes down to the sea floor. The experiment is designed to serve as a pilot field study for the Global Atmospheric Research Program (GARP) of the World Weather Watch. Later, in the early 70's, the Tropical Meteorological Experiment (Tromex) is scheduled, and some consideration is being given to expanding it to a Tropical Environmental Experiment. In FY 1971, the satellite systems Im- proved TOS N and O and Advanced Polar Orbiting Satellites (APOS) A and B may carry laser altimeters for determining variations of sea level for geodetic purposes. 44 The distant future, however, is more nebulous. For example, since the cost of keeping aircraft in the air is extremely high, we have considered the concept of "aircraft of opportunity" as a possible means of reducing such long-term costs. Many airlines run over the oceans on daily schedules, both night and day. The possibility of equipping such aircraft with sensors where all the commercial pilot has to do is flip a few switches to turn them on and off has a certain amount of merit. However, the ocean is an international problem, and to exploit the global surveillance capability of spacecraft will require international co- operation, possibly under a central cooperative control, where as auto- mated data are displayed and critical changes in meteorological and oceanographic effects or patterns are detected aircraft and ships in the area can be sent to monitor a region in greater detail. It is understood that the problems are many, and industry's scientific effort is needed just as much as its tools. There is a long way to go, but we feel that a start has been made. 1. Allison, L. J., L. L. Foshee, G. Warnecke, and J. C. Wilkerson, 1966: "An Analysis References of the North Wall of the Gulf Stream Utilizing Nimbus 2 High Resolution Infrared Measurements," Gulf Stream Symposium, Am. Geophysical Union, April 1 7-2 1 . 2. Clark, H., 1967: (Private Communication), U. S. Naval Research Laboratory, Ap- plied Oceanography Branch, Washington, D.C., "Clear Air Convection Cells," March. 3. Ewing, Dr. G. C, 1966: "The Use of Film as a Sensor," Minutes of the Fourth Meeting Ad Hoc Spacecraft Oceanography Advisory Group, Spacecraft Ocean- ography Project, U. S. Naval Oceanographic Office, October 18-19, p. 12. 4. McAlister, E. D., 1964: "Infrared-Optical Techniques Applied to Oceanography: 1 Measurement of Total Heat Flow from the Sea Surface," Applied Optics, 3, pp. 609-612. 5. McAlister, E. D. and W. L. McLeish, 1965: "Oceanographic Measurements with Airborne Infrared Equipment and Their Limitations," Oceanography from Space, Woods Hole Oceanographic Institution, Woods Hole, Mass., pp. 189-214. 6. NASA, Goddard Space Flight Center, (Private Communication). 7. Oshiver, A. H., G. A. Berberian, J. R. Clark and R. B. Stone, 1965: "Factors in Measurement of Absolute Sea Surface Temperature by Infrared Radiometry," Pro- ceedings of the Third Symposium on Remote Sensing, Univ. of Mich., Ann Arbor, pp. 737-762. 8. Smith, G., 1963: "Color - A New Dimension in Photogrammetry," Photogram- metric Engineering, Nov. 1963, Figure 7, pp. 999-1013. 9. Stommel, H. M„ W. S. Von Arx, D. Parson, and W. S. Richardson, 1953: "Rapid Aerial Survey of Gulf Stream with Camera and Radiation Thermometer," Science, 1 17, pp. 639-640. 45 Reprinted from Hot Brines and Recent Heavy Metal Deposits in the Red Sea, Spri nger-Verl ag , New York, 18-21. A Fourth Brine Hole in the Red Sea? FEODOR OSTAPOFF Atlantic Oceanographic Laboratories Sea Air Interaction Laboratory Miami, Florida 76 Abstract This paper discusses some of the results of the OCEANOGRAPHER (USC & GSS) cross- ing of the Red Sea. A possible new hot hole was observed 617km north-northwest of the original hot brine area. Three reflecting layers were observed in the Atlantis II Deep that are apparently related to tne different brine layers. Recently a number of publications (Swallow and Crease, 1965; Krause and Ziegenbein, 1966; Miller et ai, 1966; Hunt et ai, 1967; Ross and Hunt, 1967; and Munns et ai, 1967) have dealt with the interesting problem of the hot brine holes in the Red Sea. Three such hot brine holes were discovered, documented and subsequently named Atlantis II Deep, Discovery Deep and Chain Deep. All three are located in a small area of less than 10 by 10 nautical miles. In May, 1967 the USC & GSS OCEA- NOGRAPHER traversed the Red Sea on her scientific Global Expedition. A sta- tion in the Atlantis II Deep was occupied at the position 21°25'02"N and 38°03'03"E to obtain large volume water samples and cores for specialized analysis. The depth recorder was operating all the time. Posi- tions were determined by satellite fixes taken every few hours. The OCEANOGRAPHER is equipped with a General Electric narrow beam (2.66° at 3db) mechanically stabilized sound trans- ducer system and operates on 19KHz. The recording is made on a precision fath- ometer recorder (Raytheon PFR-193A). The calibration is set at 1,463msec"1. Fig. 1 is a sample of the PFR record, recorded while on station in the Atlantis II Deep. Three characteristic sound reflections in- dicate the presence of the hot brine. The weakest reflection at 1 ,034 fathoms (1,891m), and two stronger reflections are found at 1,041 and 1,057 fathoms (1,904 and 1,933m), respectively. All depths quoted in this paper are uncorrected. The OCEANOGRAPHER's fathogram may be compared with a number of similar records which were obtained by METEOR 800 fms.j 900 fms. 1000 fms. REFLECTIONS 1100 fms. 1200 fms. Fig. 1. Narrow-beam echo-sounder record obtained on OCEANOGRAPHER while on station in Atlantis II Deep at 2r25'2"N and 38°13'13"E. Depth scale uncorrected. 18 A Fourth Brine Hole in the Red Sea? 19 and published by Krause and Ziegenbein (1966). The METEOR carried the ELAC narrow-beam sounder 1 CO operating at the frequency of 30KHz with a beam width of 2.8° at 3db. The transducer is mechani- cally stabilized and calibrated for a sound speed of l^OOmsec^1. Considering the instrumental limitations and differences, the agreement between the OCEANOGRAPHER's PFR record and the METEOR'S PDR record is rather good. The travel time of the sound waves be- tween the surface and the first reflection for the METEOR instrument and the OCE- ANOGRAPHER instrument are about the same (estimated as less than 4m). The METEOR station was located less than 4km to the south-southwest of the OCEA- NOGRAPHER's station. Thus, the OCE- ANOGRAPHER found, about two years later, conditions similar to those observed by the METEOR as far as the layering structure is concerned. Table 1 presents scaled distances in meters between the identifiable reflec- tors. Individual differences appear to be relatively large, although the distance be- tween the first and the third reflecting sur- face is very little. The differences may arise from the fact that one echo-sounder operates on 19KHz, the other on 30KHz; thus, different scatterers may have been involved. The three different reflecting layers cor- relate well with the temperature struc- ture observed by Ross (1969). These lay- ers occur at depths of large temperature and salinity changes (Table 2) and are probably due to the increase in density associated with these changes. The narrow-beam deep echo-sounding systems used on the METEOR and OCEANOGRAPHER thus proved to be use- ful tools in detecting, among other things, the hot brine holes. Scanning the PFR Table 2 Comparison of Depths of Reflecting Layers and Temperature Structure as Observed by Ross, 1969 (All depths uncorrected fathoms) Reflecting Layers Depth Temperature Structure Depth 1 1 ,034 Start of hot brine 1 ,025 2 1,041 Start of 44°C water 1,037 3 1,057 Start of 5 6°C water 1,054 records for specific characteristic features revealed an interesting reflection in a very narrow hole located some 617km north- northwest of the original hot brine area. It was named Oceanographer Deep. A re- production of the original record is pre- sented in Fig. 2. The bottom of the hot hole was observed at 785 fathoms ( 1 ,446m). The Oceanographer Deep measures on top 5.5km and is at the bottom about 1.0km wide along the trackline. East-west dimen- sions are unknown. Possibly the course of the OCEANOGRAPHER may have crossed the hole as its outer edge. The reflection can 800 fms. Fig. 2. Narrow-beam echo-sounder record obtained on OCEANOGRAPHER showing one reflecting layer. Depth scale uncorrected. Table 1 Distances in Meters Between Reflecting Layers for the METEOR and OCEANOGRAPHER Records lst-2nd layer 2nd-3rd layer lst-3rd layer METEOR OCEANOGRAPHER 8m 13m 31m 29m 39m 42m 20 35 Feodor Ostapoff 40° ::;;:p';?p' ' ! W^^^ • ' ." * "' * ' ' ■' * • '' '** Fig. 3. Trackline of the OCEANOGRAPHER through Red Sea showing geographic locations of Atlantis II Deep and Oceanographer Deep; 500m and 1,000m contour lines after Drake and Girdler (1964). A Fourth Brine Hole in the Red Sea? 21 be clearly identified and seems rather strong, raising the suspicion of a possible hot hole in an unsuspected area and at a shallower depth than the other three known holes. Most of the available records from the other holes show multiple reflections un- like the one from the Oceanographer Deep, which reveals only one reflecting layer at an uncorrected depth of 741 fathoms or 1,355m (Fig. 2). Krause and Ziegenbein (1966) published a record obtained at Meteor station 28 (21°17.2'N, 38°02.5'E) from the eastern edge of the Discovery Deep with only one reflecting layer. Fig. 3 shows the trackline of the OCEANOGRAPHER, the location from which the PFR record (Fig. 2) was obtained in relation to the Atlantis II Deep where the record (Fig. 1) was obtained. Indeed, if the Oceanographer Deep does contain hot brine, for the proof of which we must await further research, then a new area of hot holes has been found, probably belonging to a separate system. Acknowledgment The author would like to thank participating scientists and the crew of the USC & GSS OCEANOGRAPHER for their efforts; in par- ticular, Mr. W. Moore of New York State Uni- versity at Stony Brook, Long Island and Dr. J. Swinnerton of the Naval Research Laboratory, Washington, D.C., for their assistance search- ing the voluminous records. References Drake, C. L. and R. W. Girdler: A geophysical study of the Red Sea. Geophys. J. Royal Astro. Soc, 8, 473 (1964). Hunt, J. M., E. E. Hays, E. T. Degens, and D. A. Ross: Red Sea: detailed survey of hot brine areas, Science, 156,514(1967). Krause, G. and J. Ziegenbein: Die structurdes heissen salzreichen Tiefenwassers im Zentralen Rotem Meer. METEOR-Forschungsergebnisse Reihe A. 1, Gebr. Borntraeger, 53 (1966). Miller, A. R., C. D. Densmore, E. T. Degens, J. C. Hathaway, F. T. Manheim, P. F. McFarlin, R. Pocklington, and A. Jokela: Hot brines and recent iron deposits in deeps of the Red Sea. Geochimica et Cosmochimica Acta, 30, 341 (1966). Munns, R. G., R. J. Stanley, and C. D. Densmore: Hydrographic observations of the Red Sea brines. Nature. 214, 1215 (1967) Ross, D. A.: Temperature structure of the Red Sea brines. In: Hot brines and recent heavy metal de- posits in the Red Sea, E. T. Degens and D. A. Ross (eds.). Springer-Verlag New York Inc., 148-152 (1969). Ross, D. A. and J. M. Hunt: Third brine pool in the Red Sea. Nature, 213, 687 (1967). Swallow, J. C. and J. Crease: Hot salty water at the bottom of the Red Sea. Nature, 205, 165 (1965). Reprinted from Journal of Marine 77 Research, Vol. 27, No. 1, 24-31. Deep Water Properties and Flow in the Central North Pacific R. K. Reed Pacific Oceanographic Research Laboratory Environmental Science Services Administration Seattle, Washington 98102 ABSTRACT Values of potential temperature, salinity, and dissolved oxygen at deep levels in the central North Pacific are presented and discussed, and the direction of flow is inferred. Deep water from the south appears to spread into the northern region by way of a western route rather than directly through the central region. Introduction. The flow of Pacific deep water has been inferred by Knauss (1962) from the distribution of temperature, salinity, and radioactive carbon. He concluded that all water below 2500 m in the Pacific is from a single source to the south, that the flow is predominantly northward, and that the return flow occurs in the upper layers as a result of rising water in the North Pacific. At a given depth, the general trend is for temperature to increase and for salinity and dissolved oxygen to decrease toward the north, primarily be- cause of mixing with overlying water that is warmer, less saline, and contains less oxygen than the source water. The effect of heat flow from the earth's interior was deemed by Knauss to be of less importance than a modification by upper water. Recently, numerous deep measurements have been made in the central North Pacific. Many of the measurements were taken by the Coast and Geodetic Survey (C &GS) and by the Pacific Oceanographic Research Labora- tory (PORL) as part of an ocean-survey program (SEAMAP). Although plans call for further work in this area and for an extension to the entire Pacific, it seems desirable at this time to present the results derived from ex- isting data. Methods. The C&GS-PORL cruises were designed so that certain sites were reoccupied during the 1 961 -1966 period. Table I is a summary of the 1. Accepted for publication and submitted to press 14 August 1968. 24 1969] Reed: Deep-water Properties and Flow 27 Table I. Deviations from the means of potential temperature, salinity, and dissolved oxygen at reoccupied sites (C&GS-PORL cruises, 1 961 -1966) at levels of 3, 4, and 5 km. The sites are indicated in Figs. 1 and 2 by bars over the plotted values. Potential temperature (°C) ^ Salinity (%<>) ^ Dissolved oxygen (ml/1) Deviation Number of Deviation Number of Deviation Number of from mean values from mean values from mean values 0.00 0.01 0.02 33 38 16 4 2 0.000-0.004 0.005-0.008 0.009-0.012 52 29 4 0.00-0.04 0.05-0.08 0.09-0.12 0.13-0.16 0.17-0.18 36 33 12 0.03 0.04 total 85 3 2 total 93 total 86 Number of values exceeding Number of values exceeding Number of values exceeding 0.02°C = 6<>/o of total. 0.008 %o = 5% of total. 0.12 ml/1 = 6% of total. deviations from the mean values found at these sites at depths of 3, 4, and 5 km. Approximately 95% of the temperatures do not vary from the means by more than o.02°C; comparable values for salinity and dissolved oxygen are 0.008 °/0o and 0.12 ml/1. These values, except for dissolved oxygen, are close to most estimates of the random errors in these oceanographic measure- ments. Carritt and Carpenter (1966), however, showed that random and systematic errors in oxygen data may be as great as 1 ml/1; thus a value of 0.12 ml/1, coupled with the absence of trends, does not appear significant. Furthermore, temperature data taken over a span of more than a decade revealed no temporal changes of sufficient magnitude to influence the fol- lowing analysis. Consequently, data from various periods and sources were used. Examination of all of the data allowed some random and systematic errors to be detected. The data are identified in Table II and Fig. 1. Figs. 1 and 2 show the distribution of potential temperature (computed according to FofonofF 1962), salinity (obtained with a salinometer), and dissolved oxygen at 5 and 4 km. The bathymetry shown is from Rechnitzer and Terry (1965). Discussion. Fig. 1 shows that water colder than i.o5°C occurs in the southern sector of the area. Temperatures lower than 1 . 1 o° C appear in zones just north of the Hawaiian Rise and just south of the Aleutian Islands; be- tween these areas the water is about o.05°C warmer. As expected, the less- saline and less-oxygenated water generally coincides with the warmer water. Although dissolved oxygen is subject to change by biological processes, the fact that its distribution pattern is very similar to the distribution of temper- ature and salinity suggests that oxygen may be treated as a conservative property Reed: Deep-water Properties and Flow 25 1969] Reed: Deep-water Properties and Flow 27 Table I. Deviations from the means of potential temperature, salinity, and dissolved oxygen at reoccupied sites (C&GS-PORL cruises, 1 961 -1966) at levels of 3, 4, and 5 km. The sites are indicated in Figs. 1 and 2 by bars over the plotted values. Potential temperature (°C) ^ Salinity (°/00) ^ Dissolved oxygen (ml/1) Deviation Number of Deviation Number of Deviation Number of from mean values from mean values from mean values 0.00 0.01 0.02 33 38 16 4 2 0.000-0.004 0.005-0.008 0.009-0.012 52 29 4 0.00-0.04 0.05-0.08 0.09-0.12 0.13-0.16 0.17-0.18 36 33 12 0.03 0.04 total 85 3 2 total 93 total 86 Number of values exceeding Number of values exceeding Number of values exceeding 0.02°C = 6»/o of total. 0.008°/oo = 5% of total. 0.12 ml/1 = 6°/0 of total. deviations from the mean values found at these sites at depths of 3, 4, and 5 km. Approximately 95% of the temperatures do not vary from the means by more than o.02°C; comparable values for salinity and dissolved oxygen are 0.008 °/0o and 0.12 ml/1. These values, except for dissolved oxygen, are close to most estimates of the random errors in these oceanographic measure- ments. Carritt and Carpenter (1966), however, showed that random and systematic errors in oxygen data may be as great as 1 ml/1; thus a value of 0.12 ml/1, coupled with the absence of trends, does not appear significant. Furthermore, temperature data taken over a span of more than a decade revealed no temporal changes of sufficient magnitude to influence the fol- lowing analysis. Consequently, data from various periods and sources were used. Examination of all of the data allowed some random and systematic errors to be detected. The data are identified in Table II and Fig. 1. Figs. 1 and 2 show the distribution of potential temperature (computed according to FofonofF 1962), salinity (obtained with a salinometer), and dissolved oxygen at 5 and 4 km. The bathymetry shown is from Rechnitzer and Terry (1965). Discussion. Fig. 1 shows that water colder than i.05°C occurs in the southern sector of the area. Temperatures lower than i.io°C appear in zones just north of the Hawaiian Rise and just south of the Aleutian Islands; be- tween these areas the water is about o.05°C warmer. As expected, the less- saline and less-oxygenated water generally coincides with the warmer water. Although dissolved oxygen is subject to change by biological processes, the fact that its distribution pattern is very similar to the distribution of temper- ature and salinity suggests that oxygen may be treated as a conservative property ig6g] Reed: Deep-water Properties and Flow 25 -,;:»* 105 .12 •'" rfJ L1.10" i^ifi ^•1.15 / »i 01 f * ••• rssi A107 1C811 J.0 6 1.05-4 ■1-021 * ** u3o - 1«H • , >i.oo 89 • -CGS O-Senp i-Stnp ■» ? ' r"i ■•Ottia STRANSPAC1953 SCHINO0K.195S SMUKLUK.1957 'WoShir,gt0n.1957 ioa1959 eatVe.1966 SZETES 19GG (NOOC;i935-19G6 ^0.95 0 ^ Figure 1. The distribution of potential temperature (0), salinity (S), and dissolved oxygen (Oxy) at 5 km. Values on all charts representing the average from reoccupied sites are denoted by overbars. 170» 180 150* solved oxygen (Oxy) 28 Journal of Marine Research [27>! Table II. Identification of data used. Source PORL files (unpublished; available at NODC) Data C&GS-PORL Scripps Transpac Scripps Chinook Scripps Mukluk Year(s) 1961-1968 1953 "J 1956 1957 Univ. of Washington .... Canadian BCF Seattle 1957 1959 1966 "Oceanic Observations of the Pacific Bureau of Commercial Fisheries Report (unpublished) Scripps Zetes 1966 Unpublished report, SIO Ref. 66-24 Other (NODC) 1935-1966 fNational Oceanographic Data Center * Scripps Instituion of Oceanography, Univ. of Calif. Press, Berkeley and Los Angeles, t Various stations: Japanese, Swedish, Scripps, Russian, and U.S. Navy. in the deep water in this region. Ranges of salinity and dissolved oxygen are about o.02°/00 and 0.4 ml/1, respectively, over the area north of the Hawaiian Islands. The distribution at 4 km is shown in Fig. 2. A significant difference in the potential temperature patterns in Figs. 1 and 2 is the lack of a widespread cold zone south of 30°N at 4 km. Except for one value, the temperature increase from south to north at 4 km is only a few hundredths of a degree compared with a temperature range of at least o. I5°C at 5 km. Perhaps the water at 4 km is more uniform because of the lack of major bathymetric impediments to the flow. A 3-km chart was also prepared, but it is not shown because of its similarity to the distribution at 4 km. Because all of the deep water is from a single source region, the differences in observed properties are usually considered to be a result of residence time in the Pacific, and the path of flow is assumed to be from areas of colder (newer) to areas of warmer (older) water. The temperature distribution at 5 km in- dicates that the warmer water in the central region cannot be the source of the colder water to the north, but this distribution does not preclude a northward flow below this level. The deepest water in the central region, however, is not as cold as water in the northern region at the bottom or at a depth of 5 km (see Figs. 3 and 1). Thus the deeper water in the northern region must arrive by way of a route other than one that would pass directly through the central region. Figs. 1 and 2 reveal an increase in temperature from west to east between 45°N and 5o°N. Salinity and oxygen exhibit comparable decreases toward the east. This fact, plus the marked similarity in properties on either side of the rise along I70°E (Bureau of Commercial Fisheries, unpublished data, 1966), suggests that the deeper water found near the Aleutians entered from the west, through a break in the rise between 46°N and 48°N. The inferred circulation is summarized in Fig. 4. 26 Journal of Marine Research [27>' Figure 2. The distribution of potential temperature (0), salinity (S). and dissolved oxygen (Oiy) 28 Journal of Marine Research [27> Table II. Identification of data used. Data C&GS-PORL Scripps Transpac Scripps Chinook Scripps Mukluk Year(s) 1961-1968 1953 \ 1956 1957 Univ. of Washington .... Canadian BCF Seattle 1957 1959 1966 Scripps Zetes 1966 Other (NODC) 1935-1966 Source PORL files (unpublished; available at NODC) "Oceanic Observations of the Pacific Bureau of Commercial Fisheries Report (unpublished) Unpublished report, SIO Ref. 66-24 fNational Oceanographic Data Center * Scripps Instituion of Oceanography, Univ. of Calif. Press, Berkeley and Los Angeles, f Various stations: Japanese, Swedish, Scripps, Russian, and U.S. Navy. in the deep water in this region. Ranges of salinity and dissolved oxygen are about o.02°/oo and 0.4 ml/1, respectively, over the area north of the Hawaiian Islands. The distribution at 4 km is shown in Fig. 2. A significant difference in the potential temperature patterns in Figs. 1 and 2 is the lack of a widespread cold zone south of 30°N at 4 km. Except for one value, the temperature increase from south to north at 4 km is only a few hundredths of a degree compared with a temperature range of at least o. I5°C at 5 km. Perhaps the water at 4 km is more uniform because of the lack of major bathymetric impediments to the flow. A 3-km chart was also prepared, but it is not shown because of its similarity to the distribution at 4 km. Because all of the deep water is from a single source region, the differences in observed properties are usually considered to be a result of residence time in the Pacific, and the path of flow is assumed to be from areas of colder (newer) to areas of warmer (older) water. The temperature distribution at 5 km in- dicates that the warmer water in the central region cannot be the source of the colder water to the north, but this distribution does not preclude a northward flow below this level. The deepest water in the central region, however, is not as cold as water in the northern region at the bottom or at a depth of 5 km (see Figs. 3 and 1). Thus the deeper water in the northern region must arrive by way of a route other than one that would pass directly through the central region. Figs. 1 and 2 reveal an increase in temperature from west to east between 45°N and 50CN. Salinity and oxygen exhibit comparable decreases toward the east. This fact, plus the marked similarity in properties on either side of the rise along i70°E (Bureau of Commercial Fisheries, unpublished data, 1966), suggests that the deeper water found near the Aleutians entered from the west, through a break in the rise between 46°N and 48°N. The inferred circulation is summarized in Fig. 4. 1969] Reed: Deep-ivater Properties and Floiv 770° jep- 29 10° Figure 3. Bottom potential-temperature distribution. Prepared from temperature data obtained within 300 m of the bottom. Values for depths of less than 100 m from the bottom are denoted by the station symbol in parentheses. Water depths at these stations generally ranged from 5500 to 6000 m, except in the Aleutian Trench, where depths exceed 7000 m in the western part. Considerations for the Future. Although direct current measurements have yielded interesting results, they have not given reliable values of the net trans- port of Pacific deep water. Because of fluctuating barotropic flows of 1 cm/sec 3° "Journal of Marine Research l>7>! 150° ,60° Figure 4. Schematic representation of the inferred circulation at 5 km and below. or more (Barbee 1965) and deep tidal currents probably at least this great, it is very difficult to resolve net velocities on the order of o. 1 cm/sec (Knauss 1962, Bien et al. 1965). Thus the distributions of physical and chemical properties, plus results from isotope dating, are likely to remain for some time our main source of information on deep circulation in the Pacific. The data presented here suggest an interesting and unanticipated path for 1969] Reed: Deep-water Properties and Flow 31 the deep water; northern water appears to arrive from the west instead of from the south. Ultimately, very precise measurements from strategic locations throughout the Pacific may yield a convincing circulation pattern for the entire basin. Acknowledgments. I wish to thank W. James Ingraham, Jr., Bureau of Commercial Fisheries, Biological Laboratory, Seattle, for use of data from the RV George B. Kelez cruise, winter 1966. Dr. Kilho Park, Oregon State University, kindly furnished unpublished oxygen data. Cdr. W. D. Barbee, N. P. Laird, and T. V. Ryan read the manuscript and offered helpful sugges- tions. REFERENCES Barbee, W. D. 1965. Deep circulation, Central North Pacific: 1961, 1962, 1963. Cst. geod. Surv. Res. Pap.; 104 pp. Bien, G. S., N. W. Rakestraw, and H. E. Suess 1965. Radiocarbon in the Pacific and Indian oceans and its relation to deep water move- ments. Limnol. Oceanogr., 10 (Redfield Suppl.) : R25-R37. Carritt, D. E., and J. H. Carpenter 1966. Comparison and evaluation of currently employed modifications of the Winkler method for determining dissolved oxygen in sea water; a NASCO report. J. mar. Res., 24 (3): 286-318. FOFONOFF, N. P. 1962. Physical properties of sea-water, in The Sea, Vol. 1, pp. 3-30. M. N. Hill, Editor. Interscience, N.Y. 864 pp. Knauss, J. A. 1962. On some aspects of the deep circulation of the Pacific. J. geophys. Res., 67 (10): 3943-3954- Rechnitzer, A. B., and R. D. Terry 1965. Bathymetry of the Pacific Basin. Printed by North American Aviation/Autonetics, Anaheim, California, 1 p. Printed in Denmark for the Sears Foundation for Marine Research, Yale University, New Haven, Connecticut, U.S.A. Bianco Lunos Bogtrykkeri A/S, Copenhagen. Denmark Reprinted from Journal of Acoustic America, Vol. 46, No. 5, 1382-1384 LETTERS TO THE EDITOR Society of 78 Received 30 August 1969 11.2; 13.4, 13.5 Diffraction of a Plane Acoustic Pulse by a Free Orthogonal Trihedron (Three-Dimensional Corner) Richard P. Shaw* and Daniel F. Courtine Division of Interdisciplinary Studies and Research, Stale University of Xew York at Buffalo, Buffalo, New York 14214 The normal velocity field on arbitrary three-dimensional scattering surfaces struck by a weak acoustic plane wave, is considered. A numerical solution for a right-angle corner (i.e., three orthogonal edges of infinite length i is found for a step-incident pressure wave, while the wavefront normal is taken to form equal angles with the three orthogonal edges. The scattering obstacle is assumed to have a free surface (i.e., pressure is zero). We consider here a numerical solution to the problem of a plane weak shock wave striking a three-dimensional exterior right- angled corner, i.e., an orthogonal trihedron (see Fig. 1), with a pressure-release (free) boundary condition. The incident wave is taken to be symmetric with respect to the three orthogonal sides. The approach is described elsewhere1 (in a report form of this paper) and is based on an integral equation formulation2 of wave problems, which allows for solution on the scattering surface separately from the remainder of the solution. The total velocity potential, - with similar expressions on xo = ^npv— Y, <"iZvj2 = aiVi{x,0,z,t), (4) ■ («o+yo)/v5]2, on y0 = 0, (5) = 0 and so = 0 — with the restriction that all values of x0, yo, z0 remain positive (or zero). A rectangular area of width Ax and height Az over a time interval I to t-\-At is used with a velocity value corresponding to that calculated at the center of the rectangle and time t. Areas that fall completely within S are included directly, but those through which the boundary INCIDENT PLANE WAVE FRONT INTERSECTION WITH SIDES OF TRIHEDRON X V 50 Fig. 2. Velocity at / = 10 sec. 40 30 20 -0.61 J_ 0.61 n/t The Journal of the Acoustical Society of America 1383 LETTERS TO THE EDITOR Fig. 3. Free corner :t = 10 sec; 7 = 15° 30°, 45°. defining the domain of dependence, Eq. 5, passes must be treated as special cases in order to include that portion of the source area which lies within 5 in the calculations, as mentioned above. For the corner problem, three distinct types of solution are expected in three different regions. They are the "infinite-plane solution" in that region of the surface not affected by any of the edges of the trihedron, the "infinite-wedge solution" in that region affected by only one edge, and the solution for those remaining areas that are affected by more than one edge (see Fig. 1). The results obtained are in very good agreement with known solutions in the areas corresponding to the infinite-plane and the infinite- wedge solutions. There is no exact solution to which the corner area may be compared, but the results (see Figs. 2 and 3) show higher velocities than those in the corresponding infinite-wedge solution, as would be expected. For fixed arbitrary y, where y is the angle between the x axis and an arbitrary line passing through the origin on the xz face, and d is the distance from the origin along this line, plots of velocity against d/i yield essentially the same results for several different valus of / (e.g., see Fig. 4 for 7 = 45°), as they should, since time and space dimensions are coupled; i.e., there is no representative length in the problem.6 Acknowledgment : This research was supported in part by the Office of Naval Research. * Presently on leave at Hawaii Inst, of Geophys., Univ. of Hawaii, Honolulu, Hawaii 96822. 1 R. P. Shaw and D. F. Courtine. "Diffraction of a Plane Acoustic Pulse by a Free Orthogonal Trihedron." Rep. No. 32, Div. of Interdisciplinary Studies and Res.. State Univ. of New York at Buffalo (May 1968). 2 M. B. Friedman and R. Shaw, "Diffraction of Pulses hv Cylindrical Obstacles of Arbitrary Cross Section." J. Appl. Mech. 29, 40-46 (1962). * R. P.Shaw, "Diffraction of Pulses by Obstacles of Arbitrary Shape with a Robin Boundary Condition: Part B: Semi-Free Case," Rep. No. 12. Div. of Interdisciplinary Studies and Res., School of Eng., State Univ. of New York at Buffalo (April 1066^ ; J. Acoust. Soc, Amer. 41, 855-859 (19671. 4 R. P. Shaw and M. B. Friedman. "Diffraction of Pulses by Deformable Cylindrical Obstacles of Arbitrary Cross Section," Proc. U. S. Nat. Congr. Appl. Mech., 4th, June 1962, pp. 371-376. 'J. B. Keller and A. Blank. "Diffraction and Reflection of Pulses by Wedges and Corners," Commun. on Pure and Appl. Math. 4. 75-94 (1951). Received 13 January 1969 12.3, 12. 3i 0 05 10 1.225 d/t Fic. 4. Free corner, : y =45°, (=8,9, 10 sec. Damping-Material Effectiveness Measured by the Geiger-Plate and Composite-Beam Tests T. J. Dudek Lord Manufacturing Company, Erie. Pennsylvania 19511 The Geiger thick-plate test and the vibrating composite-beam te.-t lor the evaluation of vibration damping materials are briefly reviewed, and the advantages and disadvantages of both methods are analyzed. The results 1384 Volume 46 Number 5 (Part 2) 1969 79 Reprinted from Journal of Acoustic Society of America, Vol. 46, No. 3, 649-654. Received 10 June 1968 11.2, 11.3, 11.7 Transmission of Plane Waves through Layered Linear Viscoelastic Media R. P. Shaw and P. Bugl Division of Interdisciplinary Studies and Research, Slate University of New York at Buffalo, Buffalo, New York 14214 The two-dimensional propagation of time-harmonic plane waves through a plane horizontally layered viscoelastic medium is discussed. The problem is formulated as the equivalent elastic plane-strain case with modified Lame constants, which are complex and frequency dependent, replacing the usual elastic Lame constants. Rather than use potentials, incident angles, etc., we formulate the problem directly in terms of stresses and displacements and solve it by using matrix methods. This approach is felt to be more direct and leads to some interesting conclusions. If the incident wave is not attenuated in the direction parallel to the layering, interface waves can be generated only if one of the layers is "pseudoelastic," i.e., has at least one real wave speed. In this case, the interface waves are generated in the same manner as in the purely elastic case. Such a physical problem would exist, for example, if the incident waves were to travel through a semi-infinite elastic half-space before striking the plane viscoelastic layers. If the incident wave is attenuated in the direction parallel to the layering, interface waves can be generated at specific angles of incidence and specific combinations of material parameters. INTRODUCTION The transmission of time-harmonic plane waves through layered linear elastic media is a problem of great interest and much study.12 In addition, there has been much recent interest in the reflection and trans- mission of plane waves in a linear viscoelastic medium.3 It is a relatively straightforward task to combine these topics into a single treatment. Insofar as the mathe- matical manipulations are concerned, the primary dis- tinction between the elastic and the viscoelastic cases is that the latter will have modified Lame constants, a and p., which are complex and frequency dependent.4 The governing equations, continuity conditions at the inter- face between layers, etc., remain unchanged, except that some care must be taken in physical interpretation of the results. A modification of the usual technique of solution for the elastic (or viscoelastic using X and p.) problem is introduced in an attempt to clarify the mathematical manipulations involved. Results are left in a form re- 1 L. M. Brekhovskikh, Waves in Layered Media (Academic Press Inc., New York, 1960). 2 M. Ewing, W. Jardetsky, and F. Press, Elastic Waves in Layered Media (McGraw-Hill Book Co., New York, 1957). 3 H. F. Cooper, Jr., "Reflection and Transmission of Oblique Plane Waves at Plane Interface Between Viscoelastic Media," J. Acoust. Soc. Amer. 42, 1064-1069 (1967). * W. Nowacki, Dynamics of Elastic Systems (John Wilev & Sons, Inc., New York, 1963), p. 315. lating the displacements and stresses in any layer to those at the uppermost (2 = 0) interface that separates the layered media, z>0, from a half -space, z<0, through which some incident wave travels. Since the displace- ments and stresses at this 2=0 interface also depend on the waves transmitted from below (z>0) by reflections at other interfaces, these "initial" values cannot be de- termined until the entire problem has been specified, i.e., the number of layers, the appropriate physical parameters in each layer, etc. Nevertheless, some useful conclusions can be drawn regarding interface waves directly. I. ELASTIC CASE Consider a stratified medium consisting of parallel plane-homogeneous elastic layers of different thickness and material properties (Fig. 1). The z axis is oriented Fig. 1. Geometry of z=z, layered medium. : d, />, X, /J, ! do pi^i The Journal of the Acoustical Society of America 649 S H A W A X D B U G L in a direction normal to these planes with x and y form- ing a right-handed Cartesian-coordinate system. The problem considered will be restricted to a plane-strain case, such that none of the variables depend on the co- ordinate y. This uncouples the SH wave, which is not considered. In any one layer, the displacement (u) equation of motion is given as PjU= (Xy+/x>)V(V •!!)+/*, V2!!, (1) where p, is the density, and Xy,/xy are the Lame constants for the yth layer. Along the upper surface 2=0, the dis- placements and stresses of an incoming plane wave are given. Using the continuity of the normal stress, shear stress, normal displacement, and tangential displace- ment at the interface between layers, the reflected and transmitted fields may be calculated. The assumption of a solution in the form ux= U{z) exp{ik[cl— x~\), uy=0, uz=W{z) txp{ik\_ct— x~]}, (2) implies a frequency u=kc and a phase velocity c in the x direction. The normal and shear stresses are, respectively, Txz=n[uXtt\-Uz,^\=S{z) txp{ik[_cl—x~\), tZz = \ux,x+(\+2ij.)uz,z = T(z) exp{ik[ct— x~\) . (3) In any given layer (leaving out the j subscript for convenience at this point), a set of four coupled first- order ordinary different equations on U, W, S, and T can be found. In matrix form, these are U,. ikX A+2M -£2[A2+pC2(X+2p.)-(X-f2M)2] X+2m 0 or, in a condensed form, (d/dz)X=AX, (5) where X is a vector whose components are (U, W, S, T) and A is the coefficient matrix given above in Eq. 4. While Eq. 5 can be solved directly, a transformation is convenient. Consider V=BX or X^BrW. (6) Equation 5 is then dV/dz= BdX/dz= B(AX) = BAB-1F= EV. (7) If B can be determined so as to make E diagonal, E = diag[7J, (8) then 7 could be obtained directly from Eq. 7 : 7= col[A, exp7iz] = QA', (9) A' = col[A^]= 7(0)= BX(0) (10) Q = diag[exp(7i2)]. (11) where and If the first layer is between z = 0 and z=zh X(zi) can be evaluated ; A'(2l) = Br17(z1) = Br1Qi(21)B1A'(0), (12) 650 Volume 46 Number 3 (Part 2) 1969 ik 1 0 0 0 1 X+2m 0 0 ik\ X+2M k2pc2 ik 0 (4) where the subscript 1 indicates that B, Q, etc., are evaluated using the material properties of Layer 1. Similarly, X(z2) may be found in terms of X(zi) and therefore in terms of X(0). This may be generalized to X(zn) =lf B/^Qyfe-zy-O ByA'(O) =n Ry*(0), (13) where 2y is the coordinate of the interface between the jth and (_/+ 1 ) th layers. The eigenvalues ?i, y-., y3, and 74 and the matrix B can be determined directly from the condition that BAB-'=E. A straightforward calculation gives 7i,2=±z'ya2-&2)i]}2 (22) which has aactuai equal to the elastic wave speed a only if a and k are real. (A similar equation holds for rota- tional waves with /3 replacing a.) Thus, the actual wave speed will depend, in general, on the angles of the inci- dent wave, 9 and 9', as well as the material properties of the layers. The conditions under which interface waves may exist are now considered. A. Viscoelastic Layers under an Elastic Half-Space If the half -space s<0 through which the incident waves travel is elastic, k and c will be real quantities, e.g., k = ks-sm9 andc=o>/&, where ks is the wavenumber for elastic rotational waves, 9 is the angle of incidence, and c is the phase velocity in the x direction for an inci- dent rotational wave, with similar expressions for an incident dilational wave. Then, the existence of interface waves is specified by having terms in the dependent variables that have only a real exponential dependence on z; i.e., in the Q term, at least one of the eigenvalues 7, must be a pure real number. Obviously, this implies that 71, 72, and/or 73, 74 must be real and that, by Eq. 15, a and/or b must be pure imaginary. This requires that a/ and/or /3/ be real, positive, and less than c2 or that a/ and/or /3/ be real, negative, and greater than — c2. The former case corresponds to the usual elastic case. The latter appears physically unrealistic, since it would require ju and/or X+2jK to be pure imaginary. If fi is imaginary, so is Ys. This implies that rotational waves will not propagate in such a material. Similarly, if X+2# is imaginary, so is |[FV-|-2FJ. But this implies that dila- tational waves will not propagate. Therefore, neither of these latter possibilities is considered. Therefore, for the case of viscoelastic layers lying under an elastic half-space through which the incident wave travels, it is concluded that interface waves cannot be generated unless one of the lasers is "pseudoelastic," in which case they may be generated under the same conditions as in the usual elastic case. B. Viscoelastic Layers under a Viscoelastic Half-Space The primary distinction between this case and the previous one is that the incident wave may now be attenuated in the x direction, and, therefore, k and c in Eq. 2 will be complex such that kc=co is real. The same requirement as before on 7,- holds for the existence of interface waves, but, since k is complex, some 7,- can be real by having ka and/or kb a pure imaginary number. This implies that (ka)2 and/or (kb)2 is a real negative number. From Eq. 16, (ka)2= (w/a)2-k2; (kb)2= (w/0)2-k2. (23) First consider the "dilatational" interface wave. The requirement is then Re[(w/a)2-£2]<0, (24a) Im[(w/a)2-£2] = 0. (24b) This corresponds to p(L)w2 Re[A(L)+2M]/ 1 \«>+2m(L) j 2 <{Re[/t]}2-{Im[^]}2, (25a) P(L)a.2Im[X(L) + 2M(L)]/|X(L>+2M(L):2 = 2ReKJ-ImKJ. (25b) The corresponding equations for the "rotational" inter- face wave are pco2 Re[Ma']/'U(L)|2<{Re[/fe]}2-{Im[^]}2, (26a) p], (26b) where the superscript L denotes the material properties of the layer in question, while values without a super- script refer to properties of the ''incident" half-space. Consider an incident SV wave decaying in the direc- tion of propagation, i.e., a "damped" plane wave. The exponential dependence of the incident potential, dis- placement, stress, etc., will have the form exp{/[>'/ — £s(xsin0-fzcos0)]}, where ks is a complex, shear wavenumber and 9 is a real angle of incidence. An equiv- alent form would be exp{/[w/— Re[£„.](.v sin0+; COS0)] — Im[&s](.rsin0-r-zcos0)}, such that Re(£,) sin0 ex- presses the real phase velocity in the x direction, while Im(£s) sin0 is the attenuation factor in the x direction. Clearly, from Eq. 2, k-kt>sm9, (27) such that Re(k) = Re(ks) sin0andImOC> = Im(A\/) sin0-*. 652 Volume 46 Number 3 (Part 2) 1969 TRANSMISSION THROUGH VISCOELASTIC MEDIA are known in terms of the complex Lame parameters for the "incident" half-space and may be written as k?= {Re[02-{Im[>s]}2+2; Re[*J Im[*.] = w2p[Re[p]WIm[p]]/!p:|2. (28) Equations 25 and 26 can then be examined in detail. Equation 25b requires p + 2MU) | 2 = par ImfjuQ sin20/ 1 p, | 2, (29) which, in turn, requires a definite relationship between the angle of incidence 0 of the incident plane wave and the material properties of the various layers. Equation 25a requires p(L>a>2Re[X(L, + 2M(L)]/|\(L) + 2/u(L)|2 < sin20 • par Re[p]/ | p | 2, (30) whereupon, using Eq. 29 to define the appropriate angle 9, Re[Xt— ils(x sin0+s cos0) — //(.t sin0'+z cos0')}, where k in Eq. 2 is given by ls sm8—ils' sin0'. The governing differential equation would require that k2=l2-l,'2-2il,l/ cos(0-0'), (34) which implies /s2-/s'2 = po,2Re[p]/[M|2, (35a) 21,1,' cos(0-0') = pw2 Im[p]/|p!|2. (35b) Then Eqs. 25b and 26b become P(L)o>2 Im[X(L'+2p(I-»] pco2 sin0-sin0' Im[p] and |X(L,-f2pu2 Im[p(/-')] pw2 sin0-sin0' Im[p] AL)\2 cos(0-0')|p|2 (36) (37) respectively. Given 0 and 0', these equations will deter- mine the material properties in the layers such that an interface wave can be generated (or vice versa). The corresponding restrictions of Eqs. 25a and 26a require p(L)w2Re[X(L»+2p]/|X(L)+2p(L)i2 i 2- — — POLYURETHANE ___^_ ■> G' ^^-^^^^ G" _-•'' POmSOBUTYLENE . •- " 20 20 log u Fig. 2. Log G', log G" (G in dynes/square centimeter) vs log u (w in radians/second) for polyurethane and polyisobutylene. Im[/xj>0, tan arg[jQf] = ImfjuJ/RefjuQ logG'-logG"(Z-\ (40) where G'=Re[ji] and G'=Im[juJ in terms of Ref. 11. Clearly, the results will not be particularly accurate in those regions where log G' and log G" are close in mag- nitude, and this reservation must be considered in evaluating the conclusions. Reference 11 gives data for several materials in Appendix D, but unfortunately at different reference temperatures. These may be reduced to the same reference temperature11 or may be compared to other materials measured at the same reference tem- perature. As an illustration of Eq. 40, compare poly- isobutylene" with a polyurethane propellant15 at 25°C. Values of G' and G" are given in Fig. 2, while logG' — logG" is plotted in Fig. 3, over a frequency range 0 \p.\'1 Im[>lL)]-i* si n0 = ,{L)\ Im[j3] J (41) 16 T. Smith, L. Hiam, and J. Smith, "Viscoelastic Properties of Solid Propellants and Propellant Binders," Stanford Res. Inst., Quart. Rep. 5, 6 (Jan. 1963). Fig. 3. Comparison of log (G'/G") for polyurethane, •, and polyisobutylene, o. If no such real angle exists, an interface wave cannot exist for an ordinary damped incident wave, and the case of a general inhomogeneous incident wave must be considered, e.g., Eqs. 36-39. For the particular example used, p (polyisobutylene) ~1.0 while p (poh -methane) (Ref. 15) ~1.7. Thus, for w=1.0 rad 'sec, 0 = sin_1 (0.68)~43°. For inhomogeneous incident waves or for compres- sible materials, the calculations would be somewhat more complicated but follow directly from the equations developed. III. CONCLUSION A method has been presented for the calculation of stresses and displacements resulting from a time-har- monic plane wave propagating through a layered linear viscoelastic medium. Some general conclusions have been drawn concerning the types of waves transmitted and reflected, and a simple example of the conditions under which an interface wave may occur has been given. It is felt that this direct approach has an ad- vantage over usual approaches, e.g., Ref. 3, in that the complex arithmetic involved in the application of a com- plex Snell's law is avoided, giving, it is hoped, a clearer understanding of the conclusions drawn. These ire that general inhomogeneous reflected and transmitted waves will be formed even if the incident waves are not of this form (i.e., see Eq. 21), that the actual speed of propaga- tion of wavefronts differs from the usual wave speed, (i.e., see Eq. 22), that interface waves cannot exist in viscoelastic layers under an elastic half-space unless one of the wave speeds in the layer is real (i.e.. the layer is "pseudoelastic"), and that interface waves can exist in viscoelastic layers under a viscoelastic half-space under specific conditions of material properties and incident angle. ACKNOWLEDGMENT This research was supported in part by a contract with the Office of Naval Research. 654 Volume 46 Number 3 (Port 2) 1969 80 Reprinted from Journal of American Ceramic Society Vol. 52, No. 10, 539-542 (Also HIG 287). Adiabatic Elastic Moduli of Vitreous Calcium Aluminates to 3.5 Kilobars T. J. SOKOLOWSKI Environmental Science Services Administration, Pacific Oceanographic Laboratories, Joint Tsunami Research Effort, Honolulu, Hawaii 96822 and M. H. MANGHNANI Hawaii Institute of Geophysics, University of Hawaii, Honolulu, Hawaii 96822 "Pulse superposition" ultrasonic interferometry was used to measure elastic wave velocities and related elastic parameters of four vitreous calcium aluminate specimens at pressures up to 3.5 kbars at 25°C. The values obtained for the bulk (K.) and shear (/u) moduli and for Poisson's ratio (a) were much higher than those reported for silicate glasses. The bulk moduli for the calcium aluminates, however, fit quite well with the relation between bulk modulus and specific volume per ion pair suggested by Soga and Anderson for 29 glasses. The (dv,,/dP) value was highest (8.9x10"' km/(skbars)) for the SiO -doped vacuum-melted calcium aluminate and lowest (6.8X10 3 km/(s kbars)) for the BaO-doped air-melted speci- men. The BaO doping seemed to cause anomalous behavior in the shear wave velocity vs pressure relation; the (dv,/dP) value for the BaO-doped air-melted specimen was -4.1x10 3 km/(skbars). The differences in the compressibility at 1 bar and the rate of change of compressibility with pressure appear to be related to composition and melt conditions. The (dK./dP) values ranged from 4.0 to 4.7 and the (dcr/dP) values from 6.8 to 7.5 x 10 Vkbars. I. Introduction The elastic behavior of noncrystalline solids under pres- sure has been studied by several workers. Bridgman' first noted that elastic behavior was anomalous, in the sense that the compressibility increased with pressure, in several natural and artificial silica-rich glasses. Other investigators" ° reported that the moduli of such glasses decreased with pres- sure. Recently, it was shown* that the anomalous behavior of silica-rich glasses under pressure is quantitatively related to silica content. The purpose of this study was to better understand the effect of composition and conditions of glassmelting on the elastic constants of vitreous calcium aluminates by comparing the elastic parameters at normal and high pressures. Prop- ,;---,----, 1 VARIABLE MaT t E NUATOI H~ I I> 1 **■ ; £«■■_ ! — r-|T.ANiro.M»| l'":""E.n |*"| l^T.ANSOUCE. , 1 | h SPECIMEN H OETECTO. [ Fig. 1. Diagram of electronic equipment (adapted from Ref. 8). erties were measured by ultrasonic wave propagation. The elastic behavior of four specimens of vitreous calcium alumi- nate subjected to pressures up to 3.5 kbars at 25°C is re- ported. II. Method of Investigation Ultrasonic interferometry ("pulse superposition" method) was described in detail by McSkimin7 and by Schreiber and Anderson.8 Figure 1 is a diagram of the electronic equipment used. The major components are a tone-burst generator, con- sisting of a carrier wave (CW) oscillator and a pulse repeti- tion frequency (prf) oscillator, a Tektronix 545A oscilloscope, a frequency counter (Hewlett-Packard model 5246L), and an amplifier. An rf pulse "from the tone-burst generator is applied to a quartz transducer; the frequency of the CW pulse is equal to the natural frequency of the transducer. The traftsducer is attached to one of the two parallel faces of the specimen to Received November 29, 1968; revised copy received March 24 1969. Contribution No. 287 from the Hawaii Institute of Geo- physics. Supported by the Office of Naval Research under Con- tract N-00014-68-A-0387-0005 to the University of Hawaii. 540 Journal of The American Ceramic Society — Sokolowski and Manghnani Table I. Elastic Wave Velocity Measurements and Related Parameters for Calcium at 1 Bar and 25°C Parameter Relation Vol. 52, No. 10 Aluminate Classes Longitudinal velocity Shear velocity Density Bulk modulus Shear modulus Compressibility Young's modulus v„ v, P K. = P(W f v.') At = pV." /?. = 1/K. E = 9K,M/(3K. + /i) — - . — i-u-^-'l/l-^-']} Mean atomic wtf Vol/ion pair* m = M/p V = 2M/pP Glass No.» Units BS37A-A BS37A-V BS39B-A BS39B-V km/s km/s g/cm3 6.934 3.784 2.960 6.923 3.760 2.996 6.832 3.758 3.089 6.746 3.659 3.170 kbars 857.9 871.2 860.3 876.6 kbars Mbars"1 kbars 423.8 1.166 1091.6 423.6 1.148 1093.5 436.3 1.162 1119.6 424.4 1.141 1096.2 0.2879 0.2908 0.2831 0.29K g cmVmol 24.40 16.49 24.40 16.28 25.08 16.23 25.08 15.82 * BS37A-A and BS39B-A were melted in air; BS37A-V and BS39B-V were melted in vacuum. tCalculated from known chemical composition. generate elastic wave pulses. The waves so generated travel through the specimen, are reflected, and are then received by the transducer. When the interval between the applied rf pulses is equal to an integral multiple (p) of the round-trip transit time of the wave pulses, the echoes are superimposed (in the present case, p is equal to 1). By properly gating the incident pulses, the echo pulses are received. The signal of these pulses is then matched with an impedance matching device, amplified, and displayed on the oscilloscope. The prf of the applied pulse is measured with a frequency counter. Elastic wave velocity is calculated from the prf; 30-MHz X-cut and Y-cut quartz transducers were used for measuring longi- tudinal and shear wave velocities. The transducers were bonded to the specimen by a thin film of Dow Corning resin 276 V9. The pressure-generating system included a two-stage nitro- gen gas pumping system, a pressure vessel, a Harwood man- ganin pressure cell, and a Carey-Foster resistance bridge. The latter was used to measure and monitor the pressure in the vessel containing the specimen. The manganin coil was calibrated with a Harwood DWT-300 dead-weight tester to 4 kbars. The prf data were obtained at 4000 psi intervals of increas- ing and decreasing pressure; 20 to 25 min were allowed after the pressure was changed for the specimen to reach equilib- rium with the pressure and temperature in the vessel. The temperature of the specimen was maintained at 25° ±0.1°C by a constant-temperature water jacket around the vessel and was monitored with a Chromel-Alumel thermo- couple and a K-4 Leeds & Northrup potentiometer. III. Specimens The vitreous calcium aluminates* were those used by Levengood" in his studies. One glass (BS37A) is doped with SiO, and the other (BS39B) with BaO. Two specimens of each composition were prepared by the manufacturer: those identified as BS37A-A and BS39B-A were melted and cooled in air at 1 bar; those identified as BS37A-V and BS39B-V were melted and cooled at reduced pressure (100 yum air pressure), so that most of the inter- stitial dissolved gases were removed from the melt. Each sample was prepared for wave propagation velocity measure- ments by grinding and polishing the two parallel faces to within 1 part in 1x10' parts. The specimens were 10 to 11 mm long between the parallel faces. •Specimens were obtained from W. C. Levengood at the Uni- versity of Michigan; they were produced by the Barr and Stroud Company, Glasgow, Scotland. Composition of glass BS37A is CaO 57, A1,0, 28, MgO 7, SiO, 7; glass BS39B is CaO 50, AW, 34, MgO 9, and BaO 7 mol%. IV. Measurements at 1 Bar and 25 °C The pulse repetition frequencies (prf) gave the longitudinal wave velocity (vP) and shear wave velocity (v,) according to the relation v=2Jf, where v is the velocity in the specimen, I the length of the specimen, and / the prf. The effect of the phase shift due to reflection at the specimen-seal interface is less than 1° for a properly prepared seal and was neglected in the calculations. The data at 1 bar and 25°C are presented in Table I. V. Measurements at Higher Pressures The sound velocity variation in a specimen subjected to pressure is obtained from the relation v/v0 = (f/fo) (l/L>). The zero subscript denotes initial (1 bar) conditions. The prf data were obtained at regular pressure intervals to approximately 3.5 kbars. The results for both longitudinal and shear modes are shown in the plots of (///o) vs pressure (Fig. 2). The length ratio (L/l) at a given pressure can be calculated from Cook's formula10: (Ul) = 1 + 1 + A Po dP 3A - 4B where (1+A) is the ratio of the adiabatic bulk modulus to the isothermal bulk modulus, p0 the initial density, A=(vpo///o)1 for longitudinal waves, and B=(v.0/'7o): for shear waves. The quantity A is equal to ayT, where a is the coefficient of volumetric expansion, y the Griineisen parameter, and T the temperature (°K). Since a is a small quantity (<10"V°C for calcium aluminate glasses), the quantity A was ignored in the computations. The pressure derivatives of the elastic parameters are presented in Table II. VI. Results and Discussion As seen in Table I, the bulk densities and bulk moduli for vacuum-melted glasses are slightly higher than those for air- melted glasses of the same composition. This relation is con- sistent with the fact that interstitial gas and water vapor are removed from the glass when it is melted under reduced pressure. Several investigators""" have attempted to correlate bulk modulus of glasses with the various structural parameters that are basically related to the bonding forces of the atomic link- ages. One such correlation of bulk modulus, K„ shear modulus, n, and specific volume/ion pair, V (V=2M pp. where M is the molecular weight, p the number of atoms in the molecule, and p the density), was suggested by Soga and Anderson." They showed that, for 29 glasses, the bulk October 1969 Adiabatic Elastic Moduli of Vitreous Calcium Aluminates to 3.5 Kilobars 541 Table II. Pressure Derivatives of the Elastic Parameters of the Calcium Aluminate Classes PRESSURE (kb) Fig. 2. Longitudinal (solid line) and shear (dashed line) frequency ratios (///o) vs pressure for vitreous calcium aluminates. Melt condition for each specimen follows the specimen number. modulus is inversely proportional to the specific volume; their data fit a line parallel to a relation for various crystalline solids (see Ref. 14, Fig. 1). Our data for vitreous calcium aluminate, if plotted on this figure, would fall reasonably close to an extension of the line for the glasses. The bulk moduli of the BaO-doped specimens are slightly higher than those of the Si02-doped specimens (Table I). It has been suggested16 that there could be a significant effect on the elastic modulus of a glass when high-field-strength modifying ions, such as Ba, are introduced. In the present study, the bulk moduli for the glasses which contain appreciable amounts of CaO are higher than those for the silicate glasses listed in Refs. 1, 2, 4, 5, and 14. Poisson's ratio for the glasses studied varied from 0.283 to 0.292 (Table I), which is quite high compared to the values for glasses such as borosilicate" and fused silica and for fused quartz." One explanation for relatively high Poisson's ratios (>0.25) for glasses containing appreciable amounts of large alkali and alkaline-earth ions was given by Smyth12: ". . .when the modifying ions are large, they fill the interstices in which they are located so that any change in the shape of the glass means a deformation of these ions as well as the distortion of the network." The relations between compressional and shear wave veloci- ties and pressure are shown in Fig. 3. The longitudinal velocities increase linearly with pressure within experimental error for all the specimens. Values of (dvp/dP) are higher for the vacuum-melted specimens than for the air-melted specimens of the same composition (Table II). Also, the (dvp/dP) values for the SiOz-doped vacuum-melted and air- melted specimens are higher than for the BaO-doped speci- mens. The relations among the shear velocities and among Glass No. Derivative BS37A-A BS37A-V BS39B-A BS39B-V ~ (km/(s-kbar)XlO°) 8.1 8.9 6.8 7.8 ~ (km/(skbar)XlO') 1.1 0.3 -4.1 -2.3 <3K dP 4.31 4.71 4.00 4.42 dP 0.51 0.48 0.40 0.42 ^-(kbars'XlO') dP 6.9 7.5 6.8 7.1 -1 1.0002 BSJTA-Aif, _| « ^^^BTsM-V^cVum -\l0000\ PRESSURE (kb) Fig. 3. Longitudinal (solid line) and shear (dashed line) velocity ratios (v/v«) vs pressure for vitreous calcium aluminates. their pressure derivatives are not simple, however. Figure 3 shows that in the BaO-doped vacuum-melted and air-melted specimens the behavior of the shear velocity under pressure is anomalous, i.e. decreasing with pressure, and also that the behavior of the air-melted specimen is relatively more anomalous. The (dv./dP) values for the Si02-doped speci- mens are normal (positive) but low and are higher for the air-melted specimen. Anomalous behavior of shear velocity with pressure'"" has been found previously only in silicate glasses with a high silica content (>70%). Poisson's ratio is plotted vs pressure in Fig. 4. The (da/dP) values for the calcium aluminate glasses lie between 6.8X10"' and 7.5X10"' kbars"1 (Table II). The relations between bulk modulus and pressure are shown in Fig. 5. Since interstitial gas and water vapor are removed 542 Journal of The American Ceramic Society — Sokolowski and Manghnani Vol. 52, No. 10 in vacuum-melting, these glasses were expected to be less compressible than air-melted specimens, and this was con- firmed: the vacuum-melted specimens had higher bulk moduli (low compressibility), and, further, the pressure derivatives of their bulk moduli (dK./dP) are higher: 4.7 (Si02-doped) and 4.4 (BaO-doped) for vacuum-melted compared with 4.3 (SiO-doped) and 4.0 (BaO-doped) for air-melted glasses. The data also show that for both melt conditions, the BaO- doped specimen is less compressible than the Si02-doped specimen. VII. Summary and Conclusions 1. The calcium aluminate glasses studied are characterized by higher bulk and shear moduli and Poisson's ratios, in general, than the values reported for various silicate glasses. 2. The data for the calcium aluminate glasses fit well with the bulk modulus vs specific volume/ion pair relation reported for other glasses. 3. The elastic parameters of the calcium aluminate glasses and the pressure derivatives of these parameters are influ- enced by composition and melt condition. However, more data are needed to quantitatively evaluate the parameters in terms of compositional variation and melt condition. 4. At 1 bar, the vacuum-melted BaO-doped glass is the least compressible (highest K,), whereas the air-melted Si02-doped glass is the most compressible (lowest K,). 5. The anomalous behavior of shear velocity with respect to pressure in certain glasses has been attributed to high silica content; this study indicates that calcium aluminates with low silica content doped with BaO also exhibit anomalous behavior. 6. The (dK./dP) values of the calcium aluminate glasses examined range from 4.0 to 4.7, depending on composition and melt condition. The vacuum-melted and Si02-doped speci- mens have relatively higher (dK./dP) values. Acknowledgments The authors thank W. C. Levengood of the University of Michigan for providing the specimens and G. R. Miller and G. H. Sutton for constructive criticism of the paper. References 1 P. W. Bridgman, "Compressibility of Several Artificial and Natural Glasses," Am. J. Sci., 10, 81-102 (1924). 2 Francis Birch, "Effect of Pressure on the Modulus of Rigid- ity of Several Metals and Glasses," J. Appl. Phys., 8, 129-33 (1937). 30. L. Anderson and G. J. Dienes; Chapter 18 in Noncrystal- line Solids. Edited by V. D. Frechette. John Wiley & Sons, Inc., New York, 1960. ' M. H. Manghnani, "Role of Silica Content in the Anomalous Elastic Behavior of Silicate Glasses Under Pressure"; pre- sented at the 71st Annual Meeting, The American Ceramic Society, Washington, D. C, May 5, 1969 (Glass Division, No. 10-G-69); for abstract see Am. Ceram. Soc Bull., 48 [4] 434 (1969). 5 Louis Peselnick, Robert Meister, and W. H. Wilson, "Pres- sure Derivatives of Elastic Moduli of Fused Quartz to 10 Kilo- bars," J. Phys. Chem. Solids, 28 [4] 635-39 (1967). 8 M. H. Manghnani and W. E. Benzing, "Pressure Derivatives of Elastic Moduli of Vycor Glass to 8 Kilobars," ibid., 30 [9] (1969). ' H. J. McSkimin, "Pulse Superposition Method for Measur- ing Ultrasonic Wave Velocities in Solids," J. Acoust. Soc. Am., 33 [1] 12-16 (1961). 8 Edward Schreiber and O. L. Anderson, "Pressure Deriva- tives of the Sound Velocities of Polycrystalline Alumina," J. Am. Ceram. Soc, 49 [4] 184-90 (1966). " W. C. Levengood, "Stress-Induced Defects in Vitreous Cal- cium Aluminates," J. Appl. Opt, 5 [12] 1906-10 (1966). 10 R. K. Cook, "Variation of Elastic Constants and Static Strains with Hydrostatic Pressure: Method for Calculation from Ultrasonic Measurements," J. Acoust. Soc. Am., 29 [4] 445-49 (1957). u R. J. Charles; pp. 1-38 in Progress in Ceramic Science, Vol. 1. Edited by J. E. Burke. Pergamon Press, New York, 1961. 12 H. T. Smyth, "Elastic Properties of Glasses," J. Am. Ceram. Soc, 42 [6] 276-79 (1959). PRESSURE (kbl Fig. 4. Poisson's ratio as function of pressure for vitreous calcium aluminates. o - Increasing Pressure • -Decreasing Pressure PRESSURE (kb) Fig. 5. Absolute values for adiabatic bulk modulus as function of pressure for vitreous calcium aluminates. The (rfKs/dP) values are given in parentheses. 15 C. J. Phillips, "Calculation of Young"s Modulus of Elastic- ity from Composition of Simple and Complex Silicate Glasses." Glass Technoi, 5 [6] 216-23 (1964). " N. Soga and O. L. Anderson: Paper No. 37 in Proceedings of the Seventh International Congress on Glass, Brussels, Bel- gium. 1965. Vol. I; 9 pp. Institut National du Verre, Charleroi. Belgium. 1966. 15 G. Y. Onada and S. D. Brown, "High Modulus Glasses Based on Ceramic Oxides," Final Report. Contract N 00019- 67-C-301, Rocketdyne. Canoga Park. California. 1-53, 196S. 81 Reprinted from Marine Technological Society Journal , Vol . 3, No. 3, 41-46. TIDAL MODULATION OF THE FLORIDA CURRENT SURFACE FLOW John A. Smith2, Bernard D. Zetler3 , and Saul Broida' ABSTRACT A tidal current analysis has been made of surface current observations obtained by the General Dynamics Monster Buoy in 1965 in the Florida Current off Hollywood, Florida. The analysis of 15 days of hourly speeds shows that the diurnal constituents K and 0 have larger amplitudes than the semi- daily M and S , this in sharp contrast to the predominantly semidaily tide in the area. The amplitudes and phases of the diurnal constituents support the hypothesis of a diurnal stand- ing wave oscillating between the open ocean and the Gulf of Mexico with a node in the Florida Straits near the latitude of Miami. The tidal analysis indicates that the tidal modulation accounts for roughly one fifth of the variance in the obser- vations. INTRODUCTION The pulsations of tidal origin in the Florida Current have long been a subject of interest and speculation. Pillsbury (1891) found monthly current variations related to the declination of the moon, and daily oscillations amounting in some instances to as large as 128 cm/sec. He reported two periods of increase and two periods of decrease during a lunar day. Parr (1937) reported current speed fluctuations up to 50 cm/sec. apparently caused by tidal forces, both diurnal, and more dominantly, semidiurnal. From studies of electric potential measurements between Key West, Florida and Havana, Cuba, Wertheim (1954) was able to show evidence of the diurnal tidal influence on the transport through the Florida Straits. He cited the dependence of the transport on both the semidiurnal Atlantic tide and the diurnal Gulf of Mexico tide. Webster (1961) analyzed a large amount of GEK data for both the Straits of Florida and off Onslow Bay, North Carolina. He concluded that although it was probably rash to ascribe the velocity fluctuation of the Florida Current predominantly to tidal causes, the periods of the fluctuations observed were on the order of one day. Recently Schmitz and Richardson (1967) utilized a least- squares harmonic analysis of transport data (acquired over a period of three years using the free-fall instrument technique) across a section of the Florida Current. Based on the limited data available, they indicate that it is possible for fluctuations of tidal period to be the major modulation of the Florida Current transport. Their estimates of transport amplitudes are 3.5 + 1 (106m3sec1) for tidal coefficients M2, K{ and Cy and 1.5 + 1 (106m3sec"1)forS,. MONSTER BUOY DATA Late in 1965, a General Dynamics ocean buoy was moored for testing and evaluation in the Straits of Florida at Mjy 1969 41 121 NOV I 22 ' a I 24 I 25 ' 26 I 27 '26 ' 29 ' 30 ■ IOEC • 2 Figure 1 . Current Velocity versus Time Lat. 26°01'N and Long. 79°51.2'W. From November 20 to December 18, 1965, the buoy was equipped with a rotary cur- rent meter placed immediately beneath the water surface. Cur- rent speed data for one-minute averages taken approximately each hour were telemetered to the mainland and recorded. Also available for this period are wind speed, wind direction, barometric pressure and the significant wave height at the time of recording. Current direction is considered as directionally steady in the north-south orientation of the Florida Current at this location. A plot of current velocity versus time (Figure 1) reveals fluctuations of current speed on the order of 30 cm/sec. with apparent periodicity of 24 hours. Harmonic analysis of the data was conducted to determine if the fluctuations were indeed due largely to tidal effects. HARMONIC ANALYSIS Comparative tests show that the harmonic constants for the same set of constituents are slightly more accurate utilizing the least-squares method as opposed to the classical approach (Zetler and Lennon, 1967). The greatest advantage in using the least-squares method, however, is that it requires neither equally spaced data nor a synodic period, whereas the traditional Fourier tidal analysis requires both equally spaced data and a quasi-synodic period of the principal constituents (Zetler, et a I, 1965). The least-squares method has been adopted by the Coast and Geodetic Survey for the analysis of long data series but, for 15 and 29 day series, a computer program based on Fourier analysis is now in use. Also, Parseval's Theorem states that the energy of a com- posite wave is composed of the sum of the energies of each of the distinct harmonic constituents of the waves of different frequencies making up the basic wave. Thus, from the current fluctuation data, the percentage of total energy due to periodic variations was calculated and compared to the total energy of all of the fluctuations; and the total energy contributed by indi- vidual periodic components was determined. RESULTS Figure 2 presents a plot of current velocity versus time with a superimposed plot of the predicted tidal component of the current from the results of this analysis. The predicted tidal current is plotted about the mean current (167.05 cm/ sec.) indi- cating the predicted Florida Current in the absence of fluc- tuations of a non-tidal nature. The hourly predictions were pre- pared by the Coast and Geodetic Survey using a least count of 0.1 knot, hence the step characteristic of the plotted curve. Figure 3 is a plot of the residual after the predicted tidal modu- lation of the Florida Current has been removed. As can be seen from Figure 1, the second half of the current data series is of much poorer quality than the first half. Gaps in the record were due to telemetry and recording failure. The intense abrupt fluctuations seem to be indicative of a gradual failure of the current meter. Data obtained from the first fifteen days of this period are continuous, and the current meter one-minute speed averages were available for each hour. 195 jrfl75 1 155- 135- | 21 NOV | 22 NOV | 23 NOV | 24 NOV | 25 NOV | 26 NOV | 27 NOV | 28 NOV | 29 NOV | 30 NOV | I DEC | 2 DEC | 3 DEC | 4 DEC | 5 DEC | PREDICTED TIDAL CURRENT OBSERVED CURRENT Figure 2. Current Velocity versus Time with Superimposed Plot of Predicted Tidal Modulation 42 MTS Journal v 3 n 3 21 NOV I 22 NOV I 23 NOV I 24 NOV I 25 NOV I 26 NOV I 27 NOV I 28 NOV I 29 NOV I 30 NOV I I DEC I 2 DEC I 3 DEC I 4 DEC I 5 DEC I WIND DATA (MPH) 04 9 14 3 13 6 12 9 12 2 II 7 SE WNW NW SE SE SSE SSE 10 6 170 22 3 20 7 19 7 10 1 II 5 NNE W N E NE SE SSE SSW ENE S E Figure 3. Plot of the Residual After Tidal Modulation is Removed An initial computer analysis of the entire data series utilizing a least-squares program indicated that the diurnal tidal constituents, K and 0 , are the predominant contributors to the tidal fluctuations of the current. The results of the least- squares analysis for the diurnal constituents for the first fifteen days and the entire period are compared in Table 1. That the amplitudes and phase angles agree reasonably well in the two separate analyses is indicative that the diurnal tidal components are in fact significant and that our results are not due to random fluctuations. Because the second half of the data series was of marginal reliability, it is not included in the remainder of the analysis. Table 2 indicates that three techniques for solving for the major tidal constituents produce relatively small differences. These can be accounted for based on the method of each tech- nique. The Fourier computer analysis was selected for determining the harmonic constants contained in Table 3. A total of 24 constituents, of which 15 were inferred from the 4 major constituents, were then recombined to produce the pre- dicted tidal modulation of the Florida Current for the period 2 1 November through 5 December 1965. TABLE 1 Comparison of least-squares harmonic analysis of the first half of the data series with that of the entire series 1. 15 DAY ANALYSIS Kl 01 (360 Data Entries) Amplitude* Phase Amplitude* Phase 0.11 59.8° 0.12 273.5° 2. ENTIRE DATA SERIES Kl 01 (596 Data Entries) 0.15 43.5° 0.13 296.5° *Amplitude is in knots. Note: Amplitudes and phases are values prior to correcting for equilibrium argument, interference effects, etc. These comparative results will slightly differ from those found elsewhere in this paper as during the above analysis the constituent N was included in the calculations. TABLE 2 Comparison of results of harmonic analysis on the first 1 5 day data period using different analysis methods METHOD M2 S2 Kj O, Amp* Phase Amp* Phase Amp* Phase Amp* Phase 1. Hand Analysis (C&GS Spec. 0.063 55.73° 0.048 300.07° 0.125 60.43° 0.103 277.27° Pub. No. 98) 2. Least-Squares Analysis 0.066 57.2° 0.047 301.8° 0.115 59.6° 0.119 274.0° 3. Fourier Computer Analysis 0.063 59.64° 0.047 301.46° 0.132 55.94° 0.106 281.42° •Amplitude is given in knots. Note: The amplitudes and phases given are values prior to correcting for equilibrium argument, interference effects, etc. May 1969 43 TABLE 3 Harmonic constants from Florida current data CONSTITUENT** AMPLITUDE (H) (cm/sec) KAPPA*** (a) DIURNAL CONSTITUENTS Ki Pt Q, J, Mi 00, RHO, 2Q, (b) OTHER CONSTITUENTS M„ M, M4 M8 T2 NU2 L2 2N2 LAMBDA2 R. 5.710 5.551 1.888 1.075 0.437 0.396 0.237 0.211 0.144 3.400 2.500 1.101 0.679 0.664 0.658 0.458 0.304 0.278 0.149 0.129 0.098 0.087 0.026 0.020 24.49° 12.25° 24.49° 6.13° 30.61° 18.37° 36.74° 6.98° 0.00° 114.95° 309.40° 159.88° 309.40° 277.76° 203.68° 236.23° 41.08° 290.55° 309.40° 191.79° 26.22° 292.41° 38.13° 309.40° **Nomenclature and constituent speeds are in accordance with the classical Doodson classification. ***The phases are referred to tidal flow to the north; for a south direc- tion apply +180°. To convert to Greenwich Epoch (G), add the product of the longitude (79.85°) times the value of the constituent subscript. Astronomical data for the period are given in Table 4. It can be seen that the predicted tidal modulation is in agreement with the astronomical data for the period. The additive effect of M2 and S2 on November 22 is not readily apparent due to the semi-diurnal components being over-shadowed by K and O as they approach phase agreement on November 26. The pre- dominant diurnal modulation becomes negligible as K and O come into opposition on December 3, leaving only semi-diurnal tidal modulation of less than usual amplitude because M and S were in phase opposition on December 1. TABLE 4 Astronomical data for period 21 November through 17 December 1965* 22 November 26 November 29 November 1 December 3 December 8 December 10 December 1 1 December 1 5 December 16 December New moon Moon farthest south of equator Moon in apogee Moon in first quarter Moon at equator Full moon Moon farthest north of equator Moon in perigee Moon in last quarter Moon at equator *From American Ephemeris and Nautical Almanac. Fluctuations of the observed and predicted current are in excellent agreement and clearly show that the tidal modulation is the major periodic fluctuation of the current during the period 23 through 30 November. During the remainder of the data series, correlation with the predicted tidal modulation re- mains fairly good, but the mean current speed is raised or lowered, apparently in response to local wind stress, or possibly in response to atmospheric variations over the water regions which are coupled to the Florida Straits. Figure 3 is a plot of the residual after the predicted tidal modulation has been removed from the data. Included is the mean local wind speed and average wind direction at the buoy location in the Straits during each day from midnight to mid- night. It would appear that response of the current to wind stress from either the east or west is negligible , and further that the current responds fairly rapidly to winds from a southerly direction. Response of the current to northerly winds appears more complicated, with the indication from this limited data series being that the current initially is slow to respond to northerly winds; but once the response commences, the current speed is greatly lowered and recovery to normal conditions is quite gradual. The seemingly erratic period, November 30 through December 3, contained the highest wind speeds, and rough seas were prevalent. Table 5 presents statistical results from the 15 day analysis of the current data. During this period the tidal modu- lation accounted for 21.35 per cent of the total fluctuations, with the remainder being fluctuations of an apparent non- periodic nature. 44 MTS Journal v 3 n 3 DISCUSSION TABLE 5 The analysis of the surface current data reveals large diurnal tidal modulation of the Florida Current. This is in agree- ment with the tidal analysis performed on the transport of the Florida Current by Richardson and Schmitz (op. cit. ) and tidal analysis of transport fluctuations from studies of electric po- tential measurements by Wertheim (op. cit). It is further in agreement with Project MIMI's results, where underwater acoustic signals transmitted across the Straits of Florida over long periods of time have shown prominent diurnal phase changes (Steinberg and Birdsall, 1966), (Clark and Yarnall, 1967). Recently, Zetler (1968) calculated the amplitude of the K tidal current in the Florida Straits required to conform to observations of the oscillating diurnal tidal water transport in the Gulf of Mexico. The Kt amplitude of 0.11 knots found from the harmonic analysis of the Monster Buoy data is re- markably close to his calculated value of 0.12 knots. Zetler concluded, after consideration of the known K and (^am- plitudes and phase angles at shore stations along either side of the Straits of Florida, that there is a strong indication of a longitudinal standing wave for the major diurnal tidal com- ponents in the Straits of Florida, with a node close to the latitude of Miami. The large amplitudes of the diurnal constituents of the tidal modulation of the Florida Current at the Hollywood latitude are in agreement with this concept, as the tidal current should be maximum at the node. Zetler and Hansen (1968) have used the Kl phase of the tidal current observed at the Monster Buoy as additional evidence of a stand- ing wave. The current observations near the node should have a phase 90° earlier than the observed tide in the Gulf of Mexico. Because of differences in longitude, it is more meaningful to use phase angles referred to the same meridian, usually Greenwich. An approximate generalized Greenwich phase for K in the Gulf of Mexico is 20°. The comparable phase of 284° for the tidal current at the Monster Buoy is about 90° earlier than the tide in the Gulf and therefore supports the hypothesis of a standing wave. Statistical results and energy calculations for the 1 5 day period 1. Mean Current Velocity 167.05 cm/sec 2. Standard Deviation 15.42 cm/sec 3. Average Fluctuation 9.23 per cent 4. Total Current Variance 237.90 cm2 /sec2 5. Predicted Tidal Current Variance 50.79 cm2/sec2 6. Fluctuations Due to Tidal Components .. 21.35 percent 7. Per cent of Item 6 Due to Major Diurnal Tidal Components (Kj andOj) 71 percent 8. Per cent of Item 6 Due to Major Semi- Diurnal Tidal Components (M2 and S2) 20 per cent 9. Energy Contributed by Individual Tidal Constituents (cm2 /sec2) Kj 16.30 Oj 15.40 M2 5.78 S2 3.12 Px 1.78 S6 0.60 Qj 0.58 Remainder Semi-Diurnal Constituents . 0.88 Remainder Diurnal Constituents 0.24 SUMMARY AND CONCLUSIONS Harmonic analysis of Monster Buoy data covering 1 5 com- plete days confirms that the tidal influence on the Florida Cur- rent surface flow does not conform to the usual Atlantic coastal tidal configuration. Instead, the influence is transitional be- tween the semi-diurnal Atlantic tide and the diurnal Gulf of Mexico tide. The tidal coupling between the Gulf of Mexico and the Atlantic Ocean, with pronounced diurnal features, can be explained at present only by a heretofore overlooked longi- tudinal, diurnal, standing wave oscillating through the Florida Straits. The obtainment and subsequent analysis of tide obser- vations at additional points along the lower third of the east coast of Florida should confirm the presence of this diurnal, standing wave. A fluctuation of 10 per cent of the mean surface current is given as representative of the Florida Current. Slightly more than one-fifth of this modulation is attributed to tidal influence. ACKNOWLEDGMENTS The authors wish to thank R. A. Cummings, C. B. Taylor, and other Coast and Geodetic Survey, ESSA, personnel at Rock- ville, Md. for providing tidal predictions and analysis. The Florida Current data were made available by General Dynamics Corp. and W. S. Richardson of Nova University. This work was supported by the Office of Naval Research under Contract Nonr 4008 (02). May 1969 45 REFERENCES LT. Smith, U.S. Navy, is currently an instructor in the Naval Science Depart- ment at the U.S. Naval Academy, Annapolis. He has a B.S., 1961, from the USNA, and an M.S. (Oceanography), 1968, from the University of Miami. Clark, John G. and J. R. Yarnall, 1967. "Long Range Ocean Acoustics and Synoptic Oceanography, Straits of Florida Results," Contribution No. 798, Institute of Marine Sciences, University of Miami. Unpublished Manu- script. Parr, Albert E., 1937. "Report of Hydrographic Obser- vations at a Series of Anchor Stations Across the Straits of Florida," Bulletin Bingham Oceanographic Laboratory, Yale University. 6 pp. 1-62. Bernard D. Zetler is Director of the Physical Oceanography Laboratory, Atlantic Oceanographic Laboratories, ESSA in Miami. He has a B.S. from Brooklyn College, and has done graduate work at George Washington University and the Department of Agriculture Grad- uate School. He has been with the Federal Government since 1938, serving in the Hydrographic Office and the Coast and Geodetic Survey. Pillsbury, John E., 1891. "The Gulfstream - A Descript- ion of the Methods Employed in the Investigation and the Results of the Research," Report of the Superintendent of the U. S. Coast and Geodetic Survey, Appendix 10. 461-620. 4. Schmitz, William J. and W. S. Richardson, 1967. "On the Transport of the Florida Current," Nova University. Un- published Manuscript. 5. Steinberg, John C. and T. G. Birdsall, 1966. "Underwater Sound Propagation in the Straits of Florida," Journal Acoustical Society of America, 39 (2), p. 301-315. Saul Broida has been on the faculty of the Institute of Marine Sciences, Uni- versity of Miami, since 1961. He has a PhD in physical oceanography. He has done extensive research in the dynamics and kinematics of the Florida Current, and has participated in Equalant II, International Cooperative Investigation of the Tropical Atlantic. 6. Webster, F., 1961. "The Effect of Meanders on the Kinetic Energy Balance of the Gulfstream," Tellus 13 (3), p. 392-401. 7. Wertheim, G. K., 1954. "Studies of the Electric Potential Between Key West, Florida and Havana, Cuba," Trans- American Geophysical Union. 35 (6), p. 872-882. 8. Zetler, Bernard D., M. D. Schuldt, R. W. Whipple and S. D. Hicks, 1965. "Harmonic Analysis of Tides from Data Randomly Spaced in Time", Journal of Geophysical Re- search, 70 (12), p. 2805-2811. 9. Zetler, Bernard D. and G. W. Lennon, 1967. "Some Com- parative Tests of Tidal Analytical Processes," Inter- national Hydrographic Review, 44 (1). p. 139-147. 'Contribution No. 1022 from the Institute of Marine Sciences, University of Miami. Institute of Marine Sciences, University of Miami, Miami, Florida. Physical Oceanography Laboratory, Atlantic Oceanographic Labora- tories, ESSA, Miami, Florida 10. Zetler, Bernard D.. I9b8. "Tides in the Gulf of Mexico." Physical Oceanography Laboratory, ESSA, Miami. Pre- liminary Report. Unpublished Manuscript. 11. Zetler, Bernard D. and D. V. Hansen. 1%S. "Proposed Tide Program - Gulf of Mexico," Physical Oceanography Laboratory. ESSA, Miami. Unpublished Manuscript. 46 MTS Journal v 3 n 3 82 Reprinted from Deep Sea Research Vol. 16, Suppl. 447-470 Deep-Sea Research, 1969, Supplement to Vol. 16, pp. 447 to 470. Pergamon Press. Printed in Great Britain. Fluctuations of the Florida Current inferred from sea level records C. WlJNSCH*, D. V. HANSENf and B. D. ZETLERf Abstract — Power spectra and coherences were computed from simultaneous tide records at Miami, Florida ; Cat Cay, Bimini Islands ; Key West, Florida ; and Havana, Cuba, as a measure of statistical variability of the Florida Current. Diurnal and semi-diurnal tides account for most of the power in sea level variations at all stations, and approximately half of the remaining power is in the annual variation. Power levels are generally higher on the left side of the current but no significant power peaks were found between the annual and tidal frequencies. Coherence is generally low between all stations, but where significant coherence is found, it occurs with essentially zero phase, indicating that sea level tends to rise or fall together on opposite sides of the Florida Straits. The zero-phase coherence suggests a common response to local weather events. Low coherence was found between atmospheric pressure and sea level, with essentially an inverse barometer response for fluctuations of period greater than ten days. At shorter periods the response is direct barometric. Coherence between vector wind and sea level was also low, so that removal of linear weather effects (by a Wiener multichannel filter) accomplished little reduction of total power, and did not materially change coherence amplitudes or phases. A sharp result is obscured by the general lack of coherence between records, but the major conclusions are that the Florida Current is fairly steady, r.m.s. modulation at all periods between two days and one year amounting to perhaps 25 % of the mean, the annual fluctuations accounting for about 10%, and linear weather effects have only a minor influence on statistical sea level. The instantaneous fluctuations of the transport could be consider- ably larger, but the low r.m.s. values indicate that extreme transport values are unusual if they occur at all. INTRODUCTION Using ship-drift data, Fuglister (1951) has documented an annual cycle in surface current speed in the Gulf Stream system, with a range of approximately one-third the mean current speed, as shown in Fig. 1. Pillsbury (1890) observed fortnightly and higher frequency tidal modulation of flow in the Straits of Florida. Von Arx, Bumpus and Richardson (1955) suggested that visual and thermal " shingle " structures observed along the edge of the Gulf Stream northward from the Straits of Florida might be caused by fluctuations of the flow through the Straits. Dominant periods of approximately four and seven days were found in 28 days of GEK data from this region analyzed by Webster (1961). These results were all based on short records however, and therefore no conclusions could be drawn about the significance of the observed fluctuations. The only intensive study of fluctuations in flow rate and transport appears to be that of Wertheim (1954) who obtained electrical potential measurements by means of an underwater telegraph cable between Key West and Havana. The potential measurements were converted to volume transport T, by the relation r=i^ (i.i) ft ♦Department of Earth and Planetary Sciences, Massachusetts Institute of Technology, Cam- bridge, Massachusetts. tPhysical Oceanography Laboratory, Atlantic Oceanographic Laboratories, ESSA, Miami, Florida. 447 448 C. Wunsch, D. V. Hansen and B. D. Zetler jam rrn mar apr may jun jol AUG SEP 0( ;t NOV OCC V"* 1 ^p> w Y* V "•-* TRADES ^» ■-■» ' -*1 /j y" ■»^" ^^,4 — *•■; * 2 16 r — , CARIBBEAN > 14 ^,^ / IS &*' n •4 /S \\ Sf \\ 6* \i ^i — » Vi 60 ~*jr / 3 98 / > /" ^ FLORIDA 56 < «u i*^ ^ o *♦ t > ,- «r * \ X / V\ A< ' w */« V» /' o. *° k ' »^ p •» *• > 3 46 ^ A X 44 ^ 4 42 ^^* SOUTH ^~4* OF 40 J* HATTER AS 36 14 23 22 21 CO 13 12 II <*>-. jt* f* ." vs. V , — - \N 5 Vs ,> N.E. OF HATTERAS N •^ — 2* 55s •* _^* *^> ^>» 4 6 S.W. OF GRAND 10 io r 4 BANKS 3 7 SOUTH OF AZORES Fig. 1. Annual cycle in surface currents of the Gulf Stream system. After Fuglister (1951) Included is the annual variation of the Trade Wind system. Broken line represents fitted sinusoids. Fluctuations of the Florida Current inferred from sea level records 449 where His the vertical component of the earth's magnetic field, d is the mean depth of the channel, and A is the electrical potential difference measured across the channel. Annualmeansof thetransportssoobtainedvariedonlymoderately from|25 x 106 m3/sec over several years (cf. Stommel, 1957, 1959, 1961, and Broida, 1962, 1963, for later reports of these measurements). This figure is about 80% of that found in recent direct measurements by Schmitz and Richardson (1968), which suggests that the potential difference generated by the current is partially short-circuited by the con- ducting bottom. In addition to tidal period modulations, the data show large erratic transport fluctuations (Fig. 2). Changes as large as the mean transport occuring within a few days occasioned speculation about transport switching between the Florida Current and Antilles Current branches of the Gulf Stream. But the Florida Current does not fill the strait between Key West and Havana in the same sense that it does between Miami and the Bahama Banks, and there remains the possibility (raised and dismissed by Wertheim) that some of the variation observed is due to partial short-circuiting of the electrical potential by lateral movement of the axis of the stream into regions of varying depth. A series of papers by Montgomery (1938, 1941a, b) lays the foundation for our own analysis of fluctuations of the Florida Current. The first consideration, and the only one for which Montgomery had suitable data for application to the Straits of Florida, is that of the Bernoulli relation between sea level and the speed of the flow on a surface streamline, Vs2 + 2gl = constant, (1.2) where Vs denotes surface current speed in the stream axis, g is gravitational accelera- tion and £ is local sea level. Montgomery (1938, 1941a) in applying (1.2) to the Straits of Florida between Key West and Miami found that the mean sea level difference between these stations determined by a precise leveling survey was sub- stantially less than required to explain the observed acceleration of the current between these stations. The monthly means of sea level difference between the two places occasionally indicated a negative slope, leading to the conclusion that sea level variations on one coast are not a useful indication of the strength of the Florida Current. Nonetheless, assuming sea level is relatively invariable somewhere upstream and that the speed of the stream in the axis of the current is the controlling measure of the strength of the flow, we expect local sea level to respond to changes in current speed approximately as X - vs r^/ — 0-2 sec iVs g more or less uniformly across the stream. Tide gauges installed at Havana, Cuba and Cat Cay, B.I., provide data, unavailable to Montgomery, on variations of sea level across as well as along the current. In a geostrophic flow, the Coriolis effect associated with the surface current is in near balance with the transverse pressure gradient, requiring a difference in sea level across the stream, H=f-Vs (1.3) g where the overbar denotes the average value across the stream, L is the width of the stream, and f is the Coriolis parameter. Studies by Iselin (1940), Hela (1952), and 450 C. Wunsch, D. V. Hansen and B. D. Zetler o 2? UJ o |— u _) T3 < L- CO >- o O -a a: o. UJ o a ^ 0- (/> 1-1 >- in < g 5 01 or 10 en < 3 o 2 3 a o. < £ (3»s/ ui oDiaOdSNVHl Fluctuations of the Florida Current inferred from sea level records 45 1 Stommel (1953) of monthly mean sea level at these stations are summarized by Stommel (1965). Sea level at all stations and cross-stream differences of sea level are greatest in July when the flow is strongest. Geodetic leveling does not span the Florida Straits with sufficient precision to enable direct determination of absolute differences in sea level, so we consider only the variation of sea level difference implied by the geostrophic relation H =f_L IV. g ' which amounts to approximately 0-5 sec and 0 8 sec at Miami-Cat Cay and Key West- Havana respectively. In the simplest interpretation, the sea level change should be of the same amplitude and opposite sign on the two sides of the channel. Curvature associated with meandering of the stream within the straits introduces perturbations ± g R into (1.3), where R is the radius of curvature of the flow. Since very little is known of the magnitude and cross-stream coherence of curvature occuring in the stream, we have estimated the possible importance of this effect from 17 six-hour drogue trajec- tories from the Gulf Stream at mean Lat. 32°N.*, where the flow is presumably subject to less severe lateral constraint than in the Straits of Florida. The mean curvature in these trajectories is 0 0056 km-1, in accord with that of the eastward turning of the stream at this latitude, and the standard deviation is 0004 km-1. Using Vs2 r* 1 m2/sec2, the perturbation of sea level difference is estimated as «-^(J)-w(fMiH- a potentially significant contribution, but probably an overestimate. The absolute difference of sea level across the Straits of Florida is useful as a reference against which to measure the observed fluctuations. By applying (1.3) to the current measurements by Pillsbury (1890), Montgomery (1941b) and Hela (1952) estimated the cross stream difference in sea level at Havana and Miami as 52 and 58 cm, respectively. Using the recent transport measurements reported by Schmitz and Richardson (1968) we compute a sea level difference of 66 cm at Miami. Little is known about the representativeness of these measurements except that monthly mean sea level at Miami was near normal at about 5 cm below the annual mean when most of the observations by Schmitz and Richardson were made. We have investigated in greater detail the question of variation of the Florida Current as evidenced in sea level records. In particular, we have used hourly values instead of monthly means to seek fluctuations of comparatively high frequencies. The record pairs are not simultaneous. Although Hicks and Shofnos (1965) show that smoothed secular trends at Miami and Key West are quite similar, the annual sea level values fluctuate greatly over short periods and therefore the spectral ♦These observations were made by the U.S. Coast and Geodetic Survey Ship Peirce, 1965-1966. The data is on file at Atlantic Oceanographic Laboratories, ESSA, Miami, Fla. 452 C. Wunsch, D. V. Hansen and B. D. Zetler estimates in the very low frequencies may vary considerably depending on the epoch being used. We wish to re-emphasize that the sea level differences strictly relate only to surface speed of the current, but the assumption will be made throughout that this is a reflec- tion of total transport changes. The geostrophic assumption is applied only to changes of sea level with periods exceeding two days. For shorter periods we have not attempted to relate sea level changes to transport, as geostrophy is unlikely to be valid. 2. METHODS OF ANALYSIS AND DISCUSSION OF RESULTS The discussion of our results is divided into parts. In the first part we work only with the observed sea level variations across and along the Florida Current axis. In the second part we attempt to improve our results by taking the effects of local weather into account. The conclusions change very little. v KEY WEST -gj&i. ■■■"' 24° S T" *l 82° 80° 79° Fig. 3. The Florida Current region of the Gulf Stream. The records at our disposal were hourly values of sea level from the tide gauges at Miami and Cat Cay (1938-1939), Key West and Havana (1953-1956), and Key West and Miami (1957-1962). A chart of the general area and detail charts of tide- gauge location are shown in Figs. 3 and 4. Our time-series methods are nearly standard, and we will only outline the proce- dures here. The hourly sea level values were edited for miscellaneous errors by a procedure described in Zetler and Groves (1964). Daily values of sea level were then obtained in a two-step procedure. An ordinary 35-term convolution filter was first used to remove the semi-diurnal and diurnal tides [the so-called D35, described by Groves (1955)]. In order to avoid aliasing the continuum between the tidal lines, a recursive low-pass filter was then applied. Fluctuations of the Florida Current inferred from sea level records 453 SECTION OF CSCS CHART 547 CAT CAY, BAHAMAS, 8WI rs or FLORIDA LOCATION OF TIDE GAUGE HAVANA HARBOR, CUBA t-AT 2V09N-LONC 92*20 W Fig. 4. Locations of tide gauges used in this study. Let /(to) be the Fourier transform of the filter. Then the filter transfer function was |/(-)| 2 — 1 + e2 r32 (a>) (2.1) where 7s (to) is the 3rd order Chebyschev polynomial, Cis a normalization constant and e is a constant controlling the degree of " ripple " in the filter pass-band. For a discrete time low-pass filter we put 2(1 -z) (1 +*) (2.2) z being the discrete-time z-transform variable. A discussion of the high-speed recur- sion (feed-back) application of the filter may be found in Shanks (1967). The Chebyschev response is discussed in Weinberg (1962), and the distortion due to the mapping (2.2) is discussed in Golden and Kaiser (1964). The doubly filtered, hourly values were then resampled at 24-hour increments yielding the working time series. The spectra and coherences were all computed from Cooley-Tukey Fourier transforms, using the perfect Daniell (rectangular) frequency window. Owing to the 454 C. Wunsch, D. V. Hansen and B. D. Zetler rapid low-frequency rise of the sea level power, the transforms were, in practice, computed in two sections to avoid a leakage of power from the low-to-high frequency end of the spectrum. The low-frequency transforms were performed directly on the 24-hour samples. The high-frequency transforms were performedon the 24-hour samples after they had first been filtered with a high-pass filter of the form of (2.1). To obtain a high-pass recursive filter from (2.1) one simply lets (1+z) 2(1 -z) (2.3) The effects of the three filters involved have been removed from the spectra. All spectra are shown as power instead of the more common power density. They may be converted to power/cpd by multiplication by 128/cpd for the spectra based on daily values, and by 3152/cpd (Fig. 5 only) for the ones based on hourly values. Approximate 95 % confidence limits are shown on all spectra, and the 95 % signifi- cance levels for the zero-hypothesis are shown on the coherences. These are from the Ml A HI POWER 40 I I I I l I I I I I I I CAT CAY POWER 20 40 *%. /*.•. . .„. CYCLES/HOUR CYCLES/HOUR Fig. 5. High frequency pair spectra at Miami and Cat Cay. Peaks are due to semi-diurnal tides and their harmonics. Miami shows a small diurnal peak. Fiuctations of the Florida Current inferred from sea level records 455 tables of Amos and Koopmans (1963). The confidence limits for coherence phase and amplitude are large and depend upon the values of the coherence amplitude. They may be estimated from the tables of Amos and Koopmans (1963) and Groves and Hannan (1968). We have not corrected the small positive bias in the coherence amplitude estimates ; the phase estimates are unbiased. In retrospect the spectra and coherences were run at too high a resolution. We were searching for a nonexistent frequency structure and might as well have sacri- ficed resolution for statistical reliability. The consequences of this are most severe for the coherences, as indicated by the high 95 % level for the hypothesis of zero coherence. The scatter in the phases of coherence give good eye estimates of true level of coherence. Table 1. The total power and r.m.s. amplitude for each station over the entire record. Spectrum Root-mean-square amplitude (cm) Non-seasonal r.m.s. (cm) Miami 100 81 Cat Cay 5-9 5-2 Miami- Cat Cay 8-7 — Havana 8-7 5-5 Havana residual 7-6 5-3 Key West 91 6-8 Key West residual 8-9 6-5 Havana-Key West 8-4 7-1 Havana-Key West residual 7-2 6-3 Key West-Miami 9-4 — Bermuda 11-4 — In each section, Miami-Cat Cay, Key West-Havana, and Key West-Miami, we have shown in Table 1 the r.m.s. amplitude of each station over the entire record. This includes the energy lying in periods from the total record length to two days (the filter cutoff). We also show the difference power between the station pairs, and in some cases the " annual " power and amplitude. As a comparison with a totally differ- ent oceanic regime, we have included similar results at Bermuda. The power in the difference is explicitly related to the coherence. Let £\ () be the transforms of two tide records £1 (f ) and £2 (0- Then the power spectra are the brackets denoting ensemble averages (in practice, of course, we use frequency- band averages). Then the power spectrum of the difference of £1 and £2 is = *!>(«) = #11 (w) + 022 (w) — 2RI #12 (<") = #11 (w) + #22 (w) — 2 Rl Cohi2 \/(#ii #22) where Cohi2 is the coherence between £1 and £2. The difference power in the case of zero-coherence is the sum of the powers. If £1 and £2 tend to be coherent with 180° phase, #z> ((a>) approaches 456 C. Wunsch, D. V. Hansen and B. D. Zetler 0n _|_ 022 _ 2 \/(&n #22), a lower bound, which will be zero if 12 24 36 46 60 1 1 1 1 1 1 1 1 | 1 1 | | 1 1 1 -• • •• •. /"• 1 a -•-• »— 5— • -* _ _ 4 _ '"/-.• *. *". _ 0 ibo .-.•* • •* •• " - - . ~ • CAT CAY LEADS " 120 • " 60 - * • • - . • • * • • •• • 0 • • * .•* !•••* . ■ * • • * • -.. . s • • - -60 - • • "- - • . • - • ~ 120 - - - MIAMI LEADS _ - I'll! - CAT-CAY SEA LEVEL POWER 95% CONFIDENCE INTERVAL CYCLES/DAY MIAMI-CAT CAY SEA LEVEL DIFFERENCE POWER • • • . •.*. . . ••• • • • • • • • • 1 ' ' 95\ CONFIDENCE LIMITS • • • • • CYCLES/DAY CYCLES/DAY Fig. 6. Results at Miami and Cat Cay. 458 C. Wunsch, D. V. Hansen and B. D. Zetler KEY WEST St A- LEVEL POWER HAVANA SEA-LEVEL POWER .6 iJl • ORIGINAL POWER A RESIDUAL POWER 95% CONFIDENCE INTERVAL A* jN.» * A.A A4* ^ .'* CYCLES/ DAY KEY WE ST -HAVANA COHERENCE 32 ~T KEY WEST LEADS -4 - * i 4 > A Aa A'A . HAVANA LEADS aft* ••A • ORIGINAL COHERENCE A RESIDUAL COHERENCE CYCLES/OAT • ORIGINAL POWER A RESIDUAL POWER > 95% _ CONFIDENCE - INTERVAL A 1 a A »A X#. • s* •. A. A A„ - ^.> *A A ** \A^A. V.A*.A. A * A 4 -J* A A A 1 1 • 1 1 1 CYCLES /DAY KEY WEST- HAVANA SEA-LEVEL DIFFERENCE (Si 6 • ORIGINAL POWER 4 RESIDUAL POWER ll 40 • A 1 95% o • CONFIDENCE "A* INTERVAL j • 4". A *• * A • • • to M •• • - A ' •a 4 . A 1 * * A* A A* • '.V A A A • [ 4W* A. %. ' * • CYCLES /DAY Fig. 7. Results for Key West and Havana. Fluctuations of the Florida Current inferred from sea level records 459 KEY WEST SEA LEVEL POWER MIAMI SEA LEVEL POWER 1 I 1 1 ! 1 1 1 1 1 1 1 1 1 95% CONFIDENCE _ INTERVAL * • • - . ,•• •■» „ •» * • i : i i > 1 — l — i — r i ■ T--r i i i iiii 95% CONFIDENCE - • INTERVAL ••• m *•* Vj 0 10 •* io"1 i • *•• • • - • •• • •• • i i i i CYCLES/DAY COHERENCE MIAMI a KEY WEST SEA LEVEL CYCLES/ DAY KEY WEST- MIAMI SEA LEVEL DIFFERENCE POWER I I i i i i : i i 1 1 1 1 0; 5! e 4 V.- .;.?;.-- -\-y-r.r; ••• - 180 - 120 : • KEY WEST LEADS ; - 60 * • - . . • • - 0 -60 -120 • • • * * • " . - $ * • •• ' • - MIAMI LEADS _ - -ISO i i l i i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 - - 6 10° ' •**". 95% CONFIDENCE - INTERVAL '•"•.•• 10 1 * *■ •* •. 1 :•: 1 *' I 1 CYCLES/DAY CYCLES /DAY Fig. 8. Results for Key West and Miami. 460 C. Wunsch, D. V. Hansen and B. D. Zetler BERMUDA SEA- LEVEL POWER 126 DAYS 2 DAYS T 1 14 DAYS 1 ' • 95 V. CONFIDENCE INTERVAL • ^ • • • - • * * f ' 1 1 •• •• • 1 I CYCLES/DAt Fig. 9. The Bermuda sea level spectrum. (d) Bermuda 1953-1957 This result is in Fig. 9 as a comparative study. The spectral levels are about the same as for the other four locations, with slightly greater energy at periods of 5-10 days. Discussion There are three obvious conclusions we can draw from the results thus far: (1) The power levels are very low. There is no possibility of 50% fluctuations of the Gulf Stream transport as suggested by Wertheim (1954). If the sea-surface slope measurements reflect transport changes, then the transport varies by at most 25%, of which about 1/4 is a seasonal change. This is in agreement with the findings of Schmitz and Richardson (1968) drawn from wholly different methods and data. (2) There is no real structure in the fluctuations; there are no distinct fortnightly or other major frequency components. The monotonic rise in power toward lower frequencies is a demonstration that calculations based upon monthly means are a good indicator of the long-period fluctuations. In particular, the seasonal oscillation we have found is in good agreement in amplitude and phase with that calculated by Pattullo, Mink, Revelle and Strong (1955) (Fig. 10) and with the surface currents tabulated by Fuglister (1951), (Fig. 1). (3) The small fluctuations that do exist appear to be basically incoherent. To the extent that cross-stream records are coherent (in particular Havana-Key West for periods of 2-10 days), the phase is zero, indicating that the two sides of the stream oscillate up and down together, perhaps as a result of the Bernoulli effect. Let us postulate a model of the Gulf Stream in which the sea surface is fixed at Havana and permitted to oscillate at Key West. Then the power is zero at Havana. Now suppose that the Havana side moves only in response to the Bernoulli effect so Fluctuations of the Florida Current inferred from sea level records 461 MONTHLY MEAN SEA LEVEL- after Patullo et al. cm + 20 + 10 0 -10 + 10 0 -10 JFMAMJJAS0ND -« — •- "• — • MIAMI CAT CAY + 10r- . . o— •— • * * • * « . CAT CAY-MIAMI -10- • m -20 - + 20 - + 10- . * . o , 9 M * • KEY WEST -ioL • • • + 10p • o -10L • • + 10i- • • HAVANA 0 -10 + 10- 0 — -10- + 10i- ~9 •" Jt •_ • • • 9 • • •" -. HAVANA-KEY WEST -• KEY WEST- Ml AM I o 10 i , * •— •— • , , «——•—, HAVANA- CAT CAY Fig. 10. Annua! changes in sea level based on monthly means. After Pattullo, Munk, Revelle and Strong (1955). that Havana fluctuations are due only to the non-linearity. Associated with a core speed of twice the mean surface speed, we then expect that Havana sea level will move up and down with Key West with about 33 % of the Key West amplitude. Let us now write 462 C. Wunsch, D. V. Hansen and B. D. Zetler Ch (0 = AUw (0 + n (0 where t,H is Havana sea level, law is Key West sea level, and n(t) is that part of Havana sea level unrelated to (incoherent with) Key West. A is a constant scale factor. If Havana responds primarily to Bernoulli effects, we expect that the power at Havana coherent with Key West should be about 10% of the power at Key West. In fact, the coherence is about 04 on the average, and thus the coherent power at Havana is about 16% of the Key West power. A is about 0-36, which is a reasonable value under the Bernoulli hypothesis. One could equally well postulate that the Key West side is geostrophically anchored and Havana moving; we cannot choose between these possibilities or some intermediate case on the basis of the available data, as long as the nature of the incoherent fluctuations remains obscure. The lack of downstream coherence, Key West-Miami, can be rationalized in several ways. One interesting idea is as follows: due to the shoaling and narrowing of the channel from Key West to Miami, the current accelerates downstream. Using a mean current speed (over the whole water column) at Key West of 25 cm/sec, the speed at Miami is 63 cm/sec. Suppose there exist disturbances in the stream at Key West with a frequency a (to an observer at rest) with a characteristic wavelength of A = 250 km. Then the apparent frequency to an observer fixed at Miami is a' = a + U2tt/X where U is the difference between the surface speeds at the two locations. Putting in the numbers, we find a shift in frequency Aa-277^= 10-6/sec. (2.5) A The coherencies were computed with a resolution frequency 8^2Wky-s^3-6Xl°_8/SeC a6) almost two orders of magnitude sharper than the frequency shift. Depending upon the generation mechanism for stream disturbance, i.e. the Q of the system, the coher- ence could be totally destroyed. This Doppler shifting could be an important effect, but it should be pointed out that there are several other ways to destroy coherence between two records. In particular, the cyclostrophic effects discussed in the introduction need not be coherent with transpou changes. If meandering within the straits is important (and this is the best explanation of Wertheim's large voltage fluctuations), the coherence we measure both across and downstream is reduced; the power in the sea level variations then also overestimates the transport changes. We have no quantitative measure of these effects of meandering. 3. WEATHER The zero-phase difference between the record pairs suggests that sea level is re- sponding to local weather effects, perhaps the barometric fluctuations. The low coherence amplitude between stations suggests that one station might be responding to one component of wind, and the other station to the other component. To the Fluctuations of the Florida Current inferred from sea level records 463 extent that the wind components are incoherent, the sea level records would be incoherent, and might account for the occasional negative slope between Key West and Miami. In an attempt to explore the relationship between weather and sea level, we obtained hourly values of wind and atmospheric pressure at Key West and Miami. Before proceeding we would like to emphasize that we are dealing with small numbers KEY WEST ATMOSPHERIC PRESSURE 95% CONFIDENCE INTERVAL CYCLES/ DAY COHERENCE KEY WEST PRESSURE 8 HAVANA SEA LEVEL COHERENCE KEY WEST PRESSURE a SEA LEVEL ^ Q 8 Jl t; » • - •-. ••-•-•-•-. — 0. 4 0 180 ,.* # . • • • H *••••-# * • \ • • • * - • • - — 4 • " — 120 • - - 60 - • • - — • • ~ • • • S" 0 ^ .. •*• • . •• * ..• •..•• <». " •• • . • - -60 • • • • . •••■ • -120 - • • • % 1*1 1 1 1 ■ CYCLES/DAY CYCLES /DAY Fig. 11. Pressure power spectrum from Key West and the coherence with sea level at Key West and Havana. 464 C. Wunsch, D. V. Hansen and B. D. Zetler in proportion to the mean difference in sea level across the Florida Current. Any " removal " of weather effects will reduce the power in what is already a very small fluctuation of the current, but perhaps will unmask frequency structure in these fluctuations. The wind records are reported on the basis of hourly speed and a 16-point compass direction code. These were converted to east and north component of wind. The 16-point code introduces a high background noise — the least count error. Owing to the erratic behavior of the wind, the error checking was abandoned. It was extremely difficult to determine when a change in wind direction and speed was not real. There ke r west east wind power KEY WEST NORTH WIND POWER 1 1 I 1 • • • • ••• • 1 95X CONFIDENCE INTERVAL • • • • • • V • • •..>• 1 L_ 1 l l 1 1 1 I ■- 1 1 • ****A. •• 95% . *> • CONFIDENCE .* •• INTERVAL • • m •V.\ % 1111, CYCLES/DAY CYCLES/DAY COHERENCE KEY WEST EAST WIND a SEA LEVEL COHERENCE KEY WEST NORTH WIND a SEA LEVEL - • - — S£A LEVEL LEADS * _ —■• • - -^ I ~ • • . • * — - - . *. • . • • • • • • - • . • . • — - NORTH WIND LEADS • - ■ * "' 1 L__. 1 ! ! " CYCLES/ DAY CYCLES/DAY Fig. 12. Power in the two components of wind at Key West and the coherence with the sea level there. Fluctuations of the Florida Current inferred from sea level records 465 is a possibility, which we cannot evaluate, of aliasing from high frequency wind changes. The pressure records are probably more reliable, as the spectrum of pressure computed by Gossard (1960) shows a steep rise toward low frequencies. We deal primarily with the weather record at Key West in the period 1953-1957. As the Havana weather record was unavailable, we have used Key West weather to compare with the Havana tide gauge. The power spectrum of Key West pressure is shown in Fig. 1 1 ; the most obvious feature is that it is much flatter than the equivalent sea level spectrum. Coherence with Key West sea level and Havana sea level is shown in the figure as well, and is quite low. At the lower frequencies, periods about 128 days to 10 days, the phase tends to be near ± 180°, indicating an isostatic inverted barometer effect at both locations. The coherence level is too low to make calculations of the actual " baro- meter factor " meaningful. At the higher frequencies on the contrary, the average phase tends to be zero, a direct barometer effect. The cause of this change is not apparent and is in distinction to the results of Groves and Hannan (1968), who found an essentially isostatic response at all frequencies, for two Pacific islands. On the other hand, Hamon (1966) found non-static barometer effects at some Australian locations. We note that the coherence involved is low; and, in general, the contribution of atmospheric pressure to the sea level oscillations is small. The coherence between the two components of wind and sea level is shown in Figs. 12 and 13. The level is about the same as for pressure. We note that the phase between Key West sea level and east component of wind is generally positive at high frequencies, indicating that either sea level fluctuations lead the wind or that an increase in wind leads to a drop in sea level. The latter conclusion would appear to COHERENCE KW EAST WIND a HAVANA SEA- LEVEL 0 16 32 18 64 Si i 8 .4 0 ISO ..T *• . «- - • . " "" • • . . • * - SL. LEADS * '." " 120 . * . * 60 • • • • 0 •*•*.. .' • • '•• ••': •• • -60 - . - • -120 " WIND LEADS -ItO i l »i I r COHERENCE KW NORTH WIND 8 HAVANA SEA-LEVEL 0 16 32 4S 64 e T 1 ■ 1 1 ! . 4 0 180 . * S L LFJSQS • m - 120 . ," - 60 " . . - 0 -60 " •' . • *•• • # - ■'• -120 "• • . WIND LEADS -180 I l 1.. _l 1 CYCLES/DAY CYCLES/DAY Fig. 13. Coherence of Key West wind and Havana sea level. 466 C. Wunsch, D. V. Hansen and B. D. Zetler be more acceptable except that it is difficult to reconcile with the chart in Fig. 4, which places the gauge on the eastern side of the harbor. At Havana there is a change over from 180° (acceptable for a gauge on the western side of the harbor) to zero- phase at intermediate frequencies. At the highest frequencies there is a trend back toward 180° but with reduced coherence. It is difficult to generalize about these results. In a variation on the coherence calculation, and in an effort to raise the coherence between these two stations, we removed the linear wind effects from sea level by constructing the Wiener optimum filters relating sea level and wind at each location. We then computed the residuals at each location and compared the power and coherence with the non residual results. In particular, let £j* be discrete-time sea level at the zth place, and let et and nt be east and north wind at Key West. Then using the daily values we put Ne N„ £,< = Z aKl et-K + Z bKl nt-K + it* (3-2) where ft* = {at1, bA is a finite approximation to the multi-channel Wiener optimum filter and &* is " noise," or that part of sea level incoherent with the wind. In practice Ne and Nn were equal, and after a little experimentation were chosen as either 9 or 10, corresponding to a maximum time lag of sea level response to wind of nine days. Note that the a? and bt* are zero for t less than 0, requiring that sea level respond only to past or present values of wind and not to future values. The validity of this causal assumption depends upon the absence of an " ocean-driven wind circulation," investigation of which is outside the scope of this paper. A discussion of the finite, discrete, Wiener optimum filter, and the recursive solution for it may be found in Levinson (1947) and in Wiggins and Robinson (1965). Due to the finite filter length, the filter characteristics are principally determined by the spectral components of the data with the most power. For this reason the operation of removing the wind was performed on both the low- and high-passed versions of sea level discussed above, and the power spectra patched together as before. In each case equation (3.2) is solved for the residual noise (Za^et-K + ZbKirtt-A. (3.3) Since the filters are of necessity of finite length, they are broad-band in frequency, operating in those frequency bands where sea level and weather may be incoherent. For this reason, we expect that the power in £tl will exceed the power in £t* in regions of sea level wind coherence. The power should be less where there is true coherence, and the wind correctly removed. The results are shown in Fig. 7 where the residual power is plotted for comparison wiih the original results. Generally speaking the power has decreased by a small amount; the totals are given in Table 1. The decrease is at most 20%, a figure we could have anticipated from the coherence levels. The small increase in power at the high frequencies indicates that here the filters were ineffective, presumably due to the very small power levels associated with these frequencies. The remedy for this is to high-pass the data, leaving only these frequencies, and compute a Wiener filter for this region of the spectrum. We deemed this unnecessary since the power involved is very Fluctuations of the Florida Current inferred from sea level records 467 small. The total decrease in power is of the same order as found for Kwajalein and Eniwetok in the mid-Pacific by Groves and Hannan (1968), using a much more elaborate procedure and dispensing with the causality condition. The coherence between the residuals dropped slightly at low and high frequencies with the phases remaining scattered about zero degrees. At intermediate frequencies there was a slight increase in coherence with a subsequent small decrease in the phase scatter about zero degrees. The residual difference power in Fig. 7 reflects these changes. The very slight change we made in the power levels led us to drop any further experimentation along these lines. Discussion The weather variables account for no more than 20 % of the total sea level varia- tion or about 5 % of the total mean cross-stream pressure head. At the lowest fre- quencies, the weather effects are essentially static; they are definitely nonstatic at periods shorter than about ten days. It is plainly possible to explain these results in terms of a dynamic model of the response of this region to large scale weather systems, but we will not pursue the subject further here. The weather regression could undoubtedly be improved by using longer filters, more weather variables from more locations, and perhaps by using the geostrophic wind as well as observed wind. There is little reason to anticipate any qualitative improvement ; however, we did make one attempt at exploring another approach as described below. 4. A STRESS EXPERIMENT The calculation of coherences and convolution relations between sea level and wind depend for their interpretation upon an assumption of a linear response of water to wind. A commonly accepted relation for stress on the sea surface is the expression t = 0-0025 joaw|w | (4.1) w being vector wind, t the vector stress, pa the density of air. Steady winds are normally implied. This is, of course, a nonlinear relation, and (4.1) represents a complicated transformation of the frequency structure of the non-steady winds. To the extent that sea level responds to stress and not to wind directly, there would be a low coher- ence between wind and sea level. On the other hand, if the stress law (4.1) can be linearized, there will be no difference between stress and wind coherence with sea level. Note that (4.1) tends to emphasize the importance of strong winds. To study the applicability of (4.1), we used the 2048 days of available Miami wind and sea level. The unnormalized time series (ret, rut) = (et, nt) (et2 + «<2)* (4.2) were computed from the daily values of the wind. The filtering involved in computing the daily values is involved in a complicated way in the frequency structure of (4.2). The power in each component of stress and the coherence between wind and stress (east stress on east wind, north stress on north wind) and coherence between stress and sea level at Miami and at Key West were computed. Some of the results, which are puzzling, are shown in Fig. 14. 468 C. Wunsch, D. V. Hansen and B. D. Zetler For north stress (not shown) there is no problem. The coherence with sea level is low, and the coherence with north wind is high. Since the coherence of north wind with sea level is also low, north stress is apparently sufficiently represented by a linearization of (4.1). For east stress the picture is quite different (Fig. 14). The stress-sea level coherence is markedly higher than the wind-sea level coherence, in several peaks. But most striking is the essentially linear-phase relationship between stress and sea level, as indicated by the dashed lines on the coherence-phase plot. Such a law is characteristic of a system with pure delay. Let t (/) be a stress component with Fourier transform t (co), and let £ (t ) = — t (/ — /0) be sea level. It is easy to see that £ (to) = — e"""'° f (a>) yielding a coherence phase difference, (to) = — o»/0 + tr, linear in frequency with value 77(180 degrees) at w = 0. to is ambiguous up to multiples of 2 n. From the slope of the phase curves in Fig. 14, we find the smallest possible value of to is about thirteen days. Such a delay time is difficult to rationalize, but Stommel (1965) estimates that a change in the North Atlantic wind system would be reflected in the Florida Current MIAMI EAST WIND POWER POWEP IH MIAMI EAST COMPONENT OF STPESS COHERENCE MIAMI EaST WIND a MIAMI SEJ -LEVEL «B 60 CYCLES /DAr COHERENCE MIAMI EAS! STRESS 3 MIAMI SEA-LEVEL CTCLCS/Dtr Fig. 14. Results of the computation on stress and sea level at Miami (see text). Fluctations of the Florida Current inferred from sea level records 469 about fifteen days later. The agreement is presumably fortuitous. If Stommel's idea were correct, we would expect a similar relationship between Miami stress and Key West sea level. We found no significant coherence, which we could have antici- pated from the low Key West-Miami sea level coherences. The result remains a puzzle, There is a low coherence between east stress and east wind at Miami in the range where the stress-sea level coherence is highest, and a somewhat higher coherence' where the stress-sea level coherence is lower. This is consistent with the low wind-sea level coherence. Since the filtering effects from computing daily values of wind are included in a complicated way in the computation of (4.1) and (4.2) (and the spectra are uncor- rected for this effect), we attempted to investigate the effects of this on the results by computing stress from hourly values of wind, and then low-pass filtered to obtain daily east stress values. The result was a very low coherence between stress and sea level, and the phase was essentially random, implying that high frequency wind fluctuations are not effective in exerting a stress on the ocean. If, in fact, stress is directly related to sea-state as is often hypothesized, and if sea-state is primarily determined by winds of many hours' duration, then our result is reasonable. Since the law (4.1) is postulated for steady winds and is of itself somewhat arbitrary, any further exploration of stress-sea level effects should be done systematically to determine empirically the best form of stress law. We are currently investigating techniques to do so. Acknowledgements — This work was supported by the National Science Foundation through Grant GA-434 with the Massachusetts Institute of Technology. We are indebted to the United States Coast and Geodetic Survey, Rockville, Maryland, for making the sea level records available, and for their continued cooperation throughout. Prof. Henry M. Stommel contributed a great deal to this study in continual discussions of our results and we are highly indebted to him. The data analysis was performed at the Information Processing Center at MIT. The bulk of the work was done while we were visiting the Woods Hole Oceanographic Institution and we thank them for their hospitality. REFERENCES Amos D. E. and L. H. Koopman (1963) Tables of the Distribution of the coefficient of coherence for stationary bivariate Gaussian processes. Sandia Corp. Monogr, SCR-483. Broida S. (1962) Florida Straits transports. April 1960-January 1961. Bull. mar. Sci. Gulf Carib., 12, 168. Broida S. (1963) Florida Straits transports. May 1961 -September 1961. Bull. mar. Sci. Gulf Carib., 13, 58. Fuglister F. C. (1951) Annual variations in current speeds in the Gulf Stream System. J. mar. Res., 10, 119-127. Golden R. M. and J. F. Kaiser (1964) Design of wideband sampled— data filters. Bell Syst. tech. J., 43, 1533-1545. Gossard E. E. (1960) Spectra of atmospheric scalars. /. geophys. Res., 65, 3339-3351. Groves G. W. (1955) Numerical filters for discrimination against tidal periodicities. Trans. Am. geophys. Un., 36 (6), 1073-1084. Groves G. W. and E. J. Hannan (1968) Time series regression of sea level on weather. Rev. Geophys., 6 (2), 129-174. Hamon B. V. (1966) Continental Shelf waves and the effects of atmospheric pressure and wind stress on sea level. J. geophys. Res., 71 (12), 2883-2893. Hela I. (1952) The fluctuations of the Florida Current. Bull. mar. Sci. Gulf Carib., 4, 241-248. Hicks S. D. and W. Shofnos (1965) Yearly sea level variations for the United States. /. Hydraul. Div., ASCE, 91, (Proc. Pap. 4468) 23-32. 470 C. Wunsch, D. V. Hansen and B. D. Zetler Iselin C. O'D. (1940) Preliminary report on long period variations in the strength of the Gulf Stream System. Pap. Phys. Oceanogr. Meteorol., 8 (1), 1-40. Levtnson N. (1947) The Wiener r.m.s. error criterion in filter design and prediction, appendix to N. Wiener (1947) Extrapolation, Interpolation and Smoothing of Stationary Time Series, MIT Press, 163 pp. Montgomery R. B. (1938) Fluctuations in monthly sea level on eastern U.S. coast as related to dynamics of western North Atlantic Ocean. J. mar. Res., 1 (2), 165-185. Montgomery R. B. (1941a) Sea level difference between Key West and Miami, Florida. J. mar. Res., 4 (1), 32-37. Montgomery R. B. (1941b) Transport of the Florida Current off Havana. J. mar. Res., 4 (3), 198-220. Pattullo J., W. Munk, R. Revelle and E. Strong (1955) The seasonal oscillation in sea level. J. mar. Res., 4 (2), 88-155. Pillsbury J. E. (1890) The Gulf Stream — A description of the methods employed in the investigation, and the results of the research. U.S. Coast Geodetic Survey Rep. for 1890, Appendix No. 10, 461-620. Schmitz W. J., Jr and W. S. Richardson (1968) On the transport of the Florida Current. Deep-Sea Res., 15, 679-693. Shanks J. L. (1967) Recursion filters for digital processing. Geophysics, 32 (1), 33-51. Stommel H. M. (1953) Examples of the possible role of inertia and stratification in the dynamics of the Gulf Stream System. /. mar. Res., 12, 184-195. Stommel H. M. (1957) Florida Straits transports, 1952-1956. Bull. mar. Sci. Gulf Carib., 7, 252-254. Stommel H. M. (1959) Florida Straits transports : June 1956-July 1958. Bull. mar. Sci. Gulf Carib., 9, 222-223. Stommel H. M. (1961) Florida Straits transports : July 1958-March 1959. Bull. mar. Sci. Gulf Carib., 11,318. Stommel H. M. (1965) The Gulf Stream. University of California Press, 2nd. edn. 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. Webster F. (1961) A description of Gulf Stream meanders off Onslow Bay. Deep-Sea Res., 8, 130-143. Weinberg L. (1962) Network Analysis and Synthesis. McGraw-Hill Co., New York, pp. 692. Wertheim G. K. (1954) Studies of the electrical potential between Key West, Florida, and Havana, Cuba. Trans. Am. geophys. Un., 35 (6), 872-882. Wiggins R. A., and E. A. Robinson (1965) Recursive solution to the multichannel filtering problem. /. geophys. Res., 70 (8), 1885-1891. Zetler B. D. and G. W. Groves (1964) A program for detecting and correcting errors in long series of tidal heights. Int. Hydrogr. Rev., 41 (2), 103-107. 83 Reprinted from Handbook of Ocean and Underwater Engineering North American Rockwell, Inc., (McGraw-Hill Inc. New York). TIDES B. D. Zetler Tides and tidal currents give rise to periodic changes in the ocean level and are the result primarily of lunar and solar gravity influences on the water masses of the oceans. Pole Pole * To moon To moon (o) (b) Fig. 1-38 Lunar tidal effects: (a) moon on equator; (6) moon at maximum declination. A simplified (although fictitious) model permits a useful delineation of the forces involved in tidal theory. If a rigid earth is considered to be completely covered by a deep layer of ocean, the magnitude and direction of the tidal forces can be related to the various motions of the moon and sun.476' Friction and inertia are disregarded, so it is assumed that the waters respond instantly to the attraction of the tide-produc- ing body. SEA MOTION 1-75 In the earth-moon system there is a high-water bulge at both points where the line connecting the centers of earth and moon intersects the surface of the earth. There is a low-tide belt circling the earth between these points (Fig. 1-38). There is a similar tide caused by the sun, but its amplitude is only 46 percent of the lunar tide. From a fixed point on earth, both the moon and sun vary in longitude, declination, and distance. These changes are cyclical, and therefore the tide at a given time and place can be calculated as the sum of a series of cosine curves representing tidal con- stituents whose amplitudes, periods, and phases are known. These are the bases of some tidal constants used in tide prediction. However, the earth does not have a surface of water that is either uniform or of the required depth to validate this equilibrium theory. Furthermore, friction, inertia, viscosity, and the continental masses make meaningless any theoretical determinations of amplitude and phase. Mathematicians have made remarkable use of the identi- fication of tidal frequencies. With this knowledge and a sufficiently high signal/noise ratio, sophisticated analysis techniques have been developed. Tidal records that are ordinarily continuous hourly heights (Fig. 1-39) are subjected to a Fourier analysis modified by the knowledge of tidal frequencies and utilizing theoretical ratios of am- plitudes and phase relationships for a refinement of results. Although methods have been developed for obtaining harmonic constants from a tidal series as short as only a few days, a year of hourly heights is desirable for a satisfactory determination and resolution of the tidal components. Tidal Components The U.S. Coast and Geodetic Survey considers 37 components in its analysis and prediction procedures.64 Some European tide-predicting agencies use more than 60 components, the larger number being related primarily to additional shallow-water tidal components (nonlinear combinations of tidal frequencies) that are found signifi- cant in their home waters. The following important tidal components are described to illustrate the concept. Lunar and Solar Components. The principal lunar semidiurnal component has an average period of 12 hr and 25 min; the principal solar semidiurnal component has a period of 12 hr. These two components will be in phase at new and at full moon, causing spring tides (high waters appreciably higher than average and low waters lower than average) about every 15 days. They are opposed (out of phase) at the first and last quarters of the moon; the resulting smaller than average ranges are called neap tides. The moon does not remain at a fixed distance from the earth. A lunar elliptic semidiurnal component with a period of 12.66 hr is in phase with the principal lunar constituent at perigee (moon closest to the earth) and out of phase at apogee (moon farthest from the earth). Perigean and apogean ranges are approximately 20 percent larger and smaller, respectively, than the mean range. In Fig. 1-39 the larger spring ranges for New York at times of new and full moon are quite apparent.46 Perigee occurs at the same time as full moon, making the ranges appreciably larger than the spring tides 2 weeks earlier, when new moon and apogee are just 1 day apart. To take care of diurnal inequalities in the tide associated with large declinations of moon and sun, diurnal components are introduced whose periods are such that they are in phase at extreme declination and opposed when the moon (or sun) is on the equator. Figure 1-39 illustrates the importance of extreme declination of the moon in the larger inequalities at Seattle, Los Angeles, and Honolulu. At Pakhoi the tide is completely diurnal, except for a few days when the moon is near the equator. Nonastronomical Components. Some tidal components do not have astronomical causes. Estuaries may be considered to consist of various superimposed basins, each of which has a vibration period determined by its length and depth. Although the period of an enclosed basin'is 2L/(gh)M, where /. is the length, g is gravity, and h the depth, a bay open to the ocean has a period twice as long. If the opening of the bay is large compared to the basin length, its period is even longer.2 When the period of a basin approximates a harmonic of a tidal period, it introduces a repetitive disturbing wave that more or less persistently distorts the shape of the tidal curve. The irreg- ular dimensions of real basins make it difficult to estimate their effect on the tide. 1-76 BASIC OCEANOGRAPHY N E 9 u c c P £ September c Os I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 _ e •, new moon; J.firstquorter; Qfull moon ;(, lost quorter; E, moon on the Equator; N.S.moon torthest north or south of theEquctor; A,P, moon in apogee or perigee; Oj.sun ot autumnal equinox. x=chart datum Fig. 1-39 Tidal variations at various places during a month. SEA MOTION 1-77 Higher harmonics of the largest components are calculated and introduced in the predictions to simulate the observed shape of the curve. In general, the tide in an estuary is a progressive wave, high water occuring later with distance upstream. The range of tide depends on the cross-section dimensions, the phasing of the incoming wave with a reflected wave from the head of the estuary, and the damping coefficients.62 The tidal current floods upstream and ebbs down- stream, going through slack water before each reversal. Ordinarily the characteristics of the tide or tidal current for a particular place are best determined from observations. See Hurricanes and Typhoons for a discussion of storm tides. Cotidal Charts After tides were observed and analyzed at many places, tidal mathematicians found they could draw cotidal charts, which have lines indicating places at which high waters of a particular component occur simultaneously. Many fit the data with the concept of a progressive wave (wave advancing horizontally with a fixed period between successive crests). Others used superimposed stationary waves (the back-and-forth sloshing observed on a rectangular pan of water, one end of which is raised and quickly lowered). In the latter concept, when it is high water at one end of a basin, it is low water at the other, and at the middle there is a nodal line with no rise or fall of the water. Dietrich1 favors the progressive- wave idea in theoretically projecting the tidal lines offshore. Along some coasts the cotidal lines are thickly clustered and thereby describe large changes in time of tide in relatively short distances. On the East Coast of the United States the semidiurnal cotidal line is more or less parallel to the shoreline, showing that high water occurs almost simultaneously all along the outer coast. On the West Coast these lines are somewhat normal to the coast, showing a progressive change in time of high water with distance along it. Thus these charts can be used for estimat- ing the tidal regime at places for which no observations are available, whereas estimat- ing from only a few nearby stations may be extremely unreliable. Measurement of Tides Tide Level. Tides are ordinarily measured by gages which use floats in wells to orient the position of a pencil or stylus on an analog record. A limited orifice at the bottom of the well dampens the high-frequency wind-wave effect. These gages can be portable or permanent, and various types of pressure sensors are used when a pier or piling is not available for mounting the equipment above the water surface. If necessary, hourly observations can be made visually in a graduated vertical scale, averaging crest and trough splash marks for an observation at any given time. A short series obtained in any of these ways furnishes a rough estimate of average range and sea level, particularly if obtained during ordinary meteorological conditions. In- asmuch as a very short series may include only a limited period, such as spring tides, more reliable values can be obtained if the observations are reduced by comparison with data for a station of similar tidal characteristics for which better-determined mean values are available. Chart Datum. The datum of a nautical chart is the level to which all soundings on the chart are referred. In principle, it is desirable to have a level such that the tide seldom or never drops below it. In that case we would not have negative-tide pre- dictions, and the mariner could always count on having at least the charted depth of water. For historic, legal, and engineering reasons, the U.S. Coast and Geodetic Survey61 has not followed this principle, using mean low water on the East Coast and mean lower low water on the West Coast. Thus on the East Coast half of all low waters fall below chart datum ; on the West Coast, half of all of the lower of the two low tides a day fall below the datum. Many countries use appreciably lower datums, some using a level chosen arbitrarily such that the tide is unlikely to fall below it. Seasonal changes in various meteorological parameters (wind, pressure, and temper- ature) result in slow cyclical changes in sea level. Monthly mean values of sea level averaged over a number of years are analyzed for an annual and a semiannual varia- 1-78 BASIC OCEANOGRAPHY tion, which are in turn introduced in the predictions to reproduce the seasonal change in sea level. Tidal Currents. There has not been an intensive effort on the part of oceanographcrs to measure tidal currents in the ocean because these measurements are not only expensive but also somewhat unreliable. Instrumental contributions to the observa- tions may be almost as great as the relatively low velocities observed. Unlike tidal- current predictions in estuaries and rivers, tidal currents in most of the ocean have little or no significance to navigators. Theoretically it is possible to predict tidal currents in the open ocean from cotidal charts if water depth and Coriolis force are considered.2 This prediction assumes that the tide is a progressive wave with maximum current occurring at times of high and low LL+3h North L.2J1H-3 LL+2 LL+1 L-3 H+3 Scale in knots 0.0 0.2 04 0.6 0.8 1.0 (a) 0.1 0.2 0.3 Scale in knots (b) Fig. 1-40 Rotary-current plot (current rose) : (a) mean current curve, Nantucket Shoals Light Vessel, July, 1920; (b) tidal-current curve, San Francisco Lightship referred to predicted time of tide at San Francisco (Golden Gate), California. water. However, in a stationary wave maximum current occurs at mean water level, exactly out of phase with a progressive wave. If the tides in the open ocean are considered to be some combination of progressive and stationary waves, there is no satisfactory method of inferring the tidal current from cotidal charts. There have been numerous long series of surface-current observations obtained from lightships in coastal waters.4960 Analysis of these data shows a rotary change in direction and a cyclical change in velocity during a tidal period. The simpler type of semidiurnal rotary current can be drawn as a current rose, a series of hourly vectors starting from a fixed point whose extremities can be described by an ellipse (Fig. l-40a) . The major axis of the ellipse describes the maximum flood and ebb of the tidal current; the minor axis represents the minimum currents in lieu of the slack water found with reversing currents. When rotary tidal currents are diurnal or have a large diurnal component, the current rose is unsymmetric and very complex (Fig. 1-406). 60 REFERENCES General 1. Coker R. E.: "This Great Wide Sea," University of North Carolina Press, Durham, N.C., 1949; reprinted by Harper & Row, Publishers, Incorporated, 1962. REFERENCES 1-79 2. Dietrich, G.: "General Oceanography," Interscience Publishers, Inc., New York, 1963. 3. Hill, M. N. (ed.): "The Sea," vol. I, Physical Oceanography; vol. II, Composition of Sea Water; vol. Ill, The Earth Beneath the Sea; Interscience Publishers, Inc., New York, 1962, 1963. 4. King, C. A. M.: "An Introduction to Oceanography," McGraw-Hill Book Com- pany, New York, 1962. 5. "Handbook of Oceanographic Tables, 1966," U.S. Navy Oceanographic Office Special Publication #68, 1967. 6. Sears, M. (ed.): Progress in Oceanography, Pergamon Press, New York (published annually). 7. Sverdrup, H. U., M. W. Johnson, and II. H. Fleming: "The Oceans: Their Physics, Chemistry, and Biology," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1942. 8. Weigel, II. L.: "Oceanographical Engineering," Prentice- Hall, Inc., Englewood Cliffs, N.J., 1964. 9. "Climatological & Oceanographic Atlas for Mariners," U.S. Government Printing Office, Washington, D.C., 1961. Physical Oceanography 10. Defant, A.: "Physical Oceanography," Pergamon Press, New York, 1961. A large two-volume work with examples, theory, and thoroughness. 11. Fuglister, F. C.: "Atlantic Ocean Atlas: Temperature and Salinity Profiles and Data from the International Geophysical Year," Woods Hole Oceanographic Institute, Woods Hole, Mass., 1960. A graphical summary of extensive series of temperature and salinity measurements made in the Atlantic during the Inter- national Geophysical Year. A comprehensive and well-printed collection of actual data. 12. LaFond, E. C: Processing Oceanographic Data, U.S. Navy Oceanog. Off.Publ. 614, 1951. A convenient set of instructions for computing densities and currents from classical temperature and salinity values. 13. Neumann, G., and W. J. Pierson, Jr.: "Principles of Physical Oceanography," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. Physical oceanography with a strong slant toward meteorology and waves. A big modern book with much information and mathematical material, both descriptive and pictorial. 14. Pickard, G. L.: "Descriptive Physical Oceanography," Pergamon Press, New York, 1963. An excellent paperback book on the title subject. 15. Pounder, E. R.: "The Physics of Ice," Pergamon Press, New York, 1965. An excellent paperback description of ice and its properties in the laboratory and at sea. 16. von Arx, W. S.: "An Introduction to Physical Oceanography," Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1962. An introduction to ocean- ography that was written by an oceanographer with the engineering student in mind. Chemical Oceanography 17. Barnes, H.: "Apparatus and Methods of Oceanography," pt. 1, Interscience Publishers, Inc., New York, 1965. 18. Harvey, H. W.: "Chemistry and Fertility of Sea Water," Cambridge University Press, Cambridge, England, 1957. 19. Mero, J. L.: "The Mineral Resources of the Sea," American Elsevier Publishing Company, New York, 1965. 20. Riley, J. P., and G. Skirrow (eds.): "Chemical Oceanography," vols. 1 and 2, Academic Press, New York, 1965. Geological Oceanography 21. Bascom, W.: "Waves and Beaches," Anchor Books, Doubleday & Company, Inc., Garden City, New York, 1964. 1-80 BASIC OCEANOGRAPHY 22. Krumbein, W. C, and F. J. Pettijohn: "Manual of Sedimentary Petrography," Appleton-Ccntury-Crofts, Inc., New York, 1938. 23. Kuenen, Ph. II.: "Marine Geology," John Wiley & Sons, Inc., New York, 1950. 24. Menard, II. W.: "Marine Geology of the Pacific," McGraw-Hill Book Company, New York, 1964. 25. Shepard, F. P.: "Submarine Geology," Harper & Row, Publishers, Incorporated, New York, 1963. Meteorological Oceanography 26. Bolin, B. (ed.): "The Atmosphere and the Sea in Motion," Rockefeller Institute Press, Oxford University Press, New York, 1959. 27. Gentry, It. C.: Current Hurricane Research, Weatherwise, 17: 180 (1964). 28. Pettersscn, S.: "Introduction to Meteorology," McGraw-Hill Book Company, New York, 1958. 29. Redfield, A. C, et al: "Interaction of Sea and Atmosphere," Meleorol. Monographs, 2 (10) (1957). 30. Sverdrup, H. U.: "Oceanography for Meteorologists," Prentice-Hall, Inc., Engle- wood Cliffs, N.J., 1943. 31. Taylor, G. F.: "Elementary Meteorology," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1954. 32. Annual Tropical Storm Report, 1963, U.S. Navi/ Fleet Weather Facility, Miami, Rept., OPNAV 3140-9, 1964. 33. Annual Typhoon Report, 1963, U.S. Fleet Weather Central/ Joint Typhoon Warning Center Rept., Guam, 1964. 34. "The Application of Oceanography to Subsurface Warfare," chaps. 5 and 7, National Defense Research Council, reprinted by Commission on Undersea War- fare of the National Research Council with Office of Naval Research, 1951 Sea Motion Waves 35. Bretschneider, C. L.: Wave Variability and Wave Spectra for Wind-generated Gravity Waves, U.S. Army Corps Engrs. Beach Erosion Board Tech. Memo. 118, 1959. 36. Bretschneider, C. L.: "Modification of Wave Spectra over the Continental Shelf," Proc. Eighth Conf. Coastal Eng., 1963. 37. Bretschneider, C. L.: Generation of Wind: State of the Art, Natl. Eng. Sci. Co. Rept. SN 134-6, 1965. 38. Cornish, V.: "Ocean Waves and Kindred Physical Phenomena," Cambridge, England, 1934. 39. Darbyshire, J.: The Generation of Waves by Wind, Proc. Roy. Soc. (London), Ser. A, 216: 299 (1952). 40. Jeffreys, H.: On the Formation of Water Waves by Wind, Proc. Roy. Soc. (London), Ser. A, 107: 189 (1924). 41. Kelvin, Lord: On the Waves Produced by a Single Impulse in Water of Any Depth, or in a Dispersive Medium, Proc. Roy. Soc. (London), 42 (1887). 42. Kitaigorodski, S. A., and S. S. Strekalov: Contribution to the Analysis of the Spectra of Wind-caused Wave Action, /. Izv. Geophys., 1962, p. 1221. 43. Pierson, W. J., Jr., and L. Moskowitz: A Proposed Spectral Form for Fully Devel- oped Wind Seas Based on the Similarity Theory of Kitaigorodski, N.Y. Univ. Tech. Rept. 63-12, 1963. 44. Russell, R. C. EL, and D. H. MacMillan: "Waves and Tides," Hutchinson's Scientific and Technical Publications, New York, 1952. Tides and Currents 45. Stommel, H.: "The Gulf Stream: A Physical and Dynamical Description," University of California Press, Berkeley, Calif., 1965. 46. Bowditch, N.: "American Practical Navigator," U.S. Navy Oceanographic Office, Washington, D.C., 1958. REFERENCES 1-81 47. Darwin, G.: "The Tides and Kindred Phenomena in the Solar System," W. H. Freeman and Company, San Francisco, 1902. 48. Doodson, A. T., and II. 1). Warburg: "Admiralty Manual of Tides," Admiralty Ilydrographic Department, London, 1941. 49. Ilaight, F. J.: Coastal Currents along the Atlantic Coast of the United States, U.S. Coast Geodet. Sur. Spec. Publ. 230, 1942. 50. Maimer, II. A.: Coastal Currents along the Pacific Coast of the United States, U.S. Coast Geodet. Sur. Spec. Publ. 121, 1926. 51. Manner, II. A.: "Tidal Datum Planes," U.S. Coast Geodet. Sur. Spec. Publ. 135, 1951. 52. I ted field, A. C: The Analysis of Tidal Phenomena in Narrow Embayments, MIT Woods Hole Oceanog. Inst. Papers Phys. Oceanog. Meteorol., 11(4) (1950). 53. Russell, II. C. H., and 1). H. MacMillan: "Waves and Tides," Hutchinson's Scientific and Technical Publications, New York, 1952. 54. Schureman, P.: "Manual of Harmonic Analysis and Prediction of Tides," U.S. Coast Geodet. Surv. Spec. Publ. 98, 1958. 55. Fckart, C: "Hydrodynamics of Oceans and Atmospheres," Pergamon Press, New York, 1960. TIDE FORECASTING B. D. Zetler Prediction of tides and tidal currents is a highly specialized technique which an engineer ordinarily will not wish to master. He will generally use the published tables and tidal-current charts to obtain required predictions. These tables and charts furnish a time-dependent correction to the depths published on nautical charts by the U.S. Coast and Geodetic Survey and the U.S. Navy Oceanographic Office. The tables,31 in four volumes covering different geographic areas, arc published by the U.S. Coast and Geodetic Survey and may be purchased from that agency and various sales agents. There are two related tidal-current tables published annually and a series of tidal-current charts for specific areas, showing current speeds and direction at various points for each hour in the tidal cycle. A list of publications relating to tides and currents and a list of sales agents may be obtained by writing directly to the U.S. Coast and Geodetic Survey, Uockville, Maryland 20852. Table 1 of the tide tables (Fig. ll-5Uo), an example of which is reproduced here from Itef. 31, furnishes the times and heights of high and low waters for a number of places in the area of coverage. The heights are added to the depths shown on nautical charts to obtain the total depth at the particular time. Note that if the tidal height is a minus quantity it should be subtracted from the chrrted depth. Table 2 (Fig. 11-506), an example of which is reproduced here from Ref. 31, furnishes tidal differences (time differences and height differences or ratios) for many additional places. The differences are applied to the predictions for a designated reference station in Table 1. Regardless of the time zone listed for the reference station, the predicted time of high and low water for a place in Table 2 will be in the time zone listed in Table 2 for that place. Supplemental tables are furnished for estimating the height of the tide at times in between high and low water. Predicted heights in these tables are compatible with the chart datum on the largest-scale nautical chart of the place for which the predictions are prepared. Table 1 of the tidal-current tables (Fig. ll-51o) furnishes daily predictions for a limited number of stations. The predictions consist of times of slack water and times and velocities of maximum floods and ebbs. "Flood" refers to the current movement from the ocean into an estuary, and "ebb" refers to the opposite current movement. In some complex geographical locations, as in a strait between two basins both connected directly to the ocean, the designated flood and ebb directions are chosen somewhat arbitrarily. Table 2 (Fig. 11-516) permits daily predictions for additional places by listing differences to be applied to the daily predictions for designated reference stations. In some places the tidal current turns cyclically in a clockwise or counterclockwise direction, during which it has maximum and minimum speeds rather than maximum and slack water of the reversing currents described in the previous paragraph. The tidal-current tables furnish hourly values of direction and speed for these rotary currents. The extremities of those plotted hourly vectors describe the current roso (nee Tidal Currents in Sec. 1). The tidal-current charts arc referred to predicted tides (high and low waters) or predicted currents (either maximum flood and ebb or slack waters). They are used in conjunction with predicted tables for the particular year in which the infor- mation is needed. The charts, which supply a visual generalized composite of cur- rents in an area, are a useful supplement to the tables. However, inasmuch as they are referred to only two phases in the tidal cycle, as opposed to four in the tidal- current tables, they are not ordinarily so accurate as the latter. 11-110 NEM TOKK ITHE BATTERY), M.T.i 1961 TIMES AND HEISHT5 OF MICH »N0 LOU MATERS OCEAN OPERATIONS 0»Y TIME H.N. NT. FT. OAV TIME H.M. HT. FT. OAT TIME H.M. HT. FT. OAY TIME H.N. H7. FT. OAT TIME H.M. HT. FT. OAT TINE H.N. HI ft t N 0248 0906 1MO 2136 -0.7 3.2 -1.0 4.0 16 TU 0236 0842 1316 2112 -0.2 *.a -0.7 3.T 1 TH 0*00 1018 1630 22*6 -0.5 4.6 -0.7 4.2 16 F 0336 09*2 1600 2212 -0.8 *.8 -0.9 *.6 1 F 03*2 09*8 153* 2212 -0.5 *.5 -0.6 *.* 16 SA 0318 0924 1336 21*2 -0 0 ■) .1 2 2 TU 0336 093* 1610 2230 -0.6 3.0 -0.9 4.0 IT M 0312 0918 1334 2134 -0.3 4.T -0.7 3.0 2 F 0**2 1100 1706 2336 -0.3 4.3 -0.3 4.1 17 SA 0*18 1030 16*2 2300 -0.7 *.6 -0.8 ♦ .7 2 SA 0*16 1024 1630 22*8 -0.3 *.2 -0.3 4.1 17 SU 0406 1012 1612 2236 -0 .9 .7 .7 .2 3 u 0424 1048 1T00 232* -0.4 4.T -0.7 4.0 16 TH 039* 1006 1630 2236 -0.4 4.6 -0.6 4.0 3 SA 092* 11*2 17*2 0.0 4.0 -0.2 16 SU 0306 1116 1716 23*8 -0.6 *.* -0.6 *.7 3 SU 0**8 1106 165* 2330 0.0 3.4 0.0 4.2 1* M 0448 1106 163* 2330 -0 .7 .4 .5 .0 * TH 0312 1136 1T48 -0.1 4.4 -0.4 19 F 0430 1046 1706 2324 -0.3 4.5 -0-6 4.1 4 SU 0018 0606 122* 182* 4.0 0.4 3.7 0.1 19 M 033* 1212 1806 -0.3 4.1 -0.3 4 N 0530 11*2 172* 0.3 3.6 0.1 19 TU 03*2 1200 1748 -2 .4 .1 .1 3 F 0012 0600 122* 1(36 3.9 0.2 4.1 -0.1 20 SA 0312 1136 1742 -0.2 4.3 -0.4 3 M 0100 0706 1306 1912 3.9 0.6 3.4 0.4 20 TU 00*2 0706 1306 1912 4.6 0.0 3.8 0.0 5 TU 0006 0606 1218 17*8 4.0 0.6 1.3 0.6 20 a 0024 06*8 1300 1854 .8 .0 .8 .3 4 SA 0100 0700 1306 1930 3.6 0.3 3.8 0.1 21 SU 0012 0606 1230 1830 4.2 -0.1 4.1 -0-3 6 TU 01*2 0812 13*8 2012 3.8 0.8 3.1 0.6 21 H 01*2 062* 1*12 2030 *.3> 0.2 3.3 0.2 6 M 00*2 0706 1300 1618 3.4 0.8 3.1 0.6 21 TH 0130 0612 1*06 202* .6 .2 .6 .5 T SU 01*6 0606 133* 202* 3.a 0.6 3.3 0.2 22 M 0106 0718 1316 1936 4.3 0.1 3.9 -0.1 T M 022* 0918 1**2 2118 3.7 0.8 2.9 0.7 22 TH 02*8 0936 132* 21*6 *.* 0.1 3.* 0.2 7 TH 012* 0830 135* 2012 3.6 0.9 2.9 1.0 22 F 0236 092* 1518 2136 .2 .5 ,4 a n 0236 0906 1**2 2118 3.8 0.7 3.3 0.3 23 TU 0200 0842 1418 2048 4.4 0.1 3.6 -0.1 6 TH 032* 1018 155* 2212 3.7 0.6 2.6 0.6 23 F 0*00 10*2 16*2 22*6 *.* 0.0 3.* 0.0 8 F 022* 0936 1306 2136 3.7 0.6 2.9 1.0 23 SA 03*8 \02* 1630 22*2 .3 .1 .7 .3 9 TU 032* 1000 13*2 2206 3.6 0.6 3.1 0.3 24 M 0306 0948 1330 2134 4.4 0.0 3.5 -0.1 9 F 0*2* 1106 1700 2306 3.8 0.4 2.9 0.5 24 SA 0512 1136 17*8 23*6 *.3 -0.2 3.T -0.2 9 SA 0336 1036 162* 2236 3.8 0.6 3.0 0.6 24 SU 0*5* 1118 1730 2336 -o .4 .1 .0 .0 10 M o*ia 103* 1636 223* 3.9 0.4 3.1 0.2 23 TH 0412 1034 1648 2300 4.5 -0.2 3.5 -0.3 10 SA 052* 1200 1600 4.0 0.1 3). 2 29 SU 0612 1230 16*2 *.7 -0.* 4.0 10 SU 0**2 112* 172* 2330 *.o 0.3 3.4 0.4 29 M 053* 1206 162* -0 .) .3 .3 11 TH 0312 11*2 1736 2336 4.0 0.2 3.1 0.2 26 F 0318 11*6 175* 233* 4.7 -0.4 3.6 -0.4 11 SU 0000 0612 12*8 16*6 0.3 4.3 -0.1 3.5 26 H 00*2 0700 1318 1930 -0.4 4.9 -0.6 4.3 11 N 03*2 1212 1812 4.3 0.0 3.6 26 TU 0024 06*2 123* 1904 -0 .2 .7 .4 .* 12 f 0600 1230 112* 4.3 0.0 3.2 2T SA 0618 12*6 18*8 4.9 -0.6 3.0 12 M 00*8 0700 1330 192* 0.0 4.6 -0.4 3.6 2T TU 0130 07*6 1*06 2012 -0.3 4.9 -0.8 4.4 12 TU 0016 0630 125* 165* 0.1 4.6 -0.3 4.2 2T H 0112 072* 1336 19*8 -0 .3 .7 .5 .8 13 SA 002* 06*2 1312 1912 0.1 4.3 -0.2 3.4 28 SU 005* 0712 1336 19*2 -0.3 5.1 -0.8 4.0 13 TU 0130 07*2 1*12 2006 -0.2 4.8 -0.6 4.0 26 0218 0630 1**2 205* -0.6 4.9 -0.8 4.9 13 H 0106 0712 1336 1936 -0.3 4.8 -0.6 4.4 28 TH 015* 0800 1*12 202* -0 .4 .6 .5 .1 14 SU 0112 072* 1*00 193* 0.0 4.6 -0.4 3.3 29 N 01*2 0800 1*2* 2030 -0.6 5.1 -0.9 4.2 14 M 0212 0816 1**8 20*8 -0.3 4.9 -0.8 4.3 29 TH 0300 0906 152* 2130 -0.6 4.T -0.7 4.9 14 TH 015* 073* 1*16 2016 -0.7 3.0 -0.8 4.9 24 F 0236 06*2 1**6 2100 -0 .4 .5 .4 .1 IS M 013* 0800 1436 2030 -0.1 4.T -0.6 3.4 30 TU 11 N 0236 06*8 1312 2116 0316 0936 13*6 2206 -0.7 5.0 -1.0 4.2 -0.6 4.6 -0.9 4.2 15 TH 0300 0900 132* 212* -0.7 4.9 -0.9 4.S 19 F 0236 0636 1*5* 2100 -0.4 5.0 -0.9 9.1 10 SA 31 SU 0316 0916 152* 2136 0348 093* 155* 2204 -0 -0 .4 .3 .3 .7 .2 .1 .1 .6 TINE MERIDIAN T5* w. 0000 IS NIDNICHT. 1200 IS NOON. HEIGHTS ARE RECKONED FROM THE DATUM OF SOUNDINCS ON CHARTS OF THE LOCALITY WHICH IS MEAN ION MATER. Fig. ll-50a Representative Table 1 from "Tide Tables: High and Low Water Predictions, U.S. Coast and Geodetic Survey, Rockville, Maryland (published annually). WAVE, TIDE, AND WEATHER FORECASTING 11-111 TABLE 2.-T1DAL DIFFERENCES AND OTHER CONSTANTS POSITION long DIFFERENCES High water low water Height High water low water Spring Mean Tide level 1451 1453 1455 1457 1459 1461 146J 1465 1467 1469 1471 147J 1475 1477 1479 1481 1483 1485 1487 1489 1491 1493 1495 1497 1499 1501 1503 1505 1507 1509 1511 1513 1515 1517 1519 1521 1523 1525 1527 1529 1531 1533 1535 NEW YORK— Continued Long Island, South Side — Continued Hempstead Bay Deep Creek Meadow Green Island Cuba Island Bellmore, Bellmore Creek Neds Creek Freeport Creek Freeport, Baldwin Bay Long Beach Long Beach, outer coast Bemps t ead Bay — Con tlnued East Rockaway Woodmere, Brosewere Bay East Rockaway Inlet Jamaica Bay Plumb Beach Channel Barren Island, Rockaway Inlet — Beach Channel (bridge) Motts Basin Norton Point, Head of Bay New York International Alrport-- Grassy Bay (bridge) Canarsle Mill Basin HEW YORK and NEW JERSEY New York Harbor Coney Island Norton Ftolnt, Gravesend Bay Fort Wadsworth, The Narrows Fort Hani Iton, The Narrows Bay Ridge — — — ----- St. George, Staten Island——-— — - Bayonne, New Jersey-— — — — — Governors Island—— — — — — NEW YORK (The Battery) Hudson RiverJ Jersey City, Ffe. RR. Ferry, N. J New York, Desbrosses Street New York, Chelsea Docks- Hoboken, Castle Fbint, N. J- Weehawken, Days Point, N. J- New York, Union Stock Yards New York, 130th Street George Washington Bridge — — — Spuyten Ouyvil, West of RR. bridge- Tarrytown— — — — — — — - 40 36 40 37 40 37 40 40 40 37 40 38 40 38 40 36 40 35 40 38 40 37 40 36 40 35 40 35 40 35 40 37 40 38 40 37 40 39 40 38 40 37 40 34 40 35 40 36 40 37 40 38 40 39 40 41 40 40 40 42 40 42 40 43 40 43 40 45 40 45 40 46 40 47 40 49 40 51 40 53 40 56 41 01 41 05 73 32 73 30 73 31 73 31 73 33 73 34 73 35 73 39 73 39 73 40 73 42 73 44 73 55 73 53 73 49 73 46 73 45 73 47 73 50 73 53 73 55 73 59 74 00 74 03 74 02 74 02 74 04 74 06 74 01 74 01 74 01 74 02 74 01 74 01 74 01 74 01 74 00 73 58 73 57 73 56 73 54 73 53 73 52 k. m. k. m. fttt fttt on SAHDY HOOK, p. 70 I I I Time meridian, 75'V. •0.52 0.41 0.50 0.43 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 +1 02 +1 09 •0.52 +1 22 + 1 29 •0.41 +1 08 +1 20 •0.50 +1 29 +1 56 •0.43 +0 50 +0 52 -1.9 +0 34 +0 27 -1.5 +0 38 +0 53 -1.6 +0 19 0 00 -0.7 -0 29 -0 35 -0.1 +0 42 +0 45 -0.7 +0 35 -K) 48 -0.7 -0 06 -0 16 -0.5 +0 03 -0 05 +0.3 0 00 -0 06 +0.4 +0 38 +0 22 +0.5 +0 40 +0 46 +0.8 +0 39 +0 43 +0.8 +0 26 +0 43 +0.7 +0 44 +0 45 +0.6 +0 28 +0 06 +0.6 +0 29 '+0 02 +0.6 -0 0$ -0 19 +0.1 -0 03 +0 01 +0.1 +0 02 +0 12 -0.3 +0 03 +0 05 +0.1 on NEW YORK, p. 62 -0 24 -0 24 +0.1 -0 21 -0 18 0.6 -0 19 -0 08 0.0 -0 19 -0 15 -0.1 -0 11 -0 06 -0.1 Dai ly predictions +0 07 +0 07 -0.1 +0 10 +0 10 -0.1 +0 17 +0 16 -0.2 +0 17 +0 16 -0.2 +0 24 +0 23 -0.3 +0 27 +0 26 -0.3 +0 37 +0 35 -0.5 +0 46 +0 43 -0.6 +0 58 +0 53 -0.7 +1 09 +1 10 -0.8 +1 29 +1 40 -1.1 +1 45 +1 54 -1.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 feet 2.4 1.9 2.3 2.0 2.7 3.1 3.0 3.9 4.5 3.9 3.9 4.1 4.9 5.0 5.1 5.4 5.4 5.3 5.2 5.2 5.2 4.7 4.7 4.3 4.7 4.6 4.5 4.5 4.4 4.4 4.5 4.4 4.4 4.3 4.3 4.2 4.2 4.0 3.9 3.8 3.7 3.4 3.2 /«( 2.9 2.3 2.8 2.4 3.3 3.8 3.6 4.7 5.4 4.7 4.7 5.0 5.9 6.0 6.2 6.5 6.5 6.4 6.3 6.3 6.3 5.7 5.7 5.2 5.7 5.5 5.4 5.4 5". 3 5.3 5.4 5.3 5.3 5.2 5.2 5.0 5.0 4.8 4.6 4.5 4.4 4.0 3.7 feet 1.2 0.9 1.1 1.0 1.3 1.5 1.5 1.9 2.2 1.9 1.9 2.0 2.4 2.5 2.5 2.7 2.7 2.6 2.6 2.6 2.6 2.3 2.3 2.1 2.3 2.3 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.1 2.1 2.1 2.1 2.0 1.9 1.9 1.8 1.7 1.6 •Ratio. JValues for the Hudson River above George Washington Bridge are based upon averages for the six months May to October, when the fresh water discharge is a minimum. Fig. 11-506 Representative Table 2 from "Tide Tables: High and Low Water Predictions," U.8. Coast and Geodetic Survey, Rockville, Maryland (published annually). U-112 OCEAN OPERATIONS THC NARROWS, NEW YORK HARBOR, N.Y. , 1968 F-F10O0, OIR. 3*0° TRUE E-ESB. OIR. 160* TRUE SLACK MA «| HUH SLACK HAXIHUH SLACK HAXI HUH SLACK HAXIHUH WATER CURRENT HATER CURRENT WATER CURRENT WATER CURRENT TIKE TIHE VEl. TIHE TIHE VEl. TIHE TIHE VEL. TIHE TIHE VEl. OAY DAY DAY OAY M.M. H.H. KNOTS H.H. H.H. KNOTS H.H. H.H. KNOTS H.H. H.H. KNOTS 1 0206 2. IE 16 01*8 2.5E 1 0300 1.9E 16 0306 2.5E F 0536 0606 1.7F S* 0518 0748 2. OF H 0642 0854 1.3F TU 0646 0906 1.7F 1112 1*2* 2. IE 1054 1406 2.*E 115* 1506 l.TE 1206 1516 2.2E ITS* 2030 1.7F 1T2* 2012 2.2F 1836 2116 1.6F 1836 2130 2.2F 2336 2318 2 02*8 2.0E W 0236 2.5E 2 0030 03*2 l.SE IT 004S 0*00 2.3E sa 0618 08*8 1.5F SU 0606 0836 1.9F TU 0736 0942 I. IF w 0T48 1006 l.SF 11*8 1506 2.0E 1136 1**6 2.3E 1236 1546 1.6E 1300 1612 2.0E 1836 2112 1.7F 1812 2100 2.2F 1918 2200 l.SF 19*2 2230 2. OF 3 0018 0330 1.9E 18 0012 032* 2.*E 3 0112 0424 1.7E 18 01*2 0*5* 2. IE su 0T06 0930 l.*F H 0700 0930 1.7F M 0630 1036 l.OF TH 08*8 1112 1.4F 1230 15*2 1.9E 122* 1536 2.2E 1324 1630 l.*E 1*00 1712 l.SE 1918 215* 1.6F 1900 215* 2. IF 2012 2254 1.5F 20*8 2330 l.SF * 0100 0*12 1.8E 19 0106 0*18 2.2E * 0200 0518 1.6E 19 02*2 0600 1.9E H oeoo 1018 1.2F TU oeoo 102* 1.5F TH 092* 112* l.OF F 095* 1216 1.3F 1306 1618 1.7E 1316 1630 2.0E 1*12 172* 1.3E 1500 162* l.SE 2006 22*2 1.5F 2000 2248 2. OF 2106 23*2 l.*F 215* 5 01*8 0500 1.6E 20 0200 0512 2.0E 5 025* 0618 l.SE 20 0036 1.7F TU 0900 1106 1.1F N 0906 112* l.*F F 1016 1218 0.9F SA 03*2 0712 1.9E 135* 1706 1.5E 1*12 1730 1.8E 1506 1830 l.SE 105* 1330 1.3F 205* 2330 1.5F 2106 23*8 1.9F 2206 1612 2300 1936 1.6E 6 0236 055* 1.5E 21 0300 062* 1.9E 6 0036 1.4F 21 01*8 1.6F u 095* 115* l.OF TH 1012 122* 1.2F SA 03*6 072* 1.5E SU 0**8 0612 1.9E 1**2 1806 l.*E 1512 18*2 l.TE 1112 1312 l.OF 11*8 1**2 l.*F 21*8 2212 1612 2306 1936 l.SE 1718 2036 1.7E 7 0018 l.*F 22 00*8 1.7F 7 0130 1.4F 22 0006 0306 l.SF Th 0330 0700 l.SE F 0*06 0730 l.SE SU 0**8 0818 1.7E M 05*8 0906 1.9E 10 5* 1248 0.9F 1118 1336 1.2F 1200 1*12 1. IF 12*2 15*2 l.SF 1536 1912 1.3E 1624 194 8 l.TE 1712 2030 l.SE 1818 2130 1.8E 22*2 2318 e 0112 l.*F 23 0206 1.7F 8 0000 0230 1.4F 23 0100 0406 1.6F F 0*30 0800 l.SE SA 0512 0836 1.9E M 0546 0906 1.8F TU 06*2 0954 2.0E 11*8 13*2 0.9F 1218 1500 1.2F 1248 1512 1.3F 1330 1636 1.7F 16*2 2006 l.*E 1736 205* l.SE 1806 212* 1.7E 1912 2224 1.9E 2336 9 0206 l.*F 2* 0018 0330 1.7F 9 0054 0336 1.6F 2* 0154 0*5* 1.6F SA 0530 085* 1.6E SU 0618 0930 2.0E TU 0636 0954 2.0E w 072* 10*2 2.0E 12*2 1*5* 0.9F 1312 1612 l.*F 13 30 1606 l.SF 1*12 1718 l.SF 1T*2 2100 l.SE 1836 21*8 1.9E 1900 2212 2.0E 195* 2306 2.0E 10 0030 0312 1.5F 25 one 0*30 1.8F 10 0148 0*2* 1.7F 2S 02*8 0536 1.6F SU 062* 09*2 1.8E H 0712 102* 2.0E u 0724 10 36 2. IE TH 0606 112* 1.9E 1330 1600 1. IF 1400 1700 1.6F 1412 16*8 l.SF 1*5* 175* 1.9F 1836 21*8 1.7E 1930 22*2 1.9E 1946 2300 2.2E 2036 235* 2.0E n 012* 0*12 1.6F 26 0212 0518 1.8F 11 0236 0512 1.9F 26 0330 0612 1.6F M 0T12 102* 1.9E TU oeoo 1112 2. IE TH 0806 112* 2.2E F 08*8 1206 1.9E 1*12 16*2 l.*F 1446 17*2 1.7F 14 5* 1730 2. IF 1536 1818 1.9F 192* 2236 l.SE 2018 2330 2.0E 2030 23*6 2.4E 2118 12 0212 0500 1.8F 27 0306 0600 1.8F 12 032* 055* 2. OF 27 0036 2.0E TU oeoo 1112 2. IE M 0842 115* 2. IE F 085* 1206 2.3E SA 0*12 06*2 1.5F 1*5* 172* 1.6F 1530 1818 1.6F 1536 1812 2.3F 092* 12*2 1.9E 2012 2330 2.0E 2100 2118 1612 215* ie*e 1.9F 13 0 300 05*2 2. OF 28 0018 2. IE 13 00*2 2.5E 26 one 2.0E V 08*2 115* 2.2E TH 0346 0636 1.8F SA 0*12 06*2 2. OF SU 0*5* 0712 l.*F 1536 1800 1.9F 0918 1236 2. IE 0936 125* 2.4E 1006 132* l.SE 2100 1606 2142 18*8 1.9F 1612 2206 1900 2.*F 16*6 2236 1918 l.SF 14 0018 2.2E 29 0100 2. IE 14 0130 2.6E 29 0200 2.0E TH 03*8 0618 2. IF F 0436 0706 1.7F SU 0500 0T2* 2. OF H 0536 07*6 1.3F 092* 12*2 2.3E 1000 1318 2.0E 102* 13*2 2.4E 10*2 1*00 1.7E 1612 18*2 2. OF 1642 1918 l.BF 165* 19*2 2.*F 172* 2000 l.SF 21*2 222* 2 300 2318 15 0100 2.*E 30 01*2 2. IE IS 021S 2.6E 30 0236 2.0E F 0*30 0700 2. IF SA 0518 0736 1.6F H 05*8 0812 l.SF TU 062* 0630 1.2F 1006 132* 2.*E 1036 135* 2.0E 1112 1430 2.3E 1124 1**2 1.6E 16*8 192* 2.2F 1718 195* l.SF 17*2 2036 2.3F 1800 20*2 l.TF 22 30 31 SU 2 306 0600 1112 175* 23*6 022* 0812 1*30 2030 2.0E l.*F 1.9E 1.7F 235* TIHE MERIDIAN 75° W. 0000 IS MIONIGHT. 1200 IS NOON. Fig. ll-51o Representative Table 1 from "Tidal Current Tables," U.S. Coast and Geodetic Survey, Rockville, Maryland (published annually). WAVE, TIDE, AND WEATHER FORECASTING 11-113 TABLE 2. -CURRENT DIFFERENCES AND OTHER CONSTANTS Long. TIME DIF- FERENCES Slock water VELOCITY RATIOS Hood ebb MAXIMUM CURRENTS Direc- tion {true) (iru.l 'ty knots 2250 2255 2260 2265 2270 2275 2280 2285 2290 2295 2300 2305 2310 2315 2320 2325 2330 2335 2340 2345 2350 2355 2360 2365 2370 2375 2380 2385 2390 2395 2400 2405 2410 2415 2420 2425 2430 2435 2440 2445 2450 2455 LONG ISLAND, South Coast— Continued Sh I nnecock I n I et Fire I. Inlet, 0.5 mi. S. of Oak Beach Jones Inlet Long Beach, Inside, between bridges East Rockaway Inlet Ambrose Channel Lightship Sandy Hook App. Lighted Horn Buoy 2A — JAMAICA BAY Rockaway Inlet Barren Island, east of Canarsle (mldchannel , off Pier) Beach Channel (bridge) Grass Hassock Channel — NEW YORK HARBOR ENTRANCE Ambrose Channel entrance Ambrose Channel, SE. of West Bank Lt' Coney Island Lt., 1.6 miles SSW. of- Ambrose Channel, north end Coney Island, 0.2 mile west of Ft. Lafayette, channel east of—— THE NARROWS, mldchannel NEW YORK HARBOR, Upper Bay Tompk i nsv i I I e — ■ Bay Ridge Channel Red Hook Channel Robbins Reef Light, east of— — ■■■'■■ Red Hook, 1 mile west of Statue of Liberty, east of ■ ■- HUDSON RIVER, Mldchannel4 The Battery, northwest of — Desbrosses Street Che I sea Docks — — — — — — — -— Forty-second Street — — . — . Ninety-sixth Street Grants Tomb, 123d Street - George Washington Brldge- Souyten Duyvll Rtverdal e- Dobbs Ferry Tarrytown- Osslnlng- Haverstraw- Peek sk 1 1 I Bear Mountain Bridge Highland Falls West Point, off Duck Islend- 40 51 40 38 40 35 40 36 40 35 40 27 40 27 40 34 40 35 40 38 40 35 40 37 40 30 40 32 40 33 40 34 40 35 40 36 40 37 40 38 40 39 40 40 40 39 40 41 40 42 40 43 40 43 40 45 40 46 40 48 40 49 40 51 40 53 40 54 41 01 41 05 41 10 41 12 41 17 41 19 41 22 41 24 72 29 73 18 73 34 73 40 73 45 73 49 73 55 73 56 73 53 73 53 73 49 73 47 73 58 74 01 74 01 74 02 74 01 74 02 74 03 74 04 74 02 74 01 74 03 74 02 74 02 74 02 74 01 74 01 74 00 73 59 73 58 73 57 73 56 73 55 73 53 73 53 73 54 73 57 73 57 73 59 73 58 73 57 k. m. h. ' on THE NARROWS, p. 52 Time meridian, 75'V. -0 20 -0 40 1.5 1.2 ■tO 15 0 00 1.4 1.2 -1 00 -0 55 1.8 1.3 -0 10 +0 10 0.3 0.3 -1 25 -1 35 1.3 1.2 See table 5. See table 5. -1 45 -2 15 -2 00 -2 25 -1 35 -1 50 -1 20 -1 20 -1 10 -1 CO -1 10 -1 05 ( ) -0 25 -0' 10 ( ') +0 05 to 15 -0 55 -0 55 c« ) ( ) 1.1 0.7 0.3 1.1 0.6 1.0 0.8 0.5 0.8 0.9 0.6 1.3 0.9 0.3 1.0 0.5 1.2 0.9 0.8 0.9 1.0 0.5 Dal ly predictions -0 10 ■•0 20 0.9 -0 35 -0 45 0.6 -0 35 -0 35 0.6 tO 10 +0 20 0.8 +0 45 tl 00 0.8 •K) 55 +1 00 0.8 +1 30 +1 35 0.9 +1 35 +1 40 0.9 +1 30 +1 40 1.0 +1 35 + 1 45 1.0 +1 40 +1 50 1.0 +1 45 +1 55 0.9 +1 45 +2 00 0.9 +2 00 +2 10 0.9 +2 05 +2 20 0.8 +2 25 +2 40 0.8 +2 40 +2 55 0.6 +2 55 +3 10 0.5 +3 05 +3 IS 0.5 +3 20 +3 35 0.5 +3 26 +3 40 0.5 +3 35 +3 50 0.6 +3 40 +3 55 0.5 1.0 0.6 0.4 0.8 1.2 1.0 1.2 1.2 1.0 1.2 1.2 1.2 1.1 1.1 1.0 0.9 0.8 0.7 0.7 0.6 0.6 0.6 0.6 350 80 35 75 40 310 310 330 330 330 345 340 5 40 355 15 25 30 15 10 20 30 30 25 20 20 15 10 0 320 335 0 0 5 10 2.5 2.4 3.1 0.5 2.2 1.7 1.3 0 1.3 1.5 1.1 1.7 1.6 1.0 1.0 1.3 1.3 1.4 1.5 1.5 1.7 1.7 1.7 1.6 1.6 1.6 1.4 1.3 1.1 0.9 0.8 0.8 0.8 1.0 1.0 deg 170 245 215 275 225 245 190 220 225 230 110 170 145 175 170 195 160 170 220 170 205 205 205 185 200 2.3 2.4 2.6 0.6 2.3 2.7 1.7 0.7 2.0 1.0 2.3 1.8 1.5 1.9 2.0 0.9 2.0 2.0 1.1 0.7 1.6 2.3 1.9 2.3 2.3 2.0 2.3 2.3 2.3 2.2 2.1 2.0 1.7 1.5 1.3 1.3 1.2 1.1 1.2 1.1 'Current is rotary, turning clockwise. Minimum current of 0.9 knot sets SW. about time of "Slack, flood begins" at The Narrows. Minimum current of 0.5 knot sets NE. about 1 hour before "Slack, ebb begins" at The Narrows. ■Maximum flood, -O" 50"; maximum ebb, -K>* 55". 'Flood begins, -2» 15"; maximum flood, -0" 05"; ebb begins, tO* 05"; maximum ebb, -1* 50". 'The values for the Hudson River are for the summer months, when the fresh-water discharge Is a minimum. Fig. 11-516 Representative Table 2 from "Tidal Current Tables," U.S. Coast and Geodetic Survey, Rockville, Maryland (published annually). REFERENCES 11-119 Safety Afloat 13. "Recreational Boating Guide," CG-340, U.S. Coast Guard, Washington, D.C., 1961. 14. "Harbor Craft Crewman's Handbook," TM 55-501, U.S. Army, Washington, D.C., 1958. 15. SCUBA Suits, U.S. Coast Guard Commandant Instruct. 10126.1A, July, 1963. 16. Powder Actuated Tools, U.S. Coast Guard Commandant Instruct. 10290. 1A, September, 1963. 17. "U.S. Navy Safety Precautions," Government Printing Office, Washington, D.C., 1961. 18. "U.S. Navy Diving Manual," Government Printing Office, Washington, D.C., July, 1953. 19. Knight, A. M., "Modern Seamanship," D. Van Nostrand Company, Inc., Princeton, N.J., 1966. 20. "Aids to Navigation Manual," CG-222, U.S. Coast Guard, Washington, D.C., 1953. 21. "National Search and Rescue Manual," CG-308, U.S. Coast Guard, Washington, D.C., July, 1959. 22. "Accident Prevention Manual for Industrial Operations," National Safety Council, Chicago, 1959. 23. "Fire Protection Handbook," National Fire Protection Association, Boston, 1962. 24. "Bureau of Ships Technical Manual," chap. 88, Damage Control, U.S. Navy Bureau of Ships, Washington, D.C., April, 1959. 25. "Bureau of Ships Technical Manual," chap. 93, Fire Fighting, U.S. Navy Bureau of Ships, Washington, D.C., April, 1959. Marine Communications 26.'Bcnnett, W. R., and J. R. Davey: "Data Transmission," McGraw-Hill Book Company, New York, 1965. 27. Davies, K.: "Ionospheric Radio Propagation," National Bureau of Standards, 1965. 28. International Radio Consultative Committee, CCIR Doc. Ninth Plen. SesS., Los Angeles, 1959. 29. "Fundamentals of Single Sideband," Collins Radio Company, Cedar Rapids, Iowa, 1960. 30. "Point-to-point Radio Relay Systems," Radio Corporation of America, Camden, N.J., 1962. Tide, Wave, and Weather Forecasting 31. "Tide Tables: High and Low Water Predictions," U.S. Coast and Geodetic Survey, Rockville, Maryland (published annually). 32. Bretschneider, C. L.: Revision in Wave Forecasting: Deep and Shallow Water, Proc. Sixth Conf. Coastal Eng., 1957, p. 30. 33. Neumann, G.: On Ocean Wave Spectra and a New Method of Forecasting Wind- generated Sea, U.S. Army Corps Engrs. Beach Erosion Board Tech. Memo. 43, 1952. 34. Pierson, W. J., Jr., G. Neumann, and It. W. James: Observing and Forecasting Ocean Waves by Means of Wave Spectra and Statistics, U.S. Navy Hydrographic Off. Publ. 603, 1955. 35. Sverdrup, H. U., and W. H. Munk: Wind, Sea, and Swell: Theory of Relations for Forecasting, U.S. Navy Hydrographic Off. Pub'. 601, 1947. 36. Wilson, B. W.: Graphical Approach to the Forecasting of Waves in Moving Fetches, U.S. Army Corps Engrs. Beach Erosion Board Tech. Memo. 73, 1955. 37. Petterssen, S.: "Introduction to Meteorology," McGraw-Hill Book Company, New York, 1958. 38. Taylor, G. F.: "Elementary Meteorology," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1954. qa Reprinted from Proceedings of the Symposium on Tides organized by the International Hydrographic Bureau, Monaco, 1967, with permission UNESCO and the International Hydrographic Bureau. COMPUTER APPLICATIONS TO TIDE AND CURRENT ANALYSIS IN THE COAST AND GEODETIC SURVEY Bernard D. ZETLER Physical Oceanography Laboratory, Institute for Oceanography, ESSA The U.S. Coast and Geodetic Survey is now using a digital tide gage (Barbee, 1965 which outputs a punched paper tape with information on tidal height in a stilling well every six mi- nutes (each tenth of an hour). The paper tape is fed through a translator which converts the information to punched cards suitable for processing in electronic computers. The availability of the data in this format led to the development of computer programs to routinely do the reduction processing previously done manually from the traditional ana- log tide records. A changeover of this type must be done carefully. The data must be edi- ted to insure that erroneous values are not included in the processing ; previously a man had scaled a continuous curve and would have detected a malfunction in the gage or the re- cording equipment. Furthermore, the temptation to do the processing exactly as it had been done before must be resisted. Sometimes the standard procedures are based on man's limi- tations and opportunities to do things better with our new powerful tools must be sought. For example, we get into the habit of looking up information in tables to save the time involved in obtaining the answer from a formula. Unless a table is used repeatedly, it may be more efficient for an electronic computer to work with a formula and, in addition, precious space in the memory core is not used for storing the table. The editing procedures are primarily to compute third differences in the data, a pro- cess which multiplies an error by three, thereby making it stand out above small random fluctuations. In the initial testing, errors were found due to failure of the punch to pierce the paper tape for certain digits and to translator errors. The editing procedure checks time and date sequence on successive cards and outputs a diagnostic if the cards are arranged wrong and if values are missing. The format of each card is also checked in the routine editing. The tide heights are read to four significant digits (hundredths of a foot) and the editing by differences is not likely to find an error in the last digit. A program was written that counts the number of times each digit occurs in the last place and severe departures from a rectangular distribution for the about 7,000 values each month can be interpreted as evidence of a systematic failure. However, the information furnished by the program is not concidered sufficiently significant to be used routinely. The major problem in the reduction lay in deciding on a method of choosing times of high and low waters. In preparing tide tables, the predicted heights are routinely compared to select the extremes (high and low waters). However, the presence of noise makes this method unacceptable with observations. Serious consideration was given to using a low pass filter to smooth high frequency noise but this was rejected on the basis that this modifies the data on a subjective basis (the choice of filter) and it is not possible now to anticipate future uses of the data that might be affected by the choice of the filter. Furthermore, there is the problem that the records are frequently used as legal records and a smoothed value might have a questionable value in a court of law. In addition, the response of the smoothing function must be exactly unity in the tidal frequencies ; otherwise the analysed ranges would be incorrect. It appeared logical and simple to identify a limited period of an extreme and then to fit a parabola by least squares to these data. The first derivative of Y = ax2 + bx + c , in which a, b, and c are the unknowns to be obtained by a least square procedure, can be set equal to zero (2ax + b = 0) to obtain a linear solution for the times of high or low water. However, this implies a model curve symmetric to a line parallel to the Y axis, a solution that is not valid for the skewed curve found in many estuaries where the duration of rise is shorter than the duration of fall. Instead, we settled on a tilting board type of approach , using a given time as a fulcrum, adding four adjacent heights on either side and subtracting one sum from the other. At times of extremes, this difference is closest to zero. The me- 75 thod stemmed from an approach of fitting a line to the same data by a regression formula and choosing the slope closest to zero but the latter method weights each height by its dis- tance from the fulcrum, making the distant points most important. The method accepted gives equal weight to each height used in the computation. Times are treated cumulatively during a month and the program sums these times for both high and low waters. The sum of the moon's transits for the month has already been prepared on the same basis using a formula which takes into account the dates of the two days with only one transit due to the lunar progression in solar time. The instruction card which precedes the data contains this sum of transits as well as the number of days in the month. Also included is the designated option of reducing the data as (1) semidiurnal, (2) mixed, and (3) diurnal (only one high and low water during some days of the month). With the first option, the output lists times and heights of all high and low waters , mean lunitidal intervals, mean high water, mean low water, mean tide level, mean sea le- vel (river level in estuaries), mean range, hourly heights (these are outputted on punched cards as well) and monthly extremes. Option two chooses the higher high and lower low water and the inequalities to the output. It had been customary in U.S. Coast and Geodetic Survey procedures (1965) to check the higher high and lower low of each solar day, adding a check or omitting it on the days of one tide per solar day in accordance with sequence on either side (day before and after). This led invariably to either 29 or 31 higher highs in a 60 tide month, an expedient but unsatisfactory result of tabulating a lunar phenomenon in solar time . It would have been difficult to program this method ; furthermore it was not good science . It was easier and more satisfactory to pair the high waters in sets of two (two per lunar day) and to select the higher of each pair for inclusion as higher high. A comparable treat- ment is applied to the low waters. With both of these options, the program damands the pro- per number of high and low waters (2 less than twice the number of days). It does not sum the last tide in a month if it is superfluous and it advances to the early hours of the first day of the following month if another tide is needed. A diagnostic is outputted if there are too many or too few calculated high and low waters in a given month. The diagnostic includes information identifying the problem dates. With the third option (sometimes diurnal), the program calculates the times and heights of all high and low waters and outputs them according to day of month. It also outputs and punches hourly heights and lists monthly extreme high and low. It does not reduce the data nor does it check the number of highs and lows. The procedures used in the program to locate times of extremes makes it possible to identify other anomalous tide conditions. Inasmuch as it is impossible to anticipate and cor- rect for any possible contingency, the program outputs diagnostics giving the approximate time of the occurrence and categories of what may be wrong. Thus, if a float sticks to the side of the well, the resulting straight line is detected and reported. If a storm surge obli- terates a high or low tide, the failure to change sequence or the wrong number of tides is reported. Under these circumstances, a man must examine the data and decide on how the processing must proceed. Simple points of inflection or stands are handled within the pro- gram. Numerous changes have been made in the analysis procedures as well. Some of these have already been described (Harris et al. , 1963) but they will be summarized here. A least square analysis program is used routinely for series of one year, solving for 37 traditional harmonic constants (Schureman, 1958). The decision to adopt the program was supported by some comparative tests (Zetler and Lennon, 1967). The program is dimensioned for 41 cons- tituents and when a larger number is needed, more than one analysis is made (Zetler and Cummings, 1967). This is done without, loss of significant accuracy by including all fre- quencies in a particular species (cycles per day) in the same solution. The Vo + u phase corrections and the node factors are applied to the results as they have been in the past . An evaluation of the least squares approach was made with twelve consecutive 2!) day series, using the results from the year as the criteria for accuracy, but the results were not significantly better than comparable analyses made by traditional methods, now program- med for an electronic computer (both 29 and 15 day analyses). 76 Unlike the analysis for a year, only M , S2, N , K , and O , are in the 29 day solu- tion and corrections must be made in the results for contributions from nearby frequencies (those with synodic periods greater than the length of series being analyzed). These include P on K,, K2 and T2 on S2 (1^ is disregarded), and Nu2 on N2. Equilibrium ratios and phase relationships were used in the corrections in the calculations made thus far. It may be that if local relationships established from nearby places are used, the results could be impro- ved sufficiently to warrant a change in procedure. In a few cases where the data are obtained in random time, a least square solution is a method whereby the harmonic constants can be obtained (Zetler et al. , 1965). A comparable automation in the processing of tidal current observations has been achieved. Current speed and direction are obtained every ten minutes for a 29 day series on a Geodyne meter. The photographic record is translated under contract and the Coast and Geodetic Survey is furnished a magnetic tape with the data in BCD code. A plot and a non- harmonic reduction provide the azimuth of the major axis of the current ellipse. This di- rection is subtracted from the observed directions and by multiplying the speeds by the cosine and sine respectively of the resulting angles, we obtain series of vectors parallel to and normal to the major axis. These are then analysed using the computer program to furnish harmonic constants in the two orthogonal directions. It has been found that it is more sa- tisfacotry to align the axis of the solution to match the tidal ellipse rather than north and east components because, if the amplitudes along the minor axis are small, these constants may be disregarded and satisfactory predictions may be prepared from the harmonic cons- tants for the vectors parallel to the major axis. The analysis also furnished the non-tidal current in both directions. These are the algebraic means for each set of vectors. Some- times the clock is not precise and an adjustment is needed for a sampling interval that is not exactly ten minutes. A simple compensation for clock error is made by adjusting the frequencies sought to correspond to the true sampling interval. Some of the procedures described in this paper represent radical departures from the practices described in various U.S. Coast and Geodetic Survey manuals. The need to update the manuals appears to be imperative but I have strong doubts that we have reached a new plateau of achievement that will result in stabilized procedures for even a few years. Tidal authorities in many countries are going through similar changes in their programs. It is good that we are getting together to discuss these changes and all of us should benefit by this exchange of ideas. REFERENCES BARBEE, W.D. (1965) - Tide Gages in the U.S. Coast and Geodetic Survey, unpublished manuscript, U.S. Coast and Geodetic Survey. HARRIS, D.L., PORE, N. A., and CUMMINGS, R. (1963) - The Application of High Speed Computers to Practical Tidal Problems, Abstracts of Papers, VI, IAPO, XIII General Assembly, IUGG, Berkeley. SCHUREMAN, Paul (1958) - Manual of Harmonic Analysis and Prediction of Tides, U.S. Coast and Geodetic Survey Spec. Pub. No. 98. U.S. Coast and Geodetic Survey (1965) ; Manual of Tide Observations, Pub. No. 30-1. ZETLER, B.D. and CUMMINGS, R.A. (1967) - A Harmonic Method for Predicting Shallow water Tides, Journal of Marine Research, Vol. 25, No. 1, pp. 103-114. ZETLER, B.D. and LENNON, G.W. (1967) - Some Comparative Tests of Tidal Analytical Processes, International Hydrographic Review, Vol. XLIV, No. 1, pp. 139-147. ZETLER, B.D. , SCHULDT, M. D. , WHIPPLE, R.W., and HICKS, S. D. (1965) - Harmo- nic Analysis of Tides from Data Randomly Spaced in Time, J. Geophy. Res. , 70 pp. 2805-2811. DISCUSSION Le PRESIDENT remercie M. Zetler de sa communication et propose d' entendre les exposes de M. A. C.M. Van ETTE et du Pr SCHOEMAKER, qui se rapportent, comme les deux premieres com- munications, a l'utilisation pratique dee ordinateurs pour l'analyse des marees. Voir ci-apres. Reprinted from Proceedings of the Symposium on Tides organized gg by the International Hydrographic Bureau, Monaco, 1967, with permission UNESCO and the International Hydrographic Bureau. SHALLOW-WATER TIDE PREDICTIONS Bernard D. ZETLER An objective method for identifying significant hidden frequencies and thereby deve- loping a harmonic method of predicting shallow-water tides is described by Zetler and Cummings (1967). The method was devised to improve predictions at Anchorage, Alaska, where the tidal range is about eight meters and the routine tide predictions were not sufficiently accurate for the navigation needs of deep-draft oil tankers. Inasmuch as the port freezes during the winter, the available length of record was 192 days of hourly heights, too short for Doodson's method (1957) of shallow water analysis or that of the German Hydrographic Office. The paper describes a standard U.S. Coast and Geodetic Survey analysis of the data, a prediction for the same period that is subtracted from the data, a power spectrum analysis of the residuals, and a high resolution Fourier analysis of the frequency bands in which the spectral energy is high. Wherever large values stood out above the continuum in a plot of the Fourier amplitudes, an effort was made to identify an integral combination of frequencies of constituents known to be important that closely matched the frequencies of these peaks. The least square analysis program was then repeated using the larger set of constituents, the number in this study being 114. The resul- ting predictions (with 114 constituents) matched the observed high and low waters better in times and mean range, the difference between tide level and sea level was better, and the residual variance (using hourly heights) was sharply reduced. The question of consistency of phase was considered in the paper by applying the same approach to tide data at Philadelphia for the years 1946, 1952 and 1957. It was found that the phases were not sufficiently consistent for a number of constituents that included the sum of K2 and N2 but that, if the sum of M2 and L2 is substituted (a difference of .009*/hour or one cycle in about 4. 5 years), the phases matched satisfactorily and the residual variances wore reduced. The paper questions why l,a, theoretically u small constituent, should be so large at Philadelphia that it contributes significantly to the interaction constituents. Since publication of the paper, it has come to my attention that Horn (1960) determined that the large amplitudes found for the L2 frequency in shallow water ports are primarily for the compound term, 2MN2, which has exactly the same speed. This does not change the solution by least squares but it does modify the "f and u" nodal factors and phase correc- tions. Consequently all of the affected constituents shown in the paper should be changed, deleting L2 and adding (2M2 - N2) in the source column. The Doodson numbers and the speeds are unchanged. It is interesting to note that the method followed in this study forced a con- sideration of a particular frequency even though the inadequate physics in the original model omitted this particular frequency as a possible contributor to the compound constituents. Another aspect of the solution would be considered if the study was re-examined. No attempt was made to seek significant constituents in the low frequencies (species zero) because a previous study. Groves and Zetler (1964), had failed to find any significant additional frequencies although about fifty years of data and an extremely high resolution (. 0005 cpd) were used. However, this was done with stations having very little shallow-water effect ; I am informed that with stations such as Anchorage, it is very likely that a number of com- pound 'orms would be found with amplitudes significantly above the continuum. 163 The residual variance would be appreciably reduced if these constituents are included in the least square solution but the effect on the accuracy of future daily predictions would be very small. When a line extends above a continuum, the solution gives the amplitude and phase of a trigonometric identity which is the vectorial sum of the signal and the white noise (continuum). The relationship of the phase lags of the two is unknown and cannot be resolved. Therefore, all that is known is that the true amplitude of the signal lies somewhere in between the sum of the analyzed amplitude and the continuum level in the vicinity of the line and their difference. The most likely value is probably in the middle of this range, namely the analyzed value, but the level of the continuum (highest in the low frequencies and peaking at or near zero) is a good index of possible error. Furthermore, the phase of the particular continuum sample contaminates the determined phase of the constituent. Hence, although the residual variance of a self- predictor is reduced by introducing the added constituent, there is little expectation that the use of the constituent for a future prediction would provide a comparable reduction in the variance. With reference to tide predictions, the species zero constituents are not important in determining the times of high and low waters because the first derivatives are weighted by the constituent speeds, so their only significant contribution is to the heights. Finally, it appears that the computing effort in searching for significant hidden fre- quencies could be greatly reduced by using the "Fast Fourier Transform" (Cooley and Tukey, 1965) on the residuals rather than the power spectral analysis of the residuals followed by the high resolution Fourier analysis in particular frequency bands. The estimated number of computer operations for the "Fast Fourier Transform" is estimated as 2N Log2 N whereas the traditional Fourier method requires N2 operations, where N is the number of data points . Therefore the relative computing time is the factor 2N Log^/N2. There are 4 608 hours in 192 days. If the data are normalized in the sense that the mean is made equal to zero, the ends tapered, and enough zeros are added at both ends to bring the total number of points to 8 192 (the next power of 2), the factor becomes about 1/300. In this particular study, the sav- ings would not have been quite as great because only particular portions of the spectrum were examined, but nevertheless it appears that the savings in computer time would have been quite large. I thank D.E. Cartwright, G.W. Lennon and W. Horn for calling some of the above points to my attention. REFERENCES COOLEY, J.W. and TUKEY, J.W. (1965) - An Algorithm for the Machine Calculation of Fourier Series, Mathematics of Computation, 19 : pp. 297-301. DOODSON, A.T. (1957) - The Analysis and Prediction of Tides in Shallow Water, Interna- tional Hydrographic Review, 34, pp. 5-46. GROVES, G.W. and ZETLER, B. D. (1964) - The Cross Spectrum of Sea Level at San Francisco and Honolulu, Journal of Marine Research, 12, pp. 269-275. ZETLER, B. D. and CUMMINGS, R.A. (1967) - A Harmonic Method for Predicting Shallow- water Tides, Journal of Marine Research, 2*3, pp. 103-114. DISCUSSION Mr. van ETTE (Netherlands) wanted to ask a question about the Fourier analysis, because there was a registration of a certain time which consisted not only of tidal constituents but also of all kinds of noise. It was true that when the Fourier analysis had been made results were found, and since every result had to have a variable the results had a certain standard deviation. It was well known that the standard deviation of results obtained by means of harmonic analysis, in its proper sense, was very high and could be approximated by a Chi2 distribution with only 2 degrees of freedom. What value, therefore , 164 could be attached to the results of a calculation of that Fourier analysis ? Was anything known about the statistical behaviour of the results ? If not, the following device might be considered. A long series of results might be split up into equal parts and the same computation done for each of the parts. If that were done, were approximately the same results obtained for each of the parts 9 Mr. ZETLER (U.S.A.) replied that the data at Anchorage had been too short to truncate and they had needed the utmost resolution that they could possibly get. What they had had was barely enough and so they had not been able to afford the luxury of that particular test. The frequencies of the Fourier analysis had not been used ; they were merely a guide. Obviously the non- linear terms which the had been looking for would not fall on the accidental exact harmonics of a particular record length. They had been looking for values which obviously extended significantly above the continuum. When they had been found they were not necessarily on a line ; in fact, ordinarily they were distributed between lines and it was obvious that there was energy there of a frequency of approxi- mately so much. That could be determined from the frequency assigned to each harmonic. They had then looked for a combination of significant frequencies such as the 2MS6 which had been a new frequency to them. When they found energy that apparently corresponded to what they would get by adding twice the frequency of M2 to that of S2, and it appeared to be approximately right, they had merely included that in their model for the next least square analysis. Had they been wrong they would have got a side band of what they were looking for and not the true thing. However, it was a somewhat systematic search in that there were a very limited number of terms which they had attempted to use as input to the search. They had used only the important ones. That was why they had been off on L2 when they added L2 and M2 in place of K2 and N2 on the fourth, sixth and eighth diurnal terms that they had happened to correct. When a subsequent residual analysis had been done it had been found that the residual energy had been reduced in the three different species by the change that had been made. There was, therefore, satisfactory documentation that the renaming of the constituents was an improvement. With regard to the question of what was a significant amount over the continuum, that again was something which had to be judged by eye and there seemed to be a difference of opinion in the group as to how good a tool an eye was. So far as the fifth diurnal was concerned, those particular points stood out well above the continuum and it was not a normal distribution with an occasional value 3 sigma away from the mean. They were more than that. There was, therefore, a geophysical reason for the changes. There was a tidal line, and they were allowed to identify it and put it into their solution. Mr. van ETTE (Netherlands) referred to the fact that Mr. Zetler had only had a fairly short period of 192 days and had really had to use them all, and suggested that between computations it would be worth while to try to split them up and consider whether the results which had been obtained did indeed have some value. In the end, of course, all the data available could be used. Mr. ZETLER (U.S.A.) made the point that subsequently they had succeeded in putting a bottom recorder in the location, substituting it for a tide gauge, and had obtained a year of data of which only about three months overlapped with the 192 days which had been described in the paper. It was a pleasant surprise that the analyzed constants for the full year agreed very well with what had been done previously. Mr. HORN (Federal Republic of Germany) wanted first to congratulate Mr. Zetler because he had a laboratory which they would all like to have with a range of 10 metres and tides of an almost fixed character. This was desirable for analyzing tides and doing research. Unfortunately it froze up, and Mr. Horn wondered whether something could be done through international cooperation to make it per- manent. A careful comparison had been made between Mr. Zetler's results and the German results over a period of 25 years and there was a range of only 3 metres. They could not go as far as Mr. Zetler had done, but they had also included the twelfth order species. What was perhaps remarkable was that they had found more or less the same orders of magnitude for the individual constituents that he had found . They had called some of them by different names, but the wording was something which would soon have to be gone into. As to the identification of L2, 2M and N2, that was something to which Mr. Horn had drawn attention in 1958 and it was one of the outstanding points. L2 was only 10 per cent of the total amplitude. It was really surprising that Mr. Zetler had found results from such a short series which could be confirmed by such a long analysis, and it seemed probable that he was perfectly right in what he had done. Mr. GODIN (Canada) suspected that the proof of the analysis was in the prediction, and asked how the prediction went. Mr. HORN (Federal Republic of Germany) replied that in analyzing the tides they had found a twelfth order species. According to Sei's law, which had often been quoted by Dr. Doodson, the number of 165 constituents of almost the same order in one species should increase as any three in the order of the species. The table of results which had been shown was not in harmony with that law because the number decreased instead of increasing indefinitely. It was obvious that they were all mixed up with the noise. If the high and low water times were to be investigated, where there had to be a differentiation with respect to time, the combined influence of those things would be found in the high and low water intervals. That was one of the reasons why he had given up the direct harmonic analysis and had decided to analyze high and low waters directly, or lunar or hourly heights. Mr. ZETLER (U. S. A. ) agreed completely with what Mr. Horn had said. It was apparent that the combinations multiplied up very rapidly. That was obvious even in the spread in frequency within species. The species were no longer so far apart in the higher order of species. At the same time they tended to get smaller in size. There were more of them but they tended to get smaller and one began to wonder whether they were not merging with the continuum to form part of it. There were so many and they were small, so that instead of having a random meteorological process there might be a process which was not random but was hardly worth working with to extract all of the additional terms. It came back to the proDlem which Mr. Zetler had mentioned at the beginning. One wondered at what point to stop punching holes in the continuum in the hope that one was doing something meaningful. Any set of data could obviously be described by a Fourier transform and there would be no residuals . One could therefore keep punching the continuum had getting more and more constituents. The imagina- tion could run wild in the higher species on the number of combinations which one could allow oneself to use. It became a subjective process. Mr. Zetler had tried to limit himself in most cases to something that obviously protruded. He believed that, in what Mr. Horn was saying, the continuum was part of the non-harmonic grouping in the higher species. Mr. LKNNON (United Kingdom) commented that he had done an exorcise very similar to Or. Zetler's when dealing with two ports in tho llivcr Thames. It had been found that, as ono proceeded Into the higher species, the situation was not that one had more and more constituents which merged with the noise but that one had relatively few constituents which stuck out bright and clear above the noise. In fact, the highest species were the easiest to handle and the most difficult ones were the semi-diurnals and the fourth-diurnals where there was considerable pseudo-tidal noise. Mr. HORN (Federal Republic of Germany) replied that that did not entirely meet the point which he had made. Mr. Lennon was perfectly correct when he spoke of approximating to the total tide curve, but the higher species had an influence on the times of high and low waters that could not be represented by that method. That was why he had said that it was necessary to choose the things that they wanted to predict in a tide table and try to represent them directly. Dr. Doodson had always said that if eight diurnals had to be included the situation would probably become hopeless because there would be too many. Mr. Lennon had said that he did not entirely agree, which implied that he did partly agree. Mr. Horn himself agreed with Dr. Doodson to a somewhat higher degree. The situation became difficult if there were too many shallow water corrections which all influenced the high water times, because in the derivative with respect to times they appeared multiplied by a factor of 3, 4, 6, 8 and so on. That was of importance. They could be found, but only by finding their combined effect not the individual effect. Mr. ZETLER (U.S.A. ) recalled the statement of Dr. Doodson's which Mr. Horn had quoted, but he also remembered that in his Manual he had talked about the convergence and the possibility of working with higher order terms. He had specifically stated that there was a physical limitation on how many cons- tituents could be used on a mechanical tide predicting machine. Using the cut-off that he used he had thought that it was virtually impossible to go beyond 60 constituents on a tide predicting machine without introducing so much friction that the tide predictions suffered in the process. Mr. CARTWRIGHT (United Kingdom) thought that the list of high order interaction terms was impressive, but it had occurred to him that there was one type of interaction term which could not be included in that scheme. Many people had observed, as he had done himself around Great Britain or in the North Sea, that many of the important tidal lines had a seasonal modulation. That meant that if one took a special analysis one found, surrounding the M2 line, some lines at one cycle per year difference. Admittedly, in the full development of the potential, there was a seasonal change, or a change which depended on the sun's perigee for its true expansion, but it was very small and the observed modulation was larger than that. It would be almost impossible when choosing the dominant tidal terms to choose a combination of terms which would give one cycle per year difference among them. Possibly in many sea areas that was not at all important, but in certain areas where, for some reason, there was a large seasonal modulation, another type of interaction would have to be introduced, possibly something which involved the product of SA, the annual term and the leading lineal terms. 166 Reprinted from GO Boating, Miami 86 TIPS TALK By Bernard D. Zetler Atlantic Oceanographic Laboratories, Miami. January Tide Talk The Coast and Geodetic Survey recently completed one hundred years of providing published tide predictions to navigators. As early as 1844, the Coast Survey provided information (mean high water lunitidal intervals and ranges) that could be used with a nautical alma- nac to provide an approximate tide prediction. Although reasonably accurate tide predictions are taken very much for granted today, the development of the science was an outstanding scientific achievement in the nineteenth century. GO FEBRUARY 1969 TALK By Bernard D. Zetler Atlantic Oceanographic Laboratories, Miami. During World War II an intensive effort was made to improve tide predictions, particularly for amphi- bious operations in strategic areas. Landing craft moving onto a beach needed as much water as possible in order to carry both men and sup- plies as far up on the beach as pos- sible. However, it was desirable to come in just before high water so that if a boat did run aground on a shoal, after a short wait a little more water was available to make it float again. The heavy toll in the Tarawa landing, when many landing craft were hung up for long periods on shoals, emphasized the need for more accurate tide predictions. Needless to say, the improvement was given a high priority. The tide tables contain daily predictions for a few particular places and Table 2 GO JANUARY 1969 This is another illustration of nece- ssity being the mother of invention. The Coast Survey was given the responsibility of preparing nautical charts for the safety of navigation. A chart shows the depth of water at any particular place within the geographic limits of the chart. But, the water column does not remain fixed. Instead it rises and falls in some periodic fashion related to the transits of the moon and sun. How does one measure something that won't stand still? Obviously, one needs to correct the measure- ment at a given time to some fixed datum; on our east coast, we use mean low water. In the same sense, the navigator must apply (add or subtract, depending on the sign) a tide prediction to a charted depth to know the depth of water at the time he plans to be there. lists differences and ratios for many subordinate places. The choice of a reference station for these subordin- ate places frequently involves a comprcmise, that is a selected best possible reference station but one which may not be a satisfactory one. Furthermore a reference station which may be adequate for ordin- ary navigation may not be accep- table for a military landing opera- tion. As an example, the pre-war tide tables used two reference tables, Manila and Cebu, for the Philippines. This was expanded to six reference stations in special mil- itary reports. Predicting the addi- tional four stations on a crash basis was not a tremendous task but remaking Table 2 to go along with the augmented coverage required a considerable effort, first deciding on the appropriate reference stations and then recomputing the time and height differences. The post-war tide tables included many of the additional reference and subordinate stations prepared for military purposes during the war. GO MARCH 1969 By Bernard D. Zetler Atlantic Oceanographic Laboratories, Miami. In 1965 the Coast and Geodetic Survey's tide prediction machine finally yielded to electronic com- puters after more than a half cen- tury of distinguished service. Those of us who were involved in the changeover to an electronic com- puter felt some measure of remorse for terminating its remarkable car- eer. The tide predicting machine, completed in 1910, was designed to sum continuously 37 cosine curves, draw a combined curve and select automatically its maxima and mini- ma (times and heights of high and low waters). Although the periods involved in the tide calculations varied from one cycle per year to eight cycles per day, the gearing for these various input curves was so precise that the maximum allow- able error was 2 degrees in a year. A man could set the dials on the machine, turn a hand crank (stop- ping to record each high and low water) and complete a year of pre- dictions in an eight hour day. Because the machine was both unique and indispensible, there was considerable anxiety during World War II and in the post-war years that it might be harmed by bomb- ing or sabotage. Although special tables were prepared to facilitate crude predictions that could be computed on a desk calculator, the only significant safeguard was achieved by running the machine overtime to build up a stockpile of four years of advance predictions. Needless to say, when the Coast Survey purchased its first electro- nic computer, an IBM 650, about fifteen years ago, designing a pro- gram for predicting tides was given careful consideration. I remember meeting an IBM executive about a year later at a social event where I described the tide-predicting mach- ine. When he asked incredulously whether the almost fifty year old machine had a hand crank, I replied in the affirmative with the further comment that it turned out tide predictions faster than his men had been able to achieve on the 650. It was a losing battle, however, as electronic computers rapidly be- came faster and cheaper to operate. In 1965 the Coast and Geodetic Survey changed over to a computer program that predicts a year of tides in three minutes and outputs the data in a format ready for re- production. Furthermore there is greater flexibility in that there is no longer a constraint to a unique 37 periods (114 have been used in a special research study) and there is far greater security in no longer de- pending on one unique set of hard- ware. Nevertheless — it was a won- derful machine! GO APRIL 1969 By Bernard D. Zetler Atlantic Oceanographic Laboratories, Miami. Tides generally are classified in three categories, semidaily, mixed and daily. Miami residents are some- what uniquely in a position to see a all three without going far from home. The semidaily tides are found closest, at Miami Beach, Biscayne Bay and nearby waters. There is very little difference between the heights of the two high waters or between the two low waters on a particular day. Tidal ranges are lar- gest at times of new and full moon and at times of perigee (moon clo- sest to the earth, about once a month). If new or full moon and perigee come on about the same day, the ranges are particularly large. GO MAY 1969 If we go west across the Tamiami Trail to Naples or Marco Island, we find the diurnal tides are much more important and when the moon is near extreme declination, there may be only one high and one low tide a day. The tide tables use St. Marks River Entrance as the reference sta- tion for predictions in this area; the predictions for April 9, 1969 call for only one high and one low tide. Farther to the north at St. Peters- burg the tides are even more diur- nal and, at Pensacola, the diurnal tide is so predominant that one finds two highs and two lows only on a few days each month when the moon is near the equator. If we go south to Key West, we find the mixed type of tide. Both the daily and semidaily tides are im- portant and usually there is a signi- ficant difference between the height of the two highs on a particular day and/or between the two lows on that day. This inequality will be greatest when the moon is near extreme declination and smallest when the moon is near the equator. These sharp changes in type of tide within short distances demon- strate the problem implicit in set- ting up Table 2 in the tide tables. Obviously, the changes in type are not abrupt but rather gradual in a geographic sense. Nevertheless, in preparing Table 2, it is necessary to have arbitrary limits which indicate that all places to some point A fit Miami, from there on to point B, Key West is used, beyond B St. Marks is used, etc. **♦#***»** sea level values even more carefully in the next decade looking for evi- dence of a continuance, leveling off, or even a reversal of the rising trend that has been recorded so far in this century. ¥BE)E 7AILE1 By Bernard D. Zetler Atlantic Oceanographic Laboratories, Miami. The Miami Herald on April 13, had a feature article on a signifi- cant lowering of the world temp- erature due primarily to man-made contamination. It made me wonder if a related trend has been record- ed on tide gauges spanning the world's oceans. We have known for some time that mean sea level is a misleading term for geodetic purposes because sea level does not stand still, even on an average basis. If we average hour- ly tidal heights over a period of a year (about 9,000 values), this should average out reasonably well tides, waves, storm induced changes, etc. But not only do annual means show large variations from year to year but, over the past fifty years, there has been a significant upward trend, about 0.01 foot per year on our east coast. It has not been the same along all coastlines and an approxi- mation of a world rate Would be somewhat smaller, possibly 0.005 foot per year. Areal differences in trend have generally been attributed to differential land sinking or up- lift. The principal point, however, is that sea level has been rising. The usual explanation has been that the earth has been warmed by the increased supply of carbon dioxide and this warming has reduced the polar ice-caps. In support of this theory has been some documenta- tion of the retreat of glaciers and similar phenomena. The scatter (non-systematic vari- ation) between annual sea level val- ues is sufficiently large that a valid trend cannot bo determined from just the past few years. Oceano- graphers will be watching annual GO JUNE 1969 GO JULY 1969 By Bernard D. Zetler Atlantic Oceanographic Laboratories, Miami. Most people viewing an earth-moon diagram for the first time have little or no trouble in accepting on faith the tidal bulge on the earth directly beneath the moon. How- ever, the cause of the comparable bulge (high tide) on the oppos- ite side of the earth is far less ob- vious and usually leads to quest- ions, primarily, "How come?" We know from physics that the earth and moon attract each other and that it requires an equal and opposite force to keep them apart. The latter is centrifugal force direct- ed away from the moon. However, this centrifugal force is the same at all points on the earth's surface whereas the gravitational force is greatest at that point on the earth just under the moon and least at a point on the other side farth- est from the moon. The difference between the attractive force and the centrifugal force is therefore a small net force toward the moon just under the moon, zero at the center of the earth, and a small net force away from the moon on the far side of the earth. These net differences are responsible for the two high water bulges (two high tides each lunar day as the earth rotates under the moon). There are similar high waters on either side of the earth due to the sun but the much greater distance of the sun than the moon makes the solar tide slightly less than half the lunar tide. #«»■»#»«»*» electronic computer permitted the use of any reasonable set and, in this case, we went from 37 to 1 14 periods to achieve our results. Shortly after our improved predic- tion program was ready for use, Eng- lish tidal experts arrived at virtually the same solution for a comparable problem in the Thames. By Bernard D. Zetler Atlantic Oceanographic Laboratories, Miami. I note with interest the recent pro- posal to deepen the channel into Dodge Island to permit larger draft vessels to use the Port of Miami. There is a strong trend toward build- ing larger ships, particularly oil tank- ers for the trip around Africa since the closing of the Suez Canal. In some ports where the tidal range is large, the advent of these larger ships has led to a requirement for increased accuracy in tide predic- tions. If channel depth combined with the tide adds up to marginal clearance, the need for extreme accu- racy becomes obvious. It was such a requirement that recently led to some quite interesting research. The tide at Anchorage, Alaska, averages about 25 feet. For many years the Coast and Geodetic Survey prepared predictions for Anchorage based on summer observations only as the port freezes in winter. Then oil was discovered in Cook Inlet bringing deep-draft oil tankers into the area. The published tide tables were found to be not sufficiently accurate for navigational purposes and all existing techniques were investigated and found inadequate. A technique was developed for identifying and analyzing signific- ant additional tide constituents and these were then incorporated into the prediction method to achieve improved accuracy. In this case, the timing was very fortunate. Less than two years before, the Coast and Geodetic Survey had changed from using its mechanical tide predic- tion machine to an electronic compu- ter. The mechanical machine used 37 predetermined tidal periods for prediction and there was virtually no way to add additional periods to the calculation without years of precise preparation of appropriate gears.The GO AUGUST 1969 ¥i©E By Bernard D. Zetler Atlantic Oceanographic Laboratories, Miami. A frequent question on tides is whether a particular body of water is large enough to have a tide and my response is that you can have a tide in a tea cup. This means that the tide producing forces act on any body of water and, if measurements could be made sufficiently precise and if all other forces affecting the level of water are eliminated, we would indeed find a tide in any ba- sin. The smallest basin in which, to my knowledge, a tide has been documen- ted is the David Taylor Model Basin, an enclosed rectangular tank about 2700 feet long, 52 feet wide and 22 feet deep, along the Potomac River near Washington, D.C. The tank is used for extremely precise measure- ment of the characteristics of ship models towed in the tank. The de- mand for precision is so great that the tracks used for the towing ve- hicles were leveled to the curvature of the earth rather than purely hori- zontal. I recall that in 1947 when we we- re asked to compute the theoretical tide in the basin, we made a quick calculation of "less than .005 inch." We were quite surprised by the respon- se, "Yes, but how much?" During a seven day period when the basin was not used, we installed registering floats at either end and had volunteers bicycle back and for- th around the clock reading the gauges each half hour. The observed mean range was .00181 inch and the plotted tide curve was quite smooth, the only other bvious change being a downward drift due to seepage. Tides have been measured on the Great Lakes but it requires a long re- cord to clearly identify the small ti- dal range that is usually masked by other changes due to meteorological variables. Using tide table on Page 2 which is Miami Beach (ocean). Port Everglades entrance (jetties), and Miami Harbor entrance, add or subtract as indicated. Differences Place High Water Low Water Miami Harbor Entrance Fort Pierce Inlet St. Lucie I nlet Jupiter Inlet Palm Beach (ocean) Hillsboro Inlet Port Everglades Cape Florida Fowey Light Pumpkin Key, Card Sound Molasses Reef Alligator Reef Light Key West Channel Sombrero Light American Light Sand Key Light East Cape Sable Shark River Pavilion Key Barron River Cape Romano Marco Naples Fort Myers Pine Island Captiva Island Boca Grande Miami Yacht Basin 79th St. Csywy Ft. Laud. (Andrews Ave. Bridge) Cape Fla. (west side) Riviera (Lake Worth) Key Biscayne Card Sound Key Largo (Garden Cove) Plantation Key (Tavernier) Key West Sombrero Key Light Marathon (No. side) Flamingo Big Sable Creek White Water Bay •No data -0 14 -0 18 -0 20 -0 21 + 1 04 + 1 38 -0 21 -0 18 + 0 13 +0 36 + 0 02 + 0 02 + 0 49 + 1 02 +0 03 + 0 02 +2 53 + 3 03 +0 16 +0 11 + 0 13 +0 26 +2 10 + 1 34 +0 51 + 0 44 + 0 58 + 0 38 + 1 08 +0 50 + 5 59 +6 11 + 5 23 + 6 06 +5 29 + 5 45 + 6 58 +8 19 -7 16 -7 00 -7 03 -7 05 -8 00 -8 06 -3 39 -3 37 -6 17 -7 05 -6 33 -6 41 -6 59 -8 17 + 1 28 + 1 47 + 1 45 +2 13 + 1 06 +0 49 +0 49 + 2 53 +0 36 +0 34 +2 10 +0 51 +7-32 +7 38 + 1 28 + 1 02 + 1 02 +3 03 + 1 09 +0 39 + 1 34 + 0 44 + 6 15 +8 56 GO SEPTEMBER 1969 GO OCTOBER 1969 tipe By Bernard D. Zetler Atlantic Oceanographic Laboratories. Miami The tide measurements described last month for the David Taylor Mod el Basin introduced me for the first time to tidal variations in the crust of the earth. When we compared a computed tide curve with the obser vations, there were consistent small variations in phase and in range. A study showed the reason was the yielding of the earth's crust to the tidal forces. At the latitude of Washington, D.C., the earth tide averages about six inches. It would not be possible to measure this by ordinary geodetic instrumentation because the extent of the tidal bulges is so great that the differential change that can be measured directly between any two points is much less than the possible error of the observation. As with ocean tides, the semidaily ranges are larger at new and full moon and when the moon is at perigee. The diurnal tides are larger when the moon is at exteme declination. The earth also responds in a more devious and indirect way to tide-pro- ducing forces because the crusa yields due to tidal loading on the sea floor. The degree to which the earth yields depends on the geological structure in the area and to the range and extent of the ocean tide. Al- though Washington, D.C. is about a hundred miles from the ocean, the loading effect was found to be 5 to 10% of the tide-producing force. At some places near the coast where the tidal ranges are quite large, the loading effect has been found to be the most important contributor to- the observed earth tide. The principle benefit of earth tide measurements is that by docu- menting the response of the earth to known forces, it becomes possible to evaluate the structural strength of the earth's crust. 7BBI By Bernard D. Zetler Atlantic Oceanogiaphic Laboratories. Miami Engineers are constantly trying to harness the energy of the oceans, us- ually concentrating on tides although attempts have also been made to use wave motion and temperature grad- ients. There has never been a ques- tion of the engineering possibilities of tidal power; the principal restrain- ing consideration has been econmon- ics. In places where the tidal range is large, such as the Bay of Fundy where the average range exceeds 35 feet, it is readily feasible to trap the water at high tide and use the head as wa- ter level falls on the outside to gen- erate power. This is the simplest form of tidal power and the prin- ciple defect is that the power supply is intermittent. A more complex system of multiple basins can be de- signed so that a sufficient head al- ways exists somewhere in the system, thereby making possible a contin- uous supply of power. Other more complex systems are conceivable such as using power during the available periods to pump water into a storage basin and thereby establishing a head as a source of supply during other periods in the tidal cycle. The re- cently constructed French power plant produces power from the cur- rent as the waters in Ranee River rush upstream and then uses the trapped head to produce power on the falling tide. "We are just on the threshold of our knowledge of the oceans. Knowledge of the oceans is more than a matter of curiosity. Our very survival may hinge on it. ' ' . John F Kennedy GPO 830 - 693 L