DEPARTMENT OF COMMERCE CHARLESSAWYER, Secretary WEATHER BUREAU F. W. REICHELDERFER, Chief MONTHLY WEATHER REVIEW Editor,JAMES E. CASKEY, lr. Volume 78 MARCH 1950 Closed May 5, 1950 Number 3 Issued June 15, 1950 FORECASTING LOCAL SHOWERS IN FLORIDA DURING THE SUMMER ROBERT C. GENTRY Weather Bureau Office, Miami. Fla. [Manuscript received April 3, 19501 ABSTRACT July and August precipitation records for 5 years from 10 stations within 25 miles of Miami are analyzed to obtain an indication of the frequency of summer showers in that area. Several meteorological parameters for fore- casting showers are examined. A quasi-objective method is developed which can be used to forecast the proportion of the Miami area which should expect showers during a 24-hour period 9 to 33 hours in advance. Several parameters are listed which were tested, but did not improve the forecasts. Verification results using independent data are included. CONTENTS Page 41 42 42 43 44 44 46 46 46 46 47 48 48 49 49 49 papcr presents an approach to making precipitation fore- cast's for Florida in the summer months that will have moremcaning. It is a pilot project worked out for an area of about 25 miles radius centered around Miami. However, it is hoped that ideas which were found to work for this area will also work, when properly applied, to other sections of the Florida Peninsula. An examination of climatological data reveals that there is a shower somewhere in Florida almost every day during the summer season. However, the percentage of stations reporting showers during any 24-hour period varies widely from day to day. Data from 10 raingages located near Miami (fig. 1) werecompiled for July and August for 5 years. Thus there were data for 310 days. , Table 1 gives the frequency that showerswere observed during July and August, 1944, 1945, 1947, 1948, and 1949. INTRODUCTION TABLE 1,"Frequency of showersreported by stations near *fiami, J u ~~J and August, 1944, 1945, 1947, 1948, and 1949 Localshowers occur so frequently in Florida during the =~. I summer that most forecasters give up trying to forecast variations in shower activity and instead put out a sta,ndard forecast-['Partly Cloudy with Scattered Show- ers"-every day, except for the very rare occasion when fair weather is indicated. Although this forecast of partly cloudy with scattered showers will verify for Florida about 90 percent or more of the time, it doesn't give the public much information not already known. As a result, the Florida public consults the .weather foremst infrequently during the summer, unless there is a tropical storm. This 885753-50-1 i Namher 0 ................................................. 4". .............................................. 24 3 ................................................. 19 2." .............................................. 28 1. ................................................ 32 27 10 ................................................ 37 9.". ............................................. 35 7". .............................................. 20 5 .. ............................................... 31 6 ................................................. 25 8 ................................................ 32 ~-___ Pcrrent of ail days 10.3 9 .0 6 .1 7. 7 10.0 6.5 10.3 11.3 11.9 8.1 8.7 Percent of days har- ing value or less "" 10 19 25 33 13 50 GO 71 79 91 100 - I1 42 M O N T H L Y W E A T H E R R E V I E W MAWH 1950 I \ I FIGWILE 1.-Location of stations near Miami at which precipitation was observed. During this period, there were almost equal numbers of days in which no stations reported rain, 4 stations reported rain, 10 stations reported rain, etc. The standard fore- cast of partly cloudy with scattered showers would have verifled about 90 percent of the time; and, if it is assumed that some showers occurred without rain falling in any of the 10 raingages, the forecast would have verified over 90 percent of the time. However, data in table 1 show how meangingless is the “standard” forecast. Price [l] has emphasized the usefulness of the probability forecasts of thunderstorms. The present writer believes that Miami forecasts would have more meaning than the “standard” forecast and be of more service to the public if they contained a statement indicating the proportion of the area that was expected to have showers during the period. The forecast procedure explained in this paper is adaptable to that type of forecast. SELECTION OF DATA To insure that the precipitation records used in develop- ing the forecast procedure would be representative of the area, data from 10 stations near Miami (fig. 1) were examined and compiled. Some of the stations were operated by cooperative observers of the Weather Bureau, and the rain was measured once a day-usually at about 0800 EST. At the Miami Beach station the accumulated precipitation was measured at about 1700 EST, and during part of the period records were available showing the amount measured at about 0700 EST. At the Miami Airport measurements were made a t about 0115, 0715, 1315, and 1915 EST. At stations where recording rain- gages were used, hourly amounts of precipitation were available. Since raingages do not record traces, a trace was considered as no rain. Since at several of the stations measurements were made at about 0700 or 0800 EST, it was decided to use a 24-hour period from 0730 EST on 1 day to 0730 EST of the following day. The only station that presented difficul- ties in using this period was the one at Miami Beach. During the period when records of the 0700 EST measure- ments were available, its data could be easily adjusted to be approximately concurrent with the others. During the time when 0700 EST measurements were not available, times of occurrence of precipitation were noted a t neigh- boring stations and a decision was made as to which 24- hour period rain measured at 1700 EST should be assigned, Of course this introduces some errors, and the fact that observations at all stations were not made regularly at the same time, i. e., 0730 EST, would introduce some errors, However, it is believed that none of these would be great enough or occur frequently enough to seriously affect any of the results. Although 10 stations were used in the study, occasion- ally one or two were missing. For such days the percent- age of the rema.ining stations reporting was computed and that percentage was used. Data used in making the forecasts were the upper air data observed a t about 0330 GMT, and surface data observed at about 0030 GMT. The forecast period was for the 24-hour period beginning at 0730 EST (1230 GMT). Thus the forecast period began about 9 hours after the latest observations were taken. As already noted, this period was chosen because of convenience in handling the precipitation records. However, the forecasting method should work about as well for any other period, because none of the forecast parameters (see p. 44-46) vary very much diurnially with the possible exception of the average relative humidity above Miami. SELECTION OF PARAMETERS Following the selection of data for use in developing the forecast procedure, meteorological parameters useful in segregating the days of general showers from those with few or no showers were sought. Since very few air mass changes occur in south Florida in the summertime, one would suspect high correlation between number of showers, and the lapse rate and humidity. An examination of about 150 July and August soundings taken a t Miami, however, showed that the lapse rate was always between the wet and dry adiabatic lapse rates. Furthermore, there seemed to be very little correlation between the degree of conditional instability and the number of stations having showers. This agrees with results that Chalker [2] . MAWH 1950 MONTHLY 43 obtained when studying thunderstorm occurrence throughout the United States. Further analysis of the soundings indicated that percentage of stations reporting rain could not be determined with much accuracy from purely thermodynamic considerations even when the moisture content was also considered. A large group of soundings were analyzed, using both the parcel and slice methodsof analysis. Both methods gave consistently poor results. This agrees with studies of the Thunder- storm Project as reported by Byers and Rodebush [3]. They concluded that in each case of widespread thunder- storm activity attributed to insolation in earlier literature there must be a dynamically induced source of low-level convergence, perhaps in some cases related to the diurnal heating. Since high-moisture content through a deep layer results from low-level convergence, that conclusion is in agreement with the well-known correlation between thunderstorm areas and the locations of moist tongues on isentropic or related charts. From the vorticity theorem [4] it can be argued that horizontal convergence is associated with polar troughs, waves in the easterlies and closed cyclonic circulations. Polar troughs occasionally reach as far south as Miami during July and August, particularly at the 5,000-ft. and 10,000-ft. levels. Also waves in the easterlies affect the Miami vicinity frequently during the average July and August. Infrequently, but a t least once almost every summer,closed cyclonic circulations-usually tropical storms-pass near enough to Miami to affect its weather. In addition to these, Byers and Rodebush [3] point out the low-level horizontal convergence which is due to the sea breeze. They maintain that this is particularly effec- tive in Florida which, being a peninsula, has a sea breeze coming onto land from three sides. Summer air masses over Miami are nearly always con- ditionally unstable and are usually convectively unstable. There is usually sufficient daytime heating to release any convective instability. The sea breeze blows on most days in July and August, and it should cause enough horizontal convergence near the surface to release the convective instability. For these reasons, it would appear, there should be general showers nearly every day. How- ever, as indicated in table l, there is a wide variation in the number of stations reporting showers from day to day. The problem then seemed to be (1) to identify general circulation patterns that encourage the release of convec- tive instability and/or bring in moist air during the fore- cast period, and (2) to identify general circulation patterns which tend to suppress convective instability and/or bring in dry air during the forecast period. Types of circulation which will usually give horizontal convergence are troughs approaching Miami, easterly waves approaching, cyclonically curved streamlines, and tropical storms. Types of circulations which will usually cause horizontal divergence and thus inhibit ascending motion, are ridges centered right over Miami, strong anticyclonically curved streamlines, and back sides of FIGURE 2.-Schematicrepresentation of criteria for typing 700-mb. maps. Point D is is the 700-mb. contour line. at Miami, chords DE and DF are equal to 5" of latitude (25"-30°) and the arc EDF easterly waves and polar troughs. Any pattern which causes low-level horizontal convergence will probably increase the moisture in air over Miami. After a number of parameters indicative of the circu- lation-stability-moisture conditions had been tried, the following were found to be most helpful in segregating the days of general showers from those with few or no showers: (1) the relative humidity, (2) distance from Miami of 700-mb. ridge, (3) degree and type of curvature of 850-mb. and 700-mb. contour lines near Miami, (4) direction and distance of nearest easterly wave, if any, (5) direction and distance from Miami of nearest tropical storm, if any, (6) direction and distance from Miami of nearest polar trough at 700 mb., and (7) general trajectory of air coming to Miami. TYPING OF MAPS The next step in developing the forecasting method was to type the 700-mb. maps so that application of the meteorological parameters would be to data for similar synoptic situations. The maps were divided into three types: A-mapsof predominantly zonal flow or of weak meridional flow; B-maps of moderate to strong meri- dional flow with Miami being under the flow from the south; C-maps of moderate to strong meridional flow with Miami being under the flow from the north. Since an effort was being made to make the method objective, definitions were set up to rigidly assign the maps to the respective types. Type B is illustrated in figure 2. Chords DE and D F are each equal to the distance between lati- tude circles 25 and 30. The point D is at Miami and the arc EDF is the 700-mb. contour line which passes over Miami. level maps to constantpressuremaps. For convenienes, the map will he called the 1 During the period from 1944 to 1949 the WeatherBureauchangedfromconstant 7OO-mh. map or 850-mb. map, etc., even though data from 1" and 1946 were taken from BO the 4,Wft. maps were used instead for July and August, 1944 and lM5.) lO,OO@-ft. maps or 4,Wft. maps. (6,Wft. maps were not easily obtainable for the study, 44 XONTHLY WEATHER REVIEW MARCH 1950 Type B is defined by the folloiving crit'eria: 1. The north component of EF is greater than the east or west component'. 2. EF is greater than DG. 3. The height of the 700-mb. surface at Miami (D) is a t least 50 feet greater than at H (26" N. 90' W.); or, if there is a minimum height between D and H, the height a t D is at least 50 feet higher than tmhe height a t the minimum point. Type C is similar to B, except that the chord EF will be oriented toward the south rather than the north, and the height at H will be at least 50 feet higher than a,t D. Type A includes all cases not included in types B and C. This includes all cases in which the east or west component of chord EF is greater than t'he north or sout'h component'. It also includes all cases in which the nort'h or south component is greatest but in which the east-west' pressure gradient measured along a line from D to H is weak, or in which the anticyclonic curvature of the contour line from E to F is unusually intense. CONSTRUCTION OF FORECASTGRAPHS I n developing the forecast method, graphs (scatter diagrams) similar to those given in figures 3-9 were pre- pared from data for July 1944, 1945, and August 1944, 1945, 1947. Data for July 1947, 1948, 1949, and August 1948 and 1949wereused as independent data to test results presented in the graphs. The graphs in figures 3-9, which give the basic forecasts, were prepared later and include all data both dependent and independent'. How- ever, they differ in minor details only from the original graphs. Details of the construction of the graphs for each 700-mb. map type follow. TYPE A FORECASTS Most of the maps were type A. The basic forecasts for type A are given in figures 3, 4, and 5. Forecast number 1A (fig. 3) uses average relative humidit'y as one param- eter, entered on the graph as the abscissa. After various humidity measurements had been tried, it was decided that best results were obtained by using an average value. On the forecast charts (figs. 3, S), relative humidity refers to the average of relative humidity values at 5,000 ft., 10,000 ft., and 15,000 ft. for 1944 and 1945 data, and for the average of humidity values at the 850-mb., 700-mb., and 500-mb. levels for the remainder of the data. Forecast IA (fig. 3) uses distance from Miami to the 700-mb. ridge as t'he second parameter, entered on the graph as the ordinate. If the 10,000-ft. wind at Miami has a westerly component, the ridge.used is the one nearest to the south. If t'he 10,000-ft. wind a t Miami has an easterly component, the ridge used is the one nearest to the north. The dist,ance to the ridge line is measured along the meridian passing through Miami in units north or south of Miami. For convenience, a unit of distance equal to 1' of latitude (25" to 2S0) wasused for the measurements. On the graph (fig. 3) at the intersection of the abscissa and ordinate values was plotted a number whichgives tenths of stations near Miami reporting rain during the 24-hour period. After the data were plotted, isolines were so drawn that the majority of days on one side of a line have values 2n, and the majority of days on the other side have values n and the majority of numbers on the other side have values 4 7 ' b W a a 0 4 a 0 5 I 4 OR LESS 2;: , ; I 6 7 8 9 RADIUS OF CURVATUREFACTOR AT 85Omb IO F O R E C A S T 2 A (f r o m fig.4) FIGURE 4.-Scatter diagram for type A, forecast 2A. Graph is constructed in same way FIGURE 5.-Scatter diagram for type A, forecast 3A. Parameters used here are the as figure 3. forecasts obtained from curves in figures 3 and 4. This is the basic forecast for type A. 46 MONTHLY MABCH 1950 TYPE B FORECASTS Forecast graphs for type B given in figures 6, 7, and 8 were made in a fashion similar to those for type A, except that distance to the ridge was measured along the latitude circle passing through Miami and was measured only to the east. Similar conclusions to those for type A can be drawn for type B maps after a study of figures 6 and 7. Showers are more frequent when the humidity is high and when the ridge is several units distant from Miami. Type B as a whole is more showery than type A; so showers occur on almost all days except when the relative humidity is very low or when the ridge is within 4 units of Miami. The radius of curvature factor has about the same effect on type B cases as on type A. Showers are frequent when the factor gives cyclonic curvature or when the anti- cyclonic curvature is slight. Chances for showers get progressively less with increase in the intensity of the anticyclonic curvature, i. e., decrease in the radius of curvature factor. TYPE C FORECASTS Forecasts for type C used a parameter not used in the type A and B forecasts. With Miami as the center, and a radius of 5 units, a mark was made upstream on the 700-mb. contour line passing over Miami. Another mark was made 10 units upstream. The longitude a t each of these marks was read and the values averaged. The average value is the quantity used as the ordinate in fore- cast 1C (fig. 9). There were very few cases of type C, so reliability of the forecast 1C is somewhat doubtful. However, figure 9 indicates more probability of rain when the humidity is high and when the average trajectory estimated by the longitude factor is such as to have brought t.he air over water for a long distance before it reaches Miami. This seems logical and agrees with observations of experienced meteorologists. MODIFICATION O F BASIC FORECASTS CORRECTION RULES Some other parameters were tested and found to improve the basic forecasts given in figures 5, 8, and 9. These other parameters do not occur every day. I n fact, there were insufficient cases to justify drawing additional graphs. It was believed that about as good results could be obtained by stating them in forecast rules as corrections of the basic forecasts. Perhaps when additional data have been studied there will be sufficient cases to justify Cyclonic IC e d' 0 E I ;E 0 t! W 3 E ' =I Y 0 $6 n a 5 4 or less 40 :ss FIQIJBE B.--Seatterdiagram for type B, forecast 1B. Graph is constructed in same way as figure 3. FIGURE 7.-Scatter diagram for type B, forecast 2B. Graph is constructed in same way as figure 3. MUOH 1950 MONTHLY WEATHER REVIEW 47 drawing additional graphs and preparing more accurate solutions. These rules are based partially on results found in studying the dependent data and partially on experienceof the Miami forecasters. They are stated as corrections to the basic forecasts given in figures 5, 8, and 9. The rules follow: (1) If there is an easterly wave at 2,000 ft. whose axis is located within 2 units to the west of Miami or within 6 units (1 unit equals 1 degree of latitude) to the east of Miami, add one-tenth to the basic forecast. (See Dunn [5] for a discussion of easterly waves.) (2) If there is an easterly wave at 2,000 ft. whose axis islocated within 4 to 8 units to the west of Miami, subtract two-tenths from the basic forecast. (3) If there is an easterly wave at 2,000 f t . whose axis is within 2 to 6 units to the north or northwest of Miami, subtract two-tenths from the basic forecast. (4) If Miami is in the westerlies at 700 mb. and there is a trough over Miami or within 10 units to the west, add one-tenth to the basic forecast. (5) If Miami is in the westerlies at 700 mb. and there is a trough within 5 units to the northwest or 4 units to the north, add one-tenth to the basic forecast. (6) If Miami is in the westerlies at 700 mb. and there is a trough 3 or 4 units to the east, subtract two-tenths from the basic forecast. (7) When a t 10,000 ft. there is a shear line north of Melbourne and the 10,000-ft. wind a t Tallahassee is on or between ESE and ENE, subtract two-tenths from the basic forecast (fig. 10). Do not use this rule for those cases in which the streamline or contour line is curved cyclonically continuously from Miami to Tallahassee. (8) If there is a tropical storm in areas X or Y (fig. 1 1), subtract the number of tenths indicated on the map. OTHER PARAMETERS Many other parameters were tried and found to have either little correlation with the number of showers or such a high correlation with the parameters already used in forming the basic forecasts that they added little or nothing to the skill. A list of these follows: 1. Sign of the curvature of the 850-mb. and 700-mb. 2. Occurrence of precipitation up wind 12-18 hours contour lines at Miami. preceding the forecast period. AVERAGE RELATIVE HUMIDITY ABOVE MIAMI - 0400 GMT (%I FIQUBE 8.-Scatterdiagramfor type B, forecast 3B. Parametersused areforecasts obtained from curves in figures 6 and 7. This is the basic forecast for type B. FIGURE S.--Scatter diagram for type 0, forecast IC. The ordinate is the average of the two values of longitude read at points 5 and 10 units upstream from Miami at 10,OOOft. 48 MONTHLY W E A T H E R R E V I E W MARCH 1950 2 10 000' Streomlines shaped o; obove reduce probobility of showers neor Mtoml. I FIGURE lO.-Schematic representation of rule number 7. FIGURE 11.-Diagram showing correction to be made to bmic forecast if tropical storm is centered in either of areas X or Y (rule 8). 3. Direction and speed of 2,000-ft. winds a t Miami. 4. Direction and speed of 5,000-ft. winds at Miami. 5. Direction and speed of 10,000-ft. winds at Miami. 6. Direct,ion and speed of 20,000-ft. winds at Miami. 7. Direction and speed of 8,000-ft. winds. 8. Wind shear from 2,000 ft. to 10,000 ft. and 5,000 ft. to 10,000 ft. (See Byers and Battan [6].) 9. 24-hour surface pressure change at hfiami for 24 hours preceding forecast period. 10. Rain a t Miami in preceding 24-hour period. 11. Direction of the chord EF (fig. 2). 12. Humidity a t 5,000 ft. 13. Humidity a t 10,000 ft. 14. Humidity a t 15,000 ft. 15. Humidity a t 20,000 ft. 16. Convergence in wind field over area immediately preceding forecast period. (Computed for a few cases only by a method developed by Bellamy PI.) 17. Instability as computed by slice method [SI. 18. Instability as computed by parcel method 191. SUMMARY OF FORECAST PROCEDURE The forecast procedure which has beendeveloped is summarized schematically in table 2. TABLE 2.--Summary of forecast procedure Type A (Zonal flow at 700 mb. or weak meridional flow).' Type I3 (Moderate to strong meridional flow from some southerly component).l Type C (Moderate to strong meridional flow from some northerly component).l Parameters Distance to 700-mb. ridge. Average relative humidity. Radius of curvature factor at 700 mb. Radius of curvature factor at 850 mb. Distance eastward to 700-mb. ridge. Average relative humidity Radius of yrvature factor at 100 mb. Radius of curvature factor at 850 mb. 700-mb. air trajectory (longitude factor). Average relative humidity. 1 See paga 43 for detailed criteria for typing 700-mb. maps. - Forecasts 2 applicable. 2 Forecasts 3A, 3B, and l C are to be modified by use of rules 1-8 (see p. 47) when TESTS As stated previously, the basic forecasts and the rules weredeveloped using 5 months of dependent data and checked with the 5 months of independent data. If we accept as correct those forecasts which were within two- tent,hs of what was observed, i. e., a forecast of four-tenths being accepted as correct if two- to six-tenths were ob- served, the skill score is 55. ~ 2 Skill scores were computed from the formula S= KO. correct-chance expectancy Total-chance expectancy x loo served classes. In a contingency tahle with subtotals P; for predicted and 0; for observed Chance expectancy was determined by the marginal totals of both predicted and ob- and a total of Ncases, the chance expectancy is z (Pi x Oil N MARCH 1950 MONTHLY W E A T H E R R E V I E W 49 Table 3 gives the number of days of independent data forwhich the forecasts were exactly correct, t.he number and percentage of days that were within one-tenth of the observed, the number and percentage of days that were within two-tenths of the observed, etc. The eight-step error and all of the seven-step errors except onewere cases in which frequent showers had been forecast and few or none occurred. TABLE 3.-Tabulation of number and percentage of d a y s w i t h various step errors in forecasting from independent data Step errors in forecasts (tenths) Sumbcr 01 days 0.. ........................................................ 3.. ........................................................ 36 2.”” ..................................................... 38 1.. ........................................................ 41 14 4 .......................................................... 8 5 .......................................................... 9 6 .......................................................... 2 I .......................................................... 6 8. ......................................................... 1 9 .......................................................... 0 10. ........................................................ 0 Pcrccqtage of days having this crror or less 2G 51 74 83 88 91 96 99 100 100 1 no If it is desired not to make forecasts in t8erms of tenths or percentage, but to forecast either showers or no showers, the method can still be used. Since showers occur so frequently, we decided to test the method by assuming that any time two-tenths or less of the area was expected to have showers to give a forecast of no rain. Likewise, in verifying it was assumed that two-tenths or less would verify as no rain. With these assumptions, the skill score for the independent data was 57, and the forecasts were correct 86 percent of the time. Although most of the skill in the forecasts comes from the objective portions of the method, the forecast rules 1 through 8 added some skill. For example, the forecasts made from figures 5 , 8, and 9 gave a skill score for independent data of 47 compared to the 57 for the forecasts when modified by the rules. As stated previously, the graphs given in figures 3-9 were made with all of the data-bot,h dependent and in- dependent. Using them and the rules given for correct- ing the basic forecasts, with the exception of rules number 4 and 5 which didn’t add any skill to forecasts made by the charts which were based on all data, the skill score for the two-step errors was 58. Assuming two-tenths or less as no rain, and forecasting either rain or no rain, the skill score was 63 with 87 percent of the forecasts correct. CONCLUSIONS It is concluded that by using the forecast procedures - developed in this paper, one can forecast’ summer showers ~~ ~ in Florida with a high degree of accuracy. It is not nec- essary to forecast, “Partly Cloudy with Scattered Show- ers” for southern Florida almost every day in the summer. The forecaster can give the public much more information by predicting what percentage of the area will have show- ers during the period, and he can do it with considerable accuracy. ACKNOWLEDGMENTS The author is grateful to Mr. Grady Norton, Official- in-Charge, Miami Weather Bureau Office, for encourage- ment and many helpful suggestions offered during the preparation of this paper. Also thanks are due Mr. George Collins and Miss Evelyn Perlich for preparing the figures and the manuscript; and to Mr. Collins, Mr. Charles Gardner, Mrs. Margaret Moore, Mr. Howard Ellis, Mrs. Philo Gwin, and hiIiss Martha Coster, all of the Miami Weather Bureau, for assistance with the statistical and clerical work. REFERENCES I . Saul Price, ‘LThunderstorm Today?-Try a Probability Forecast,” Weatherwise, vol. 2, No. 3, June 1949, 2. Wm. R. Chalker, ‘Vertical Stability in Regions of Air Mass Showers,” Bulletin of the American Meteoro- logical Society, vol. 30, No. 4, April 1949,pp. 145-147. 3 . H. R. Byers and H. R. Rodebush, “Causes of Thunder- storms of the Florida Peninsula,” Journal of Me- teorology, vol. 5, No. 6, December 1948, pp. 275-280. 4. C.-G. Rossby, “Planetary Flow Patterns in the Atmos- phere,” Quarterly Journal of the Royal Meteorological Society, vol. 66, Supplement, 1940, pp. 68-87. 5 . Gordon E. Dunn, “Cyclogenesis in the Tropical Atlan- tic,” Bulletin of the American Meteorological Society, vol. 21, No. 6, June 1940, pp. 215-217. 6. H. R. Byers and Louis J. Battan, “Some Effects of Vertical Wind Shear on Thunderstorm Structure,” Bulletin of the American Meteorological Society, vol. 30, No. 5, May 1949, pp. 168-175. 7. John C. Bellamy, “Objective Calculations of Diver- gence, Vertical Velocity and Vorticity,” Bulletin of the American Meteorological Society, vol. 30, No. 2, February 1949, pp. 45-49. 8. Norman R. Beers “Atmospheric Stability and In- stability” in Handbook of Meteorology, ed. by F. A. Berry, Jr., E. Bollay, and N. R. Beers, McGraw-Hill Book Co., Inc., New York, 1940, pp. 693-725. 9. Sverre Petterssen, Weather Analysis and Forecasting, McGraw-Hill Book Co. Inc., New York. 1940. pp. 61-63.