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ARCHIVFUR METEOROLOGIEGEOPHYSIK UNDBIOKLIMATOLOGIE<c> by Springer-Verlag 1980
Arch.
Met. Geoph. Biokl., Ser. A. 29,1-40 (1980)
551.515.4Department of Environmental Sciences, University of Virginia, Charlottesville, U. S. A.
On Cumulus Mergers
Joanne Simpson, Nancy E. Westcott, R. J. Clerman, and R. A. Pielke
With 11 Figures
Received July 9, 1979
Summary
Joining together or merging is postulated to be a major way in which convective cloudsbecome larger, enhancing their transports and impacts upon their environment. Cumulusshower merger is defined in terms of echoes from a calibrated digitized 10-cm radarreviewing a 0.9 x 105 km2 area in south Florida, U. S. A., which encompasses a1.3 x 1~ km2 experimental area for randomized seeding.A detailed physical and statistical study is reported for three relatively undisturbed un-treated days in the summer of 1973, the driest of which was a randomly selected controlday for the experiment. Mergers are found to produce more than an order of magnitudemore rain than unmerged echoes, while mergers of mergers (second order mergers)produce still an order of magnitude more rain. On the three days studied, merged systemsproduced about 86% of the rainfall over the area. Duration, echo area and rain depthsare also compared for merged and unmerged systems. Each day is then analyzed individ-ually, indicating a correlation between organization and rain amount, confirmed by otherresearch reviewed briefly.1:he location and time of merger is related to the seabreeze convergence zones as pre-dicted by the University of Virginia Mesoscale Model with overall good agreement.Physical hypotheses suggesting the importance of downdrafts in cumulus merging aredeveloped. The relevance of mergers to hydrology, weather modification and the large-scale impacts of convective clouds is discussed.
Zusammenfassung
tlber das Verschmelzen von Cumulus-Wolken
Das Zusammenwachsen oder Verschmelzen yon Cumulus-Wolken wild als einer delHauptgriinde fliT fur Wachstum sowie fliT ihren EinfluE auf ihre Umgebung und auf dieduTch sie bewerkstelligten Transportprozesse angesehen. Das Verschmelzen yon Cumulus-Schauern wild auf Grund del yon einem kalibrierten und digitisierten 10-cm-Radarempfangenen Echos definiert. Das Radargeriit iiberblickt fine Fliiche yon 0.9 x 105 km2
1 Arch Met. Geoph Biokl. A. Bd 29, H 1-2
0066-6416/80/0029/0001/$08.00
2 Joanne Simpson et al.
imStidenFloridas(U.S.A.),dieeinExerimentaigebietvon 1.3 x I~ km2 flirrando-misierte Wolkenimpfung umgibt.Eine detaillierte physikalische und statistische Studie fliT drei relativ ungest6rte Tageohne Wolkenimpfung wiihrend des Sommers 1973 Wild hiermit vorgelegt. Der trockenstediesel Tage war willkiirlich als Kontrolltag fliT das Wolkenimpfungsexperiment gewiihltworden. Verschmelzungsprozesse weisen urn mehr als eine Gr6/!'enordnung mehr Nieder-scWag auf als unverschmolzene Echos, wiihrend Verschmelzungen yon Verschmelzungen(Verschmelzungen zweiter Ordnung) nochmals eine Gr6/!'enordnung mehr Regen ergeben.An den drei untersuchten Tagen produzierten verschmolzene Systeme ungef!ihr 86% deslibel clem Untersuchungsgebiet beobachteten Regens. Andauer, Echoausmal!, und Nieder-schlagsh6he werden fliT verschmolzene und unverschmolzene Wolkensysteme vergiichen.Jeder Tag Wild individuell analysiert, wobei eine Korrelation zwischen Wolkenorganisa-tion und Niederschlagsbetrag angedeutet wild, die auch yon anderen, kurz erwiihntenForschungsarbeiten bekraftigt wurde.art und Zeit des Verschmelzens hangen yon del Seewind-Konvergenzzone ab, welchedUTCh das mesoskalare Rechenmodell del University of Virginia gut vorhergesagt wurde.Eine physikalische Hypothese libel die Wichtigkeit del Absinkbewegung wahrend desCumulus-Verschmelzungsprozesses Wild dargelegt. Die Bedeutung del Verschmelzungs-vorgange flir die Hydrologie, fUr die ktinstliche Wetterbeeinflussung und fliT den gro/!'-raumigen Einflu/!' konvektiver Wolken wild diskutiert.
1. Introduction, Historical Perspective and Motivation
I
An important frontier in meteorology concern$ the factors controlling thesizes of cumulus clouds. The correlation between heights and widths ofcumuli has been well documented [28,48]. As they become larger, cumulusclouds produce more rain, release more heat and transport more energyaloft. Critical size also appears necessary for severe storm events, such assqualls, hail.and torI}adoes, with the Browning :'supercell" [6, 27] theultimate giant of the spepies. The processes forcing cumulus clouds aresuspected to control their size, but theserelatioriships are not yet wen under-stood. Cumulus models so far must assume the dimensions of an initial per-turbation [9, 49]. For parameterizing cumulus effects in th~ large-scalemodels, size controls are among the most vital unknowns.This paper adds a link to understanding cumulus relations to their forcingby examining the growth of cumulus showers by merging or aggregation,which is hypothesized to be a main mechanism of producing larger clouds.Merging has been observed on a hierarchy of scales, with the element dia-meters ranging from a few hundred meters to tens of kilometers. We examinethe merging of showers in the vicinity of Florida, U. S. A., in the size rangeobserved by a lo-cm radar, namely about I to 100 km in horizontaldimension.Merger was actually first documented in Florida by the ThunderstormProject [7] and by Malkus over the tropical oceans [32,34]. In the latter
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333.5 km
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cJ FACE TARGET AREA
~ UVo MESONETWORK
333.5 km(180nmi)
RAINGAUGE
CLUSTER
Fig. 1. The study area is the truncated circle within the squares bounded by 333.5 by333.5 km domain, the 100 n mi (183.5 km) radar range marker and the 25 n mi(46.3 km) radar range marker. The large quadrilateral in the upper left is the FACEseeding target,- showing within it the University of Virginia mesonetwork. The fiverain gauge clusters are denoted by dots, one per gauge ,
start for the cumuli, which usually decay as the heating declines after sunset.Pielke and colleagues [10, 11, 30,41] have evolved the University of VirginiaMesoscale Model (UVMM) of the boundary layer and seabreezes which hasbeen improved, applied and tested extensively in Florida, as well as in severalother areas [44,45,46]. Over Florida the strength and patterning of theconvergence zones are sensitive to the imposed windspeed and direction.Although the model does not yet include water substance phase changes,good agreement between the positions of large radar echoes and predictedconvergence zones have been found, which improve as the daily cycleprogresses [43, 46]. Typical scales of the seabreeze convergence zones are300 by 30 km along the coast lines, with core magnitudes of about 10-4
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to shower fonnation, as suggested in Section 1. Secondly, the visual cloudbody containing the shower studied could merge prior to echo merger.Several cases [14, 24] suggest this difference to be 5 minu tes or less in themiddle levels although a visible low cloud "bridge" between towers com-monly occurs still earlier (Figs. 9-11).Radar echoes of rainshowers are chosen for this study both because of thelesser laboriousness of acquisition of a meaningful sample than in the caseof visible clouds and updrafts and because of the inherent importance ofthe rainfall. However, the subjects of visual cloud and updraft mergerwarrant intensive study in relation to those of echoes; efforts are 'beingpursued with photogrammetry and multiple doppler data in the FACEanalyses [14, 16] and with other tools in examining the clouds of the easternAtlantic in the GATE! [4,26,40,62].
The Data and Methods of the Research
2.1
The Radar Data
In 1972 the National Weather Service Miami 10-cm WSR-57 radar wasdigitized and calibrated for quantitative rain measurements, in part to serveas the main rain-measuring tool in the FACE 1 program in 1973, 1975 and1976. A Miami reflectivity-rainfall relationship had been developed andadapted [21, 22, 55], which underwent extensive further testing in thesummer of 1973 [74,75]. It was shown that when rain gauge clusters areused to adjust the radar rainfall estimates, significant improvement inaccuracy is obtained. This finding has received stronger confirmation inthe second phase of FACE (begun in 1978) when a network of 100 re-cording gauges was established over the entire seeding target [58].The data studied here are from the 1973 season when daily adjustmentsfor the radar were obtained from the five clusters in Fig. 1. Results weretested against the values obtained by the 229 closely spaced gauges in theirregular-shaped mesonetwork shown within the target. The 1973 and 1978tests indicate that the rain differences of importance in this research lieoutside the margin of errors in the measurements [1, 58, 71,74,75].The WSR-57 radar radially scans with a beam width of 2° at an antenna tiltranging between 0.0° and 0.5°. The area within the 46.3 km (25 n.mi) rangemarker, generally filled with ground clutter, is omitted from the analysis.The region outside of the 185.3 km (100 n.mi) range marker is also ex-cluded because of beam filling problems. Cloud base averages about 860 mduring the summer months over south Florida. Beyond 185.3 km range, the
GATE denotes GARP Atlantic Tropical Experiment.GARP denotes Global Atmospheric Research Program.
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study will be analyzed in the context of existing products of STATS inSection 7.With the output of PEAKS, considerable comparative human analyses hadto be performed using the 5 minute photographs of the PPI scope. Detailsare described by Westcott [64, 65].Because of the labor described above combined with that of documentingthe larger-scale cloud environment, only 3 days in the summer of 1973have been analyzed in depth. Near the end of the paper, these will be placedin the context of 16 additional summer days analyzed from a populationrather than a tracking viewpoint using the STATS program.
2.3 Echo Analysis Products
As each echo is tracked, its location, rain rate and area are recorded. If anecho splits, the components are considered to be a continuation of theparent echo, and are included in the computation of the parent echo'slife span, mean and accumulated characteristics. If an echo is said to merge,the component echoes'life histories are terminated, and the consolidatedsystem's history begins at the time of merger. Three echo-types are de-scribed, the single echo, the first order merger, and the second order merger.The duration, the meaQarea, the maximum area, the mean and maximumfive minute rainfall and the accumulated rainfall are determined for eachecho.The mean, standard deviation and standard error are calculated for each ofthe three echo categories (Table 2). The initial purpose of this investigationhas been to investigate the difference in the mean characteristics of the threetypes of echoes without further stratification and to apply statistical teststo determine the significance of these differences. T,he six variables de-scribing each echo have been stratified by echo type and analyzedwith respect to the best fit distribution by means of a program [15] com-paring the fit of nine different distributions to the data. In the majority ofcases, on each day and for the combined days, the raw data follow eithera log-normal, or gamma-like distribution. These are heavy tailed distribu-tions which are skewed to the right, that is, there are many more small thanvery large values. Both the raw data, and the natural log transformed datadifferences are tested for their significance. The log transformed data areapproximately normally distributed because of the near log-normal characterof the untransformed distribution.
2.4 Preliminary Discussion of the Three Selec ted Days
Three summer days have been chosen, mainly on the basis of data quality,to investigate the duration, rainfall and area characteristics of radar- echoes.The dates are July 1, August 4 and July 17, 1973, in order of descendingwhole-day rainfall over the study area. The synoptic and mesoscale situations
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Table 2. Combined Days -Properties of Unmerged and Merged Showers
Standard Deviation Standard ErrorMeanSingle echoes (615 cases):
Duration (min)Mean area (krn2)Max. area (krn2)Acc. rain (105 m3)Mean rain (105m3)Max. rain (105m3)
Depth (cm)
23.522.240.9
3.380.280.59
0.950.901.67
.14
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243144
1
4.8615.4024.252.590.210.31
First order mergers (60 cases):
Duration (min) 58.4Mean area (km2) 183.5Max. area (km2) 266.6Acc.rain(105m3) 14.7Mean rain (105m3) 1.4Max. rain (IOSm3) 2.2Depth (cm) .07
Second order mergers! (11 cases):
Duration (min)Mean area (km2)Max. area (km2) ]
Acc. rain (105m3)Mean rain (105m3)Max. rain (105m3)
Depth (cm)
37.7119.3187.820.7
1.62.4
49.7697.3
1040.3434.0
12.817.9
14.98210.26313.66131.0
3.875.40
132.5851.8[415.3
302.09.5
17.211
Underestimates, see text.
..The total area was derived from the numbers in Table 2 by multiplying themean area (km2) by the mean duration (min) by the mean number of echoesin that category and dividing by 5. The area had been recorded at5-minute intervals and is then summed approximately every 5 minutes. Thisis a rough estimate of the total area covered per day. Single echoes and first-order mergers contribute similar proportions of total area and of total rain-fall. The total accumulated rainfall was derived simply by multiplying themean accumulated rainfall, summed every 5 minutes, by the mean numberof echoes in each category. Second-order mergers contribute about 68%of the rainfall during these 3 days and account for 53% of the area coveredby echo. The outstanding result is that 86% of the rain volume fell frommerged systems (first or second order) while only 14% was produced by non-merged showers; echo area is 80% produced by mergers. The opposite is
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In the example of a second order merger outlined in Fig. 3, it is easier toenvision the evolution of cell interaction. The total estimated rainfall derivedfrom this second order merger which began at 1230 LST (1730 GMT) is368.8 x 1 OS m;1. The 5 minute rainfall maximum, 20.5 x 1 OS m3, occurs at1335 LST when the system also reaches its largest areal coverage, 2068.3 km2At 1545 LST, this system remerges with 2 other second order mergers tothe west.
The duration of the average second order merger is presented as 132.5minutes (Table 2). This is an underestimate of the actual echo life span,as the data for 2 of the 11 second order mergers were truncated at 1930 LSTwhen the radar digitizer was shut off for the day. A particularly largesystem on 1 July 1973 which lasted for more than 4 hours was artificiallyterminated two hours prior to complete dissipation. The maximum in rain-fall and areal coverage appear to have occurred within the first two hoursof its existence. On 17 July a small system which had been in existence for3 hours was terminated 45 minutes early. The mean duration for the secondorder merger should be approximately 150 minutes. The mean area andmean 5 minute rainfall are overestimated, and the accumulated rainfallfor the second order merger is underestimated by perhaps 15 percent [65].Nevertheless, it is clear that the average second order merger extends over4 to 5 times more area than the first order merger. In a 5 minute period,8 to 10 times more rain is yielded by a second order merger. More than anorder of magnitude difference is found between its total rainfall and thatof the first order merger.
Three statistical tests have been applied to the data and its log transforma-tions. The F test is applied to analyze for differences in variance. At aprobability level better than 0.001, the variances of all tabulated propertiesare different for the single echo and first-order merger. Except for duration,the same result holds for first-order versus second-order merger. This resultmeans that to test for differences in means, we must use the modified t orWelch test which allows for different variances between samples [56, 63].This test shows that for the means between single echoes and first-ordermergers the null hypothesis (that the means do not differ) can be rejectedat probability levels of 10-7 to 10-11. In comparing mean values for firstand second-order mergers, the probability level ranges from .012 for maxi-mum rain to .0004 for duration.
Since the data are skewed and thus far from normally distributed, theseresults need confirming with similar tests on a log-transformation, whichrender the distributions very nearly normal. The F test shows that whenthe data are transformed, the variances of the area and rainfall propertiesof single and merged echoes satisfy the null hypothesis, i. e. they can beassumed equal, as is the case comparing first and second-order mergers.
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A graphical type of "analysis of variance" is presented for the untransfonneddata in Fig. 4. Plotted are the sample means, plus or minus 2 standard errorsfor the single, merged and doubly merged echo systems. These dramaticallyillustrate the difference in the means of the three population samples.Similar graphs (not shown) were plotted for the log transfonnations, withsimilar results.Actual one-way analyses of variance calculations were also perfonned usingthe transfonned data (since the test assumes equal sample variance). Themeans of all the echo characteristics for each echo type differ to a p levelbetter than 0.001. The duration is again the least significant variable.'Since the means (but not the variances) differ significantly for the log-transfonned data, it can be concluded that the differences in populationmeans are multiplicative rather than additive (when logarithms of numbersare added, the numbers are multiplied, so a scale difference in the log trans-fonn of a variable implies a multiplicative difference in the untransfonnedvariable). In other words, there is a synergistic increase in precipitationresulting from the more organized convective systems. The difference induration means, however, seem additive perhaps because several of thedouble mergers were artificially truncated.Comparing the rainfall depths per echo we see that they also increasewith merger level but only by about a factor or two (between single echoesand second-order mergers) rather than an order of magnitude.
4. Results Stratified by Day and Merger Level
4.1
Characteristics of the Three Days Studied
According to the half hourly sample, August 4 yielded about double andJuly 1 triple the total amount of rainfall produced over the area on 1,. July.There were also differences in the 0700 LST (1200 GCT) soundings, in thetime, location and intensity of convective activity and in cirrus coveragebetween and three days, which are summarized briefly.July 1: This was an ideal seabreeze day, although showers developed toolate for the FACE experiment. The University of Virginia Mesoscale Modelreceived intensive successful testing on this day, as reported by Pielke andMahrer [46] who also show the synoptic charts and soundings. At 0700 LSTthere was drying between 900 hPa and 700 hPa, and above 500 hPa. Theprofile of 6e showed the convectively unstable lower portion of the cloudlayer (hereafter called "lower cloud layer") to extend to the 785 hPa level.Both 17 July and 4 August were more convectively unstable. The windswere light on 1 July, at 2.5 m sec-l or less up to 700 hPa increasing to7 m sec-l at 500 hPa, and vacillating between 2.5 and 7.5 m sec-l
16 Joanne Simpson et at.
above. The winds veered from 3600 at the surface to 800 at 500 hPa, backedto 3050 at 400 hPa and again became more northwesterly above.There was little echo activity until 1400 LST, with a large system developingafter 1630 LST due west of Miami. A maximum of rainfall occurred overthe peninsula at 1800 LST. This was the wettest of the 3 days, though the0700 LST sounding indicated the most suppression.Small variable amounts and thicknesses of cirrus were reported along theeast coast of Florida from 0700 LST (1200 GCT) on. No cirrus was foundon western portion of peninsula. Satellites showed little cirrus over t~e peninsulasouth of Lake Ok~echobee up to 1500 LST, increasing to about 50 percentcoverage by 1604 LST particularly in northern part of the area. No mergersoccurred after about 1600 LST. The northwest winds aloft blew earlymorning coastal cirrus out to sea. The cirrus which covered the northern partof the area by late afternoon consisted of blow-offs from a cloud clusternorth of Lake Okeeschobee.July 17: This day, the only one of our three selected for the FACE experi-ment, had relatively strong upper winds, producing substantial cirrus anvilcoverage by midafternoon. In testing the University of Virginia MesoscaleModel on this day, Pielke and Cotton [43] present the synoptic situationand model results. They show that feedback from active convection, cirrusand rain had some effect upon the seabreeze convergence patterns. The 0700LST moisture profile indicated there was drying around 850 and 600 hPa.The 8e profile showed the lower cloud layer reached to 585 hPa, and that17 July was slightly more convectively unstable than 1 July. The winds werelight, 3-4 m sec-l up to 500 hPa, with a steady increase of speed up to16.5 m sec-l at 200 hPa. The winds veered from 360u at the surface to 950at 850 hPa,'-and became more north-easterly above.Relative to the other FACE 1 days of 1973, an average amount of rain fellon July 17 though it is the least convectively active of the three days studiedhere. At 0800 LST a second order merger was already present south of theFlorida mainland which dissipated at 1100 LST and was not included in theecho-history analysis. Two other second order mergers occurred over theAtlantic late in the afternoon. These were the only two which occurred overwater during the three study days. Convective activity began over thepeninsula at 1130 LST, with a maximum at 1530 LST and a substantialdecrease in activity over land at 1730 LST.Cirrus was reported at 1000 LST along the east coast of Florida. Both theMiami 1200 and 1800 GCT (0700 and 1300 LST) soundings show strongnortheast (10-15 m sec-l ) winds from 400 hPa up. The DAPPS satellitepicture (Fig. 8) showed the southeastern quarter of the area covered byanvils by 1237 LST. The A TS satellite series showed the area virtuallyentirely cirrus covered by 1445 LST; however comparison with aircraftand ground photographs from the FACE 1 project showed this satellite
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Table 3. Half Hour Data Sample Results by Days
Area (km2)Amount
Rain (105m3)Amount %% %
6973.25199.9
18367.730540.8
22.817.060.1
100.0
75.373.05
320.0468.35
25.334.540.2
100.0
72.119.18.8
100.0
11408.29871.55
10214.6
31494.35
36.231.332.5
100.0
40.455.264.2
159.8
Echo-type EchoesNumber
1 July 73 (0830-1930 LST):Single 1251st order merger 212nd order merger 41Total 187
17 July 73 (0800-1930 LST)Single 2711st order merger 722nd order merger 33Total 376
4 August 73 (1030-1730 LST)Single 2191st order merger 692nd order merger 48Total 336
11058.311418.527227.349704.1
22.223.054.8
100.0
40.362.9
218.4321.6
12.519.667.9
100.0
65.220.514.3
100.0
On 1 July, only 187 echoes were observed, compared with 336 on 4 Augustand 376 on 17 July. The proportions of areal coverage and rainfall yieldcontributed by each echo-type were quite similar on 1 July and 4 August,the two largest rain producing days. August 4 was sampled from1030-1730 LST.The half hourly data results reveal that single echoes played a larger rolein rainfall pr0ductio~ on drier 17 July, than on. either wetter 1 July or4 August. Single echoes on 17 July (1) were found in larger nQmbers,(2) covered the largest proportion of area and (3) contributed the greatestpercentage of rainfall. The proportion of echo coverage and rainfall yieldwas most evenly divided between the 3 echo categories on 17 July, the dayleast productive of rainfall. The half hourly sample on 17 July included thehours of 0800 through 1930 LST.On the wetter days, 17 July and 4 August, single echoes and first-ordermergers produced similar total amounts of rainfall, as well as coveringnearly the same total area. Second order mergers on 4 August, however,yielded more than 3 times more precipitation and covered nearly 3 timesmore area than on 17 July. The total echo coverage was smallest for eachecho category on 1 July, though the total amount of rain produced by singleechoes and echoes resulting from first and second order mergers was largeston this day, a feature which is clarified below.
16.115.668.3
100.0
66.811.321.9
100.0
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Joanne Simpson et al.20
Table 5.17 July 1973 (Driest) -Properties of Merged and Unmerged Echoes
Mean Standard DeviationSingle echoes (243 cases):
Duration (min)Mean area (km2)Max. area (km2)Acc. rain (105m3)Mean rain (105m3)Max. rain (105m3)
Depth (cm)
29.3530.3543.0
.867
.098
.166
.032
27.020.437.2
1.60.120.221
First order mergers (21 cases):
Duration (min) 67.95Mean area (krn2) 159.3Max. area (krn2) 228.3Acc. rain (105m3) 13.9Mean rain (105m3) .830Max. rain (105m3) 1.31Depth (cm) .052
Second order mergersl (4 cases):
Duration (min) 115.5Mean area (km2) 622.2Max. area (krn2) 789.75Acc. rain (105m3) 109.0Mean rain (105m3) 4.02Max. rain (105m3) 6.46Depth (cm) .065
lOne second-order merger artificially terrilinated.
37.9133.1182.7520.0
.9751.46
59565599119
35
the mean depth of the rain produced by the single echo is 40 to 50 percentthat of the second order merger, and the mean rain depth from the firstorder merger is 67 to 80 percent that from the second order merger.It is important to note that the number of single and first order mergedechoes of 1 July was approximately half that found on each of the otherdays. It appears that wetter days are characterized by fewer, larger echounits. Ulanski and Garstang [61] have shown a similar difference betweenwet and dry seasons in a smaller portion of the same area.Within each day, the same statistical tests were performed as for the com-bined days of Table 2 with essentially the same results (for details see [65]).The differences in rainfall means between single echoes and first-ordermergers are significant. Only on August 4, which has the largest sample ofboth merger types, are means significantly different between first andsecond-order mergers.
.6
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Joanne Simpson et al.
these two echo-types are larger than on 4 August, though of comparablesizes. The accumulated rainfall values of the single and merged echoes arealso larger on 17 July. The maximum area and rainfall properties are larger,however, on 4 August. Duration is a critical factor in the larger accumulatedrainfalls of 17 July. Second order mergers are considerably smaller than oneither I July or4 August.The most important result of this section concerns the relationships be-tween echo merger and rain production, which goes up with organization.July I was the rainiest and most convectively intense of the 3 study days,though it appeared to be the most severely suppressed at 0700 LST(1200 GCT). Rainfall activity began and ended later in the day than oneither July 17 or August 4. Fewer but more intense echoes of each echo-type were found. The echoes are of average duration, as compared with17 July and 4 August. Both the average area and rainfall characteristicswere larger for single and first order merged echoes, and the mean rainfallof the second-order mergers was also larger than found on the other twodays.Single echoes developing on 17 July were of longer duration than singleechoes on I July and 4 August, and contributed a larger proportion of thetotal rainfall on this day which was least convectively intense. The singleechoes on I July, however, were larger and more intense. The percent echocoverage and total rainfall contribution was rather evenly divided amongthe 3 echo types on July 17.On I July and 4 August, the larger rain producing days, 50 to 60 percentof the echo coverage is of echoes resulting from second order mergerswhich produce 68 percent of the rainfall. Single and first-order mergedechoes covered nearly the same percent of area and yielded the same pro-portion of precipitation on these two days. Both single echoes and first-order mergers played a iarger role in rainfall generation on 17 July; however,second order mergers still contribute the largest proportion of rainfall.,Statistical results further indicate that not only in combining the days,but also on each individual day, there is a multiplicative difference in areaand rainfall property means in going from single echoes to the larger moreorganized first and second order mergers.The differences noted here between organization on wet versus dry con-ditions have been supported by other evidence, to be cited in Section 7.Comparisons have been made of merger characteristics over the Floridapeninsula versus those over the surrounding waters. These results are re-ported elsewhere [66] together with a comparison of those echoes whichdissipate without merger versus those which merge. The relevant resultsto this study are that merging systems have, class for class, about 50-100percent larger echo area and 2-3 times the rainfall of nonmerging systems(the lower figure for single echoes; the high figure for first-order mergers).
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Table 7 .Model, Analysis andEchoMotion Parameters
Geostrophic wind Model start timeSpeed Directionm sec-1 degrees LST
July 1, 1973 4.3 120 1850 June 30July 17,1973 6.0 100 0640August 4,1973 6.2 135 0700
Analysis period Echo motion
LST
Date
0830-19300800-19300130-1730
no motionmotionmotion
of July 1, 1973, model-predicted moisture flux through cloud base levelprecedes the occurrence of rain by about 4 hours during morning and earlyafternoon, while fluxes and rainfall are more in phase in the late afternoon[46]. This may explain in part the apparent increased control with timeexerted on showers by model-predicted convergence. Also mechanisms forpositive feedback between convection and convergence have been proposed[.19,43].Table 7 gives information on model initiation, analysis periods and echomotion for the three study days.
5.2 Purpose and Method of Analysis
This analysis was designed to determine the degree to which mergerscoincide in time and space with updraft zones at 1.22 kIn elevation predictedby the University of Virginia Mesoscale Model. Updrafts are calculated fromthe predicted horizontal convergence by the continuity equation. Agreementis measured by the areal percent of merger echo falling within a hierarchy ofmodel-predicted vertical velocity isopleths. At each time the PEAKSprogram defined a merger event, the echo was traced on a scaled Florida mapfrom the projected PPI radar photograph. This map was then enlargee to thescale of the vertical velocity field maps generated by the model, on whichthe echoes were outlined. Each merger echo was plotted on the hourlyvertical velocity diagram closest in time to its occurrence. The percent ofeach merger echo within a specified vertical velocity range was determinedby the weight-area ratio method.
5.3 ResultsThe main results are shown in Figs. 5-7 and in Table 8. On July 17 andAugust 4, some mergers occurred over or downwind from the offshoreBahama islands, or over water. These are not treated by the model andshould be ignored in the comparisons. With this omission, the parentheticfigures in the right-hand column in Table 8 shows excellent coincidence ofmergers with model-predicted mesoscale ascent (regions with vertical
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Fig. 8. DAPP Satellite photograph of the Florida peninsula at 1237 LST (1737 GCT)on July 17, 1973. The black region is Lake Okeechobee
the convergent zones, with suppression outside: Fig. 8 shows a satellite viewof this process in progress on July 17, 1973. Fritsch [18] and Fritsch andChappell [19] have suggested and modelled positive convective feedback tothe mesoscale convergence by means of pressure gradient forces created bythe convection. We believe cumulus organization by merger plays animportant role in this feedback, as postulated below in a preliminary fashion.
6.2 Postulate Concerning Merger Mechanisms of Showering Cumuli
The merging of small non-precipitating trade cumuli, especially along linesroughly parallel to the shear, has been documented photographically and
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cloud has opposite relative motion to that of an older downdraft-dominatedcloud. Looking at surface fields, investigators using the Florida mesonetworkdata [25, 59, 60] have commonly detected large cumulus-scale coupledcenters of surface convergence and divergence associated with cumulonimbiin the stages of Figs. 9-11 ; these are probably the "seeds" of meso-high andmeso-low pressure areas since they are seen enlarge to the meso-scale asthe cloud systems organize by combined growth and merger to the second-order merged complex stage [25]. Since three-dimensional effects probablycannot be ignored, pursuit of the simplified hypotheses proposed here mustbe carried out using multi-doppler radars and three-dimensional simulations,together with detailed surface field observations. Among the first importantpoints to follow up are the role of downdrafts in merging, the differencesin merger processes as a function of wind and windshear and criteria forcontinued merging to the mesoscale system.
7. Context, Relevance and Conclusions of This Research
7.1 Research Results in Context of Related Work
A hint has come from our results, particularly the tables in Section 4, thatheavier convective rainfall is produced not by more shower elements butby fewer, larger and more organized elements. However, a sample of threedays is inadequate proof, so that other evidence must be examined.Ulanski and Garstang [61] compared two whole summer seasons of showerstructure using densely spaced raingauges in the mesonetwork of Fig. I.The very dry summer of 1971 was contrasted with the three:timeswettersummer of 1973. Total duration and intensity of rainfall was about thesame in both years. Days With few well-organized large storms prodbcedmore rain than those With more, smaller showers. The summer of 1973was wetter by virtue of larger showers, which processed water more effi-ciently. We have shown that merger is an important factor in producinglarge organized showers; rainy days Will be those With conditions forcingor permitting the large showers.The above deduction receives further support from use of more of thesouth Florida radar data with the same computer programs described here,adding the statistical program STATS (Section 2). Wiggert et al. [68] madea statistical merger study of 16 summer days from the seasons of 1973,1975 and 1976. All 16 days were experimental days in the randomizeddynamic seeding program (FACE I). The main purpose of the study wasto identify differences in echo structure and merging behavior as a functionof echo motion and Windspeed. Differences in these variables appear to be
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7.4 RecommendationsImprovements in model and remote sensing capability offer opportunity tomake vast advances in understanding, predicting and even in beneficiallymodifying cloud merger. Remote sensing is a necessary component, since themotions in and around cumuli must be documented to understand theirinteraction. A flat heated peninsula like south Florida is an ideal laboratoryto study cumulus growth and organization because I) the daily forcingfactor, the seabreeze, has been identified, successfully simulated and relatedto cloud organization 2) the mesoscale forcing ends each night and beginsagain next morning, so that early, less complex, more readily measurablestages of cloud interaction and merging are available for study in a limitedtarget and 3) relatively light winds and wind shears keep the systems in aehosen study area long enough for their life cycles to be encompassed bya limited number of sensors and platforms. Experimentation, jointly withmodelling, should be pursued in Florida and in similar sea-breeze-dominatedlocations elsewhere, focussing attention on motion fields which can now bemeasured over substantial volumes as a function of time.
AcknowledgementsThis research has been supported by Grants DES-75-03984, ATM-78-10087 andATM-78-21763 from the National Science Foundation. We are deeply grateful to thedirectors and scientists of NOAA's Florida Area Cumulus Experiment (FACE) for data,discussions, help and constructive criticism, especially P. Gannon, R. L. Holle, R. I. Sax,V. Wiggert and W. L. Woodley. Ron Holle kindly provided Fig. 9. We also thankW. R. Cotton for valuable model information, a synoptic analysis of August 4, 1973and for providing Fig. 8.Our University of Virginia colleagues R. Biondini, H. Cooper, G. D. Emmitt, W. Frank,M. Garstang, R. H. Simpson and C. Warner provided valuable discussions, ideas andcriticisms which we greatly appreciate.Sandy Smith, Gloria Adams and Carol Wagner prepared the many drafts of the..manu-script. Robert Clerman, Stephen Garstang and Tom Adams drafted the diagrams. Weare grateful for their patience and competence.
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40 Joanne Simpson et aI.: On Cumulus Mergers
64. Westcott, N. E.: Radar Characterization of South Florida Convective Rainfall. Proc.Sixth Conf. on Planned and Inadvertent Weather Modification, pp. 190-193.Champaign-Urbana"Illinois. Amer. Met. Soc. (1977).
65. Westcott, N. E.: Radar Characterization of South Florida Rainfall, 74 pp.M. S. Thesis, Dept. of Environmental Sciences, University of Virginia, Charlottesville,Virginia (1977).
66. Westcott, N. E., Simpson, J.: Population Study of Radar Echoes Over South Florida.Submitted to J. Appl. Met. (1979).
67. Wiggert, V., Andrews, G. F.: Digitizing, Recording, and Computer ProcessingWeather Data at EML. NOAA Tech. Memo. ERL WMPO-17, pp. 1-25 (1974).
68. Wiggert, V., Lockett, G. J., Ostlund, S.: Radar Rainshower Growth Histories andTheir Variation With Wind Speed and Echo Motion Over South Florida. Submittedto Mon. Weath. Rev. (1979).
69. Wiggert, V., Ostlund, S.: Computerized Rain Assessment and Tracking of SouthFlorida WSR-57 Weather Radar Echoes. Bull. Amer. Met. Soc. 56,17-26 (1975).
70. Wiggert, V., Ostlund, S., Lockett, G. J., Stewart, J. V.: Computer Software forthe Assessment of Growth Histories of Weather Radar Echoes. NOAA Tech.Mem. ERL WMPO-35 , 85 pp. Boulder, Colorado (1976).
71. Wilson, J. W.: Evaluation of Precipitation Measurements With the WSR-57 WeatherRadar. J. Appl. Met. 3,164-174 (1964).
72. Woodley, W. L., Jordan, J. A., Simpson, J., Biondini, R., Flueck, J.: NOAA's FloridaArea Cumulus Experiment Rainfall Results: 1970-1976. In press
73. Woodley, W. L., Norwood, J., Sancho, B.: Some Aspects of South Florida Showersand Thunderstonns. Weatherwise 24, 106-113 (1971).
74. Woodley, W. L., Olsen, A., Herndon, A., Wiggert, V.: Optimizing the Measurementof Convective Rainfall in Florida. NOAA Tech. Mem. ERL WMPO-18, 9? pp.Boulder, Colorado (1974).
75. Woodley, W. L., Olsen, A. R., Herndon, A., Wiggert, V.: Comparison of Gage andRadar Methods of Convective Rain Measurement. J. Appl. Met. 14,909-928(1975).
76. Woodley, W. L., Sax, R. I.: The Florida Area Cumulus Experiment: Rationale, Design,Procedures, Results and Future Course. NOAA Tech. Rept. ERL 354-WMPO 6,204 pp. (1976).
77. Woodley, W. L., Simpson, J., Biondini, R., Berkeley, J.: Rainfall Results, 19.70-1975:Florida Area Cumulus Experiment. Science 195, 735-742.
78. Woodley, W. L., Simpson, J., Biondini, R., Jordan, J.: NOAA's Florida Area CumulusExperiment Rainfall Results 1970-1976. Sixth Conf. on Inadvertent and PlannedWeather Modification, pp. 206-209. Champaign-Urbana, Illinois, Amer. Met. Soc.(1977).
Authors' addresses: Dr. Joanne Simpson, Goddard Laboratory of Atmospheric Sciences,National Space and Aeronautics Administration, Greenbelt, MD 20771, U.S.A.;R. A. Pielke, Department of EnvirOtlrnental Sciences, University of Virginia;Charlottesville, VA 22903, U.S.A.; Nancy E. Westcott, Atmospheric Sciences Section,Illinois State Water Survey, Urbana, IL 61801, U.S.A.; R. J. Clerman, The MitreCorporation, McLean, VA 22101, U.S.A.
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