On cumulus mergers

ARCHIV Arch. Met. Geoph. Biokl., SeE A, 29, 1-40 (1980) Ff]R METEOROLOGIE

GEOPHYSIK UND BIOKLIMATOLOGIE

�9 by Springer-Verlag 1980

551.515.4

Department of Environmental Sciences, University of Virginia, Charlottesville, U. S. A.

On Cumulus Mergers

Joanne Simpson, Nancy E. Westcott, R. J. Clerman, and R. A. PMke

With 11 Figures

Received July 9, 1979

Summary

Joining together or merging is postulated to be a major way in which convective clouds become larger, enhancing their transports and impacts upon their environment. Cumulus shower merger is defined in terms of echoes from a calibrated digitized 10-cm radar reviewing a 0.9 x 105 km 2 area in south Florida, U. S. A,, which encompasses a 1.3 x 104 km 2 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 control day for the experiment. Mergers are found to produce more than an order of magnitude more 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 systems produced about 86% of the rainfall over the area. Duration, echo area and rain depths are also compared for merged and unmerged systems. Each day is then analyzed individually, indicating a correlation between organization and rain amount, confirmed by other research reviewed briefly. T, he location and time of merger is related to the seabreeze convergence zones as predicted by the University of Virginia Mesoscale Model with overall good agreement. Physical hypotheses suggesting the importance of downdrafts in cumulus merging are developed. The relevance of mergers to hydrology, weather modification and the large- scale impacts of convective clouds is discussed.

Zusammenfassung

[2ber das Verschmelzen von Cumulus-Wolken

Das Zusammenwachsen oder Verschmelzen von Cumulus-Wolken wird als einer der Hauptgrtinde Far ihr Wachstum sowie far ihren Einflug auf ihre Umgebung und auf die durch sie bewerkstelligten Transportprozesse angesehen. Das Verschmelzen von Cumulus- Schauern wird auf Grand der yon einem kalibrierten und digitisierten 10-cm-Radar empfangenen Echos definiert. Das Radarger~it iiberblickt eine Fl~iche yon 0.9 x 10 s km 2

1 Arch, Met. Geoph. BiokI. A. Bd. 29, H, 1 2

0066-6416/80 /0029 /0001 /S 08.00

2 Joanne Simpson et al.

im Siiden Floridas (U. S. A.), die ein Exerimentalgebiet von 1.3 x 104 km 2 ftir rando- misierte Wolkenimpfung umgibt. Eine detaitlierte physikalische und statistische Studie ftir drei relativ ungestorte Tage ohne Wolkenimpfung wahrend des Sommers 1973 wird hiermit vorgelegt. Der trockenste dieser Tage war willkiirlich als Kontrolltag ftir das Wolkenimpfungsexperiment gewNdt worden. Verschmelzungsprozesse weisen um mehr als eine Gr6t~enordnung mehr Nieder- schlag auf als unverschmolzene Echos, wNarend Verschmelzungen yon Verschmelzungen (Verschmelzungen zweiter Ordnung) nochmals eine Gr6f~enordnung mehr Regen ergeben. An den drei untersuchten Tagen produzierten verschmolzene Systeme ungefahr 86% des tiber dem Untersuchungsgebiet beobachteten Regens. Andauer, Echoausma$ und Nieder- schlagsh6he werden far verschmolzene und unverschmolzene Wolkensysteme verglichen. Jeder Tag wird individuell analysiert, wobei eine Korrelation zwischen Wolkenorganisa- tion und Niederschlagsbetrag angedeutet wird, die auch yon anderen, kurz erwahnten Forschungsarbeiten bekr/iftigt wurde. Ort und Zeit des Versctunelzens h~ingen yon der Seewind-Konvergenzzone ab, welche dutch das mesoskalare Rechenmodell der University of Virginia gut vorhergesagt wurde. Eine physikalische Hypothese tiber die Wichtigkeit der Absinkbewegung w~ihrend des Cumulus-Verschmelzungsprozesses wird dargelegt. Die Bedeutung der Verschmelzungs- vorg~inge ftir die Hydrologie, f'tir die ktinstliche Wetterbeeinflussung und ftir den grog r~iumigen Einfluf5 konvektiver Wolken wird diskutiert.

1. Introduction, Historical Perspective and Motivation

An impor tant frontier in meteorology concerns the factors controlling the sizes o f cumulus clouds. The correlation between heights and widths o f cumuli has been well documented [28, 48]. As they become larger, cumulus clouds produce more rain, release more heat and transport more energy aloft. Critical size also appears necessary for severe s torm events, such as squalls, hail and tornadoe s, with the Browning "supercell" [6, 27] the ultimate giant o f the species. The processes forcing cumulus clouds are suspected to control their size, but these relationships are not yet well under- stood. Cumulus models so far must assume the dimensions o f an initial per- turbat ion [9, 49]. For parameterizing cumulus effects in the large-scale models, size controls are among the most vital unknowns. This paper adds a link to understanding cumulus relations to their forcing by 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 o f kilometers. We examine the merging of showers in the vicinity o f Florida, U. S. A., in the size range observed by a 10-cm radar, namely about 1 to 100 km in horizontal dimension. Merger was actually first documented in Florida by the Thunders torm Project [7] and by Malkus over the tropical oceans [32, 34]. In the latter

On Cumulus Mergers 3

studies, by instrumented aircraft and time-lapse movies, cloud groups were often seen to begin their visible lives as random-appearing bunches of small cloudlets a few hundred meters across. These would commonly grow by aggregation with their near neighbors. This aggregation process has been simulated in a model by Hill [23], in which the "ent rapment" of a cumulus in the circulation of a neighbor does not require any superposed flow field, convergent or otherwise. Another visually observed growth-enhancing mode is lines of small cumuli which often grow by merging along the lines [36]. The Ludlam-Scorer bubble theory [28, 50] and aircraft data of the 1950's showed related aspects of how bigger clouds were composed o f the amalgamation of smaller ones. Evidence that medium-sized (tops 2 - 3 km) tropical cumuli were made up of aggregates was documented by aircraft [34]. Vertical holes were found between updraft elements in the lower port ion of most clouds; at higher levels the elements merged into widening updrafts within continuous cloud matter. In mid-latitudes Malkus and Scorer [37] mapped the merging of numerous bubbles or "thermals" by time-lapse tracings, which confirmed that the larger towers formed by the aggregation of several smaller ones.

1.1 Convergence, Merger and Precipitation

In 1949, Byers and Braham [7] presented evidence from Florida that surface convergence cells on the order of 10 -20 km 2 with peak convergence of 1 - 2 • 10 -3 sec -1 coincided with cumulus development and preceded precipitation by 1 - 2 hours. In the 1960's it was recognized [36, 38] that wide towers occurred in synoptic-scale convergent regions; the time sequence and causality between the convergence and cloud development, however, was unclear until the 1970's. In the past decade, observational evidence has been accumulating to show that low-level convergence (meso and/or synoptic-scale) is a necessary pre-condition for penetrative precipitating convection [24, 62]. In Florida, Ulanski and Garstang found [59, 60] that convergence zones of 2 - 5 0 km 2 precede shower-type precipitation for a sufficient time to permit use in short-period forecasting. Furthermore, the precipitation amounts are predictable from the size and duration of the convergence. A relation between convergence and merging has been demonstrated in a few case studies [ 14, 24] and warrants extensive further research.

1.2 Motivation of Radar Studies of Florida Mergers

Florida's flat heated peninsula (Fig. 1) and surrounding waters make an ideal laboratory for studying all aspects o f convective clouds, particularly in relation to their forcing. In periods unaffected by synoptic-scale disturb- ances, the seabreeze convergence zones develop each day providing a fresh

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355,5 km (180 nrni)

166.7 km (90 nmi)

166.7 km 333.5 km (90 nmi) (180 nmi)

~ FACE TARGET AREA

UVe MESONETWORK

RAIN GAUGE CLUSTER

Fig. 1. The study area is the truncated circle within the squares bounded by 333.5 by 333.5 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 FACE seeding target; showing within it the University of Virginia mesonetwork. The five rain 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 Virginia Mesoscale Model (UVMM) of the boundary layer and seabreezes which has been improved, applied and tested extensively in Florida, as well as in several other areas [44, 45, 46]. Over Florida the strength and patterning of the convergence 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 predicted convergence zones have been found, which improve as the daily cycle progresses [43, 46]. Typical scales of the seabreeze convergence zones are 300 by 30 km along the coast lines, with core magnitudes of about 10 .4


sec -1. An elliptical zone 100 by 40 km with double these magnitudes is common near the southwest tip of the peninsula. A main objective of this paper is to compare radar-viewed merger locations with the model-predicted seabreeze convergence zones. An important question is whether the smaller convergence zones found by Ulanski and Garstang [59, 60] are within these seabreeze convergence regions or whether the latter are merely an aggregate or average of smaller-scale and shorter-lived convergence cells. The data base for this merger study has been mainly provided by NOAA's Florida Area Cumulus Experiment (1970-1976) called FACE 1 [76, 77]. The core objective of these experiments is to determine by a randomized dynamic seeding program [52, 54, 72, 78] whether convective rainfall can be increased over the 1.3 x 104 km 2 quadrilateral in the upper left of Fig. 1. Since preliminary radar, photographic and aircraft cloud studies in Florida [53, 73] suggested that perhaps most of the summer reason rainfall comes from merged complexes rather than from isolated showers, enhanced merger is a major objective of the seeding program.

1.3 Specific Objectives o f This Research

This study examines comparatively the size, rainfall and duration of isolated showers versus merged systems. The objectives are three-fold: First, to provide an initial step toward understanding, modelling and predicting the properties of convective systems in relation to their forcing processes. Second, rain distributions are needed in themselves to construct statistical/ physical models of precipitation, in order to incorporate its controls and impacts in large-scale simulations. Third, enhanced merger is a major objective in dynamic seeding for rain augmentation, so that documentation of natural merging is essential to learn how to enhance this process and to evaluate, in an experimental context, whether merger has been or can be augmented deliberately.

1.4 Precipitation Modelling, Merger Definition

Precipitation systems are modelled here as being composed of single echoes, first-order merger echoes and second-order merger echoes, as depicted on a calibrated 10-cm weather radar. A merger is defined as the consolidation of two previously separate echoes at the 1 mm hr -1 isopleth of rain rate. A first-order merger is the result of the joining of two or more previously independent single echoes, and a second-order merger is formed by the juncture of two or more first or second-order mergers at the 1.0 mm hr -1 rain rate contour level. We recognize that shower merging is studied here, which may differ from the merger of visually detected clouds or of cloud-scale vertical motions. Firstly, several stages of visual cloud merging may have occurred prior


to shower formation, as suggested in Section 1. Secondly, the visual cloud body containing the shower studied could merge prior to echo merger. Several cases [14, 24] suggest this difference to be 5 minutes or less in the middle levels although a visible low cloud "bridge" between towers commonly occurs still earlier (Figs. 9-11) . Radar echoes of rainshowers are chosen for this study both because of the lesser laboriousness of acquisition Of a meaningful sample than in the case of visible clouds and updrafts and because of the inherent importance of the rainfall. However, the subjects of visual cloud and updraft merger warrant intensive study in relation to those of echoes; efforts are being pursued with photogrammetry and multiple doppler data in the FACE analyses [ 14, 16] and with other tools in examining the clouds of the eastern Atlantic in the GATE 1 [4, 26, 40, 62].

2. The Data and Methods of the Research

2.1 The Radar Data

In 1972 the National Weather Service Miami 10-cm WSR-57 radar was digitized and calibrated for quantitative rain measurements, in part to serve as the main rain-measuring tool in the FACE 1 program in 1973, 1975 and 1976. A Miami reflectivity-rainfall relationship had been developed and adapted [21, 22, 55], which underwent extensive further testing in the summer of 1973 [74, 75]. It was shown that when rain gauge clusters are used to adjust the radar rainfall estimates, significant improvement in accuracy is obtained. This finding has received stronger confirmation in the second phase of FACE (begun in 1978) when a network of 100 recording gauges was established over the entire seeding target [58]. The data studied here are from the 1973 season when daily adjustments for the radar were obtained from the five clusters in Fig. 1. Results were tested against the values obtained by the 229 closely spaced gauges in the irregular-shaped mesonetwork shown within the target. The 1973 and 1978 tests indicate that the rain differences of importance in this research lie outside 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 tilt ranging between 0.0 ~ and 0.5 ~ The area within the 46.3 km (25 n.mi) range marker, 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 m during the summer months over south Florida. Beyond 185.3 km range, the

1 GATE denotes GARP Atlantic Tropical Experiment. GARP denotes Global Atmospheric Research Program.


lower edge of the beam is more than a kilometer above cloud base. In Florida, the low cloud base and high humidity in the subcloud layer are important in the good agreement between radar and rain gauge rain estimates. Case studies, however, show merger of raincells as delineated by surface gauges to lag the mergers of the "cloud base" shower echoes by 5 to 15 minutes [24]. Quantitative measurements can be made over a 93061 km 2 area between the inner and outer circle in Fig. 1. This area comprises about 40% peninsula and 60% surrounding waters. The FACE seeding target occupies 15% of the area, while the target-contained mesonetwork studied by Ulanski and Garstang [59, 60] covers less than 1%.

2.2 Computer Products Utilized

Over the years extensive software has been developed to obtain specific properties of the rain-producing echoes from the records of the digitized radar [67, 69, 70]. Shower properties are documented both individually and in populations. The products provide information on location, area and rain rate (resolution 1.85 by 1.85 km) for a field of individually tracked shower echoes every five minutes throughout the daylight hours. Three key programs, developed by Wiggert, Ostlund and collaborators, are called UNPACK, KART and PEAKS. UNPACK normalizes the average power returned data in each of the 200 half mile by 2.0 ~ azimuthal increment bins. This corrects for the increasing distance from the antenna. The bin's power is normalized to what it would be at 215 km (125 n.mi). The range normalized data is then converted into reflectivity and this into rain rate by the aforementioned relationships in the KART program. The polar coordinate system is also transformed into a Cartesian grid of 1 n.mi 2 squares [6]. PEAKS, the third program, isolates echoes using the 8-surrounding points search method. The internal rain rate distribution of each echo is described by the moment method, where local maxima within an echo are taken into account. This technique is described by Wiggert et al. [70]. Individual echoes are then matched from frame to frame and the tracked information updated, providing continuity between frames. The end product consists of (1) a 5 minute rain rate map covering the 333.5 km x 333.5 km area, and (2) a listing of the echoes present during that particular scan. The spatial and temporal resolutions are 1.85 km and 5 minutes. The location, area, rain rate, accumulated rain volume, and status (new echo, merging echo, splitting echo, lost echo, result of a merger, or result of a split) of each echo is also provided. A fourth program called STATS supplies end-of-hour and whole day sum- maries of echo and rain parameters broken down by a number of desired stratifications, such as windspeed, land versus water etc. Results of our

8 Joanne Simpson et ~d.

study will be analyzed in the context of existing products of STATS in Section 7. With the output of PEAKS, considerable comparative human analyses had to be performed using the 5 minute photographs of the PPI scope. Details are described by Westcott [64, 65]. Because of the labor described above combined with that of documenting the larger-scale cloud environment, only 3 days in the summer of 1973 have been analyzed in depth. Near the end of the paper, these will be placed in the context of 16 additional summer days analyzed from a population rather 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 an echo splits, the components are considered to be a continuation of the parent echo, and are included in the computation of the parent echo's life span, mean and accumulated characteristics. If an echo is said to merge, the component echoes'life histories are terminated, and the consolidated system's history begins at the time of merger. Three echo-types are described, the single echo, the first order merger, and the second order merger. The duration, the mean area, the maximum area, the mean and maximum five minute rainfall and the accumulated rainfall are determined for each echo. The mean, standard deviation and standard error are calculated for each of the three echo categories (Table 2). The initial purpose of this investigation has been to investigate the difference in the mean characteristics of the three types of echoes without further stratification and to apply statistical tests to determine the significance of these differences. The six variables de- scribing each echo have been stratified by echo type and analyzed with respect to the best fit distribution by means of a program [ 15 ] comparing the fit of nine different distributions to the data. In the majority of cases, on each day and for the combined days, the raw data follow either a log-normal, or gamma-like distribution. These are heavy tailed distributions which are skewed to the right, that is, there are many more small than very large values. Both the raw data, and the natural log transformed data differences are tested for their significance. The log transformed data are approximately normally distributed because of the near log-normal character of the untransformed distribution.

2.4 Preliminary Discussion of the Three Selected 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 descending whole-day rainfall over the study area. The synoptic and mesoscale situations


are similar in several respects on these days. The 1200 GCT (0700 Local Standard Time) soundings indicate that conditions are neither suppressed nor disturbed with a ridge present in the low and middle levels. A typical early morning surface inversion is found. The winds are generally from the east, though veering in the lower layers and backing with height above. Up to 500 hPa, the wind speed is between 2.5 and 7.5 m sec -1 [57]. During the day, convective rainfall is organized by the sea breeze circulation. A maximum of rainfall activity occurs over the peninsula between 1330 and 1830 LST. Over the surrounding waters, a minimum in convective activity occurs during the late morning and afternoon. Single echoes, first order mergers, and second order mergers appear on each of the days. In view of these similarities, the echo history data have been combined to display the general characteristics of south Florida convective rainfall. Later, differences in meteorological conditions and in echo characteristics will be discussed. It is noteworthy that only the driest day, namely July 17, was selected as a suitable experimental day for the FACE seeding, for reasons to be examined.

3. Overall Results Stratified by Merger Level Only

On the days selected, echoes were tracked, and their properties documented from the normal beginning to the end of the diurnal shower cycle, namely about 0800 LST (1300 GCT) to about 19-2000 LST. On August 4 the study period was truncated by about two hours at each end owing to antenna and false echo problems with an estimated loss of about 7% of the total rainfall and no mergers. Major overall results are shown in Tables 1 and 2. Table 1 presents an estimation of the average daily contribution of each echo category to total area covered by rainfall and to total daily rainfall, and shows the average number of echoes in each category. Since only those echoes which were tracked during their entire lifespan are included (except in the case of 2 second-order mergers), the values are a slight understate- ment.

Table 1. Number, Area and Total Accumulated Rainfall Averaged Over 3 Days 5-Minu te Sample Summation

Number % Area (kin 2) % Acc. Rain (107m 3) %

Single echo 205 89.6 31651 20 2.32 14 lst-order merger 20 8.8 42866 27 2.94 18 2nd-order merger 3.7 1.6 82767 53 11.07 68 Total 228.7 100 157284 100 16.33 100


Table 2. Combined Days - Properties o f Unmerged and Merged Showers

Mean standard Deviation Standard Error Single echoes (615 cases):

Duration (min) 24.2 23.5 0.95 Mean area (km 2) 31.9 22.2 0.90 Max. area (km 2) 44.5 40.9 1.67 Acc. rain (10sin 3) 1.13 3.38 .14 Mean rain (10 s m 3) .14 0.28 .01 Max. rain (10Sm 3) .26 0.59 .02 Depth (cm) .05 - -

First order mergers (60 cases):

Duration (rain) 58.4 37.7 4.86 Mean area (kin 2) 183.5 119.3 15.40 Max. area (km ~ ) 266.6 187.8 24.25 Acc. rain ( 10 s m 3 ) 14.7 20.7 2.59 Mean rain (10 s m 3) 1.4 1.6 0.21 Max. rain (10Sm 3) 2.2 2.4 0.31 Depth (cm) .07 - -

Second order mergers 1 (11 cases):

Duration (min) 132.5 49.7 14.98 Mean area (km 2) 851.8 697.3 210.26 Max. area (km 2) 1415.3 1040.3 313.66 Acc. rain (10Sm 3) 302.0 434.0 131.0 Mean rain (105m 3) 9.5 12.8 3.87 Max. rain ( 10 s m ~ ) 17.2 17.9 5.40 Depth (cm) .11 - -

1 Underestimates, see text.

The to ta l area was derived f rom the numbers in Table 2 by mul t ip ly ing the mean area (km 2 ) by the mean dura t ion (min) by the mean number o f echoes in that ca tegory and dividing by 5. The area had been recorded at 5-minute intervals and is then summed approx ima te ly every 5 minutes. This is a rough es t imate o f the to ta l area covered per day. Single echoes and first- order mergers con t r ibu te similar p ropor t ions o f total area and o f to ta l rainfall. The to ta l accumula ted rainfall was derived s imply by mul t ip ly ing the mean accumula ted rainfall , summed every 5 minutes , by the mean n u m b e r of echoes in each category. Second-order mergers con t r ibu te abou t 68% of the rainfall during these 3 days and account for 53% of the area covered by echo. The ou ts tand ing result is that 86% of the rain volume fell f rom merged systems (first or second order) while only 14% was p roduced by non- merged showers; echo area is 80% p roduced by mergers. The oppos i te is


A FIRST ORDER MERGER, AUGUST 4, 1973

I 5 nmi I

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42 1 3 2 9

1 3 5 3

1 3 1 7 1321 1 3 2 5

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Fig. 2. An example of a first order merger as depicted by the WSR-57 radar. The merger of the 1 mm hr -1 isopleth (not corresponding to any of the radar contours shown) occurs at 1225 LST or 1725 GCT

true of echo numbers , in tha t near ly 90% were unmerged and only abou t 10% merged. Table 2 gives the key da ta on the sample o f each type o f system for the combined days. In examining the mean proper t ies o f the single echo in Table 2, i t is found tha t the average life span is 24 minutes , which is consis tent wi th earlier s tudies by Byers and Braham [7] and Bat tan [27]. The average mean area is 32 km 2 , and m a x i m u m area, 44.5 km 2 . I t mus t be r emembered tha t a m i n imum area threshold o f 13.7 km 2 is imposed . The average mean rainfall in tegra ted over a 5 minu te per iod is 0.45 x 10Sm 3, and the average accumula ted rainfall , 1.13 x 10 s m 3 . Each o f the six descript ive variables is best fi t by a heavy tai led d is t r ibut ion , skewed toward the larger values. The s tandard deviat ions for the dura t ion and area variables are less than the mean values. The rainfall p roper t ies on the o ther hand vary widely. The average echo character is t ics are derived f rom 615 single echoes, 60 first o rder an 11 second order mergers. The first order merger is found to have a mean dura t ion of one hour , twice tha t o f a single echo. The mean and m a x i m u m areas are bo th a fac tor o f six more extensive than those o f a single echo. The average rainfall characteris t ic o f a first order merger sys tem are an order o f mangi tude greater than those of the single echo. The rainfall p roper t ies again have s tandard deviat ions which are larger than the mean values, and the o ther variables deviate less widely f rom the mean. A n example o f a first o rder merger as dep ic ted by the WSR-57 radar is presented in Fig. 2. The merger o f 1 mm-hr -1 isopleths occurs at 1215 LST (1725 GMT) with rainfal l peaking at 1250 (1.32 x 10Sm 3) and area (206 km 2) at 1300 LST.

12 Joanne Simpson etN.

In the example of a second order merger outlined in Fig. 3, it is easier to envision the evolution of cell interaction. The total estimated rainfall derived from this second order merger which began at 1230 LST (1730 GMT) is 368.8 x 10Sm ~. The 5 minute rainfall maximum, 20.5 x 10Sm 3, occurs at 1335 LST when the system also reaches its largest areal coverage, 2068.3 km z . At 1545 LST, this system remerges with 2 other second order mergers to the west.

The duration of the average second order merger is presented as 132.5 minutes (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 LST when the radar digitizer was shut off for the day. A particularly large system on 1 July 1973 which lasted for more than 4 hours was artificially terminated two hours prior to complete dissipation. The maximum in rainfall and areal coverage appear to have occurred within the first two hours of its existence. On 17 July a small system which had been in existence for 3 hours was terminated 45 minutes early. The mean duration for the second order merger should be approximately 150 minutes. The mean area and mean 5 minute rainfall are overestimated, and the accumulated rainfall for the second order merger is underestimated by perhaps 15 percent [65]. Nevertheless, it is clear that the average second order merger extends over 4 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 an order of magnitude difference is found between its total rainfall and that of the first order merger.

Three statistical tests have been applied to the data and its log transformations. The F test is applied to analyze for differences in variance. At a probability level better than 0.001, the variances of all tabulated properties are different for the single echo and first-order merger. Except for duration, the same result holds for first-order versus second-order merger. This result means that to test for differences in means, we must use the modified t or Welch test which allows for different variances between samples [56, 63 ]. This test shows that for the means between single echoes and first-order mergers the null hypothesis (that the means do not differ) can be rejected at probability levels of 10 .7 to 10 -11 . In comparing mean values for first and second-order mergers, the probability level ranges from .012 for maximum rain to .0004 for duration.

Since the data are skewed and thus far from normally distributed, these results need confirming with similar tests on a log-transformation, which render the distributions very nearly normal. The F test shows that when the data are transformed, the variances of the area and rainfall properties of single and merged echoes satisfy the null hypothesis, i. e. they can be assumed equal, as is the case comparing first and second-order mergers.


A SECOND ORDER MERGED SYSTEM, AUGUST 4, 1973

5 nmi �9 0

3.3 kr. ~?~ 0 o ~ ~ o | ~| 0

1112 LST 1225 1237 1250

1 3 0 2 1 3 1 5 1 3 2 8 1 3 4 0

1353 ~ 1 4 0 6 ~ 1 4 1 5 0 1425

1440 1449 1506 1510

1522 1535 1548

1612 1632 1645

% 1 6 0 0

Fig. 3. Example of a second order merger as depicted by the WSR-57 radar. Second-order merger occurred at 1230 LST or 1730 GCT


A graphical type of "analysis of variance" is presented for the untransformed data in Fig. 4. Plotted are the sample means, plus or minus 2 standard errors for the single, merged and doubly merged echo systems. These dramatically illustrate the difference in the means of the three population samples. Similar graphs (not shown) were plotted for the log transformations, with similar results. Actual one-way analyses of variance calculations were also performed using the transformed data (since the test assumes equal sample variance). The means of all the echo characteristics for each echo type differ to a p level better than 0.001. The duration is again the least significant variable. Since the means (but not the variances) differ significantly for the log- transformed data, it can be concluded that the differences in population means are multiplicative rather than additive (when logarithms of numbers are added, the numbers are multiplied, so a scale difference in the log trans- form of a variable implies a multiplicative difference in the untransformed variable). In other words, there is a synergistic increase in precipitation resulting from the more organized convective systems. The difference in duration means, however, seem additive perhaps because several of the double mergers were artificially truncated. Comparing the rainfall depths per echo we see that they also increase with merger level but only by about a factor or two (between single echoes and second-order mergers) rather than an order of magnitude.

4. Results Stratified by Day and Merger Level

4.1 Characteristies of the Three Days Studied

According to the half hourly sample, August 4 yielded about double and July 1 triple the total amount of rainfall produced over the area on 17 July. There were also differences in the 0700 LST (1200 GCT) soundings, in the time, location and intensity of convective activity and in cirrus coverage between and three days, which are summarized briefly. July 1: This was an ideal seabreeze day, although showers developed too late for the FACE experiment. The University of Virginia Mesoscale Model received intensive successful testing on this day, as reported by Pielke and Mahrer [46] who also show the synoptic charts and soundings. At 0700 LST there was drying between 900 hPa and 700 hPa, and above 500 hPa. The profile of 0e showed the convectively unstable lower portion of the cloud layer (hereafter called "lower cloud layer") to extend to the 785 hPa level. Both 17 July and 4 August were more convectively unstable. The winds were light on 1 July, at 2.5 m sec -1 or less up to 700 hPa increasing to 7 m sec -1 at 500 hPa, and vacillating between 2.5 and 7.5 m sec -a


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above. The winds veered from 360 ~ at the surface to 80 ~ at 500 hPa, backed to 305 ~ at 400 hPa and again became more northwesterly above. There was little echo activity until 1400 LST, with a large system developing after 1630 LST due west of Miami. A maximum of rainfall occurred over the peninsula at 1800 LST. This was the wettest of the 3 days, though the 0700 EST sounding indicated the most suppression. Small variable amounts and thicknesses of cirrus were reported along the east coast of Florida from 0700 LST (1200 GCT) on. No cirrus was found on western portion of peninsula. Satellites showed little cirrus over the peninsula south of Lake Okeechobee up to 1500 LST, increasing to about 50 percent coverage by 1604 LST particularly in northern part of the area. No mergers occurred after about 1600 LST. The northwest winds aloft blew early morning coastal cirrus out to sea. The cirrus which covered the northern part of the area by late afternoon consisted of blow-offs from a cloud cluster north of Lake Okeeschobee. July 17: This day, the only one of our three selected for the FACE experiment, had relatively strong upper winds, producing substantial cirrus anvil coverage by midafternoon. In testing the University of Virginia Mesoscale Model on this day, Pielke and Cotton [43] present the synoptic situation and model results. They show that feedback from active convection, cirrus and rain had some effect upon the seabreeze convergence patterns. The 0700 LST moisture profile indicated there was drying around 850 and 600 hPa.

]'he ee profile showed the lower cloud layer reached to 585 hPa, and that 17 July was slightly more convectively unstable than 1 July. The winds were light, 3 - 4 m sec -1 up to 500 hPa, with a steady increase of speed up to 16.5 m sec -1 at 200 hPa. The winds veered from 360 ~ at the surface to 95 ~ at 850 hPa, and became more north-easterly above. Relative to the other FACE 1 days of 1973, an average amount of rain fell on July 17 though it is the least convectively active of the three days studied here. At 0800 LST a second order merger was already present south of the Florida mainland which dissipated at 1100 LST and was not included in the echo-history analysis. Two other second order mergers occurred over the Atlantic late in the afternoon. These were the only two which occurred over water during the three study days. Convective activity began over the peninsula at 1130 LST, with a maximum at 1530 LST and a substantial decrease in activity over land at 1730 LST. Cirrus was reported at 1000 LST along the east coast of Florida. Both the Miami 1200 and 1800 GCT (0700 and 1300 LST) soundings show strong northeast (10-15 m sec- ~ ) winds from 400 hPa up. The DAPPS satellite picture (Fig. 8) showed the southeastern quarter of the area covered by anvils by 1237 LST. The ATS satellite series showed the area virtually entirely cirrus covered by 1445 LST; however comparison with aircraft and ground photographs from the FACE 1 project showed this satellite


imagery greatly exaggerated cloud coverages on all three study days, apparently due to failure to distinguish between cirrus and cumulus. No merging over the peninsula occurred after 1540 EST. Also after this time convective echoes had virtually disappeared over the southeastern two-thirds of the area, which was heavily cirrus covered. August 4: Detailed investigation of this day using aircraft, satellite, model and surface network information [42] revealed a north-northeast to south- southwest oriented synoptic-scale shear line (not detectable by conventional analyses) superimposed on the seabreeze circulation. The 0700 LST (1200 GCT) Sounding indicated a considerable amount of moisture up to 650 hPa, with a large decrease above 500 hPa. The 0 e profile showed 4 August to be much more convectively unstable than either the 1 st or 17th of July, with a lower cloud layer reaching 550 hPa. The winds were variable, between 2.5 and 7 m sec -1 up to 250 hPa, and increased above to a maximum at 150 hPa of 14.5 m sec -1 . The winds veered slightly from the surface to 850 hPa, from 120 ~ to 130 ~ back to 90 ~ at 500 hPa, and remained easterly above. Echo activity began to increase at 1230 LST, with a maximum at 1400 LST, and a termination at about 1700 LST over the peninsula. Cirrus blow-offs to west and northwest associated with shear line cumulonimbus covered about one-fourth of the studied area of the peninsula by 1200 LST. Miami 1200 GCT winds showed no increase until the 200 hPa level. Upper winds decreased by 1800 GCT. Thin to medium cirrus covered most of the area by 1500 LST [421. On August 4, no mergers occurred between 1430-1530 LST. It is possible that the two which occurred between 1530-1630 LST were superimposed by the shear line convergence rather than the seabreeze convergence which may have been greatly diminished by the spread of cirrus by late afternoon.

4.2 Half-Hourly Summed Data Results by Days

For each of the three days, the number of echoes in the study area, their echo-type, location, area and 5 minute rainfall estimate have been noted every one half hour. Presented here are the total number of echoes sampled on a particular day, the percentage of echoes in each category, the percent of total echo coverage by an echo-type, and the percent contribution to the total sample rainfall by each echo class (Table 3). Between 0830 and 1930 LST on 1 July, single echoes made up 66.8 percent of the total number of echoes, covering 21.9 percent of the area with echoes, and yielding 16.1 percent of the total rainfall sampled. First order mergers were found in fewer numbers, but their total areal coverage and precipitation recorded in the half hourly 5 minute periods were comparable to those of the single echo category. Echoes resulting from second order mergers comprised 60.1 percent of the area covered by echoes, and produced 68.3 percent of the total rainfall.

2 Arch. Met. Geoph. Biokl. A. Bd. 29, H. l ~

3,8 Joanne Simpson et aL

Table 3. Half Hour Data Sample Results by Days

Echo-type Echoes Area (kin 2 ) Rain (10 s m 3) Number % Amount % Amount %

1 July 73 (0830-1930 LST): Single 125 66.8 6973.2 22.8 75.3 16.1 1st order merger 21 11.3 5199.9 17.0 73.05 15.6 2nd order merger 41 2 1 . 9 18367.7 60.1 320.0 68.3 Total t87 100.0 30540.8 100.0 468.35 t00.0

17 July 73 (0800-1930 LST) Single 271 72 .1 11408.2 36.2 40.4 25.3 1st order merger 72 19 .1 9871.55 31.3 55.2 34.5 2nd order merger 33 8.8 10214.6 32.5 64.2 40.2 Total 376 100.0 31494.35 1 0 0 . 0 159.8 100.0

4 August 73 (1030-1730 LST) Single 219 65 .2 11058.3 22.2 40.3 !2.5 1st order merger 69 20 .5 11418.5 23.0 62.9 19.6 2nd order merger 48 14,3 27227.3 54.8 218,4 67.9 Total 336 190.0 49704.1 100.0 321.6 100.0

On 1 July, only 187 echoes were observed, compared with 336 on 4 August and 376 on 17 July. The proportions of areal coverage and rainfall yield contributed by each echo-type were quite similar on 1 July and 4 August, the two largest rain producing days. August 4 was sampled from 1030-1730 LST. The half hourly data results reveal that single echoes played a larger role in rainfall production on drier 17 July, than on either wetter 1 July or 4 August. Single echoes on 17 July (1) were found in largernumbers, (2) covered the largest proportion of area and (3) contributed the greatest percentage of rainfall. The proportion of echo coverage and rainfall yield was most evenly divided between the 3 echo categories on 17 July, the day least productive of rainfall. The half hourly sample on 17 July included the hours of 0800 through 1930 LST. On the wetter days, 17 July and 4 August, single echoes and first-order mergers produced similar total amounts of rainfall, as well as covering nearly the same total area. Second order mergers on 4 August, however, yielded more than 3 times more precipitation and covered nearly 3 times more area than on 17 July. The total echo coverage was smallest for each echo category on I July, though the total amount of rain produced by single echoes and echoes resulting from first and second order mergers was largest on this day, a feature which is clarified below,


Table 4. I July 1973 (Wettest) - Properties of Merged and Unmerged Echoes

Mean Standard Deviation Single echoes (122 cases):

Duration (min) 26.55 23.4 Mean area (km z) 40.1 32.0 Max. area (km ~) 59.9 62.0 Acc. rain (10Sm 3) 3.05 6.77 Mean rain (10Sm 3) .364 .536 Max. rain ( i 0 ' m 3) .694 1.17 Depth (cm) .091 -


Duration (min) 43.85 31.3 Mean area (km 2) 243.4 126.8 Max. area (km 2) 341.85 216.9 Acc. rain (105 m 3) 26.7 29.4 Mean rain (10Sm 3) 3.50 2.29 Max. rain ( 10 s m 3) 5.05 3.29 Depth (cm) .144 -


Duration (rain) I 16.7 43.7 Mean area (kin 2) 895.7 1149. Max. area (km 2) 1240. 1410. Acc. rain (10sin 3) 540. 838. Mean rain (10Sm 3) 17.2 24.7 Max. rain (10sin 3) 25.7 31.7 Depth (cm) .192 -

1 One second-order merger artificially terminated, see text.

4. 3 Echo History Sample Results by Day

Table 3 compares the 3 days by half-hourly summed data and Tables 4 - 6 are analogs o f Table 2, except for each day separately. In viewing the echo history statistics on each of the three days, it is immediately evident that the isolated echo and the first order merged echo on 1 July (wettest day) were of larger area, and produced more rain than on either 17 July or 4 August, al though their duration was o f average length. The mean depths further emphasize the difference in convective intensity present on the 3 days. The mean rain depths on 1 July were largest, increasing in size f rom single to second order merger. Those on 4 August were approximately 30 percent o f the values o f 1 July. These clearly indicate that 1 July echoes produced the most intense rain in each echo category, followed by 4 August, which in turn is followed by 17 July. In each case,

2*


Table 5.17July 1973 (Driest) - Properties o f Merged and Unrnerged Echoes


Duration (min) 29.35 27.0 Mean area (km 2) 30.35 20.4 Max. area (km 2) 43.0 37.2 Acc. rain (10sin 3) .867 1,60 Mean rain (105m 3) .098 .120 Max. rain (10Sm 3) .166 .221 Depth (cm) ,032 -


Duration (rain) 67.95 37.9 Mean area (kin 2) 159.3 133.1 Max. area (kin 2) 228.3 182.75 Acc. rain (10 s m 3) 13.9 20.0 Mean rain (10sin 3) .830 .975 Max. rain (10sin 3) 1.31 1.46 Depth (cm) .052 -


Duration (min) 115.5 59.6 Mean area (kin 2) 622.2 565.3 Max. area (km 2) 789.75 599.1 Acc. rain (105m 3) 109.0 119.0 Mean rain (10sin 3) 4.02 3.82 Max. rain (10Sm 3) 6.46 5.16 Depth (cm) .065

i One second-order merger artificially terminated.

the mean depth o f the rain produced by the single echo is 40 to 50 percent that o f the second order merger, and the mean rain depth from the first order merger is 67 to 80 percent that f rom the second order merger. It is impor tant to note that the number o f single and first order merged echoes of 1 July was approximately half that found on each of the other days. It appears that wetter days are characterized by fewer, larger echo units. Ulanski and Garstang [61 ] have shown a similar difference between wet and dry seasons in a smaller port ion o f the same area. Within each day, the same statistical tests were performed as for the combined days o f Table 2 with essentially the same results (for details see [65]). The differences in rainfall means between single echoes and first-order mergers are significant. Only on August 4, which has the largest sample of both merger types, are means significantly different between first and second-order mergers.


Table 6 . 4 August 1973 (Intermediate Wetness) - Properties of Merged and Unmerged Echoes


Duration (rain) 17.7 Mean area (km 2) 28.8 Max. area (kin 2) 38.4 Acc. rain (10sin 3) .4575 Mean rain (10sin 3) .084 Max. rain (10sin 3) .136 Depth (cm) .0455


Duration (min) 56.5 Mean area (km 2) 175.7 Max. area (kin 2) 262.8 Acc. rain (105m 3) 9.96 Mean rain (10sin a) .838 Max. rain (10sin 3) 1.58 Depth (cm) .074

Second order mergers (4 cases):

Duration (min) 161.3 Mean area (km 2) 1 048,4 Max. area (kin z) 2165,2 Acc. rain (105m 3) 316,13 Mean rain (10sin 3) 9.16 Max. rain (10 s m a) 21 A9 Depth (cm) .111

17.7 16.4 27.6

1.03 .100 .196

37.9 98.4

175.1 11.9

.703 1.47

40.9 '545.2 789.2 202.

5.30 10.8

Within all three days, it is found that the differences in echo properties (except for duration) are multiplicative. This impor tant result is thus appli- cable within days - merging multiplies rainfall by a factor, rather than simply encouraging an additive increment. When the log-transformed data are subjected to the student t test, the average maximum area, accumulated and maximum 5 minute rainfall differences in mean are significant. These are the most reliable o f the second order merger echo characteristics. There is a multiplicative difference between the means of the first and the second order mergers for these 3 echo properties. The results o f the 17 July (the only day qualifying for the FACE experiment) echo history statistics are revealing (Table 5). The mean duration o f both the single echo and the first order merged echo are greater than on either July 1 or August 4. The mean area and rainfall characteristics o f


these two echo-types are larger than on 4 August, though of comparable sizes. The accumulated rainfall values of the single and merged echoes are also larger on 17 July. The maximum area and rainfall properties are larger, however, on 4 August. Duration is a critical factor in the larger accumulated rainfalls of 17 July. Second order mergers are considerably smaller than on either 1 July or 4 August. The most important result of this section concerns the relationships between echo merger and rain production, which goes up with organization. July 1 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 on either July 17 or August 4. Fewer but more intense echoes of each echo- type were found. The echoes are of average duration, as compared with 17 July and 4 August. Both the average area and rainfall characteristics were larger for single and first order merged echoes, and the mean rainfall of the second-order mergers was also larger than found on the other two days. Single echoes developing on 17 July were of longer duration than single echoes on 1 July and 4 August, and contributed a larger proportion of the total rainfall on this day which was least convectively intense. The single echoes on 1 July, however, were larger and more intense. The percent echo coverage and total rainfall contribution was rather evenly divided among the 3 echo types on July 17. On 1 July and 4 August, the larger rain producing days, 50 to 60 percent of the echo coverage is of echoes resulting from second order mergers which produce 68 percent of the rainfall. Single and first-order merged echoes covered nearly the same percent of area and yielded the same proportion of precipitation on these two days. Both single echoes and first- order mergers played a larger 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 area and rainfall property means in going from single echoes to the larger more organized first and second order mergers. The differences noted here between organization on wet versus dry conditions have been supported by other evidence, to be cited in Section 7. Comparisons have been made of merger characteristics over the Florida peninsula versus those over the surrounding waters. These results are reported elsewhere [66] together with a comparison of those echoes which dissipate without merger versus those which merge. The relevant results to this study are that merging systems have, class for class, about 5 0 - 1 0 0 percent 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).


This result suggests a relationship between merging and the external processes which cause clouds to join. The forcing factors and merger mechanisms are examined in the next two sections.

5. Mergers and Their Forcing - Mesoscale Model Comparisons

On undisturbed days, the formation and growth of showers in south Florida have been associated observationally [ 17] and theoretically with the seabreeze-produced convergence zones. We postulate that merging is also favored by mesoscale convergence, due not only to more closely spaced clouds, but possibly also to convergence-caused changes in their dynamics [8, 12]. An important step to understand the conditions for and processes of merging is to relate merger times and locations to low-level mesoscale convergence zones. Since this scale of velocity field characteristics is not readily measurable, we use the University of Virginia Mesoscale Model (UVMM) [10, 11, 30, 41] for the comparison.

5. l Relevant Features of the University o f Virginia Mesoscale Model (UVMM)

This three-dimensional time-dependent mesoscale model of the airflow over south Florida, originally developed by Pielke in 1974 [41 ], has since been improved, tested and applied to other areas, including hilly terrain [ 11, 29, 30, 44, 45]. For the simulations of the south Florida seabreezes used in the current comparison, the relevant model features are: 1) Horizontal grid 11 km spacing, 33 by 36 points. 2) Vertical levels, 8, closer together at low elevations. 3) Detailed boundary layer parameterization, with eddy transfer coefficients dependent upon stability and altitude. Prognostic equation for boundary layer depth. 4) Diagnostic equation for surface temperature enabled by heat budget, including long- and short-wave radiative fluxes. 5) Cubic spline method used to calculate advective terms. 6) Vertical shear of horizontal wind included. 7) Initiation by the Miami 1200 GCT radiosonde and by the geostrophic wind as estimated from that sounding together with the synoptic pressure field. Results are sensitive to both the speed and direction of the geostrophic wind. 8) Omission of cumulus processes, water substance phase changes and cloud effects on radiation. Gannon [20] has shown with a 2-dimensional version o f the model that major impacts upon convergence patterns may be made by cirrus anvils and variations in soil thermal and moisture capacities. Despite these omissions in the model, one of the most significant results of comparing its predictions with radar observations [41, 42, 46] is that the good agreement between predicted convergence zones and shower distributions actually improves during the afternoons, optimizing at about 1 6 0 0 - t 7 0 0 LST. In a case study


Table 7. Model, Analysis and Echo Motion Parameters

Geostrophicwind Model start time Speed Direction

Date m sec -1 degrees LST

July 1, 1973 4.3 120 1850 June 30 July 17, 1973 6 .0 t00 0640 August 4, 1973 6.2 135 0700

Analysis period Echo motion

LST

0830-1930 no motion 0800-1930 motion 0130-1730 motion

of July 1, 1973, model-predicted moisture flux through cloud base level precedes the occurrence of rain by about 4 hours during morning and early afternoon, while fluxes and rainfall are more in phase in the late afternoon [46]. This may explain in part the apparent increased control with time exerted on showers by model-predicted convergence. Also mechanisms for positive feedback between convection and convergence have been proposed [19, 431. Table 7 gives information on model initiation, analysis periods and echo motion for the three study days.

5.2 Purpose and Method o f Analysis

This analysis was designed to determine the degree to which mergers coincide in time and space with updraft zones at 1.22 km elevation predicted by the University of Virginia Mesoscale Model. Updrafts are calculated from the predicted horizontal convergence by the continuity equation. Agreement is measured by the areal percent of merger echo falling within a hierarchy of model-predicted vertical velocity isopleths. At each time the PEAKS program defined a merger event, the echo was traced on a scaled Florida map from the projected PPI radar photograph. This map was then enlarged to the scale of the vertical velocity field maps generated by the model, on which the echoes were outlined. Each merger echo was plotted on the hourly vertical velocity diagram closest in time to its occurrence. The percent of each merger echo within a specified vertical velocity range was determined by the weight-area ratio method.

5.3 Results

The main results are shown in Figs. 5 - 7 and in Table 8. On July 17 and August 4, some mergers occurred over or downwind from the offshore Bahama islands, or over water. These are not treated by the model and should be ignored in the comparisons. With this omission, the parenthetic figures in the right-hand column in Table 8 shows excellent coincidence of mergers with model-predicted mesoscale ascent (regions with vertical


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............. i .............. A JULY 17, 1973 1641-1740 LST

Fig. 6. Model predictions for vertical motions at 1.22 km elevation for 17 July, 1973. Values in cm sec -1 , isopleths at intervals of 8 cm sec -1 . First order mergers are black. Second order mergers ,are stippled, a) 0841-0940 LST (1341-1440 GCT), b) 0941-1040 LST (1441-1540 GCT), c) 1041-1140 LST (1541-1640 GET), d) 1141-1240 LST (1641-1740 GCT), e) 1241-1340 LST (1741-1840 GCT), f) 1341-1440 LST (1841-1940 GCT), g) 1441-1540 LST (1941-2040 GCT), h) 1541-1640 LST (2041-2140 GCT), i) 1641-1740 LST (2141-2240 GCT)

velocity upward). An hour-by-hour breakdown (tables not reproduced) shows a trend toward better coincidence as the day advances particularly strong for second-order mergers. In examining the diagrams together with the hierarchy of ascent magnitudes in Table 8, we see that the center o f predicted ascent isopleths is of ten displaced from merger location. If cirrus cover, soil characteristics and the imposed synoptic-scale convergence on August 4 were taken into account in the model, the coincidence could be

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Fig. 7. Model predictions for vertical motions at 1.22 km elevation for August 4, 1973. Values in cm sec -1 , isopleths at intervals of 8 cm sec -1 . First order mergers are black. Second order mergers are stippled, a) 1031-1130 LST (1531-1630 GCT), b) 1131-1230 LST (1631-1730 GCT), c) 1231-1330 LST (1731-1830 GCT), d) 1331-1430 LST (1831-1930 GCT), e) 1431-1531 LST (1931-2030 GCT), 0 1531-1630 LST (2031-2130 GCT)

Joanne Simpson et al.: On Cumulus Mergers 29

Table 8. Relationship Between Mergers and Model-Predicted Updraft Zones

Percent of total area in vertical velocity zones: (units cm sec -1 )

Date Total area(km z) ( - ) (0-8) (8-16) (16-24) (24-32) > 0

First order mergers:

1 July 3798 6 57 29 8 - 94 17 July 6444 46 27 12 11 4 54(83) 1 4 August 12593 27 47 20 6 - 73(90) 1

Second order mergers:

1 July 5038 17 40 20 14 9 83 17 July 3625 48 32 7 9 3 51(91) 1 4 August 5356 10 37 28 18 7 90

Numbers in parentheses are results with over-water mergers omitted.

expec ted to improve marked ly [20]. Pielke and col labora tors have examined in detai l possible reasons for discrepancies be tween the model predic t ions and observat ions o f radar echoes, winds and t empera tu res on each of the days [42, 43, 46]. F r o m these results i t is clear tha t mesoscale convergence provides the necessary ambience for shower merging and that the Universi ty o f Virginia Meso- scale Model well predic ts the loca t ions of the convergent regions. I t is nex t necessary to proceed to the mechanisms by which convergence encourages mergers and those processes by which mergers occur.

6. Merger Mechanisms

6.1 Relationships Between Mesoscale Convergence and Mergers

Some o f the reasons tha t mesoscale convergent areas are favorable sites for mergers are obvious, namely low-level inf lux of warm mois t air providing the source for sustained b u o y a n t ascent and the release o f the slice m e t h o d [5, 13] const ra in t so that a larger f ract ion of the area can be filled with b u o y a n t ascent. Thus more vigorous pene t ra t ive clouds can be located closer toge ther than in neutral o r divergent regions. Moreover, two and three d imensional models o f individual cumuli [8, 12] show tha t convergence gives rise to taller, fa t ter , longer-lived and more heavi ly raining cumuli . P lank 's s tudy [47] shows an early morn ing irregular or banded d is t r ibut ion o f small cumul i over the peninsula, clearly m o d u l a t e d by local surface anomalies. Gradua l ly the sea breeze sets in, so tha t by local noon obvious organiza t ion and merger o f these c loudle ts in to larger systems has begun in


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 view of this process in progress on July 17, 1973. Fritsch [18] and Fritsch and Chappell [ 19] have suggested and modelled positive convective feedback to the mesoscale convergence by means of pressure gradient forces created by the convection. We believe cumulus organization by merger plays an important 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 lines roughly parallel to the shear, has been documented photographically and


partially explained by Malkus and Riehl [36]. The model of Hill [23] simulates small cumuli merging without shear. In this paper we are con- sidering the mergers of showers, and hence must be concerned with the dynamics of cumuli large enough to precipitate; in Florida this commonly requires tops to 4 km or above, with tower widths of the order of a kilometer or more. We postulate that the downdraft or gust front interaction is the primary mechanism of shower merger. This postulate has been developed in more detail by Simpson [51] in relation to dynamic seeding effects; it also believed to be the merger mechanism of natural showers. The approach or collision of gust front/downdrafts from adjacent clouds can force upward warm moist air which in tropical air masses is both conditionally and convectively unstable. An excellent case study showing this with production of a tornado has been documented by Holte and Maier [25]. The dynamics of gust fronts have been discussed and modelled elsewhere [27, 39]. Crucial clues to the role of downdrafts in the merging process are illustrated in Figs. 9 -11 . The first photograph in Fig. 9 shows the precursor "bridge" between cloud towers which virtually always precedes radar echo merger. New towers surge up from the bridge filling the gap, as the downdrafts approach and collide. Fig. 9 depicts a situation with weak wind and weak shear. Fig. 10 is a schematic digram illustrating the downdraft interaction envisaged to trigger the bridge from which spring new towers between those pre-existing. A detailed case study of this situation with surface radar and photographic observations [24] shows that merger as defined here occurred 14 minutes following the first photograph (Fig. 9a). Ulanski and Garstang [60], working in the same observational mesonetwork, found that stronger gust fronts were associated with moving, in contrast to stationary, showers. With wind shear, the merger process should be different and possibly more effective in joining and organizing cloud systems. Our proposed schematic illustration is Fig. 11. The winds are easterlies decreasing upward which are typical ot a Florida summer, with backing to stronger northerlies at anvil level. A young cloud (right) contains mainly updrafts and moves westward (leftward) faster than the cloud layer wind. It feeds and grows on the upshear side [3 I, 32, 33]. The gust front spreads fairly symmetrically below cloud base at this stage. As a cumulonimbus ages, down fluxes predominate [3, 27, 35] so that in a negatively sheafing wind field the cloud's relative motion becomes slower than the ambient wind. Thus the gust front spreads out mainly on the downshear side (right in Fig. I 1 ) setting off new towers which may become a bridge to the younger cloud. The bridge formation is aided by the mesoscale convergence line which commonly extends between the major clouds, having initiated their development. Thus, in the sheared case, relative motion as well as pro- pagation can bring clouds closer together, since a young updraft-dominated

32 Joanne Simoson et al.

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MERGER PROCESS WITHOUT SHEAR

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Fig. 10. Schematic illustration relating downdraft interaction to bridging and merger in case of light wind and weak shear

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jt : I

o OLDER CUMULONIMBUS o YOUNG CUMULONIMBUS = HEAVY SHOWERS * LIGHT SHOWERS �9 DOWNSHEAR GROWTH = UPSHEAR GROWTH

DOWN FLUX SPREADS, INCR, ~.- UP FLUX >DOWN FLUX .'. REL, CLOUD MOTION ~ " .'. REL, CLOUD MOTION

NOTE', GUST FRONTS ICE SHOWERS .;~,~,",'

Fig. 11. Schematic illustration relating downdraft interaction to bridging and merger in case of moderate shear opposite to wind direction through most of the vertical extent of cloud layer. Younger cumulonimbus on right has predominate upmotions, moves faster than the wind. Older cumulonimbus on left has predominate downmotions, moves slower than wind so clouds move and propagate toward each other. Interaction of downdrafts enhances bridge development

3 Arch. Met. Geoph. Biokl. A. Bd. 29, H. 1L2

34 Ioanne Simpson et al.

cloud has opposite relative motion to that of an older downdraft-dominated cloud. Looking at surface fields, investigators using the Florida mesonetwork data [25, 59, 60] have commonly detected large cumulus-scale coupled centers of surface convergence and divergence associated with cumulonimbi in the stages of Figs. 9 -11 ; these are probably the "seeds" of meso-high and meso-low pressure areas since they are seen enlarge to the meso-scale as the cloud systems organize by combined growth and merger to the second- order merged complex stage [25]. Since three-dimensional effects probably cannot be ignored, pursuit of the simplified hypotheses proposed here must be carried out using multi-doppler radars and three-dimensional simulations, together with detailed surface field observations. Among the first important points to follow up are the role of downdrafts in merging, the differences in merger processes as a function of wind and windshear and criteria for continued merging to the mesoscale system.

7. Context, Relevance and Conclusions of This Research

7.1 Research Results in Context o f Related Work

A hint has come from our results, particularly the tables in Section 4, that heavier convective rainfall is produced not by more shower elements but by fewer, larger and more organized elements. However, a sample of three days is inadequate proof, so that other evidence must be examined. Ulanski and Garstang [61 ] compared two whole summer seasons of shower structure using densely spaced raingauges in the mesonetwork of Fig. 1. The very dry summer of 1971 was contrasted with the three-times wetter summer of 1973. Total duration and intensity of rainfall was about the same in both years. Days with few well-organized large storms produced more rain than those with more, smaller showers. The summer of 1973 was wetter by virtue of larger showers, which processed water more effi- ciently. We have shown that merger is an important factor in producing large organized showers; rainy days will be those with conditions forcing or permitting the large showers. The above deduction receives further support from use of more of the south Florida radar data with the same computer programs described here, adding the statistical program STATS (Section 2). Wiggert et al. [68] made a statistical merger study of 16 summer days from the seasons of 1973, 1975 and 1976. All 16 days were experimental days in the randomized dynamic seeding program (FACE 1). The main purpose of the study was to identify differences in echo structure and merging behavior as a function of echo motion and windspeed. Differences in these variables appear to be


associated with different natural and seeded rainfall distributions. The 16 days, with about two or three exceptions, were drier than the three days studied here. A greater average number of smaller echoes were found, with a smaller percentage contribution by merged systems to average total daily rainfall. The merged systems contributed only about four to seven times the rain volume as did unmerged showers. No distinction was made between first and second-order mergers. The days studied here were above average in wetness and cloud organization for undisturbed seabreeze conditions. August 4, in fact, showed evidence, as we saw, of a larger-scale convergent system superimposed upon the seabreeze.

7. 2 Conclusions

Our most important conclusion is that shower size and organization is the crucial factor in convective precipitation production over south Florida and probably elsewhere. The merging process is a major factor in producing large organized shower complexes. While the merging process is not fully under- stood, we have related merging to a forcing function (seabreeze convergence calculated from a numerical simulation) and proposed downdraft interaction as a key mechanism. The merging of convective showers is preceded by a "bridge" of visible smaller cumuli (Figs. 9 -11 ), implying a low-level convergent forcing.

7. 3 Relevance o f Resul ts

Fhe results o f merger studies are relevant to every aspects of convective rainfall, since this is a major process creating the "heavy tail" in rain distributions. Heavy convective rainfall implies organization by merger so that merger is relevant to rain models, flash floods, water resource management, hydrology and rain modification, both deliberate and inadvertent. In order to increase cumulus rain, it appears promising to a t tempt to promote merger, as is being carried out experimentally in the FACE projects. I f merging were prevented or delayed, rainfall would be decreased. Numerical experiments underway with the University of Virginia Mesoscale Model are exploring forcing function alterations which might be produced by cirrus cover, vegetation changes, ground heat and moisture changes etc. Section 5 suggests that forcing function alterations might indeed alter merging behavior. Less obvious but also important are possible alterations of the other impacts of convective cloud systems that are altered by merging. Larger, taller clouds transport more water vapor, momentum and energy to higher levels, and also have greater impacts on the layers below cloud. Merging must be an essential process in the formation of severe convective storms, and in driving the large- scale circulations, particularly in the tropics.

3*


7.4 Recommendations

Improvements in model and remote sensing capability offer opportunity to make vast advances in understanding, predicting and even in beneficially modifying cloud merger. Remote sensing is a necessary component, since the motions in and around cumuli must be documented to understand their interaction. A flat heated peninsula like south Florida is an ideal laboratory to study cumulus growth and organization because 1) the daily forcing factor, the seabreeze, has been identified, successfully simulated and related to cloud organization 2) the mesoscale forcing ends each night and begins again next morning, so that early, less complex, more readily measurable stages of cloud interaction and merging are available for study in a limited target and 3) relatively light winds and wind shears keep the systems in a chosen study area long enough for their life cycles to be encompassed by a limited number of sensors and platforms. EXperimentation, jointly with modelling, should be pursued in Florida and in similar sea-breeze-dominated locations elsewhere, focussing attention on motion fields which can now be measured over substantial volumes as a function of time.

Acknowledgements

This research has been supported by Grants DES-75-03984, ATM-78-10087 and ATM-78-21763 from the National Science Foundation. We are deeply grateful to the directors 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 thank W. R. Cotton for valuable model information, a synoptic analysis of August 4, 1973 and 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 and criticisms 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. We are grateful for their patience and competence.

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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 Environmental 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 Mitre Corporation, McLean, VA 22101, U.S.A.

On cumulus mergers

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