1 Structural and Evolutionary Aspects of Trade Wind Cumulus Determined from Dual-polarization Radar Measurements
Charles A. Knight, L. Jay Miller, and Robert A.Rilling National Center for Atmospheric Research,* Boulder, Colorado
July 13, 2007 Submitted to: Journal of the Atmospheric Sciences
______ * The National Center for Atmospheric Research is sponsored by the National Science Foundation.
______ Corresponding author address: Dr. Charles A. Knight, National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado, 80307-3000. E-mail:
[email protected]
2
ABSTRACT
Early radar echo development in trade wind cumulus clouds is studied using the equivalent reflectivity factor, Ze, combined with the differential reflectivity, Zdr. The measures used for analysis are values calculated for entire, constant elevation angle sweeps through the clouds and entire volume scans, not maximum, single pulse volume values. The radar echo evolution follows fairly closely the Marshall-Palmer distribution with some scatter towards higher values of Zdr especially in the earliest stages of echo intensification, where some of the scatter is caused by size sorting. The data provide no evidence for an important role of ultra-giant aerosols in initiating coalescence, and are in strong contrast with similar data from northern Alabama, that do suggest a major role for UGA in producing several-mm-diameter raindrops that dominate the radar echo, though the amount of rainfall in the Alabama case was insignificant.
3 1. Introduction
a. RICO
RICO (Rain In Clouds over the Ocean) featured a two-month field campaign (Nov. 23, 2004 to Jan. 25, 2005) focused on trade wind cumulus, with emphasis on understanding their precipitation behavior and its implications at all scales (Rauber et al. 2007). The National Center for Atmospheric Research S-Pol radar was operated on Barbuda in the Northeastern Caribbean Sea so that clouds approaching from NE or E, as they nearly always do there, would be largely unaffected by land and could be considered oceanic, trade wind cumulus. The radar scanned continually to record the behavior of a large number of clouds in a consistent manner. The objective of the study reported here has been to characterize the first echo behavior of individual clouds using both the equivalent reflectivity factor (Ze) and the differential reflectivity (Zdr) at S band (3 gHz, 10 cm wavelength). The purpose has been to establish both the average behavior and the variability of precipitation initiation in trade wind cumulus from the radar viewpoint, and draw from the results whatever conclusions may be warranted.
b. Scientific background, mainly microphysical
Malkus (1962) wrote: “Rainfall in the trade stream is the least reliable of its properties. Even casual observers have noted that a skyful of trade cumuli on some days produces plentiful showers from clouds of all sizes, while on other days with apparently
4 similar cloud conditions no drop of rain appears.” This statement most likely was based upon the visual appearance of the clouds and rain shafts, and prior to RICO there had been no extensive, systematic, and detailed observations of trade wind cumulus with a sensitive radar. Thus an initial question for RICO is simply whether such a great variability in precipitation behavior could be documented using radar, and if so, if it could be related to other observables such as aspects of the aerosol or of local soundings of thermodynamic variables and wind. A specific microphysical problem that had historical significance in motivating RICO involves the length of time it takes for precipitation to initiate by coalescence of water drops: the warm rain mechanism. This has been perceived as a major problem, based upon the widely quoted observation that precipitation takes only about 20 to 30 minutes to form in small, warm cumulus, because numerical models of the liquid coalescence process did not seem to allow for it to form that fast. There is abundant room for skepticism regarding the observations, which are largely anecdotal and perhaps based more upon seeing very small cumulus that do rain quite hard than upon careful assessment of lengths of time. The best time measurements are those of Saunders (1965), a radar and visual study of cumulus near Barbados in August, the wet season. The start time was defined as the time when a cloud started to grow “from fractocumulus” and the ending time was the appearance of a radar echo of 13 to 20 dBZ. Saunders found the time period to be 25 to 35 minutes for 20 cases. It is of course open to question whether the starting time used is appropriate for comparison with the calculations, and there are also grounds for skepticism of the calculations themselves, of how much time it should take for precipitation to “initiate”,
5 regardless of how one defines the starting and ending times. But whether or not the problem of reconciling the time to precipitation with numerical models is well posed, the variability of natural precipitation formation and its causes is fundamental and deserves study. We prefer to justify the present study in these general terms. One specific effect that has concerned researchers is the extent to which ultragiant aerosol particles have an influence upon precipitation development. Ultragiant aerosols * are large enough to have appreciable collision efficiencies for coalescence _____ * It is common to assign specific size ranges to qualitative adjectives, such as “large,” in writing about aerosols. Thus large aerosols have radii of 0.1 to 1μm; “giant”, 1 to 10; and “ultragiant”, >10. These thresholds obviously do not correspond to anything physically significant. It is convenient in some contexts to have such specific thresholds, but in this paper it is inconvenient not to have a qualitative word available in the context of the “onset” of coalescence – itself a qualitative threshold. The ultragiant category was introduced in just this context (Johnson, 1976), and in this paper we continue that usage, but we do not use it to imply a specific, fixed, lower size limit. To the extent that it might be possible to set a meaningful, lower size limit for UGA in this context, that limit would depend upon updraft velocity and the collision efficiencies. _____ growth within cloud with little or no further growth by condensation being required. If present in large-enough concentrations, they would speed precipitation formation significantly. This idea fits well with Woodcock’s (1952) hypothesis of sea salt particles initiating rainfall. Importance for UGA received some support in a radar study by
6 Illingworth (1988), in which he found the early precipitation in a small, growing cumulus in northern Alabama to be composed largely of small concentrations of large drops. This is what would be expected from rapid growth on small concentrations of UGA that would grow rapidly by capturing the smaller cloud droplets, while the smaller droplets themselves grow much more slowly. The size information was deduced from the differential reflectivity, Zdr, combined with the normal radar reflectivity factor, Ze. (Zdr is the ratio between Ze with horizontally and vertically polarized beams, which gives a measure of the flattening of the rain drops and therefore an estimate of raindrop size, since the larger raindrops are the more flattened.) This radar technique was applied later to a small number of first echoes in Florida, again finding an apparently anomalous presence of large raindrops very early in the formation of warm rain (Knight et al. 2002). The objectives of the present analyses are to record the Zdr and Ze histories of trade wind cumulus to see what the data reveal about the early development of precipitation. The plan has been to analyze enough cases to enable a solid generalization about the behavior of trade wind cumulus to be made and to start assessing the variability. The results will be discussed with reference to the possible importance of UGA, and in relation to the previous, much more limited observations in Alabama and Florida, where the clouds may be assumed to have been more continental.
2. Operation of the radar
7 The objective, acquiring complete radar histories of many clouds that produce significant amounts of precipitation, placed very strong restrictions upon how the radar could be operated. Since there was no way to predict which cloud might grow and precipitate, a large volume had to be scanned continually. This mandated that the PPI mode (constant elevation angle sweeps over an azimuth sector at discrete elevation angles) be used almost exclusively, and the trade-offs in planning the scanning were the size of the sector covered, the number of elevation angles, and a combination of scanning rate and the number of pulses averaged per beam, which would determine the azimuthal resolution of the data and the accuracy of the Ze and Zdr values. The scanning routine that was adopted covered a sector of at least 180o centered approximately North but often adjusted to be about normal to the low level (trade) winds. The half-power beam width of the radar was 0.91o (Keeler et al. 2000) and ten elevation angles were planned, 0.5, 1.5, 2.5, 3.5, 4.5, 5.8, 7.5, 9.8, 12.5 and 16.5 degrees, but in practice one or more of the higher angles often were deleted and sometimes the lower angles were spaced a little closer, sacrificing complete coverage of nearby clouds for the sake of getting better time resolution. The time between volume scans was nearly always closer to 3 than 4 minutes, range gates were 150 m, fifty pulses were averaged per beam for both horizontally and vertically polarized radiation, and the beam spacing was between 0.5 and 1o in azimuth. The compromises embodied in this scanning plan appear to have been quite good for the objectives of the project, though in retrospect it might have been better to keep the elevation angle menu completely fixed over the two months. Having a truly uniform data set would have been convenient for this kind of study.
8 The radar site chosen was more than one km inland in all directions, at or perhaps slightly below sea level. The data are free of sea clutter at antenna elevation angles above 0.5o. The radar was operated continually except for servicing.
3. The clouds and their sampling
“Trade wind cumulus” for the purposes of this paper means the cumulus clouds studied in RICO, restricted only by excluding the very few cases of convection that extended substantially above the freezing level (4-5 km MSL). Rauber et al. (2007) is a source for generalities about cloud and meteorological conditions during RICO. In this paper a “trade wind cumulus” or a “cloud” refers to a radar echo feature. It was common to be able to track distinct echoes that probably correspond to visual clouds for an hour to an hour and a half, with the coverage often truncated at one or both ends by the useful radar range. Most clouds cannot be traced back to distinct and isolated “first echoes*” ______ * “First echo” in this paper will be used literally, for the first appearance of a specific radar feature being tracked backwards in time. “First precipitation echo” will mean the first echo that is judged to be definitely due to precipitation, and “early echo” means that we do not want to be that specific (since weak echoes often are ambiguous). ______ but there were many that could be, especially by being generous with “isolated”, and with 24-hour radar operation there were many more potential first echo cases than were analyzed.
9 The objective was to analyze several cases for each day of the project on which clouds occurred, and 58 of the 64 days yielded at least one case. Individual clouds were picked for analysis by selecting first appearances of distinct precipitation echoes using the second elevation angle scan (1.5 or 1.3o), and then following the cloud echo forwards and backwards as far as possible, changing elevation angles to find the best levels for tracking. Generally, higher angles are best during early stages of precipitation formation and lower angles both before that (when the cloud is small and the echo probably mostly from Bragg scattering), and later (as the cloud is dying). This can be done rather quickly using the SOLO II program (Oye et al. 1995) with its ability to run the PPIs forward and backward in time at fixed elevation angles. Selection or rejection for analysis was based upon the observations made during this process. The clouds chosen were ones with maximum Ze usually over 35 and often over 45dBZ, with their growing phase in favorable radar range (roughly 15 to 40 km), and usually with relatively isolated first echoes, always with relatively isolated first precipitation echoes. Isolation is a matter of degree, of course, and the bias toward isolation was purposely relaxed as the analysis progressed, especially on days with many suitable clouds, to examine whether the degree of isolation made any noticeable, systematic difference. No obvious differences were seen, though a more detailed and formal examination of this would be required for a firm conclusion. The main result for this paper will be the overall combination of all of the suitable cases. (In doing a lengthy analysis of this kind it was found that many cases invited very close scrutiny, a case study approach. Aside from the fact that there is never enough data
10 for a good case study, the temptation to go into more detail had to be suppressed for the sake of getting enough cases in a reasonable time.) At first in the analysis, Zdr was purposely ignored in the selection process. Later, as the Zdr behavior proved not to be extremely variable, if there was any bias it was toward including any case that seemed unusual. Variability was hoped for, since variations provide more information to work with in figuring out what is important. While the emphasis in the analysis is on the growing phase of the cumulus (that is, intensifying Ze, starting at the first precipitation echo), clouds were studied, when possible, over essentially their complete life-cycles. This was not possible when they came too close to the radar to be scanned adequately, or when they grew into much bigger convective complexes with multiple updrafts, but all cases include the first precipitation echo and its intensification. It needs to be emphasized that trade wind cumulus present as much variety and complexity in their organizations as do mid-latitude thunderstorms. The frequent impossibility of distinguishing and tracking individual convective cells in thunderstorms has its counterpart except at a smaller scale in many of the actively-precipitating trade wind cumulus. In several cases of what one might call small convective complexes, the analysis was performed on individual cells that could be distinguished as well as on the complex as a whole, treated as a single “cloud.” The whole-complex view provides only one growing event, whereas the individual cells provide several, sometimes very similar to each other and sometimes different. When both analyses were performed, only the individual cells are included in the overall results.
11 We emphasize that the data used here represent a very small subset of trade wind cumulus clouds, highly selected to represent growing stages of the clouds that have distinct histories (“relatively isolated”) starting at least as low as 0dBZ and growing to produce significant precipitation. Most of the actual precipitation in RICO was on a few days with widespread, complicated convection (Rauber et al. 2007) that offered few clouds that could be selected for this analysis.
4. Treatment of the radar data
a. Measures of Ze and Zdr
Comparing the development of reflectivity and Zdr in a cumulus cloud poses difficulties. Both are functions of space as well as time and the spatial correlation between them can be poor, especially in the early stages of echo intensification. Figure 1 shows examples of both good and poor spatial correlation. Poor correlation is common in the RICO data, undoubtedly because the big drops fall a lot faster than the small ones. Time histories of Ze in cumulus clouds generally have used maximum values, presumably to reflect storm intensity. Here, however, we are interested in combining Ze and Zdr to produce information about drop size distributions, so it is obvious that we need to have them refer to the same volume of cloud. Figure 1 illustrates how misleading that could be, when the pulse volume with the maximum value of Ze has a very low value of Zdr, while much higher values of Zdr are found elsewhere in the same scan. Our interest is to reveal characteristics of how clouds produce precipitation, and we do not want size
12 sorting dominating the results unless it influences the overall precipitation from the cloud, so we estimate the overall precipitation directly. Thus the analysis here is designed to estimate values of Ze and Zdr that are characteristic of levels within a cloud and of entire clouds. In fact, the calculated values are what one would get if single radar pulse volumes were fitted in space to whole sweeps or to whole clouds (Knight et al. 2005). These might be thought of roughly as averages: of Ze, transmitted and received horizontally polarized, averaged over either sweeps through cloud or entire cloud volumes and then expressed in dB; and the “average” Zdr is the ratio of the average horizontal Ze to its average vertically polarized equivalent, the ratio likewise expressed in dB. The area and volume values for the RICO data were calculated from all the recorded values of Ze (which is always horizontal polarization unless otherwise specified) and Zdr for each cloud. Equations for these quantities, AZe and AZdr for total sweep, or areal values, and VZe and VZdr for cloud volume averages, follow.
AZe or VZe = 10 log10 (∑ Ze)
1)
AZdr or VZdr = 10 log10 (∑ ZeH/∑ZeV),
2)
and
where the values on the left sides of the equations are expressed in dBZ, while those on the right are in mm6m-3, and Ze = ZeH is the equivalent reflectivity factor using horizontally polarized radiation. The summations are over all the pulse-volume values in
13 entire sweeps through a cloud or over entire volume scans. Subscript V refers to vertical polarization in the last term in Eq. 2 and in the Appendix, but everywhere else in this paper V refers to cloud volume. Calculating the cloud volume quantities requires weighting factors to be applied to the sweep (A) quantities in order to compensate for varying distances between sweeps. The 0.5o elevation angle scan is not used here, so the calculated volumes start at 1o height from the radar. For the purposes of the calculation, the elevation angles are low enough that considering the sweeps as horizontal through the reflectivity-weighted center of the cloud echo of each sweep is a good approximation. Since Ze and Zdr are recorded as logarithms, obtaining the A and V values requires recalculating the recorded data back to linear Ze, both horizontal and vertical; averaging, and then calculating forward again. This mode of analysis is required by the meteorological objectives, but it has the important added benefit of making the numbers reliable enough to be useful. Figure 2 is a scatter diagram of Ze vs. Zdr for all 377 pulse volumes of a single sweep at 1.2km height through a cloud at 20km range producing light rain. The “average” values of Zdr (in the same sense that AZdr is the “average” for all Zdr values in a sweep, given by eq. 2), grouped in 2dBZ intervals, are given by the heavy dots, and do not deviate significantly from zero except above about 26dBZ. The point here is to note the scatter of the individual points in samples that collectively do not depart significantly from zero Zdr. Since the individual pulse-volume values below zero cannot be meteorologically significant they must be noise of some kind. When they average consistently to zero, we must also ascribe the positive ones to noise. Thus using maximum pulse-volume values seriously overestimates the true maximum, just as the use of minimum values would
14 underestimate the true minimum, which is zero. Note that the numeral 3 (the data are from the third elevation angle of the volume scan) represents the point (AZe, AZdr) for the entire sweep, and AZdr is significantly positive. Its placement illustrates the dominance of the higher dBZ values in the “average,” due to the logarithmic scale.
b. Data thresholding
The sensitivity of the radar at close ranges extends below -20dBZ, which presents a problem because values below about 5dBZ are ambiguous due to Bragg scattering. These ambiguities are discussed in detail in Knight and Miller (1998). Thus in order to simplify the analysis a Ze threshold is applied, below which both Ze and Zdr are deleted. This is done using SOLO II (Oye et al. 1995) before drawing a boundary around the cloud echo, after which all data outside the boundary are deleted. Then lists of Ze, Zdr, azimuth and range for each sweep through the designated cloud are produced and programs operate on the lists to produce the reduced data. The -1dBZ threshold was established early, rather arbitrarily, and was retained because the reduced data were found to be very insensitive to it. Higher thresholds could be set in the program, and concern about possible importance of contamination by Bragg scattering led to tests comparing thresholds of -1 and 10dBZ, since the higher value eliminates any contributions from Bragg scattering. (No Ze values approaching 10dBZ were ever seen in the mantel echoes observed in RICO. Mantel echoes contain the most intense Bragg scattering.) Comparison of the V and A values of Ze and Zdr between data thresholded at -1 and at 10 dBZ revealed almost no difference at all: hundredths of a dB
15 in Zdr at most, and less than one or two dBZ in Ze. The lack of sensitivity seemed quite surprising at first, but it is due to the dominance of the higher values of Ze and the logarithmic scale. Data at very low values of Ze are still valuable in providing information on cloud age, however, and in fact some clouds can be tracked back in time for tens of minutes with echo completely below the -1dBZ threshold.
c. Further editing The other editing job after deleting all data outside a cloud of interest was deleting bird echoes. The frigate birds from the nesting colony on Barbuda provided many strong echoes, mostly in the 0.5o scans, especially in roll circulations to the North of the island. In daylight hours the birds commonly soared within cumulus, sometimes up to cloud top. If retained, they would dominate the A and V values in some cases in the early phases, but usually their Zdr and/or radial velocity was so anomalous that their identification was certain. They were edited out pixel by pixel, and the 0.5o scans were routinely excluded from the analysis both for this reason and because they were not needed in the context of early precipitation formation. In a few cases editing the birds within cloud echo could have a small influence because the process necessarily deletes some cloud echo, but this is insignificant for the present study.
5. Analysis products: discussion of an example
Computer programs produced many different graphs and scatter diagrams. Several of these products are presented here as the basis for discussion of the data, from a
16 single case selected to represent as many significant aspects of the data as possible. The nature of the variability is also significant, and will be discussed and illustrated in the following section. The basic, complete radar data for each case are in the form of timeheight diagrams and these are greatly reduced into scatter diagrams for much of the overall discussion.
a. Time-height diagrams
Six time-height diagrams are produced for each case. Figure 3 shows three: a) AZe, b) AZdr, and c) number of data points for each sweep, along with listings of the volume data. The three others, not shown, are maximum Ze and Zdr values and sweep area. In Fig. 3c, when the number of pulse volumes -- independent data points -- is less than, say, 5, we feel quite free to disregard values of AZe and AZdr when they seem anomalous, but the data are not deleted because they do indicate that the cloud echo exists on radar at that time and height. (The existence of cloud in this and other cases does not rely upon just a few points. There are usually many more, but below the -1dBZ threshold.) Between about 5 and 20 data points we take the values seriously and if one seems unreasonable its PPI is examined critically to see if there is any evidence suggesting that it should be deleted or altered. This very seldom happens, but occasionally a bird echo had been overlooked. With more than about 20 we consider them to be well established, with Ze probably correct within 1 or 2 dBZ and Zdr within 0.1 dB. A common exception to this rule is at echo top, where the values of Zdr are often
17 consistently negative. Presumably this is because the H and V antenna patterns are slightly mismatched. (Beam mismatch had been minimized, but it cannot be eliminated entirely; it is most evident when there are strong reflectivity gradients across the beam, and that occurs most often and most systematically at cloud top.) The AZdr value (-0.8) in Fig. 3b at 40min., 3.3km is an example and the data at 58min, 3.4km in Fig. 3 are missing because a 360o low-level surveillance scan was inserted in place of the top PPI of that volume. The present analysis concentrates on AZe and AZdr, shown in Fig. 3a and b and especially their cloud volume counterparts listed across the tops of the diagrams. The case chosen for Figs.3 and 5, 050106_e, is a cloud that is larger than average for the RICO sample but well below the largest. The higher values of both AZe and AZdr are among the highest of the entire sample. The lifetime of this case, a little more than one hour, was not unusually long for the analyzed population, which contained examples from less than 30 minutes to two hours, but it is perhaps surprisingly long for most people’s prior expectations of trade wind cumulus. The steadiness of its mature phase is remarkable but not unusual: for roughly 30 minutes, from 0540 to 0610, there was not a lot of change in AZe or AZdr, either with time or with height up to about 2km MSL. Clouds maintaining a fairly constant level of intensity for up to about 30 minutes were not uncommon in the sample analyzed, although one would not call most of them single cells. This particular case was unusual in the sample in its small time between first breaching the -1dBZ threshold and attaining AZe of 20dBZ and greater. Many of the
18 cases have much longer “gestation periods,” some being trackable for nearly an hour with AZe below 10dBZ before suddenly intensifying. The cloud of Fig. 3 passed about 30 km north of the radar traveling E to W at 9.5 ms-1, a nearly ideal location for a cloud this size, providing little change in the elevation of each sweep. The elevation angles in this case were 1.3, 2.0, 2.8, 3.5, 4.3, 5.0, and 6.0o. The 6.0o angle, was barely high enough to be adequate for this cloud. In general the coverage is considered adequate only if the values of AZe in all the highest-elevation scans were lower than those of the next highest. This case does not quite conform to that rule for every volume, but the period of nonconformity is brief and it does not appear to be serious. Note the effect of the dB scale here once again. Leaving out the entire top two sweeps through a cloud that is actively precipitating has a negligible effect upon the values of VZe and VZdr, which are the main results of the analysis.
b. Scatter diagrams
Scatter diagrams are the final stage in reducing the data to a more easily digestible form. Figure 4 contains scatter diagrams of VZe against maxZe, the maximum pulsevolume values, not A values of Ze within each volume, and the same for VZdr, drawing from the case in Fig. 3 but including all the rest of the analyzed cases as well. Figure 4a shows a consistent correlation between VZe and maxZe; from 1:1 close to the threshold (necessarily), to the maximum value being about 10dB higher when VZe = 5dBZ and then gradually increasing to nearly 20dB higher at VZe = 35dBZ. A reasonably good estimate of maxZe is directly available from VZe. In contrast, there is no useful
19 correlation between VZdr and maxZdr (Fig. 4b). This provides further justification for not using the maximum values, although further justification is not needed. Figure 4 plotted with A instead of V values shows the same scatter. Figure 5 contains the kind of information that has been the main objective from the start (that is, getting this kind of result for many clouds): Zdr plotted against Ze, using whole-cloud values in a) and sweep values in b). Plots of this kind contain potentially useful information about the onset of precipitation, and provide strong constraints on the development of raindrop size distributions. Figure 5a includes the 21 volume scans of the example case, numbered in order. With the volume scans about 3 minutes apart, this represents the time history of the precipitation development in the entire cloud. The negative Zdr values for points 1 and 2 can be discounted, so the first five points are not significantly different from 0dB Zdr. Point #6 has a VZdr of 0.5dB with about VZe 23dBZ, a big jump from the previous volume scan with 8dBZ. The large jumps in dBZ between points 5 and 6 and 7 are typical especially of the clouds that attain high VZe values: rapid echo intensification and Zdr increase, which leaves the value of VZe at which VZdr first departs significantly from 0 quite uncertain. Here it must be above 8 but could be as high as about 20dBZ. Two reference curves are included in Fig. 5 and will be included in later figures of the same type. The curve to the left is a representation of Zdr for each Ze value of a Marshall-Palmer distribution, calculated as described in the Appendix. The one to the right is the curve that would result from one raindrop per m3, of the size that produces the corresponding Ze. This is meant to approximate an extremely bi-modal distribution for which the smaller mode contributes negligibly to Ze and the larger mode is sparse
20 raindrops. In the extreme this is the kind of distribution that one might expect if all of the drop coalescence involved one per m3 of ultragiant aerosols sweeping out small cloud droplets. These curves serve the purpose of giving the eye a reference for comparing figures, and the M-P curve, to the left, can be viewed as approximating average rainfall (as in Illingworth, 1988). We do not see any reason to expect initial rainfall from small cumulus to have similar size distributions to average rainfall, but it will be seen that it represents fairly well an upper limit of the data, and in fact a significant amount of the whole data set. Most of the data points in Fig. 5b, the A values of Ze vs. Zdr, are close to the V values in Fig. 5a, but there are some outliers. S1 through S5 are the lowest two points in the volume scan starting at 41 minutes and the lowest three points in the one starting at about 38 minutes. (The decimal represents the data location and the lowest scan is the start.) These are obviously size sorting – the largest drops falling out first, partially separated from the smaller drops (Figs. 3a, b). N1 and N2 are the -0.3 and -0.4dB values of AZdr near 30 minutes, 0.8 km and 25 minutes, 1.2 km, and are not meaningful. T1 – T3 are the three points at cloud top between 40 and 50 minutes that have negative values of AZdr presumably from beam mismatch. The contrasts between Figs. 5a and b are common in the data: the early fallout of big drops often is found on the A plots of Ze vs Zdr is significant, but these early big drops are only occasionally apparent in VZe. This will be important in the discussion, below. The most extreme example of this in the data set happens to be chronologically the very last case, and is shown in Fig. 6a. Here the portion of the curve representing intensifying cloud echo lies as much as 10dBZ below the decaying portion, producing a hysteresis-like pattern. It is not uncommon to see a
21 barely detectable trace of this hysteresis in the plots of VZe vs. VZdr, but obvious examples constitute only a small handful of the total sample of 171 cases. It was noted above that case 050106_e (Figs. 3 and 5) started unusually quickly. Figure 6 represents a case that started unusually slowly, with 18 volume scans, about 40 minutes preceding the rapid intensification. The average case lies somewhere not far from the middle, in between these two. While the weak radar echo being tracked for these long periods is always distinct, there can be little doubt that it never represents a single, continuous updraft. It must result usually from a moving source of updraft or, more likely, a successive regeneration of updraft pulses.
6. Extremes of cloud variability
Case 050106_e, shown in Figs. 3 and 5, contrasted with the case in Fig. 6 illustrate the range “cloud lifetimes” before significant precipitation formation -- with a start time defined by the -1dBZ threshold -- and of the “hysteresis” in VZe vs. VZdr. (Cloud lifetime is qualified by quotes to emphasize that it is based upon radar tracking, and its physical meaning is ambiguous to a degree that might not be evident to some readers.) Presentation of a few examples does not do justice to the variability of trade wind cumulus in general, or to that within the exceptionally precipitation-rich sample selected for analysis here. However, one more example illustrates the extreme of variability in the co-development of reflectivity and Zdr in the earliest accessible stages of precipitation formation. The two cases in Fig. 7, from different times on the same day, are quite
22 different from each other in that the VZdr in the case in panels a) and b) departs from zero at an exceptionally low value of VZe, whereas in the case in the last two panels, VZdr is much lower throughout the range from 5 to 25dBZ. This illustrates rather well the range of variability in the early-echo trends of VZdr vs. VZe in this data set.
7. Results from all cases combined
The data comprise 171 analyzed cases with 2709 volume scans and 12098 sweeps. All cases have complete initiation stages starting from the first echo exceeding -1dBZ, but termination of a case is never at the complete disappearance of the echo. The analysis often was terminated when there was obviously nothing but weak fallout remaining with essentially no dynamic support, as in the 050106_e case, Figs. 3 and 5. A substantial number of cases were terminated earlier than that because of approaching too close to the radar. Thus the data set as a whole is weighted rather heavily toward growing stages at the expense of the dying stages. The mature stage often lasted a surprisingly long time with relatively constant values of VZe and VZdr, as seen for example in Fig. 3; and the clouds themselves often lasted a surprisingly long time. Usually the increase in VZe from roughly 5 to 20 dBZ was rapid, and in this respect the case in Figs. 7a and b is about the slowest in the whole sample. Figures 8a and b are scatter plots of both the V and the A values of dBZ vs. Zdr for all the data. In Fig. 8b, any A values with Zdr below -0.2dB or with fewer than ten individual data points have been excluded, and only every fifth point has been included, resulting in 2,419 points to compare with the 2709 in Fig. 8a. This assures that any
23 appearance of greater scatter in Fig. 8b compared with Fig. 8a is not just caused by the number of points. (The overall selection is essentially random, since in the complete data list the first volume scan of each cloud except the very first one comes at irregular intervals.) Comparing the V and A diagrams, a) and b) of Fig. 8, it is evident that the scatter toward higher Zdr values is greater in the A diagrams. This is consistent with the discussion relating to Fig. 5 in Section 5.b, ascribing this tendency to earlier fallout of larger drops, but with little evidence that the larger drops dominate VZe and VZdr from the whole cloud. (Recall that VZe and VZdr are the values one would get from a single radar measurement if the pulse volume fit the entire cloud – here, the entire cloud above 1o elevation and above -1dBZ.) Figure 9 reveals the height dependence of the scatter in Fig. 8b. The much greater scatter in Fig. 9a (below 2km) than in Fig. 9b (2km and above) is probably due in large part to size sorting. A lot of the points in Fig. 8 are close to the Marshall-Palmer, “average rainfall” distribution, though many of them fall outside the rainfall rate range for which that distribution is justified (Marshall and Palmer, 1948).
8. Conclusions from RICO alone
Section 1.b started with a quote claiming great variability in the precipitation behavior of trade wind cumulus. That was kept in mind during the field program, but in spite of watching for evidence of this variability the qualitative impression gained from the two months of observations was just the opposite. Bigger or deeper clouds appeared to have bigger, denser-looking rain shafts and larger and more intense radar echo. (There
24 undoubtedly would be a correlation between radar echo strength and cloud depth, but it would be revealed by a different kind of analysis from that used here. The radar data do not define cloud top heights well for individual clouds.) No anomalous differences between different days were evident. No attempt to quantify this impression has been made, and we can only counter the original, also-qualitative impression with the contrary one, and wonder why they are so different. The main result of the present study is the overall scatter diagram of Figure 8 a), the relation between VZe and VZdr for clouds throughout their whole cycles, though the sampling is biased toward the intensifying at the expense of the weakening stages. The clouds do not show much variability with respect to VZe vs. VZdr. The discussion of case 050106_e (Figs. 3 and 5) indicates that some of the scatter toward higher values of Zdr can be caused by size sorting, the earlier fallout of bigger drops as clouds develop. In surveying the overall results there is little suggestion of significant variation on time scales of one or a few days: the kind of variation that would be needed in order to find a correlation with the aerosol population or with an aspect of the local sounding. That is not to say that there definitely is no such variation, but that more cases more closely spaced in time and a statistical treatment would be needed to demonstrate one. A problem in attempting that would be that it requires determining a numerical response variable, and the limited temporal and spatial resolution of the radar data would limit the precision with which this could be done. Thus we are not optimistic about finding any significant correlations involving the early development of the drop size distributions (as indicated by the V or A values of Ze and Zdr), and have not attempted to do so. However, the overall result in Fig. 8 a) appears to be solid for trade wind cumulus in
25 general. The next section shows that it can be useful for comparison with similar data on clouds in other regions. It can be concluded that the results do not provide evidence for UGA being important in the precipitation process of trade wind cumulus. They appear to be generally unimportant either for determining the early values of Ze or in influencing total amounts of rainfall. If there were a great reluctance for precipitation to form by coalescence in trade wind cumulus, only overcome by the presence of UGA, then in the extreme one might find that some clouds produce only small concentrations of large drops and no other rainfall; or, early, large drops might be followed after some time interval by smaller-drop rainfall (lower Zdr). The results both from Alabama (Illingworth, 1988) and Florida (Knight et al. 2002) provided some support for this; but the results from trade wind cumulus do not. This is not to say that they contradict any role for the larger end of the aerosol size spectrum, but that they indicate a “not very important” role. The only way of quantifying what “not very important” really means would have to be via numerical models, not direct interpretation of field data alone. During the RICO field campaign it was obvious both at the radar and visually that trade wind cumulus clouds and their precipitation are very different from the previous clouds investigated, either in Florida in PRECIP 98 (Knight et al. 2002) and in SCMS (Knight and Miller, 1998) or in northern Alabama (Illingworth, 1988). That is the topic of the next section.
9. Comparison with previous data and conclusions
26 Superficial comparison of the RICO results represented in Fig. 8a with data from a small, warm cumulus in Alabama in Fig. 1 of Illingworth (1988) shows a truly spectacular difference. The latter has data points as far out as (Ze, Zdr) = (9dBZ, 2.6dB) and (25dBZ, 5dB), far from any points on Fig. 8a or 8b, from trade wind cumulus. However, the mode of analysis is very different. In order to compare the RICO data with the two other studies that offer worthwhile comparisons, Illingworth (1988) and Knight et al. (2002), the data have to be treated similarly, and since the latter used RHI scanning exclusively and the former used both RHIs and PPIs, the RHI data had to be separated into 500m height intervals for the analysis. Starting with the original radar data, this has been applied to the case of Fig. 1 in Illingworth (1988) and the cases of Figs. 5 and 7 of Knight et al. (2002). Illingworth’s case using the RICO style of analysis is shown in Fig. 10, with timeheight diagrams of AZe and AZdr in Figs. 10a and b, and scatter plots for the V and A values of Ze vs. Zdr in Figs. 10c and d. The numbers of independent data points in the 14 volumes range from 450 to 4000. The differences with the RICO data are perhaps even more spectacular when they are plotted alike, because AZe never exceeds 12dBZ, while AZdr reaches above 3dB and VZdr above 1.5 dB. Nothing anywhere near this was ever seen in RICO (and this is from many more than the 171 cases used here, because either at the radar in the field or going through the data later, this kind of Ze/Zdr response would have been immediately obvious). It is worth noting that while the Alabama case does support a role for UGA influencing the early radar echo development in small cumulus over land, it provides no evidence of their being important for rainfall in significant amounts because the cloud produced virtually no rainfall.
27 Figure 10 (and 12, below) uses data thresholded at -1dBZ as in the RICO cases, but especially in Fig. 10 the Bragg scattering could be more significant. This is largely because the A and V values of dBZ are very low, but also because the Bragg echo can be more intense than in the maritime clouds. The air mixing with the cloud is likely to be drier. The Bragg echoes (mantel echoes) in continental cumulus are only rarely as strong as 10dBZ in our experience, but the possible influence of Bragg scattering deserves a more detailed examination for this case. Time-height and scatter diagrams of AZe were produced for thresholds of 0 to 18dBZ in 3dB steps, with the result that the very low echo values -- presumably largely Bragg scattering -- are seen to be more important than in RICO, but the contrast with all the RICO cases remains very strong. Figure 11 shows the VZdr vs. VZe plots for thresholds of 0, 9, and 15dBZ, illustrating the trend toward stretching out VZdr toward higher values and gradually increasing VZe as the threshold increases. In this case the spatial correlation between Ze and Zdr was very strong, or the effect would not have been this simple. Our judgment is (aided somewhat by examination of the X-band reflectivity data in the MIST case, which for several reasons does not remove very much of the ambiguity at low levels of Ze) that with the threshold at 0dBZ the ambiguity of interpretation caused by the Bragg scattering is probably quite significant quantitatively, especially above about 3 km height. However, at the 9dBZ threshold it is probably negligible considered in the context of the present analysis, and at 15dBZ there is no ambiguity at all. The two Florida cases shown in Fig.12 also had hundreds of independent measurements per volume scan. In the 980803 case, Figs. 12a and b, the three points
28 with VZe under 15dBZ and VZdr over 0.5dB are at the high-VZdr edge of the scatter in Fig. 8a and a number of the points with high values in the AZe vs. AZdr diagram are outside the scatter in the RICO data shown in Fig. 8b. Here too, the reflectivity factors are very weak compared with anything from a cloud of comparable height (the top height was 5 km in this case) in RICO. The 980805 case, Figs. 12c and d, is similar except that this cloud attained 6 km, which is well above the freezing level. Ice was probably involved in scans 5-7 but probably not in scan 4, at which time the top just reached about 5 km, and certainly not in scans 1-3. Here too some of the A values are outside the RICO scatter, and the V values for scans 3 and 4 are also somewhat outside the RICO data. This case is the earliest of two neighboring cases (cell 2 of Fig. 6 in Knight et al. 2002) and the 980803 case is the one illustrated in Fig. 5 of the same reference. The contrast between the first echo behavior of the few Alabama and Florida cases with the many cases from trade wind cumulus is certainly significant even without having an adequate sample from either Alabama or Florida, because of the very large RICO sample. While there were no aerosol measurements in the more continental areas, one might easily explain it in terms of continental vs. maritime CCN along with ultragiant aerosol. Using the standard reasoning, more continental CCN means more but smaller cloud droplets, slowing the onset of coalescence in general, but not nearly as much for collection on drops started by the UGA. The result could be just this contrast between these cases and RICO: the early echo primarily from a few big drops, giving high VZdr with low VZe. However, that may be too facile an interpretation to rely upon, because the dynamic histories of the clouds are different too, not just (presumably) the aerosol.
29 One other possible source for data to compare with RICO is the TRMM-LBA project in central Brazil in 1999. The S-Pol radar recorded Ze and Zdr, and there would have been many good cases except that the 12 minute interval between volume scans was too long. Nevertheless examination of those data provided more material reinforcing the strong contrast between the dynamic behavior of small cumulus over land and the trade wind cumulus over the ocean. The small cumulus over land are strongly diurnal, forced by solar heating (and in Florida also by a sea breeze front). They are typically more vigorous than the maritime cumulus and the ones that remain below the freezing level are typically short lived. They much more often extend well above the freezing level. The contrast with the dynamics of the maritime cumulus could hardly be greater. The trade wind cumulus are hardly diurnal at all, they commonly last longer, sometimes much longer, their updrafts are probably considerably weaker on the average, and they rarely extend above the freezing level. In the TRMM LBA data the metaphor embodied in the phrase “popcorn cumulus” seems completely appropriate, whereas it would never come to mind observing trade wind cumulus on radar. The trade wind cumulus that produce precipitation are more like miniature, traveling storm systems with various degrees and kinds of organization: not at all like the random-looking, popcorn-like, continental cumulus. (While “popcorn cumulus” may more often be applied to small, non-precipitating, fair-weather cumulus, it also is useful here in distinguishing precipitating trade wind cumulus from their counterparts over land.) Thus seeking a full understanding of the precipitation behavior of small cumulus involves the familiar quandary of sorting out the relative influences of the aerosol and the
30 cloud kinematics. It is clear that eventually better modeling and probably better observations as well will be needed for that. From the standpoint of the radar data alone, both the cloud dynamics and the aerosol effects are likely to contribute importantly to the Ze/Zdr histories of the clouds. In order to have a chance of detecting a positive Zdr value the droplets responsible for the radar echo need to have radii exceeding several hundred microns, which puts their terminal velocities at least into the 3-4 ms-1 range. Thus as a very rough estimate, updrafts larger than that may be required to produce much detectable, positive Zdr. A possible experimental approach toward evaluating the independent effect of aerosols on the precipitation behavior of trade wind cumulus could involve seeding clouds with CCN. Trade wind cumulus could be especially suitable for that, inasmuch as many cases can be depended upon over restricted areas in fairly short times. The clouds themselves are not simple, but there would be a strong potential for getting statistical significance from a seeding experiment. Finally, after this extensive a study of precipitation from trade wind cumulus clouds, one feels almost obliged to say something about the famous microphysical problem noted in the introduction, of explaining the time to the onset of precipitation in warm cumulus. RICO data include a complete visual record during daylight hours from a video camera mounted on the radar antenna as well as a systematic record of 35 mm film coverage for some portions of most days during the project. The obtaining of these data was motivated in part by the “time-to-precipitation” problem, which was also part of the overall motivation of RICO. It is planned to survey the visual data with this as well as
31 other issues in mind, but with little optimism that a meaningful time to precipitation will be accessible except perhaps in very rare instances.
Acknowledgments. S-Pol is fielded by NCAR's Earth Observing Laboratory. We are indebted to virtually the entire radar support group of NCAR, not only during the two-month field campaign, but also for the additional months of often less than-pleasantwork including the set-up and take-down phases for the radar operation. Don Ferraro was lead S-Pol project engineer, and resident supervising engineer for S-Pol operations on Barbuda; special appreciation is extended to those who provided expert technical/operational support while maintaining excellent attitudes under trying field conditions: Alan Phinney, Mike Strong, Chris Golubieski, Kyle Holden, Jonathan Emmett, and Lou Verstraete. We thank all the NCAR engineers, software engineers, and field scientists who made this radar project a success. We thank the people of Barbuda for their hospitality during our stay on their island. J. Vivekanandan provided useful advice on aspects of the Zdr analysis, and S. Lasher-Trapp made many valuable suggestions on an early version of this paper. We thank Greg Holland for extra support without which the data reduction would not have been possible, and Bonnie Slagel for help with the figures.
32 APPENDIX A Reference Curves for Zdr vs. Ze For a dual-polarization radar, the differential reflectivity Zdr is defined as Z dr = 10 log10 ( Z H / Z V ),
(A1)
where ZH (ZV) is the radar reflectivity factor at horizontal (vertical) transmit-receive linear polarizations. At radar wavelength, λ, both horizontal and vertical reflectivity factors can be obtained by a summation over all drops within a unit volume: Z H ,V =
λ4 π 5 | K |2
∑ N ( D)σ
H ,V
( D)δD ,
(A2)
Vol
where |K|2 is the dielectric constant, D is the raindrop diameter (the spherical-equivalent diameter), N(D)δD is the number of drops with diameter between D and D + δD, and σH,V(D) is the backscattering cross-section for incident radiation of horizontal or vertical polarization. For small (D 15dBZ. With increasing threshold values, the influence of Bragg scattering on VZe decreases (see text).
Fig. 12. Scatter diagrams of a) VZe vs. VZdr and b) AZe vs. AZdr for the 980803, PRECIP-98 case in Florida, showing higher AZdr values coupled with low Ze than found in RICO. Scatter diagrams of c) VZe vs. Zdr and d) AZe vs. AZdr for the 980805, PRECIP-98 case in Florida, also showing higher AZdr values coupled with low Ze than were found in RICO. In volumes 5, 6, and 7 the cloud top was at about 6 km, and ice probably was present.
41
Fig. 1. Two cases illustrating extremes of the relationship between Ze and Zdr in trade wind cumulus. The case in a) and b), PPIs of Ze and Zdr respectively, thresholded at 1dBZ, range 32 km, height 2.5 km MSL, shows the maximum of Zdr, about 3dB, at the location where Ze is about 0dBZ, while the maximum Ze is about 40dBZ. The case in c) and d), range 22 km, height about 1 km MSL, has the maxima of Zdr and Ze nearly coincident.
42
Fig. 2. Scatter diagram of Zdr vs. Ze for all 377 pulse volume values in a single sweep through a typical trade wind cumulus, 1.2 km MSL. Since Zdr cannot be negative, the scatter in Zdr up to about Ze = 20dBZ must represent measurement error. Zdr was recorded with 0.1dB resolution. The large, larger, darker points represent “averages” in the sense of Eq, 2, of Zdr, for Ze separated into 2dB intervals. The numeral 3 represents the area “average” for the entire sweep. While this Figure illustrates the error of individual Zdr values, these arise partly from errors in Ze. Reflectivity factor values from the Ka-band radar with the same beamwidth were much smoother than those at S-band, suggesting that the noise in Ze at S-band is several dBZ, compared with several tenths of a dB noise in Zdr.
43 Fig. 3. Time-height diagrams for case 050106_e: a) shows AZe (dBZ) with VZe across the top; b) shows AZdr with VZdr across the top; and c) shows the number of data points in each value, with the number of points in the V values across the top, in multiples of 100, rounded. The contours in a) and b) are handdrawn, at 10 and 30dBZ in a) and 0.5 and 1.5db in b).
44
Fig. 4. Scatter diagrams, a) VZe vs. the maximum Ze in each volume, and VZdr vs. the maximum Zdr in each volume, for all 171 cases. The scatter is nearly identical using A instead of V values.
45
Fig. 5. Scatter diagrams for case 050106_e, a) VZe vs. VZdr, and b) AZe vs. AZdr. In a) the points are numbered in time from 1 to 21, with 11 and 12 at the highest Zdr and Ze and the descending points following approximately the ascending ones. The bulk of the area-average points in b) follow the same path as the V values in A, but with outliers discussed in the text, and identified by volume scan # as well as other data, described in the text. Of the two curves, the one on the left represents the Marshall-Palmer distribution, and the one on the right the VZe vs. VZdr relation for a range of drop sizes at concentration 1 m-3 (see text and Appendix).
46
Fig. 6. Scatter diagrams similar to Fig. 5 except a different case that shows the ascending and descending points in the V diagram (a) distinctly separated. A small percentage of the cases show this tendency, none more distinctly than this one. Note the long period (points 1 to 18 bunched at about 3dBZ) before VZe started to intensify.
47
Fig. 7. Scatter diagrams for two cases at different times on the same day, like those in Figs. 5 and 6, illustrating the extent of variability of VZe vs. VZdr. The case in a) and b) shows VZdr becoming significantly positive at about 5dBZ, while that in c) and d) always has low VZdr, departing only slightly from zero.
48
Fig. 8. Scatter diagrams for all of the cases together, VZe vs. VZdr (a) and AZe vs. AZdr (b). All 2701 volume scans are included in a), but only one out of five of the 12,098 sweeps are in b), to facilitate comparison of the scatter.
49
Fig. 9. The data from Fig. 8b are stratified according to height, with Fig. 9a below and 9b at and above 2 km. Sweeps with less than 3 data points are not included, and in a, only every third sweep is included so as to get approximately equal numbers of sweeps in a and b. The greater scatter below 2 km is consistent with size sorting.
50
Fig. 10. The data from the case used for Fig. 1 of Illingworth (1988), analysed in the same way as the RICO cases: a) and b) are time-height diagrams of AZe and AZdr, with the V values across the top, and c) and d) the corresponding, V and A scatter diagrams. Note the very low Ze values coupled with high Zdr values, not seen in trade wind cumulus.
51
Fig. 11. This is the scatter diagram of Fig. 10c, with the original data thresholded at three values of Ze, 0, 9, and 15 dBZ, to explore the influence of Bragg scattering. All the points with 0dBZ threshold lie close to VZe = 5dBZ (almost identical to Fig. 10c, thresholded at -1dBZ). With the threshold at 9dBZ all the points lie between VZe = 9 and 15dBZ, and at 15dBZ volume scans 1 to 8 are no longer present and all the values are, of course, VZe > 15dBZ. With increasing threshold values, the influence of Bragg scattering on VZe decreases (see text).
52
Fig. 12. Scatter diagrams of a) VZe vs. VZdr and b) AZe vs. AZdr for the 980803, PRECIP-98 case in Florida, showing higher AZdr values coupled with low Ze than found in RICO. Scatter diagrams of c) VZe vs. Zdr and d) AZe vs. AZdr for the 980805, PRECIP-98 case in Florida, also showing higher AZdr values coupled with low Ze than were found in RICO. In volumes 5, 6, and 7 the cloud top was at about 6 km, and ice probably was present.
