Systematic Variation of Observed Radar Reflectivity Rainfall Rate Relations in the Tropics

Transcription

1 2198 JOURNAL OF APPLIED METEOROLOGY Systematic Variation of Observed Radar Reflectivity Rainfall Rate Relations in the Tropics EYAL AMITAI Joint Center for Earth Systems Technology, University of Maryland, Baltimore County, Baltimore, Maryland, and NASA Goddard Space Flight Center, Greenbelt, Maryland (Manuscript received 30 September 1999, in final form 9 March 2000) ABSTRACT The Tropical Rainfall Measuring Mission Global Validation Program provides a unique opportunity to compare radar datasets from different sites, because they are analyzed in a relatively uniform procedure. Monthly observed radar reflectivity rainfall rate (Z e R) relations for four different sites that are surrounded by tipping bucket gauge networks (Melbourne, Florida; Houston, Texas; Darwin, Australia; and Kwajalein Atoll, Republic of Marshall Islands) were derived. The radar and gauge data from all sites are controlled for quality using the same algorithms, which also include an automated procedure to filter unreliable rain gauge data upon comparison with radar data. The relations are generated by two different methods. The first method is based on using a power law Z e R with a fixed exponent of 1.4, and the second is based on matching unconditional probabilities of rain rates as measured by the gauge to radar-observed reflectivities and is known as the window probability matching method (WPMM). Both methods tune the radar observations to a network of quality-controlled gauges to adjust the total monthly rainfall to match the gauges. Separate relations are generated for convective and stratiform rain, as classified by the horizontal reflectivity structure. In the WPMM-based Z e R relations, a given Z e was matched to a much lower R in convective rainfall than in stratiform rainfall. These relations were found to be curved lines in log log space rather than a straight-line power law. The WPMM-based Z e R curves demonstrated systematic variation between the convective and stratiform rain, but the power law based Z e R curves showed no systematic trend. The systematic variation in the relations shown here contradicts previous findings in which the classification is based only on the existence or nonexistence of brightband signature. The latter indicates a higher reflectivity in stratiform rain as compared with that in convective rain, for a given rain rate. Recent studies, based on disdrometer data, suggest that during a typical event there are three principal types of rain (convective, transition, and stratiform), each characterized by a different type of Z R relation. The current study suggests that to distinguish each type, both the horizontal and the vertical reflectivity field structure should be analyzed. 1. Introduction Considerable effort has gone into the development of methods for classification of tropical precipitation (e.g., Szoke et al. 1986; Houze 1993; Rosenfeld et al. 1995a; Steiner et al. 1995; Williams et al. 1995; Atlas et al. 2000). The two major objectives of these studies are 1) to distinguish the various rain types associated with different latent heating profiles within the atmosphere and 2) to distinguish the different rainfall types associated with different observed radar reflectivity rainfall rate (Z e R) relations. These different needs may demand different classification algorithms. The latter studies, which are aimed at providing different Z e R relations to improve radar rainfall estimates, are based on disdrometer Corresponding author address: Dr. Eyal Amitai, NASA Goddard Space Flight Center, Code 912.1, Greenbelt, MD eyal@radar.gsfc.nasa.gov data (e.g., Tokay and Short 1996; Black et al. 1997; Atlas et al. 1999), on airborne particle-image probe data (Yuter and Houze 1997), and on radar data (e.g., Austin 1987; Rosenfeld et al. 1995b; Amitai 1999a), using different methods to relate reflectivities to rain rates and different methods for rain type classification. As part of the Tropical Rainfall Measuring Mission (TRMM) Ground Validation (GV) program, a rain type classification scheme based on the horizontal reflectivity structure is used. Two different schemes that relate radar reflectivities to rain rates are tested. The first method is based on using a power law Z e R relation with a fixed exponent of 1.4, and the second is based on matching unconditional probabilities of rain rates as measured by the gauge to radar-observed reflectivities. Both methods tune the radar observations to a network of qualitycontrolled (QCed) gauges to adjust the total monthly rainfall to match the gauges. This paper describes these procedures in brief, then describes the resulting rela American Meteorological Society

2 DECEMBER 2000 AMITAI 2199 tions. A distinct systematic trend in the obtained relations that is opposite to previous findings is discussed. Based on recent studies on the evolution of drop size distribution (DSD)-based Z R relations, an explanation for the discrepancies is suggested (note that Z represents the calculated reflectivity as opposed to Z e, which is the observed reflectivity). 2. The radar and rain gauge data Thirty-one months of TRMM GV data were available for this study. This dataset includes 13 months (December 1997 December 1998) of data from the Melbourne, Florida, GV site; 5 months (December 1997 April 1998) from the Kwajalein Atoll, Republic of Marshall Islands, site; 11 months (December 1997 October 1998) from the Houston, Texas, site; and 2 months (December 1997 January 1998) from the Darwin, Australia, site. The radar and gauge data from all sites were QCed and analyzed using the same algorithms. The QC of the radar data, the extraction of the radar data over the locations of rain gauges, and the merging of rain gauge and radar data in time and space was done by the TRMM GV Data Processing Group (DPG), as part of the TRMM GV operations. A description of the QC algorithm and performance can be found in Kulie et al. (1999). For each volumetric radar scan, the radar gauge merged data files that were available contain 1) 9 (arranged 3 3) 2 km by 2 km horizontal pixels centered over each gauge that include both the reflectivity value at a 1.5-km constant-altitude plan position indicator (CAPPI) and their corresponding rain type and 2) 15 values of 1-min gauge-measured rain rate taken from a time window of 15 min centered at the radar scan time. The rain type was defined using the Steiner et al. (1995) classification scheme, which was selected as the primary TRMM algorithm for generating the convective/stratiform GV site maps. The classification is based on the horizontal reflectivity field structure. In general, an echo is convective if it is either very intense (exceeds a given high threshold reflectivity) or if it forms a peak value in relation to background echo intensity. Any echo that is not convective by one of these criteria is classified as stratiform. An automated procedure to filter unreliable rain gauge data upon comparison with radar data using the merged datasets was developed by the author. The main filtering parameters (P1 P4) that are calculated for each gauge separately for a given month are as follows. R The monthly fraction of rain depth, as measured by the radar (P1), at times when the gauge measured no rain (for every minute in the 15-min time window centered at the time of the scan). This value is calculated only when all of the 3 3 reflectivity pixels exceeded a given threshold to ensure that the rain is not local and therefore should be represented by the gauge. R The monthly fraction of rain depth, as measured by the gauge (P2), at times when the radar did not observe precipitation echoes above the gauge. R The correlation coefficient between the center radar pixel and the 7-min averaged gauge-measured rain rate centered at the time of the radar scan, for all pairs during the month (P3). R Monthly normalized radar gauge rain accumulation bias (P4). The normalization is performed with respect to the overall radar gauge bias calculated from all gauges combined. The monthly parameters mentioned above represent the total accumulation derived from each of the 7-min accumulations centered at the time of the radar scan they are not aimed at representing the actual monthly values. All parameters had to be within a defined range of values in order to accept the monthly gauge data for generating the Z e R relations. The threshold/range values, for each of the four parameters listed above are: P1 0.4, P2 0.2, P3 0.15, and 0.5 P If the individual gauge fails to meet any one of these criteria, its data were removed for the entire month. Note that the overall radar gauge bias in P4 is calculated only from gauges that met each of the first three criteria. In general, almost all rejected gauges were detected by the first and also by the fourth criterion. The other two criteria rejected few gauges, most of which were already rejected by the other criteria. For example, for the Melbourne, August 1998, dataset, 15 gauges were rejected by the filtering parameters out of 77 that were available within 100 km of the radar. The criterion for P1 rejected 14 gauges, 2 of which were not rejected by any of the other three criteria; the criterion for P4 rejected 12 gauges, 1 of which was not rejected by any of the other three; however, the criteria for P2 and P3 rejected only 2 and 6 gauges, respectively, all of which were rejected also by at least one of the other two criteria. A similar pattern was found with respect to most of the other months. It is worthwhile mentioning that the radar data were also compared with the gauge data several minutes after the radar scan, because it takes several minutes for raindrops to fall 1.5 km. However, although the correlation coefficient was slightly higher for about half of the gauges and smaller for the others, the same 15 gauges for August 1998 were rejected again, with the correlation coefficient criterion rejecting the same 6 gauges. The large overlaps of rejected gauges by the different criteria increase our confidence in the algorithm. However, the evaluation of the automated quality control (AQC) algorithm was done by using a graphical display in which the time series of gauge and radar accumulations are compared. The graphical display was not intended for determining total accumulations, because the radar accumulations are computed using a nominal fixed Z R relationship. It was used for pattern matching between the radar and gauge to determine geometrical and timing errors and other gauge measurement errors.

3 2200 JOURNAL OF APPLIED METEOROLOGY Example of such a display can be found in Rosenfeld et al. (1995a, see their Fig. 5). Upon a joint effort with DPG, the algorithm is now being used in the TRMM GV operation in the process of generating reference rain maps (Marks et al. 1999). Future work will further examine and try to optimize the algorithm. 3. The Z e R relations Once a monthly QC-merged dataset was produced, other products could be generated. Figure 1a shows an example of the distribution of rain volume by rain rate measured by the gauges during the period of August 1998 for the Florida GV site. These probability density functions (PDF) were generated separately for each of the rain types using the Steiner et al. (1995) classification procedure. The PDFs were constructed according to the relative contribution made by each rain intensity to the total rain volume attributed to that rain type. The volumetric PDF(R) is defined as the sum of the rain rates for a given 1-dBR interval {dbr 10 log [R/(1 mm h 1 )]; R: mmh 1 } divided by the total sum of the rain rates. The rain rates were averaged over 7-min time windows. The cumulative distribution function for each rain type is shown in Fig. 1b. In general, the two PDFs are distinctly different. However, a large fraction (14%) of the stratiform rain was contributed by R 10 mm h 1. This fraction represents only 2.5% of the total rainfall contributed by R 10 mm h 1. However, for other months where the fraction of stratiform rain was larger, a larger fraction of the rain contributed by R 10 mm h 1 was also defined as stratiform, such as 23% for February Similar features were found for the other months and for the other locations, suggesting misclassification of some fraction of the convective rain as stratiform. This result suggests that a fraction of the convective rain has horizontal reflectivity properties similar to those of the stratiform rain. The selection of 10 mm h 1 as the maximum in stratiform rain, used in the discussion above, is based on previous studies, such as Tokay et al. (1999). Monthly Z e R relations were obtained using the window probability matching method (WPMM) of Rosenfeld et al. (1994). This method relies on matching unconditional probabilities of rain rates and radar reflectivity using rain gauge and radar data, respectively. The center pixel of the 3 3 reflectivity array centered over a given rain gauge location (taken from a 1.5-km CAP- PI) and the 7-min averaged gauge-measured rain rate centered on the time of the radar scan are taken to construct the PDFs. Then, the R and Z e having the same cumulative probability are matched. This procedure was done separately for convective and stratiform rain type using the Steiner et al. (1995) classification procedure. The selection of 7 min as the time period for averaged gauge-measured rain rate is based on a study by Zawadzki (1975) that has shown that the spatial smoothing FIG. 1. (a) Distribution of rain volume by 7-min averaged rain rate (dbr) as measured by the Melbourne, Florida, rain gauge network during Aug 1998 for stratiform and convective rain. (b) The cumulative distribution functions for the same dataset. (c) The power law based Z e R relation currently implemented in the operational algorithm and the WPMM-based Z e R. Note, dbr 10 log[r/(1 mm h 1 )] R: mmh 1.

4 DECEMBER 2000 AMITAI 2201 of the radar beam over an area of A km 2 is analogous to the smoothing of the rain gauge measurements in time T according to T 1.3A 1/2 /V, where V (km h 1 ) is the horizontal velocity of the rainfall system. With A 4km 2 and V of km h 1, then T 7 min. An adjusted power law Z e R with a fixed exponent of 1.4 was also derived for each rain type by comparing the radar gauge coincident pairs to adjust the total monthly rainfall to match the gauges. This bulk adjustment procedure modifies the linear coefficient A in Z A R 1.4 (A is the initial choice). The adjusted A is derived by multiplying the base A by a factor of ( R/ G) 1.4, where G is the gauge 7-min average rain rate centered at the time of the radar scan, and R is the radar-estimated rain rate from the pixel directly over the gauge location using A. The summation is done over all gauge radar pairs obtained during the month. The latter procedure, including the use of a fixed exponent of 1.4, is currently implemented in the TRMM GV operational algorithm (Marks et al. 1999). A fixed exponent of 1.4 with A 300 was developed for convective rainfall during the Florida Area Cumulus Experiment (Woodley et al. 1975). The Z R relation of Z 300R 1.4 is also being used as a standard operational parameter in the Next-Generation Weather Radar (NEXRAD) Weather Surveillance Radar-1988 Doppler (WSR-88D) precipitation accumulation algorithm (Fulton et al. 1998). It is emphasized that this study is not aimed at comparing the rain-rate estimates upon application of the best power law and of the WPMM-based Z e R relations nor at determining the best relations to estimate rain rate from radar measurements. The improved accuracy of radar WPMM estimates of rainfall over other techniques has been demonstrated in previous papers (e.g., Rosenfeld et al. 1994, 1995b; Crosson et al. 1996; Haddad and Rosenfeld 1997; Xin et al. 1997; Rosenfeld and Amitai 1998). The objective of this study is to investigate systematic variations in the WPMM-based Z e R relations upon rain-type classification. However, operationally, a fixed exponent of 1.4 is still widely used and therefore was selected for comparison. The Z e R relations for Melbourne, August 1998, are shown in Fig. 1c. In both methods reflectivities are taken from a 1.5-km CAPPI. Figures 2a l show the WPMMbased Z e R for each of the 12 months during The adjusted coefficient A for Z AR 1.4 is written in each legend. Figure 3 represents an example of a two-month time period for each of the four GV sites. The total rainfall amount from all gauges combined used to derive each curve is specified in the legend. This number was found to be very useful as an indication of the stability of the Z e R relation. Rosenfeld et al. (1995b) showed that a small sample size is required to achieve a stable Z e R relation (standard deviation of 15% of R for a given Z e ) about 200 mm of rainfall accumulated in all gauges combined, for each classification. The relations for Kwajalein are not stable, as is evident from the legend of Fig. 3d, because of the small sample of data that was available to generate them. Note that the WPMM-based stratiform curves are not stable at high rain rates. This dynamic range is derived from a very small sample size, probably because of misclassification of convective rain. In the figures presented here, both the stratiform and the convective curves are drawn for intensities where at least one gauge radar pair is still found for each 0.5- dbz interval. This requirement is to eliminate the unstable and thus unreliable portion of the curves at high rain rates. For example, in the stratiform rain type in Melbourne, August 1998, out of 5033 pairs that were matched to R 0 (in addition to several thousand pairs that were matched to R 0), only the 5 pairs matched to the highest intensities are not depicted. These pairs have been left only in Fig. 1c to be compared with Fig. 2h. This criterion removed a relatively large dynamic range of rain rates that was caused by the interpolation of a few matched pairs at high rain rates (usually, less than 10 pairs out of several thousands for the entire dynamic range). Site specific differences, such as radar calibration, could have an effect on Fig. 3. They probably explain differences in the Z e R relations from site to site with regard to the specific rain-rate value that corresponds to a given reflectivity. However, the site-specific differences will likely not have a significant effect on the interpretation of Fig. 3 with regard to the existence of systematic variation between convective and stratiform Z e R. 4. Systematic variations of Z e R relations In general, in the WPMM-based Z e R relations, a given Z e is matched to a much lower R in convective than in stratiform rainfall. This trend was observed in all datasets that were analyzed. These relations were found to be curved lines in log log space rather than a straight-line power law. The WPMM-based Z e R curves demonstrated systematic variation between the convective and stratiform rain, but the power law based Z e R curves showed no systematic trend (see the A values in Figs. 2 and 3). It is envisaged that over large time space domains both methods will result in similar rainfall estimates, because both methods tune the radar observations to a network of QCed gauges on a monthly basis. However, when the rain intensities or the rain depth over a small space time domain is of concern, the application of the power law based Z e R will yield systematic estimation errors that will not balance out. For a consistency check, the pre-aqc merged datasets were tested. Here also the same systematic trends were found. However, for several monthly datasets, the AQC algorithm filtered out data from more than half of the gauges and changed the Z e R relations (both power law and WPMM) in such a way that the total rainfall amounts have changed significantly (up to 20% 30%). Having a radar gauge QC algorithm that will detect only reliable data should be a major concern when the radar

5 2202 JOURNAL OF APPLIED METEOROLOGY FIG. 2. Monthly WPMM-based Z e R relations for convective and stratiform rain as classified by the horizontal reflectivity structure. The relations are for the Melbourne GV site, for each of the months during 1998, as derived by radar and gauge data up to 100 km from the radar. The total rainfall amount from all gauges combined used to derived each curve is specified in the legend. Also specified is the adjusted coefficient A for Z AR 1.4. estimates are based on Z e R relations that are tuned to a local rain gauge network (Steiner et al. 1999). The total rainfall estimates over a large space time domain may be more affected by changes in the Z e R relations resulting from the use of a QC algorithm rather than from the particular method being used to relate R to Z e (i.e., power law or WPMM). Another classification scheme that is also based on the horizontal reflectivity field structure was tested. The data were classified according to the horizontal reflec-

6 DECEMBER 2000 AMITAI 2203 FIG. 3. WPMM-based Z e R relations classified by rain type for each of the four primary TRMM GV sites during Dec 1997 Jan 1998 for radar and gauge data up to 100 km from the radar. The total rainfall amount from all gauges combined used to derive each curve is specified in the legend. Also specified is the adjusted coefficient A for Z AR 1.4. tivity gradients within the 3 3 array at the 1.5-km CAPPI level. The Z e R relations as classified into strong and weak reflectivity gradient categories, for the Florida site, are shown in Amitai (1999b). The relations for strong and weak gradients are found to have similar properties, with some variation, to those of the convective and stratiform based on the Steiner et al. (1995) scheme, respectively. This result is perhaps not surprising, because convective rain, in general, is characterized by horizontal reflectivity gradients that are larger than those of stratiform rain (e.g., Zawadzki 1973; Rosenfeld et al. 1992, 1995a see their Table 2 and Fig. 16; Klazura et al. 1999). The Steiner et al. (1995) classification scheme used in this study is also based on this property of convective rain, that is, the relatively inhomogeneous horizontal reflectivity structure. Although several studies have presented analyses that showed horizontally inhomogeneous reflectivity structure within stratiform regions, such as the existence of fallstreaks with continuous brightband features in Tropical Ocean and Global Atmosphere Coupled Ocean Atmosphere Response Experiment (TOGA COARE) data (Yuter and Houze 1997), the fallstreaks usually did not reach the surface. Thus, when analyzing data from the lower CAPPI using these classification schemes, one probably will classify such radar data as stratiform. Nevertheless, other studies reported that when a brightband signature was present, large horizontal reflectivity gradients were rarely observed (Rosenfeld et al. 1995a see their Fig. 12; Amitai 1999a refer to Table 1). 5. Discussion The systematic variation in the Z e R relations shown in this study is in agreement with various previous studies such as the relations usually recommended for convective storms (Jones 1956), as opposed to the Marshall and Palmer (1948) relation widely used for stratiform

7 2204 JOURNAL OF APPLIED METEOROLOGY rain. It is also in agreement with recent studies based on DSD properties [refer to Fig. 3 in Salles et al. (1999)] and based on comparison of NEXRAD WSR-88D estimates (Z 300R 1.4 ) to gauge measurements for high and low horizontal reflectivity gradient precipitation events (Klazura et al. 1999). In the latter study, it was found that the radar overestimates the rain for the high reflectivity gradient cases (i.e., convective), and vice versa for the low reflectivity gradient cases (stratiform). Similar findings were earlier reported by Klazura (1981) who has shown empirically that large radar overestimates were obtained in high rain-rate gradient storms. In other words, in all the above-mentioned studies, it is suggested that a given reflectivity should be related to a lower R in convective than in stratiform rainfall. It is also worth mentioning that the same systematic variation in the Z e R relations was found for reflectivities above the freezing level and surface rain rates when the rain was classified according to the horizontal reflectivity gradients at these high elevations [refer to Fig. 5 in Amitai (1999a)]. However, the systematic variation in the relations shown here contradicts previous findings based on disdrometer data (Tokay and Short 1996) and based on Z e R relations that are classified by the existence or nonexistence of a brightband signature (Rosenfeld et al. 1995b). The latter relations are presented in Figs. 4a and 4b, respectively. As in our study, the Z e R relations in Fig. 4b are based on WPMM in which the reflectivities also are taken from a 1.5-km CAPPI. Both studies (i.e., Tokay and Short 1996 and Rosenfeld et al. 1995b) indicate higher reflectivities in stratiform rain as compared with that in convective rain, for a given rain rate. Caution is therefore suggested when applying any of these relations to radar data, especially when the partition of stratiform and convective rainfall amount is of concern. The inverse trends in the relations might be related to the different classification schemes. Black et al. (1997), in their manuscript on underwater acoustical methods, showed a time-labeled scatterplot for Z versus R, based on disdrometer data from Miami, Florida, that indicated different Z R relations for the various phases of the mesoscale convective system (early convective, convective, transition, and stratiform see Fig. 4c). Remarkably, nearly identical results recently have been reported for Singapore and Papua New Guinea [refer to Fig. 4 in Wilson et al. (1999)]. The separate Z R relations for convective and stratiform FIG. 4. Previous studies on Z R relation for convective and stratiform rain. (a) Disdrometer-based Z R for Kapingamarangi Atoll during TOGA COARE [after Tokay and Short (1996)]. (b) WPMM-based Z e R curves for the Darwin area, as classified by three categories of brightband fraction (BBF). BBF 0.6 is defined as stratiform [after Rosenfeld et al. (1995b)]. (c) Disdrometer-based Z R for a case study in Miami, Florida, demonstrated by a time-labeled scatterplot over 35 min ( ) [after Black et al. (1997)].

8 DECEMBER 2000 AMITAI 2205 rainfall indicated in their study are consistent with the findings of Tokay and Short (1996). However, in the early convective phase a given rain rate is matched to a much higher reflectivity, as a result of a relatively large sample of large drops. A distinct difference in the Z R relations between the initial convective and the trailing transition regions was recently also suggested by Atlas et al. (1999). Their study, based on the behavior of the representative drop sizes (median diameter of the distribution of water content D 0 ), used the same disdrometer dataset from Kapingamarangi Atoll that was previously studied by Tokay and Short (1996). They concluded that the previously reported Z R relation for convective rain is primarily representative of the transition rain that was erroneously included in the convective class. They also used profiler data and reported no sign of a bright band during the transition phase. The conceptual model of the two-dimensional precipitation trajectories by Biggerstaff and Houze (1991; illustrated in their paper in Fig. 18) stratified the rain also into three categories of events: convective, transition, and stratiform, with a transition zone void of bright band. Those studies, based on disdrometer data, in general suggest that, during a typical event, there are three principal types of rain (convective, transition, and stratiform), each characterized by a different Z R relation. In the study described here, the classification is based solely on the horizontal reflectivity field structure without the use of any information on the existence or nonexistence of a brightband (BB) signature. Based on the current study and those previously mentioned, it is suggested that, to distinguish all three types, both the horizontal and the vertical reflectivity properties must be used to classify the rain. Whereas a classification scheme based on the horizontal structure is needed to distinguish between the initial convective regime and the other regimes, a classification scheme based on the vertical structure is needed to distinguish the stratiform rain that is marked by a bright band from the transition rain that is not. To this point, it is worth mentioning that, although several studies have clearly recognized the existence of a transition zone, only one, as far as the author is aware, subclassified the stratiform rain type as defined by the Steiner et al. (1995) scheme to transition and stratiform rain. Sempere-Torres et al. (1999) conducted a DSD analysis for different storm phases over Barcelona, Spain, following a preclassification of rainfall type from radar analysis. They stratified the rain into three categories of events convective, transition, and stratiform using both the horizontal and the vertical reflectivity structure. They defined transition rain at times when it could not be considered as convective according to the Steiner et al. (1995) scheme but also when there was not a clear brightband signature. Each phase was found to be characterized by a different DSD shape. However, no attempt to generate Z R relations for each storm phase has been made. FIG. 5. (a) WPMM-based Z e R as in Fig. 1c, but as classified by range in addition to rain type. (b) WPMM-based Z e R as in Fig. 1c (thin lines), and only for reflectivities that have been classified into the same rain type as their surrounding eight pixels (each pixel size: 2 km by 2 km, bold lines). The trend in the relations between the convective and the stratiform rain is more prominent by radar observation than by disdrometer measurement, because of beam-filling effects. These effects increase with range and with horizontal reflectivity gradient (Zawadzki 1982; Rosenfeld et al. 1992). The latter are larger in the early convective phase and decrease as the rain becomes more stratiform (Zawadzki 1973). Figure 5a demonstrates the dependence of the Z e R relations on the range. Note that the reflectivities are taken from the same CAPPI at all ranges. The dependence is clearly observed in the convective rain, for which partial beamfilling (PBF) effects are more dominant. In general, as

9 2206 JOURNAL OF APPLIED METEOROLOGY a result of this effect, low reflectivities are being overestimated by the radar and peak reflectivities are being underestimated as seen in Fig. 5a and simulated numerically by Rosenfeld et al. (1992, see their Figs. 2 and 4). Unlike WPMM, a bulk adjustment procedure with a fixed exponent will detect only the overall effect resulting in a larger A that matches a given Z e to a smaller R. The following explanation is suggested for this effect. Let Z e be the radar-observed (effective) reflectivity and Z t the true reflectivity, as would be observed with an infinitely narrow beam. Because of PBF, Z e is greater than Z t at the peripheries of reflectivity peaks. One may actually have Z e greater than 0 above nonrainy areas (i.e., where R 0, or Z t 0). As PBF errors increase (these are proportional to the distance from the radar, reflectivity gradients, and beamwidth) larger Z e s will be related to R 0. However, at reflectivity peaks, Z e is less than Z t (i.e., the true reflectivities are underestimated). Because of nonlinearity between Z and R, upon application of the same power law on both Z t and Z e fields and integrating the estimated Rs throughout the entire dynamic range of Z, the true total rain amount will be overestimated; that is, R(Z e ) is greater than R(Z t ). The latter is true for any Z AR b as long as b is greater than 1, and the reflectivity field is not 100% uniform (Rosenfeld et al. 1992). However, in our bulk adjustment procedure (or WPMM), upon classification by range from the radar (and other properties related to PBF) we are not overestimating the true rain any more. We are matching a larger A and relating a given R to a larger Z e. It is important to know that, as the PBF errors increase, an adjusted power law will relate a given Z e to a smaller R for the entire dynamic range of the intensities. However, when relating by WPMM, the weak to medium Z e s, which are overestimated, are related to a smaller R, and the very high Z e s, which are underestimated, are related to a larger R, as seen in Fig. 5a. Therefore, the shape of the desired relations depends not only on the classification scheme implemented but also on the technique being used to relate the reflectivities to rain rates (i.e., disdrometer measurements, bulk adjustment power law, or WPMM). The DSD-based Z R relations are generated from Z R pairs for which by definition both parameter values are either positive or zero, and thus any given Z greater than 0 is related to R greater than 0. The Z e R relations based on radar observations and gauge measurements are affected by PBF, gauge radar time, and geometrical matching errors, and sampling volume discrepancies, and thus are being derived from Z e s that differ from Z t. The radar gauge pairs include also Z e greater than 0 observed at times when the gauge-measured R is equal to 0 (and vice versa). For the given example of Melbourne, August 1998, the number of radar gauge pairs for which the gauge-measured R was greater than 0 was However, an additional 2775 pairs with Z greater than 20 dbz, for example, existed. In the bulk adjustment procedure, which still artificially enforces a power-law Z R relation and thus means a given reflectivity must be related to an R greater than 0, the adjustment is performed with respect to the integral rain depth and will affect the entire dynamic range of the intensities in the way described in the previous paragraph. However, in WPMM the calibration is performed with respect to rain intensities, and the matching of the radar and rain gauge accumulation is a mathematical outcome. The Z e R relations obtained by WPMM are not artificially enforced to a power law and thus are able to account for the true shape of the Z e R relations. By definition of WPMM, unlike any power law, the distribution of R, as derived from the reflectivities above the gauges, is identical to the distribution of the gauge rates, and thus relatively high reflectivities in convective rain and far from the radar may still be matched to R equal to 0. A unique PDF(Z e ) for each rain type is determined by analyzing the reflectivity field. However, the classification of the gauge data and thus the PDF(R) for each type is determined, not by analyzing the gaugemeasured rain-rate properties, but solely by the matching procedure. Sampling limitation might introduce systematic errors in the PDF(R) that affect the desired relations. The PDF(R) of the convective rain might be contaminated by stratiform rain characterized by a smaller R value, and thus a given Z e in the convective class would be underestimated, and vice versa for the stratiform rain type. To ensure that these systematic variations in the relations are not statistical artifacts, WPMM-based Z e R relations have also been generated using only the reflectivity pixels that have been classified into the same rain type as their surrounding eight pixels (each pixel size: 2 km by 2 km), as shown in Fig. 5b. The bold solid curve represents a relatively pure convective rain type, where mismatching is less likely to occur. Indeed, the trend in the relation is even more dominant here, and therefore the systematic variations in the relations are not due to statistical artifacts but rather are due to physical effects (e.g., large drops, partial beam-filling effects). 6. Summary and conclusions In this work, 31 months of gauge and radar data from four different TRMM GV sites were used to study systematic variations in the Z e R relations. The radar and gauge data from all sites were processed in a uniform procedure that also includes an automated procedure for detecting unreliable rain gauge data upon comparison with radar data. In general, a given Z e was matched to a lower R in convective rain than in stratiform rain when the rain was classified according to the horizontal structure of the radar reflectivity field. These relations, based on WPMM, were found to be curved lines in log log space rather than a straight-line power law. The WPMM-based Z e R curves demonstrated systematic variation between the convective and stratiform rain; a

10 DECEMBER 2000 AMITAI 2207 power law based Z e R relation, with a fixed exponent of 1.4 and a coefficient that was tuned to the gauge network so as to adjust the total monthly rainfall to match the gauges, had no systematic trend. It is envisaged that, over large time space domains, both methods will result in similar rainfall estimates because both methods tune the radar observations to a network of QCed gauges on a monthly basis. However, when the rain intensity or the rain depth over a small space time domain is of concern, the application of the power law based Z e R relation is expected to yield systematic estimation errors that will not balance. The systematic variation in the relations shown here contradicts previous findings in which the classification is based only on the existence or nonexistence of BB signature. The latter is indicating a higher reflectivity for a given rain rate when a melting-layer signature exists. Recent studies, based on disdrometer data, suggest that during a typical event there are three principal types of rain (convective, transition, and stratiform), each characterized by a different type of Z R relation. The systematic variation in the Z R relations found in those studies, combined with the findings based on classification by BB signature, suggests that only the third stage is associated with BB, although the transition stage may still contain high rain rates. The latter is also supported in this study by erroneously classifying a fraction of the high rain rates as stratiform. Therefore, based on this study and the studies previously mentioned, it is suggested that, in order to distinguish each type, both the horizontal and the vertical reflectivity field structures must be analyzed. These rain types and their associated radar properties are as follows. 1) Early convective: characterized by large drops, large horizontal reflectivity gradients ( H Z e ) and no BB signature, where a given Z e is related to a lower R. The latter is more prominent in radar observations than in disdrometer measurements because of strong beam-filling effects at this stage. 2) Transition: characterized by small H Z e and no BB signature, where a given Z e is related to a relatively larger R. 3) Stratiform: characterized by small H Z e and a BB signature, where a given Z e is related to a larger R than in case (1) but to a smaller R than in case 2. It is emphasized that some of the latter assumptions were drawn from combined studies based on both radar and disdrometer data, in which observed and calculated reflectivity from different altitudes were used. Deriving Z e R relations upon classification by both vertical and horizontal reflectivity field properties using the same dataset is a future goal. Also, comparison with Z R relations based on disdrometer data following a preclassification to rain type by the 3D radar reflectivity field structure, where also the stage of the storm can be detected, is planned. Acknowledgments. The author is deeply grateful to Dr. David Atlas, a Distinguished Visiting Scientist at NASA Goddard Space Flight Center (GSFC), for his advice and helpful discussion. The author also appreciates the useful comments by David B. Wolff and Brad Fisher of Science Systems and Application, Inc., at NASA GSFC and by Dr. Donald Martin of Howard University. Thanks to Mike Robinson, David Marks, and Mark Kulie of the TRMM GV Data Processing Group at NASA GSFC, led by Dr. Brad Ferrier, for processing the radar and gauge data and making them available for this study. 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