Experimental Test of the Effects of Z R Law Variations on Comparison of WSR-88D Rainfall Amounts with Surface Rain Gauge and Disdrometer Data

Transcription

1 JUNE 2001 NOTES AND CORRESPONDENCE 369 Experimental Test of the Effects of Z R Law Variations on Comparison of WSR-88D Rainfall Amounts with Surface Rain Gauge and Disdrometer Data CARLTON W. ULBRICH Department of Physics and Astronomy, Clemson University, Clemson, South Carolina NEIL E. MILLER Science Department, Lander University, Greenwood, South Carolina 26 June 2000 ABSTRACT Reflectivity factors and rainfall rates found from Level II WSR-88D data for the National Weather Service (NWS) radar in Greer, South Carolina (KGSP), are compared with similar parameters found from disdrometer data collected at the Clemson Atmospheric Research Laboratory. These comparisons are used to determine experimentally the sensitivity of rainfall amounts found from the WSR-88D data to variations in the parameters A and b of the Z R law (Z AR b ) that is used in analysis of the data. Analyses of data for nine storms in upstate South Carolina are described. These nine cases encompass a variety of rainfall types including stratiform rain, airmass thunderstorms, and strong cold front convective activity. It is found, after correction of the radar reflectivity factors for obvious calibration offset, that the rainfall depths found by radar are in good agreement with those found from the disdrometer when the NWS default values of A and b (A, b 1.4) are used. If the values of A and b found from an empirical Z R analysis of the disdrometer data are used, then, as expected, the agreement is even better. It is important to recognize that this good agreement was obtained only after adjustment of the radar-measured reflectivity factors for calibration offset. A similar analysis is also described for one other storm but with the addition of rain gauge data from locations in upstate South Carolina, which are remote from the Clemson laboratory and where there are no collocated disdrometers. The radar data are used to determine rainfall amounts for each of the rain gauge locations as well as for the Clemson laboratory. It is found that the agreement between radar-measured rainfall amounts and those found from the rain gauges is very good, even when the default values of A and b are used. Again, this agreement is obtained only after correction of the radar data for the calibration offset found from comparison of the radar reflectivity factors determined from the WSR-88D data and disdrometer data at the Clemson laboratory. When the values of A and b determined from the disdrometer data are used, the agreement is further improved. It is concluded that the commonly observed large differences between KGSP WSR-88D-measured rainfall amounts and surface rain gauge data are not due primarily to variations in Z R law parameters but are the result of hardware calibration offsets. These offsets could probably be eliminated by performing an accurate calibration of the WSR-88D with special emphasis on antenna gain. The results are also of importance to the ground validation field campaigns, which are a part of the Tropical Rainfall Measuring Mission operated by the National Aeronautics and Space Administration. Similar large differences between WSR-88D and surface measurements have been found in these field campaigns. 1. Introduction National Weather Service (NWS) Weather Surveillance Radars-1988 Doppler (WSR-88Ds) estimate rainfall amounts by employing a relationship between radar reflectivity factor Z (mm 6 m 3 ) and the rainfall rate R (mm h 1 ) of the form Z AR b. (1) Corresponding author address: Carlton W. Ulbrich, Department of Physics and Astronomy, Clemson University, Clemson, SC cwulbr@hubcap.clemson.edu The default values of the coefficient A and exponent b used by the NWS are A and b 1.4, which apply to most meterological situations (Hunter 1996). Variations in these parameters are permitted for rain from isolated thunderstorms and for tropical storms. The importance of allowing for such variations has been stressed by Atlas et al. (1999) who show that there can be dramatic changes in Z R law parameters within an individual storm as well as between storms. The latter work also shows that these changes are systematic within storm structure and are clearly identified with the physical processes acting to form rain. Even when such variations in A and b are employed, some NWS radars commonly underestimate rainfall by a factor of 2 or 2001 American Meteorological Society

2 370 WEATHER AND FORECASTING VOLUME 16 more when compared with rain gauge measurements at the surface, especially in stratiform rain (Ulbrich and Lee 1999). Similar differences have been found between WSR-88D cumulative rainfall amounts and those found using the radar, which is a part of the National Aeronautics and Space Administration s Tropical Rainfall Measuring Mission (TRMM; Datta et al. 1999). The purpose of the present work is to assess experimentally the effects of variations in A and b (and thus in the raindrop size distribution) on the accuracy with which the WSR-88D can measure rainfall and to determine the extent to which such variations can account for the large differences observed in the aforementioned experiments. This is done using radar data from the WSR- 88D at the Greer, South Carolina (KGSP), National Weather Service Forecast Office together with disdrometer data from the Clemson Atmospheric Research Laboratory at Clemson University. A comparison is also made of radar-estimated rainfall amounts with those found from rain gauges at three locations in upstate South Carolina. It is found that the radar can estimate rainfall amounts with good accuracy and that the effects of the observed variations in A and b are of minor importance compared to the error due to radar calibration offset. Methods of eliminating such offets are discusssed in Ulbrich and Lee (1999). It must be recognized that the present work does not constitute an effort to validate any exisiting Z R law or to derive a new one to be used in future analyses of WSR-88D data to measure rainfall. This work consists of an analysis of disdrometer and radar data to determine the senstivity of rainfall estimates to variations in A and b and whether such variations can explain the large differences observed between KGSP WSR-88D estimates and surface rain gauge data. 2. Experimental arrangement The location of the disdrometer used in this work is the Clemson Atmospheric Research Laboratory, which is located 60 km to the SW of the KGSP radar and is completely free of any ground clutter surrounding the radar at the lowest radar elevation scan (0.5 ). At this range from the radar the pulse volume is only a few hundred meters above the surface and is well below the freezing level for all the storms considered in this work. Measurements of raindrop size spectra were made using a standard Joss drop disdrometer. The data consist of numbers of raindrops n i of diameter D i in 20 categories ranging in size from 0.35 to 5.25 mm. Computation of the reflectivity factor and rainfall rate from these data involves the simple summations over drop size categories of the form D i i i i 1 Z 10 DN(D ) D and (2) 3 RD 0.6 (D i)din(d i) D i. (3) i 1 These quantities carry the subscript D to indicate that they were determined from disdrometer data. Here, N(D i )(m 3 mm 1 ) is the drop size distribution found from the n i using n i N(D i ), (4) (D i)a Di where (D i )(ms 1 ) is the fall speed in still air of a drop of diameter D i (cm), A (m 2 ) is the area of the disdrometer, (s) is the sampling time, and D i (cm) is the width of the ith category. It is valid to use the fall speed in still air for (D i ) in Eq. (4) since the disdrometer measurements are made at the earth s surface. In this work the sampling time 60 s. A correction was applied to the N(D i ) to account for the dead time associated with the recovery time of the disdrometer s transducer. This correction is described by the manufacturer of the instrument and is summarized by Sauvageot and Lacaux (1995). In this work it was found that there was very little difference between the Z and R values found by the two methods. The conclusions found here are therefore not affected by whether or not this correction is applied. Values of Z measured by the KGSP radar were found from Level II data stored on tape. These values were determined by displaying the lowest (0.5 ) elevation scans at highest resolution and finding the reflectivity factor corresponding to the location of the Clemson laboratory. Careful visual screening of the radar data was performed to avoid observations, which involved highreflectivity gradients near the boundaries of rain areas and other inhomogeneous regions. This was done to find rain areas that were relatively uniform over the location of the disdrometer thereby maximizing the probability that the disdrometer measurements at the surface were representative of that which was measured aloft by the radar. Values of reflectivity factor and rainfall rate determined from such analysis will be refered to henceforth as Z R and R R, the subscript R indicating that they were measured by the radar. For all the storms examined, the temperature at the surface was greater than 60 F during the entire period of observation, thus ensuring that the pulse volume was well below the freezing level. The rain gauge data used in section 4 of this work were obtained from the National Climatic Data Center and are a part of the weather observing sites administered by the National Weather Service. Only data from gauges that made hourly observations were used. 3. Comparisons using disdrometer data In this work radar data for five storms in 1997 and four in 1998 were compared with disdrometer data collected at the Clemson laboratory. A temporal record of the reflectivity factor for one of these storms is shown in Fig. 1a. The solid curve is the record of Z D and the solid circles represent Z R, that is, the reflectivity factor as measured by the radar. It is apparent that the Z R lie

3 JUNE 2001 NOTES AND CORRESPONDENCE 371 FIG. 1. (a) Reflectivity factor Z (dbz) vs time (HHMM) for a storm over the Clemson Atmospheric Research Laboratory on 23 Feb The solid curve depicts Z D as determined from disdrometer data. The solid circles represent Z R, i.e., measurements by the KGSP WSR- 88D. (b) Plot of Z R vs Z D at the same times for the storm in (a). The solid line is the locus of points for which Z R Z D. The dashed line represents a constant offset of Z R below Z D by an amount shown in Table 1 ( 5.4 db). systematically below the Z D, therefore implying that the calibration of the radar is incorrect or that the disdrometer measurements are in error. This is also shown in Fig. 1b, which is a plot of Z R versus Z D. The solid line is a 1:1 line along which all the data would lie if Z R Z D. The dashed line shows the offset of the Z R from the Z D of 5.4 db. The correlation coefficient for these data is 0.97 and the standard deviation is 0.9 db. Very similar results were obtained for all nine storms considered in this section. The average offset for all nine storms is 4.7 db. It is possible to plot all the data for all nine storms on a plot like Fig. 1b; however, a similar plot is shown in Ulbrich and Lee (1999) and is not repeated here. For some of the storms a tipping bucket rain gauge was operated about 10 m from the disdrometer, which produced results for rainfall rates and cumulative depths that were in good agreement with those found from the disdrometer data (Table 1). It is very unlikely then that the disdrometer measurements are significantly in error. In view of the obvious systematic offset of the Z R below the Z D, the effects of variations in the Z R law have been investigated in several ways. First, the total depth of rainfall was determined from the radar data using the default NWS Z R relation, Eq. (1), with A, b 1.4. This was compared with the total depth of rainfall measured by the disdrometer, which is shown in the Table 1 as H (mm). The percent deviation of the radar-measured depth from the disdrometer-measured depth is shown in the column labeled H 1. It is apparent from Table 1 that the use of the default NWS Z R relation with raw Z R data and with no adjustment for possible calibration offset produces rainfall amounts that are a factor of 2 or more too small. In the second method, the rainfall depth was determined using a Z R relation found from standard logarithmic least squares analysis of the Z D and R D disdrometer data acquired at the Clemson laboratory. The latter relation involves a coefficient and exponent A D and b D as shown in Table 1 and was found using only those disdrometer data that lie within the time intervals shown in the table for each date. As before, the radar-measured total depth of rainfall was found using this new Z R relation and the percent deviation of the radar depth from the disdrometer depth is shown in Table 1 as H 2. For all nine storms investigated there is very little or no improvement in the radar-measured rainfall depth TABLE 1. Parameters derived from disdrometer data at the Clemson laboratory and associated radar quantities found from KGSP radar data for the dates and times indicated. Here, N D and N R are the numbers of data points for the disdrometer and radar, respectively: H(mm) the total depth of rainfall measured by the disdrometer; (db) offset of radar Z values from the disdrometer values; A D,b D coefficient and exponent in Z R relation found from the disdrometer data; H 1, H 2 offsets (%) from H of rain depths determined from radar data with (A, b) (, 1.4) and (A, b) (A D,b D ), respectively; H 3, H 4 same as H 1 H 2 but with the offset applied before using the Z R law; H G difference (%) of tipping bucket rain gauge measurement from H; and not available. Date Time (LT) N D N R H A D b D H 1 H 2 H 3 H 4 H G 3 May Jul Nov Nov Dec Jan Jan Feb Feb

4 372 WEATHER AND FORECASTING VOLUME 16 relative to the disdrometer measured depth when use is made of this Z R relation appropriate to the rainfall, that is, when account is made of variation in the Z R law parameters from the default NWS values. In the third and fourth methods the average offset of the radar-measured Z R values from the disdrometer-measured values was found. This value was then used to adjust the radar values of Z R before determining the rainfall depth from the relevant Z R relation. The results found in this way using the default NWS Z R relation and the Z D R D relation for each storm are shown in Table 1as H 3 and H 4, respectively. The values for H 3 demonstrate that the default NWS Z R relation measures rainfall amounts adequately, but only after adjustment for possible calibration offset has been performed. The results shown for H 4 show that some further improvement is possible when a Z R relation is used that is known to apply to the rainfall event under observation. It should be noted that the above analyses do not involve the use of the NWS tropical Z R relation with A 250, b 1.2. It was deemed improper to consider the use of such a relation in this work since all of the storms analyzed were midlatitude in character and none was distinctly tropical in nature. 4. Comparisons using disdrometer and rain gauge data An analysis similar to that described in the previous section was performed using WSR-88D data together with disdrometer and rain gauge data collected on 7 January The principal difference between the earlier analysis and that described here is that rainfall depths were estimated using WSR-88D data over three NWS rain gauges at locations in upstate South Carolina, remote from the Clemson laboratory. These radar-estimated rainfall depths are then compared with those measured by the rain gauges. Each of the three locations used in this work lies at a range from the radar similar to that for the Clemson laboratory (but at different azimuth) thus ensuring that the radar measurements are well below the bright band. The temporal behavior of Z and R for the storm of interest was fairly smooth for the period LT. Some rain fell during an earlier period ( LT) on this day but the behavior of the integral parameters during this period was not as smooth as during the later times. The approximate uniformity of the rainfall field during the period LT was also reflected in the plan position indicator displays of the WSR-88D data. As indicated earlier, choosing a period of approximate uniformity tends to avoid problems associated with mismatch of the radar sampling volume aloft and the disdrometer and rain gauge sampling volumes at the surface. Using the Z D and R D values calculated from the disdrometer data collected at the Clemson laboratory, an empirical Z R analysis was performed for the data FIG. 2. Empirical Z R analysis of disdrometer data for a storm over the Clemson Atmospheric Research Laboratory on 7 Jan collected during LT, which yielded the values shown in Fig. 2, namely, A D, b D. Note that total depth of rain for the specified time period is large (52.7 mm) and that most of the rainfall rates were large. This behavior and the smoothness of the temporal behavior of the integral parameters referred to above tends to avoid problems associated with mismatch of the sampling volumes aloft and at the surface. Almost all of the radar Z R values during the period of interest lie below the disdrometer values and involve an average offset of the radar Z R below the disdrometer Z D of db. This value is similar to that found from analysis of the storms described in the previous section. As a result, the radar values of R R found by assuming A, b 1.4 lie systematically below the disdrometer data and yield a radar estimate of total rainfall depth of 18.8 mm, about 64% below the disdrometer value. If the Z R relation found from the disdrometer data for this day and time period (i.e., A D, b D ) is applied to the radar data, it is found that the radar-estimated rainfall depth is 20.7 mm, a difference from the disdrometer value of 61.7%. The latter result is quite similar to that found with A, b 1.4 thus indicating that use of the empirical values of A D and b D has very little effect on improving the agreement between radar and disdrometer. If the analysis is performed using the default A and b values but with the radar Z R values increased by the offset of 5.1 db, then somewhat better agreement is found between the disdrometer and radar-derived rainfall rates. The total depth of rainfall found by the radar is 43.7 mm, a difference from the disdrometer value of only 17%. Finally, if the analysis is done using the disdrometer values of A D and b D and the calibration offset is also applied, then the results show even better

5 JUNE 2001 NOTES AND CORRESPONDENCE 373 TABLE 2. Summary of disdrometer, rain gauge, and radar-deduced parameters for a rainfall event in South Carolina on 7 Jan 1998 during the time period LT. The first column lists the station name, under which is given the range and compass bearing of the station from the KGSP radar. Here, A and b are the coefficient and exponent in the empirical Z R law used in analysis of the radar data; Z is the offset of the radar Z values from those found from the disdrometer data (db); H R is the value of the rainfall depth as deduced from the radar-measured Z values using the A and b values shown on the same line; H G is the rainfall depth found from the surface instrument (disdrometer for the Clemson station, rain gauge for the other three); and H is the deviation of H R from H G in percent. Station Clemson (60 km, 246 ) Longcreek (95 km, 264 ) Jocassee (78 km, 278 ) Calhoun Falls (95 km, 201 ) Start time (LT) End time (LT) Z H G A b H R H (%) agreement with a total radar-derived depth of rainfall equal to 47.0 mm, a difference of less than 11% from the disdrometer value. Consequently, adjustment of A and b to account for their natural variations in this storm helps to improve the radar estimate but by a minor amount compared to the error due to calibration offset. The results described here are summarized in Table 2, where H R and H D are the total depths of rainfall found using the radar and disdrometer, respectively; H is the difference between H R and H D in percent; Z is the offset of the radar Z values from the disdrometer values (db); and A and b are the values used in the Z R relation in determining the radar-measured rainfall depth. Similar results are obtained when radar-measured rainfall amounts are compared with rain gauge data where no disdrometer is available at the location of the rain gauge. To illustrate this point, three rain gauges in upstate South Carolina have been used that are at locations remote from the Clemson laboratory. All of these gauges are at similar ranges (but different azimuths) from the radar and all radar measurements are well below the bright band. Each involves large and therefore useful amounts of rainfall for this storm. The locations of the gauges are at Jocassee, Longcreek, and Calhoun Falls, South Carolina, and are a part of the network of precipitation gauges supervised by the National Weather Service. Data for these stations were obtained from the National Climatic Data Center. Each of these stations has a gauge that records hourly amounts of precipitation and they are the only gauges in upstate South Carolina within range of the KGSP radar, which made such measurements for this storm. The comparisons of rain gauge amounts with radarmeasured amounts are similar for all three stations. The results for one of the stations (Longcreek) is shown in Fig. 3. The solid line connects hourly measurements made by the rain gauge. The solid circles represent the rainfall amounts determined from the radar data using the Z R method described earlier and with A, b 1.4. The radar Z R values used in this method have been offset or corrected by the radar calibration offset Z db as determined from the disdrometer data acquired at the Clemson laboratory. The agreement between the rainfall amounts determined by the two methods is very good. The radar-estimated cumulative depth of rainfall, as shown in Table 2, differs from the gauge amount by only about 23%. If the values of A D and b D found from analysis of the disdrometer data collected at the Clemson laboratory are used in the analysis, then the difference between radar and rain gauge estimates is only 16%. Similar behavior is found for the other two locations shown in Table 2. It is interesting to note that the agreement between rain gauge and radar amounts for the Calhoun Falls station is better when the default values of A and b 1.4 are used rather than the values determined from the disdrometer data. In summary, this analysis has shown that the KGSP WSR-88D has the potential to measure rainfall amounts with good accuracy. The highest accuracy is obtained by allowing for adjustment of the coefficient A and exponent b in the Z R law for the type of rain being observed. It has demonstrated, however, that in order to achieve this level of accuracy it is necessary to account for any calibration offsets in the radar data that may exist and these have been shown to be the major contributor to the difference between radar and surface measurements. Ulbrich and Lee (1999) discuss methods by which such calibration offsets can be eliminated. The

6 374 WEATHER AND FORECASTING VOLUME 16 FIG. 3. (top) Rainfall depth H vs time at a rain gauge site in upstate SC for a storm on 7 Jan The solid curve represents the depth as measured by a rain gauge administered by NOAA and the solid circles are the cumulative rainfall depth as measured by the KGSP WSR-88D. Here, A, b are the parameters of the Z R law used to determined rainfall rates from the WSR- 88D data; H G and H R are the rainfall depths found from the rain gauge data and from analysis of the radar data, respectively. (bottom) Plot of the radar-measured Z R as a function of time. The offset of db of Z R from Z D as found from analysis of disdrometer data at the Clemson Atmospheric Research Laboratory has been applied to the radar data. most important of these methods is accurate determination of the antenna gain. 5. Conclusions It has been found here that, for the storms investigated in this work, variations in the coefficient A and exponent b in the Z R law used to determine rainfall amounts using WSR-88D data cannot account for the large differences between radar-measured and surface rain gauge measured rainfall observed with the KGSP WSR-88D in Greer. However, it has been shown that dramatic improvement results when adjustment of the measured radar reflectivity factors is performed to allow for possible calibration offset. This has been demonstrated through comparison of disdrometer-measured reflectivity factors with those measured by the KGSP radar. This analysis probably also explains similar large deviations observed with other WSR-88D as well as those found in comparison of SA TRMM precipitation radar data with WSR-88D data. The most accurate method of removing the calibration offset is through hardware calibration of the radar, as discussed by Ulbrich and Lee (1999). Since current NWS calibration procedures involve careful analysis of all components up to the antenna, the most likely source of error is inaccurate determination of antenna gain. Once this factor is determined accurately the performance of the radar can be checked periodically using methods described in this work. Acknowledgments. C. Ulbrich s participation in this work was supported by Contract S with the SA Goddard Space Flight Center. REFERENCES Atlas, D., C. W. Ulbrich, F. D. Marks Jr., E. Amitai, and C. R. Williams, 1999: Systematic variation of drop size and radar-rainfall relations. J. Geophys. Res., 104 (D6), Datta, S., B. Roy, L. Jones, T. Kasparis, P. Ray, and D. Charalampidis, 1999: Evaluation of TRMM precipitation radar rainfall estimates using NEXRAD and rain gauges in central and south Forida. Preprints, 29th Int. Conf. on Radar Meteorology, Montreal, PQ, Canada, Amer. Meteor. Soc., Hunter, S. M., 1996: WSR-88D radar rainfall estimation: Capabilities, limitations and potential improvements. Natl. Wea. Dig., 20, Sauvageot, H., and J.-P. Lacaux, 1995: The shape of averaged drop size distributions. J. Atmos. Sci., 52, Ulbrich, C. W., and L. G. Lee, 1999: Radar measurement error by WSR-88D radars due to variations in Z R law parameters and the radar constant. J. Atmos. Oceanic Technol., 16,