1306 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 15

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1 1306 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 15 The Effect of Vertical Air Motions on Rain Rates and Median Volume Diameter Determined from Combined UHF and VHF Wind Profiler Measurements and Comparisons with Rain Gauge Measurements DEEPAK K. RAJOPADHYAYA, PETER T. MAY,* ROBERT C. CIFELLI, SUSAN K. AVERY, CHRISTOPHER R. WILLAMS, AND WARNER L. ECKLUND Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado KENNETH S. GAGE National Oceanic and Atmospheric Administration, Boulder, Colorado (Manuscript received 19 June 1997, in final form 22 December 1997) ABSTRACT Two different frequency radar wind profilers (920 and 50 MHz) were used to retrieve rain rates from a longlasting rainfall event observed near Darwin, Northern Territory, Australia, during the wet season. In this technique, 50-MHz data are used to derive the vertical air motion parameters (vertical velocity and spectral width); the 920-MHz data are then used to obtain the precipitation characteristics with the vertical air motion corrections. A comparison of the retrieved rain rates with rain gauge measurements shows excellent agreement. A detailed examination of the mean vertical velocity and spectral width corrections in the rain retrieval shows that the error due to an uncorrected mean vertical velocity can be as large as 100%, and the error for an uncorrected spectral width was about 10% for the range of mean vertical velocity and spectral width considered. There was a strong functional dependence between the retrieved mean vertical velocity and percentage difference between observed and retrieved rain rates with and without vertical air motion corrections. The corresponding functional dependence with and without the spectral width corrections was small but significant. An uncorrected upward mean vertical velocity overestimates rain rates, whereas an uncorrected downward mean vertical velocity underestimates rain rates. Uncorrected spectral width estimates have a tendency to overestimate rain rates. There are additional errors in the width correction because of antenna beam mismatching. A method is discussed to quantitatively evaluate this effect, and it is shown to be relatively small compared to the first-order mean vertical velocity correction. 1. Introduction The ability of wind profilers (UHF or VHF) to estimate size distributions of raindrops has been demonstrated by several investigators using various techniques (Wakasugi et al. 1986; Gossard 1988; Rajopadhyaya et al. 1993). The VHF profiler operating at 50 MHz is sensitive to Bragg scattering from clear-air turbulence and to Rayleigh scattering from precipitation greater than about 5 mm h 1 but is unable to resolve raindrops less than about 1 mm in diameter (Rajopadhyaya et al. 1993). On the other hand, the UHF profiler operating * Current affiliation: Bureau of Meteorology Research Center, Melbourne, Australia. Current affiliation: TRMM Office, Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, Maryland. Corresponding author address: Dr. Deepak K. Rajopadhyaya, CI- RES, Campus Box 216, Boulder, CO drajopad@numbat.colorado.edu at 920 MHz is primarily sensitive to the precipitation echoes and is capable of resolving small drops (1 mm). At low rainfall rates or low altitudes, both the vertical air motion that is derived from the clear-air echo associated with the Bragg scattering and the precipitation echoes can be observed in the UHF spectra; however, the precipitation echo completely overwhelms the echo due to Bragg scatter in moderate to heavy rain at heights above about 1.5 km. This sensitivity suggests that there are significant advantages to be gained by using combined 50/920-MHz rain retrievals. Validation of the characteristics of precipitation is a significant problem. Rogers et al. (1993) compared profiler observations with in situ measurements using an instrumented aircraft. Another possible method is to compare rain rates derived from the profiler retrievals with surface rain gauge data. However, profiler estimation of rain rates and the resulting comparisons with rain gauges has been reported by only a few investigators (Currier et al. 1992; Maguire and Avery 1994; Klugmann and Richter 1995; Chu and Song 1998) American Meteorological Society

2 DECEMBER 1998 RAJOPADHYAYA ET AL TABLE 1. Profiler specification. Profiler specification UHF VHF Latitude Longitude Frequency Peak power Antenna type Antenna aperture One-way beamwidth Vertical resolution Sample spacing Spectral points Data recording 12.43S E 920 MHz 500 W Microstrip array 1.8 m 1.8 m m 300 m 128 m Full spectra optical disk 12.43S E 50 MHz 30 kw COCO array 100 m 100 m m 300 m 256 m Full spectra optical disk These comparisons are important in order to test the profiler s ability to estimate the precipitation parameters such as size distribution, rain rate, and water content. Instead of using a profiler at either VHF or UHF by itself, Currier et. al (1992) and Maguire and Avery (1994) used the vertical air motion information from the VHF profiler to estimate the size distribution in the corresponding UHF profiler data. In the present study, we use this approach to evaluate rain-rate estimation in high and low intensity rain regions of precipitating clouds. The method assumes a drop size distribution (DSD) shape. A gamma distribution is used in all the results shown in this paper. A theoretical model is fitted to the radar spectrum and is used to estimate the size distribution of raindrops. The derived rain rates are then compared with the tipping-bucket surface rain gauge values recorded at the profiler site. The rain gauge resolution is mm per tip. The results indicate that there is an excellent agreement between the observed and retrieved rain rates. Rogers (1967) indicated that the mean vertical air motion velocity is a key factor for the accurate determination of the size distribution of raindrops. Atlas et al. (1973) discussed the accuracy of the mean vertical air motion velocity needed for the accurate measurement of median volume diameter from a theoretical standpoint. This paper includes a detailed examination of the errors associated with both mean vertical motion and spectral width in the retrieval process with observational data as well as the effects on rain-rate estimates. For this reason, rain rates are first retrieved using the full vertical air motion corrections (both mean vertical velocity and spectral width) and then rain rates are obtained by correcting one factor at a time. This method provides a measure of what accuracy in the measured vertical air motion parameters is needed and how large the induced errors are in the determination of the size distribution of raindrops and rainfall rates when the vertical air motion information is neglected. 2. Methodology a. Data used The data we used for this study are from collocated profilers near Darwin, Australia. The UHF profiler collected data in two different modes (high and low height coverage) alternately switching between each mode. The low height mode has a vertical resolution of 100 m, whereas the high height mode has a vertical resolution of 500 m that is sampled at 300-m intervals and 128 spectral points. For the purpose of this study, only the high mode UHF data were used. The time resolution of the UHF high mode data is about 100 s because the profiler was alternating between low height coverage and high modes and cycling between beams, so that coverage was not continuous. The vertical resolution of the VHF data is also 500 m sampled at 300-m intervals. Time resolution is 166 s and each spectrum has 256 spectral points. Description of radar characteristics is given in Table 1. A well-developed mesoscale convective system passed over Darwin on 28 December 1993 during an active monsoon period. This storm consisted of alternating periods of high and low rain rates. A distinct precipitation echo was visible in the UHF Doppler spectra for almost an entire day (16 h) with intense rainfall observed from 1000 to 1200 UTC. Figure 1 shows a time height profile of the vertical velocity for the period UTC. Well-developed convective cells with upward velocities exceeding 3ms 1 (actual values with 4 5ms 1 that do not show in the shading in the figure) were observed between UTC and UTC above the melting layer (5 km). Relatively homogeneous vertical velocities of about 0.5 m s 1 are visible after 1200 UTC, which is consistent with widespread stratiform conditions during this time. Figure 2 shows a time height profile of reflectivity (dbz) estimated from the signal-to-noise ratio of the returned signals for the period UTC. The height coverage is from 0.75 to 7.0 km. Relatively large reflectivities (above 35 dbz) are seen up to about 5 km between 0930 and 1200 UTC. High reflectivities (above 35 dbz) from 1330 to 1700 UTC between about 4 and 5 km indicate the presence of a bright band. However, the bright bands are not continuous, mainly due to the occasional occurrences of mixed convective regions in the low rain-rate regions (Williams et al. 1995). Occasionally, very weak reflectivities are observed in the lower height level from 0500 to 0900 UTC.

3 1308 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 15 FIG. 1. Time height cross section of vertical velocities from the 50-MHz profiler in the high and low rain-rate regions. b. Retrieval technique The radar reflectivity factor Z is proportional to the sixth power of the diameter of the hydrometeors and is expressed as (Doviak and Zrnic 1984) 6 Z N(D)D dd, (1) 0 where N(D) is the number of particles in the diameter range between D and D dd. We shall assume that the DSDs have the form of a gamma function. The gamma distribution form of N(D )is N(D) N 0 D e D, (2) where and represent the shape and slope factors of the distributions. Maguire and Avery (1994) have also applied these techniques assuming a Gaussian-shaped DSD. While the gamma distribution is the more realistic, the Gaussian distribution has some computational advantages and may be a reasonable approximation when only bulk parameters, such as rain rate and median volume diameter, are needed. Although all the analysis in the study has been performed using a gamma distribution, the rainfall rate comparisons between retrieval and gauge differ only slightly when a fit to a Gaussian DSD is performed. The reflectivity-weighted fall speed spectrum for still air P(w) is smeared by various effects, such as turbulence, beam broadening, and wind shear, but these are all the same processes that broaden the vertical air motion spectrum G(w). Hence, the observed spectrum can be expressed as (Wakasugi et al. 1986) S(w) [G(w w) G(w) * P(w w)] * F n, (3) where w is the terminal speed of precipitation particles, w is the mean vertical velocity, n is the noise level, F is the data window function, and the asterisk (*) stands for the convolution operation. The terminal velocity is related to the diameter through the empirical relation of Beard (1976, 1977): and [ ] 9 i D 0 i i0 10 w exp C ln (4)

4 DECEMBER 1998 RAJOPADHYAYA ET AL FIG. 2. Time height cross section of reflectivity (dbz) from the 920-MHz profiler in the high and low rain-rate regions w w, where w 0 is the terminal fall velocity at sea level in meters per second, drop diameter D is in millimeters, and C i are polynomial-fit coefficients listed in Beard (1977). The variables 0 and are the densities of air at sea level and at the height of observation. The mean vertical velocity and spectral width are estimated using the VHF (50 MHz) data that is interpolated in time and height to match the UHF (920 MHz) sampling. Here, G(w) A0 exp (5) 2 2 and 1 dd 6 P(w) N(D)D, (6) Z dw where A 0 and are the respective amplitude and spectral width of the vertical air motion spectrum that has been normalized to unit area. Note that this has implicitly assumed that the spectral width of the vertical air motion spectrum measured by the profilers will be the same at both frequencies. In general this will not be the case, which is an issue that is discussed in section 3e. The amplitude of the vertical air motion echo detected 0 w 2 by two radars operating at two different frequencies (50 and 920 MHz) is not the same due to the wavelength dependence of Bragg scatter. Additionally, the clear-air portion of the UHF spectrum is often very difficult to observe, as noted in the introduction. For this reason, the mean vertical velocity and spectral width information obtained from the VHF spectrum is used to locate the position of the vertical air motion echo in the UHF spectrum and assign a minimal signal strength (noise level) to this portion of the spectra. Thus, by incorporating the VHF data, the precipitation component of the UHF spectra can be isolated. The vertical air motion information is extracted by fitting a Gaussian curve to the VHF spectra. However, the observed height and time of the VHF spectra often does not match with the corresponding height and time of the UHF spectra. As an example, Fig. 3 shows the four VHF spectra just before, after, above, and below the UHF observation time and range gate. A Gaussian fit to the spectrum is shown by the dotted lines. Even though the time resolution of the VHF spectra is just 166 s, there is a change of mean vertical motion from around 1.9ms 1 to about 1.3 m s 1. The change in spectral width is also considerable (1.3 to 2.2 m s 1 ). Therefore, a two-dimensional interpolation technique is applied to obtain an average estimate of the mean vertical velocity and spectral width. Finally, a model precipitation drop size distribution

5 1310 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 15 FIG. 3. Four VHF spectra just before and after the UHF time and below and above the UHF range gate. Negative velocities are defined as toward the radar so that a positive value is an updraft. Precipitation echoes will, in general, have negative velocities. is converted to a reflectivity-weighted fall speed spectrum [Eqs. (4) and (6)] and then convolved with G(w) [Eq. (5)]. A least squares technique is used to find a best fit to the observed spectrum by varying the parameters N 0,, and using Eq. (3). This process was first described by Currier et al. (1992) and is similar to that described by Wakasugi et al. (1986) except that a more general form of the DSD is used as well as the two different frequency radars. The precipitation rate R (mm h 1 ) and water content M (g m 3 ) are related to the size distribution of raindrops N(D) through and R N(D)D w(d) dd (7) w M N(D)D dd, (8) where w is the density of the drop. These parameters can be easily determined once N(D) is established through the fitting procedure just described. 3. Results a. Preliminary comments Next we will discuss the four experiments described in Table 2. The first experiment will examine the accuracy of the full retrievals against rain gauge data. The next two experiments use the full retrievals as truth and examine the effect of the vertical air motion and spectral broadening. The last experiment examines the TABLE 2. Summary of experiments. Experiment Corrections in the retrieval Truth Vertical air motion and broadening Broadening only Vertical air motion only Vertical air motion and modified broadening Rain gauge Vertical air motion and broadening Vertical air motion and broadening Vertical air motion and broadening

6 DECEMBER 1998 RAJOPADHYAYA ET AL FIG. 4. Time height cross section of water content (g m 3 ) below the freezing level in the (top) high rain-rate and (bottom) low rain-rate regions. effect of the beam mismatch on the retrievals by introducing a modified spectral broadening. Before discussing the intercomparisons it is useful to describe some of the observed features of the 28 December case. These features are shown in the time height cross sections of the water content in the high and low rain-rate conditions (Fig. 4). In each case there is considerable structure and high-frequency variations. However, it is clear that the fluctuations have spatial and temporal coherence. This provides confidence that

7 1312 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 15 FIG. 5. A time series of rainfall rate estimated using a Z R relationship and rain gauge (dotted line). FIG. 6. A time series of retrieved rainfall rate (solid line) and gauge rainfall rate (dotted line). the fluctuations we observe are real manifestations of the precipitating systems and are not associated with noise in the retrieval process. The primarily vertically oriented structure also validates the idea of comparing the retrieved data with surface (gauge) measurements, although some differences due to the evolving precipitation field structure over the profiler will be evident. Section 3b will examine whether these data can be used quantitatively as well. b. Experiment 1: Profiler versus rain gauge intercomparison For the intercomparison of profiler retrieved rain rates and rain gauge measurements, UHF data from 1.9 km is used because it is just above the lowest VHF range gate unaffected by ground clutter. The air temperature at this level is typically about 33C for a tropical wind environment. Figure 5 is a time series of rainfall rates (solid line) estimated using a simple Z R relation (Z 200R 1.6 ) where the reflectivity has been estimated using the signal-to-noise ratio. The gauge rainfall rate is shown by the dotted line. The time resolution of the gauge data is about 35 s. The gauge data are smoothed by a sixpoint running mean, and the profiler data are smoothed by a three-point running mean. The different averaging is to account for differences in the sampling rate between the model retrieval and the rain gauge. Additionally, there is a time lag between the precipitation event at the ground and the profiler precipitation retrieval at 1.9 km. For this reason, the retrieved rain-rate series has been shifted to the right by about 5 min (the time required for a typical drop to fall from 1.9 km to the ground). The two time series are highly correlated ( 0.78), demonstrating that the temporal variations of the rainfall rates match in both estimates. However, the total accumulated rain using the Z R values is just 53 FIG. 7. Time series of rainfall rates with (solid line) and without (dotted line) considering the vertical air motion effect in the (top) high rain-rate and (bottom) low rain-rate regions.

8 DECEMBER 1998 RAJOPADHYAYA ET AL FIG. 8. Scatterplot of relative percentage difference in expt 2 [defined as 100 (test retrieval truth)/truth] in the rain-rate retrieval (with and without considering the vertical air motion effect) vs the vertical air motion velocity. mm, which is very low compared to the rain gauge total of 145 mm. The Z R relation that we used here serves as an illustration of the technique. It is valid only for the Marshall Palmer distribution with rainfall rate greater than 10 mm h 1. Because there are so many Z R relations for various precipitating conditions, all determined empirically but as a parameterizing in mean DSD, one must be careful in choosing a correct relationship. With profiler data we actually measure the DSD. In general we have found that the Z R rainfall estimates using various relationships is low compared to the rain gauge estimates. Figure 6 is a time series plot of the retrieved rain rate (solid line) and the gauge rain rate (dotted line) that shows much better agreement, although there are some discrepancies during the time of high rainfall ( UTC). There are numerous reasons to expect differences. The profiler measurement is a volume sample 1.9 km above the earth s surface compared with the essentially point measurement of the rain gauge. Therefore, time and spatial variability can cause these discrepancies. There are a large number of gaps in the data due to the sampling sequence between the vertical and oblique beams and only the high height mode of the 920-MHz profiler data is used, so further differences can be expected, particularly in highly variable convective rain. The difference between the two measurements could also depend on atmospheric conditions, such as background humidity and temperature, which determine the rate of evaporation of the drops that fall from 1.9 km (retrieved height) to the ground (gauge). The estimated total rainfall is 151 mm, which is very close to the gauge total (145 mm) for the same period. c. Experiment 2: The effect of mean vertical velocity corrections Atlas et al. (1973) have shown theoretically that the error in retrieving DSDs from radar data can be very FIG. 9. Schematic showing the effect of an error in fall speed. The corrected spectrum is the solid line, and the spectrum for uncorrected updrafts is the dotted line. The top frame shows the returned power spectrum followed by the corresponding size spectra. Note that the two curves have equal area. The lower frames show D 3.67 N(D)(rain rate) and N(D), which both increase as D 0 is shifted to smaller values in an uncorrected updraft (dashed line). large if the vertical air motions are not properly taken into account. It is easily seen that if there is an uncorrected upward velocity, then the apparent fall speed is reduced, leading to an estimate where there is a large number of small drops (since Z remains constant and is proportional to D 6 ). Atlas et al. (1973) showed that errors in assigning diameters and number of drops exceeded 100% for situations where the uncorrected vertical air velocities exceeded 1 m s 1. However, no detailed analysis has been done to discriminate the effects of the mean vertical velocity and spectral width in the retrieval process on real data. Nor there has been an analysis of the integrated error effect on realistic DSDs. We will consider the full retrievals as truth for examining the effect of vertical motion and spectral width on rainfall retrievals because of the excellent agreement between the profiler retrieved rain rates and the rain gauge trace. Figure 7 is a time series plot of retrieved rain rates

9 1314 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 15 FIG. 10. (a) The top frame shows the time series of the median diameter in high and low rain-rate regions. The middle frame shows the time series of the percentage difference of retrieved median volume diameter with and without corrections for the magnitude of the vertical air motion. The bottom frame shows the time series of vertical air motion velocity.

10 DECEMBER 1998 RAJOPADHYAYA ET AL FIG. 10. (b) Scatterplot of retrieved median volume diameter vs mean vertical air motion velocity. The thick solid line represents the theoretical results of Atlas et al. (1973) for a median diameter ranging from 0.5 to 2 mm. at 1.9 km with full corrections (solid lines) and without considering the vertical air motions (dotted lines) in the high and low rain-rate regions. Note that the instantaneous difference in rain rates can differ by 100% or more when the vertical air motion is large (top panel) and that even when the vertical velocity is small, such as in the low rain-rate regions, the differences can be as large as 25%. The total rainfall accumulation estimate has been reduced from 151 to about 101 mm for the time period of UTC, and the correlation coefficient between the retrieved and gauge rain rate is Figure 8 is a scatterplot of the relative percentage difference [defined as 100 (test retrieval truth)/ truth] of rain rates at 1.9 km with full corrections and with spectral width corrections alone as a function of the magnitude of the vertical air motion velocity for the period of UTC. This plot clearly illustrates the almost linear dependence of the retrieval accuracy with the strength of the mean vertical velocity when the velocity is less than about 1 m s 1. For larger velocities, the uncorrected updrafts produce larger errors. This is at least partly a result of the D 6 dependence on reflectivity. For an uncorrected updraft, the spectrum is shifted toward smaller velocities and hence a very small drop diameter regime. Consequently, many more small drops are needed to produce the same reflectivity. However, for downdrafts, the spectrum is shifted to higher fall speeds, and hence larger diameters, but the integrated effect is less. The shift in DSDs is shown in Fig. 9. Note that D 6 N(D) must remain constant, so that N(D) must increase for an uncorrected updraft. The rain rate is approximately related to D 3.67 N(D) (Ulbrich 1983), so it too increases. It is important to note the effects of improperly corrected mean vertical velocity on different parts of the drop size spectrum. The terminal fall speed of raindrops is related to their diameters, but the speed changes little for diameters greater than about 4 5 mm. Thus, a small change in velocity results in a large (small) change in the diameter in the large (small) diameter regime. For this reason, uncorrected vertical velocities result in more changes to the large drop diameter part of the spectrum. Figure 10a shows a time series of the median diameter (top panel) and percentage difference (defined as before) in median diameters (middle panel) at 1.9 km with and without corrections for vertical motions along with the vertical air velocities (bottom panel). These differences are largest in the high rain-rate regime, where the vertical velocities are largest with the diameters biased downward in an updraft evident around 1100 UTC. Figure 10b shows a scatterplot of the percentage difference in median diameter against the mean vertical air velocity for the period of observations. There is an almost linear dependence of the relative accuracy of median diameter with the magnitude of the mean vertical velocity. It is notable, however, that these errors are only about 20%, even for a vertical velocity of 1.3 m s 1 with a peak error of about 50% when the vertical velocity is 2.3 m s 1. The theoretical results (thick solid lines) of Atlas et al. (1973) are shown for comparison. They are in reasonable agreement for small velocities but tend to be larger than our results for large vertical velocities. This may be a result of their assumption of the Marshall Palmer drop size distribution. In addition to errors induced by the shift of the median diameter, there is an additional problem in fitting a reflectivity-weighted fall speed spectrum that is illustrated in Fig. 11. Drop fall speeds lie between velocity limits of 0.0 and 9.6 m s 1 for small and large drops at mean sea level pressure. If the DSD is in an uncorrected (or improperly corrected) updraft, part of the drop spectrum lies at fall speeds greater than 0ms 1, which is physically unrealistic. The fitting procedure used here does not allow for such errors, and poor fits to the observed radar spectrum result. Similarly, if there is an uncorrected downdraft, part of the spectrum may lie at velocities exceeding physically allowable fall speeds, and again the fitting procedure breaks down. Similar errors may also arise if the spectral broadening due to turbulence and antenna beamwidth is very large and uncorrected, so that the broadened fall speed spectrum has significant amplitude at physically unrealistic velocities. Note that these errors have the opposite sign to that of the mean velocity correction errors. This effect is also one of the reasons for the total errors in D 0 being less than the theoretical calculations of Atlas et al. (1973) (Fig. 10b) for large uncorrected vertical motions. These comparisons have relevance to the full retrievals because errors in the vertical motion will produce errors similar to the cases where we have neglected the vertical motion. Also note that the difference in sampling between the profilers will induce errors associated

11 1316 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 15 FIG. 12. Time series of retrieved rain rates in expt 3 in which full corrections (solid line) are compared with retrievals with no spectral width corrections (dotted line). d. Experiment 3: The effect of spectral width corrections As noted above, there are two components of the vertical air motion information that are used in the retrieval process: the mean vertical velocity and spectral width contributions [see Eqs. (3) and (5)]. The mean vertical air motion correction is obviously important, as shown in the previous section, but the impact of the spectral width is less clear. This effect will now be examined. Figure 12 is a time series of retrieved rain rates at 1.9 km during the period of relatively intense rain with and without spectral width corrections. The dotted line represents the retrieved rain rates without spectral width corrections, which is compared with the retrieved rain rates (solid lines) using full corrections (spectral width and mean vertical air velocity). Clearly, the spectral width has a minimal effect on the retrieval compared to the mean vertical air motion. Figure 13 is a plot of the relative percentage difference in retrieved rain rate with and without considering the vertical air motion smearing effect. In most cases, FIG. 11. Schematic showing (top) a Doppler spectrum that has been properly corrected for vertical motion so that the fit to the spectrum (shaded region) matches the curve, (middle) an uncorrected updraft so that some drops have a positive fall speed, and (bottom) uncorrected downdraft so that some drops have fall speeds greater than is possible. The dark shading represents the retrieval fit to the spectrum in these uncorrected cases. with rapid (nonlinear) changes in vertical motion as well as statistical errors in the measurement. FIG. 13. Scatterplot of relative percentage difference in the rain rate for expt 3 vs the vertical air motion spectral width.

12 DECEMBER 1998 RAJOPADHYAYA ET AL FIG. 14. Time series of percentage difference of retrieved median volume diameter in the high and low rain-rate regions in expt 3. FIG. 15. Scatterplot of UHF precipitation spectral width vs VHF precipitation spectral width. the errors are negative, which indicates that the retrieved rain rates are higher when the spectral width is not included. This effect also can be seen in Fig. 12. The percentage difference in most cases is 10% or less. An almost linear increase in the percentage difference of rain rates with spectral width is clearly seen when the spectral widths are small (1 ms 1 ). To further examine the apparent weak effects of the spectral width, the median volume diameter is investigated. Figure 14 shows a time series of the percentage difference in the median volume diameter at 1.9 km with and without vertical air motion spectral width corrections for an 8-h period. Note that there are variations (15%) in the median volume diameter in the high rainrate region with the uncorrected data biased toward small median diameters. This result is because when the vertical air motion widths are large the precipitation peak is spread and more energy is put into velocities corresponding to small and large diameters. However, the D 6 reflectivity dependence means that this spread produces many more small drops in the retrieval (and only a small number of large drops) so that the median diameter is biased toward smaller drops. Small variations can be seen in the low rain-rate region (5%), but the random errors are comparable. Thus the variation of the median volume diameter seems to be larger if the spectral width is not corrected compared to the variation of rain rates (10%). Overall, this variation in the median volume diameter is small but is a definite bias. e. Experiment 4: The effect of beam mismatching The precipitation spectral width is equal to the square root of the sum of the air motion width squared and the precipitation width in still air squared. Because the corrections due to the vertical air motions spectral width are small, this indicates that the UHF precipitation width is significantly wider than the vertical air motion width measured by the VHF radar. Now, the question arises whether the VHF vertical air motion spectral width can be taken as the representation of the UHF vertical air motion spectral width in the retrieval process. The beamwidth of the VHF profiler is about 3, whereas the beamwidth of the UHF profiler used here is about 9. This difference means that the spectral broadening characteristics due to the beamwidth will not be the same for both profilers. Horizontal velocity information can be used to calculate beam broadening, but the velocity during strong convection is highly variable. An alternative way is to compare the UHF precipitation width with the VHF precipitation width or UHF vertical air motion width with the VHF vertical air motion width. In the present dataset the UHF vertical air motion echoes were so weak that they were not visible at the height of interest. However, there are many cases, mainly in light rain conditions, in which two distinct spectral peaks are visible in the VHF dataset one for the vertical air motion and another for the precipitation. Thus, it is possible to compare (statistically) the precipitation components of the UHF spectra with the precipitation component of the VHF spectra in order to assess beam broadening effects. In the analysis procedure, the VHF precipitation peak has been separated from the vertical air motion peak and the spectral width of the precipitation echo is obtained by fitting a Gaussian curve to the precipitation component. Figure 15 is a scatterplot of the UHF precipitation width versus the VHF precipitation width. The scatter points are clustering above the solid (y x) line, which indicates that the UHF width is significantly wider than the VHF width. Note that the signal-to-noise ratio of the VHF is quite low, so that much of this scatter is associated with random statistical errors (Doviak and Zernic 1984). The median position of the points in Fig. 15 indicates that the UHF precipitation spectral width is about 10% higher than the VHF precipitation spectral width. Note that in the high rain-rate periods, this difference is likely to be less because convective turbulence

13 1318 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 15 width becomes wider, the potential for error will increase. However, in strong convection, where turbulence will be intense and beam broadening less important, then FIG. 16. Time series of retrieved rain rates at 1.9 km for expt 4 in which a correction for the beam broadening due to antenna beam mismatching (dotted lines) compared with retrieved rain rates (solid line) without including the effect of antenna beam mismatching. will be much higher and will be a greater contributor to the spectral width than during stratiform conditions. We can estimate a correction factor using the results of Fig. 15. In still air, the precipitation spectral width will be determined only by the DSD. We denote this width as p. We seek an estimate of the 920-MHz vertical air motion width denoted by 920 and can measure the 50-MHz air motion width 50. The observed 920- MHz spectral width 920ob is dominated by precipitation, so we have 920ob 920 p. Using the result of Fig. 15 we can write ob 920 p ( 50 p ). (9) Therefore, p. (10) Using the observed 920-MHz precipitation width 920ob in place of p will cause us to overestimate 920 because 920ob is broadened with respect to p due to smearing by vertical air motion and beamwidth effects. However, assuming Gaussian-shaped spectra we can correct the width using 50, that is, substitute 2 p 2 2 E into Eq. (10) to give 920ob ob E, (11) where E is the error associated with the assumption that We can incorporate an iteration procedure to further reduce the error, but the accuracy and scatter of the widths and their differences do not warrant this type of analysis. We can now use Eq. (11) to substitute a corrected vertical air motion width into the retrievals. Figure 16 shows the retrievals with the modified width correction. The effect is small, so that in practice the errors induced by the beam mismatch will not be important. In cases where the vertical air motion spectral 4. Conclusions The excellent agreement in the retrieved rain rates with the gauge rain rates shows that UHF and VHF wind profilers can be used as a ground-based remote sensing tool to estimate rainfall. Moreover, it follows that the median volume diameter estimated from the retrievals must also be reasonably accurate because the rainfall is approximately related to the 3.67 moment of the DSD (Ulbrich 1983), and the drop volume is related to the third moment of the DSD. The evolution of the DSD with height and the vertical gradient of water content can also be reliably estimated. It has been verified with observational data that the correction for the magnitude of the vertical air velocity is very important for accurate retrievals. The correction for the spectral broadening effects is of second order but is a bias. If the upward (downward) vertical air motion velocity is not corrected, then the retrieval process overestimates (underestimates) rain rates. Uncorrected updrafts (downdrafts) causes an underestimation (overestimation) of D 0. If the spectral width is not corrected, a positive bias in D 0 results. In the present study, only one dataset is considered. For further validation of work, many datasets in different environmental conditions should be considered. Acknowledgments. Helpful comments from the reviewers are greatly acknowledged. This work was supported in part by NASA Grant NAGW REFERENCES Atlas, D., R. C. Srivastava, and R. S. Sekhon, 1973: Doppler radar characteristics of precipitation at vertical incidence. Rev. Geophys. Space Phys., 11, Beard, K. V., 1976: Terminal velocity and shape of cloud and precipitation drops aloft. J. Atmos. Sci., 23, , 1977: Terminal velocity adjustment for cloud and precipitation drops aloft. J. Atmos. Sci., 34, Chu, Y. H., and J. S. Song, 1998: The observations of precipitation associated with the cold front using VHF wind profiler and ground-based optical rain gauge. J. Geophys. Res., 103, Currier, P. E., S. K. Avery, B. B. Balsley, K. S. Gage, and W. L. Ecklund, 1992: Combined use of 50 MHz and 915 MHz wind profilers in the estimation of raindrop size distributions. Geophys. Res. Lett., 19, Doviak, R. J., and D. S. Zrnic, 1984: Doppler Radar and Weather Observations. Academic Press, 458 pp. Gossard, E. E., 1988: Measuring drop-size distributions in clouds with a clear-air-sensing Doppler radar. J. Atmos. Oceanic Technol., 5, Klugmann, D., and C. Richter, 1995: Correction of drop shapeinduced errors on rain rates derived from radar-measured Doppler spectra at vertical incidence. J. Atmos. Oceanic Technol., 12,

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