Raindrop size distribution (DSD) parameters are retrieved from dual-frequency (UHF and VHF) wind profiler measurements made at Gadanki, India, in a summer monsoon season. The convoluted UHF spectra are first corrected for vertical air motion and spectral broadening (using VHF measurements) and later are used for deriving DSD parameters. Two distinctly different case studies, a mesoscale convective system and a pure stratiform precipitation system, have been considered for a detailed study. DSD parameters obtained in these case studies reveal systematic variations of DSD from case to case and also from one rain regime to another within the same precipitating system. A statistical study has been carried out using the profiler data collected during the passage of 16 rain events. The retrieved DSD profiles are divided into separate rain regimes (stratiform and convection), based on reflectivity, to examine salient microphysical characteristics and the vertical variability of DSD in different precipitation regimes. The distribution of DSD parameters is, in general, wider in the convective rain regime than in the stratiform regime, particularly below 2.4 km. The vertical variation of the gamma parameter distribution in the stratiform rain regime is minimal, indicating that the microphysical processes (growth and decay), which alter the rain DSD, may be in equilibrium. On the other hand, the distribution in the convective rain regime appears to be more complex, with the mean profile of the shape parameter varying significantly with height. The observed vertical variability of the gamma parameters and the median volume diameter in the convective rain regime is attributed to two major microphysical processes: evaporation and breakup. The role of other processes, like drop sorting and collision–coalescence, in altering the DSD parameters is also discussed. The present statistics, representing continental monsoon rainfall, are compared with the existing statistics at Darwin, Australia, and the results are discussed in light of DSD differences in oceanic and continental monsoon precipitation.
Knowledge of raindrop size distribution (DSD) and its variability is essential for understanding the processes associated with precipitation growth–decay, radio communications, microwave remote sensing, and cloud modeling. Measurements of DSD with in situ devices have been made for a long time, but the remote sensing of DSD, in general, and the retrieval of the vertical profile of DSD, in particular, are difficult tasks. Rapid developments in wind profiler technology in the past few decades have led to a variety of new applications to meteorological problems, including the retrieval of DSD. Vertically pointing Doppler radars operating at VHF and UHF can provide information about ambient air motion and the structure of hydrometeors, respectively, in the precipitating clouds that are present overhead. As a result, one can directly determine the fall velocity spectrum of hydrometeors. By using accepted empirical relationships, the DSD can be estimated accurately from its fall velocity spectrum.
Using middle- and upper- (MU) atmospheric radar data collected during moderate rain, Wakasugi et al. (1986) first retrieved the DSD using a nonlinear least squares method. They assumed an exponential size distribution of raindrops and modified the resulting reflectivity-weighted fall speed spectrum into rain DSD. This procedure, though simple, requires the use of some initial guess values in order to retrieve the required parameters. This problem was later resolved by Sato et al. (1990), who developed an automated computer algorithm for guessing the initial values for the retrieval of DSD. Rajopadhyaya et al. (1993) have shown that the retrieval technique involving VHF profiler data may not be able to resolve drops smaller than about 1 mm in diameter. Using simulations and the data collected with the boundary layer VHF radar at Buckland Park, South Australia, Lucas et al. (2004) investigated the sensitivity of the technique and its accuracy. They found a negative bias of 10%–20%, on average, across the retrieved DSD at diameters greater than 1 mm with a maximum bias at the lower drop end.
On the other hand, Gossard (1988) and Gossard et al. (1990) employed a UHF profiler for retrieving DSD, but limited their studies to light rain. During moderate to heavy rain, the UHF returns from precipitation overwhelm the clear-air portion of the Doppler spectra and make it difficult to get the ambient vertical air motion information. However, recent studies show that it is possible to retrieve DSD from a UHF profiler alone using the Sans Air Motion (SAM) model even during moderate to heavy rain (Williams 2002). The SAM model uses the precipitation spectrum to estimate the ambient air motion, spectral width, and DSD. The inherent limitations in the technique limit the applicability of the SAM model to only the bulk parameters of rainfall, like mass-weighted mean diameter, Dm, and rain rate. Williams et al. (2000) compared the DSD parameters obtained from two surface disdrometers with those retrieved from a UHF profiler after correcting for vertical air motion. They found good agreement between these measurements for the drops with diameters (D) greater than 1.5 mm, while at smaller drops (D < 1.5 mm), the agreement is poor, particularly during heavy rain. They attributed this difference to instrumental errors as well as the radar retrieval technique, mainly turbulence correction.
The applicability of the techniques discussed above, employing single-frequency radar, is limited to either moderate rain to heavy rain or light rain depending on the frequency of the radar and its sensitivity to precipitation. On the other hand, the techniques involving the dual-frequency radars are highly successful in deriving the DSD (Currier et al. 1992; Maguire and Avery 1994; Rajopadhyaya et al. 1998; Cifelli et al. 2000; Schafer et al. 2002) at all rain rates. A comparison between single-frequency (∼50 MHz) and dual-frequency (∼50 and ∼915 MHz) techniques reveals that the single-frequency technique often overestimates the median volume diameter (Rajopadhyaya et al. 1999) because of its inability to resolve the small-drop end of the spectrum accurately (Rajopadhyaya et al. 1993).
Most of the studies cited above generally follow one of the two approaches available for the retrieval of DSD, that is, the parameterization method or deconvolution. The first approach assumes a functional form for DSD, either an exponential (Wakasugi et al. 1986; Sato et al. 1990) or a gamma (Currier et al. 1992; Rajopadhyaya et al. 1998; Cifelli et al. 2000), then convolutes with the known clear-air spectrum. This model spectrum is then fitted, using nonlinear least squares fitting, to the observed precipitation spectrum to retrieve DSD parameters. The deconvolution method obtains the true precipitation spectrum from the observed precipitation (UHF) spectrum by deconvolving it with the clear-air (VHF) spectrum (Rajopadhyaya et al. 1993; Kobayashi and Adachi 2005). Schafer et al. (2002) compared these two approaches for dual-frequency retrievals and found that the deconvolution methods generally performed better for a broader range of median volume diameters (D0).
Barring a few studies (Cifelli et al. 2000; McKague et al. 1998), most of the earlier investigations are based on one or two precipitation events. However, knowledge of the statistical characteristics of DSD is vital for understanding many microphysical processes. For instance, earlier DSD statistics, obtained from VHF and UHF measurements made at Darwin, Northern Territory, Australia, have been used to obtain rain rate–radar reflectivity (Z–R) relations as a function of height (Cifelli et al. 2000) and to test the sensitivity of passive microwave retrievals on DSD variations (McKague et al. 1998). In the present study, the data collected during 16 rain events were used to derive DSDs and the statistics are presented separately for stratiform and convective rain. The Indian mesosphere–stratosphere–troposphere (MST) radar and lower-atmospheric wind profiler (LAWP) measurements have been used to derive the DSD in the height range of 1.5–3.9 km. Further, the DSD statistics from Darwin represent the oceanic monsoon precipitation, while the present statistics are for continental monsoon precipitation. This allows us to compare the DSD variations (with height) and statistics in the context of continental versus oceanic monsoon rainfall.
A brief description of the Indian MST radar, LAWP, and disdrometer is given in section 2. This section also includes an overview of the rain events, including information on their times and lengths of observation, types of the system, and so on used in the present study. The method of DSD retrieval used in this study is briefly outlined in section 3. An error analysis is carried out to study the effects of clear-air information upon the retrieval of DSD and subsequently on physical rain parameters like R and median volume diameter D0. Two case studies (a mesoscale convective system and widespread stratiform rain) are presented and discussed in section 4. Statistical characteristics of rain DSD are presented separately for stratiform and convection in section 5. The results are summarized and discussed at length in section 6.
2. System description and database
The Indian MST Radar, LAWP, and disdrometer are located at Gadanki (13.5°N, 79.2°E), in the southeastern part of India. The Indian MST radar operates at a frequency of 53 MHz and with a peak power of 2.5 MW. The antenna array consisting of 1024 crossed yagi antennas and generates a radiation pattern with a half-power beamwidth of 3°. A complete description of the Indian MST radar can be found in Rao et al. (1995). The operating frequency of the LAWP is 1357.5 MHz. The phased antenna array consists of 24 × 24 elements and transmits a peak power of 1 KW. The antenna beam can be positioned, through electrical phase switching, at three fixed orientations, namely, zenith, 15° down to east, and north. A complete description of the system can be found in Reddy et al. (2001). LAWP operates in two modes, low and high mode, alternatively, to provide better height coverage. In the low mode, radar samples are taken up to 4.8 km with a range resolution of 150 m, while in the high mode the data are collected up to 9.0 km with the same range resolution as in the low mode. In the present study, we have used only the vertical beam data collected in the high mode. The specifications of the MST radar and LAWP parameters are given in Table 1.
A Joss–Waldvogel (JW) disdrometer (RD69) is used for measuring DSDs at the ground continuously and automatically every minute. The surface disdrometer records the number and size of raindrops hitting the 50 cm2 sensor head, enabling the direct estimation of reflectivity, rain rate, liquid water content, and the median volume diameter. The range of drop diameters that can be measured spans from 0.3 to 5 mm in 20 drop-size classes.
The data collected during the 2000 summer monsoon season (June–September; however, one event is in April) have been used for this study. Although LAWP operates and provides data continuously, the Indian MST radar data are not continuous. The MST radar time is distributed to several scientific and technical experiments based on users’ scientific proposals. As a result, simultaneous radar data (both MST as well as LAWP) are available for only 16 rain events. Table 2 provides an overview of the data used in the present study. As can be seen from Table 2, the time span of each event ranges from 11 min to 6 h. The type of rainfall is also not uniform: some of the cases are purely stratiform, some are purely convective, and others belong to the mesoscale convective system (MCS) category.
3. Retrieval technique and error analysis
The Indian MST radar and LAWP observe Bragg scatter from turbulent irregularities in the radio refractive index and Rayleigh scatter from precipitation in the presence of precipitating clouds. The observed VHF/UHF spectrum can be represented by the convolution of clear-air echoes and precipitation echoes during precipitation. The measured Doppler spectrum can be mathematically represented as (Wakasugi et al. 1986)
where G(w) is the clear-air Doppler spectrum, G0(w) is the normalized clear-air spectrum [=(1/2πσw) exp(w2/2σ2w)], P(w) is the reflectivity weighted fall speed spectrum, w is the mean vertical air motion velocity, F is the data window function, and the asterisk denotes the convolution operator. The first term in the above equation is almost negligible at UHF, because the precipitation echo overwhelms the clear-air contribution in most cases. The second term is mostly affected by two factors in a nonquiescent atmosphere: 1) nonzero wind, as any nonzero wind component can shift the entire spectra and, thus, corrupt DSD retrievals significantly, and 2) spectral broadening, as turbulence can alter the drop fall velocity and, thus, can widen the spectrum even if the drops have the same fall velocity. In addition to turbulence, some nonturbulent processes—finite beamwidth (beam broadening), wind shear across the pulse volume (shear broadening), etc—broaden the spectrum. Therefore, information on vertical air motion and clear-air spectral width is essential for the accurate retrieval of DSD from the convoluted spectrum.
In the present study, the clear-air information is gathered from the corresponding VHF spectrum. In other words, the UHF and VHF spectra are matched in both space and time. A typical example of the spectrum obtained with UHF (dash–dot line) and VHF (solid line) radars during convection is shown in Fig. 1a. Here, both the VHF and UHF spectrums are normalized with the maximum power in that altitude. It is evident from the VHF spectrum that there exist an updraft of 3–4 m s−1 and also a precipitation echo with comparable signal strength with the clear-air echo. The Doppler velocity of the precipitation echo observed with the MST radar matches reasonably well with that of the LAWP. The small discrepancy between the precipitation spectra measured by the LAWP and MST could be due to the differential integration time involved in constructing their respective spectra. Although we have utilized data (MST and LAWP) collected at the same time, their probing times are slightly different. As a result, there could be a slight shift in the spectra of one radar from that of the other, particularly in convection. One can clearly notice that some of the spectral points in the uncorrected LAWP spectra are showing upward motion (>0 m s−1), which is unrealistic. This happens because of the presence of strong updrafts at that altitude. This clearly demonstrates the importance of vertical air motion correction for accurate retrieval of DSD.
To extract the vertical air motion and spectral width due to turbulence and other effects, the VHF spectrum is fitted with a Gaussian distribution:
where A0 and σw are the amplitude and spectral width of the Bragg scatter. The dashed line in Fig. 1a shows the Gaussian fit to the clear-air echo.
To remove the broadening contribution due to turbulence and other nonturbulent processes from the UHF spectrum, it is deconvolved with the VHF spectrum. Two methods are generally used for this purpose and are discussed at length in Rajopadhyaya et al. (1993) and Schafer et al. (2002). They are 1) the Fourier transform technique (FT) and 2) an iterative technique. Rajopadhyaya et al. (1993) have shown that the FT technique performs better than the iterative technique through their simulation studies. We chose to use the FT technique to deconvolute the LAWP spectra (Schafer et al. 2002):
where Ppc = G0(w) * P(w − w), FFT denotes the fast Fourier transform, FFT−1 represents the inverse of FFT, SHIFT represents the mean shift of the Doppler spectra based on the vertical air velocity [obtained from Eq. (2)]. Since, the amplitudes of the spectra are different for LAWP and MST radars, they are normalized to their peak power, before deconvolving the LAWP spectra. Note that the deconvolution involves division of the Fourier series, and the division of small numbers associated with the noise will amplify the sidelobes significantly. To avoid these problems, either we have to low-pass filter the Fourier series by truncating the high-frequency components or use an optimal filter [Φ(w)]. Following Schafer et al. (2002), we have applied the optimal filter on the Fourier series of the convoluted spectra. The resulting spectra, Sp(w), can be treated as the velocity-corrected deconvolved spectra. Figures 1b and 1c show the spectrum at different stages of the above operations.
The spectra thus obtained, that is, reflectivity-weighted fall speed spectra from hydrometeors, can be, theoretically, represented in terms of the drop diameter with the following equation:
where D is the diameter of the drop, w is the terminal velocity, and Ze is the radar reflectivity factor, estimated from LAWP measurements. Surface disdrometer measurements were used for absolute calibration of the LAWP backscattered power (i.e., for obtaining the radar reflectivity factor, Ze), following Gage et al. (2000). The value of dD/dw is estimated using the empirical relation between the terminal fall speed and drop size (Atlas et al. 1973):
where ρ and ρ0 are the atmospheric densities at the height of observation and near the ground, respectively. The constants used in the equation are valid only when w is in meters per second and D is in millimeters.
To represent a broader range of raindrop size distributions, the DSD is often approximated to follow a gamma distribution of the following form (Ulbrich 1983):
where μ is the shape parameter, Λ is the slope parameter, and N0 is the intercept parameter.
where K is a scaling factor dependent on Ze, μ, and Λ (Schafer et al. 2002).
The reflectivity-weighted fall speed spectrum in Eq. (7) is fitted to the “pure” precipitation spectrum [Eq. (3)] using a nonlinear least squares fitting method (Wakasugi et al. 1986) by giving initial values to the gamma parameters. An iterative procedure is performed to minimize the chi-square values between the fitted and the observed (pure precipitation) spectra. Because of the exact matching of the VHF and UHF spectra in both space and time, the DSD retrievals are performed with 300-m heights and 11-min temporal resolutions. Further, the retrievals are confined only to the rain region, that is, between 1.5 and 3.9 km.
In the present study, the reflectivity-weighted fall speed spectrum is assumed to follow the gamma distribution. It has been widely accepted that the gamma distribution better represents the instantaneous DSD and its variations over a wide range of scales (Ulbrich 1983). However, there are several reports available in the literature with different functional forms for representing DSD, for example, Maguire and Avery (1994), for a Gaussian distribution, Wakasugi et al. (1986; 1987) and Sato et al. (1990), for an exponential distribution. In addition, more complicated spectra have been observed in situ as well as with radars, where more than one spectral peak has been observed (Gossard et al. 1990). Although the functional form differs in the above studies, the estimated rainfall bulk parameters (rainfall rate R and median volume diameter D0) are more or less equal irrespective of the functional form. These parameters can be estimated from the retrieved DSD, using the following formula:
As seen above, the Doppler spectra are corrected for vertical air motion and spectral broadening before retrieving the DSD. The affect of these parameters on the accuracy of DSD retrievals has been recognized for a long time. Atlas et al. (1973) showed theoretically that vertical velocity correction is essential for the accurate retrieval of DSD, in particular in convective rain. Later, Rajopadhyaya et al. (1998) quantified the errors in median volume diameter and rain-rate estimations by comparing these parameters estimated after correcting the spectra for vertical velocity and spectral width with the parameters obtained by correcting one factor at a time. They reported that the error could be as large as 100% in rain rate if the vertical velocity is not properly taken into account. They, however, reported that the spectral width has minimal effect on the retrieval of DSD parameters and also on rainfall bulk parameters (less than 10% in R and D0).
In the present analysis, a quantitative study has been set up to see the effects of vertical velocity on DSD retrievals, in general, and rainfall bulk parameters, in particular. Spectral width effects are not considered for error analysis as they have minimal effect on DSD retrievals. However, the spectra are corrected for spectral width, as shown above, for DSD retrieval. Figure 2 shows the percentage difference in rain rate and median volume diameter estimated simply using the following expressions: R%diff = (Rsw – Rfull)100/Rfull and D0%diff = (D0sw – D0full)100/D0full, where the suffix “%diff” represents the difference in percentage, “sw” indicates that the spectra are corrected for the spectral width alone (in other words, not corrected for vertical air velocity), and “full” indicates that the spectra are corrected for both vertical air motion and spectral broadening. DSD retrievals made in all 16 rain events are included in Fig. 2. It is clearly evident from the figure that the error (in R and D0) is increasing with the vertical air velocity. Although there exists some scatter in the diagram, the majority of the points show a linear dependence of the error on vertical velocity. It is interesting to note that the percent difference in R and D0 seems to be different for the same velocity. For instance, for an uncorrected velocity of 0.5 m s−1, the error in the rain rate is 25%–30%, while for the same velocity the error in D0 is only 10%.
From Fig. 2, one may also notice that the error in rain rate is positive in the presence of an updraft, while it is negative during downdraft periods. A reverse trend is seen in the median volume diameter with smaller (larger) values of rain rate (median volume diameter) than the true value in the presence of a downdraft. This is physically realistic and is explained as follows: updrafts reduce the Doppler velocity of raindrops and move the entire Doppler spectra toward a smaller-drop regime. Thus, a large number of smaller drops are required to keep the reflectivity constant. A large number of smaller drops will yield high rain rates for the same reflectivity. At the same time, a large number of smaller drops will drag the median volume diameter toward the lower end. The converse is also true with downdrafts, which increase the Doppler velocities of raindrops and thus affect the bigger-drop end of the spectra.
4. Case studies
In this section, two distinct rain events are considered for a detailed study. These events include a mesoscale convective system and a pure stratiform precipitating system. Drop size distributions retrieved for these rain events are presented in this section. The variations in the DSDs with height as well as with the type of system are discussed at length.
a. A mesoscale convective system
On 22–23 June 2000, a well-developed mesoscale convective system passed over the radar site. It lasted for about 9 h and the accumulated rainfall during this period was ∼40 mm. The mesoscale system showed a high degree of variability in its structure as well as rainfall during this period. There were three short bursts of intense rain, with the first one lasting for more than 80 min (2140–2300 LT) producing more than 20 mm of rainfall. However, the other two were short lived (15 and 20 min each, producing rainfall amounts of 3 and 6 mm, respectively) and occurred after midnight (0021–0031 and 0056–0116 LT).
Figure 3 shows the height–time contour of (a) the reflectivity factor (dBZe), (b) the Doppler velocity (m s−1), and (c) the spectral width (m s−1) of the hydrometeors. The measurements made with the LAWP during 1830–0930 LT on 22–23 June 2000 have been used to construct the above figure, in which LAWP clearly shows precipitation echoes for about 9 h, that is, between 2140 and 0630 LT. For comparison, corresponding surface rain rate and reflectivity estimates from disdrometer measurements are shown in Fig. 3d. As indicated above, both the LAWP and disdrometer measurements show highly varying rainfall patterns. Figure 3a clearly shows strong reflectivities of the order of 40 dBZe and higher in the initial phase of the event, that is, during 2130–2230 LT. Corresponding spectral widths show high values, of the order of 2–3 m s−1, while Doppler velocity profiles show strong gradients with height during this period. Surface rainfall rate and reflectivity values are high during this period with maximum R and Z values reaching 70 mm h−1 and 51 dBZ, respectively. After 2230 LT, all of the moments and surface measurements clearly show a gradual decrease in their strength with time. Precipitation has stopped (or may be too weak to reach the ground) for about 20 min around midnight.
During 0021–0116 LT, the vertical profiles of the reflectivity and spectral width and the surface rainfall rate and reflectivity all show an increase in their magnitudes in two short spells. The reflectivity (both at the surface and aloft) is often >38 dBZ during this period. Furthermore, a sharp enhancement in the reflectivity profile is seen around 5 km. Corresponding Doppler velocity and spectral width profiles show strong gradients around 5 km. After 0116 LT, the R and Z values at the surface are well within 5 mm h−1 and 35 dBZ, respectively. The reflectivity profile shows a clear enhancement of about 10 dBZe at around 4.5 km. At the same altitude, a sharp gradient is observed in the Doppler velocity and spectral width profiles.
UHF profiler measurements can be used to classify the precipitating systems unambiguously (Williams et al. 1995; Rao et al. 2001). The initial phase of the event (between 2130 and 2230 LT), where the profiler shows strong reflectivity and spectral width while the disdrometer measurements show a high surface rainfall rate and reflectivity, can be identified as convection. Note that, during this period, the bright band is completely absent, as expected. The intermediate region or transition region can be identified as the region where all of the moments show a gradual decrease in their strength. Also, the rain can be considered to be transition precipitation, if it shows signatures of both convection and stratiform. One can see, during 0021–0116 LT, both the radar bright band and strong reflectivities. So the entire dataset collected between 2230 and 0116 LT is labeled as transition rain in the present study. The bright band, which is a signature of stratiform rain, is clearly apparent, from Fig. 3, after 0116 LT around the height of the melting layer.
To retrieve DSDs corresponding to different rain regimes, information on clear-air velocity and spectral width during that period is required. Fortunately, the MST radar was operational for more than 6 h (2210–0430) during this event. Figure 4 show time–height sections of the vertical air motion and the spectral width of clear-air echoes obtained with the MST radar for the above period. Though MST radar measurements are available up to a height of 21 km, we restricted the plot to a height of 4 km as the DSD retrievals are performed only between 1.5 and 3.9 km. During this convective period, MST radar observations show strong up- and downdrafts of approximately 2 and −4 m s−1, respectively (Fig. 4). The vertical air velocity and spectral width plots show high variability with height and also with time during the transition period. In the initial phase of the transition region, the radar parameters are smaller in magnitude but show large values in later part, particularly in lower altitudes. Spectral width values of the order of 2 m s−1 are also seen during this period. However, in the stratiform rain regime, the vertical air motions are well within ±1 m s−1 and, in addition, the spectral width values are relatively less.
Using the information obtained from the UHF and VHF profilers, DSD retrievals are performed in the rain region during 2215–0430 LT. The retrievals are performed only when the VHF and UHF measurements are synchronized in time. Figure 5 shows the time–height contours of the gamma parameters (N0, μ, and Λ). It is clearly apparent from the figure that DSD parameters vary significantly from one rain regime to another even within a system. It also shows spatial and temporal coherency in all of the DSD parameters. From Fig. 5, the shape parameter of the gamma distribution is found to be in the range 2–6 in the convective rain regime. During the transition regime, μ not only varied over a wide range but also showed maximum values of the order of ∼12. In the initial phase of the stratiform rain region, μ is found to be less but its value increased with time and reached ∼7 at the end of the observation. The slope parameter shows features similar to those of the shape parameters in all regimes, albeit with different magnitudes. The intercept parameter also shows similar features except for the stratiform rain regime. Here, we have not seen any significant change in the intercept parameter with time. Further, most of the structures seen in the time–height intensity plots of the LAWP and DSD parameters are oriented vertically, perhaps because of the low resolution of the LAWP measurements (11 min in this study). Measurements with better temporal resolution than used here may show inclined structures normally associated with the evolving systems.
The bottom panel in Fig. 5 shows a comparison of the median volume diameter estimated from DSD measurements made by the disdrometer at the surface and by the radar at 1.5 km. It is important to test the profiler-retrieved rainfall parameters with those measured independently by some other source, like a rain gauge or disdrometer. These comparisons will give an indication of the measurements’ accuracy and, thus, ensure the ability of the profilers to estimate the rainfall parameters accurately. The median volume diameter is preferred over other gamma parameters for comparison as it is a more stable parameter than μ or Λ. The D0 at the surface is estimated using DSD measurements made with the disdrometer following two methods. The first method fits the gamma function to the raindrop distribution and estimates the gamma parameters and, then, employs Eq. (9). The second method follows the Tokay and Short (1996) scheme, that is, the method of moments. In Fig. 5, both of the curves are included and they show very good agreement.
For better comparison with the profiler measurements, DSD measurements made by the disdrometer are integrated over 11 min to match the temporal resolution of the profiler. Further, following Rajopadhyaya et al. (1998), the time series data of D0 have been shifted right in time for about 4 min (the time required for a drop with a fall velocity of 6 m s−1 to reach the ground from 1.5 km). Note that the time shift is calculated by assuming that the vertical air motion is zero and any deviation from this assumption (as often happens in convection) will change the time shift. From Fig. 5, one can see the excellent agreement in the D0 values, except for a few data points, derived from disdrometer and profiler measurements. The discrepancy between the disdrometer and radar measurements is not really surprising considering the following factors: 1) the huge differences in sampling volumes, as profiler measurements are integrated over a large volume (depends on beamwidth, range, and pulselength), while disdrometer measurements are point measurements (sampling area is 50 cm2); 2) the advection of precipitation—if the horizontal winds are strong, the profiler-sampled rain may fall at some other location far from the disdrometer, while the disdrometer may sample a completely different DSD; in this study, no correction has been made for the movement of the storm; and 3) the change in the DSD distribution itself during its descent. For instance, several microphysical processes can occur between 1.5 km and the ground, such as evaporation. Several earlier studies have shown that evaporation plays a dominant role in the continental precipitation, particularly in the lower part of the troposphere, that is, below 2 km (Ferrier et al. 1996). The rate of evaporation depends on the background atmospheric conditions, like temperature and the humidity fields. The excellent agreement (in D0) between the disdrometer and profiler measurements reinforces the accuracy of the retrieval technique and the validity of assumptions (DSD following gamma distribution, etc.) involved in the technique.
b. Case 2: Stratiform precipitation
A widespread stratiform rain was observed for 2 days (3–4 July 2000) with very low surface rainfall. Except for a period of 16 min, between 1228 and 1244 LT on 4 July 2000, the surface rainfall rate never exceeded 5 mm h−1 (92% of observations show a rain rate <2 mm h−1). The rainfall was seen for more than 24 h in these 2 days, producing an accumulated rain of 12.5 mm (including 3.3 mm of rainfall that occurred in 16 min).
Though LAWP measurements are available for most of the above time period, except for 15 h on 4 July 2000, MST radar measurements are not made continuously. They are available only in short spells with the duration of each spell ranging from 90 min to 4 h. Time–height sections of the reflectivity, Doppler velocity, and spectral width of hydrometeors as measured by LAWP are shown in Fig. 6. Similar plots for the vertical air motion and spectral width observed with the MST radar are shown in Fig. 7. The boxes in the reflectivity plot (Fig. 6) indicate the time, when we have MST radar measurements. Since disdrometer measurements are not available on this day, the rain rate information has taken from a collocated instrument, optical rain gauge (ORG-815; Scientific Technology, Inc.). The bottom panel in Fig. 6 shows the variation of R with time for the above 2 days.
It is clearly evident from Fig. 6 that there exists a clear bright band, almost throughout the observational period, with sharp enhancement in the reflectivity and strong gradients in the Doppler velocity and spectral width plots at about 4.2 km, indicating that the rain is associated with stratiform clouds. Vertical winds, wherever available, measured with the MST radar (Fig. 7), are also less (within ±1 m s−1). Except at some heights and on some occasions, the spectral width is relatively small. Note that the radar bright band is not continuous throughout the observational period. There exist some breaks in between, which may be associated with the transition region. In addition, on occasion, the cloud tops do not reach the 0°C isotherm level (like warm rain).
As indicated above, MST radar measurements are not continuous (in this case). As a result, the time–height section map shows (not included here) lot of gaps. Hence, we decided to examine the DSD variations (gamma parameters) statistically. Figure 8 show histograms of the gamma parameters and the median volume diameter obtained in the height region 1.5–3.9 km during the above period. The shape parameter shows both positive and negative values with 93% of the values lying between −3 and 2. It also shows a peak close to zero, closely following the classical exponential distribution (Marshall and Palmer 1948). This result is consistent with earlier studies reporting a large number of smaller drops in stratiform rain. For about 96% of the slope, values are found to be in the range 1–7 mm−1 with 72% of the values lying between 3 and 5. This value is close to the value reported by Marshall and Palmer (1948) for stratiform rain. The major portion (∼90%) of the median volume diameter distribution lies within 0.5–1.2 mm, with a mean value of 0.86 mm.
5. Statistical characteristics of DSD
In this section, the DSD information obtained from all 16 rain events is combined to discuss the variation of DSD with height and also with the type of rain system. For the present analysis, nearly 110 stacked simultaneous (MST and LAWP) profiles were used. Obviously, these data may not be sufficient for a detailed classification and discussion of the DSD variations as a function of rain system. We may not have enough samples for each group to discuss the statistical variations in a meaningful way. To overcome this problem, we have divided the DSD data into two groups (stratiform and convection) based on the reflectivity. The profile is considered to be convective if the reflectivity at any height (below 4 km) is more than a threshold value of 38 dBZe. We arrived at this threshold after browsing through several research reports available in the literature.
Figure 9 shows contour frequency by altitude diagrams (CFADs) for the intercept, slope, and shape parameters and also for the median volume diameter corresponding to (a) stratiform and (b) convective rain. Mean profiles are estimated for all of the parameters and are overlaid on CFADs. The abscissa for the shape and slope parameters is limited to ranging from −3 to 12 and from 0 to 15, respectively, in Fig. 9. Although we have observed values outside the above limits (in case studies), the percent occurrence of those values is less. Moreover, for μ > 9, the spectrum becomes narrower and the fitting becomes unrealistic. This may happen in the presence of intense turbulence, where the spectral width correction makes the UHF spectra narrow. Similarly, in the case of light rain, it is possible that the clear-air echo will corrupt the DSD retrievals. This increases the smaller number of drops drastically, thus reducing the median volume diameter and μ. In our analysis, we have either taken care of this effect, wherever possible, or omitted the spectra from retrieving DSDs. At most of the heights and also for most of the parameters in both of the rain regimes, the mode and mean of the distribution are nearly equal, indicating that the mean of the distribution can be used to describe or characterize the distribution.
Comparisons of gamma parameters and the median volume diameter obtained in convective precipitation with those obtained in stratiform precipitation revealed many interesting features.
There is significant overlap between the parameter distributions; however, their mean values show large differences between the stratiform and convective rain. The distribution of μ, D0 is, in general, broader in convection than in stratiform rain, particularly below 2.5 km. Note that μ values obtained in case 2, sometimes (∼10%), are found to be negative during stratiform precipitation. However, after compiling all of the stratiform events, it is found that the percentage occurrence of negative μ values is less than 10% at most of the heights. Manual inspection of the data reveals that the percent occurrence of negative μ values in stratiform rain is about 5%–8% in the height region considered. However, more than 10% of the negative μ values are found in convective rain. Several earlier studies have shown that negative μs are generally associated with orographic rain (Ulbrich 1983). As expected, and also as seen in our case studies, the median volume diameter is slightly more for convective rain than for stratiform precipitation at different heights. The spread of the N0 distribution is more or less similar in both of the rain regimes; however, the mean N0 (not shown here) is higher in the convection than in the stratiform rain regime. This result is consistent with published disdrometer studies (Tokay and Short 1996). Tokay and Short (1996) have observed a sudden jump in N0 values from one rain regime to other and, in fact, they used this property to separate the convection from the stratiform precipitation.
In addition, the vertical variation of the above parameters is distinctly different in different rain regimes. For instance, during convection μ and Λ changed significantly with altitude, whereas such a significant variation is not seen in the stratiform rain regime. The parameters show a decreasing trend with height, indicating that there is significant evaporation occurring in most of the cases considered here. A detailed discussion of this point is presented in the next section. We see a small decreasing trend in stratiform rain, but in convection it is considerable. The evaporation seems to be significant in the lower troposphere (below 2.4 km) as we see large gradients in this height region. Experiments conducted at Darwin also indicated that the evaporation dominates in the lower troposphere, below 2 km, particularly for continental rain (Ferrier et al. 1996).
6. Summary and discussion
The data collected with the Indian MST radar and the LAWP during a rainy season (southwest monsoon) in 2000 have been used to study the variations of the drop size distribution (and parameters) with height and also with the type of precipitating system. Sixteen events are considered for the present study, from which two distinctly different case studies have been presented in detail. They include a mesoscale convective system and a pure stratiform precipitating system. The dual-frequency algorithm has been employed to retrieve the DSD accurately. The major advantage of this algorithm is that it utilizes the sensitivities of the VHF and UHF radars to refractivity fluctuations and precipitation, respectively, in the best possible way. A detailed statistical error analysis of the effects of vertical air motion on DSD retrievals revealed that the error in rain rate could be as large as 50% for an uncorrected vertical velocity of 1 m s−1. Rajopadhyaya et al. (1999) have done a similar analysis for a rain event in Darwin and arrived at a similar conclusion. They have also shown that the spectral width corrections are of second-order importance, but they, indeed, remain as a bias.
The statistical plots of the gamma parameters and the median volume diameter show large differences from stratiform rain to convective rain. Note that such differences are also seen in our case studies, presented in section 4. As expected, the variations of the DSD parameters with height are much more pronounced in the convective category compared to those in the stratiform regime. Although there exists considerable overlap in the DSD parameter distribution in the two rain regimes, mean profiles are distinctly different. Furthermore, mean values of μ and Λ are found to increase with decreasing height in both rain regimes, albeit with different slopes. The decrease in μ with increasing height indicates that there may be evaporation taking place in the cases considered here. The evaporation seems to be more in the case of convection as the slope of μ is large in convection, in particular below 2.4 km. A numerical study by Ferrier et al. (1996) confirmed this particular effect of evaporation is greater below 2 km. The other physical processes one can think of for the narrowing of DSD are drop sorting by updrafts, breakup of bigger drops, and the loss of smaller drops through a collision and coalescence mechanism. It is well established that the medium-size drops increase their mass by collecting smaller drops while descending. Drop sorting by updrafts also needs to be considered here. Present observations are taken from the southwest monsoon season, when the ground temperatures and convection are high. The strong updrafts normally associated with these convective cells will not allow the smaller drops to fall, but may not hold bigger drops aloft because of their weight. As a result, at lower heights, there will be a shortage of smaller drops. In general, the absence or decrease of smaller drops results in an increase in the median volume diameter (Rajopadhyaya et al. 1993). So, one can expect an increase in the median volume diameter with decreasing height. However, our measurements show a completely opposite D0 profile with large values of D0 at higher heights and small values at lower heights. This could be possible only if there is a loss of larger drops through some breakup mechanism (collisional or spontaneous breakup). The likelihood of this, indeed, is very high. Note that the mean profile of Λ looks nearly similar to that of μ, corroborating the above idea.
The results obtained in the present study can be compared and discussed in light of similar studies reported elsewhere (McKague et al. 1998; Cifelli et al. 2000). McKague et al. (1998) has not stratified the rain DSD statistics as a function of rain type but, rather, presented the mean and standard deviation of the rain DSD parameters estimated from the VHF and UHF wind profiler measurements made at Darwin. The mean (standard deviation) μ and D0 obtained by McKague et al. (1998) are, respectively, 4.56 (3.08) and 1.12 (0.388) and match well with our results for the stratiform rain regime. Cifelli et al. (2000) used the same dataset and separated the precipitation into three rain regimes based on a modified Williams et al. (1995) classification scheme. The comparison of the shape parameter distribution obtained here with that reported at Darwin reveals some interesting features. First, the mean μ profile is strikingly similar at both the places with a decreasing trend with increasing height. At both the places, this trend is much more pronounced in the convective category, particularly below 2.4 km. However, the vertical profile of D0 observed in the present study seems to be different from that observed at Darwin. The mean D0 profile at Gadanki shows an increasing trend with height, while an opposite feature (decreasing trend) is seen at Darwin. This difference is clearly visible in the convective rain regime. The observed increase in D0 (and also μ) with a decrease in altitude at Darwin is ascribed to evaporation (Cifelli et al. 2000). However, at Gadanki, as explained above, other microphysical processes like the breakup of bigger drops may be occurring concomitantly with evaporation.
Earlier studies using JW disdrometer measurements made at Gadanki clearly demonstrated that there exist systematic differences in rain DSDs from the southwest monsoon (June–September) to the northeast monsoon season (October–November) (Rao et al. 2001; Kozu et al. 2006). The latter have observed fewer smaller drops in the southwest monsoon than in the northeast monsoon. As seen above, the present observations show a decreasing trend of μ with increasing height, indicating significant evaporation during the raindrop descent. In other words, the evaporation reduces the smaller drops considerably and this result is consistent with those reported by Kozu et al. (2006). However, we were not able to study the vertical variation of rain DSDs in different seasons, as our observations are limited to the southwest monsoon in the present study. Such a study has been planned and will be carried out in the near future. Nevertheless, the present observations provide an opportunity to characterize the rain DSDs in the southwest monsoon season and to study the DSD variations as a function of height and rain type. These kinds of statistics are imperative in order to study the vertical variation of relationships between integral parameters of the gamma distribution (Rao et al. 2006) and also the Z–R relation (Cifelli et al. 2000).
* Current affiliation: Space Physics Laboratory, Trivandrum, India
Corresponding author address: Dr. T. Narayana Rao, National Atmospheric Research Laboratory, SVU Campus, P.O. Box No. 123, Prakasham Nagar, Tirupati, 517 502, AP, India. Email: email@example.com, firstname.lastname@example.org