a. L-band wind profiler

In the present study, an L-band wind profiler is utilized to classify the type of precipitating systems and to estimate the rain integral parameters from its Doppler spectra. The basic features of the profiler and experimental specification file (ESF) information during precipitation studies are presented in Table 1. The three moments of the Doppler spectra, namely the zeroth, first, and second, are calculated by the offline data processing. The three moments have physical meaning such as returned power (in arbitrary unit), Doppler shift (which subsequently gives the radial velocity of the target and its diameter), and variance or spectral width of the spectrum, respectively (Ralph et al. 1996). For the vertical incident beam of profiler, the fall velocity of raindrop is given by the following expression:

View Expanded

where F_d is the Doppler shift of the precipitation echoes spectrum and λ is the wavelength of the radar signal.

From the wind profiler, the mean drop diameter (D_mean) is calculated by utilizing the equation as given by Atlas and Ulbrich (1977):

View Expanded

where γ = 17.67 m s⁻¹ cm^−0.67 and V_t is the terminal velocity of the raindrops.

During convective precipitation, the presence of updrafts–downdrafts has a direct effect on the fall velocity of the hydrometeor particles. In this regard, Cifelli and Rutledge (1994) studied the composite profiles of vertical air motion during convective, transition, and stratiform rain. In a convective region they reported the double-peaked ascent profile with a peak located near 3 and 9 km. The reported peaks of the composite profiles are of the order of 1–2 m s⁻¹. The composite profile in the transition region showed subsidence throughout the majority of the troposphere with dual peaks of comparable magnitudes at upper and lower levels. In the stratiform region, the composite profiles showed descending motion occurring below ∼8.5 km, with a peak near the melting level, and double-peak ascent structure in the upper troposphere, with a magnitude of ≤0.5 m s⁻¹. It is important to mention that during the convective situation the magnitude of the vertical air velocity is <1.0 m s⁻¹ at lower heights, and during transition and stratiform rain it is <0.5 m s⁻¹. Similar results are also reported by Balsley et al. (1988) and Kishore et al. (2005). These results are important in the context that for the present study the rain integral parameters are estimated with the help of the L-band wind profiler at 0.6 km, thereby they are least affected by the clear-air vertical air motion. Therefore, for the present study it is assumed that from 0.6 km the raindrops are falling with terminal velocity and therefore that mean diameters from the profiler are estimated without applying the vertical air motion correction. Rajopadhyaya et al. (1998) reported that there is an almost linear dependence of the relative accuracy of median diameter with the magnitude of mean vertical velocity. It is notable that these errors are about 20% for a vertical velocity of 1.3 m s⁻¹, and when the vertical velocity is 2.3 m s⁻¹ the error is of about 50%. Kirankumar et al. (2008) pointed out that for an uncorrected velocity of 0.5 m s⁻¹ the error in median diameter is around 10%. Sharma et al. (2008) have reported that during convective rain, when the vertical clear-air velocity correction is applied, the root-mean-square error (rmse) of D_m estimation by the L-band profiler at 1.8 km is reduced by ∼11%. Similarly during the stratiform rain it is reduced by ∼7%.

Further, for the meteorological applications, the wind profilers suffer from certain limitations. During clear-air measurements the clear-air wind profiler receiver has a linear response. However, during rain, when the backscattered signal is very strong, the profiler receiver has a nonlinear response; that is, an increase in the incident power produces only a small increase in the measured signal power (Ralph et al. 1995). At some point the receiver even becomes completely saturated and further increase in incident power leads to no measurable increase in signal power. Therefore, it becomes very difficult to calibrate the wind profilers, which implies that radar reflectivity factor (Z) cannot be determined directly. For the present study the L-band wind profiler is calibrated with the help of JWD by using the nonparametric method as described by Konwar et al. (2008). For the L-band wind profiler the measured parameters are available from 300 m onward, but because of the presence of ground clutter data from 600 m onward only are considered.

b. VHF wind profiler

The VHF profiler (53 MHz) is sensitive to clear-air echoes because of the refractive index gradient in clear air. The main features of VHF profiler and ESF information during precipitation studies are also presented in Table 1. The estimation of clear-air vertical velocity during rain is carried out with the help of the zenith beam of the profiler. For the rain events under study, separate peaks for precipitation and clear-air echoes are observed during heavy rain. The clear-air spectral peaks are analyzed after separating them from the rain echoes. Further, the clear-air vertical velocity is calculated by using the Eq. (1). The positive and negative Doppler shifts signify the downdrafts and updrafts, respectively.

c. Joss–Waldvogel disdrometer

The JWD is a standard tool for precipitation measurements such as DSD, rainfall intensity R, rain accumulation, and radar reflectivity factor Z (Waldvogel 1974). The range of drop diameters that can be measured spans from 0.3 to 5.0 mm with an accuracy of 5%. The limitation of JWD is that it is sensitive to background noise. Laboratory measurements have revealed that a noise level of 50 dB or less had little effect on signals corresponding to drop diameters of 0.3–0.4 mm, whereas a noise level of 55 dB reduced the detected number of such sized drops significantly. When noise level reached 70 dB, detection of drops of 0.3–0.8 mm-diameter is almost completely suppressed (Tokay et al. 2003). During high rain, lower channels, that is, first and second, show the zero number of drops that are considered because of the dead time error. During the Tropical Rainfall Measuring Mission (TRMM) ground validation field campaign in central Florida, it is observed that JWD underestimates the number of small drops relative to the 2D video disdrometer (Williams et al. 2000). It is also noticed that a continuous increase in the number of drops toward smaller size was only evident in video disdrometer at rain rate above 20 mm h⁻¹ (Tokay et al. 2001). Despite these limitations, JWD is still considered a standard tool for the measurements of the bulk descriptors of rainfall. The bulk descriptors of rainfall such as rainfall intensity (R), radar reflectivity factor (Z), mass weighted mean diameter (D_m), and scaling parameter for concentration or normalized intercept parameter (N*₀) (Testud et al. 2001) are calculated by the following expressions:

View Expanded

View Expanded

View Expanded

View Expanded

where A is a collecting area of JWD, T is the integration time, and n_i and D_i are number of drops and drop diameter (mm) of the ith channel of JWD, respectively. The υ(D_i) is the terminal velocity (m s⁻¹) of the raindrops in the ith channel and is estimated by V(D_i) = 9.65 – 10.3 exp(−6.D_i) (Gunn and Kinzer 1949). LWC is the liquid water content, that is, the third moment of the DSD spectra, and ρ_w is the density of the water.

For the validation of JWD, the rain intensity measured by JWD is compared with optical rain gage (ORG) measurements. From the available simultaneous dataset of JWD and ORG, the comparison is carried out for seven rain events. For the present study, the rain intensity ≥0.5 mm h⁻¹ are considered to be rainy minutes. The scatterplot for overall JWD- and ORG-measured rain intensity is shown in Fig. 1. A linear fit is carried out to the scatterplot. The error statistics is provided in the figure panel. The bias is estimated with respect to JWD observations. It is observed that the gradient of the linear fit is 1.30. The positive bias indicates that the JWD-measured rain rate is overestimated relative to ORG measurements. The correlation coefficient is reasonably good between these two measurements. Further, for individual rain events, the linear fit parameters and error statistics for the simultaneous measurements of rain intensity from these two measuring systems are provided in Table 2. The total rain accumulation of rain with JWD and ORG is compared with varying statistical errors. It is noticed that the JWD is consistently overestimating the rain intensity. At Gadanki, similar results are also reported by Rao et al. (2001).

d. Intercomparison of the L-band profiler and JWD estimated rain integral parameters

The intercomparison of the L-band profiler and JWD-measured mean diameter (D_mean) and reflectivity (dBZ) are also carried out for all the selected events. The D_mean from L-band wind profiler and JWD are estimated by using the Eqs. (2) and (5), respectively. The L-band profiler measurements are at 0.6 km. To make the near-simultaneous data points of these two systems, a time lag is incorporated because of the falling raindrops from a height of 0.60 km. The time lag is calculated with the help of a fall velocity parameter (V_D) at 0.60 km. To match the different integration time of the two systems, averaging of the DSD spectra at ground is carried out. The integration time for each vertical beam of profiler is nearly 3 min. Therefore, DSDs from JWD are averaged for 3 min. Hence, the mean D_m measurements from both the sensors are the average value of 3 min. The scatterplots for overall JWD- and profiler-measured D_mean and dBZ are shown in Figs. 2a and 2b, respectively. A linear fit is carried out to these scatterplots. The error statistics is provided in the respective figure panels. Bias is estimated with respect to JWD observations. As evident from the negative bias in both the panels, although overall JWD measurements are underestimated relative to profiler measurements, reasonably good agreement is found between these two measurements. The observed negative biasing may be attributed to the various factors such as (i) no correction of clear-air vertical velocity to the hydrometeor fall velocities, as the clear-air vertical air motion at the lower heights is not available; (ii) the effect of evaporation while raindrops fall from 0.6 km to the ground; (iii) different approach of measurements, that is, while profiler measurements are reflectivity weighted (∼D⁶) and JWD measurements are mass weighted (∼D³); and (iv) different sampling volumes of the two systems.

a. Characteristics of rain integral parameters during convective, transition, and stratiform rain at Gadanki

From the prepared dataset of DSDs, the occurrence of D_m is studied in terms of frequency distribution during three types of rain. The frequency distribution of D_m during convective rain is divided into two groups: convective I (R ≤ 10 mm h⁻¹) and convective II (R > 10 mm h⁻¹). The frequency distributions of the occurrence of D_m during convective I, convective II, transition, and stratiform rain are shown in Figs. 4a, 4b, 4c, and 4d, respectively. The mean values of D_m during convective rain for these two ranges are 1.56 and 2.18 mm, with a standard deviation (std dev) of 0.35 and 0.49 mm, respectively. During the transition and stratiform rain, mean values of D_m are found to be 1.56 and 1.62 mm with a standard deviation of 0.39 and 0.26 mm, respectively. During convective II (R > 10 mm h⁻¹), larger drops are observed quite significantly compared to convective I, transition, and stratiform rain. It is interesting to note that, for R < 10 mm h⁻¹, D_m is larger for stratiform rain compared to convective I events. To further study the variability of D_m with respect to R, the scatterplots of D_m versus R during convective, transition, and stratiform rain are shown in Figs. 5a, 5b, and 5c, respectively. The power-law equations are fitted to these scatterplots. The coefficient and exponent values of the fitted power-law equations are provided in the respective figure panels. For D_m–R plots, the coefficients and exponents are in the order of S > C > T and T > C > S, respectively. This nature of variation of coefficient and exponent indicates that, for a given rain rate, overall mean raindrops are bigger during stratiform regimes but the sensitivity of D_m with respect to R is minimum in stratiform rain. This result is consistent with the fact that, at lower rain intensity, the stratiform regime has larger mean drops compared to convective and transition regimes, but, on the other hand, at higher rain intensity range the D_m is larger in convective rain relative to other two types of rain, as noticed in Figs. 4a–d also. To study the variability of D_m with respect to Z, the scatterplots for D_m versus Z during convective, transition, and stratiform rain are shown in Figs. 6a, 6b, and 6c, respectively. The power-law equations are fitted to these scatterplots. The values of the coefficient and exponent of the derived power-law equations for each type of rain are provided in the respective figure panels. The coefficients and exponents are in the order of S > C > T and T > C > S, respectively, thereby indicating that overall mean raindrops are bigger during the S regimes, but by virtue of the lowest value of the exponent the sensitivity of the D_m with respect to Z is minimum. These results are similar to D_m–R relations. The characteristic of D_m at Gadanki is very similar in nature to the results reported by Testud et al. (2001). They studied the frequency distribution of the occurrence of D_m with respect to types of rain as well as rain intensity over the west Pacific Ocean under the TOGA COARE program. In the range of rain intensity 0 < R ≤ 10 mm h⁻¹, they reported the mean values of D_m for stratiform and convective rain to be 1.30 and 1.19 mm, respectively. For convective rain, in the rain intensity range of 10 < R ≤ 30 mm h⁻¹ the mean value of D_m is 1.40 mm, and for the 30 < R ≤ 100 mm h⁻¹ it is found to be 1.78 mm. It is also important to point out that the higher value of D_m for the convective rain (R ≥ 10 mm h⁻¹) at Gadanki relative to the TOGA COARE observation may be due to the classification of the rain into three types of rain at Gadanki, whereas for the latter work, rain events were classified only as convective and stratiform. At lower rain intensity, similar results were also reported by Tokay and Short (1996) and Atlas et al. (2000). For the stratiform rain, Maki et al. (2001) also reported larger drop spectrum and reflectivity trough for the same liquid water content, relative to the convective center. It is pointed out by Stewart et al. (1984) that the aggregation of hydrometeors at the height of the bright band produces large raindrops in the stratiform region.

The scatterplots for Z versus R during convective, transition, and stratiform rain are shown in Fig. 7a, 7b, and 7c, respectively. The power-law equations are fitted to these scatterplots and the values of coefficients and exponent for each type of rain are provided in the respective figure panels. It is observed that coefficients for Z–R relations are predominantly larger during convective and stratiform rain compared to transition rain. For the overall Z–R relations the coefficients and exponents are in the order of C > S > T and T > C > S. The similar nature of the result is also pointed out by Atlas and Ulbrich (2006). The coefficient and exponent of the Z–R relation for each type of rain for the selected rain events are estimated separately and are provided in Table 4. It is observed that, eventwise, there is no systematic variation of coefficients and exponents among these three different regimes. It is also noticed that there are wide variations in the coefficient values during the convective rain compared to stratiform rain. The large difference in the coefficients between 18 August (1865) and 22 June (129) may be attributed to the different magnitudes of the prevailing updrafts–downdraft. The general observed feature of stratiform rain, that is, large coefficients and small exponents, may be attributed to the melting of large snow flakes below a strong bright band (Atlas and Ulbrich 2006). In their study of microphysical interpretation of the Z–R relation, Steiner et al. (2004) pointed out that the variability of the raindrop size distribution is bounded by either size or number controlled conditions, with conditions of a coordinated mixed control embedded in between those extremes. On the basis of raindrop spectra observations from JWD, Smith and Krajewski (1993) found the limiting values of the exponent b for number controlled and size controlled to be 1 ≤ b < 1.79. From our observations at Gadanki, on average it is found that the microphysical process are different for convective, transition, and stratiform rain, but by virtue of low values of the exponent b (in Z = AR^b), the convective and stratiform events are primarily number controlled, and by virtue of a high value of b, transition events are either size or mixed controlled phenomena. Furthermore, the variability of the coefficient and exponents of Z–R relations during these three types of rain at Gadanki are compared with the results reported by various researchers over different regions of the globe. The numerous Z–R relations, as developed by various researchers, for individual as well as for combined rain events are provided in Table 5. The proposed Z–R relations for individual rain events by Ulbrich and Atlas (2007) and Atlas et al. (1999) are at Arecibo, Puerto Rico, and Kapingamarangi Atoll, respectively. The proposed Z–R relations for individual and combined rain events by Rao et al. (2001) are at Gadanki, India. At Gadanki, for the combined rain events, the DSD observations are during September–December 1997 and May–August 1999. Maki et al. (2001) derived the Z–R relations from the 15 continental squall lines events. Their observations are during 26 December 1997 to 3 March 1998 at Darwin, Australia. It is clear that even for each type of rain there is no distinct Z–R relation. For example the coefficient A in the convective rain is varying from 99 to 906 and exponent b is varying from 1.08 to 1.51. Similarly for stratiform rain the values of the coefficient and exponent are found to be varying from 89 to 865 and 1.01 to 1.90, respectively. These variations indicate that different microphysical processes are involved from system to system, which results in wide ranges of DSDs. It is also obvious from the reported results that the two extreme microphysical processes, that is, number controlled (b ∼ 1.0) and size controlled (b ∼ 1.80), occur both in convective as well as in stratiform rain.

The variability of DSDs during these three rain regimes can also be understood with the help of normalized intercept parameter N*₀. The scatterplots for N*₀ versus R during convective, transition, and stratiform rain are shown in Figs. 8a, 8b, and 8c, respectively. The values of the coefficient and the exponent of fitted power law are shown in the respective figure panels. The coefficients and exponents are in the order of T > C > S and S > T > C, respectively. The N*₀–R relations shows distinct characteristics for the three types of rain. The smallest value of the coefficient of N*₀–R relation during stratiform rain indicates the presence of larger mean raindrops (N*₀ proportional to 1/D_m) compared to convective and transition rain. During stratiform rain, the maximum value of the exponent signifies the maximum sensitivity of N*₀ with respect to R. It indicates that, by virtue of the least sensitivity of D_m with respect to R during stratiform rain, the term LWC/D_m in the N*₀ expression is not constant and therefore R is directly proportional to LWC. The correlation coefficients during convective, transition, and stratiform rain are found to be 0.20, 0.24, and 0.46, respectively. The maximum value of the correlation coefficient during stratiform rain for N*₀–R relative to convective and transition rain further signifies the maximum sensitivity of N*₀ with respect to R during stratiform rain. A similar result is also reported by Testud et al. (2001). They pointed out that, when no distinction is made between convective and stratiform rain, the correlation coefficient for N*₀–R is reported around 0.40 with an exponent value of 1.31. However, after separating the convective and stratiform DSD spectra, the correlation coefficient reduced significantly for the convective, that is, almost to 0, with a very small value of exponent. Whereas for the stratiform spectra the correlation coefficient is reduced to 0.22, but the exponent increased to 2.48.

b. Case study for the variability of rain integral parameters with respect to different microphysical process in the convective and stratiform rain

The comparison of the temporal variation of mean diameter as measured from the JWD and L-band wind profiler is carried out for different rain events. The temporal variation of D_m,(profiler) and D_m,(JWD) on 17–18 May, 26 August, 21–22 June, 22–23 June, and 18 August are shown in Figs. 9a, 9b, 9c, 9d, and 9e, respectively. The classification of the different types of rain, as proposed by Williams et al. (1995) and Testud et al. (2001), are also shown in the same figure. The overall error statistics in terms of correlation coefficient and bias is provided in the respective figure panels. The biases are estimated with respect to JWD measurement. In all the cases the correlation coefficients are found to be ≥0.81 and bias is found to be ≤−0.73 mm. The negative bias indicates that JWD measurements are underestimated with varying magnitudes relative to profiler measurements. The maximum bias is observed on 17–18 May (Fig. 9a). On this day the bias is quite significant during convective and stratiform rain relative to transition rain. The minimum bias is found to be −0.15 mm on 21–22 June. It is to be mentioned that on this day measurements are available for stratiform rain only. Similarly, the temporal variations of radar reflectivity factor (dBZ) as measured from the JWD and profiler for the rain event on these five days are shown in Figs. 10a, 10b, 10c, 10d, and 10e, respectively. The overall error statistics in terms of correlation coefficient and bias is provided in the respective figure panels. In all the cases, the correlation coefficients are found to be ≥0.80 and bias is found to be ≤−4.18 dBZ. The negative bias indicates that JWD measurements are underestimated compared to profiler measurements, though with varying magnitudes. The maximum bias of the value −4.18 dBZ is observed on 17–18 May (Fig. 10a) and the minimum of −0.92 dBZ is observed on 22–23 June (Fig. 10d). For the dBZ measurements, the correlation is better compared to mean diameter measurements. It is attributed to the calibration of the profiler with the JWD. The mean values of D_m and dBZ along with their standard deviation during each regime for these five rain events are provided in Table 6. In all the cases the convective rain is dominated by bigger raindrops relative to stratiform rain. The mean D_m > 2 mm is observed during all the convective regimes, except on 22–23 June where it is found to be 1.71 mm. In the stratiform regimes the largest mean raindrop is found on 17–18 May and the minimum on 26 August. In both the situations, that is, convective and stratiform, there is no consistency in the proportionality of D_m and dBZ values.

For better understanding of the variability of rain integral parameters, a detailed case study of some of the rain events is carried out during convective and stratiform rain. For the convective situations, two rain events on 18 August 1999 and 22 June 2000 are selected, where distinctly different characteristics of the studied parameters are observed. The variability of rain integral parameters during convective events is studied with the help of clear-air vertical velocity from VHF wind profiler. Similarly, stratiform rain events on 17–18 May 1999, 26 August 1999, and 23 June 2000 are selected where the distinct characteristics of rain parameters are observed. The stratiform rain events are studied with the help of the characteristics of the bright band as observed from the L-band wind profiler.

c. The Z/D_m–R relation and its application in rain retrieval

As a result of these variations in rain integral parameters, even for each type of rain, there are constraints to propose a generalized empirical relation between the rain integral parameters, that is, D_m–R or Z–R. In convective rain these constraints are due to different prevailing microphysical process by virtue of different physical and dynamical natures of storms that governed the characteristics of DSDs, that is, coalescence, breakup, evaporation, strength of updrafts–downdrafts, and sorting of drops by drafts (Rosenfeld and Ulbrich 2003). Even for stratiform rain, which is considered to consist of homogeneous and uniform rain, there is significant variation in the DSDs because of the variation of the thickness of the bright band. Therefore it is assumed that the different microphysical processes are appropriately manifested in the drop size distribution and thereby on mean drop diameter D_m. As the empirical relations involving a single measured parameter may not give desired rain retrieval accuracy (Testud et al. 2001), one more parameter in term of D_m, which is very much a direct indicator of microphysical processes, is considered in the new empirical relation. In the present study the Z has been normalized by the D_m. The empirical relations are found out by fitting the power-law equations to Z/D_m–R scatterplots for each rain type. The scatterplots of Z/D_m versus R for total data during convective, transition, and stratiform rain are shown in Figs. 13a, 13b, and 13c, respectively. The values of the coefficients and exponents of the fitted power law are provided in the respective figure panels. The coefficients and exponent of these relations are in the order of S > C > T and T > C > S, respectively. The values of the coefficients and exponents of the power law for individual rain events are provided in Table 7. Furthermore, the correlation coefficients during each type of rain for all developed empirical relations are provided in Table 8. It is observed that, for each type of rain, the correlation coefficients are in the order of Z/D_m–R > Z–R > D_m–Z > D_m–R. It is also observed that, during different types of rain, there is a systematic variation in the exponent for each relation. They are in the order of T > C > S. As the overall correlation coefficient is maximum for the Z/D_m–R relations, thereby signifying the better estimation of rain intensity by using the Z/D_m–R relation compared to other relations. The Z/D_m–R relation will be suitable for estimating the rainfall intensity by scanning polarimetric radar or vertically looking profiler radars where multivariable measurements such as Z and D_m are possible to measure.

The comparison of the rain intensity as estimated from Z–R and Z/D_m–R relations, during each type of rain, is carried out on 22 and 23 June 2000. For this purpose, Z and D_m are estimated by the DSD spectra from the JWD measurements and the rain retrieval is validated with the observed rain rate by JWD. The temporal variation of estimated rain intensity from Z–R and Z/D_m–R relations and its comparison with observed values during convective, transition, and stratiform rain are shown in Figs. 14a, 14b, and 14c, respectively. The error statistics of this retrieval in terms of correlation coefficient and rmse is provided in the respective figure panels. For each type of rain, rmse is reduced and correlation coefficient is increased for the Z/D_m–R relation compared to the Z–R relation. The intercomparisons of rain retrieval by Z–R and Z/D_m–R relations for the other selected rain events are provided in Table 9. From these error statistics, it is very clear that there is an improvement in rain retrieval by using the Z/D_m–R relation compared to conventional Z–R relation. The rmse for rain retrieval even found to reduce by 46% in some events irrespective of types of rain. The minimum reduction in rmse is found to be by 19%. Huggel et al. (1996) reported that the rmse in rain retrieval is reduced by 20%–40% relative to conventional Z–R relation by using the dual parameter, Z and ΔZ_e. Testud et al. (2001) also found that there is a significant improvement in the error statistics of the rain retrieval with the normalized approach. They reported that by taking into account the normalization by N*₀ (for all types of data) the correlation coefficient for rain retrieval is increased from 0.84 to 0.98 and the standard deviation parameter is reduced from 0.26 to 0.12.