Raindrop Size Distributions of North Indian Ocean Tropical Cyclones Observed at the Coastal and Inland Stations in South India

: The current study summarizes the raindrop size distributions (RSDs) characteristic of the North Indian Ocean (NIO) tropical cyclones (TCs) measured with ground ‐ based disdrometers installed at the coastal (Thiruvananthapuram, 8.5335°N, 76.9047°E) and inland (Kadapa, 14.4742°N, 78.7098°E) stations in south India. The NIO TCs observed at the coastal station showed more mid ‐ and large ‐ size drops (>1 mm) than the inland station. On the other hand, for both inland and coastal stations, small and mid ‐ size drops (<3 mm) primarily contributed to the total number concentration and rainfall rate. The RSDs of the NIO TCs segregated into precipitation types (stratiform and convective) demonstrated the presence of more mid ‐ and large ‐ size drops at the coastal station. The RSD relations of the NIO TCs, which are used in rain retrieval algorithms of remote sensing (global precipitation measurement) radars, exhibited contrasts between the coastal and inland station. Further, the NIO TCs’ rainfall kinetic energy relations, which are crucial in rainfall erosivity studies, estimated for the coastal station revealed dissimilar characteristics to that of the inland station. The conceivable thermo ‐ dynamical and microphysical processes that are accountable for the disparities in the NIO TC RSDs measured at the coastal and inland stations are also elucidated in this work.


Introduction
Raindrop size distribution (RSD) information from the ground-based disdrometers has profound applications in meteorology, hydrology, and rain attenuation studies. For instance, knowledge about the RSD is useful in offering accurate RSD models for satelliteborne remote-sensing radar and ground-based weather radar rain-retrieval algorithms [1,2]. Moreover, rainfall kinetic energy-intensity relations computed from the RSDs are useful in evaluating rainfall erosivity factor, one of the key parameters of soil erosion calculation [3,4].
In terms of understanding the microphysical features of TCs, globally, there has been increasing interest in TC RSD studies. There have been attempts in understanding TCs' RSD features over the Atlantic Ocean [17], Northwest Pacific Ocean [18][19][20][21], and South Indian Ocean [22] using ground-based disdrometers, and these studies were conducted using Joss-Waldvogel disdrometer [17,22], 2-Dimensional video disdrometer [20], and Parsivel disdrometer [18,19,23] measurements. Furthermore, over the North Indian Ocean (NIO), the disparities in the RSDs of TC rainfall to the monsoon rainfall, one TC to another TC, as well as between their pre-and post-landfall were well documented [8,9,24,25].
There have been studies on the rainfall characteristics of NIO TCs using remote sensing and model simulations [26,27]. Moreover, previous researchers demonstrated substantial variations in the seasonal rainfall RSDs measured between the coast and inland stations [28][29][30][31]. However, there have been no such studies documented for the TCs, especially for the NIO TCs, which led us to conduct the present work with the following questions: 1) do the RSDs of NIO TCs exhibit similar/dissimilar characteristics if they are measured at the coastal and inland station? 2) If there are any disparities in the RSDs of the NIO TCs at the coastal and inland sites, what could be the conceivable microphysical processes responsible for such disparities? 3) In assessing the rainfall estimation algorithms, do we need to adopt unique/different RSDs empirical relations at the coastal and inland sites? 4) do the rainfall kinetic energy-intensity relations, which are worthwhile in soil erosion studies, readily available at the existing literature are adequate to estimate the rainfall kinetic energy of the NIO TCs? Moreover, while assessing the rainfall kinetic energy, do we need to adopt same/different rainfall kinetic energy empirical relations for the NIO TCs at the coastal and inland locations? To answer the above-mentioned question, the present study is carried out by collecting the RSDs of the NIO TCs rainfall at the coastal (Thiruvananthapuram) and inland (Kadapa) sites in south India using ground-based disdrometers.
With this introduction, this article is prepared as follows. Section 2 details the data and methods used, Section 3 provides the results on RSDs features of the NIO TCs measured at the coastal and inland sites, followed by discussion in Section 4, and the summary and conclusions are given in Section 5.

Tropical Cyclones
In the current study, the RSDs of eight NIO TCs

Parsivel Disdrometer
The Parsivel [32,33] disdrometer can measure liquid (0.2−5 mm) and solid (0.2−25 mm) precipitating particles, their velocity (0.2−20 ms −1 ), and records them in a raindrop size and velocity matrix of 32 by 32. The Parsivel uses 650 nm laser beam (length, width, and height of 180 mm, 30 mm, and 1 mm, respectively) and 3 mW power. The basic working principle and pros and cons of the Parsivel were detailed by Löffler-Mang and Joss [33], Battaglia et al. [34], Jaffrain and Berne [35], Friedrich et al. [36], and Tokay et al. [37]. The Parsivel is prone to some instrumental errors, such as marginal effect and splashing effect. To overcome these limitations, quality-control procedures, mentioned below, were applied to the RSD measurements of the disdrometers in the inland and coastal sites. In the present work, the first two size bins of disdrometer are not considered in the RSD computations, and the RSD samples with rainfall rate < 0.1 mm h −1 were removed from the analysis [38]. Moreover, drops of diameter > 6 mm and fall speeds with ±60% of fall velocity-diameter relation were discarded [35,39].
The raindrop concentration (N(Di), m −3 mm −1 ) of NIO TCs are estimated using below calculation [36,37]. ΔDi (mm) [33,34,37,39]. The integral RSD parameters, like radar reflectivity (Z), rainfall rate (R), total number concentration (Nt), and liquid water content (W) are expressed as: The water density is denoted with ρw, which is equal to 1 g cm −3 . The gamma distribution function as given below is fitted with the NIO TC RSDs measured at the coast and inland [40]: here, No is the intercept parameter (m −3 mm −1-μ ), μ is shape parameter (-), and Λ is the slope parameter.
The intercept parameter No is given by [41]: The RSD n th moment, Mn (mm n m −3 ) is given as The above equation can provide the 3rd, 4th, and 6th moments of the RSDs if n = 3, 4, and 6, respectively.
where G is (11) Ʌ µ 4 (12) 4 10 Apart from the above-mentioned meteorological parameters, we evaluated the rainfall kinetic energy relations for the NIO TCs. The rainfall kinetic energy expenditure (KEtime, J m −2 h −1 ) and the rainfall kinetic energy content (KEmm, J m −2 mm −1 ) are expressed as [44]: where, R is the rainfall intensity in mm h −1 .

Reanalysis Data
Along with the disdrometer measurements, convective available potential energy (CAPE) (J Kg −1 ), vertical integral of water vapor (Kg m −3 ), air temperature and relative humidity profiles from the European Centre for Medium-Range Weather Forecasts interim re-analysis are adopted [45].

Results
The quality-controlled data of the Parsivel disdrometers showed 3901 and 3715 1min RSD samples of the NIO TCs, respectively, at the coastal (Thiruvananthapuram) and inland (Kadapa) stations. Distributions of mean raindrop concentrations for the coast and inland stations are shown in Figure 2. In the current study, drops of diameter <1 mm, 1 mm to 3 mm, and >3 mm [8,9,17,25] are classified as small-, mid-, and large-size drops, respectively. The concentration of the raindrops above 1 mm diameter is greater for the coastal station than the inland station. Examination of the coast and inland stations' RSDs for different TCs intensities (depression, deep depression, cyclonic storm, and severe cyclonic storm) also showed raindrops above 1 mm diameter are more at the coastal station than the inland station (figure not shown). The NIO TCs at the coastal station are found to have higher R (mm h −1 ), Dm (mm), and lower log10Nw (Nw in mm −1 m −3 ) values than the inland station ( Figure 2). Larger Dm values at the coastal station are due to the presence of more mid-and large-size drops than the inland station. Previously reported Dm and log10Nw values for the TCs measured at different parts of the globe are given in Table 1 [10,12,17,18,20,22,23,46,47]. Owing to geographical variations or different types of disdrometers, the Dm values of other oceanic TCs are different from those of the NIO TCs measured at the coastal and inland stations. If we compare the NIO TCs' Dm and Nw values with those of the Northwest Pacific Ocean TCs, it is obvious that NIO TCs have smaller (larger) Dm (Nw) values. The presence of more convective clouds in the Northwest Pacific Ocean TCs than the NIO TCs could be the reason for the occurrence of more large-size drops in the Northwest Pacific Ocean TCs [18]. The variations of log10R, log10W, Dm, and log10Nw with their probability distribution functions (PDF) for the NIO TCs measured at the coastal and inland stations are depicted in Figure 3. TCs' rainfall at the inland site shows peak rainfall rates distribution at log10R = 0 and at the coastal site s shows peak distribution at log10R = 0.2 ( Figure 3a). Rainfall rates of the inland site show higher distribution than the coastal station for log10R < 0.4 and for log10R > 0.4 the coastal station showed a higher distribution than the inland station ( Figure 3a). The PDF distributions for the liquid water content at the coastal show a relatively greater frequency for log10W > -0.76 than at inland station (Figure 3b). A remarkable difference in the PDF distributions of Dm between the coastal and inland sites can be attributed to more raindrops of diameter > 1 mm at the coast than the inland site ( Figure 3c). The inland station's Dm values have peak PDF at 0.98 mm and the coastal station's Dm values have peak PDF around 1.2 mm. Similar to Dm, the log10Nw also demonstrated distinct dissimilarities in PDF distributions between the coastal and inland sites (Figure 3d). The TCs' rainfall at the coast have higher PDF values for log10Nw < 4 than the inland, and the inland site showed higher PDF values for log10Nw > 4.0 than coastal site ( Figure 3d). Furthermore, to corroborate the variations in these four rain parameters of the inland and coastal sites, the statistical student's t-test was conducted at 0.01 and 0.05 significant levels and the test results rejected the null hypothesis confirming that the NIO TCs' rain/RSD parameters at the coast are different from that of the inland site.

Contribution of Raindrop Diameters to Nt and R
To appraise the NIO TCs RSDs variability between the coastal and inland stations, the contribution of drop diameter classes (as shown in x-axis labels of Figure 4) to total number concentration (Nt, m −3 ) and rainfall rate (R, m h −1 ) are portrayed in Figure 4. For both the locations (coast and inland), with the increase in drop diameter classes, contribution to total number concentration decreased, while that to rainfall rate increased and then decreased, and this characteristic is alike with the findings of Chen et al. [10] for the Pacific Ocean TCs measured in Japan. Small-size drops predominantly added to a higher Nt (> 80% and > 70% for the NIO TCs measured at the inland and coastal stations, respectively) and contributed to about 30% of the rainfall rate at the inland station, and 11% of rainfall rate at the coastal station. The contribution of raindrops with diameters 1−2 mm to number concentration is around 13% (26%), and their contribution to rainfall rate is around 54% (55%) for the NIO TCs measured at the inland (coastal) station. The contribution of drops with diameters 2−3 mm to number concentration is negligible (<2% and <0.5% for the NIO TCs measured at the coastal and inland stations), and the contribution to rainfall rate is around 13% for the inland station and 25% for the coastal station. Figure 4a,b clearly demonstrates that raindrops with diameter < 3 mm contributed to a higher percentage of total number concentration and rainfall rate for the NIO TCs measured at both stations.

RSDs in Precipitation Types
Microphysical characteristics of precipitating clouds were found to vary profoundly with precipitation types (stratiform and convective), which have a major influence on microphysical parameterizations and rainfall retrieval algorithms [42]. There have been reports on different approaches in classifying the rainfall into stratiform and convective types [42,43,48]. We classified the NIO TCs' rainfall at the coastal and inland stations to convective and stratiform type using the classification method of Bringi et al. [43]. If the mean R of 10 successive 1-min RSD samples was > 5 mm h −1 (>0.5 mm h −1 ) and the standard deviation > 1.5 mm h −1 (<1.5 mm h −1 ), then those samples were considered as convective (stratiform) type. With the above-mentioned classification criteria, 64% (36%) of data points are stratiform (convective) type for the NIO TCs at the coastal station, and they contributed to 15% (85%) rainfall accumulation, respectively. For the NIO TCs at the inland station, around 85% (15%) of data points are stratiform (convective) type, and they contributed to rainfall accumulations of 46% (54%), respectively.
Distributions of mean N(D) with raindrop diameters in two precipitation regimes of the NIO TCs at the coastal and inland stations are shown in Figure 5a. For both the coastal and inland stations, a higher number of raindrops greater than 1 mm in diameter was observed for convective regimes than for stratiform regimes. The convective regimes of the inland and coastal stations showed broader distributions than the stratiform regimes, which could be owing to the large drops' collisional breakup in convective regimes [49]. A nearly exponential distribution can be seen for the stratiform RSDs at the coastal region. Furthermore, for both stratiform and convective regimes, the TCs at the coastal station have more raindrops of diameter > 1 mm as compared to the inland station. Mean values of mass-weighted mean diameter and normalized intercept parameter in stratiform and convective regimes for the coastal and inland stations are provided in Figure 5b. Compared to stratiform type, the convective type has a larger Dm and log10Nw values. On the other hand, in both convective and stratiform regimes, larger log10Nw and smaller Dm values can be seen at the inland as compared to the coastal station. In Figure 5b, the range of log10Nw and Dm values for the continental and maritime precipitations of Bringi et al. [43] are drawn with rectangular boxes. When comparing present TCs with the precipitation clusters described by Bringi et al. [43], the Dm and log10Nw distributions have smaller values of Dm than the maritime convective clusters (except in the coastal station convective regime). The log10Nw values in convective regimes of both locations fell under the maritime convective clusters.

Dm−ZKu/ZKa and Dm−Nw Relations
The GPM DPR that operates at Ka-and Ku-band can provide the radar reflectivities at these two frequencies and are denoted, respectively, as ZKa and ZKu. The RSDs (Dm and Nw) and the rainfall parameters for the GPM DPR can be inferred from the difference between the radar reflectivity at two frequency bands, known as the differential frequency ratio (DFR, in dB) [50]. The ZKu and ZKa are evaluated from the RSD measurements from the coastal and inland station using T-matrix simulations with 20 °C temperature [51,52]. The scatter plots of DFR with Dm values at the coast and inland are depicted in Figure 6. Parallel to the results reported in the literature, DFR-Dm plots for both the locations showed a "double solution" problem, which leads to the ambiguity in the estimation of Dm [1,50]. This double solution problem arises due to the dominance of Rayleigh scattering at Ka-band and Ku-band reflectivities during the weak rain, which is mostly associated with small-size raindrops [53]. Due to the dual-value problem with DFR, rather than deriving the empirical relations between Dm and DRF, like previous researchers [2,54,55] Figure 7. The derived Dm relations with Zku, Zka, and Nw clearly demonstrate that they differ substantially from the coast to the inland station, which hints at the need to adopt different empirical relations while estimating the DSD parameters for the NIO TCs from the GPM DPR measurements.

Rainfall Kinetic Energy Relations
Rainfall kinetic energy (KE) is an important parameter in soil erosion studies that is used in estimating the rainfall erosivity factor [56]. Because of the expensive experimental requirement for the direct measurement of rainfall KE, alternative methods have been adopted by previous researchers [57,58]. Alternatively, rainfall KE can be estimated from the RSD information measured with the disdrometers [44]. For the locations where there is no availability of RSD information, the KE and the rainfall erosivity factor can be estimated using the empirical relations between rainfall KE and rainfall intensity (KE-R relations) [3,59]. These relations showed diversity with the geographical location and weather systems [3,21,60,61], which requires one to deduce region-specific relations. Moreover, in India, due to the lack of indigenous KE relations, previous studies adopted the relations of other areas [62], which can result in overestimation or underestimation of KE. Henceforth, in the present work, for the first time, the NIO TCs rainfall KE relations are obtained in terms of R (rainfall intensity, mm h −1 ), and Dm (mass-weighted mean diameter, mm).
Distributions of rainfall kinetic energy (KEtime and KEmm), with R for the inland and coastal stations are depicted in Figure 8. The relations between KEtime and rainfall intensity for the NIO TCs are obtained based on the least square method in power and linear forms. The fit lines and the corresponding equations for power and linear forms are also provided in Figure 8a,b. The coefficients of KEtime-R relations (power law: KEtime = aR b ; linear: KEtime = aR +b) and their correlation coefficient (R 2 ), root mean square error (RMSE), and normalized RMSE (NRMSE) for the coastal and inland stations are provided in Table  2. Both the power and linear form of equations fitted well at lower rainfall rates, however, at higher rainfall rates, the power fit line showed better performance than the linear form. Moreover, despite a higher correlation coefficient for power and liner fits, the power law revealed smaller RMSE and NRMSE than the linear form. The empirical relations between the rainfall content (KEmm) and the rainfall intensity (R) are derived in power (KEmm = aR b ), logarithmic (KEmm = a + b log10R), and exponential (KEmm = a [1 − b exp(−cR)]) forms for the NIO TCs, and the respective fit lines and equations are illustrated in Figure 8c,d. The statistical parameters of these three forms of equations are provided in Table 2. The present result on the NIO TCs KE-R relations exhibited analogous behavior to those of the previous studies [63,64]. Table 2. Empirical relations of rainfall kinetic energy (KEtime: kinetic energy expenditure/time specific kinetic energy; KEmm: kinetic energy content/volume-specific kinetic energy) with rainfall rate (R, mm h −1 ), mass-weighted mean diameter (Dm, mm), and GPM DPR radar reflectivity (Zku/Zka, dBZ).  With the recent advancements in precipitation measurements from the space, remote-sensing instruments like GPM DPR can provide the radar reflectivity (at ka-band: Zka and ku-band: Zku) and drop size information (mass-weighted mean diameter: Dm) globally [65,66]. By means of empirical relations between rainfall KE and the GPM DPR parameters like Dm, Zka, and Zku, one can estimate the rainfall KE at the locations where there are no ground-based measurements. Here, we tried to formulate the empirical relations between rainfall KE and GPM DPR rain parameters (Dm, Zka, and Zku), which are depicted in Figures 9 and 10. The empirical relations' values and their statistical parameters for the KE and GPM DPR parameters are given in Table 2. In the KE and Dm distribution plots for the NIO TCs at the coastal and inland station, the second order polynomial equation fits better than the power form. Moreover, the NIO TCs' rainfall kinetic energy expressed in terms of Dm and GPM DPR reflectivities (Zku and Zka) showed distinction between the coast and inland stations.

Discussion
In order to reveal the conceivable mechanisms that explain the disparities between the coastal and inland stations' RSDs, the CAPE and total column water vapor from the EAR-interim reanalysis are used for the NIO TCs measured at the coastal and inland stations, and are portrayed in Figure 11. From the figure, it is obvious that the TCs measured at the coast were associated with more water vapor content and strong convection, with stronger updrafts and downdrafts than the inland. Intense convection can enhance the raindrops growth through collision-coalescence and drop sorting processes, and raises the hydrometeors to higher altitudes, which can lead to the possible growth of ice particles (snowflakes) to a larger size (via vapor deposition and aggregation) than at the inland station [43,67]. Drop sorting and intense updrafts can inhibit the small drops from reaching the ground by suspending them aloft, which in turn allows adequate time for collision and coalescence processes leading to the growth of mid-size drops at the expense of small-size drops [49,68]. Furthermore, the vertical profiles of air temperature and relative humidity evidently illustrate that, during the NIO TC measurements, the coastal station had relatively drier conditions than the inland station (Figure 12), and hence, the rate of evaporation of small drops, which were produced through the collision breakup processes, was higher at the coastal station than at the inland station, allowing mostly the mid-size and large drops to reach the surface. The above-stated thermodynamical and microphysical processes resulted in more mid-and large-size drops at the coastal station than the inland station, resulting in higher Dm and lower Nw values, as depicted in Figures 2 and 5.

Summary and Conclusions
This study concentrated on the NIO TCs' raindrop size distribution (RSD) features measured at the coastal and inland stations using ground-based disdrometers. The NIO TCs at the coastal station have more raindrops of diameter > 1 mm than those at the inland station, resulting in higher Dm and smaller log10Nw values at the coastal station. The contribution of small drops to rainfall rate is relatively higher in the inland station than the coastal station, and opposite characteristic is noticed for raindrops greater than 1 mm in diameter. When comparing Dm, and Nw values of NIO TCs with Pacific Ocean TCs, the NIO TCs have a greater number of small-and mid-size drops. Distributions of Dm and log10Nw values at the coastal and inland stations in convective and stratiform types have lower Dm and higher log10Nw values as compared to the continental clusters. The GPM DPR relations assessed for both the coastal and inland stations demonstrated distinctions between these two locations. Furthermore, the rainfall kinetic energy expressed in terms of rainfall rate and remote-sensing radar parameters also exhibited dissimilarities between the coast and inland. The association of relatively higher evaporation rate and intense convection with strong updrafts and downdrafts to the NIO TCs at the coast than inland region resulted in dissimilarities in the RSDs between the two considered sites, which suggests that we ought to adopt region-specific (coast and the inland region) empirical relations while estimating NIO TCs' RSD/rainfall parameters from remote sensing radar and rainfall kinetic energy.

Conflicts of Interest:
The authors declare no conflict of interest.