Vertical Characteristics of Raindrops Size Distribution over Sumatra Region from Global Precipitation Measurement Observation

The climatology of the vertical profile of raindrops size distribution (DSD) over Sumatra Region (10 S – 10 N, 90 E – 110 E) has been investigated using Global Precipitation Measurement (GPM) level 2 data from January 2015 to June 2018. DSD's vertical profile was observed through a vertical profile of corrected radar reflectivity (Ze) and two parameters of normalized gamma DSD, i.e., mass-weight mean diameter (Dm) and total drops concentration (Nw). Land-ocean contrast and rain type dependence of DSD over Sumatra were clearly observed. The values of Dm and Nw were larger in the land than in the ocean. Negative and positive gradients of Dm toward the surface were dominant during stratiform and convective rains, respectively, consistent with the Z gradient. Moreover, the negative gradient of stratiform rain in the ocean is larger than in land. Thus, the depletion of large drops is dominant over the ocean, which is due to the break-up process that can be observed from the increase of Nw. Raindrop growth of convective rains is more robust over the ocean than land that can be seen from a larger value of Dm gradient. The BB strength is slightly larger over land and coastal region than over the ocean, indicating that the riming process is more dominant over land and coastal regions than the ocean.

February 2014 [22]. The GPM is an advanced Tropical Rainfall Measuring Mission (TRMM) project that provides some precipitation parameters, including DSD parameters.
This work uses GPM data to investigate the vertical characteristics of DSD over Sumatra region. Sumatra is located in the tropical region's warm pool, which is the most active convective area in the world [23]. Several studies have been conducted to study the vertical profile of DSD over Sumatra [18,24,25]. Renggono et al. [24] observed DSD's vertical profile using Equatorial Atmospheric Radar (EAR). Marzuki et al. [25] and Ramadhan et al. [18,20] observed the vertical profile of DSD using Micro Rain Radar (MRR). Using this instrument, they found the rainfall type and diurnal variation of DSD in Sumatra. However, all previous studies were only conducted at one location, namely, at the Equatorial Atmosphere Observation, which is located in Kototabang, West Sumatra (0.20°S, 100.32°E; 865 m above sea level). Therefore, to describe DSD's vertical characteristics over the whole Sumatra Region, we used the data of GPM level 2. The GPM data provide two parameters of normalized gamma DSD, i.e., mass-weight mean diameter (Dm) and total drops concentration (Nw). The performance of GPM to estimate the DSD parameters has been examined by several studies [26][27][28].

2-Data and Methodology
The region of interest is Sumatra and the surrounding ocean (10 S -10 N, 90 E -110 E). The GPM level 2 data of the study area from January 2015 to June 2018 are used. GPM carries Dual-Frequency Precipitation Radar (DPR) that was Ku-band (13.6 GHz) and Ka-band (35.5 GHz) frequency radar [22,29]. The type of DPR scanning proceeds three modes of data, i.e., Normal Scan (NS), Match Scan (MS), and High-sensitivity Scan (HS). This mode is produced from different scanning in which NS is from Ku-band scanning while MS and HS are from Ku and Ka combinations. Although NS was produced only from Ku-band scanning, previous studies show good performance of NS scanning for DSD observation in comparison with a ground radar [28,30]. Ku band has 125 m vertical resolution with 176 range bin and 49 swath with 5×5 km resolution approximately.
The GPM DPR level 2 data are classified into convective and stratiform rains using the classification method, which is available in the classification (CSF) module of GPM [31]. The GPM algorithms consist of the preparation (PRE) module, the vertical (VER) profile module, the classification (CSF) module, the drops size distribution (DSD) module, the surface reference technique (SRT) module, and the solver (SLV) module [32]. This paper used GPM level 2 data version 5 (V05) that was released in May 2017. This version included precipitation at the surface and additional parameters like some parameters and flag, freezing level altitude, and land surface type [33]. The CSF modules used in this study were type precipitation, quality BB, quality rain type precipitation, height BB, bin of BB top, and bin of BB bottom. We only analyze the data if quality BB and quality rain type precipitation are 1. Finally, we also used the precipitation near surface, Z factor corrected (Ze), and DSD parameter data, which are obtained from the SLV module.
GPM provides mass-weight mean diameter (Dm) in mm and total drops concentration (Nw) in dBNw unit. These parameters are belong to normalized gamma distribution [34] expressed by: where D is drops diameter in mm, N(D) is the number of density in m -3 mm -1 , and f(µ) is a function of shape parameter (μ): Parameter Nw in mm -3 is the ratio between liquid water content (W) in gm -3 and parameter Dm [35], while Dm is the ratio for the fourth to third moment from DSD. The parameter Nw is expressed by: where ρw is the density of water in gm -3 . This study does not retrieve the DSD parameters manually, we use Dm and Nw that the GPM has been provided. These parameters were calculated from the rainfall rate (R)-Dm relationship that tends to Ze observation [36]. Details theoretical basis of this algorithm can be seen in Iguchi et al. [37]. This study investigated the vertical structure of DSD over the Sumatra region by filtering the data for near-surface rainfall greater than 0.1 mm/h. We used the precipitation classification from the GPM level 2 data to divide rainfall types into stratiform and convective rain. The spatial distribution of data was given in Figure 1. It contained 5,325,630 data for all rainfall event (Figure 1a), 1,389,261 data for stratiform rain (Figure 1b), and 3,936,369 data for convective rain (Figure 1c). Usually, the number of stratiform rain profiles is the largest [18,20], but we found the stratiform rain profile is smaller than convective rain in this study. We compared both stratiform and convective DSD characteristics for several locations, including land, coastal, strait, and ocean, to find the variability. Figure 2 shows the spatial distribution of the vertical profile of reflectivity gradient (VPRG) above and below the melting layer. It can be used to identify the growth of hydrometeors. Above the melting layer, the gradient was calculated in 5-7 km rain column, while below the melting layer, the VPRG was calculated at the altitude of 1-3 km. All gradients above the melting layer are positive (downward increasing toward the surface, hereafter DI) both for both stratiform and convective rain (Figures 2a and 2c).

3-Results
Stratiform rain has larger DI above melting layer than convective rain, consistent with characteristics of the convective-stratiform formation. Although DI above the melting layer is positive for convective and stratiform, below the melting layer, stratiform has negative VPRG, while convective rain has positive values.  VPRG for stratiform and convective rains show a regional variation. Above the melting layer, the stratiform's DI gradient is larger over the ocean than over land (Figure 2a). A slightly larger DI gradient of stratiform rain over the land was observed on Sumatra's western coast, which is consistent with the previous study in Indonesia Maritime Continent (IMC) [38,39]. Otherwise, the DI gradient of convective rain is larger over the land than over the ocean, especially in the western region of Sumatra ( Figure 2c). Thus, the growth of hydrometeor for convective rain is more robust over land, while for stratiform rain, it is more dominant over the ocean [40]. A larger positive DI gradient (positive VPRG) is observed below the melting layer during convective rain over the ocean, indicating that the increase of large-size drops concentration is more significant over the ocean. On the other hand, stratiform rain shows a larger negative gradient of VPRG over this region (Figure 2b), indicating the decrease of large-size drops concentration, consistent with the Dm gradient for the below-melting layer (Figure 3). Gradients of Dm and Nw for stratiform and convective are given in Figure 3. The gradients were calculated in the rain column 1.5-4.0 km. A negative gradient was observed for the vertical profile of Dm during stratiform rain (Figure 3a). It means there is a decrease of large-sized drops toward the surface during stratiform rain over Sumatra region, which is consistent with the VPRG trend ( Figure 2b). The decreasing Dm trend for stratiform rain is followed by Nw's increase that indicates the break-up process [42]. This result is different from previous studies at Kototabang in west Sumatra using MRR [18,20,42]. It may be due to a small-scale variability of vertical DSD over Sumatra. Therefore, we analyze the DSD for ten selected locations include Kototabang in Section 3.1.  Figure 3b and d show the spatial distribution of Dm and Nw gradients for convective rain. It can be seen that convective rain has a positive gradient for both Dm and Nw parameters, consistent with the VPRG pattern (Figure 2d). The Dm gradient is smaller over the land than over the ocean. This confirms a smaller increase of large drop concentration over land, as indicated by a small VPRG gradient (Figure 2d). The increase of Dm for convective rain coincides with an increase of gradient Nw. The increase of large-sized drops with the increasing total number of raindrops is likely due to several microphysical processes such as the accretion break-up and coalescence [41]. Break-up and coalescence processes occur during the convective rain over the ocean and land. However, the break-up processes are more dominant, especially over the ocean, indicated by a more significant increase of Nw. Figure 4 shows the vertical profile of the corrected radar reflectivity factor (Ze) during stratiform rains from GPM observation for several locations over Sumatra. The selected area locations are given in Figures 3a and 3b, and the data distribution for these regions was presented in Table 1. The bright band (BB) appears for all rainfall intensities (R). To identify rainfall intensity dependence of vertical structure of stratiform precipitation, the data are classified into several classes of intensity i.e., very light rain (0.1R˂1), light rain (1R˂2), moderate rain (2 R˂5), and heavy rain (5 R˂10) [2]. We calculated the BB strength (∆Z) by taking the difference in the average value of Ze between Bright Band Height (BBH) and BB-bottom. The strength of BB is necessary to identify the number and size of the raindrop during their formation [43].

Figure 5. Vertical profile of mass-weight mean diameter (Dm) for ten selected locations of stratiform rain for a) very light rain, b) light rain, c) moderate rain, and d) heavy rain.
The . Thus, very light rain has a larger ∆Z than heavy rain, which indicates a more dominant break up or riming process [44]. The strength of ∆Z is closely related to the decrease of large-sized drop soon after the ice crystal melts. There is a significant rain intensity dependence of VPRG below the melting layer. Very light rain has a negative gradient, while heavy rain has a positive gradient (Figure 4). This feature indicates the decrease of large-sized drops concentration during very light rain over Sumatra. The values of ∆Z during heavy rain for several coastal areas such as CSM1, CSM2, and CSM3 are larger than in other regions. Figure 5 shows the vertical profile of Dm for all classes of stratiform rain. The values of Dm increase with an increasing rainfall rate. This is typical of DSD characteristics in the tropics [2,14]. The value of Dm over land (SM1, SM2, SM3) is larger than other regions, indicating a smaller growth of raindrops over land than ocean, coastal, and strait, as observed in Figure 2. For very light to moderate rain, the larger value Dm was observed over land (SM2 and SM3). The larger Dm over land is associated with a smaller value of Nw ( Figure 6). A similar pattern is also observed in the coastal region (CSM3). Thus, the DSD of stratiform rain over land comprises more large-sized drop concentrations with a small number of raindrop total. This fact is consistent with weak BB over land (Figure 4). Figure 7 shows Ze's vertical profile during convective rains for several locations, which are indicated in Figures 3a  and 3b. The data distribution for these regions was presented in Table 2. We classified convective rain into six rain intensities i.e. very light rain (0.1R˂1), light rain (1 R˂2), moderate rain (2 R˂ 5), heavy rain (5R˂10), very heavy rain (10  R˂20), and extreme rain (R ≥ 20) [2]. High rainfall intensity is associated with a larger positive VPRG above the melting layer. Below the melting layer, a positive gradient of Ze was observed for almost all classes. The negative gradient of Ze was observed only for very light rain (Figure 7a). Very light rain also shows a clear BB pattern in the melting layer (~5 km), which may indicate a miss classification of convective rain by the CSF module. The GPM is less sensitive to weak precipitation [45]. The gradient becomes positive when the rainfall intensity increases. The largest Ze value was observed over land, and the smallest one was observed offshore (IOC). Although the largest Ze value was observed over land, the VPRG value below the melting layer in this region is smaller (Figure 2). Thus, a larger raindrop size is found over land, but the raindrop growth is small in this region.    Figure 8 shows the vertical profile of Dm for convective rain. It can be seen that the positive gradient of Dm for higher rain intensity is larger than others, consistent with the vertical profile of Ze (Figure 7). Furthermore, the larger positive gradient of Nw was observed for the lower intensity of convective rain for all locations (Figure 9). This pattern contrasts with the pattern of Nw for stratiform rain in which a larger positive gradient is observed for higher rain intensity. A smaller Dm gradient in lower intensity (very light to light rain) is associated with a larger Nw gradient, indicating a more dominant break up process during raindrop's fall. The coalescence process becomes dominant when the rainfall intensity increases, which can be seen from the increase of the Dm gradient and the decrease of Nw gradient.

3-2-Vertical Characteristics of Convective Rain
The largest Dm was observed over land, and the lowest one was observed over offshore (IOC). Such contrast is more obvious for a higher rain intensity. A larger Dm over land is associated with its smaller gradient in the rain column ( Figure 3). Thus, intense convective rain, which is indicated by larger Ze (Figure 7), having larger drops (indicated by large Dm), is dominant over land. This is consistent with the variability of intense convective study in the tropical region [38,46]. A larger Dm value was also observed over the Malacca strait (SMAL area). Intense convective rain is also frequently generated in this region [47]. The vertical profile of Nw for convective rain is similar to stratiform rain. The largest Nw value is observed over offshore (IOC), and the smallest one is observed over land ( Figure 8). Thus, the DSD of convective rain over land comprises more large-sized drop concentration with a small number of raindrop total, as observed during stratiform rain.

4-Conclusion
This study reinforces the regional variation and rain type dependence of the vertical profile of precipitation over Sumatra. The DSD over land comprises more large-sized raindrop concentration with a small number of raindrop total, indicated by a larger Dm and smaller Nw over land than over the ocean. The land-ocean contrast of raindrop growth is visible. For convective rain, the increase of large-sized drops over the ocean is more significant than over land, indicated by a larger positive Dm gradient toward the surface. On the other hand, the reduction rate of large size drop is more significant over the ocean than over land, indicated by a larger negative Dm gradient toward the surface. Ze, Dm, and Nw's vertical profile is also dependent on the rainfall intensity, especially for convective rain. A smaller Dm gradient in lower rain intensity (very light to light rain) is associated with a larger Nw gradient, indicating a more dominant break up process during the raindrop's fall. The coalescence process becomes dominant when the rainfall intensity increases, which can be seen from the increase of Dm gradient and the decrease of Nw gradient. In this study, we also found the shortcoming of rain classification of the CSF module. Some profiles classified as convective by the CSF module may be stratiform, indicated by strong BB pattern in the melting layer. The DSD over Sumatra is influenced by diurnal, intraseasonal, and seasonal variability of the atmosphere. The characteristics of the vertical profile of DSD in terms of these variabilities are being conducted and will be reported in other papers.

5-2-Data Availability Statement
Publicly available datasets were analyzed in this study. This data can be found here: www.gpm.nasa.gov/data.

5-4-Acknowledgements
Thanks to NASA for providing open-source GPM Level-2 data.

5-5-Conflicts of Interest
The authors declare that there is no conflict of interests regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies have been completely observed by the authors.