Global Distribution of Three Types of Drop Size Distribution Representing Heavy Rainfall from GPM/DPR Measurements

1School of Earth and Environmental Sciences, Seoul N ational University, Seoul, Korea 2National Institute of Meteorological Sciences, Kore a Meteorological Administration, Jeju, Korea Collaborative Innovation Center on Forecast and Eva luation of Meteorological Disasters, Nanjing University of Information Science & Technology, Nan jing 210044, China Key Laboratory for Aerosol-Cloud-Precipitation of C hina Meteorological Administration School of Atmospheric Physics, Nanjing University o f Information Science & Technology, Nanjing 210044, China


Introduction
The drop size distribution (DSD) of rainfall is important for estimating rain intensity and latent heating profiles using remote sensing data (Chapon et al., 2008;Liao et al., 2014;Nelson et al., 2016) and for parameterizing rain microphysics in numerical weather forecasting models (Lim & Hong, 2010;Zhang et al., 2006Zhang et al., , 2008. It also helps in understanding and interpreting physical processes related to rain development (Chen et al., 2011). Thus, better understanding of its global characteristics can significantly advance our meteorological knowledge.
Previous DSD-related studies mainly used ground observations where the regional DSD characteristics were examined (Bringi et al., 2003;Dolan et al., 2018;Gatlin et al., 2015;Tang et al., 2014;Thompson et al., 2015;Ulbrich & Atlas, 2007;Zhang et al., 2020). Although these studies provided fundamental results by identifying DSD characteristics in various precipitation regimes, certain limitations exist when characteristics at any particular region is concerned, especially with regard to the understanding of rain processes over remote areas, such as in an open ocean. Furthermore, generalizing DSD characteristics has been challenging owing to the differences in the measuring instruments, study regions, time periods, and methodologies used in various studies. Thus, acquiring general characteristics applicable to any local area is necessary.

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This article is protected by copyright. All rights reserved. 4 Satellite measurements seem to be an appropriate solution for examining such spatially and temporally varying DSD behaviors across diverse precipitation regimes.
Tropical Rainfall Measuring Mission (TRMM) was the first space-borne radar dedicated to rainfall measurement. The diameter parameter for DSD was retrieved using the precipitation radar (PR) measurements of reflectivity at a single , assuming that the DSD can be characterized by the diameter parameter itself (Iguchi et al., 2000). However, as DSD variations cannot be fully expressed as a single parameter, rain rates (RRs) retrieved from single frequency radar measurements have often been found to prone to errors and biases (Iguchi et al., 2010).
Global Precipitation Measurement (GPM) satellite, a successor to TRMM, launched on February 27, 2014, carries a dual-frequency precipitation radar (DPR) and is much better at detecting DSDs as compared to the single band approach of PR (Iguchi et al., 2010). Difference between the radar reflectivities of the two frequencies (Ku-band: 13.60 GHz, Ka-band: 35.55 GHz) enables the retrieval of the two DSD parameters, mass-weighted mean diameter (Dm) and normalized intercept parameter (or normalized scaling parameter for concentration, Nw). This has enabled applications in different types of studies, for example, in the study of vertical structures of DSDs for stratiform and convective precipitation (Sun et al., 2020), microphysical features of tropical cyclones (Huang & Chen, 2019), and different DSD features between land and ocean (Kumar & Silva, 2019, Radhakrishna et al., 2016. Well-known features, such as difference between Dm of continental area and oceanic region was confirmed using globally retrieved DSD data (Seto et al., 2016;Yamaji et al., 2020). With large amount of accumulated data, comparing DPR-retrieved DSDs with in situ ground observations and understanding the comprehensive features of DSD across various rainfall regimes are more plausible. In particular, examining the

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This article is protected by copyright. All rights reserved. 5 behavior of DSD characteristics in two-dimension carries significant importance. Note that in remote areas, such as open oceans or rain forest areas, which are presumably under different atmospheric environments, DSD features are difficult to obtain using the conventional disdrometer and polarimetric approaches.
In this study, we analyze the global DSD characteristics of heavy rainfall using multi-year DPR-retrieved DSDs and evaluate the remote sensing analysis results against ground observations provided in the literature. The obtained results can improve our understanding of cloud development and rain formation microphysics across global convection and rainfall regimes. This study can also further improve microphysical parameterizations needed for numerical models owing to the understanding of regionally different heavy rainfall microphysics.

Data and Methodology
In this study, GPM DPR-retrieved near-surface RR, Dm, Nw at clutter-free bottom level, and attenuation-corrected radar reflectivity profiles at the Ku-band (version 6) over the entire observation domain (65° N-65° S) during 2014-2019 are used (see Iguchi & Meneghini, 2016 for detailed DPR-retrieved parameters). Solid or mixed precipitation is not considered as the focus here is rain precipitation. We use the inner swath data of the matched scan mode where reflectivities are measured at both the Ku-and Ka-bands.
For the initial version of DPR-retrieved DSD data, it has been reported that the uncertainty is high for RR > 8 mm h -1 cases, compared to the disdrometer measurements over Gadanki, India (Radhakrishna et al., 2016). From the validation of the updated version 4 data over the Mediterranean region, D'Adderio et al. (2019) reported that probability distribution of DPRretrieved Dm is well matched with disdrometer measurements, but logNw is subject to uncertainties.

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This article is protected by copyright. All rights reserved. 6 For the latest version (i.e., version 6), agreement is good between retrievals and disdrometer measurements over the central China for Meiyu monsoon events; correlation coefficient is higher than 0.6 with no significant mean bias (Sun et al., 2020), satisfying the DSD measurement requirement of 0.5 mm error range for the GPM mission (Skofronick-Jackson et al., 2017). Indirect validation of was undertaken about the microphysical assumption used for the DSD retrievals (version 6), using disdrometer measurements from numerous NASA's Ground Validation (GV) field campaign sites over the United States and Department of Energy-Atmospheric Radiation Measurement (DOE-ARM) mobile facility deployments over the globe (Chase et al., 2020). It was demonstrated that employed microphysical assumption of rain-drop size relationship for the rain is in good agreement with disdrometer measurements, further assuring the quality of version 6 DPR-retrieved DSD retrievals.
The DSD function for raindrops (N(D)) is normally described by the gamma distribution function (Ulbrich, 1983) and its normalized form (Testud et al., 2001) can be written as follows: where μ, D, and N(D) are the shape parameter, diameter bin in mm, and number concentration in mm -1 m -3 . Dm is the mass-weighted mean diameter in mm, and Nw is the normalized intercept parameter in mm -1 m -3 . In this study, the shape parameter μ = 3 is used as in other studies (Liao et al., 2014;Seto et al., 2013). By using the values of Dm and Nw retrieved from DPR measurements, the corresponding number concentration N(D) is calculated using Eq. (1).
The procedures for data construction needed for examining the global DSD characteristics are shown in Figure S1. We first define an equal-area grid, equivalent to the 5° × 5° grid area over

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This article is protected by copyright. All rights reserved. 7 an equatorial region such that the number of heavy rain pixels and corresponding Dm and Nw values can be saved at each equal-area grid. If there exist more than one pixel showing the RR greater than 10 mm h -1 at a given equal-area grid (about 5° × 5° area at the equator), the grid is considered to have a heavy rain event. An RR of 10 mm h -1 exhibits a threshold separating the stratiform rain type from the convective one (Tokay & Short, 1996). Subsequently, the Dm, Nw, and RR data of all heavy rain pixels at a given grid and time are constructed. After repeating the data constructing procedure over the entire domain and analysis period, we construct a raw dataset containing the Dm, Nw, and RR of all the heavy rain pixels over the 65° N-65° S observation domain and six year period (2014-2019). However, considering the high visiting frequency of the GPM satellite in higher latitudes, the raw dataset will have a bias of more samplings in higher latitudes. Samplings are therefore homogenized to construct the final dataset that is used for the clustering analysis.
After counting the visiting frequency of the satellite depending on the latitude, the number of samples for each latitude are scaled using the ratio of the visiting frequency at each latitude to the visiting frequency at the equator. Afterwards, heavy rain events at a given latitude are randomly selected to equate the scaled number at the latitude to reduce uneven sampling problem. As a result, 328,391 heavy rain events (or number of grids showing heavy rain) and 6,258,800 heavy rain pixels over the study domain are collected for analysis. Finally, heavy rain pixels within a grid are averaged to yield mean Dm and logNw for that specific grid. The constructed data of Dm and logNw for heavy rain events are used for classifying the DSD types based on Gaussian mixture model (GMM; Bishop, 2006). GMM is a statistical model that is used to group the sample data into clusters assuming the presence of a certain number of Gaussian distributions in the sample data.
Thus, each classified type best satisfies its own Gaussian distribution with associated mean and

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This article is protected by copyright. All rights reserved. 8 standard deviation. Details on how classification was carried using GMM are found in the Supplementary Information.

Three classified DSD types
For classifying the DSD types, we examine whether the constructed Dm and logNw satisfy the Gaussian distributions for estimating the applicability of GMM. The distributions of Dm and logNw were found be similar to Gaussian distributions (not presented). The number of classified types can be subjective, but the types must be consistent with known meteorological features.
Three types appear most relevant when the DSD characteristics and associated geographical features are estimated. Figure 1a-c show the frequency distributions of Dm and logNw for the three heavy rainfall types classified using GMM. It can be seen that Dm reduces from Type 1 to Type 3, whereas logNw increases. The mean ± standard deviations for Dm for the three types are 2.25 ± 0.49, 1.62 ± 0.34, and 1.25 ± 0.27 mm, respectively and corresponding logNw mean ± standard deviations are 3.49 ± 0.49, 4.15 ± 0.45, and 4.64 ± 0.47 m -3 mm -1 . Dm for Type 1 exhibits a high frequency at 3 mm because the maximum value for Dm retrieved from the DSD algorithm was set to 3 mm (Seto et al., 2016). As the DSD types of heavy rainfall are classified based on the frequency histograms of the events, the range of one standard deviation between Type 1 (Type 2) and Type 2 (Type 3) overlaps by 9.5% (17.0%).
To obtain the DSD distributions corresponding to the three Dm-logNw types, the respective Dm and logNw values are inserted in Eq. (1), given μ = 3. Obtained results are given in Figure 1df. As a form of gamma function, the number concentration increases until a certain diameter (i.e.,

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This article is protected by copyright. All rights reserved. 9 an inflection point) and subsequently decreases. The diameters at the inflection points for the three types are 1.0, 0.6, and 0.4 mm. The number concentration around these diameters appears lowest for Type 1 and highest for Type 3. In contrast, toward the larger diameter side (e.g., D > 3 mm), Type 1 shows the highest number concentration, whereas Type 3 shows the lowest. However, Type 2 and Type 3 resemble each other. Geographical distributions of Dm and logNw that support the description provided in Figure 1 are displayed in Supplementary Figure S2.
DSD at the surface should be closely linked to the vertical structure of the cloud system.
In this study, we examine vertical structures of clouds for three DSD types. For this, the frequency of Ku-band radar reflectivity is provided in the reflectivity-height coordinates (Figure 1g-i). It is indicated that the cloud develops highest for Type 1 and lowest for Type 3, suggesting the strongest convection intensity for Type 1 and weakest for Type 3. Compared with the normalized distributions of the storm height for three types ( Figure S3), showing the minimum reflectivity at approximately 12-15 dBz (Hamada & Takayabu, 2016) highest for Type 1 and lowest for Type 3, the surface mean reflectivity seems to be proportional to the storm height as well as convection strength. The vertical shapes of reflectivity for first two types given in Figure 1g-i are consistent with the results of previous studies on precipitation characteristics representing continental and oceanic types (Liu et al., 2007;Hamada et al., 2015;Sohn et al., 2013;Song & Sohn, 2015;Xu & Zipser, 2012;Zipser et al., 2006).
The diurnal variations in convective rainfall have been well-established to be distinctly different between continents and oceans; maximum precipitation over continents and oceans occur at 15-18 and 03-06 LST, respectively (Liu & Liu, 2016;Nesbitt and Zisper, 2003;Song & Sohn, 2015;Takayabu, 2002;Yang & Smith, 2006;Zipser et al., 2006). The diurnal variations for DSD Type 1 and Type 2 are similar to those noted for the continent and ocean (Figure

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This article is protected by copyright. All rights reserved. 10 S4). Thus, the DSD characteristics for Type 1 and 2 should represent the continental and oceanic types of heavy precipitation, respectively. Type 3 shows similar variations to Type 2, but with smaller amplitudes.

Global distributions of three classified DSD types
The spatial distributions of occurrence frequencies and volumetric heavy rainfalls associated with each DSD type can be drawn and the dominant DSD types can be examined from this at any given location of the domain (Figure 2). Compared to surface-based DSD studies conducted at limited regions, which provided the most dominant DSD features, this study provides information related to a combination of DSD types or the dominant DSD type at any given location. Type 1 shows a relatively high frequency in Africa, Europe, US and South America, and western Pacific maritime continent, thereby confirming that Type 1 rainfall is mostly the continental type (Figure 2a).
Type 2 shows the dominant occurrence frequency for heavy rainfall over the tropical oceanic regions. Southeast Asian and east Asian monsoon regions as well as north Atlantic Ocean also show a prevalent Type 2 rainfall. Thus, Type 2 mainly represents the ocean type. It should also be noted that the Amazon rainforests fall into oceanic Type 2, with a less frequent continental Type 1 also evident in these forests. The dominant ocean type behaviors of rainfall over the Amazon have been well recognized in previous studies (Williams et al., 2002;Zipser et al., 2006).
Geographical distributions of Type 3 (Figure 2e) mostly overlap with Type 2, indicating that oceanic convections causing heavy rainfall comprise of deep as well as shallow convection.
Thus, heavy rainfall over the ocean regions may be characterized by a bimodal distribution with two main modes of Type 2 and Type 3, with Type 2 being the dominant one. Despite the overlapping tendency of Type 3 with Type 2, the main locations for Type 3 are toward the

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This article is protected by copyright. All rights reserved. 11 subtropical high regions off the dominant regions for Type 2, except the equatorial eastern Pacific region where Type 3 is also prevalent.
Obtained results of Dm and logNw for three DSD types are found to be consistent with known microphysical processes of precipitation. In the continental regions where Type 1 occurs most frequently, it is well known that abundant ice particles including graupel and hail are present in clouds due to the strong convection. Such clouds generally produce larger raindrops at the surface, after experiencing the melting and collision-coalescence processes (Cecil, 2011;Cecil et al., 2012;Sohn et al., 2015;Xu & Zipser, 2012;Zipser et al., 2006 among many others). Thus, larger raindrop sizes (and smaller number concentration) found in this study are consistent with general rain characteristics found over the land. In tropical oceanic regions where Type 2 is dominant, ice water content is relatively small (Cecil, 2011;Sohn et al., 2015) while liquid water content is abundant (Wood et al., 2002), in comparison to the land type. With the convection intensity weaker than the land type, collision-coalescence processes are known to be the main rain growing physics (Xu & Zipser, 2012), resulting in drop sizes smaller than the land type. The Type 3 mostly found over the subtropical subsidence region and equatorial eastern Pacific appears to be largely associated the warm rain processes under weaker and shallow convection, giving relatively lower cloud top, smaller drop size, and larger number concentration Sekaranom & Masunaga, 2019;Xu & Zipser, 2012).
In this study, we examine the rainfall amount at each grid contributed by each DSD type.
For this, the volumetric heavy rainfall is calculated at each grid by summing all the selected pixellevel RRs within the grid. Results are shown in Figure 2b, d, and f. It can be seen that 63.5% of the total rainfall is contributed by Type 2, which is predominantly from oceans. Another 18.3% of the total heavy rainfall is contributed by Type 3, mostly over the oceans as well, and the remaining

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18.2% of the total heavy rainfall is contributed by Type 1 mostly over the land regions. Again, the eastern Pacific ITCZ area show nearly compatible amounts of heavy rainfalls from both Type 2 and Type 3. Overall, the spatial distribution analysis mentioned above brought a conclusion that Type 1, Type 2, and Type 3 should be linked to continental convection, oceanic deep convection, and oceanic shallow convection, respectively.
We also examine the seasonally varying occurrence frequencies and volumetric rains for the three aforementioned types. In the boreal summer, occurrence frequency and volumetric heavy rainfall for the continental type occurred for most continents in the Northern Hemisphere, except Sahara and Arabia desert regions ( Figure S5a Contrastingly, in the boreal winter, the continental type is most commonly found in the Southern Hemispheric land regions, whereas the oceanic type is most commonly found in the Indo-western Pacific Oceans and Amazon area ( Figure S6c-f). Despite the seasonally varying geographical distributions of occurrence frequencies and volumetric rains, the results obtained for annual means of DSD parameters, as depicted in Figure 1, are found to be persistent.

Comparison with ground-based DSD observations
These globally classified DSD types are important to comprehensively interpret the DSD results of previous studies that have often represented local/regional characteristics. The global mean Dm and logNw values for the three types ( Figure 1) are compared with the results of previous studies ( Figure 3 and Table S1). Note that heavy rains as presented in Table S1 represent the cases with rain rates stronger than 10 mm h -1 (as observed in this study), whereas convective rains represent the cases with rain rates higher than 5 mm h -1 and standard deviations greater than 1.5 mm h -1 observed over a certain time period (Bringi et al., 2003).

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The values of Dm and logNw of the continental convective type (2.25 ± 0.49 mm and 3.49 ± 0.49 m 3 mm -1 , respectively) are consistent within a one standard deviation, based on the results obtained from Colorado US, Austria, Sydney Australia, and Puerto Rico (Bringi et al., 2003), the United Kingdom and Greece (Montopoli et al., 2008), northern China (Chen et al., 2016), and Tibetan Plateau (Chen et al., 2017). Furthermore, the values of Dm and logNw of the oceanic deep convective type (1.62 ± 0.34 mm and 4.15 ± 0.45 m 3 mm -1 , respectively) are found to be in good agreement with the results obtained from India (Lavanya et al., 2019;Radhakrishna et al., 2020), Indonesia (Marzuki et al., 2013), southern China (Huo et al., 2019Sun et al., 2020), Taiwan (Seela et al., 2018), South Korea (Suh et al., 2016), Japan (Montopoli et al., 2008), Darwin Australia, Papua New Guinea (Bringi et al., 2003), western Pacific (Bringi et al., 2003;Huang & Chen, 2019), and Amazon regions (Bringi et al., 2002).  (Wen et al., 2018) and India (Janapati et al., 2017;Janapati et al., 2020). The typhoon generally shows features of the oceanic shallow convective type, but seems to depend on the location or development stage (Janapati et al., 2020). The lack of observations associated with the oceanic shallow convective type is likely due to the fact that this type is mostly found over the open oceans near the subtropical subsidence regions, equatorial eastern Pacific, and equatorial Atlantic Ocean.
These classified types are also in good agreement with three DSD groups for convective precipitation based on ground-based disdrometer measurements covering diverse meteorological

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14 regimes from the tropics to the high latitudes (Dolan et al., 2018); Type 1, 2, and 3 are very similar to their 'ice-based convection', 'warm rain with high liquid water content', and 'weak convective warm rain shower' groups. Since the comparison of the classified results with ground-based measurements should be an indirect validation of DPR DSD products, the close agreement of classified rain types with results from ground-based measurements further assures the DPRretrieved data quality and obtained results.

Conclusions and discussion
In this study, we examined the global characteristics of two DSD parameters of heavy Results from this study are important because the DSD characteristics of heavy rainfall in any region can be interpreted as a combination of different DSD types with origins closely associated with the cloud-scale processes and environments. Furthermore, the global distributions of means and standard deviations of Dm and logNw for the three types, associated distributions of the occurrence of each type, and contribution to total heavy rainfall will help in understanding the physical processes of heavy rain formation, particularly over remote areas, such as open oceans where conventional observations cannot be readily made.
In spite of classification results compromising overall DSD features noted over the globe, we admit caveats of statistically-based DSD classifications. The same resultant DSD type could be attributed to many different physical reasonings responsible for the rain. For example, if there are dominant breakup processes over the continent, then DSD types without physical consideration may be interpreted as an ocean type although physical processes responsible for the ocean type can be quite different from the continental type. Thus, more future studies are needed for better understanding of the precipitation microphysics, especially combined with regionally-based physical processes such as collision and breakup processes, water vapor convergence, aerosol loadings, and so on.
While main discussions in this study have been made for interpreting three classified DSD types and their geographical distributions, obtained results can further envision studying climate change features, validating climate models, and improving cloud microphysical parameterization.

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For example, results obtained in this study may allow us to examine how two oceanic types of rainfall revealed in this study respond to changes in tropical circulations over the Pacific such as Walker circulation. And separated rain types and their contributions to the total rainfall can be used for the validation of climate model simulations, which should be more useful than the simple total rainfall comparison. The obtained results may also provide more insights on how specific rain types are linked to specific cloud structures at a given area. It is because precipitation cannot be separated from cloud microphysics.