Precipitation Microphysical Characteristics of Typhoon Mangkhut in Southern China Using 2D Video Disdrometers

: The microphysical characteristics of tropical cyclones vary in di ﬀ erent rain regions, which a ﬀ ects not only the dynamic and thermodynamic mechanisms of the typhoon system but also the development of tropical cyclones. This study analyzed the raindrop size distribution (DSD) and the gamma DSD parameters associated with Typhoon Mangkhut using three two-dimensional (2D) video disdrometers from the Longmen Field Experiment Base for Cloud Physics, China Meteorological Administration in Guangdong, China during 16–17 September 2018. According to the observed track and radar reﬂectivity, this process can be divided into three distinct segments: the outer rainband before landfall (S1), the inner core (S2), and the outer rainband after landfall (S3). The outer rainband mainly produces stratiform rains, while the inner core mainly produces convective rains. The temporal and spatial variations in the rain rate, radar reﬂectivity, and DSD parameters of the di ﬀ erent segments were analyzed and compared at three sites. Although the DSD characteristics are distinctly di ﬀ erent in the three segments, the DSD characteristics of the same segment were similar at di ﬀ erent sites. In the inner core (S2), the precipitation contains smaller drops (around 0.5 mm) and the concentrations are higher within each size bin compared with those of the other segments, resulting in the maximum rain rate (11.66 mm h − 1 ), radar reﬂectivity (34.53 dBZ), liquid water content (0.65 g m − 3 ), and number concentration (4.12 mm − 1 m − 3 on a logarithmic scale) occurring in this segment. The N w –D m scatter pairs have maritime-like convection, which increases outward from the inner core (S2). The relationship between the shape ( µ ) and slope ( Λ ) was also investigated. The microphysical characteristics determined in this study provide useful information for understanding microphysical precipitation processes and for improving the precision of numerical weather prediction models.


Introduction
The raindrop size distribution (DSD) is a key parameter for cloud and precipitation microphysical process analysis, which is essential for creating numerical weather prediction models [1,2].

Instruments and Dataset
In this study, the datasets were collected using the 2DVD from the Longmen Field Experiment Base for Cloud Physics, China Meteorological Administration. The three 2DVDs at the Enping (EP), Fogang (FG), and Xinfeng (XF) sites were used during Typhoon Mangkhut's passage over Guangdong on 16-17 September 2018 (Figure 1). The 2DVDs performed high-speed scanning with light line arrays in two mutually perpendicular directions (55 kHz). The rectangular sample area was about 10 × 10 cm 2 , and the sampling interval of the particle sizes was 0.2 mm (from 0.1 to 8.1 mm) in diameter. The details of the 2DVD instrument can be found at www.distrometer.at.
was controlled using Tokay's method [27]. For every 1 minute, if the rain rate was less than 0.1 mm h -1 or the total number of raindrops was less than 10, the data point was removed to ensure data quality. The processed 2DVD observation data are consistent with that of a rain gauge, which has been assessed by Feng et al. [28]. Moreover, the number concentration of raindrops with diameters in the range of a unit size interval ( ) is calculated as follows: where is the effective sampling area (about 10 × 10 cm 2 ); ∆ is the sampling time (1 min); , (m s -1 ) is the fall speed in the ith size bin and in the number of raindrops bin j; ( ) is the number of raindrops in each bin; and ∆ is the sampling interval of the particle sizes (0.2 mm).
In addition, an S-band polarimetric radar was used to collect the radar reflectivity at the Guangzhou site (GZ). The S-band polarimetric radar simultaneously transmits and receives horizontally and vertically polarized scattered signals with the resolution range increasing from 1000 to 250 m. The S-band polarimetric radar was processed into a six-minute resolution dataset, and its quality was controlled using the method of Liu [13].

2DVD Data Processing
The gamma distribution of the DSDs is expressed as where (mm -1 m -3 ) is the intercept; is the shape; and Λ (mm -1 ) is the slope. The curve decreases when > 0, and it increases when < 0. When = 0, it degenerates into an exponential First, the 2DVD data were processed into a one-minute resolution dataset, and then, its quality was controlled using Tokay's method [27]. For every 1 minute, if the rain rate was less than 0.1 mm h −1 or the total number of raindrops was less than 10, the data point was removed to ensure data quality. The processed 2DVD observation data are consistent with that of a rain gauge, which has been assessed by Feng et al. [28]. Moreover, the number concentration of raindrops with diameters in the range of a unit size interval N(D i ) is calculated as follows: where A is the effective sampling area (about 10 × 10 cm 2 ); ∆t is the sampling time (1 min); V i,j (m s −1 ) is the fall speed in the ith size bin and in the number of raindrops bin j; n(i) is the number of raindrops in each bin; and ∆D i is the sampling interval of the particle sizes (0.2 mm). In addition, an S-band polarimetric radar was used to collect the radar reflectivity at the Guangzhou site (GZ). The S-band polarimetric radar simultaneously transmits and receives horizontally and vertically polarized scattered signals with the resolution range increasing from 1000 to 250 m. The S-band polarimetric radar was processed into a six-minute resolution dataset, and its quality was controlled using the method of Liu [13].

2DVD Data Processing
The gamma distribution of the DSDs is expressed as Atmosphere 2020, 11, 975 4 of 18 where N 0 (mm −1 m −3 ) is the intercept; µ is the shape; and Λ (mm −1 ) is the slope. The curve decreases when µ > 0, and it increases when µ < 0. When µ = 0, it degenerates into an exponential distribution. The exponential distribution with N 0 = 8000 mm −1 m −3 is known as the Marshall-Palmer DSD [29]. When N(D i ) is calculated using Equation (1), the radar reflectivity factor Z (mm 6 m −3 ), the rain rate R (mm h −1 ), the liquid water content LWC (g m −3 ), and the total raindrop number concentration N t (m −3 ) can be calculated using the following equations: where L is the total number of bins (L = 41); D i (mm) is the equivalent spherical raindrop diameter in the ith size bin; ∆D i (mm) is the corresponding diameter interval; and The nth-order moment of the DSD is defined as The mass-weighted mean diameter D m (mm) is defined as the ratio of the fourth to the third moment of the size distribution as shown in (8): The generalized intercept parameter N w (mm −1 m −3 ) is given by where ρ ω (g cm −3 ) is the density of water (1 g cm −3 ), and W (g m −3 ) is the rainwater content.

Overview of the Typhoon
Typhoon Mangkhut formed over the western north Pacific Ocean on 14 September 2018 and made landfall in Guangdong Province at 16:00 BST on 16 September 2018. Its maximum wind speed was 45 m s −1 , and its minimum central pressure was 955 hPa. It moved northwest at 25-30 km h −1 . The typhoon caused heavy rainfall in western Guangdong, eastern Guangdong, and the Pearl River Delta. The typhoon weakened and dissipated on 17 September 2018. During its passage over Guangdong, Typhoon Mangkhut passed through the disdrometer site.
The National Centers for Environmental Prediction's (NCEP) reanalysis data with a 0.25 • × 0.25 • spatial resolution at 08:00 BST on 16 September (Figure 2a,b), and the convective available energy (CAPE) for the three 2DVDs from the nearest sounding data at Yangjiang station and Heyuan station (Figure 2c,d) were used to analyze the precipitation system. The western Pacific subtropical high is  (Figure 2b). The main airflow came from the southeasterly jet from the Bay of Bengal, which is located near the equatorial convergence zone (5-15 • N). The southeasterly jet continuously transported more moisture with a wind velocity greater than 7.5 m s −1 and a moisture flux divergence greater than 12 g cm −1 hPa −1 s −1 . The large moisture flux divergence in the typhoon's center was greater than 60 g cm −1 hPa −1 s −1 . In the outer rainband, before landfall (Figure 2c,d), the water vapor content was high in the lower layer and low at 850-700 hPa. The CAPE values at two stations were greater than 930 J kg −1 . The wind direction transitioned from northly near the ground layer to easterly in the low layer, transporting the warm, moist air in the atmospheric boundary layer. The dry, cold airflow in the mid-high level, the warm, moist airflow in the low level, and the high CAPE values were beneficial to thermal development [30][31][32].
Atmosphere 2020, 11, x FOR PEER REVIEW 5 of 18 The CAPE values at two stations were greater than 930 J kg -1 . The wind direction transitioned from northly near the ground layer to easterly in the low layer, transporting the warm, moist air in the atmospheric boundary layer. The dry, cold airflow in the mid-high level, the warm, moist airflow in the low level, and the high CAPE values were beneficial to thermal development [30][31][32].  Figure 3 shows the observed track of Typhoon Mangkhut and the radar reflectivity of the constant altitude plan position indicator (CAPPI) at an elevation angle of 0.5° at the GZ site based on the S-band polarimetric radar with a 200 km range. According to the observed track and the radar reflectivity, this process can be divided into three distinct segments: the outer rainband before landfall (S1), the inner core (S2), and the outer rainband after landfall (S3). To make it more clear, the movement direction and the direction perpendicular to the movement are shown in Figure 3b-e. It should be noted that during the passage of Typhoon Mangkhut, the time series of the disdrometer data at the FG and XF sites reveal two different segments (S1 and S3) associated with these geographic positions. The standard to distinguish between S1 and S3 is whether the perpendicular (solid red arrow) passed the site or not. The specific time periods of the three segments at the three sites are presented in Table 1.  Figure 3 shows the observed track of Typhoon Mangkhut and the radar reflectivity of the constant altitude plan position indicator (CAPPI) at an elevation angle of 0.5 • at the GZ site based on the S-band polarimetric radar with a 200 km range. According to the observed track and the radar reflectivity, this process can be divided into three distinct segments: the outer rainband before landfall (S1), the inner core (S2), and the outer rainband after landfall (S3). To make it more clear, the movement direction and the direction perpendicular to the movement are shown in Figure 3b-e. It should be noted that during the passage of Typhoon Mangkhut, the time series of the disdrometer data at the FG and XF sites reveal two different segments (S1 and S3) associated with these geographic positions. The standard to distinguish between S1 and S3 is whether the perpendicular (solid red arrow) passed the site or not. The specific time periods of the three segments at the three sites are presented in Table 1. Note: The terms S1, S2, and S3 represent the outer rainband before landfall, the inner core, and the outer rainband after landfall, respectively. The distance is that between the tropical cyclone's center and each disdrometer site (S1, S2, and S3). The temporal variability of the instantaneous wind speed and the hourly rain rate at the EP, FG, and XF sites obtained from the National Ground Observation Station of China are shown in Figure 4. The maximum instantaneous wind speed (23.3 m s -1 ) and the hourly rain rate (47.6 mm h -1 ) occurred at the EP site during S2. Compared to S1, S3 had a lower instantaneous wind speed and a higher hourly rain rate.  Note: The terms S1, S2, and S3 represent the outer rainband before landfall, the inner core, and the outer rainband after landfall, respectively. The distance is that between the tropical cyclone's center and each disdrometer site (S1, S2, and S3).
The temporal variability of the instantaneous wind speed and the hourly rain rate at the EP, FG, and XF sites obtained from the National Ground Observation Station of China are shown in Figure 4. The maximum instantaneous wind speed (23.3 m s −1 ) and the hourly rain rate (47.6 mm h −1 ) occurred at the EP site during S2. Compared to S1, S3 had a lower instantaneous wind speed and a higher hourly rain rate. The temporal variability of the instantaneous wind speed and the hourly rain rate at the EP, FG, and XF sites obtained from the National Ground Observation Station of China are shown in Figure 4. The maximum instantaneous wind speed (23.3 m s -1 ) and the hourly rain rate (47.6 mm h -1 ) occurred at the EP site during S2. Compared to S1, S3 had a lower instantaneous wind speed and a higher hourly rain rate. In general, coastal Southern China was affected by a positive vorticity at 500 hPa, a low pressure at 850 hPa, and a high moisture content in the lower layer, which improved the development of the tropical cyclone. In addition, the wind was strong, and the rain rate was heavy during S2. In general, coastal Southern China was affected by a positive vorticity at 500 hPa, a low pressure at 850 hPa, and a high moisture content in the lower layer, which improved the development of the tropical cyclone. In addition, the wind was strong, and the rain rate was heavy during S2.
In the following sections, the characteristics of the DSDs during the three segments are analyzed to determine the microphysical process of Typhoon Mangkhut. The DSDs at the three sites are also compared to reveal any spatial variations. Figure 5 shows the time series of the DSDs observed by the three 2DVDs. The average DSD parameters for each segment are presented in Table 2. When we focused on the EP site (Figure 5a-c), we found that the evolution trends of the rain rate, radar reflectivity, and number concentration were consistent. The radar reflectivity and number concentration increase with increasing rain rate. Compared with the other segments, S1 exhibited the minimum radar reflectivity of 29.10 dBZ and mass-weighted mean diameter of 1.30 mm, and a relatively low rain rate (5.28 mm h −1 ) and liquid water content (0.28 g m −3 ) on average. The main characteristics of S1 were the relatively low concentrations of small and midsize drops (<3 mm) and the narrowest raindrop spectra (maximum diameter of about 3 mm). The raindrops with diameters of <1 mm, 1-3 mm, and >3 mm are defined as small, midsize, and large drops by Tokay et al. [27] and Janapati et al. [25]. We used the same size classification criteria in this study. After this, the precipitation system became stronger, and the rain rate initially increased and then decreased rapidly during S2. S2 exhibited the highest radar reflectivity of 34.53 dBZ, rain rate of 11.66 mm h −1 , liquid water content of 0.65 g m −3 , and number concentration of 4.12 mm −1 m −3 (on a logarithmic scale) on average. S2 was characterized by a high concentration of small and midsize drops (<3 mm) with a maximum diameter of about 3.9 mm. Finally, the precipitation system became weaker and the rain rate decreased slightly during S3. S3 exhibited the minimum rain rate of 5.05 mm h −1 , liquid water content of 0.26 g m −3 , and number concentration of 3.34 mm −1 m −3 (on a logarithmic scale) and the maximum mass-weighted mean diameter of 1.52 mm. The DSDs showed a high concentration of small and midsize drops (<3 mm) with a larger diameter (about 4 mm).

Temporal Evolution and Variations in the Raindrop Size Distribution (DSDs)
The time series of DSDs showed the same characteristic at the FG and XF sites (Figure 5d-i). First, the precipitation system was weak, and the rain rate varied slightly during S1. S1 exhibited a low rain rate, liquid water content, and number concentration. The maximum concentration of the small drops was about 4 mm −1 m −3 (on a logarithmic scale). Then, the precipitation system became stronger and the rain rate increased slightly during S3. The maximum concentration of the small drops increased to about 5 mm −1 m −3 (on a logarithmic scale) during S3. Compared with S1, S3 was characterized by a higher concentration of small and midsize drops (<3 mm) with a maximum diameter of about 5 mm.
In general, the DSDs at the three sites exhibited some similar characteristics during the three segments. During S1, they experienced weak precipitation and a smaller maximum diameter (<3 mm). During S2, they experienced strong precipitation with the highest number concentration of small and midsize drops (<3 mm) with a maximum diameter of about 3.9 mm. During S3, they exhibited a maximum diameter of about 4.0 mm and a high number concentration of small drops (<1 mm).
In the following sections, the characteristics of the DSDs during the three segments are analyzed to determine the microphysical process of Typhoon Mangkhut. The DSDs at the three sites are also compared to reveal any spatial variations. Figure 5 shows the time series of the DSDs observed by the three 2DVDs. The average DSD parameters for each segment are presented in Table 2. When we focused on the EP site (Figure 5a-c), we found that the evolution trends of the rain rate, radar reflectivity, and number concentration were consistent. The radar reflectivity and number concentration increase with increasing rain rate. Compared with the other segments, S1 exhibited the minimum radar reflectivity of 29.10 dBZ and mass-weighted mean diameter of 1.30 mm, and a relatively low rain rate (5.28 mm h -1 ) and liquid water content (0.28 g m -3 ) on average. The main characteristics of S1 were the relatively low concentrations of small and midsize drops (<3 mm) and the narrowest raindrop spectra (maximum diameter of about 3 mm). The raindrops with diameters of < 1 mm, 1-3 mm, and > 3 mm are defined as small, midsize, and large drops by Tokay et al. [27] and Janapati et al. [25]. We used the same size classification criteria in this study. After this, the precipitation system became stronger, and the rain rate initially increased and then decreased rapidly during S2. S2 exhibited the highest radar reflectivity of 34.53 dBZ, rain rate of 11.66 mm h -1 , liquid water content of 0.65 g m -3 , and number concentration of 4.12 mm -1 m -3 (on a logarithmic scale) on average. S2 was characterized by a high concentration of small and midsize drops (<3 mm) with a maximum diameter of about 3.9 mm. Finally, the precipitation system became weaker and the rain rate decreased slightly during S3. S3 exhibited the minimum rain rate of 5.05 mm h -1 , liquid water content of 0.26 g m -3 , and number concentration of 3.34 mm -1 m -3 (on a logarithmic scale) and the maximum mass-weighted mean diameter of 1.52 mm. The DSDs showed a high concentration of small and midsize drops (<3 mm) with a larger diameter (about 4 mm).

Temporal Evolution and Variations in the Raindrop Size Distribution (DSDs)
The time series of DSDs showed the same characteristic at the FG and XF sites (Figure 5d-i). First, the precipitation system was weak, and the rain rate varied slightly during S1. S1 exhibited a low rain rate, liquid water content, and number concentration. The maximum concentration of the small drops was about 4 mm -1 m -3 (on a logarithmic scale). Then, the precipitation system became stronger and the rain rate increased slightly during S3. The maximum concentration of the small drops increased to about 5 mm -1 m -3 (on a logarithmic scale) during S3. Compared with S1, S3 was characterized by a higher concentration of small and midsize drops (<3 mm) with a maximum diameter of about 5 mm.
In general, the DSDs at the three sites exhibited some similar characteristics during the three segments. During S1, they experienced weak precipitation and a smaller maximum diameter (<3 mm). During S2, they experienced strong precipitation with the highest number concentration of small and midsize drops (<3 mm) with a maximum diameter of about 3.9 mm. During S3, they exhibited a maximum diameter of about 4.0 mm and a high number concentration of small drops (<1 mm).  Note: The terms R, Z, Dm, lgNw, and LWC are the rain rate, radar reflectivity, mass-weighted mean diameter, normalized number concentration, and liquid water content, respectively.

DSD Parameters
Scatterplots of the shape parameter (μ), mass-weighted mean diameter (Dm), slope parameter (Λ), and total concentration (Nt) versus the rain rate (R) for the three segments are shown in Figure  6. Segments S1, S2, and S3 are shown as red dots, green dots, and blue dots, respectively. The range decreases with increasing rain rate, and it becomes more stable at higher rain rates at the EP site (Figure 6a). The values of μ and Λ decrease, while Dm and Nt increase with the increasing rain rate. The differences between the three segments are significant. When R< 10 mm h -1 , the ranges of μ, Dm, Λ, and Nt are greater during S1 and S3. This indicates that the microphysical process is complicated during S1 and S3. When R > 25 mm h -1 , during S2 and S3, the values of μ and Λ remain nearly

DSD Parameters
Scatterplots of the shape parameter (µ), mass-weighted mean diameter (D m ), slope parameter (Λ), and total concentration (N t ) versus the rain rate (R) for the three segments are shown in Figure 6. Segments S1, S2, and S3 are shown as red dots, green dots, and blue dots, respectively. The range decreases with increasing rain rate, and it becomes more stable at higher rain rates at the EP site (Figure 6a). The values of µ and Λ decrease, while D m and N t increase with the increasing rain rate. The differences between the three segments are significant. When R < 10 mm h −1 , the ranges of µ, D m , Λ, and N t are greater during S1 and S3. This indicates that the microphysical process is complicated during S1 and S3. When R > 25 mm h −1 , during S2 and S3, the values of µ and Λ remain nearly constant, and the values of D m converge, while the values of N t increase with the increasing rain rate. In addition, when R > 25 mm h −1 , there were no raindrops measured by the 2DVD during S1. For high rain rates, the raindrop size distributions evolve into an equilibrium distribution under the action of coalescence and breakup [33]. Under these equilibrium conditions, the value of D m remains nearly constant, and the increase in the raindrop concentration is mainly due to the increase in the rain rate [18]. When we focused on the probability density function (PDF), we found that the majority of the raindrop sizes (D m ) were 1-2 mm in three segments. The distributions of the four parameters have the same characteristics for the FG and XF sites (Figure 6b,c). The difference is that there were no raindrops at the XF site when R > 60 mm h −1 . This is probably because of the different location. The characteristics of D m and N t in our study show that the heavy precipitation in the typhoon was mainly composed of high concentrations of small and midsize drops (<2 mm), which is consistent with the results of Chang et al. [17], Wen et al. [20], and Janapati et al. [25]. In addition, when R > 25 mm h -1 , there were no raindrops measured by the 2DVD during S1. For high rain rates, the raindrop size distributions evolve into an equilibrium distribution under the action of coalescence and breakup [33]. Under these equilibrium conditions, the value of Dm remains nearly constant, and the increase in the raindrop concentration is mainly due to the increase in the rain rate [18]. When we focused on the probability density function (PDF), we found that the majority of the raindrop sizes (Dm) were 1-2 mm in three segments. The distributions of the four parameters have the same characteristics for the FG and XF sites (Figure 6b,c). The difference is that there were no raindrops at the XF site when R > 60 mm h -1 . This is probably because of the different location. The characteristics of Dm and Nt in our study show that the heavy precipitation in the typhoon was mainly composed of high concentrations of small and midsize drops (<2 mm), which is consistent with the results of Chang et al. [17], Wen et al. [20], and Janapati et al. [25]. To make it clearer, Figure 7 shows the relative contribution of each size class to the total raindrop concentration (Nt) and R. The relative contributions of Nt and R at the EP site show that the small drops (<1 mm) dominate Nt (>90%) and the midsize drops (1-2 mm) dominate R (>45%) in all three segments. When we focused on the small drops (<1 mm), we found that the relative contributions of Nt and R initially increased and then decreased from S1 to S3. More significantly, the drops that were 1-3 mm in diameter contributed to the rain rate in S2. The large drops (>4 mm) contributed less than 3% during S2 and S3, and their contribution was negligible during S1. Except for the larger size drops (4 mm), the relative contributions of Nt and R at the three sites exhibit similar behaviors. This is consistent with the conclusion drawn from Figure 6 that the small and midsize drops dominated the typhoon's precipitation. Segments S1, S2, and S3 are shown as red dots, green dots, and blue dots, respectively.
To make it clearer, Figure 7 shows the relative contribution of each size class to the total raindrop concentration (N t ) and R. The relative contributions of N t and R at the EP site show that the small drops (<1 mm) dominate N t (>90%) and the midsize drops (1-2 mm) dominate R (>45%) in all three segments. When we focused on the small drops (<1 mm), we found that the relative contributions of N t and R initially increased and then decreased from S1 to S3. More significantly, the drops that were 1-3 mm in diameter contributed to the rain rate in S2. The large drops (>4 mm) contributed less than 3% during S2 and S3, and their contribution was negligible during S1. Except for the larger size drops (4 mm), the relative contributions of N t and R at the three sites exhibit similar behaviors. This is consistent with the conclusion drawn from Figure 6 that the small and midsize drops dominated the typhoon's precipitation.
Atmosphere 2020, 11, x FOR PEER REVIEW 11 of 18 Overall, the characteristics of the DSD parameters were different in the three segments because of the different dynamic and thermodynamic mechanisms of rain formation in the different rain regions [34][35][36][37]. As a result of the different locations, the characteristics of the DSD parameters in the same segment were not completely the same for the EP, FG, and XF sites. In the following section, the characteristics of the DSDs during the three segments are investigated.

Distributions of Dm and Nw
Previous studies have shown that because of the different microphysical processes during rain formation, the DSDs of different rain types vary [38][39][40][41]. The variations in the Nw-Dm values reflect the different microphysical formation mechanisms [18]. The percentage occurrence of the various rain types, which were classified using Bao's method [21], is given in Figure 8. Figure 8 shows that during S1 (S3), the stratiform rain contributed more than 70% (50%), while the convective rain contributed more than 60% during S2. Lin et al. [26] also reported that the typhoon precipitation in the eye wall region was mainly produced by convective rain. In addition, the distributions of the mass-weighted mean diameter Dm and the generalized number concentration Nw in the three segments are shown in Figure 9. The maritime-like (continental-like) cluster has Dm values of 1.5-1.75 mm (2-2.75 mm) and lgNw values of 4-4.5 (3-3.5 mm -1 m -3 ) (the two gray rectangles in Figure  9) for the convective rain, as defined by Bringi et al [18].
The mean Dm steadily increases, and the mean of the logarithmic Nw (lgNw) increases initially and then decreases from S1 to S3 (Figure 9a). The variance of Dm increases initially and then Overall, the characteristics of the DSD parameters were different in the three segments because of the different dynamic and thermodynamic mechanisms of rain formation in the different rain regions [34][35][36][37]. As a result of the different locations, the characteristics of the DSD parameters in the same segment were not completely the same for the EP, FG, and XF sites. In the following section, the characteristics of the DSDs during the three segments are investigated.

Distributions of D m and N w
Previous studies have shown that because of the different microphysical processes during rain formation, the DSDs of different rain types vary [38][39][40][41]. The variations in the N w -D m values reflect the different microphysical formation mechanisms [18]. The percentage occurrence of the various rain types, which were classified using Bao's method [21], is given in Figure 8. Figure 8 shows that during S1 (S3), the stratiform rain contributed more than 70% (50%), while the convective rain contributed more than 60% during S2. Lin et al. [26] also reported that the typhoon precipitation in the eye wall region was mainly produced by convective rain. In addition, the distributions of the mass-weighted mean diameter D m and the generalized number concentration N w in the three segments are shown in Figure 9. The maritime-like (continental-like) cluster has D m values of 1.5-1.75 mm (2-2.75 mm) and lgN w values of 4-4.5 (3-3.5 mm −1 m −3 ) (the two gray rectangles in Figure 9) for the convective rain, as defined by Bringi et al [18].
The mean D m steadily increases, and the mean of the logarithmic N w (lgN w ) increases initially and then decreases from S1 to S3 (Figure 9a). The variance of D m increases initially and then decreases, and lgN w steadily increases. When we focused on S1 (Figure 9b), we found that the lgN w -D m pairs mainly occur to the left of the stratiform line defined by Bringi et al. [18] due to the strong stratiform rain over the three sites (Figure 8). During S2, it was mainly composed of convective rain. The lgN w -D m pairs show an inhomogeneous distribution with few pairs falling in the maritime-like cluster, while some of the pairs have D m values of 0-1.25 mm and lgN w values of 4.5-5.0 mm −1 m −3 . During S3, we found that the lgN w -D m pairs were evenly distributed around the stratiform line due to the contribution of stratiform raindrops. Interestingly, few lgN w -D m pairs fall in the maritime-like cluster, and fewer lgN w -D m pairs fall in the continental-like cluster. This also indicates that the number of lgN w -D m pairs that fall in the maritime-like cluster increases from S2 to S3 because of the abundant moisture brought from the South China Sea by the typhoon.
The mean D m and lgN w values of tropical cyclones in different parts of China are presented in Table 3. The grade of the tropical cyclone reported by the Japan Meteorological Agency (JMA) (http://www.jma.go.jp/jma/index.html) is also presented in Table 3. Typhoon Mangkhut (typhoon) has a smaller raindrop diameter than and the same generalized number concentration as Typhoon Matmo (extra-tropical cyclone), which is the strongest tropical cyclone in Table 3. When we focused on the same grade of tropical cyclone (typhoon), we found that our D m is slightly larger than that of Typhoon Morakot in Fujian, while our D m (lgN w ) is larger (smaller) than that of Typhoon Hato, which made landfall in Guangdong. However, if we compare our D m and lgN w values with those of Typhoon Nida and Typhoon Pakhar (severe tropical storm), which made landfall in Guangdong, our lgN w is smaller and our D m is in between those of the other two. The sufficient water vapor brought by the typhoon from the ocean may influence the values of the DSD parameters (such as lgN w and D m ). Moreover, the strong winds shown in Figure 4 may have suppressed the collision-coalescence and breakup of the raindrops.

µ-Λ Relationship
The three-parameter (N 0 , µ, and Λ) gamma distribution is important to understanding the DSD characteristics [42,43]. The parameters µ and Λ are the shape and slope of the DSD, respectively. Furthermore, the µ-Λ relationship is useful for retrieving the DSD parameters and rain parameters from the remote measurements [41,44]. These µ-Λ relationships are dependent on the geographic location, climate, and rain type [43,45]. Thus, it is necessary to investigate the µ-Λ relationships in each region. To minimize the error, the sample data with rain rates of < 5 mm h −1 and total concentrations of N t <1000 were removed [43]. The µ-Λ relationship ( Figure 10) shows that there is a good relationship between µ and Λ. The µ-Λ relationship in this study was fitted using the polynomial least squares method. Compared with the other observation results listed in Table 3, our µ-Λ relationship is closest to that developed by Liu et al. [13] for heavy rainfall in Guangdong. In contrast, there are considerable differences among the µ-Λ relationships developed by scholars for different parts of China [16,17,19,20,43]. This indicates that the µ-Λ relationship depends on geographic location, climate, and rain type, which is consistent with the conclusions of previous studies. In addition, the µ-Λ relationship differs from that developed by Zhang et al. [43], which has been widely used to calculate the DSD parameters retrieved from polarimetric radar observations [42,46,47]. We also found that the majority of the µ-Λ pairs are characterized by µ< 0 and Λ< 2.5 mm −1 during S2, while they were characterized by µ> 0 and Λ ≈ 2.5-6 mm −1 during S1 and S3. This indicates that the microphysical processes during S1 and S3 were complicated, which is similar to the result obtained in Section 4.2.

μ-Λ Relationship
The three-parameter (N0, μ, and Λ) gamma distribution is important to understanding the DSD characteristics [42,43]. The parameters μ and Λ are the shape and slope of the DSD, respectively. Furthermore, the μ-Λ relationship is useful for retrieving the DSD parameters and rain parameters from the remote measurements [41,44]. These μ-Λ relationships are dependent on the geographic location, climate, and rain type [43,45]. Thus, it is necessary to investigate the μ-Λ relationships in each region. To minimize the error, the sample data with rain rates of < 5 mm h -1 and total concentrations of Nt <1000 were removed [43]. The μ-Λ relationship ( Figure 10) shows that there is a good relationship between μ and Λ. The μ-Λ relationship in this study was fitted using the polynomial least squares method. Compared with the other observation results listed in Table 3, our μ-Λ relationship is closest to that developed by Liu et al. [13] for heavy rainfall in Guangdong. In contrast, there are considerable differences among the μ-Λ relationships developed by scholars for different parts of China [16,17,19,20,43]. This indicates that the μ-Λ relationship depends on geographic location, climate, and rain type, which is consistent with the conclusions of previous studies. In addition, the μ-Λ relationship differs from that developed by Zhang et al. [43], which has been widely used to calculate the DSD parameters retrieved from polarimetric radar observations [42,46,47]. We also found that the majority of the μ-Λ pairs are characterized by μ< 0 and Λ< 2.5 mm -1 during S2, while they were characterized by μ> 0 and Λ ≈2.5-6 mm -1 during S1 and S3. This indicates that the microphysical processes during S1 and S3 were complicated, which is similar to the result obtained in Section 4.2. Figure 10. Scatterplots of the μ-Λ relationships during (a) S1, (b) S2, and (c) S3. S1, S2, and S3 are shown as red dots, green dots, and blue dots, respectively. The black lines denote the fitting curves of the filtered samples. In addition, the μ-Λ relationships from Chang (2009), Chen (2012), Liu (2018), Wang (2016), Wen (2018), and  are provided. S1: the outer rainband before landfall, S2: the inner core, S3: the outer rainband after landfall.

Raindrop Spectra
The raindrop spectra of the three segments ( Figure 11) show a high concentration of small drops (<0.5 mm). During S2, the number concentration within each size bin is larger than those of the other segments, especially the small drops (<0.5 mm) and large drops (>4 mm), resulting in a heavy rain rate. The spectrum is wider and has a lager maximum drop diameter (5.3 mm) during S2 and S3.   are provided. S1: the outer rainband before landfall, S2: the inner core, S3: the outer rainband after landfall.

Raindrop Spectra
The raindrop spectra of the three segments ( Figure 11) show a high concentration of small drops (<0.5 mm). During S2, the number concentration within each size bin is larger than those of the other segments, especially the small drops (<0.5 mm) and large drops (>4 mm), resulting in a heavy rain rate. The spectrum is wider and has a lager maximum drop diameter (5.3 mm) during S2 and S3. During the passage of the typhoon, the size spectrum changes from narrow to wide, and the evolution of the number concentration initially increases and then decreases.
Atmosphere 2020, 11, x FOR PEER REVIEW 15 of 18 Figure 11. Raindrop spectra of the three segments.

Summary
In this study, the microphysical characteristics of the DSDs during the passage of Typhoon Mangkhut were investigated using the 2DVD data collected from the Longmen Field Experiment Base for Cloud Physics, China Meteorological Administration. Based on the observed track and radar reflectivity, this process can be divided into three distinct segments (S1-S3). Moreover, the time evolution of the raindrop size distribution reflects the different segments. This study mainly focused on the characteristics of the DSDs during the three segments to determine the microphysical processes of Typhoon Mangkhut. The DSDs at the three different sites were compared to reveal any spatial variations. In addition, the microphysical characteristics of Typhoon Mangkhut were compared with those of other tropical cyclones in different parts of China. The DSDs of Typhoon Mangkhut exhibit different characteristics in the three segments. During segment S2, the mean of the mass-weighted mean diameter (Dm) was 1.33 mm, while the variance of the Dm was larger (0.44) than in the other segments, and the mean of the generalized number concentration (lgNw) was 4.12 mm -1 m -3 , which is the largest value among the three segments. 1. During segment S1 (the outer rainband before landfall), the circulation moved northwestward.
A strong stratiform precipitation episode mixed with convective precipitation lasting more than 2 hours occurred over all three sites. The maximum drop size was less than 3 mm, and the raindrop concentration was less than 4 mm -1 m -3 (on a logarithmic scale) at all three sites. The small and midsize drops mainly contributed to the rain rate. The lgNw-Dm pairs mainly occurred to the left of the stratiform line. 2. During segment S2 (the inner core), a strong convective precipitation process occurred over site EP. This segment had the largest instantaneous wind speed (23.3 m s −1 ), rain rate (11.66 mm h −1 ), radar reflectivity (34.53 dBZ), liquid water content (0.65 g m −3 ), and number concentration (4.12 mm -1 m −3 in logarithmic scale) on average. The small drops (<1 mm) mainly contributed to the number concentration, while the small and midsize drops (1-3 mm) mainly contributed to the rain rate. The Nw-Dm scatter pairs indicate maritime-like convection. 3. During segment S3 (the outer rainband after landfall), a widespread stratiform precipitation episode mixed with convective precipitation lasted above 10 hours. The DSDs were characterized by a high concentration of small drops (<1 mm) and a few larger drops (>5 mm). The maximum drop size was greater than 4 mm at all three sites. The Nw-Dm points were mostly distributed around the stratiform rain area, with a few points falling in both the maritime-like and continental-like clusters. This study indicates that the three segments had different DSD characteristics. The outer rainband mainly produced stratiform rains, while the inner core mainly produced convective rains. The small and midsize drops (<3 mm) dominated the typhoon precipitation. The shape (μ) and slope (Λ) exhibit a good polynomial least squares relationship.

Summary
In this study, the microphysical characteristics of the DSDs during the passage of Typhoon Mangkhut were investigated using the 2DVD data collected from the Longmen Field Experiment Base for Cloud Physics, China Meteorological Administration. Based on the observed track and radar reflectivity, this process can be divided into three distinct segments (S1-S3). Moreover, the time evolution of the raindrop size distribution reflects the different segments. This study mainly focused on the characteristics of the DSDs during the three segments to determine the microphysical processes of Typhoon Mangkhut. The DSDs at the three different sites were compared to reveal any spatial variations. In addition, the microphysical characteristics of Typhoon Mangkhut were compared with those of other tropical cyclones in different parts of China. The DSDs of Typhoon Mangkhut exhibit different characteristics in the three segments. During segment S2, the mean of the mass-weighted mean diameter (D m ) was 1.33 mm, while the variance of the D m was larger (0.44) than in the other segments, and the mean of the generalized number concentration (lgN w ) was 4.12 mm −1 m −3 , which is the largest value among the three segments.

1.
During segment S1 (the outer rainband before landfall), the circulation moved northwestward. A strong stratiform precipitation episode mixed with convective precipitation lasting more than 2 h occurred over all three sites. The maximum drop size was less than 3 mm, and the raindrop concentration was less than 4 mm −1 m −3 (on a logarithmic scale) at all three sites. The small and midsize drops mainly contributed to the rain rate. The lgN w -D m pairs mainly occurred to the left of the stratiform line.

2.
During segment S2 (the inner core), a strong convective precipitation process occurred over site EP. This segment had the largest instantaneous wind speed (23.3 m s −1 ), rain rate (11.66 mm h −1 ), radar reflectivity (34.53 dBZ), liquid water content (0.65 g m −3 ), and number concentration (4.12 mm −1 m −3 in logarithmic scale) on average. The small drops (<1 mm) mainly contributed to the number concentration, while the small and midsize drops (1-3 mm) mainly contributed to the rain rate. The N w -D m scatter pairs indicate maritime-like convection.

3.
During segment S3 (the outer rainband after landfall), a widespread stratiform precipitation episode mixed with convective precipitation lasted above 10 h. The DSDs were characterized by a high concentration of small drops (<1 mm) and a few larger drops (>5 mm). The maximum drop size was greater than 4 mm at all three sites. The N w -D m points were mostly distributed around the stratiform rain area, with a few points falling in both the maritime-like and continental-like clusters.
This study indicates that the three segments had different DSD characteristics. The outer rainband mainly produced stratiform rains, while the inner core mainly produced convective rains. The small and midsize drops (<3 mm) dominated the typhoon precipitation. The shape (µ) and slope (Λ) exhibit a good polynomial least squares relationship.
In addition, the mean values of D m and lgN w were quite different among the tropical cyclones in different parts of China. Compared with the stronger tropical cyclone (Typhoon Matmo) in Eastern China, our D m and lgN w were smaller (1.33 mm and 4.12 mm −1 m −3 , respectively). The values of the DSD parameters (such as D m and lgN w ) may be influenced by the sufficient water vapor brought by the tropical cyclone from the ocean and strong winds of the tropical cyclone.
The DSDs of Typhoon Mangkhut, which made landfall in Southern China, were quite different from those of tropical cyclones in other parts of China and even within the same region. Therefore, further tropical cyclones making landfall in Southern China are worth investigating in the future.