A Case Study on Microphysical Characteristics of Mesoscale Convective System Using Generalized DSD Parameters Retrieved from Dual-Polarimetric Radar Observations

: The microphysical characteristics of a mesoscale convective system (MCS) during a summer monsoon of South Korea are investigated using the generalized drop size distributions (DSD) that are derived from S-band dual-polarization radar data. The characteristics parameters of generalized DSDs (generalized number concentration, N 0 (cid:48) and generalized mean diameter, D m ) are directly calculated from DSD’s two moments without any assumption on the DSD model. Relationships between Z DR and generalized DSD parameters normalized by Z H are derived in the form of the polynomial equation. Veriﬁcation of the retrieved DSD parameters is conducted with the 2-D video disdrometer (2DVD) located about 23 km from the radar. The standard deviations (SD) of retrieved DSD parameters are about 0.26 for log N 0 (cid:48) , and about 0.11 for D m because of the variability of DSDs. The SD of the retrieved log N 0 (cid:48) from the dual-polarimetric measurement reaches to about 0.46 (almost double) for 11 rain events while the accuracy of retrieved D m is quite higher (~0.19). This higher error in retrieved log N 0 (cid:48) is likely attributed to the larger discrepancy in radar-observed and DSD-calculated Z DR when Z H is low. This retrieval technique is applied to a mesoscale convective system (MCS) case to investigate the Lagrangian characteristics of the microphysical process. The MCS is classiﬁed into the leading edge and trailing stratiform region by using the storm classiﬁcation algorithm. The leading edge dominated by strong updraft showed the broad DSD spectra with a steady temporal increase of D m throughout the event, likely because of the dominant drop growth by the collision-coalescence process. On the other hand, the drop growth is less signiﬁcant in the trailing stratiform region as shown by the nearly constant D m for the entire period. The DSD variation is also controlled by the new generation of drops in the leading edge and less extent in the trailing stratiform during the early period when precipitation systems grow. When the system weakens, the characteristic number concentration decreases with time, indicating the new generation of drops becomes less signiﬁcant in both regions.


Introduction
Drop size distribution (DSD) is an outcome of the complex microphysical processes of precipitation particles (e.g., collision-coalescence, break-up, evaporation, etc.). The exponential DSD, N(D) = N 0 exp(−ΛD), has some limitations to describe these processes with fixed and requires measurements near the surface with a rapid update, requiring such elevation angles. The use of these angles requires careful elimination of ground clutter. A PPI has a resolution of 125 m x 1° in radial and azimuthal directions and observes up to 150 km (Table 1).  2DVD instrument captures the shadows of a falling particle using two horizontal light beams which are transmitted from two orthogonal light sources to the two-line scan cameras and provides various information of precipitation particles such as fall velocity, equivalent volume, spherical diameter, major and minor axes, canting angle, and so on [16]. Detail specification is shown in Table  2. These drops information can be contaminated by mismatching of drops in the image processing, which integrates information received from two line-scan cameras [17]. In the case of raindrops, the mismatched particles can be identified by comparing observed fall velocity (V) with calculated fall velocity (VA) with the following predefined relationship [18].
Here, the D indicates the diameter of raindrops. The observed drops are eliminated when the difference of the observed fall velocity and calculated fall velocity (VA) is larger than 40% [16]. Table 2. Specification of two-dimensional video disdrometer (2DVD). 2DVD instrument captures the shadows of a falling particle using two horizontal light beams which are transmitted from two orthogonal light sources to the two-line scan cameras and provides various information of precipitation particles such as fall velocity, equivalent volume, spherical diameter, major and minor axes, canting angle, and so on [16]. Detail specification is shown in Table 2. These drops information can be contaminated by mismatching of drops in the image processing, which integrates information received from two line-scan cameras [17]. In the case of raindrops, Remote Sens. 2020, 12, 1812 4 of 19 the mismatched particles can be identified by comparing observed fall velocity (V) with calculated fall velocity (V A ) with the following predefined relationship [18]. V A = 9.65 − 10.3 exp(−0.6D) (1) Here, the D indicates the diameter of raindrops. The observed drops are eliminated when the difference of the observed fall velocity and calculated fall velocity (V A ) is larger than 40% [16]. The 1-min DSD is then calculated from the velocity filtered drops. The discontinuity check and 3-min moving average are performed to reduce the variation caused by measurement noise. The 22,435 of 1-min DSDs from May 2014 to October 2015 in Jinchun are used to derive the theoretical relationship between dual-polarization variables and microphysical parameters (black lines in Figure 2). The maximum values of rainfall rate, Z H , and Z DR were 100 mmh −1 , 53 dBZ, and 2.5 dB. The 12,945 of 1-min DSDs during 2012 observed in KNU are used to verify retrieved characteristic DSD parameters from the dual-polarimetric radar (blue lines in Figure 2). The maximum rainfall intensity is similar to the Jinchun data set that is used to derive the relationship. However, the maximum reflectivity and differential reflectivity are higher than the Jinchun data set (max. Z H = 55 dBZ and max. Z DR = 2.8 dB). Both data sets cover various precipitation events. In particular, the Jinchun data set is from about 48 rain events that include wide-spread stratiform rain, frontal precipitation, stationary front ("Changma front"), mesoscale convective precipitation, isolated convection, and typhoon events.  Figure  2). The maximum values of rainfall rate, ZH, and ZDR were 100 mmh −1 , 53 dBZ, and 2.5 dB. The 12,945 of 1-min DSDs during 2012 observed in KNU are used to verify retrieved characteristic DSD parameters from the dual-polarimetric radar (blue lines in Figure 2). The maximum rainfall intensity is similar to the Jinchun data set that is used to derive the relationship. However, the maximum reflectivity and differential reflectivity are higher than the Jinchun data set (max. ZH = 55dBZ and max. ZDR = 2.8dB). Both data sets cover various precipitation events. In particular, the Jinchun data set is from about 48 rain events that include wide-spread stratiform rain, frontal precipitation, stationary front ("Changma front"), mesoscale convective precipitation, isolated convection, and typhoon events.
The KNU data set used for evaluation of radar retrieval parameters is composed for the 11 rain events shown in Figure 3. The ZH plan position indicators (PPIs) at 0.8° elevation angle are shown for each case. The last two events (28 August. and 30 August. 2012) are related to nearby typhoons. The five cases (30 June, 06 July, 11 July, 22 August., and 23 August. 2012) had stationary fronts passing over Korean peninsula. The other cases are linked with troughs and local heating. As shown in Figure  2, the verification data showed heavier rainfall intensity and stronger ZH than that of the Jinchun site. The mean value of rainfall intensity and ZH at KNU is larger than that of the Jinchun site. Figure 2. Histogram of (a) rainfall rate, (b) ZH, (c) ZDR calculated from 2DVD. The data set at the Jinchun site (black lines) is used to derive the retrieval equations, and that at the KNU site (blue lines) is for verifying radar retrieved DSD parameters. The KNU data set used for evaluation of radar retrieval parameters is composed for the 11 rain events shown in Figure 3. The Z H plan position indicators (PPIs) at 0.8 • elevation angle are shown for each case. The last two events (28 August. and 30 August. 2012) are related to nearby typhoons. The five cases (30 June, 06 July, 11 July, 22 August., and 23 August. 2012) had stationary fronts passing over Korean peninsula. The other cases are linked with troughs and local heating. As shown in Figure 2, the verification data showed heavier rainfall intensity and stronger Z H than that of the Jinchun site. The mean value of rainfall intensity and Z H at KNU is larger than that of the Jinchun site.

Methodology
The relationships between polarimetric variables and microphysical parameters are derived with DSDs obtained from 2DVD. The polarimetric variables are simulated from the T-matrix scattering simulation with 1-min DSDs. The generalized characteristic DSD parameters are calculated from two moments of DSDs. The empirical relationships are then derived with the generalized DSD parameters and simulated radar variables. The details are described in the following sections.

Simulation of Dual-Polarization Parameters
The polarimetric variables ( , ) are calculated with measured drop size distributions based on the T-matrix method [19,20] with assumptions in Table 3. The frequency of 2.79Hz of BSL radar (S-band) and the dielectric constant of water [21] at an environment temperature of 10 ℃ are assumed. The canting effect caused by tumbling and oscillation of falling raindrops is considered as the Gaussian distribution with the mean canting angle of 0° and the standard deviation of 10°. The axis ratio of the oblate spheroid drop was suggested by many previous studies [22][23][24]. The axis ratio of the equi-volumetric sphere diameter (D in mm) from [25] is used in the present study. The drop shape was measured by a 2DVD from the 80 m fall experiments [19]. [25] suggested the following setup: the axis ratio of [17] for D >1.5 mm, and [26] for drops smaller than 1.5 mm.

Methodology
The relationships between polarimetric variables and microphysical parameters are derived with DSDs obtained from 2DVD. The polarimetric variables are simulated from the T-matrix scattering simulation with 1-min DSDs. The generalized characteristic DSD parameters are calculated from two moments of DSDs. The empirical relationships are then derived with the generalized DSD parameters and simulated radar variables. The details are described in the following sections.

Simulation of Dual-Polarization Parameters
The polarimetric variables (Z H , Z DR ) are calculated with measured drop size distributions based on the T-matrix method [19,20] with assumptions in Table 3. The frequency of 2.79Hz of BSL radar (S-band) and the dielectric constant of water [21] at an environment temperature of 10°C are assumed. The canting effect caused by tumbling and oscillation of falling raindrops is considered as the Gaussian distribution with the mean canting angle of 0 • and the standard deviation of 10 • . The axis ratio of the oblate spheroid drop was suggested by many previous studies [22][23][24]. The axis ratio of the equi-volumetric sphere diameter (D eq in mm) from [25] is used in the present study. The drop shape was measured by a 2DVD from the 80 m fall experiments [19]. Ref. [25] suggested the following setup: the axis ratio of [17] for D eq > 1.5 mm, and [26] for drops smaller than 1.5 mm.

Calculation of Generalized DSD Parameters
Scaling normalization that uses one or two moments of the DSD as a scaling parameter has been used for compact representation of DSD [3,27]. Double-moment normalization uses two moments (i -th moment and j-th moment) as scaling parameters of the normalization as the following equation: where h(x 2 ) is the "double-moment normalized" DSD function which is less sensitive to variation of DSD. The normalized diameter ( The normalization parameters of number concentration and diameter are defined as N 0 and as D m , respectively. where D m [mm] is the generalized characteristic diameter and N 0 [m −3 mm −1 ] is the generalized characteristic number concentration. If we take 3rd and 4th moments (i=3 and j=4) as normalization parameters, the D m and N 0 are defined as the following equation; The definition of D m is the same as D m (mass-weighted mean diameter in mm) in [2]. The N 0 represents the intercept parameter that is approximated with two moments. The choice of two moments depends on the two aspects: (1) Better representation of DSDs and instrumental uncertainty in measuring DSDs. (2) One lower (2nd~3rd) and one higher (6th~7th) moments are desired for the better representation of DSDs. On the other hand, the 2DVD suffers from instrumental uncertainty, in particular, measuring smaller sizes, thus leading to high uncertainty in lower moments [28,29]. Ref. [30] showed that the accuracy of R from 2DVD is the best among different disdrometers with 4 min integration time. However, this is not true in Z due to small sampling volume [30]. Thus, the choice of 3rd and 4th moments is rather a practical approach by considering the data set from which the retrieval relationships are derived.
The empirical relationships are derived with simulated radar variables and calculated microphysical parameters. The microphysical parameters, total number concentration (N T ), and median volume diameter (D 0 ) were expressed as a polynomial fit in terms of radar measurements [11,12]. The relationships in this study also consists of a polynomial function of Z dr , and the generalized characteristic DSD parameters are normalized with Z H .
where the Z h and Z dr are a linear scale of Z H and Z DR , respectively. The coefficients were derived from the calculated N 0 and D m and simulated radar variables from 22,435 DSDs from the Jinchun site.

Characteristics of Generalized DSD Parameters
The generalized DSD parameters calculated from the verification data set are distributed from 0.37 to 3.33 mm for D m and from 0.43 to 13,804 m −3 mm −1 for N 0 (Figure 4). Ref. [13] investigated the average values of log N W and D m for different climate regions ( D m ∼1.5mm, log N W ∼ 3.25 in stratiform rain, D m ∼1.75mm, log N W ∼ 4.25 in maritime convective rain, and D m ∼ 2.5 mm, log N W ∼ 3.25 in continental convective rain). The mean values of D m and logN 0 are within the stratiform rain range in [13]. The vertical dashed line in Figure 4b is calculated from Marshal-Palmer (MP) distribution (logN 0 = 2.27 m −3 mm −1 , [1]). The mode and mean value are smaller than those of the M-P in this data set. There are second peaks in smaller D m (= 0.5 mm) and higher logN 0 (= 3.3) that represent drizzle mode.
Remote Sens. 2020, 12, x FOR PEER REVIEW 7 of 20 where the ℎ and are a linear scale of and , respectively. The coefficients were derived from the calculated N 0 ′ and D m and simulated radar variables from 22,435 DSDs from the Jinchun site.

Characteristics of Generalized DSD Parameters
The generalized DSD parameters calculated from the verification data set are distributed from 0.37 to 3.

Relationships Between Dual-Polarization Variables and Generalized DSD Parameters
The shows a good correlation with N 0 ′ and D m normalized with a linear scale of ( Figure 5). The D m (logN 0 ′ ) monotonically increases (decreases) with the . The larger than 0.2dB is used in the regression analysis. The relationships are derived from the third-order polynomial regression.
where ℎ and are linear scale of and . These equations are used to retrieve the N 0 ′ and D m .

Relationships between Dual-Polarization Variables and Generalized DSD Parameters
The Z DR shows a good correlation with N 0 and D m normalized with a linear scale of Z H ( Figure 5). The D m (logN 0 ) monotonically increases (decreases) with the Z DR . The Z DR larger than 0.2dB is used in the regression analysis. The relationships are derived from the third-order polynomial regression.
where Z h and Z dr are linear scale of Z H and Z DR . These equations are used to retrieve the N 0 and D m .
Remote Sens. 2020, 12, x FOR PEER REVIEW 8 of 20 Theoretical accuracy is evaluated with the same data set measured in the Jinchun. This accuracy should be considered as a theoretical limit in this retrieval method because of the variability of DSD.   Theoretical accuracy is evaluated with the same data set measured in the Jinchun. This accuracy should be considered as a theoretical limit in this retrieval method because of the variability of DSD. In general, both N 0 and D m show high frequency in the one-to-one line, indicating a good accuracy generally ( Figure 6 Theoretical accuracy is evaluated with the same data set measured in the Jinchun. This accuracy should be considered as a theoretical limit in this retrieval method because of the variability of DSD.

Evaluation of Retrieved Generalized DSD Parameters
A total of 11 rainfall cases (Table 3) during the summer season in 2012 are used to verify the retrieved generalized DSD parameters from the BSL radar. To reduce the effects of measurement noise and the contamination of non-meteorological echoes, the and are only selected at the gates with a cross-correlation coefficient greater than 0.95 and they are then averaged in an area of 3° and 1.375 km in azimuthal and radial directions, respectively (~2 km 2 ). The measured and are calibrated with 2DVD. The generalized DSD parameters of 2DVD are averaged every 5 min based on the radar measurement interval.
The scatterplot of retrieved values from the radar and calculated from measured DSDs are shown in Figure 8 for the 11 rainfall cases, and Table 4 shows the error statistics (correlation coefficient, SD, and bias) of retrieved andlogN 0 ′ . The bias is almost negligible in both retrieved andlogN 0 ′ . The retrieved was well correlated with calculated from 2DVD with the overall correlation of 0.76 (case correlation of 0.56 to 0.84 shown in Table 4

Evaluation of Retrieved Generalized DSD Parameters
A total of 11 rainfall cases (Table 3) during the summer season in 2012 are used to verify the retrieved generalized DSD parameters from the BSL radar. To reduce the effects of measurement noise and the contamination of non-meteorological echoes, the Z H and Z DR are only selected at the gates with a cross-correlation coefficient greater than 0.95 and they are then averaged in an area of 3 • and 1.375 km in azimuthal and radial directions, respectively (~2 km 2 ). The measured Z H and Z DR are calibrated with 2DVD. The generalized DSD parameters of 2DVD are averaged every 5 min based on the radar measurement interval.
The scatterplot of retrieved values from the radar and calculated from measured DSDs are shown in Figure 8 for the 11 rainfall cases, and Table 4

Evaluation of Retrieved Generalized DSD Parameters
A total of 11 rainfall cases (Table 3) during the summer season in 2012 are used to verify the retrieved generalized DSD parameters from the BSL radar. To reduce the effects of measurement noise and the contamination of non-meteorological echoes, the and are only selected at the gates with a cross-correlation coefficient greater than 0.95 and they are then averaged in an area of 3° and 1.375 km in azimuthal and radial directions, respectively (~2 km 2 ). The measured and are calibrated with 2DVD. The generalized DSD parameters of 2DVD are averaged every 5 min based on the radar measurement interval.
The scatterplot of retrieved values from the radar and calculated from measured DSDs are shown in Figure 8 for the 11 rainfall cases, and Table 4 shows the error statistics (correlation coefficient, SD, and bias) of retrieved andlogN 0 ′ . The bias is almost negligible in both retrieved andlogN 0 ′ . The retrieved was well correlated with calculated from 2DVD with the overall correlation of 0.76 (case correlation of 0.56 to 0.84 shown in Table 4

Microphysical Properties of an MCS Case: 14 September 2013
Mesoscale convective systems (MCSs) that include mesoscale convective complexes (MCCs), tropical cyclones, and squall lines are the complex of thunderstorms that involves a well-organized convective region [31][32][33][34]. Their spatial dimension can reach hundreds to a thousand kilometers, and their life span can be up to 24 h [35]. Among MCSs, the squall lines are characterized by a strong convection region with strong upward motions at a leading edge and a trailing stratiform region. The The time series of the retrieved values from the BSL radar and calculated values from 2DVD are shown in Figure 9 to investigate the low accuracy of the retrieved logN 0 for the case of 17 July 2012 that has the lowest correlation. The retrieved values are well-matched with the calculated values during 0330 LST to 0430 LST when Z H and, in particular, Z DR are larger, and the rain is continuous. A significant discrepancy (Figure 9d,e) is shown in Z H and Z DR when Z H is low. This discrepancy between BSL radar and 2DVD results in a significant difference in log N 0 , subsequently lower correlation. The logN 0 shows overestimation at logN 0 larger than 2.0 m −3 mm −1 . The large scatter of logN 0 are caused by the difference between observed Z DR from radar and 2DVD likely because of the measurement height difference (radar measurement at higher than 1.1 km), measurement noise, and sampling difference.

Microphysical Properties of an MCS Case: 14 September 2013
Mesoscale convective systems (MCSs) that include mesoscale convective complexes (MCCs), tropical cyclones, and squall lines are the complex of thunderstorms that involves a well-organized convective region [31][32][33][34]. Their spatial dimension can reach hundreds to a thousand kilometers, and their life span can be up to 24 h [35]. Among MCSs, the squall lines are characterized by a strong convection region with strong upward motions at a leading edge and a trailing stratiform region. The strong updraft in the leading edge generates the abundant supercooled droplet, and the vertically developed deep convective systems promote the frequent collision-coalescence process. The well-developed leading edge is usually followed by extensive trailing stratiform regions with relatively weaker rainfall. In this section, the microphysical characteristics of the leading edge and stratiform region in MCS are investigated with the generalized DSD parameters that are retrieved from dual-polarization radar.

Description of Event
Ref. [28] suggested three primary synoptic conditions that produce heavy precipitation events over the Korean peninsula; a passage of low-level troughs or cyclones, south-westerly flow, and extended low-level troughs. The weather chart of 850 hPa isobaric surface at 0900LST 14 September 2013 shows the troughs located northwest of the Korean Peninsula and large-scale convergence along the south-westerly (not shown). The enhanced infrared imagery from the Communication, Ocean, and Meteorological Satellite (COMS) shows vertically well-developed clouds with a top temperature lower than −50 • C. The surface observation at an automatic weather station (AWS) nearby the KNU site shows the dramatic change of wind direction from easterly to westerly with the onset of rain ( Figure 10). The westerly persisted throughout the precipitation period (blue shaded). The temperature also dropped about 2 • C during the raining period. The rainfall intensity showed one dominant peak at 0950LST on 14 September 2013 with maximum 15 min average rainfall intensity of 36 mm h −1 .  Wind barbs are marked every 10 min when wind speed is higher than 2.5 knots). The rain gage is a tipping bucket type with a resolution of 0.5 mm. The shading represents the rain periods identified by the rain detector Figure 11 presents the time sequence of images for MCS on 14 September 2013. The MCS is composed of the leading edge extending from southwest to northeast and following a weak and broad stratiform region. The leading edge developed from 0800 LST to 0930LST and passed through the radar from 0930 to 1030LST. The of leading edge reached 55 dBZ. The leading-edge then dissipated after 1300LST. The stratiform rain region with relatively low is followed behind the leading-edge and shows the embedded convection with higher than 35 dBZ locally. Wind barbs are marked every 10 min when wind speed is higher than 2.5 knots). The rain gage is a tipping bucket type with a resolution of 0.5 mm. The shading represents the rain periods identified by the rain detector. Figure 11 presents the time sequence of Z H images for MCS on 14 September 2013. The MCS is composed of the leading edge extending from southwest to northeast and following a weak and broad stratiform region. The leading edge developed from 0800 LST to 0930LST and passed through the radar from 0930 to 1030LST. The Z H of leading edge reached 55 dBZ. The leading-edge then dissipated after 1300LST. The stratiform rain region with relatively low Z H is followed behind the leading-edge and shows the embedded convection with Z H higher than 35 dBZ locally. Figure 10. Timeseries of 15-min average rainfall intensity (blue), air temperature (black), and wind speed and direction (wind barbs at the top of figure) at automatic weather station (AWS) located at 1.2km southeast from the KNU for the squall line event on 14 September 2013. Wind barbs are marked every 10 min when wind speed is higher than 2.5 knots). The rain gage is a tipping bucket type with a resolution of 0.5 mm. The shading represents the rain periods identified by the rain detector Figure 11 presents the time sequence of images for MCS on 14 September 2013. The MCS is composed of the leading edge extending from southwest to northeast and following a weak and broad stratiform region. The leading edge developed from 0800 LST to 0930LST and passed through the radar from 0930 to 1030LST. The of leading edge reached 55 dBZ. The leading-edge then dissipated after 1300LST. The stratiform rain region with relatively low is followed behind the leading-edge and shows the embedded convection with higher than 35 dBZ locally.

Classification of MCS
The elevation angle of 0.8 • are used to alleviate beam blockage and ground clutter. The quality control (QC) technique based on fuzzy logic [36,37] is applied to remove the ground clutter, chaff echoes, and other non-meteorological echoes. This algorithm is constructed of the optimized membership functions and weights based on the statistical process of polarimetric feature parameters using the long-term data set. The ground clutter, anomalous propagation, chaff, and insects are successfully removed. However, we have noticed some residual of second trip echoes remains near the radar site, causing some error in retrieval of DSD parameters. In addition, the Z DR larger than 0.2dB is used. DSD retrieval is done only in rain regions. The Z H and Z DR can abruptly change within the bright band. The typical height of the bright band was about 4 km during this rain event. Thus, the radar data are only used within the 100 km range (correspond to 2.5 km altitude of the radar beam center) to avoid the bright band contamination.
The microphysical characteristics and development processes are quite different in the leading edge and extensive trailing stratiform region [15,38,39]. In this study, the leading edge is identified by the fuzzy logic algorithm for storm tracking (FAST) based on radar reflectivity [40]. This algorithm identifies the storm cells using a reflectivity threshold and tracks the cells using the fuzzy logic that utilizes the characteristics of storm cells such as cell motion speed, area change ratio, and axis transformation ratio. First, the two-dimensionally consecutive areas that exceed the reflectivity threshold of 35 dBZ are clustered as a convective cell. This step identifies the storm cells in both the leading edge and trailing stratiform region. The storm average reflectivity is smaller in the embedded cell of the trailing stratiform than that in the leading edge. The cells located at the front of the precipitation system are manually selected and are treated as a single system at the leading edge with the same characteristics. The lower panel of Figure 11 shows four snapshots of the identified leading edge (grey areas), and the upper panel shows the Z H PPIs with the identified leading edge in black lines. The leading edge is composed of many storm cells in the front of the precipitation system. The storm cells in trailing regions are excluded and are treated as the trailing stratiform region. As shown in the lower panel, its line shape is well illustrated and tracked. The DSD characteristics of the leading edge are derived from these grey areas. On the other hand, those of the stratiform region are from all areas except for the grey region. Thus, some of the weak echo areas in the leading edge is included in the stratiform region.

Microphysical Characteristics of MCS Case
The time series of averaged Z H and Z DR of leading-edge is shown in Figure 12a. The Z H values of the leading edge are high (up to 43 dBZ) in the earlier period (~0930LST). The Z H and Z DR are somewhat positively correlated in this period, and Z DR has the maximum value around 0920~0930LST. After this period, both values decrease until 1100LST. The Z H continuously decreases while Z DR increases. That is, both values are negatively correlated in the period of 1100LST to 1300LST. However, some periods such as 0827LST and 0915LST~1003LST show dramatic change of the averaged Z H and Z DR in the leading-edge, in particular, unrealistic change of Z DR . Thus, we further investigate the potential causes of this change.
Remote Sens. 2020, 12, x FOR PEER REVIEW 14 of 20 Figure 12. Time series of (a) averaged reflectivity ( , black) and differential reflectivity ( , gray) at the leading-edge and (b) averaged and for the entire area (solid line) and the circle area with the radius of 5 km centered to radar site (dashed line). The average is done in dB unit.
The averaged and for the entire observation area (including the leading edge and stratiform area) increase until 0930LST and after then, the decreased rapidly (Figure 12b). On the other hand, the values largely fluctuate during 0920~1005LST and gently decreases after 1015LST with some fluctuation (gray solid line in Figure 12b). The rapid fluctuation of is highly correlated with the around the BSL radar indicated by the average reflectivity values near radar (dashed line). In particular, the sudden increase on at 0827LST, 0915LST~1003LST, and 1012LST~1120LST is driven by the significant rain over the radar site, caused by significant differential wet radome attenuation. The vertically flowing water shield causes more considerable attenuation in vertical polarization than in horizontal polarization. The wet radome attenuation is also confirmed by the drop of average reflectivity value in the entire area (black solid line in Figure  12b) at 0827LST, 0920LST, 0931LST, and 1000LST. The sudden change of and affects the retrieved microphysical parameters (as shown in Figures 13-15). The period of significant rain over the radar site was excluded in the statistical analysis with the threshold of average near the radar (about 33 dBZ) to avoid so the wet radome attenuation. Figure 13 shows the time series of the averaged generalized DSD parameters, D m and logN 0 ′ in the leading-edge (plus symbol), trailing stratiform (diamond symbol), and overall regions (solid line). Their frequency distribution is also shown in Figures 14 and 15. The sudden change of logN 0 ′ and D m is noticed because of the wet radome attenuation and should be discarded in the analysis afterward. The logN 0 ′ in the stratiform (left panel in Figure 14) region remains nearly constant or slightly increased (average logN 0 ′ ~ 2.2 m −3 mm −1 in Figure 13a) until 0920LST and shows the temporal fluctuation in 0930~1000LST due to the wet radome attenuation. The logN 0 ′ in the leading-edge region is nearly constant until 0920LST with a higher average of 2.4 m −3 mm −1 than the stratiform Figure 12. Time series of (a) averaged reflectivity (Z H , black) and differential reflectivity (Z DR , gray) at the leading-edge and (b) averaged Z H and Z DR for the entire area (solid line) and the circle area with the radius of 5 km centered to radar site (dashed line). The average is done in dB unit.
The averaged Z H and Z DR for the entire observation area (including the leading edge and stratiform area) increase until 0930LST and after then, the Z H decreased rapidly (Figure 12b). On the other hand, the Z DR values largely fluctuate during 0920~1005LST and gently decreases after 1015LST with some fluctuation (gray solid line in Figure 12b). The rapid fluctuation of Z DR is highly correlated with the Z H around the BSL radar indicated by the average reflectivity values near radar (dashed line). In particular, the sudden increase on Z DR at 0827LST, 0915LST~1003LST, and 1012LST~1120LST is driven by the significant rain over the radar site, caused by significant differential wet radome attenuation. The vertically flowing water shield causes more considerable attenuation in vertical polarization than in horizontal polarization. The wet radome attenuation is also confirmed by the drop of average reflectivity value in the entire area (black solid line in Figure 12b) at 0827LST, 0920LST, 0931LST, and 1000LST. The sudden change of Z H and Z DR affects the retrieved microphysical parameters (as shown in Figures 13-15). The period of significant rain over the radar site was excluded in the statistical analysis with the threshold of average Z H near the radar (about 33 dBZ) to avoid so the wet radome attenuation. Figure 13 shows the time series of the averaged generalized DSD parameters, D m and logN 0 in the leading-edge (plus symbol), trailing stratiform (diamond symbol), and overall regions (solid line). Their frequency distribution is also shown in Figures 14 and 15. The sudden change of logN 0 and D m is noticed because of the wet radome attenuation and should be discarded in the analysis afterward. The logN 0 in the stratiform (left panel in Figure 14) region remains nearly constant or slightly increased (average logN 0 ~2.2 m −3 mm −1 in Figure 13a) until 0920LST and shows the temporal fluctuation in 0930~1000LST due to the wet radome attenuation. The logN 0 in the leading-edge region is nearly constant until 0920LST with a higher average of 2.4 m −3 mm −1 than the stratiform region. The overall gradual decrease is shown with slightly higher average values but significant fluctuation with time. The D m (Figure 15a) in the stratiform region is nearly constant (average D m~1 .3 mm in Figure 13b) throughout the period. The D m in the leading edge (Figure 15b) gradually increases with time until 0920LST and remains constant with the average value of 1.8 mm (Figure 13b). The values of D m are much higher in the leading edge than in the stratiform region.
also confirmed by the drop of average reflectivity value in the entire area (black solid line in Figure  12b) at 0827LST, 0920LST, 0931LST, and 1000LST. The sudden change of and affects the retrieved microphysical parameters (as shown in Figures 13-15). The period of significant rain over the radar site was excluded in the statistical analysis with the threshold of average near the radar (about 33 dBZ) to avoid so the wet radome attenuation. Figure 13 shows the time series of the averaged generalized DSD parameters, D and logN in the leading-edge (plus symbol), trailing stratiform (diamond symbol), and overall regions (solid line). Their frequency distribution is also shown in Figures 14 and 15. The sudden change of logN and D is noticed because of the wet radome attenuation and should be discarded in the analysis afterward. The logN in the stratiform (left panel in Figure 14) region remains nearly constant or slightly increased (average logN ~ 2.2 m −3 mm −1 in Figure 13a) until 0920LST and shows the temporal fluctuation in 0930~1000LST due to the wet radome attenuation. The logN in the leading-edge region is nearly constant until 0920LST with a higher average of 2.4 m −3 mm −1 than the stratiform region. The overall gradual decrease is shown with slightly higher average values but significant fluctuation with time. The Dm (Figure 15a) in the stratiform region is nearly constant (average D ~1.3 mm in Figure 13b) throughout the period. The Dm in the leading edge (Figure 15b) gradually increases with time until 0920LST and remains constant with the average value of 1.8 mm (Figure 13b). The values of D are much higher in the leading edge than in the stratiform region.   In summary, the early period in the leading edge shows the most active drop growth by the collision-coalescence process with an abundant new generation of drops. Significant skewness toward higher log 0 ′ is shown in the frequency distribution of log 0 ′ in the leading-edge ( Figure   14b). That is, the leading is characterized as higher log 0 ′ as shown in [15] and [39]. In addition, Lagrangian temporal evolution in this study indicates that the drop growth becomes more active until 0920LST in the leading edge. Furthermore, the new generation of drops becomes less important, and the drop growth by the collision-coalescence remains dominant after 0920LST, as shown by the gradual increases of D m . However, the collision-coalescence is not the dominant process in the trailing stratiform region as shown by nearly constant D m (Figure 13b). The new generation of small   In summary, the early period in the leading edge shows the most active drop growth by the collision-coalescence process with an abundant new generation of drops. Significant skewness toward higher log 0 ′ is shown in the frequency distribution of log 0 ′ in the leading-edge ( Figure   14b). That is, the leading is characterized as higher log 0 ′ as shown in [15] and [39]. In addition, Lagrangian temporal evolution in this study indicates that the drop growth becomes more active until 0920LST in the leading edge. Furthermore, the new generation of drops becomes less important, and the drop growth by the collision-coalescence remains dominant after 0920LST, as shown by the gradual increases of D m . However, the collision-coalescence is not the dominant process in the trailing stratiform region as shown by nearly constant D m (Figure 13b). The new generation of small In summary, the early period in the leading edge shows the most active drop growth by the collision-coalescence process with an abundant new generation of drops. Significant skewness toward higher log N 0 is shown in the frequency distribution of log N 0 in the leading-edge (Figure 14b). That is, the leading is characterized as higher log N 0 as shown in [15] and [39]. In addition, Lagrangian temporal evolution in this study indicates that the drop growth becomes more active until 0920LST in the leading edge. Furthermore, the new generation of drops becomes less important, and the drop growth by the collision-coalescence remains dominant after 0920LST, as shown by the gradual increases of D m . However, the collision-coalescence is not the dominant process in the trailing stratiform region as shown by nearly constant D m (Figure 13b). The new generation of small drops was significant in the early period in the stratiform region. This may be originated by the supply of new ice particles from the leading edge in which the strong updraft prevails during the early period. However, this becomes weaker after 0920LST because of the weakening of overall systems as seen by decreasing of the average Z H over the entire measurement area (see Figure 12b). The large spread of the frequency distribution of D m indicates the diversity of precipitation systems within the trailing stratiform region such as weak stratiform rain and embedded convention.
The statistical distribution of the generalized characteristic parameters is investigated for the stratiform region and leading edge in the early (0820LST) and later (1130LST) periods when the Lagrangian temporal evolution is quite different (Figure 16). The D m is larger in the leading edge with averages of 1.67~1.94 mm than in the stratiform with averages of 1.31~1.37 mm. In particular, the long tail in larger D m is prominent in the leading edge. The log N 0 is also larger in the leading edge with average values of 1.68~2.51 m −3 mm −1 than in the stratiform with averages of 1.77~2.19 m −3 mm −1 . The Lagrangian temporal evolution of log 0 ′ (D m ) shows the same trend (opposite trend) in the stratiform and leading-edge regions. That is, the log 0 ′ decreases with time in both regions (lower panel in Figure 16), caused by the significant reduction of the newly generated drops as the precipitation systems weaken. However, the D m decreases with time in the stratiform region while it becomes larger with time in the leading edge, indicating the drop growth by the dominant collisioncoalescence process in the leading-edge throughout the period. As explained in Section 5.2, the cells in the leading edge are treated as the same precipitation system in the same development stage. In fact, all cells are unlikely in the same stage. This The Lagrangian temporal evolution of log N 0 (D m ) shows the same trend (opposite trend) in the stratiform and leading-edge regions. That is, the log N 0 decreases with time in both regions (lower panel in Figure 16), caused by the significant reduction of the newly generated drops as the precipitation systems weaken. However, the D m decreases with time in the stratiform region while it becomes larger with time in the leading edge, indicating the drop growth by the dominant collision-coalescence process in the leading-edge throughout the period.
As explained in Section 5.2, the cells in the leading edge are treated as the same precipitation system in the same development stage. In fact, all cells are unlikely in the same stage. This complicates the interpretation of derived DSD parameters. Thus, the results should be understood as the evolution of the cell complex rather than that of individual cells.

Conclusions
The temporal evolution of microphysical characteristics of precipitation systems can be investigated in high temporal and spatial resolution and in Lagrangian framework by dual-polarimetric radar measurement in wide areas. We derived the relationships between differential reflectivity and generalized DSD parameters normalized by radar reflectivity derived from DSDs. The dual-polarization radar variables and generalized DSD parameters (general number concentration, N 0 , and generalized mean diameter, D m ) were derived by using the 2-D video distrometer data observed during 10 months in the Jinchun site. These relationships were applied to 11 rain events to retrieve N 0 and D m from the BSL dual-polarimetric radar, and the retrieved parameters were then verified by DSDs observed from a 2DVD located at 23 km away from the radar. A mesoscale convective system (MCS) on 14 September 2013 was classified into the two regions (the leading edge and trailing stratiform region) by the storm classification algorithm [39]. The microphysical characteristics in the two regions were then investigated with retrieved parameters from the radar in the Lagrangian frame.
The reflectivity (Z H ) and differential reflectivity (Z DR ) were simulated from DSDs with the T-matrix calculation, and the N 0 and D m are derived from the 3rd and 4th moments of DSDs with the assumption on the scaling normalization of DSDs. Then, the N 0 and D m normalized by Z H were fitted as polynomial functions of Z DR , and these fitted polynomial functions were used to retrieve N 0 and D m from the dual-polarimetric measurement. First, we calculated the theoretical accuracy of this retrieval method due to the variability of DSDs. The normalized standard deviations (NSD) of retrieved DSD parameters were in the range of 0.07 to 0.11 (average SD of 0.11) for D m and of 0.09 to 0.2 (average SD of 0.26) for log N 0 that were quite comparable with the results in [6].
However, the accuracy deteriorated when applied to the actual radar measurement. The retrieval accuracy of D m (log N 0 ) was quite high (low). The overall correlation of D m (log N 0 ) for 11 rain events was 0.76 (0.39). The SDs of D m and log N 0 were about 0.19 and 0.46. A significant overestimation was noticed at log N 0 > 2.0 m −3 mm −1 . This overall low accuracy in log N 0 was attributed to the significant discrepancy of Z H and Z DR from radar measurement and 2DVD, in particular when Z H and Z DR are low. In addition, the log N 0 is an intercept parameter that relies on the lower moments. However, the log N 0 was derived from the higher moment (Z H ) and the ratio of higher moments (Z DR ). Subsequently, the small measurement errors either in Z H and Z DR severely affect the retrieval accuracy of the log N 0 . Thus, the measurement or estimation of lower moments is key to improve retrieval accuracy and should be investigated further.
The temporal evolution of microphysical characteristics was investigated in the MCS system using retrieved values of N 0 and D m . The leading edge dominated by strong updraft showed broad DSD spectra with higher number concentration and larger characteristic diameter. The frequency distribution of log N 0 skewed negatively (tail in low concentration and peak toward higher log N 0 ). The increase of D m is noticeable in the leading edge, in particular when the precipitation system grows. This indicates that the drop growth by the collision-coalescence process was dominant in the leading edge throughout the event. In addition, the value of log N 0 (~2.5 m −3 mm −1 ) was high and steady in the leading edge for the early period when the system grows. When the system weakens, its value decreases with time. This implies that both the new generation of drops and drop growth by the coalescence was dominant in the early period of the leading-edge. However, when the system weakens, the new generation of drops becomes less significant while the growth of the drop by collision and coalescence remains.
On the other hand, the value of D m remains constant throughout the event in the trailing stratiform region. The value of log N 0 is nearly constant with a similar value of MP when the entire precipitation grows. However, its value decreases with time for the later period, similar to the leading edge. Thus, the collision-coalescence process is less important throughout the event in the trailing stratiform region. The new generation of small drops was important in the early period. This is likely due to the supply of new ice particles from the leading edge. In addition, the frequency distributions of D m and log N 0 were broader, indicating the diversity of the precipitation systems as shown by embedded convection within the stratiform region.
The Lagrangian evolution of DSDs can provide an insight into the interaction between the dynamical and microphysical processes. The separation of the leading edge and trailing stratiform is a proxy of classification of the strong updraft and steady weak upward motion. The leading edge is typically characterized by the strong updraft in the early developing period, and the strength of the updraft becomes weak as the system approaches the decaying period. The Lagrangian evolution of log N 0 and D m reflects this dynamical aspect. The Lagrangian temporal evolution of log N 0 showed the same trend in the leading-edge and trailing stratiform region. That is, the peak of the distribution shifted to smaller values. This indicates that its value is controlled by the growing and weakening of the precipitation system. However, the value of D m showed the opposite trend. That is, its value decreases with time in the trailing stratiform and vice versa in the leading-edge. Thus, we can conclude that the drop growth in the leading-edge is controlled by the collision-coalescence process for the entire event. However, the new generation of small drops is important in the drop growth in the trailing stratiform region shown in the early period.
In this study, we did not attempt to retrieve the functional form of normalized DSDs. However, the function may vary in smaller temporal and spatial scales, although it is nearly constant in a climatological sense. It is trivial that some microphysical processes, such as evaporation, will change the function of normalized DSDs. However, the change of the function becomes less significant in the normalized DSDs than that in the DSDs since the significant variation is somewhat contained in the generalized characteristic parameters. Nevertheless, exploration on the function of the normalized DSDs further merits a more detailed understanding of the microphysical evolution of precipitation systems.