Raindrop Size Distributions and Rain Characteristics Observed by a PARSIVEL Disdrometer in Beijing, Northern China

Fourteen-month precipitation measurements from a second-generation PARSIVEL disdrometer deployed in Beijing, northern China, were analyzed to investigate the microphysical structure of raindrop size distribution and its implications on polarimetric radar applications. Rainfall types are classified and analyzed in the domain of median volume diameter D0 and the normalized intercept parameter Nw. The separation line between convective and stratiform rain is almost equivalent to rain rate at 8.6 mm h−1 and radar reflectivity at 36.8 dBZ. Convective rain in Beijing shows distinct seasonal variations in log10 Nw–D0 domain. X-band dual-polarization variables are simulated using the T-matrix method to derive radar-based quantitative precipitation estimation (QPE) estimators, and rainfall products at hourly scale are evaluated for four radar QPE estimators using collocated but independent rain gauge observations. This study also combines the advantages of individual estimators based on the thresholds on polarimetric variables. Results show that the blended QPE estimator has better performance than others. The rainfall microphysical analysis presented in this study is expected to facilitate the development of a high-resolution X-band radar network for urban QPE applications.


Introduction
Characteristics of raindrop size distribution (DSD) are of great importance in various disciplinary research.They are the physical basis in the formation of clouds and precipitation [1].Understanding the DSD is critical for the microphysical parameterizations in numerical weather prediction models [2][3][4], and quantitative precipitation estimation (QPE) using remote sensing technologies, such as radar and satellite [5,6].The DSDs can also be utilized to estimate the kinetic energy of rain [7], which is a key factor in assessing the degree of soil erosion [8].To this end, numerous studies have been conducted around the world to characterize the DSD in different climate regions and rainfall types, using a variety of in situ and remote sensing instruments [9][10][11][12][13][14][15][16].

Quality control (QC)
Particle diameter and fall speed, each divided into 32 nonuniform classes, were measured by the PARSIVEL 2 disdrometer with a 1-min sampling interval.The mean values of particle diameter (0.062-24.5 mm) and fall speed (0.05-20.8 m s -1 ) are described by the manual [37].The first two size bins are not included in the analysis, because of the low signal-to-noise ratios.As a result, the smallest detectable mean diameter is 0.312 mm.The effective sampling area of PARSIVEL 2 droplet size measurements is affected by the so-called border effects, and the method of Jaffrain and Berne [38] is utilized to account for these effects.In particular, defining   (mm) as the central volume-equivalent diameter for the ith size bin, the effective sampling area can be calculated as 180 mm × (30 mm − 0.5  ).
The empirical terminal velocity-diameter (-) relationship of Gunn and Kinzer [39] with air-density correction factor ( 0   ⁄ ) 0.4 [40,41] was used to assess raindrop observations and is repeated as follows: (  ) = [9.65 − 10.3exp(−0.6 )] (  0   ) where   (  ) is the mean particle terminal velocity for the ith size bin;   and  0 (1.20 kg m -3 ) are the air density at the observation altitude and at sea level, respectively.Following the method described in Atlas et al. [40] and Foote and Toit [41], the mean value (1.008) of the correction factor was selected for simplicity.Some droplet observations may deviate from the - relationship shown in Eq. (1).A commonly used method to eliminate those abnormal particles is to set a threshold regarding Eq. (1).A value of ± 60% was selected as the threshold [20] in this study, which means droplets with velocities of  obs (  ) were discarded when they met the condition | obs (  ) −   (  )| > 0.6  (  ).In addition, the 1-min DSD spectrum with a total number of raindrops   ＜ 10 or a rain rate lower than 0.01 mm h -1 was considered to have no rain.Rain drops larger than 8 mm in diameter were also removed.Then, continuous spectra with rain-free periods of no longer than 1 h were defined as a rain event, and rain events lasting less than 5 min were eliminated to reduce the statistical errors.The dataset after quality control is further described in Section 3.1.

Quality Control (QC)
Particle diameter and fall speed, each divided into 32 nonuniform classes, were measured by the PARSIVEL 2 disdrometer with a 1-min sampling interval.The mean values of particle diameter (0.062-24.5 mm) and fall speed (0.05-20.8 m s −1 ) are described by the manual [37].The first two size bins are not included in the analysis, because of the low signal-to-noise ratios.As a result, the smallest detectable mean diameter is 0.312 mm.The effective sampling area of PARSIVEL 2 droplet size measurements is affected by the so-called border effects, and the method of Jaffrain and Berne [38] is utilized to account for these effects.In particular, defining D i (mm) as the central volume-equivalent diameter for the ith size bin, the effective sampling area can be calculated as 180 mm × (30 mm − 0.5D i ).
The empirical terminal velocity-diameter (V-D) relationship of Gunn and Kinzer [39] with air-density correction factor (ρ 0 /ρ a ) 0.4 [40,41] was used to assess raindrop observations and is repeated as follows: where V t (D i ) is the mean particle terminal velocity for the ith size bin; ρ a and ρ 0 (1.20 kg m −3 ) are the air density at the observation altitude and at sea level, respectively.Following the method described in Atlas et al. [40] and Foote and Toit [41], the mean value (1.008) of the correction factor was selected for simplicity.Some droplet observations may deviate from the V-D relationship shown in Equation (1).A commonly used method to eliminate those abnormal particles is to set a threshold regarding Equation (1).A value of ±60% was selected as the threshold [20] in this study, which means droplets with velocities of V obs (D i ) were discarded when they met the condition In addition, the 1-min DSD spectrum with a total number of raindrops C T < 10 or a rain rate lower than 0.01 mm h −1 was considered to have no rain.Rain drops larger than 8 mm in diameter were also removed.Then, continuous spectra with rain-free periods of no longer than 1 h were defined as a rain event, and rain events lasting less than 5 min were eliminated to reduce the statistical errors.The dataset after quality control is further described in Section 3.1.

Integral Rainfall Parameters
Based on the DSD data, the number concentration of raindrops per unit volume per unit diameter interval for the ith size bin, N(D i ) (m −3 mm −1 ), can be calculated using Equation (2): where n ij is the number of raindrops at the ith size bin and the jth velocity class; A i (m 2 ) and ∆D i (mm) are the effective sampling area and width of the diameter interval at size D i ; V j (m s −1 ) is the fall speed for the jth velocity class; and ∆t is the sampling time interval, which was set to 60 s in this study.
To further understand the characteristics of rainfall, the integral parameters of total number concentration N T (m −3 ), rainwater content W (g m −3 ), rain rate R (mm h −1 ), median volume diameter D 0 (mm), mass-weighted mean diameter D m (mm), normalized intercept parameter N w (m −3 mm −1 ), and mass spectrum standard deviation σ m (mm), were also calculated as follows: where ρ w is the water density (1.0 g cm −3 ).Considering the emerging development of X-band dual-polarization weather radar for urban hydrometeorological applications [42,43], a set of dual-polarization radar variables, including radar reflectivity in the horizontal (vertical) polarization Z h (Z v ) (mm 6 m −3 ), differential reflectivity Z DR (dB) and specific differential phase K DP ( • km −1 ), are derived from DSDs using the T-matrix scattering technique [44]: where f hh,vv (D i ) is the backscattering amplitude of a droplet with horizontal and vertical polarization; f hh (0, D i ) and f vv (0, D i ) are the standard forward scattering amplitudes, which is related to the depolarization factor and relative permittivity of water dielectric [45]; K w is the dielectric factor of water (0.9639); and λ (mm) is the radar wavelength (3 cm).Note that Z h (Z v ) in the unit of mm 6 m −3 is replaced by Z H (Z V ) in the unit of dBZ wherever required in this paper, and Z H,V = 10 × log 10 Z h,v .

Dataset after QC
In total, 25,499 (934) 1-minute raindrop spectra passed (failed) the QC.The validated spectra account for a total rainfall of 1013.78 mm.According to the histogram in Figure 2, DSD samples failed to pass the QC mainly appear when rain rates (R stn ) measured by collocated rain gauges at 1-min-interval were lower than 15 mm h −1 .Falling beyond the threshold of the empirical V-D relationship is the major factor leading to droplet removal from the dataset, and accounts for 3.2% of total rainfall.It was also noted that most of the removed DSD samples were characterized by abnormally rain rates (R) compared with R stn , most of which occurred when R stn < 10 mm h −1 or R stn > 100 mm h −1 (red points in the scatter plot of Figure 2).The Pearson correlation coefficient (PCC) between the pairs of (R, R stn ) was higher after QC (0.96 vs. 0.91).The linear fitting curve based on the dataset with R stn > 0 mm h −1 after QC (blue line; denoted "QC + R stn > 0") is close to the diagonal line.
where  hh,vv (  ) is the backscattering amplitude of a droplet with horizontal and vertical polarization;  hh (0,   ) and  vv (0,   ) are the standard forward scattering amplitudes, which is related to the depolarization factor and relative permittivity of water dielectric [45];   is the dielectric factor of water (0.9639); and  (mm) is the radar wavelength (3 cm).Note that  ℎ (  ) in the unit of mm 6 m -3 is replaced by   (  ) in the unit of dBZ wherever required in this paper, and  , = 10 × log 10  ℎ, .

Dataset after QC
In total, 25,499 (934) 1-minute raindrop spectra passed (failed) the QC.The validated spectra account for a total rainfall of 1013.78 mm.According to the histogram in Figure 2, DSD samples failed to pass the QC mainly appear when rain rates ( stn ) measured by collocated rain gauges at 1-min-interval were lower than 15 mm h -1 .Falling beyond the threshold of the empirical - relationship is the major factor leading to droplet removal from the dataset, and accounts for 3.2% of total rainfall.It was also noted that most of the removed DSD samples were characterized by abnormally rain rates () compared with  stn , most of which occurred when  stn < 10 mm h -1 or  stn > 100 mm h -1 (red points in the scatter plot of Figure 2).The Pearson correlation coefficient (PCC) between the pairs of (,  stn ) was higher after QC (0.96 vs. 0.91).The linear fitting curve based on the dataset with  stn > 0 mm h -1 after QC (blue line; denoted "QC+ stn >0") is close to the diagonal line.As shown in Figure 3, the distribution of raindrops is almost entirely within the threshold of ±60% based on Equation (1).The filtered particles are mainly below 3 mm in diameter.They generally have low fall speeds but with relatively large size, likely due to the influences of strong winds or splashes from instrument surface during heavy rainfall [20].The accumulated disdrometer data after QC are almost symmetric along the empirical V-D relationship of Atlas et al. [40] and the highest number concentrations of raindrops are nearly superimposed.As shown in Figure 3, the distribution of raindrops is almost entirely within the threshold of ± 60% based on Eq. ( 1).The filtered particles are mainly below 3 mm in diameter.They generally have low fall speeds but with relatively large size, likely due to the influences of strong winds or splashes from instrument surface during heavy rainfall [20].The accumulated disdrometer data after QC are almost symmetric along the empirical - relationship of Atlas et al. [40] and the highest number concentrations of raindrops are nearly superimposed.A summary of rainfall observations after QC during the experiment period is listed in Table 1.The precipitation mainly occurred from June to August, which contributed up to 81.5% of the total rainfall amount.The mean and maximum rain rates, 〈〉 and  max , were much higher during these three months than other months.The number of DSD samples,  mins , collected between June−August and in October, was much higher, contributing 78.3% of total samples.Although  mins in October was higher than June, 〈〉,  max , and the rainfall amount were much lower in October, especially  max (12.17 mm h -1 vs 84.92 mm h -1 ).The most (least) contribution of rainfall amount, as well as  max , came from July (September), while the least 〈〉 and  mins came from April and September, respectively.Compared with 2017, the precipitation intensity in 2018 was heavier with higher 〈〉 and  max but lower  mins and total rainfall amount.All these imply that the selected rainfall events consist of a wide variety of rainfall types.A summary of rainfall observations after QC during the experiment period is listed in Table 1.The precipitation mainly occurred from June to August, which contributed up to 81.5% of the total rainfall amount.The mean and maximum rain rates, R and R max , were much higher during these three months than other months.The number of DSD samples, N mins , collected between June−August and in October, was much higher, contributing 78.3% of total samples.Although N mins in October was higher than June, R , R max , and the rainfall amount were much lower in October, especially R max (12.17 mm h −1 vs. 84.92mm h −1 ).The most (least) contribution of rainfall amount, as well as R max , came from July (September), while the least R and N mins came from April and September, respectively.Compared with 2017, the precipitation intensity in 2018 was heavier with higher R and R max but lower N mins and total rainfall amount.All these imply that the selected rainfall events consist of a wide variety of rainfall types.Note: N mins is the number of 1-min DSD samples.R and R max are the mean and max rain rate, respectively.

Statistical Properties of N w -D 0
N w and D 0 are two main parameters defining the DSD [46,47], which also play an important role in retrieving precipitation microphysics on a global scale as part of the GPM mission [48,49].In fact, major microphysical processes that dominate the DSD properties can partially be recognized in the log 10 N w -D 0 domain [46].The distribution of log 10 N w vs D 0 is also an indicator to separate convective and stratiform rain types (C−S).In this study, the separation scheme described in Bringi et al. [50] (hereafter referred to as BR09) is adopted, as shown in Equation (13).Briefly, N w -D 0 pairs above (below) Equation ( 13) are recognized as convective (stratiform) rain, By using C_BR09 and S_BR09 to, respectively, denote the convective and stratiform rain, classified by Equation ( 13), Table 2 summaries a series of DSD parameters for different rainfall types.There are 1488 (24011) minutes of DSDs classified as convective (stratiform) rain, which account for 5.8% (94.2%) of the entire dataset of occurance and correspond to 54.8% (45.2%) of total rainfall amount.Generally, the means of all DSD parameters for C_BR09 are higher than those for S_BR09.[52], respectively.For example, C_BR09 and S_BR09 correspond to convective and stratiform rain classified by BR09 scheme.The number of spectra (occurrence), as well as their proportion of the entire dataset are given before and after the '/' in row 2. Row 3 is same as row 2, but for the rainfall amount.The 1th and 99th quantiles of rain rate for each dataset are listed before and after the '/' in row 5. Angle bracket stands for the sample mean.
Figure 4 shows the scatterplot of log 10 N w versus D 0 for convective (C_All, orange) and stratiform (S_All, lime) rain types, as well as the corresponding relative occurance frequency.The mean (MEAN), standard deviation (STD) and skewness (SKEW) are also indicated in Figure 4. Here, C_All (S_All) dataset equals to the dataset of C_BR09 (S_BR09) denoted in Table 2. Equation (13) are superimporsed in the scatterplot panel (dashed line).Meanwhile, another C−S separation line suggested by Thompson et al. [53] (hereafter referred to as TH15) for oceanic, tropical rain regions is also superimposed (dot-dashed line) for reference.Equation (14) shows the formula of TH15, Stratiform samples (S_All) are concentrated near the MEAN values of D 0 = 1.01 mm and log 10 N w = 3.57, whereas convective samples (C_All) are sparsely distributed above the BR09 line.It results in larger STD of D 0 and log 10 N w for convective than stratiform rain.The D 0 histograms for both rain types are positively skewed, whereas the log 10 N w histograms for convective rain exhibit a negative skewness of −0.93.Compared with stratiform rain, the D 0 and log 10 N w histograms for convective rain tend to shift toward larger values, which are in agreement with previous studies for other climate regimes [10,11,51].Similar variation tendencies of D 0 and log 10 N w histograms between "Total" dataset (blue) and stratiform rain can be found, which are due to the dominant role of stratiform rain.Figure 4 shows the scatterplot of log 10   versus  0 for convective (C_All, orange) and stratiform (S_All, lime) rain types, as well as the corresponding relative occurance frequency.The mean (MEAN), standard deviation (STD) and skewness (SKEW) are also indicated in Figure 4. Here, C_All (S_All) dataset equals to the dataset of C_BR09 (S_BR09) denoted in Table 2. Eq. ( 13) are superimporsed in the scatterplot panel (dashed line).Meanwhile, another C−S separation line suggested by Thompson et al. [53] (hereafter referred to as TH15) for oceanic, tropical rain regions is also superimposed (dot-dashed line) for reference.Eq. ( 14) shows the formula of TH15, Stratiform samples (S_All) are concentrated near the MEAN values of  0 = 1.01 mm and log 10   = 3.57, whereas convective samples (C_All) are sparsely distributed above the BR09 line.It results in larger STD of  0 and log 10   for convective than stratiform rain.The  0 histograms for both rain types are positively skewed, whereas the log 10   histograms for convective rain exhibit a negative skewness of −0.93.Compared with stratiform rain, the  0 and log 10   histograms for convective rain tend to shift toward larger values, which are in agreement with previous studies for other climate regimes [10,11,51].Similar variation tendencies of  0 and log 10   histograms The normalized frequency of DSD sample occurrence is shown in Figure 5.Note that the TH15 line in W-D 0 domain (Figure 5b) can be generated by combining Equation ( 7) and ( 14).The highest frequency of occurrence is in the ranges of D 0 about 0.8-1.1 mm and log 10 N w about 3.2-4.1,corresponding to rainwater content W within 0.02-0.11g m −3 .The distribution of normalized frequency of DSD in both log 10 N w -D 0 and W-D 0 domains are similar to the analyses in Dolan et al. [46] (their Figure 2b,e) in the midlatitudes.Therefore, this study provides new evidence from midlatitude Asian (northern China) to further support such analysis.
line in - 0 domain (Figure 5b) can be generated by combining Eqs. ( 7) and ( 14).The highest frequency of occurrence is in the ranges of  0 about 0.8−1.1 mm and log 10   about 3.2−4.1,corresponding to rainwater content  within 0.02−0.11g m -3 .The distribution of normalized frequency of DSD in both log 10   - 0 and - 0 domains are similar to the analyses in Dolan et al. [46] (their Figures 2b and 2e) in the midlatitudes.Therefore, this study provides new evidence from midlatitude Asian (northern China) to further support such analysis.In Figure 6, the log 10   −  0 pairs are color coded by rain rate  and   to investigate the interrelations among them.Similar patterns can be found in Figures 6a and 6b that the increases of both  and   are proportional to the increases of log 10   and  0 , illustrating the internal relation between rain rate and radar reflectivity, or the  ℎ - relationship that will be discussed in Section 4. The TH15 line crosses all levels of  and   , whereas BR09 line is almost equivalent to a threshold of  (8.6 mm h -1 ) or   (36.8 dBZ).Similar conclusion has been drawn for tropical, maritime regions with  = 10 mm h -1 and   = 40 dBZ [53], which are slightly higher than our results.Interestingly, fewer DSD samples fell within log 10   > 4 and  0 > 1 mm (see Figures 4−6) compared to the results observed during the Asian Summer Monsoon Season in Eastrn [14] (their Figure 6) or Southern China [54] (their Figure 6), and in tropical, oceanic islands [53] (their Figures 14a and 14b).In addition, more DSD samples exist in the range above BR09 line but below TH15 line.Referring to Dolan et al. [46] and Bringi et al. [51], warm rain with the collision-coalescence process has a great contribution to the precipitation in Eastern and Southern China during the Asian Summer Monsoon Season and tropical, oceanic regions.On the contrary, mixed phase precipitaiton processes may dominante the rainfall microphysics near the disdrometer site in Beijing.The enhanced mixed phase precipitation processes can produce larger raindrops when the ice-based hydrometers melt, which need to be further investigated in future.
Datasets for convective and stratiform rain are further divided into months, as shown in the log 10   - 0 domain in Figure 7, to see the monthly variations in DSD and better compare with previous findings.For stratiform rain, the MEAN values of log 10   and  0 in each month are all concentrated near the highest frequency of occurrences (Figure 5a), which corresponds to the "ambiguous" area in Figure 12 from Dolan et al. [46].For convective rain, those values are Interestingly, fewer DSD samples fell within log 10 N w > 4 and D 0 > 1 mm (see Figures 4-6) compared to the results observed during the Asian Summer Monsoon Season in Eastrn [14] (their Figure 6) or Southern China [54] (their Figure 6), and in tropical, oceanic islands [53] (their Figure 14a,b).In addition, more DSD samples exist in the range above BR09 line but below TH15 line.Referring to Dolan et al. [46] and Bringi et al. [51], warm rain with the collision-coalescence process has a great contribution to the precipitation in Eastern and Southern China during the Asian Summer Monsoon Season and tropical, oceanic regions.On the contrary, mixed phase precipitaiton processes may dominante the rainfall microphysics near the disdrometer site in Beijing.The enhanced mixed phase precipitation processes can produce larger raindrops when the ice-based hydrometers melt, which need to be further investigated in future.
Datasets for convective and stratiform rain are further divided into months, as shown in the log 10 N w -D 0 domain in Figure 7, to see the monthly variations in DSD and better compare with previous findings.For stratiform rain, the MEAN values of log 10 N w and D 0 in each month are all concentrated near the highest frequency of occurrences (Figure 5a), which corresponds to the "ambiguous" area in Figure 12 shown in reference [46].For convective rain, those values are distributed in a larger range from the mixed area to the ice-based area (from April to August), as well as aggregation/riming area (September and October) in Figure 12 from Dolan et al. [46].Note that for convective rain the MEAN values of log 10 N w -D 0 pairs in months from May to August are almost all around the value of 3.61 and 2.03 mm for C_All dataset with minor variations.Their STD values are also similar, which means similar microphysical processes dominated the precipitation during these months.However, such characteristics are not observed in other months.Relatively larger log 10 N w and smaller D 0 indicate relatively more warm rain processes in April, while in September and October obviously lower log 10 N w and larger D 0 indicate the relatively intense ice-based processes, such as aggregation and riming that sharply exhausting the number of small size hydrometers but slowly increasing the size of drops.Such analyses demonstrate the seasonal variation of dominating microphysical processes in Beijing.Overall, all MEAN values for both rain types in each month are below the TH15 line, illustrating that different microphysical processes are dominating the precipitation between midlatitude and Eastern and Southern China during the Asian Summer Monsoon Season, as well as tropical, oceanic regions.

Discussion on C−S classification schemes
The classification of precipitation into convective and stratiform is important in this study.Previous studies have proved that BR09 and TH15 schemes in log 10   - 0 domain are applicable based on the measurements not only from disdrometers but also from polarimetric radars [46,50,53,55,56].As such, these classification approaches are adopted.However, there are also a few other C−S classification schemes.In order to reveal the impacts of the classification approach on the analysis results, this study also applied the C−S classification schemes described in Testud et al. [52] (hereafter referred as to TE01) and Bringi et al. [51] (hereafter referred as to BR03) for comparison purpose.Both schemes are popularly used as well, and both are based on the variation of  with time and utilize 10 (5) adjacent DSD measurements at a 1-min (2-min) interval.The major difference between them is that TE01 assesses the values of  with an upper limit of 10 mm h -1 for stratiform rain, whereas BR03 evaluates the standard deviation of  ( ) with a lower threshold of 5 mm h -1

Discussion on C−S Classification Schemes
The classification of precipitation into convective and stratiform is important in this study.Previous studies have proved that BR09 and TH15 schemes in log 10 N w -D 0 domain are applicable based on the measurements not only from disdrometers but also from polarimetric radars [46,50,53,55,56].As such, these classification approaches are adopted.However, there are also a few other C−S classification schemes.In order to reveal the impacts of the classification approach on the analysis results, this study also applied the C−S classification schemes described in Testud et al. [52] (hereafter referred as to TE01) and Bringi et al. [51] (hereafter referred as to BR03) for comparison purpose.Both schemes are popularly used as well, and both are based on the variation of R with time and utilize 10 (5) adjacent DSD measurements at a 1-min (2-min) interval.The major difference between them is that TE01 assesses the values of R with an upper limit of 10 mm h −1 for stratiform rain, whereas BR03 evaluates the standard deviation of R (σ R ) with a lower threshold of 5 mm h −1 for convective rain.It should be mentioned that some DSDs may satisfy the conditions R < 5 mm h −1 and σ R ≤ 1.5 mm h −1 according to BR03, and, thus, fail to be classified as either stratiform or convective rain.
TH15 scheme is not suitable for Beijing, because no obvious peak of sample occurrences above Equation ( 14) can be found in Figure 5. Therefore, only integral rainfall parameters derived from BR09, BR03, and TE01 are listed in Table 2. Compared with BR09, both TE01 and BR03 schemes classify more convective (less stratiform) DSDs, which result in more (less) rainfall amount and a higher proportion of convective (stratiform) rain.However, almost all DSD parameter values for both rain types derived by TE01 and BR03 are not higher than those derived based on BR09, except the log 10 N w value for convective rain.Compared with Figure 4, convective rain classified by TE01 (Figure A1) and BR03 (Figure A2) in log 10 N w -D 0 domain contain much more samples under BR09 line but above TH15 line, corresponding to the DSDs with higher number concentration but smaller size.As a result, the smallest log 10 N w but highest D 0 for convective rain are obtained by BR09.
For stratiform rain, the DSD parameters from S_TE01 are higher than those from S_BR03.For convective rain, however, it is the opposite (Table 2).Further study shows that the percentage of samples with R > 5 mm h −1 in C_BR03 is higher than that in C_TE01.In other words, the lower threshold of 5 mm h −1 for convective rain set in BR03 scheme plays a key role in the different results between TE01 and BR03.
In summary, for stratiform rain, the impacts of different C−S classification schemes are not distinct relative to convective rain, due to the higher number of samples for the former than the latter.Although DSDs classified by the aforementioned three schemes in log 10 N w -D 0 domain can be separated by BR09 line in general (Figures 4, A1 and A2), the specific properties of DSDs could be different.The BR09 scheme is recommended, since it has been proved with radar observations [55,56].

Radar-Based Quantitative Precipitation Estimation
This study first computed Z h and R using Equations ( 5) and (10), based on the DSD measurements, to support weather radar applications in Beijing.The power-law relation Z h = aR b was then derived using nonlinear regression approach.It is well known that the Z h -R relationship is dependent on local DSD variability, which can be influenced by many factors, such as rainfall type, climate regime, and orographic effect [17,35,57].Finding a suitable Z h -R relation for Beijing is also critical to RMAPS model for QPE forecast [36].
Figure 8 shows a scatterplot of Z h -R pairs for both rain types classified by BR09 scheme along with the corresponding fitted power-law curves and equations.The fitted curve for the entire dataset is highlighted in black dots.For comparison, other four commonly used Z h -R relationships are also indicated in Figure 8, including those for the continental stratiform rain (Z h = 200R 1.6 ) [58], tropical systems (Z h = 250R 1.2 ) [59], operational WSR-88D radars (Z h = 300R 1.4 ) [60], and Meiyu convective rain in China (Z h = 368R 1.21 ) [11].Obviously, Z h is proportional to R in the double logarithmic domain.Based on the fitted relations for the two rain types, for a given Z h , higher R can be obtained using the stratiform relation than a convective algorithm.The relationship for the entire dataset (i.e., Z h = 265.14R1.399 ) is closer to the relationship for stratiform rain.
It is worth noting that the relationship for the operational WSR-88D (thin dashed lime line) [60] is very similar to our result based on the entire dataset, which implies that the relationship  ℎ = 300 1.4 could potentially be employed for QPE in Beijing.For convective rain, both  ℎ = 250 1.2  and  ℎ = 368 1.21 will underestimate the rainfall intensities, likely due to the smaller diameter and higher number concentration of raindrops in these two climate regions than in Beijing (as detailed in Figure 8. Scatterplot of Z h (mm 6 m −3 ) vs. R (mm h −1 ) computed from PARSIVEL 2 DSD measurements for stratiform (red dots) and convective (blue dots) rain classified using BR09 scheme.The fitted power-law curves for stratiform and convective rain, as well as the entire dataset, are indicated by thick solid dark-red, solid dark-blue, and black dotted lines, respectively.The relationships for continental stratiform rain, Z h = 200R 1.6 [58], tropical systems, Z h = 250R 1.2 [59], the operational WSR-88D, Z h = 300R 1.4 [60], and Meiyu convective rain, Z h = 368R 1.21 [11] are also indicated in thin dashed yellow, purple, lime and green lines, respectively.Equations are overlaid using the same color with the corresponding curves.
It is worth noting that the relationship for the operational WSR-88D (thin dashed lime line) [60] is very similar to our result based on the entire dataset, which implies that the relationship Z h = 300R 1.4  could potentially be employed for QPE in Beijing.For convective rain, both Z h = 250R 1.2 and Z h = 368R 1.21 will underestimate the rainfall intensities, likely due to the smaller diameter and higher number concentration of raindrops in these two climate regions than in Beijing (as detailed in Section 3.2).Compared with Z h = 300R 1.4 , Z h = 200R 1.6 has relatively larger discrepancy compared to our result.
Although a suitable Z h -R relationship can be helpful to retrieve rain rate from radar reflectivity, the dispersion of samples in Z h -R domain is still large.For example, for a given Z h = 10 3 mm 6 m −3 , R can range from 0.5-10 mm h −1 (Figure 8).To further investigate the essence of Z h -R relationships from a microphysical point of view, the scatter distribution of Z h -R pairs are color coded by D 0 and log 10 N w in Figure 9a,b.It is concluded that DSDs can be further grouped in size or number concentration in Z h -R domain, which means the QPE could be further improved when considering more physical observables.
reflectivity, the dispersion of samples in  ℎ - domain is still large.For example, for a given  ℎ = 10 3 mm 6 m -3 ,  can range from 0.5−10 mm h -1 (Figure 8).To further investigate the essence of  ℎ - relationships from a microphysical point of view, the scatter distribution of  ℎ - pairs are color coded by  0 and log 10   in Figures 9a and 9b.It is concluded that DSDs can be further grouped in size or number concentration in  ℎ - domain, which means the QPE could be further improved when considering more physical observables.In addition, dual-polarization radar variables are computed using the T-matrix method.The polarimetric measurements are proven to be capable of improving the performance of QPE.Figures 9c and 9d show the distribution of  ℎ versus , color coded by  DP and  DR , respectively.Overall, similar variation patterns can be seen compared with Figures 9a and 9b.This is not surprising, since  0 and log 10   can essentially be derived from the combination of  ℎ ,  DR , and  DP [34,45,61].
The distributions of   ,  DR , and  DP are illustrated in Figure 10.It should be noted again that   in dBZ is used in Figure 10a, while QPE estimators are fitted using  ℎ in linear scale.The details of boxplot in the center of each panel are listed in Table 3.The median value of   is about 20 dBZ, and the number of   higher than 40 dBZ is less than 5%.A large amount of  DP are smaller than 0.1 ° km -1 .The distribution of each parameter has two peaks: The first peak of   and  DP is close to their median values, while the second peaks are at about 27.5 dBZ and 0.07 ° km -1 , respectively.The two peaks of  DR are about 0.13 and 0.45 dB, and the median value lies between the two peaks.In addition, dual-polarization radar variables are computed using the T-matrix method.The polarimetric measurements are proven to be capable of improving the performance of QPE. Figure 9c,d show the distribution of Z h versus R, color coded by K DP and Z DR , respectively.Overall, similar variation patterns can be seen compared with Figure 9a,b.This is not surprising, since D 0 and log 10 N w can essentially be derived from the combination of Z h , Z DR , and K DP [34,45,61].
The distributions of Z H , Z DR , and K DP are illustrated in Figure 10.It should be noted again that Z H in dBZ is used in Figure 10a, while QPE estimators are fitted using Z h in linear scale.The details of boxplot in the center of each panel are listed in Table 3.The median value of Z H is about 20 dBZ, and the number of Z H higher than 40 dBZ is less than 5%.A large amount of K DP are smaller than 0.1 • km −1 .The distribution of each parameter has two peaks: The first peak of Z H and K DP is close to their median values, while the second peaks are at about 27.5 dBZ and 0.07 • km −1 , respectively.The two peaks of Z DR are about 0.13 and 0.45 dB, and the median value lies between the two peaks.This study also derived the polarimetric radar rainfall relations R dpr (Z h , Z DR ), R dpr (K DP , Z DR ), and R dpr (K DP ) using the least-squares method and compared with the Z h -R relationships.Here, the subscript "dpr" represents Dual-Polarization Radar for short.The obtained estimators based on the total DSD dataset are listed as follows: where α, β, and γ are generic coefficients and exponents in each relation.The specific values are listed in Table 4.In order to evaluate the application performance of various QPE estimators, the hourly rainfall amount (mm) derived using each radar rainfall relation is compared with collocated rain gauge observations (distance between disdrometer and gauge is less than 10 m). Figure 11a-d shows the scatter plots of rainfall estimated using radar relations versus gauge measurements.In addition, a set of evaluation metrics, including the Pearson correlation coefficient (PCC), standard deviation (STD), normalized mean absolute error (NMAE), and root-mean-square error (RMSE) are computed and indicated in Figure 11.
Obviously, R dpr (Z h , Z DR ) performs the best in terms of all evaluation metrics, followed by R dpr (K DP , Z DR ), R dpr (K DP ), and then R dpr (Z h ).The estimated hourly rainfall amount from R dpr (Z h , Z DR ) (Figure 11a) is the closest to rain gauge measurements at low intensities.However, R dpr (K DP , Z DR ) provides the best estimation at higher rainfall intensities, especially during severe precipitation hours.
Recent studies [5,6] demonstrated that the combination of different estimators may improve the accuracy of QPE.However, their achievements were mainly based on S-band radar measurements.In this study, we attempted to extend this strategy to X-band applications.Similar thresholds to the Dual-Polarization Radar Operational Processing System version 2 (DROPS2) [5] are used at X-band: Z H = 37 dBZ, Z DR = 0.185 dB, and K DP = 0.03 • km −1 .For clarification, this paper referred to the implemented DROPS2.0 architecture as R dpr (DROPS2-X).As expected, R dpr (DROPS2-X) (Figure 11e) provides the best results among various rainfall relations, which demonstrates the feasibility of the thresholds applied on X-band dual-polarization radar variables.Compared with Figure 11b, R dpr (DROPS2-X) inherits the advantage of R dpr (K DP , Z DR ) for all severe precipitation hours.
Nevertheless, it should be noted that except R dpr (Z h ), the differences among all other QPE estimators are not distinct: All have PCC higher than 0.98, STD and RMSE smaller than 1.0, and NMAE smaller than 0.2.

Conclusions
To investigate the microphysical properties of surface precipitation and improve the accuracy of radar QPE, 14-month continuous PARSIVEL 2 measurements during 2017-2018 in Beijing, China, were analyzed in this study.After quality control, a total of 25,499 1-min DSD spectra were obtained, corresponding to 1013.78 mm of total rainfall.The major rainy periods were from June to August, which contributed to 81.5% of rainfall amount and 78.3% of total DSD samples.The least contribution of rainfall was from September.In October, the precipitation tends to be steady with relatively long time but low intensity.
DSD dataset was classified as stratiform and convective rain types using the BR09 C−S scheme [50] in log 10 N w -D 0 domain.A large number of samples were identified as stratiform, which accounted for less than half of the total rainfall amount.The mean integral rainfall parameters, such as R , log 10 N w , D 0 , and three X-band dual-polarization variables, were higher in convective rain than stratiform rain.The occurrence of DSDs concentrated with D 0 and log 10 N w in the ranges of 0.8-1.1 mm and 3.2-4.1,respectively, which corresponds to W about 0.02-0.11g m −3 .The increases of R and Z H were proportional to the increases of log 10 N w and D 0 , and BR09 line was equivalent to R = 8.6 mm h −1 and Z H = 36.8dBZ.The comparation with other C−S classification schemes showed the similar distribution in log 10 N w -D 0 domain, but the detailed characteristics of DSDs among different schemes were different, with larger discrepancies in convective rain than stratiform rain.The different predominant microphysical processes in Beijing and other climate regions result in different DSD distributions in log 10 N w -D 0 domain, especially for convective rain.Compared to the warm rain characterized by a collision-coalescence process in Eastern and Southern China during the Asian Summer Monsoon Season, as well as in tropical, oceanic regions, the precipitation in Beijing is dominated more by mixed phase precipitation microphysical processes.The melting large ice-phase hydrometers increased D 0 but decreased N w compared to other climate regions.For stratiform rain, the mean values of log 10 N w and D 0 correspond to the high occurance ranges.For convective rain, three groups were separated, which showed distinct seasonal variations.The mean values of log 10 N w -D 0 pairs from May to August (Group 1) clustered together while those from April (Group 2) and September-October (Group 3) were distributed on the two sides of Group 1 above the BR09 line.Group 2 tends to contain more warm rain processes, while Group 3 was dominated by intense ice-based processes, such as aggregation and riming that sharply decrease the number of small size hydrometers but slowly increase the particle size.This finding provides additional insight to precipitation microphysics in midlatitude Asian (northern China) and further appends the archievements of Dolan et al. [46].
In addition, dual-polarization radar variables were computed from the DSD dataset using the T-matrix scattering method and the radar-based QPE estimators were derived through nonlinear regression analysis.The estimated rainfall products using radar rainfall relations were also independently verified using collocated rain gauge measurements.It was concluded that for single-polarization variable, the fitted Z h -R relationship, Z h = 265.14R1.399 , was almost coincident with the operational WSR-88D rainfall estimator [60], Z h = 300R 1.4 ; for dual-polarization radar applications, R dpr (Z h , Z DR ) performed the best for hourly rainfall estimation, while R dpr (K DP , Z DR ) performed the best at high rainfall intensities.In addition, a blended algorithm is derived based on the architecture of DROPS2 [5] to enhance radar rainfall estimation.It was shown that R dpr (DROPS2-X) performed better than any individual QPE estimators at hourly scale.Future work will focus on the large scale application of R dpr (DROPS2-X) for the X-band dual-polarization radar network being deployed in Beijing.

Figure 1 .
Figure 1.Topographic (m) information around the PARSIVEL 2 disdrometer site at Beijing station (BJ, the red circle).The districts of Beijing are highlighted in black curves.

Figure 1 .
Figure 1.Topographic (m) information around the PARSIVEL 2 disdrometer site at Beijing station (BJ, the red circle).The districts of Beijing are highlighted in black curves.

Figure 2 .
Figure 2. Histogram (top) of the number of 1-min raindrop spectra coinciding with rain gauge measurements (R stn ); and scatterplot (bottom) of rain rate calculated by PARSIVEL 2 disdrometer measurements vs R stn observations from rain gauge at BJ during the experiment period.The solid black line in the scatterplot is the 1:1 line.Data before (NonQC) and after (QC) quality control are indicated by red and blue dots, respectively.

Figure 2 .
Figure 2. Histogram (top) of the number of 1-min raindrop spectra coinciding with rain gauge measurements ( stn ); and scatterplot (bottom) of rain rate calculated by PARSIVEL 2 disdrometer measurements vs  stn observations from rain gauge at BJ during the experiment period.The solid black line in the scatterplot is the 1:1 line.Data before (NonQC) and after (QC) quality control are indicated by red and blue dots, respectively.

Figure 3 .
Figure 3. Scattergram of raindrop size distribution (DSD) at different diameter size and fall velocity classes after QC for the entire experiment period.The solid curve indicates the empirical - relationship described by Atlas et al. [40] which considers the air density effect; dashed curves indicate the ±60% ranges of the empirical - relationship.

Figure 3 .
Figure 3. Scattergram of raindrop size distribution (DSD) at different diameter size and fall velocity classes after QC for the entire experiment period.The solid curve indicates the empirical V-D relationship described by Atlas et al. [40] which considers the air density effect; dashed curves indicate the ±60% ranges of the empirical V-D relationship.

Figure 4 .
Figure 4. Scatterplot of log 10   vs.  0 for stratiform (S_All, lime) and convective (C_All, orange) rain in the bottom left panel, as well as the corresponding relative frequency histograms in the top and bottom right panels.The unit of   is m -3 mm -1 .Rain types were classified by BR09 scheme.The C_All (S_All) dataset equals to the dataset of C_BR09 (S_BR09) denoted in Table 2. Blue curves in each histogram indicate the relative frequency of the entire dataset for log 10   and  0 .The mean (MEAN), standard deviation (STD) and skewness (SKEW) for the entire dataset, stratiform rain and convective rain are shown in colors in each histogram panel, whereas the MEAN values of log 10   vs.  0 together with the respective ± 1 × STD values are plotted as error bars.The dashed and dot-dashed grey lines represent the C−S separation lines of BR09 and TH15, respectively.

Figure 4 .
Figure 4. Scatterplot of log 10 N w vs. D 0 for stratiform (S_All, lime) and convective (C_All, orange) rain in the bottom left panel, as well as the corresponding relative frequency histograms in the top and bottom right panels.The unit of N w is m −3 mm −1 .Rain types were classified by BR09 scheme.The C_All (S_All) dataset equals to the dataset of C_BR09 (S_BR09) denoted in Table 2. Blue curves in each histogram indicate the relative frequency of the entire dataset for log 10 N w and D 0 .The mean (MEAN), standard deviation (STD) and skewness (SKEW) for the entire dataset, stratiform rain and convective rain are shown in colors in each histogram panel, whereas the MEAN values of log 10 N w vs. D 0 together with the respective ±1 × STD values are plotted as error bars.The dashed and dot-dashed grey lines represent the C−S separation lines of BR09 and TH15, respectively.

Figure 5 .
Figure 5. Normalized occurrence frequency of DSD sample in (a) log 10   −  0 and (b)  −  0 domains.The dashed and dot-dashed lines represent the C−S separation lines from BR09 and TH15, respectively.

Figure 5 .
Figure 5. Normalized occurrence frequency of DSD sample in (a) log 10 N w − D 0 and (b) W − D 0 domains.The dashed and dot-dashed lines represent the C−S separation lines from BR09 and TH15, respectively.In Figure6, the log 10 N w − D 0 pairs are color coded by rain rate R and Z H to investigate the interrelations among them.Similar patterns can be found in Figure6a,b that the increases of both R and Z H are proportional to the increases of log 10 N w and D 0 , illustrating the internal relation between rain rate and radar reflectivity, or the Z h -R relationship that will be discussed in Section 4. The TH15 line crosses all levels of R and Z H , whereas BR09 line is almost equivalent to a threshold of R (8.6 mm h −1 ) or Z H (36.8 dBZ).Similar conclusion has been drawn for tropical, maritime regions with R = 10 mm h −1 and Z H = 40 dBZ [53], which are slightly higher than our results.Remote Sens. 2019, 11, x FOR PEER REVIEW 10 of 21

Figure 6 .
Figure 6.Scatterplots of log 10   vs.  0 color coded by (a)  and (b)   .The units of  and   are in mm h -1 and dBZ, respectively.The dashed and dot-dashed lines represent the C−S separation lines from BR09 and TH15, respectively.

Figure 6 .
Figure 6.Scatterplots of log 10 N w vs. D 0 color coded by (a) R and (b) Z H .The units of R and Z H are in mm h −1 and dBZ, respectively.The dashed and dot-dashed lines represent the C−S separation lines from BR09 and TH15, respectively.

21 Figure 7 .
Figure 7.The MEAN values of log 10   vs.  0 together with the respective ± 1 × STD values plotted as error bars for convective (triangle) and stratiform (square) rain.The dataset for both rain types, including all data, are plotted in black, whereas the monthly results are indicated by different colors.The dashed and dot-dashed lines represent the C−S separation lines from BR09 and TH15, respectively.

Figure 7 .
Figure 7.The MEAN values of log 10 N w vs. D 0 together with the respective ± 1 × STD values plotted as error bars for convective (triangle) and stratiform (square) rain.The dataset for both rain types, including all data, are plotted in black, whereas the monthly results are indicated by different colors.The dashed and dot-dashed lines represent the C−S separation lines from BR09 and TH15, respectively.

21 Figure 10 .
Figure 10.The distributions of (a)   , (b)  DR , and (c)  DP derived from DSD measurements using the T-matrix scattering approach.

Figure 10 .
Figure 10.The distributions of (a) Z H , (b) Z DR , and (c) K DP derived from DSD measurements using the T-matrix scattering approach.

Figure 11 .
Figure 11.Scattergram (based on the total rainfall observations) of hourly rainfall estimates (mm) from various radar rainfall relations vs. rain gauge measurements: (a) R dpr (Z h , Z DR ), (b) R dpr (K DP , Z DR ), (c) R dpr (K DP ), (d) R dpr (Z h ), and (e) R dpr (DROPS2-X).The grey diagonal straight line in each panel represents the 1-1 relationship.The quantitative evaluation results are also indicated in each panel, including the Pearson correlation coefficient (PCC), standard deviation (STD-mm), normalized mean absolute error (NMAE), and root-mean-square error (RMSE-mm).

Figure S1 .
Figure S1.As in Figure4, but for the TE01 classification scheme.

Figure S2 .
Figure S2.As in Figure 4, but for BR03 classification scheme.Figure A2.As in Figure 4, but for BR03 classification scheme.

Figure A2 .
Figure S2.As in Figure 4, but for BR03 classification scheme.Figure A2.As in Figure 4, but for BR03 classification scheme.

Table 1 .
Summary of rainfall during the experiment period.
Note:  mins is the number of 1-min DSD samples.〈〉 and  max are the mean and max rain rate, respectively.

Table 1 .
Summary of rainfall during the experiment period.

Table 2 .
Properties of DSDs for different rain-type classification schemes.

Table 3 .
The quantiles of polarization radar variables derived from DSDs using the T-matrix scattering method.

Table 3 .
The quantiles of polarization radar variables derived from DSDs using the T-matrix scattering method.