Evaluation of the Polarimetric-Radar Quantitative Precipitation Estimates of an Extremely Heavy Rainfall Event and Nine Common Rainfall Events in Guangzhou

The development and application of operational polarimetric radar (PR) in China is still in its infancy. In this study, an operational PR quantitative precipitation estimation (QPE) algorithm is suggested based on data for PR hydrometeor classification and local drop size distribution (DSD). Even though this algorithm performs well for conventional rainfall events, in which hourly rainfall accumulations are less than 50 mm, the capability of a PR to estimate extremely heavy rainfall remains unclear. The proposed algorithm is used for nine different types of rainfall events that occurred in Guangzhou, China, in 2016 and for an extremely heavy rainfall event that occurred in Guangzhou on 6 May 2017. It performs well for all data of these nine rainfall events and for light-to-moderate rain (hourly accumulation <50 mm) in this extremely heavy rainfall event. However, it severely underestimated heavy rain (>50 mm) and the extremely heavy rain at stations where total rainfall exceeded 300 mm within 5 h in this extremely heavy rainfall event. To analyze the reasons for underestimation, a rain microphysics retrieval algorithm is presented to retrieve Dm and Nw from the PR measurements. The DSD characteristics and the factors affecting QPE are analyzed based on Dm and Nw. The results indicate that compared with statistical DSD data in Yangjiang (estimators are derived from these data), the average raindrop diameter during this rainfall event occurred on 6 May 2017 was much smaller and the number concentration was higher. The algorithm underestimated the precipitation with small and midsize particles, but overestimated the precipitation with midsize and large particles. Underestimations occurred when Dm and Nw are both very large, and the severe underestimations for heavy rain are mainly due to these particles. It is verified that some of these particles are associated with melting hail. Owing to the big differences in DSD characteristics, R(KDP, ZDR) underestimates most heavy rain. Therefore, R(AH), which is least sensitive to DSD variations, replaces R(KDP, ZDR) to estimate precipitation. This improved algorithm performs well even for extremely heavy rain. These results are important for evaluating S-band Doppler radar polarization updates in China.


Introduction
Polarimetric radar (PR) can provide both backscatter and differential propagation phase information; therefore, this type of radar has significant advantages over single polarization radar.One of the advantages of PR is quantitative precipitation estimation (QPE) by using the PR variables.Previous studies have shown that polarimetric precipitation estimation (PPE) techniques are more robust with respect to drop size distribution (DSD) variations and the presence of hail than are the conventional Z-R relationship (here, R is the radar rainfall rate and Z is the radar-reflectivity factor) [1][2][3][4][5].However, DSD variability and hail contamination can still introduce QPE errors when only a single polarimetric variable is used in the PPE [6].To avoid large observational errors in Z DR and K DP at lower signal-to-noise ratios (SNRs) and to reduce the impact of DSD variability on the precipitation estimation, multiple relationships between polarimetric variables and rainfall (e.g., R(Z H ), R(Z H , Z DR ), and R(K DP )) are often used depending on the type of radar echo.By combining the merits of these different relationships for various rain intensities, Ryzhkov et al. [6] developed a "synthetic" algorithm that uses different combinations of radar variables depending on the rain rate estimates by using the conventional Z-R relationship; their synthetic algorithm was evaluated during the 2002-2003 JPOLE experiment conducted in Oklahoma.Cifelli et al. [7] developed a synthetic algorithm based on the thresholds of Z H , Z DR , and K DP and this algorithm was tested on the Colorado State University (CSU)-CHILL radar.
Although relationships between R and polarimetric variables are less prone to DSD variability, they must still be modified according to DSD data in different regions owing to cloud and precipitation microphysical processes that are regionally dependent [6,[8][9][10].Even in the same region, DSD can vary in terms of precipitation type (e.g., stratus clouds or convective clouds) and rainfall rate.Wu and Liu [11] statistically analyzed the DSD-R relationship in the Tibetan Plateau and in Southern China and found that DSD varies significantly with R. Wu et al. [12] and Zhang et al. [13] suggest that Z-R relationships derived from the DSD vary significantly with R even for one rainfall event.Despite many attempts to change the Z-R relationship in real time to improve QPE accuracy, the QPE performance remains unsatisfactory for heavy rain [13][14][15].
QPE for heavy rainfall is a challenge we may meet.Another challenge is the estimation of rain mixed with hail.Conventional radar rainfall estimates that were obtained from Z-R relationships deteriorate in the presence of mixed-phase and frozen hydrometeors.The R(Z H , Z DR ) relationship is less prone to DSD variability but is not immune to hail contamination.Rainfall algorithms based on K DP are more robust in the presence of hail but are not optimal for light rain in the S-band [16,17].Wang et al. [18] attempted to use H DR to determine a hail region and then estimate the liquid precipitation in the associated rain area.However, small mixtures of hail and rainfall are difficult to identify with radar reflectivity alone.Misidentification of rain and precipitation ice often leads to poorly estimated rainfall and has important implications for flood forecasting [7].The challenges of high-plain meteorological environments have led to the development of an algorithm guided by the precipitation ice fraction in the radar volume.Golestani et al. [19] developed the CSU-ICE optimization algorithm in which Z DR is used to calculate the ice-fraction index, but unfortunately it performs poorly for 38 dBZ < Z H < 45 dBZ [7].Therefore, a new rainfall algorithm was developed using hydrometeor identification (HID) to guide the choice of a particular QPE algorithm [7].Precipitation is classified as rain, mixture, and ice.Drizzle, moderate rain, and heavy rain are included in the rain category; the mixture category includes wet snow and a rain-hail mixture; and the ice category includes dry snow, graupel, and hail.QPE is conducted in a rain and mixture area.
Despite all the progress in polarimetric rainfall measurements, an algorithm that can resolve all these issues for any scenario does not exist.A synthetic algorithm that uses Z H , Z DR , and K DP can theoretically capture the full range of local DSD variability.However, when the DSD characteristics become significantly different from previous characteristics, the QPE performance will be unpredictable.As a possible radar variable for rainfall estimation, specific attenuation (for horizontal polarization) A H is more directly related to rain rate and liquid water content compared with Z H , and it is immune to radar miscalibration, partial beam blockage, and impacts of wet radomes.Compared with algorithms based on Z H , Z DR , and K DP , rainfall estimations utilizing A H are less sensitive to DSD variations [20,21].The use of R(A H ) was originally X-band and C-band motivated, but it has applied to the S-band as well, which was verified by Ryzhkov [22].R(A H ) was first used for X-band radars during the NASA Iowa Flood Studies field campaign, and was found to have excellent performance [23].A new estimator R(A H , Z DR ) was proposed by Keenan [24] for C-band estimation and proposed by Thurai et al. [25] for X-band estimation, respectively.This has also been extended to S-band by Thomposon et al. [26].Even though these estimators only offer significant skill at S-band for R(A H ) or at X band for R(A H , Z DR ), Thomposon et al. [26] states that the utility of R(A H ) or R(A H , Z DR ) provide the possibility of solving the problems discussed above.
In 2016, the new-generation S-band weather radar in Guangdong Province in China was updated to PR.On 6 May 2017, an extremely heavy rainfall event (here after this rainfall event) was observed in the low-latitude summer.During this heavy rainfall event, rain-gauge observations broke the historical record for 3-h rainfall accumulation in Guangdong and the historical record for single-day rainfall accumulation in Guangzhou City, in Guangdong Province.According to PR observations, hail and graupel melted completely and became liquid water before reaching the ground, thereby altering the DSD structure.Therefore, the QPE algorithm for this rainfall event should differ significantly from those used for previous events.The PPE performance must be examined for this extremely heavy rainfall.
So far, eight S-band PRs have been built in Guangdong Province.By 2020, more than 100 S-band PRs will be built or upgraded in China.The evaluation of PR capability to estimate rain, especially heavy rain, is an important avenue for future research.In this study, an operational QPE algorithm based on a local DSD and mixed-phase precipitation identification is proposed and applied to some rainfall events.This algorithm performs well for most rainfall events investigated in this study.However, rainfall characteristics of this event are so different from the conventional rainfall events occurred in Guangdong, in which hourly rainfall accumulations are less than 50 mm.The main motivation for this study is to analyze the PR capability for estimating severe precipitation, such as this rainfall event and to study the main factors affecting QPE.The performance of PPE and the possible reasons for biases in precipitation estimation (i.e., DSD variations, precipitation phase, and other factors) are analyzed in detail.The method to improve QPE performance on the basis of the reasons for QPE errors is also discussed in this study.
In Section 2, we introduce the measurement instruments and analysis of the rainfall event.In Section 3, we introduce our PPE algorithm, evaluation method, and the rain microphysics retrieval algorithm.In Section 4, we analyze the performance of nine rainfall events and the extremely heavy rainfall event introduced in this study, respectively.In Section 5, we explore possible reasons for biases in the precipitation estimation for this heavy rainstorm.In Section 6, we improve the algorithm and verify its effect.Finally, in Section 7, we present our conclusions.

Measurement Instruments and Rainfall Event
A heavy rainfall event occurred throughout Guangdong Province on 6 May 2017, and severe rain occurred in Guangzhou City during 1900-2400 UTC.The rainfall observed at many automatic weather stations (AWSs) broke historical records and caused numerous flooding disasters.Figure 1a shows the distribution of total rainfall during 1900-2400 UTC based on AWS observations.During this period, 78, 38, and 3 AWSs observed rain accumulations in excess of 50, 100, and 300 mm, respectively.The maximum total rainfall was 401.6 mm (station 3 in Figure 1c), whereas the maximum hourly rainfall accumulation was 184.4 mm (again station 3). Figure 1b shows the average radar reflectivity for 1900-2400 UTC, and Figure 1c shows the average reflectivity enlarged on a local scale.The average reflectivities exceeded 35 dBZ in many places, exceeding 45 dBZ in a narrow area near the radar station.Figure 1a,b clearly show the relatively concentrated spatial and temporal distributions of heavy rain and strong echoes.The locations of those AWSs where the total rainfall exceeded 300 mm are marked with plus signs in Figure 1c, along with the disdrometer (square) at Luogang and the S-band PR (triangle) at Guangzhou.The laser disdrometer (produced by Beijing Metstar Radar Co., Ltd., Beijing, China) can measure the precipitation particle diameter and terminal fall velocity simultaneously.The particle diameter is divided into 64 classes ranging from 0.2 to 30 mm, and the velocity is divided into 32 classes ranging from 0.2 to 20 m/s.The temporal resolution is 1 min.Note that the disdrometer was not located in the area of heaviest precipitation.
Updated in 2016, the S-band PR deployed in Guangzhou can measure multiple polarimetric variables such as ZH, ZDR, and ΦDP (differential phase).The radar was calibrated in the factory according to the criterion proposed by China Meteorological Administration (CMA) [27].After radar construction, a series of tests, such as built-in testing, sun-calibration, and vertical pointed calibration were conducted by the Meteorological Observation Center of CMA.The results of the tests indicated that ZH accuracy is better than 1 dB and ZDR accuracy is better than 0.4 dB.The radar operates in the conventional VCP21 volume-scan mode and completes a volume scan using nine specific elevation angles (0.5°, 1.5°, 2.4°, 3.3°, 4.3°, 6.0°, 9.9°, 14.6°, and 19.5°) in 6 min, with a 0.95° beam width, a 0.25 km radial resolution and a 460 km maximum detection range.Figures 2 and 3 show the evolution of reflectivity and radial velocity at 0.5° elevation during 1900-2400 UTC.At 2000 UTC, strong echoes reached the three AWSs and developed rapidly.During 2000-2300 UTC, echoes larger than 50 dBZ remained there and changed little in reflectivity, location, and influence area.The radial velocities at 0.5° and 1.5° elevations (not shown) indicate that gradually intensifying northerly and southerly winds converged at around 560 m above the ground at 2000 UTC.The convergence area evolved gradually into a convergence belt and reached its maximum convergence at 2200 UTC, resulting in persistent ascending motion leading to persistent strong echoes and heavy rain.The laser disdrometer (produced by Beijing Metstar Radar Co., Ltd., Beijing, China) can measure the precipitation particle diameter and terminal fall velocity simultaneously.The particle diameter is divided into 64 classes ranging from 0.2 to 30 mm, and the velocity is divided into 32 classes ranging from 0.2 to 20 m/s.The temporal resolution is 1 min.Note that the disdrometer was not located in the area of heaviest precipitation.
Updated in 2016, the S-band PR deployed in Guangzhou can measure multiple polarimetric variables such as Z H, Z DR , and Φ DP (differential phase).The radar was calibrated in the factory according to the criterion proposed by China Meteorological Administration (CMA) [27].After radar construction, a series of tests, such as built-in testing, sun-calibration, and vertical pointed calibration were conducted by the Meteorological Observation Center of CMA.The results of the tests indicated that Z H accuracy is better than 1 dB and Z DR accuracy is better than 0.4 dB.The radar operates in the conventional VCP21 volume-scan mode and completes a volume scan using nine specific elevation angles (0.5 • , 1.5 • , 2.4 • , 3.3 • , 4.3 • , 6.0 • , 9.9 • , 14.6 • , and 19.5 • ) in 6 min, with a 0.95 • beam width, a 0.25 km radial resolution and a 460 km maximum detection range.Figures 2 and 3 show the evolution of reflectivity and radial velocity at 0.5 • elevation during 1900-2400 UTC.At 2000 UTC, strong echoes reached the three AWSs and developed rapidly.During 2000-2300 UTC, echoes larger than 50 dBZ remained there and changed little in reflectivity, location, and influence area.The radial velocities at 0.5 • and 1.5 • elevations (not shown) indicate that gradually intensifying northerly and southerly winds converged at around 560 m above the ground at 2000 UTC.The convergence area evolved gradually into a convergence belt and reached its maximum convergence at 2200 UTC, resulting in persistent ascending motion leading to persistent strong echoes and heavy rain.

QPE Algorithm and Evaluation Method
In this study, we propose a localized PR QPE algorithm that accounts for hydrometeor phase classification (a flowchart is shown in Figure 4).This algorithm is designed for the operational PRs in Guangdong, which is practical and easy to implement.Based on data quality, hydrometeor phase type, and polarimetric data threshold, the QPE algorithm is conducted for poor-quality data, mixed-phase precipitation, and liquid precipitation, respectively.

QPE Algorithm and Evaluation Method
In this study, we propose a localized PR QPE algorithm that accounts for hydrometeor phase classification (a flowchart is shown in Figure 4).This algorithm is designed for the operational PRs in Guangdong, which is practical and easy to implement.Based on data quality, hydrometeor phase type, and polarimetric data threshold, the QPE algorithm is conducted for poor-quality data, mixed-phase precipitation, and liquid precipitation, respectively.An analysis of the PR data from China [27] indicates that noise can easily affect ZDR and KDP when the SNR is <20 dB, leading to large spatiotemporal variations.Therefore, under these SNR conditions, ZDR and KDP are not appropriate for precipitation estimation, and R1(ZH) is used instead.For mixed-phase precipitation (e.g., hail contamination), because the backscattering cross-section of hail is much larger than that of raindrops, ZH can be extremely large.Hail rolling results in ZDR being close to 0 dB, and hail melting results in ZDR being very large [28].However, hail makes little contribution to rain accumulation.Previous studies have shown that precipitation estimation used ZH and ZDR are not efficient in situations of hail contamination [3,6,17].Because KDP is immune to hail contamination, rainfall algorithms based on KDP are more robust in the presence of hail [3,16].In the present study, the mixed-phase precipitation is determined by ZH > 50 dBZ, KDP ≥ 1°/km, and ρHV ≤ 0.97, and its rainfall rate is estimated with KDP only.The QPE algorithm for liquid precipitation is similar to the CSU-HIDRO algorithm [7], which is denoted by the dashed frame in Figure 4.
The rainfall estimators shown in Figure 4 are expressed by: where ZH is in units of mm 6 /m 3 , ZDR is in dB, KDP is in °/km, and R is in mm/h.An analysis of the PR data from China [27] indicates that noise can easily affect Z DR and K DP when the SNR is <20 dB, leading to large spatiotemporal variations.Therefore, under these SNR conditions, Z DR and K DP are not appropriate for precipitation estimation, and R1(Z H ) is used instead.For mixed-phase precipitation (e.g., hail contamination), because the backscattering cross-section of hail is much larger than that of raindrops, Z H can be extremely large.Hail rolling results in Z DR being close to 0 dB, and hail melting results in Z DR being very large [28].However, hail makes little contribution to rain accumulation.Previous studies have shown that precipitation estimation used Z H and Z DR are not efficient in situations of hail contamination [3,6,17].Because K DP is immune to hail contamination, rainfall algorithms based on K DP are more robust in the presence of hail [3,16].In the present study, the mixed-phase precipitation is determined by Z H > 50 dBZ, K DP ≥ 1 • /km, and ρ HV ≤ 0.97, and its rainfall rate is estimated with K DP only.The QPE algorithm for liquid precipitation is similar to the CSU-HIDRO algorithm [7], which is denoted by the dashed frame in Figure 4.
The rainfall estimators shown in Figure 4 are expressed by: where Z H is in units of mm 6 /m 3 , Z DR is in dB, K DP is in • /km, and R is in mm/h.The coefficients of R1(Z H ) and R2(Z H ) are different.R1(Z H ) is used for light rain, and R2(Z H ) is used for moderate rain with low Z DR and K DP .The coefficients of R1(K DP ) and R2(K DP ) are also different.R1(K DP ) is applied to mixed-phase precipitation, whereas R2(K DP ) is applied to liquid precipitation.
The coefficients used in Equations ( 1)-( 4) were obtained from the DSD data for 27 April to 11 June 2014 from Yangjiang in Guangdong (shown in Figure 1b) [7,29].Note that the DSD data used for fitting should be chosen according to the thresholds used for the rainfall estimators.For example, DSD data that satisfy Z H > 50 dBZ and K DP ≥ 1 • /km are used to fit R1(K DP ).The coefficients of the rainfall estimators shown in Figure 4 are given in Table 1., and 0.5 • , respectively, are used to estimate the precipitation.To avoid the influences of the melting layer and the ground clutter, for evaluation, we used 558 AWSs that are within 20-180 km from the radar location.They are distributed between the two circles shown in Figure 1a.
We used the rain rate produced by the S-band PR at a temporal resolution of 6 min to calculate hourly rainfall accumulations, taking the rainfall accumulations measured at the AWSs as true accumulations.We used the average radar-estimated precipitation of the nine radar bins nearest to an AWS to evaluate the QPE performance.Because the AWS resolution is 0.1 mm, only rainfall measurements that exceeded 0.1 mm were used for evaluation.As statistical indicators of algorithmic performance, we obtained the correlation coefficient (CC), root mean square error (RMSE), normalized relative bias (NB), normalized absolute error (NE), the bias ratio of radar-estimated rainfall to AWS-observed rainfall (bias ratio), and Nash-Sutcliffe efficiency score (Eff ), which are defined as: where RA is accumulation from either radar or an AWS gauge, an overbar represents a mean value, n is the number of RA i gauge -R i radar pairs, RMSE is in millimeters, and NE and NB are both percentages.
A bias ratio larger (resp.smaller) than one indicates overestimation (resp.underestimation).Eff is a statistical measure of the variability of the error normalized by the natural variability of the estimated parameter and is scaled from −∞ to 1.A value of one indicates that the estimate is perfect.An efficiency value equal to 0 or negative indicates that the estimation is, respectively, no better or even worse than using simply the mean value of the observations [30].

Rain Microphysics Retrieval Algorithm
To analyze the factors affecting QPE, several rain variables need to be derived from PR observations.The DSD model used in the simulations is the normalized gamma distribution N(D) [31,32]: where the parameter µ is a measure of the shape of the gamma DSD, and f (µ) is a unitless function of ) is a normalized intercept parameter, and the parameter D m (mm) is the mass-weighted mean diameter.N w and D m can be expressed as where the water content W is in g m -3 , the water density ρ w is in g cm -3 , and E represents the expected value.Moment methods have been widely used to estimate these parameters for cloud and precipitation in numerical models [33].The third, fourth, and sixth moments of the DSD data are used to estimate µ, N w , and D m .Bringi et al. [34] proposed using polarimetric radar measurements of Z H , Z DR , and K DP to retrieve a normalized gamma DSD.However, Brandes et al. [35] showed that this approach is sensitive to K DP noise.In addition, K DP is derived from measurements made over many range gates and does not always match Z H and Z DR measurements well at every range gate.Therefore, the addition of K DP may result in a deterioration of the DSD retrieval at a specific range gate, especially if it is not used optimally [36].Because the three parameters of the gamma DSD distribution are not mutually independent, two PR variables can be used to retrieve the rain variables (D m and N w ) [36].In this study, only Z H and Z DR are used to retrieve rain variables.Cao et al. [37] and Brandes et al. [35] used a constraining µ-Λ relation to derive the relationships between rain variables and radar variables.However, errors may propagate through this procedure [36].Fitting directly with observations can reduce error propagation.According to the method described by Cao et al. [36], a sorting and averaging procedure based on two parameters (SATP) is introduced to mitigate the effects of sampling errors on DSD fitting.Based on Yangjiang historical DSD data processed with the SATP method, Z H , Z DR , D m , and N w were calculated for each data point.Using a three-order polynomial fit described by Cao et al. [36] for all data points, rain variables were expressed in terms of radar variables as (see also Figure 5a,b): where Z H is in mm 6 m -3 , and Z DR is in dB.CC and NB between retrieval values and observed values were calculated based on Equations ( 5) and ( 7), respectively, which are shown in Figure 5.The two variables have a small NB and a CC close to 1.These results indicate that the relationships between the rain variables (D m and N w ) and radar variables (Z H and Z DR ) in Equations ( 16) and ( 17) are valid for the rain DSD retrieval.
variables.However, errors may propagate through this procedure [36].Fitting directly with observations can reduce error propagation.According to the method described by Cao et al. [36], a sorting and averaging procedure based on two parameters (SATP) is introduced to mitigate the effects of sampling errors on DSD fitting.Based on Yangjiang historical DSD data processed with the SATP method, ZH, ZDR, Dm, and Nw were calculated for each data point.Using a three-order polynomial fit described by Cao et al. [36] for all data points, rain variables were expressed in terms of radar variables as (see also Figure 5a,b): where ZH is in mm 6 m -3 , and ZDR is in dB.CC and NB between retrieval values and observed values were calculated based on Equations ( 5) and ( 7), respectively, which are shown in Figure 5.The two variables have a small NB and a CC close to 1.These results indicate that the relationships between the rain variables (Dm and Nw) and radar variables (ZH and ZDR) in Equations ( 16) and ( 17) are valid for the rain DSD retrieval.

Result
In this section, nine rainfall events that occurred in Guangzhou in 2016 were chosen to examine the QPE algorithm for the operational PRs in Guangdong.The extremely heavy rainfall event that occurred in Guangzhou on 6 May 2017 was used to test the capability of the algorithm to estimate heavy precipitation.

Algorithm Performance for the Nine Rainfall Events
Table 2 shows the nine rainfall events that occurred in Guangzhou.These events include stratocumulus and convective precipitation, and several convective precipitation events are squall line events.
The evaluated statistical scores for QPE of the nine rainfall events are shown in Table 3.For all nine rainfall events, NE ranges from 35.20% to 43.75%, NB ranges from −17.20% to 15.19%, and Eff ranges from 0.68 to 0.78.Although some underestimations or overestimations of rainfall occurred in some rainfall events, the performance of the algorithm is good for all 24,755 RA i gauge -R i radar pairs from all nine rainfall events in terms of NB, which is close to zero (shown in Table 4).Besides NB, the other evaluated statistical scores shown in Table 4 are also satisfied for the total data pairs.The algorithm performance is also good for light-to-moderate rain.However, the algorithm severely underestimated heavy rain (hourly rainfall accumulation >50 mm).Fortunately, heavy rain pairs are very few, accounting for only 0.26% of the total pairs.The operational algorithm presented in this study was also compared with two mature operational radar systems.Multi-Radar Multi-Sensor (MRMS) is a comprehensive system operated by the American National Weather Service that combines data streams from multiple radars, satellites, surface observations, upper air observations, lightning reports, rain gauges, and numerical weather prediction models to produce a suite of decision-support products.MRMS polarimetric radar QPE product performance was evaluated for the data collected east of the Rockies during the 2014 warm season [38].Below the melting layer, the bias ratio is 1.06, which is slightly larger than that of the algorithm presented in this study.The other operational radar system is from France.For the evaluation at S-band, two precipitation events observed by the Nimes radar in 2010 are analyzed [39].NB and RMSE for the optimal polarimetric algorithm are −9% and 8.46 mm, respectively, for the intense rain (hourly accumulations > 5 mm).Compared with it, the algorithm presented in this study is slightly better in terms of identical NB (−9%) and lower RMSE (6.55 mm) for the intense rain.These comparisons show that the performance of the operational algorithm in this study is good.

Algorithm Performance for This Extremely Heavy Rainfall Event
The maximum total rainfall of the heaviest rainfall event listed in Table 2 was 207.54 mm within 24 h.However, the maximum total rainfall of the rainfall event that occurred on 6 May 2017 was 401.6 mm in only 5 h.It is a great challenge to estimate this rainfall with PR.To examine the capability to estimate extremely heavy rain, the algorithm presented in this study was applied to estimate precipitation during this extremely heavy rainfall event.Table 5 lists the evaluated statistical scores for the QPE at various hourly accumulations.There are 1341 samples of data pairs in all.Data pairs are divided into two classes to evaluate light-to-moderate rain (<50 mm) and heavy rain.The results indicate that the algorithm performs well for the light-to-moderate rain in terms of NB, which is close to 0. However, the performance for heavy rain is poor and the algorithm heavily underestimated the heavy rain.In general, regarding NB, the QPE algorithm performs better for light-to-moderate rain, but it underestimates heavy rain.The same pertains to the three stations where the heaviest rainfall occurred.

DSD Characteristics in This Rainfall Event and Their Effects on QPE
As shown in Figure 7  In general, regarding NB, the QPE algorithm performs better for light-to-moderate rain, but it underestimates heavy rain.The same pertains to the three stations where the heaviest rainfall occurred.DSD data collected during April-June 2014 were compared with DSD data collected during the target rainfall event.We calculated Z H , Z DR , and K DP based on these DSDs and then averaged them to obtain the curves shown in Figure 7, which represent the statistical (i.e., average) microphysical properties of precipitation in this region (black curve) and the specific microphysical properties of precipitation for this rainfall event (red curve).Note that the black curve and the QPE estimators are from the same DSD sources.

Analysis of Factors
As shown in Figure 7, we obtained the occurrence frequencies of ZDR versus ZH and KDP versus ZH based on a statistical analysis of the ZH-ZDR and ZH-KDP observations below 3 km (for ZDR > 1 dB, SNR > 20 dB and KDP > 1°/km, SNR > 20 dB).To analyze the DSD characteristics in this rainfall event, besides DSD data collected at Yangjiang during April-June 2014, we also used another set of DSD data collected at Luogang during this rainfall event from 1600 UTC, 6 May 2017 to 1600 UTC, 7 May 2017.DSD data collected during April-June 2014 were compared with DSD data collected during the target rainfall event.We calculated ZH, ZDR, and KDP based on these DSDs and then averaged them to obtain the curves shown in Figure 7, which represent the statistical (i.e., average) microphysical properties of precipitation in this region (black curve) and the specific microphysical properties of precipitation for this rainfall event (red curve).Note that the black curve and the QPE estimators are from the same DSD sources.Comparing the curves in Figure 7, Z DR is smaller and K DP is slightly larger for the same Z H in this rainfall event, indicating there is a slightly higher concentration of smaller raindrops in this rainfall event than the statistical microphysical properties of precipitation in Yangjiang.Theoretically, the closer the high occurrence frequencies in Figure 7a,b are to the black curve, the less-biased the precipitation estimates, and vice versa.The large difference between the high frequencies of Z H -Z DR and the black curve suggests that compared with the statistical microphysical properties of precipitation in Yangjiang, the average reflectivity is larger, the raindrops are smaller, and the number concentration is higher in this rainfall event.The large difference also suggests that there probably are some large QPE biases.
The average values of D m and log 10 N w represent the DSD characteristics more directly.According to the rain microphysics retrieval algorithm presented in Section 3.2, D m and log 10 N w are retrieved from PR observations.They are also compared with those retrieved from the DSD data observed at the Luogang disdrometer station (Figure 8).Even though there are some slight underestimations or overestimations of D m and log 10 N w , the mean biases are small, namely −0.03 mm and 0.15 dB, respectively.This indicates that the D m and log 10 N w retrieved from the PR observations are reliable.
Atmosphere 2018, 9, x FOR PEER REVIEW 13 of 23 Comparing the curves in Figure 7, ZDR is smaller and KDP is slightly larger for the same ZH in this rainfall event, indicating there is a slightly higher concentration of smaller raindrops in this rainfall event than the statistical microphysical properties of precipitation in Yangjiang.Theoretically, the closer the high occurrence frequencies in Figure 7a,b are to the black curve, the less-biased the precipitation estimates, and vice versa.The large difference between the high frequencies of ZH-ZDR and the black curve suggests that compared with the statistical microphysical properties of precipitation in Yangjiang, the average reflectivity is larger, the raindrops are smaller, and the number concentration is higher in this rainfall event.The large difference also suggests that there probably are some large QPE biases.
The average values of Dm and log10Nw represent the DSD characteristics more directly.According to the rain microphysics retrieval algorithm presented in Section 3.2, Dm and log10Nw are retrieved from PR observations.They are also compared with those retrieved from the DSD data observed at the Luogang disdrometer station (Figure 8).Even though there are some slight underestimations or overestimations of Dm and log10Nw, the mean biases are small, namely −0.03 mm and 0.15 dB, respectively.This indicates that the Dm and log10Nw retrieved from the PR observations are reliable.The occurrence frequencies of log10Nw versus Dm retrieved from PR observations above the AWSs are shown in Figure 9a.The maritime and continental convective clusters reported by Bringi et al. [40] are also shown in Figure 9a with two black rectangles.Yangjiang DSD data for convective precipitation are used to calculate the average values of Dm and log10Nw, which is shown in Figure 9a with the red "x" symbol.The method to separate stratiform and convective rain types is based on the standard deviation of rain rate over 5 consecutive DSD samples, which are 2-min averaged DSD samples [40].If this standard deviation is ≤ 1.5 mmh −1 then it is classified as stratiform, otherwise it is assumed to be convective.Finally, the average log10Nw (3.54) and Dm (1.90 mm) of The occurrence frequencies of log 10 N w versus D m retrieved from PR observations above the AWSs are shown in Figure 9a.The maritime and continental convective clusters reported by Bringi et al. [40] are also shown in Figure 9a with two black rectangles.Yangjiang DSD data for convective precipitation are used to calculate the average values of D m and log 10 N w , which is shown in Figure 9a with the red "x" symbol.The method to separate stratiform and convective rain types is based on the standard deviation of rain rate over 5 consecutive DSD samples, which are 2-min averaged DSD samples [40].If this standard deviation is ≤ 1.5 mmh −1 then it is classified as stratiform, otherwise it is assumed to be convective.Finally, the average log 10 N w (3.54) and D m (1.90 mm) of data retrieved from Yangjiang DSD data for convective precipitation are obtained.Relatively higher values of D m but lower values of log 10 N w are observed compared with the maritime-like cluster.This is likely associated with high moisture contents and sea salt aerosols.However, Dm and Nw in this rainfall event are different compared with Yangjiang data.Dm and Nw are retrieved from the polarimetric parameters ZH and ZDR based on Equations ( 16) and (17).Dm mostly ranges from 0.75 mm to 2.5 mm and log10Nw mostly ranges from 2.5 to 5.5.The average values of Dm and log10Nw are 1.44 mm and 4.06, respectively.Compared with the values of data derived from the Yangjiang DSD data, the average value of Dm in this rainfall event decreased by 24.21%, and the average value of log10Nw in this rainfall event increased by 14.69%.Relatively lower values of Dm but higher values of log10Nw are observed compared with those data derived from the Yangjiang DSD data for convective precipitation.It indicates raindrops are smaller, but they have a higher number concentration in this rainfall event.The different DSD characteristics of this extremely heavy rainfall event provide a more challenging task when attempting to obtain accurate rainfall estimates.
Data pairs are divided into two classes according to the different hourly accumulations.The light-to-moderate rain (<50 mm) and heavy rain (>50 mm) are shown in Figure 9b,c, respectively.However, D m and N w in this rainfall event are different compared with Yangjiang data.D m and N w are retrieved from the polarimetric parameters Z H and Z DR based on Equations ( 16) and (17).D m mostly ranges from 0.75 mm to 2.5 mm and log 10 N w mostly ranges from 2.5 to 5.5.The average values of D m and log 10 N w are 1.44 mm and 4.06, respectively.Compared with the values of data derived from the Yangjiang DSD data, the average value of D m in this rainfall event decreased by 24.21%, and the average value of log 10 N w in this rainfall event increased by 14.69%.Relatively lower values of D m but higher values of log 10 N w are observed compared with those data derived from the Yangjiang DSD data for convective precipitation.It indicates raindrops are smaller, but they have a higher number concentration in this rainfall event.The different DSD characteristics of this extremely heavy rainfall event provide a more challenging task when attempting to obtain accurate rainfall estimates.
Data pairs are divided into two classes according to the different hourly accumulations.The light-to-moderate rain (<50 mm) and heavy rain (>50 mm) are shown in Figure 9b,c, respectively.The corresponding rain rate observed at AWSs is also shown in Figure 9e,f, respectively.As shown in Figure 9b, the light-to-moderate rain data can be easily divided into two parts according to the results.Most data in part 1 are underestimations, whereas most data in part 2 are overestimations.This is the reason that NB is close to 0 for the light-to-moderate rain (Table 5).The two parts listed above are observable in Figure 9c, whereas some data fall into part 3, where severe underestimations occurred.The algorithm underestimated the precipitation with small and midsize particles but overestimated the precipitation with midsize and large particles.When both D m and N w have large values, underestimations occurred.Severe underestimations for heavy rain are mainly due to these data categorized into part 3.

Analysis of Factors Affecting QPE at the Three Stations
Figure 10 shows the values of R QPE (rain rate calculated with the QPE algorithm) minus R Gauge (rain rate measured at the AWS) at the three stations characterized by the heaviest rainfall.The colors represent the estimators used during this rainfall event; R1(K DP ) was used for a certain period at station 2, thus indicating that mixed precipitation existed during this period.Unfortunately, underestimations still occurred.R(K DP , Z DR ) is used most frequently, especially for stations 2 and 3.However, R(K DP , Z DR ) underestimated the rain rate most often because it is not capable of adapting to large DSD variations that characterize severe rain; i.e., the principle reason for underestimations at each station.
Atmosphere 2018, 9, x FOR PEER REVIEW 15 of 23 above are observable in Figure 9c, whereas some data fall into part 3, where severe underestimations occurred.The algorithm underestimated the precipitation with small and midsize particles but overestimated the precipitation with midsize and large particles.When both Dm and Nw have large values, underestimations occurred.Severe underestimations for heavy rain are mainly due to these data categorized into part 3.

Analysis of Factors Affecting QPE at the Three Stations
Figure 10 shows the values of RQPE (rain rate calculated with the QPE algorithm) minus RGauge (rain rate measured at the AWS) at the three stations characterized by the heaviest rainfall.The colors represent the estimators used during this rainfall event; R1(KDP) was used for a certain period at station 2, thus indicating that mixed precipitation existed during this period.Unfortunately, underestimations still occurred.R(KDP, ZDR) is used most frequently, especially for stations 2 and 3.However, R(KDP, ZDR) underestimated the rain rate most often because it is not capable of adapting to large DSD variations that characterize severe rain; i.e., the principle reason for underestimations at each station.Figure 11 shows time series of the vertical profiles of ZH, ZDR, KDP, ρHV, and Hcl (Hydrometeor classification result) at the three stations where the heaviest rainfall occurred.Hcl is obtained according to the Hydrometeor classification algorithm described in Wu et al. [27].This algorithm has been verified with the Zhuhai radar, the first operational PR in Guangdong, China.Following the approach of Mohr and Vaughan [41], radar observations (except Hcl) with SNR > 20 dB at the nine PPIs above the stations were linearly interpolated to obtain the profiles of the polarimetric variables.The vertical resolution was 0.5 km, and the temporal resolution was 6 min.The time shown on the horizontal axis is identical to Figure 6.The black lines in Figure 11 denote the heights of radar observations used for precipitation estimation, namely 1.23, 1.17, and 1.34 km at stations 1-3, respectively.The different heights correspond to the different distances between the radar and the three stations.Figure 11 shows time series of the vertical profiles of Z H , Z DR , K DP , ρ HV , and Hcl (Hydrometeor classification result) at the three stations where the heaviest rainfall occurred.Hcl is obtained according to the Hydrometeor classification algorithm described in Wu et al. [27].This algorithm has been verified with the Zhuhai radar, the first operational PR in Guangdong, China.Following the approach of Mohr and Vaughan [41], radar observations (except Hcl) with SNR > 20 dB at the nine PPIs above the stations were linearly interpolated to obtain the profiles of the polarimetric variables.The vertical resolution was 0.5 km, and the temporal resolution was 6 min.The time shown on the horizontal axis is identical to Figure 6.The black lines in Figure 11 denote the heights of radar observations used for precipitation estimation, namely 1.23, 1.17, and 1.34 km at stations 1-3, respectively.The different heights correspond to the different distances between the radar and the three stations.The sounding data obtained near the precipitation area indicate that 0 • C was located around 5600 m.However, the vertical profiles of the polarimetric variables show no significant signs of the melting layer, which is consistent with the characteristics of strongly convective precipitation.Figure 11 shows that the heavy precipitation at stations 1-3 was caused by four, two, and three convective cells, respectively.
At station 1, the four cells had similar Z H , but cells 1 and 2 had larger Z DR and smaller K DP compared with the other two cells, corresponding to a lower concentration of larger raindrops.The opposite is true for cells 3 and 4. Rain rate derived from the radar data at 1.4 h is 0, which is not correct.It is due to non-meteorological echoes at 1.4 h (Figure 11).
At station 2, the largest reflectivity (>60 dBZ) appeared at a height of 2.5 km during hours 2.4-2.5 (Figure 11b), below which were large values of Z DR and K DP and small values of ρ HV , indicating an area of mixed graupel particles, hail particles, liquid water, and larger raindrops.In Figure 10, R1(K DP ) is used to estimate precipitation at hour 2.5, which means rain mixed with hail existed at this time.This is verified by Hcl in Figure 11n.Most of the mixed precipitation detection results from both algorithms are consistent.It indicates the result of the mixed precipitation detected by the algorithm presented in this study is credible.According to the results of the two algorithms, hail existed during hours 2-3.The underestimations of R(K DP , Z DR ) at hours 2-3 (Figure 10) can probably be attributed to the abnormally large Z DR , which corresponds to larger raindrops produced by hail melting.
Compared with K DP at station 1, that at station 3 was larger most of the time during this rainfall event, especially for hours 2-3.2 (Figure 11i).The strong echo at station 3 was caused mainly by the high concentration of raindrops, which also led to the large K DP .The larger K DP mitigates the underestimations caused by R(K DP , Z DR ), which is used most of the time during this rainfall event (Figure 10c).This is the main reason why underestimation is not obvious at station 3.
Underestimations occurred at the three stations when hourly rainfall accumulation was quite large.PR data at station 1 during 2000-2400 UTC on 6 May 2017, data at station 2 during 2100-2300 UTC on 6 May 2017 and data at station 3 during 2200-2300 UTC on 6 May 2017 are used to calculate D m and N w , which are shown in Figure 9d.Pink rectangles indicate data at station 1, and red rectangles indicate data at stations 2 and 3.There are the mixtures of rain and hail at 1-1.5 km during these periods at stations 2 and 3 according to Hcl shown in Figure 11n,o.These red rectangles are found at the edge of the clusters that have relatively large D m and N w .It is probably due to the melting hail.It indicates large concentrations of big rain drops in part 3 (Figure 9c) are probably associated with the melting hail.Considering that these particles in part 3 lead to severe underestimations, the melting hail is a reason for severe underestimations.

The Improved Algorithm and Its Performance
Analyses show that DSD characteristics in this rainfall event are significantly different from that of the average DSD in Yangjiang (estimators are derived from these DSD data), which is clearly evident at the three stations where the heaviest rainfall occurred.R(K DP , Z DR ) underestimates the rain rate most often at the three stations.It indicates R(K DP , Z DR ) is still sensitive to DSD variations when the extremely heavy rain occurs.In view of this problem, specific attenuation A H is a good substitution variable for QPE.The low sensitivity of R(A H ) relation to DSD variability is well known and pointed out by Atlas and Ulbrich [20] and Matrosov [21].A method that using N w and Z H to estimate A H is used in this study [22].The relationship between x = log10(Z H /N w ) and y = log10(A H /N w ) can be expressed as where a 0 = −6.12− 0.012t, a 1 = 0.622 − 0.0002t, a 2 = 0.0250, a 3 = 0.00424, at S-band and t is temperature ( • C).Equation ( 18) was obtained from long-term disdrometer data, as described by Ryzhkov [22].Ryzhkov [22] considers A H calculated from Equation (18) as the "true" value, and we use Z H and N w derived from the radar data to calculate A H according to Equation (18).First, R-A H relation is fitted by using R and A H derived from Yangjiang DSD data with the least-squares method, which is expressed as where R is in mm/h and A H is in dB km -1 .In the improved algorithm, A H is derived from PR data and R(A H ) replaces R(K DP , Z DR ) to estimate heavy rainfall.Table 6 lists the evaluated statistical scores for the QPE estimated by algorithm before and after improvement.The improved algorithm performs better for total rain in term of NB, which is close to 0. For heavy rain, the performance of the improved algorithm is much better than the previous algorithm in terms of all the statistical indicators.After the improvement, RMSE and NE decreased by 40.29% and 37.70%, respectively.In particular, Eff changes from −0.21 to 0.57, indicating that, the QPE is worse and significantly better than the mean value of rain observed before and after improvement, respectively.As shown in Figure 12, most high rain rate data are distributed in the red circle.The extremely heavy rain data observed at the three stations and the data in part 3 (Figure 9c) are also in the red circle.After algorithm improvement, NE corresponding to the heavy rain rate data decreased dramatically.Figure 12b shows NE decreased percentage ((NE before − NE after )/NE before × 100%) after algorithm improvement of log 10 N w versus D m .Most large value data are distributed in the red circle, which explains why NE decreased significantly when hourly accumulation was > 50 mm.The same situation occurred for RMSE (not shown)., at S-band and t is temperature (°C).Equation ( 18) was obtained from long-term disdrometer data, as described by Ryzhkov [22].Ryzhkov [22] considers AH calculated from Equation (18) as the "true" value, and we use ZH and Nw derived from the radar data to calculate AH according to Equation (18).First, R-AH relation is fitted by using R and AH derived from Yangjiang DSD data with the least-squares method, which is expressed as where R is in mm/h and AH is in dB km -1 .In the improved algorithm, AH is derived from PR data and R(AH) replaces R(KDP, ZDR) to estimate heavy rainfall.Table 6 lists the evaluated statistical scores for the QPE estimated by algorithm before and after improvement.The improved algorithm performs better for total rain in term of NB, which is close to 0. For heavy rain, the performance of the improved algorithm is much better than the previous algorithm in terms of all the statistical indicators.After the improvement, RMSE and NE decreased by 40.29% and 37.70%, respectively.In particular, Eff changes from −0.21 to 0.57, indicating that, the QPE is worse and significantly better than the mean value of rain observed before and after improvement, respectively.As shown in Figure 12, most high rain rate data are distributed in the red circle.The extremely heavy rain data observed at the three stations and the data in part 3 (Figure 9c) are also in the red circle.After algorithm improvement, NE corresponding to the heavy rain rate data decreased dramatically.Figure 12b shows NE decreased percentage ((NEbefore − NEafter)/NEbefore × 100%) after algorithm improvement of log10Nw versus Dm.Most large value data are distributed in the red circle, which explains why NE decreased significantly when hourly accumulation was > 50 mm.The same situation occurred for RMSE (not shown).Figure 13 shows the hourly radar or gauge rainfall accumulations at the three stations with the heaviest rainfall.The corresponding rain rate, which was estimated using the improved algorithm, is also shown in Figure 11p-r with blue dash lines.At the three stations, the performance of the improved algorithm also becomes better in terms of both rainfall accumulations and rain rate.Even though the improved algorithm overestimates rainfall during certain periods, most hourly rainfall accumulations are close to the AWS observations.At station 2, the new algorithm significantly improves compared with previous algorithm calculations during hours 3 and 4 when the DSD is affected by hail.NEafter)/NEbefore × 100%) after algorithm improvement of log10Nw versus Dm derived from the PR data.Note that all these data are averaged from two adjacent data in time (average time: 12 min).
Figure 13 shows the hourly radar or gauge rainfall accumulations at the three stations with the heaviest rainfall.The corresponding rain rate, which was estimated using the improved algorithm, is also shown in Figure 11p-r with blue dash lines.At the three stations, the performance of the improved algorithm also becomes better in terms of both rainfall accumulations and rain rate.Even though the improved algorithm overestimates rainfall during certain periods, most hourly rainfall accumulations are close to the AWS observations.At station 2, the new algorithm significantly improves compared with previous algorithm calculations during hours 3 and 4 when the DSD is affected by hail.After improvement, the algorithm performs much better than before because of the help of R(AH).Rainfall estimation utilizing AH has many advantages compared with algorithms based on ZH, ZDR, or KDP.It is least sensitive to DSD variations and immune to radar miscalibration, partial beam blockage, and the impacts of wet radomes [22].Based on DSD-simulated data test, Thompson et al. [26] concluded that the R(AH) estimator performed as well as the top-ranking R(KDP, ZDR) estimator at S-band.However, despite recent attempts to improve ΦDP processing, reliable and robust routines for KDP estimations do not exist at the moment [22].The extremely heavy rain may make KDP more unreliable than does moderate rain in this rainfall event; therefore, R(AH) could be better than R(KDP, ZDR) when estimating the extremely heavy rain.
The improved algorithm performs well for heavy rain.How is the performance of this algorithm when it is used for light-to-moderate rainfall cases?The improved algorithm is used for the nine rainfall events listed in Table 2 to test its performance for light-to-moderate rainfall cases, and the evaluated statistical scores for these nine rainfall events are shown in Table 7.
For all nine rainfall events, NE ranges from 34.77% to 44.65%, NB ranges from -24.67% to 11.55%, and Eff ranges from 0.69 to 0.75.This improved algorithm presented for solving the heavy rain problem performed slightly worse than the original algorithm for the nine light-to-moderate rainfall cases.The performance for some rain cases becomes worse but for some becomes better.This is because the performance of R(AH) is unstable when estimating light-to-moderate rain.ZDR biases are larger for light rain than for heavy rain and the biases may propagate when AH is estimated by using Nw(ZH, ZDR) (Equations ( 17) and ( 18)).The value of AH at S-band is very small for light-to-moderate rain and the small bias of AH may bring a big bias of rain estimated by using R(AH).These make the performance of R(AH) unstable when estimating light-to-moderate rain.For all nine rainfall events, NE ranges from 34.77% to 44.65%, NB ranges from −24.67% to 11.55%, and Eff ranges from 0.69 to 0.75.This improved algorithm presented for solving the heavy rain problem performed slightly worse than the original algorithm for the nine light-to-moderate rainfall cases.The performance for some rain cases becomes worse but for some becomes better.This is because the performance of R(A H ) is unstable when estimating light-to-moderate rain.Z DR biases are larger for light rain than for heavy rain and the biases may propagate when A H is estimated by using N w (Z H , Z DR ) (Equations ( 17) and ( 18)).The value of A H at S-band is very small for light-to-moderate rain and the small bias of A H may bring a big bias of rain estimated by using R(A H ).These make the performance of R(A H ) unstable when estimating light-to-moderate rain.Considering that we have not yet figured out what kind of light-to-moderate rainfall is this new improved algorithm suitable for, this new algorithm is not suggested for light-moderate rain cases for now.

Conclusions and Discussion
In this study, we proposed a localized PR QPE algorithm that accounts for hydrometeor phase classification.The algorithm is used for nine different types of rainfall events as well as an extremely heavy rainfall event occurred in Guangzhou, China, on 6 May 2017, which is significantly different from conventional rainfall events, in which hourly rainfall accumulations are less than 50 mm.Estimates were made for total rain, light-to-moderate rain (hourly accumulation <50 mm), and heavy rain (>50 mm).The estimates at three stations where total rainfall exceeded 300 mm were analyzed in particular during this rainfall event.To analyze the reasons for QPE error, a rain microphysics retrieval algorithm was presented to retrieve D m and N w from the PR measurements.The DSD characteristics of this extremely heavy rainfall event and the factors affecting QPE are analyzed based on D m and N w .To improve the operational algorithm, R(A H ) replaces R(K DP , Z DR ) in the original algorithm to estimate heavy precipitation.The improved algorithm is also evaluated.The main conclusions are presented as follows.
(1) Persistent convergence and ascending motions occurred during this rainfall event, resulting in strong echoes that persisted for a long time.Radar echoes larger than 45 dBZ lasted for a long time and moved slowly, leading to heavy rain over some areas of Guangdong.Compared with Z DR derived from Yangjiang DSD data, Z DR in this rainfall event are smaller for the same Z H , which is more obvious for the high occurrence frequencies data.The average values of D m and log 10 N w derived from the PR data in this rainfall event are 1.44 mm and 4.06, respectively.Compared with the values of data derived from the Yangjiang DSD data, the average value of D m in this rainfall event decreased by 24.21% and the average value of log 10 N w in this rainfall event increased by 14.69%.In short, compared with the statistical DSD data in Yangjiang (estimators are derived from these data), this rainfall event was characterized by smaller average raindrop diameters and higher number concentration.These characteristics are more obvious in the heavy rainfall area.
(2) The bias ratio of MRMS for precipitation during the 2014 warm season is 1.06, which is slightly larger than that (1.00) of the algorithm presented in this study.NB and RMSE of the France operational radar system for intense rain (hourly accumulations >5 mm) in two rainfall events observed in 2010 are −9% and 8.46 mm, respectively.Compared with it, the algorithm presented in this study is slightly better in terms of similar NB (−9%) and lower RMSE (6.55 mm) for the intense rain.The performance of the operational PR QPE algorithm presented in this study is satisfied when it estimates precipitation of all nine rainfall events.Even though precipitation estimates for light-to-moderate rain performed well, this algorithm severely underestimated heavy rain.
(3) The algorithm underestimated the precipitation with small and midsize particles but overestimated the precipitation with midsize and large particles.When D m and N w are both very large, underestimations occurred, and severe underestimations of heavy rain are mainly due to these particles.It is verified that some of these particles are associated with the melting hail.Even though most mixed precipitation was detected by the operational algorithm presented in this study, R1(K DP ) underestimated mixed precipitation because it is not capable of adapting to large DSD variations for extremely heavy rain.R(K DP , Z DR ) underestimates most heavy rain at the three stations because of the same reason.
(4) Even though R(K DP , Z DR ) is less susceptible to DSD variations than R(Z H ) [6], it still performs poorly for the extremely heavy rain in this rainfall event.In the improved algorithm, R(A H ) replaces R(K DP , Z DR ).After improvement, RMSE and NE decreased by 40.29% and 37.70%, respectively, for the heavy rain in which hourly rainfall accumulations are more than 50 mm.At station 2, the improved algorithm performed much better than the previous algorithm during hours 3 and 4 when DSD is affected by hail.These indicate that R(A H ) performs well for the extremely heavy rain.
There are still scarce PR observations of such extremely heavy rain events, and further studies of similar extremely heavy rain are necessary to verify the improved algorithm.

Figure 5 .
Figure 5. Scatterplots of rain variables (Dm and Nw) and radar variables (ZH and ZDR) calculated from drop size distribution (DSD) data.The red points are mean data value, which are fitted to the black data points by using a three-order polynomial fit with the least-squares method.(a) Dm vs. ZDR (Equation (16)), and (b) ratio of Nw to ZH vs. ZDR (Equation (17)).Correlation coefficient (CC) and normalized relative bias (NB) for the retrieved rain variables versus the observations are shown in this figure.

Figure 5 .
Figure 5. Scatterplots of rain variables (D m and N w ) and radar variables (Z H and Z DR ) calculated from drop size distribution (DSD) data.The red points are mean data value, which are fitted to the black data points by using a three-order polynomial fit with the least-squares method.(a) D m vs. Z DR (Equation (16)), and (b) ratio of N w to Z H vs. Z DR (Equation (17)).Correlation coefficient (CC) and normalized relative bias (NB) for the retrieved rain variables versus the observations are shown in this figure.

Figure 6 23 Figure 6 .
Figure 6 shows the hourly radar or gauge rainfall accumulations at the three AWSs where the total rainfall exceeded 300 mm.Hours 1-5 correspond to 1900-2000 UTC, 2000-2100 UTC, 2100-2200 UTC, 2200-2300 UTC, and 2300-2400 UTC, respectively.A similar scenario occurred at all three stations.The QPE algorithm underestimated the rainfall for hourly rainfall accumulations >50 mm, especially at station 2 where the maximum hourly rainfall accumulation occurred.Atmosphere 2018, 9, x FOR PEER REVIEW 12 of 23 , we obtained the occurrence frequencies of ZDR versus ZH and KDP versus ZH based on a statistical analysis of the ZH-ZDR and ZH-KDP observations below 3 km (for ZDR > 1 dB, SNR > 20 dB and KDP > 1°/km, SNR > 20 dB).To analyze the DSD characteristics in this rainfall event, besides DSD data collected at Yangjiang during April-June 2014, we also used another set of DSD data collected at Luogang during this rainfall event from 1600 UTC, 6 May 2017 to 1600 UTC, 7 May 2017.DSD data collected during April-June 2014 were compared with DSD data collected during the target rainfall event.We calculated ZH, ZDR, and KDP based on these DSDs and then averaged them to obtain the curves shown in Figure7, which represent the statistical (i.e., average) microphysical properties of precipitation in this region (black curve) and the specific microphysical properties of precipitation for this rainfall event (red curve).Note that the black curve and the QPE estimators are from the same DSD sources.

Figure 6 .
Figure 6.Hourly rainfall accumulations at stations where the largest rainfall accumulations were observed.(a-c) show the QPE results of the algorithm at stations 1-3, respectively.The column in blue indicates an AWS observation, and the column in red indicates the radar estimate.

Affecting QPE 5 . 1 .
DSD Characteristics in This Rainfall Event and Their Effects on QPE As shown in Figure 7, we obtained the occurrence frequencies of Z DR versus Z H and K DP versus Z H based on a statistical analysis of the Z H -Z DR and Z H -K DP observations below 3 km (for Z DR > 1 dB, SNR > 20 dB and K DP > 1 • /km, SNR > 20 dB).To analyze the DSD characteristics in this rainfall event, besides DSD data collected at Yangjiang during April-June 2014, we also used another set of DSD data collected at Luogang during this rainfall event from 1600 UTC, 6 May 2017 to 1600 UTC, 7 May 2017.

Figure 7 .
Figure 7. Occurrence frequencies of (a) ZDR versus ZH and (b) KDP versus ZH from polarimetric radar.The average ZDR-ZH and KDP-ZH relationships were calculated from DSDs at the Yangjiang (black curves) and Luogang stations (red curves) for this rainfall event.

Figure 7 .
Figure 7. Occurrence frequencies of (a) Z DR versus Z H and (b) K DP versus Z H from polarimetric radar.The average Z DR -Z H and K DP -Z H relationships were calculated from DSDs at the Yangjiang (black curves) and Luogang stations (red curves) for this rainfall event.

Figure 8 .
Figure 8.(a) Dm retrieved from radar observations versus DSD data.(b) log10Nw retrieved from radar observations versus DSD data.

Figure 8 .
Figure 8.(a) D m retrieved from radar observations versus DSD data.(b) log 10 N w retrieved from radar observations versus DSD data.

Atmosphere 2018, 9 , 23 Figure 9 .
Figure 9. (a) Occurrence frequencies of log10Nw versus Dm.Two black rectangles correspond to the maritime and continental convective clusters, respectively, reported by Bringi et al. [40].The red "+" symbol indicates the average value of log10Nw (4.06) and Dm (1.44 mm) retrieved from radar data and the red "×" symbol indicates the average value of log10Nw (3.54) and Dm (1.90 mm) retrieved from Yangjiang DSD data for convective precipitation.(b) The bias between rain rate retrieved from radar data and rain rate observed at AWSs of log10Nw versus Dm for hourly accumulation <50 mm.(c) Biases for hourly accumulation >50 mm.(d) Rain rate observed at AWSs of log10Nw versus Dm.The pink rectangles indicate rain rate observed at station 1 during 2000-2400 UTC on 6 May 2017 and the red rectangles indicate rain rate observed at station 2 during 2100-2300 UTC on 6 May 2017 and that observed at station 3 during 2200-2300 UTC on 6 May 2017, during which underestimations occurred in each corresponding station.(e) Rain rate observed at AWSs of log10Nw versus Dm for hourly accumulation <50 mm.(f) Rain rate observed at AWSs of log10Nw versus Dm for hourly accumulation >50 mm.Note that all these data are averaged from two adjacent data in time (average time: 12 min).

Figure 9 .
Figure 9. (a) Occurrence frequencies of log 10 N w versus D m .Two black rectangles correspond to the maritime and continental convective clusters, respectively, reported by Bringi et al. [40].The red "+" symbol indicates the average value of log 10 N w (4.06) and D m (1.44 mm) retrieved from radar data and the red "×" symbol indicates the average value of log 10 N w (3.54) and D m (1.90 mm) retrieved from Yangjiang DSD data for convective precipitation.(b) The bias between rain rate retrieved from radar data and rain rate observed at AWSs of log 10 N w versus D m for hourly accumulation <50 mm.(c) Biases for hourly accumulation >50 mm.(d) Rain rate observed at AWSs of log 10 N w versus D m .The pink rectangles indicate rain rate observed at station 1 during 2000-2400 UTC on 6 May 2017 and the red rectangles indicate rain rate observed at station 2 during 2100-2300 UTC on 6 May 2017 and that observed at station 3 during 2200-2300 UTC on 6 May 2017, during which underestimations occurred in each corresponding station.(e) Rain rate observed at AWSs of log 10 N w versus D m for hourly accumulation <50 mm.(f) Rain rate observed at AWSs of log 10 N w versus D m for hourly accumulation >50 mm.Note that all these data are averaged from two adjacent data in time (average time: 12 min).

Figure 10 .
Figure 10.RQPE (rain rate calculated with the QPE algorithm) minus RGauge (rain rate measured at the AWS) at the three stations with the heaviest rainfall.(a-c) show the values for stations 1-3, respectively.The different colors represent the various estimators used during this rainfall event.

Figure 10 .
Figure 10.R QPE (rain rate calculated with the QPE algorithm) minus R Gauge (rain rate measured at the AWS) at the three stations with the heaviest rainfall.(a-c) show the values for stations 1-3, respectively.The different colors represent the various estimators used during this rainfall event.

Atmosphere 2018, 9 , 23 Figure 11 .
Figure 11.Time series of polarimetric radar (PR) variables at the three stations where the heaviest rainfall occurred.The columns from left to right represent stations 1-3, and the rows from top to bottom show ZH (a-c), ZDR (d-f), KDP (g-i), ρHV (j-l), and Hcl (m-o).The panels (p-r) in the bottom (sixth) row show the time series of rain rate observed (solid lines) at each station and those derived from the radar data (red and blue dash lines: estimated by using algorithms presented in Sections

Figure 11 .
Figure 11.Time series of polarimetric radar (PR) variables at the three stations where the heaviest rainfall occurred.The columns from left to right represent stations 1-3, and the rows from top to bottom show Z H (a-c), Z DR (d-f), K DP (g-i), ρ HV (j-l), and Hcl (m-o).The panels (p-r) in the bottom (sixth) row show the time series of rain rate observed (solid lines) at each station and those derived from the radar data (red and blue dash lines: estimated by using algorithms presented in Sections 3.1 and 6, respectively).The black lines denote the observation heights used for precipitation estimation.

Figure 12 .Figure 12 .
Figure 12.(a) Rain rate observed at the AWSs of log10Nw versus Dm derived from the PR data.Most high rain rate data are distributed in the red circle.(b) NE decreased percentage ((NEbefore − Figure 12.(a) Rain rate observed at the AWSs of log 10 N w versus D m derived from the PR data.Most high rain rate data are distributed in the red circle.(b) NE decreased percentage ((NE before − NE after )/NE before × 100%) after algorithm improvement of log 10 N w versus D m derived from the PR data.Note that all these data are averaged from two adjacent data in time (average time: 12 min).

Figure 13 .
Figure 13.Hourly rainfall accumulations at stations where the largest rainfall accumulations were observed.(a-c) show the results of the algorithms at stations 1-3, respectively.The column in blue indicates an AWS observation, the column in red indicates the radar estimate based on the unimproved algorithm, and the column in green indicates the radar estimate based on the improved algorithm.

Figure 13 .
Figure 13.Hourly rainfall accumulations at stations where the largest rainfall accumulations were observed.(a-c) show the results of the algorithms at stations 1-3, respectively.The column in blue indicates an AWS observation, the column in red indicates the radar estimate based on the unimproved algorithm, and the column in green indicates the radar estimate based on the improved algorithm.

Table 2 .
A list of the nine rainfall events analyzed in this study.

Table 3 .
Evaluated statistical scores for quantitative precipitation estimation (QPE) of the nine rainfall events.

Table 4 .
Evaluated statistical scores for QPE of the nine total rainfall events.

Table 5 .
Evaluated statistical scores for the QPE of this rainfall event.

Table 6 .
Evaluated statistical scores for the QPE estimated by algorithm before and after improvement.

Table 6 .
Evaluated statistical scores for the QPE estimated by algorithm before and after improvement.