A Synthetic Quantitative Precipitation Estimation by Integrating S- and C-Band Dual-Polarization Radars over Northern Taiwan

: The key factors, namely, the radar data quality, raindrop size distribution (RSD) variability, and the data integration method, which signiﬁcantly affect radar-based quantitative precipitation estimation (QPE) are investigated using the RCWF (S-band) and NCU C-POL (C-band) dual-polarization radars in northern Taiwan. The radar data quality control (QC) procedures, including the corrections of attenuation, the systematic bias, and the wet-radome effect, have large impact on the QPE accuracy. With the proper QC procedures, the values of normalized root mean square error (NRMSE) decrease about 10~40% for R(Z HH ) and about 5~15% for R(K DP ). The QPE error from the RSD variability is mitigated by applying seasonal coefﬁcients derived from eight-year disdrometer data. Instead of using discrete QPEs (D-QPE) from one radar, the synthetic QPEs are derived via discretely combined QPEs (DC-QPE) from S- and C-band radars. The improvements in DC-QPE compared to D-QPE are about 1.5–7.0% and 3.5–8.5% in R(K DP ) and R(K DP , Z DR ), respectively. A novel algorithm, Lagrangian-evolution adjustment (LEA), is proposed to compensate D-QPE from a single radar. The LEA-QPE shows 1–4% improvements in R(K DP , Z DR ) at the C-band radar, which has a larger scanning temporal gap (up to 10 min). The synthetic LEA-QPEs by combining two radars have outperformed both D-QPEs and DC-QPEs.


Introduction
Accurate radar-based quantitative precipitation estimation (QPE) has been one of the longstanding goals of meteorological radar. Marshall and Palmer [1] utilized horizontal reflectivity (Z HH , mm 6 m −3 ) and a power-law relation, Z HH = aR b (Z-R) obtained from simulated radar variables based on measured raindrop size distribution (RSD), to estimate rainfall rate (R, mm h −1 ). However, the Z-R relation varies vastly in convective, stratiform precipitation, and different climatological regions due to the natural variability in RSD [2]. Seliga and Bringi [3] proposed dual-polarization (dual-pol) radar, which is capable of transmitting horizontal and vertical electromagnetic signals. Additional dual-pol variables from a dual-pol radar, such as the differential reflectivity (Z DR ) and specific differential phase (K DP ), are utilized in QPE. Consequently, the QPE has significantly been improved by the better quality of radar data and the inclusion of the RSD information .
Diverse forms of power-law QPE relations were recommended using single to multiple dual-pol radar parameters (R(Z HH , Z DR ), R(K DP ), R(K DP , Z DR ), R(Z HH , K DP ), and R(Z HH , K DP , Z DR )); [6][7][8]11,12,25]. These QPE algorithms have shown pronounced improvements compared to the Z-R relation. More sophisticated QPE algorithms were explored to overcome various QPE issues. For instance, the variational-based algorithm is developed for attenuation correction and QPE simultaneously [13,19,26]. Moreover, the al- Table 1. The basic information for RCWF (radar code of Wu-Fanshan, NEXRAD WSR-88D S-band dual-pol radar, Ryzhkov et al. [9] from the Central Weather Bureau (CWB) and NCU C-POL) National Central University C-band polarimetric radar).

RCWF NCU C-POL
Wavelength (cm) 10 POL is a research radar upgraded from a decommission Ericsson Doppler radar and has been utilized to study the RSD characteristics of typhoon systems associated with Taiwan's complex topography [31]. Both radars have the same signal processor (Sigmat RVP8), yet they have different configurations. As shown in Figure 1, these two radars have broad overlapping coverage in northern Taiwan. In addition, different frequencies are ideal to evaluate the performance of dual-pol QPE at different wavelengths. Table 1. The basic information for RCWF (radar code of Wu-Fanshan, NEXRAD WSR-88D S-band dual-pol radar, Ryzhkov et al. [9] from the Central Weather Bureau (CWB) and NCU C-POL) National Central University C-band polarimetric radar).  Both RCWF and NCU C-POL have various data quality issues. Different distributions of PBB depending on the radar locations are displayed in Figure 1. Distinct ground clutter suppression configurations from different manufacturers induce distinct ground clutter characteristics. The degree of the attenuation effect varies according to radar wavelengths. Each radar has distinct characteristics of systematic ZHH and ZDR biases due to different maintenance and calibration procedures (e.g., transmitter and receiver). Finally, different radome materials and radar frequencies cause distinct WREs. The QC procedures for both radars shown in Figure 2 (left panel) have been applied before the QPE retrievals. These procedures include the PBB and non-meteorological signal removal, the corrections of attenuation, the systematic bias, and the WRE.

PBB Removal
Radar data with the PBB effect, mainly resulting from Taiwan's complex topography, are first identified by a beam blockage simulation [10,18,34,35]. When the central height of the radar beams, estimated by 4/3 of the Earth's radius model, is lower than the top of the terrain (50% of the power is blocked), the data and the following bins along the radial will be removed. Both RCWF and NCU C-POL have various data quality issues. Different distributions of PBB depending on the radar locations are displayed in Figure 1. Distinct ground clutter suppression configurations from different manufacturers induce distinct ground clutter characteristics. The degree of the attenuation effect varies according to radar wavelengths. Each radar has distinct characteristics of systematic Z HH and Z DR biases due to different maintenance and calibration procedures (e.g., transmitter and receiver). Finally, different radome materials and radar frequencies cause distinct WREs. The QC procedures for both radars shown in Figure 2 (left panel) have been applied before the QPE retrievals. These procedures include the PBB and non-meteorological signal removal, the corrections of attenuation, the systematic bias, and the WRE.
Despite the Doppler spectrum clutter suppression has been applied to both RCWF and NCU C-POL radars, some residual non-meteorological signals remain after the PBB removal. The standard deviation values of the differential propagation phase shift of five radar bins along a radial (Std. ) and the correlation coefficient (CC) are subsequently used to filter out non-meteorological signals. The data with the values of Std. higher than 15° or with CC less than 0.85 is removed for RCWF. The corresponding threshold values of Std. and CC for NCU C-POL are 20° and 0.8. The threshold values of Std. and CC for RCWF and NCU C-POL were obtained accordingly by examining large amounts of radar data. The values which preserve the most meteorological signal and reduce the most persistent ground clutters were selected as the threshold. The same technique has been applied to the operational Doppler dualpol radars in Taiwan [33].

Attenuation Correction
The intrinsic ZHH (Z ) and ZDR (Z ) can be obtained after attenuation and bias corrections from the observational ZHH (Z . ) and ZDR (Z . ) as bellow, The attenuation effects of ZHH and ZDR on both RCWF and NCU C-POL are corrected by the -based algorithm. The horizontal attenuation (AH, dB) and differential attenuation (AHV, dB) can be estimated as follows, The coefficients of and for S-band (C-band) radar are 0.0151 dB deg −1 (0.0727 dB deg −1 ) and 0.0025 dB deg −1 (0.0161 dB deg −1 ), respectively. These coefficients were obtained

PBB Removal
Radar data with the PBB effect, mainly resulting from Taiwan's complex topography, are first identified by a beam blockage simulation [10,18,34,35]. When the central height of the radar beams, estimated by 4/3 of the Earth's radius model, is lower than the top of the terrain (50% of the power is blocked), the data and the following bins along the radial will be removed.

Non-Meteorological Signal Removal
Despite the Doppler spectrum clutter suppression has been applied to both RCWF and NCU C-POL radars, some residual non-meteorological signals remain after the PBB removal. The standard deviation values of the differential propagation phase shift φ DP of five radar bins along a radial (Std. φ DP ) and the correlation coefficient (CC) are subsequently used to filter out non-meteorological signals. The data with the values of Std. φ DP higher than 15 • or with CC less than 0.85 is removed for RCWF. The corresponding threshold values of Std. φ DP and CC for NCU C-POL are 20 • and 0.8.
The threshold values of Std. φ DP and CC for RCWF and NCU C-POL were obtained accordingly by examining large amounts of radar data. The values which preserve the most meteorological signal and reduce the most persistent ground clutters were selected as the threshold. The same technique has been applied to the operational Doppler dual-pol radars in Taiwan [33].

Attenuation Correction
The The attenuation effects of Z HH and Z DR on both RCWF and NCU C-POL are corrected by the φ DP -based algorithm. The horizontal attenuation (A H , dB) and differential attenuation (A HV , dB) can be estimated as follows, The coefficients of α and β for S-band (C-band) radar are 0.0151 dB deg −1 (0.0727 dB deg −1 ) and 0.0025 dB deg −1 (0.0161 dB deg −1 ), respectively. These coefficients were obtained from the long-term RSD measurements in northern Taiwan. The RSD data and implementation of coefficient calculations will be discussed in Sections 3.1 and 3.2, respectively.

Z HH Systematic Bias and the WRE Correction
The next step is to correct Z HH biases including the radar systematic bias (i.e., the miscalibration of transmitter and receiver) and the WRE. The self-consistency among the Z HH , Z DR , and K DP measurements of rain has been utilized to estimate the radar systematic bias [36]. The WRE is an additional bias due to the attenuation effect of the water coated over the radome while a precipitation system is located over the radar site. It has similar characteristics to the radar systematic bias. Therefore, the Z HH biases which consist of both radar systematic bias and WRE can be calculated via the self-consistency method. The radar systematic bias is obtained by averaging the Z HH biases of no-WRE events (identified by the rain gauge measurements next to the radar site). Hence, the attenuation of Z HH from the WRE can be derived by examining the excess of estimated Z HH biases from the systematic bias. On the other hand, the WRE of Z DR measurements depends on the forms in which the rain accumulates on the radome [37][38][39][40][41]. The forms could be droplets, rivulets, or non-uniform film and cause diverse WREs of Z DR . It is difficult to estimate the WRE of Z DR, and there is no practical technique either. Consequently, Z DR is also excluded from the self-consistency algorithm for the Z HH bias estimation [36] to avoid WRE-contaminated Z DR .
Here, the attenuation-corrected Z HH (Z corr. HH , in mm 6 m −3 ) data of rain is applied to the K DP -Z HH relation to obtain the value of K DP in each radar bin as shown below, Based on the RSD measurements in Section 3.2, the coefficients a and b are 5.3 × 10 −5 (2.5 × 10 −4 ) and 0.88 (0.81) for S-band (C-band) radar. The calculated K DP of each radar bin is then integrated along a radial to derive the increments of differential phase shift (∆Φ DP ) as ∆Φ DP = 2 K DP dr = 2 aZ corr.
dr is the radial resolution of radar data [36]. Since the phase measurement (i.e., ∆Φ DP ) is not affected by the absolute calibration of the radar system and attenuation [11,36], the Z HH bias (Z bias HH ) including both the radar systematic and the WRE biases can be estimated via the calculated ∆Φ DP and the measured ∆Φ DP as In practice, the last valid ∆Φ DP and ∆Φ DP data along a radial below the freezing level (avoid non-liquid phase data) are used to calculate radial-wise Z bias HH . The values of ∆Φ DP is higher than ∆Φ DP when Z HH is over-calibrated (i.e., positive Z HH bias), and vice versa. Then the scan-wise representative Z HH bias is determined via the mean value of radial-wise Remote Sens. 2021, 13, 154 6 of 19 Z bias HH within one scan for the bias correction. Only the WRE of Z HH was considered via a self-consistency technique. The WRE of Z DR was not corrected in this study.

Z DR Systematic Bias Correction
The last remaining radar measurement error in the QC processes is Z DR systematic bias. Since both radars cannot perform vertical pointing scan (birdbath scan), the Z DR systematic bias is estimated by statistical analysis. The stratiform rain consisting of small sizes of raindrops mostly has Z DR values slightly above 0 dB. This Z DR characteristic of light rain is used for Z DR bias estimation. The mean Z DR averaged from the RSD-simulated Z DR of light rain (i.e., 0.19 dB), mainly the data with Z HH values from 10 to 20 dBZ, is considered as a reference. The difference between the mean value of radar-measured Z DR in the light rain region and the reference value is thus reasonably viewed as Z DR systematic bias. For example, the mean Z DR value in the light rain region from NCU C-POL was −0.28 dB, then the Z DR bias was determined as −0.47 dB. The Z DR biases of NCU C-POL were derived case by case and the values were within the range of −0.21 to −0.48 dB in this study. RCWF is a well-calibrated radar; therefore, Z DR calibration was not applied.

Quantitative Precipitation Estimation from S-and C-Band Dual-Polarization Radars
The RSD data obtained from the disdrometer was used to derive the coefficients for the aforementioned QC procedures and dual-pol QPE algorithms. The procedures of processing RSD data, deriving the coefficients of QPE relations, and developing different QPE (decision-tree) products are introduced. In addition, two integration methods intending to improve QPE performance are also described in this section.

Disdrometer Data
In this research, the RSD data collected by a 2D-Video Disdrometer (2DVD, [42]) located at NCU from October of 2000 to June of 2007 is used to characterize the RSD in northern Taiwan. The 2DVD records the particle diameter (D) and the terminal velocity (V t ) of each raindrop. The data is quality controlled by the V t -based filter technique [31,43,44]. The 6-min RSD is then calculated to ensure sufficient raindrop sampling numbers of each RSD [19,31,32,45]. Moreover, the rainfall rates of less than 1 mm h −1 are removed to eliminate inadequate RSD data set. There are a total of 14,314 quality-controlled minutely RSDs available for analysis.
Chen and Chen [46] has investigated the characteristics of Taiwan's precipitation systems and classified them into five distinct types. They are spring rain from March to April, Mei-Yu from May to June, summer convection from July to September, winter cold front from October to February, and typhoon systems. Most of the systems can be approximated simply by month, except typhoon is case-selected. Lee et al. [32] utilized the same classification and demonstrated unique RSD characteristics of these five types of precipitation systems. The bigger mean raindrop size (i.e., mass-weighted diameter) from Mei-Yu, summer convection, and typhoon events is found compared to spring rain and winter cold front.
The NCU 2DVD data is thus classified according to Chen and Chen [46]. The rainfall intensities of 6-min RSD for each precipitation type are summarized in Figure 3. The majority of rainfall intensities are less than 15 mm h −1 . The maximum rainfall rates of all types of precipitation are around or above 70 mm h −1 . The Mei-Yu and typhoon season have similar maximum rainfall up to 90 mm h −1 . The rainfall rates of the cold front are mostly below 5 mm h −1 . These quality-controlled and classified RSD data are consequently used to derive the coefficients of various QPE relations.
The NCU 2DVD data is thus classified according to Chen and Chen [46]. The rainfall intensities of 6-minutes RSD for each precipitation type are summarized in Figure 3. The majority of rainfall intensities are less than 15 mm hr −1 . The maximum rainfall rates of all types of precipitation are around or above 70 mm hr −1 . The Mei-Yu and typhoon season have similar maximum rainfall up to 90 mm hr −1 . The rainfall rates of the cold front are mostly below 5 mm hr −1 . These quality-controlled and classified RSD data are consequently used to derive the coefficients of various QPE relations.

QPE Coefficients
Various forms of power-law relationship using one to two dual-pol parameters were proposed to improve QPE, namely R(K DP ) [6,11,25], R(Z HH , Z DR ) [8,12], and R(K DP , Z DR ) [7,8]. The conventional Z-R and the most common dual-pol relations used in this study are shown in the following, R(K DP ) = a 3 K b 3 DP and (10) Lee [27] has shown that the RSD variability is one of the significant error sources in radar-based QPE. Thus, the correspondingly precipitation-type coefficients in dual-pol QPE relations are derived for reducing QPE error from the seasonal RSD variabilities [32]. First, the S-and C-band radar variables (i.e., Z HH , Z DR , K DP , A H , A HV ) are computed through the T-matrix scattering calculation [47] using the measured 6-min RSDs data set from NCU 2DVD, with the assumption of raindrop axis-ratio proposed by Brandes et al. [48] and Chang et al. [31] to non-typhoon cases and typhoon cases, respectively. Then the coefficients of Equations (8)-(11) for five types of precipitations (hereafter, seasonal coefficients) are derived by fitting the simulated radar variables and RSD-derived rainfall rates via the Levenberg-Marquardt algorithm [49] at both frequencies. Diverse coefficients due to the natural RSD variability among precipitation systems can be noticed. The coefficients based on the entire database (hereafter, all-season coefficients) are also obtained for comparison (Tables 2 and 3). The same procedures is also utilized to derive the coefficients of the attenuation correction and self-consistency relationship in Equations (3)-(5). Table 2. The coefficients of four power-law rain rate relations for S-band radar. The all-season coefficients are derived from the entire database measured by a 2D-Video Disdrometer (2DVD) at National Central University (NCU). The seasonal coefficients are classified into spring, Mei-Yu, summer convection, typhoon, and winter cold front. The seasonal coefficients are expected to diminish the RSD variations by considering the seasonal RSD characteristics, thus outperform all-season coefficients. The benefit of optimized QPE coefficients is first examined via the simulated data. The estimated rainfall (R est ) using seasonal and all-season coefficients, respectively, are derived from the RSDsimulated radar variables, and its performance is validated against RSD-derived rainfall rates (R t ). Since radar variables and R t are both based on the same database, namely, without radar measurement errors, the influence of the RSD variability on QPE can be investigated solely. The normalized bias (NBIAS) and normalized root mean square error (NRMSE) are calculated for validation,

All-Season
N is the number of RSD. The results in Figure 4 (upper panel) show that the values of NBIAS of QPEs using seasonal coefficients are closer to 0 than using all-season coefficients at S band, while Cband QPEs have comparable results. The NRMSEs of QPEs using seasonal coefficients are consistently lower than using all-season coefficients (Figure 4 lower panel). The improvements from applying seasonal coefficients are most pronounced in R(K DP ) and less evident in R(Z HH ). It can be explained by the fact that the seasonal variability of Taiwan RSD is mostly owing to small to medium sizes of raindrops [32] by which K DP is dominated. Moreover, the K DP -based algorithms outperform Z HH -based algorithms at both C and S bands. R(K DP , Z DR ) has the lowest NRMSE due to the additional RSD information from Z DR . The results show a good agreement with Bringi and Chandrasekar [11] and Lee [27]. Even though dual-pol radar variables have been utilized, applying seasonal coefficients in QPE relations further reduces the QPE uncertainty by diminishing the RSD variability.
N is the number of RSD. The results in Figure 4 (upper panel) show that the values of NBIAS of QPEs using seasonal coefficients are closer to 0 than using all-season coefficients at S band, while Cband QPEs have comparable results. The NRMSEs of QPEs using seasonal coefficients are consistently lower than using all-season coefficients (Figure 4 lower panel). The improvements from applying seasonal coefficients are most pronounced in R(KDP) and less evident in R(ZHH). It can be explained by the fact that the seasonal variability of Taiwan RSD is mostly owing to small to medium sizes of raindrops [32] by which KDP is dominated. Moreover, the KDP-based algorithms outperform ZHH-based algorithms at both C and S bands. R(KDP, ZDR) has the lowest NRMSE due to the additional RSD information from ZDR. The results show a good agreement with Bringi and Chandrasekar [11] and Lee [27]. Even though dual-pol radar variables have been utilized, applying seasonal coefficients in QPE relations further reduces the QPE uncertainty by diminishing the RSD variability.  The estimated rainfall rates are derived from the RSD-simulated radar variables and compared to RSD-derived rainfall rates for the theoretical verification.

Simplified Decision-Tree QPE
In practice, various dual-pol radar measurement errors cause a decline in QPE performance [27]. For instance, the noisy Z DR due to a fast-scanning radar with a low sampling rate [11,28] severely affects Z DR -based QPEs. The range-derivative K DP estimated from φ DP requires various filtering techniques [8,11,[50][51][52][53] and introduces more uncertainty in K DP -based QPEs. In the case of light rain, K DP is too small to be estimated with sufficient accuracy. The combination of different dual-pol QPE algorithms using decision-tree logic was thus proposed [8,9,14,16,54]. The superiority of this composite method over a single dual-pol algorithm has been proved [8].
Most of the decision-tree algorithms use more than two dual-pol QPE relationships. For example, studies from [14,16,54] utilize three dual-pol QPE relationships including R(Z), R(Z HH , Z DR ), and R(K DP , Z DR ) for their final QPE products. In this study, however, each dual-pol QPE algorithm is combined with R(Z) only. The purpose of utilizing simplified decision-tree algorithms is to examine the performance of specific dual-pol QPE relationships solely. In Figure 2 (right panel), the decision-tree algorithms are applied to quality-controlled plan position indicator (PPI) radar data. An additional filter of Z HH less than 10 dBZ, whose contribution to accumulated rainfall is neglectable, is applied. Each algorithm has its own criteria to assign different QPE relationships (Step C). The criteria were determined theoretically based on the dual-pol radar principle [11] and empirically adopted from previous researches. The concept is to avoid using inaccurate K DP in light rain and negative-biased Z DR due to the WRE in pure rain. For clarity, the simplified decision-tree QPE combining Z-R with R(Z HH , Z DR ), R(K DP ) or R(K DP , Z DR ) are referred to R(Z HH , Z DR ), R(K DP ) or R(K DP , Z DR ) QPEs, hereafter. To derive the composite QPE, the PPI QPE is then interpolated into the Cartesian coordinate. The lowest available Cartesian QPE is implemented as a final composite QPE product. These procedures are similar to Kwon et al. [18].

Integration Methods for Radar-Based QPE
Conventionally, the radar-based QPE is obtained by integrating each radar scan discretely, hereafter D-QPE (∆T i : time difference between two scans). The D-QPE of rapidlyevolving severe precipitation systems suffers from an inadequate radar scanning rate. Some researches proposed different solutions, namely the advection correction [15] and PCHIP interpolation [17]. Nevertheless, the influence of the evolution of the precipitation systems on QPE has not been well investigated. As aforementioned the time resolutions of RCWF and NCU C-POL were not synchronized and varied between 5 to 10 min (Table 4). To overcome this issue, the D-QPEs from asynchronous radars are "discretely" combined (hereafter, DC-QPE) to increase temporal resolution. The DC-QPE then can better reveal the evolution of precipitation than D-QPE does. Figure 5 displays an example that the NCU C-POL (red circles) and RCWF (blue crosses) D-QPEs are "discretely" combined whenever it is available (marked by black triangles). Hence, the DC-QPE has more sampling numbers.
The interval of ∆ is defined as one minute ( Figure 5 green dots) in this study. The seamless LEA-QPEs with the considerations of the advection and evolution of the precipitation systems are implemented between and .

QPE Comparison between C-and S-Band Radar
Eighteen heavy rainfall events for real case studies were selected by examining the rain gauge measurements in northern Taiwan ( Table 4). Most of the events are from the Mei-Yu season (East Asia rainy season, from mid-May to mid-June for Taiwan), since it contributes to most of the rainfall in Taiwan [46]. The most intensive hourly rainfall rate and highest event-accumulated rainfall are 103.5 mm hr −1 and 167.0 mm on 14 June, 2015. RCWF and NCU C-POL have diverse scanning strategies and configurations. RCWF has higher azimuthal and temporal resolution compared to NCU C-POL (Tables 1 and 4). The advantage of NCU C-POL is its location at a relatively lower altitude (156 m) than RCWF (766 m), providing closer observations to the surface and less vertical discrepancy than RCWF. QPE performances are evaluated against operational tipping bucket rain gauge However, not every location can be covered by two radars or more. A novel algorithm, namely Lagrangian-evolution adjustment (LEA), is developed for improving D-QPE/DC-QPE in this study. The QPEs from R T i and R T i+1 are first used to derive the advection speed and direction of precipitation movement via tracking radar echo based on the crosscorrelation (TREC, [15,55]). Thus, the R T i can be forward advected to T i+1 (= T i + ∆T i ), and the R T i+1 can be backward advected to T i . The evolution of the precipitation system between T i and T i+1 is subsequently estimated via time-weighted linear interpolation. The linear interpolated QPE (R T i +∆t j ) at T i + ∆t j is derived as follows, The interval of ∆t j is defined as one minute ( Figure 5 green dots) in this study. The seamless LEA-QPEs with the considerations of the advection and evolution of the precipitation systems are implemented between T i and T i+1 .

QPE Comparison between C-and S-Band Radar
Eighteen heavy rainfall events for real case studies were selected by examining the rain gauge measurements in northern Taiwan ( Table 4). Most of the events are from the Mei-Yu season (East Asia rainy season, from mid-May to mid-June for Taiwan), since it contributes to most of the rainfall in Taiwan [46]. The most intensive hourly rainfall rate and highest event-accumulated rainfall are 103.5 mm h −1 and 167.0 mm on 14 June, 2015. RCWF and NCU C-POL have diverse scanning strategies and configurations. RCWF has higher azimuthal and temporal resolution compared to NCU C-POL (Tables 1 and 4). The advantage of NCU C-POL is its location at a relatively lower altitude (156 m) than RCWF (766 m), providing closer observations to the surface and less vertical discrepancy than RCWF. QPE performances are evaluated against operational tipping bucket rain gauge measurements which are collected and maintained by CWB (black dots in Figure 1). For clarity, the S-and C-band QPEs will refer to RCWF and NCU C-POL QPEs hereafter.

The Influence of QC Procedures on C-and S-Band QPE
As discussed in previous studies [11], the K DP -based QPEs are immune to the systematic bias or attenuation effect and are expected to have better performance than Z HH -based QPEs. Nevertheless, Z HH -based QPEs are still applied in the simplified decision-tree QPE algorithms for specific purposes (e.g., avoid noisy K DP in light rain). Thus, it is essential to examine the impacts of various measurement errors from attenuation and the WRE on QPE.
To avoid WRE-contaminated Z DR error in the analysis, only R(Z HH ) and R(K DP ) are examined for comparison. As shown in Figure 6, both the C-band R(Z HH ) and R(K DP ) QPEs have higher values of NRMSE than the S-band when only the systematic bias is corrected. These results can be expected because of less attenuation and the WRE at longer wavelength radars. The values of NRMSE decrease dramatically at C band after the ensuing attenuation correction (brown areas), and the improvements are more pronounced than at S band. The results indicate that applying a proper attenuation correction can significantly mitigate the impacts of the attenuation effect on the C-band QPEs. The C-and S-band QPEs have a comparable performance after the systemic bias and attenuation corrections.

The Influence of QC Procedures on C-and S-Band QPE
As discussed in previous studies [11], the KDP-based QPEs are immune to the systematic bias or attenuation effect and are expected to have better performance than ZHH-based QPEs. Nevertheless, ZHH-based QPEs are still applied in the simplified decision-tree QPE algorithms for specific purposes (e.g., avoid noisy KDP in light rain). Thus, it is essential to examine the impacts of various measurement errors from attenuation and the WRE on QPE.
To avoid WRE-contaminated ZDR error in the analysis, only R(ZHH) and R(KDP) are examined for comparison. As shown in Figure 6, both the C-band R(ZHH) and R(KDP) QPEs have higher values of NRMSE than the S-band when only the systematic bias is corrected. These results can be expected because of less attenuation and the WRE at longer wavelength radars. The values of NRMSE decrease dramatically at C band after the ensuing attenuation correction (brown areas), and the improvements are more pronounced than at S band. The results indicate that applying a proper attenuation correction can significantly mitigate the impacts of the attenuation effect on the C-band QPEs. The C-and Sband QPEs have a comparable performance after the systemic bias and attenuation corrections. Figure 6. The NRMSEs of the C-band (refer to NCU C-POL) and S-band (refer to RCWF hereafter) QPEs at different levels of ZHH corrections. The height of each bar indicates the NRMSE after systematic-bias correction only. The brown color represents the reductions of NRMSE after the ensuing attenuation correction, and the yellow marks the reductions after the correction of the wet radome effect (WRE). The blue color is the final NRMSE when all QC procedures, including the systematic-bias, attenuation and wet-radome corrections, are completed.
Removing the WRE further reduces QPE errors (yellow areas). The most pronounced reduction of NRMSE can be found in the C-band R(ZHH) and R(KDP) QPEs. The C-band radar is more vulnerable to the weakening of the backscattering power due to rain over the radome. The C-band QPEs show slightly better results compared to S-band after the complete data QC procedures. The ZHH correction here is also beneficial to the R(KDP) algorithms since ZHH used in light rain is corrected, and more accurate ranges of ZHH are identified for the decision-tree criterion.

C-and S-Band Seasonal and All-Season Coefficients in QPE Algorithms
The dual-pol QPEs using seasonal and all-seasonal coefficients, respectively, in real case are first examined by comparing their NBIAS (Figure 7 upper panel). The QPEs using seasonal coefficients are consistently less biased than the ones using all-season coefficients. In terms of NRMSE (lower panel), C-band QPEs of seasonal coefficients show lower errors than all-seasonal coefficients, except for the R(ZHH, ZDR) algorithm. For the S-band QPEs, the seasonal ZDR-based algorithms have slightly higher NRMSE values compared Removing the WRE further reduces QPE errors (yellow areas). The most pronounced reduction of NRMSE can be found in the C-band R(Z HH ) and R(K DP ) QPEs. The C-band radar is more vulnerable to the weakening of the backscattering power due to rain over the radome. The C-band QPEs show slightly better results compared to S-band after the complete data QC procedures. The Z HH correction here is also beneficial to the R(K DP ) algorithms since Z HH used in light rain is corrected, and more accurate ranges of Z HH are identified for the decision-tree criterion.

C-and S-Band Seasonal and All-Season Coefficients in QPE Algorithms
The dual-pol QPEs using seasonal and all-seasonal coefficients, respectively, in real case are first examined by comparing their NBIAS (Figure 7 upper panel). The QPEs using seasonal coefficients are consistently less biased than the ones using all-season coefficients. In terms of NRMSE (lower panel), C-band QPEs of seasonal coefficients show lower errors than all-seasonal coefficients, except for the R(Z HH , Z DR ) algorithm. For the S-band QPEs, the seasonal Z DR -based algorithms have slightly higher NRMSE values compared to the all-season. It is noticed that both C-and S-band R(Z HH , Z DR ) algorithms using the seasonal coefficients perform much worse. The biased Z DR measurement due to the uncorrected WRE (visually examined, not shown in the paper) is postulated as the main reason.
Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 19 to the all-season. It is noticed that both C-and S-band R(ZHH, ZDR) algorithms using the seasonal coefficients perform much worse. The biased ZDR measurement due to the uncorrected WRE (visually examined, not shown in the paper) is postulated as the main reason. However, the R(KDP, ZDR) algorithms are less affected by ZDR than R(ZHH, ZDR). It can be explained by the more negative (more weighted) seasonal exponents of ZDR in the R(ZHH, ZDR) relations, and the less negative (less weighted) seasonal exponents of ZDR in R(KDP, ZDR). The sophisticated seasonal R(ZHH, ZDR) algorithms are sensitive to the ZDR bias in the real case. The R(ZHH, ZDR) algorithms using seasonal coefficients at S-band shows less deterioration due to the relative insensitivity of ZDR to the WRE. Overall, R(KDP) shows the most improvements after using seasonal coefficients, consistent with the result from the theoretical verification in Section 3.2.

C-and S-Band Discrete QPE Comparison (D-QPE)
The C-and S-band D-QPEs are first compared individually at different rainfall intensities to identify the best algorithm. The NRMSE (or NBIAS) as a function of rainfall intensities are derived by gradually increasing rainfall intensity thresholds in Equations (12) and (13); namely, only the data of Rt > rainfall intensity threshold are included for the calculation. In Figure 8, the R(KDP, ZDR) algorithm shows the lowest NRMSE value over other algorithms consistently at different rainfall intensities at both C-and S-band radars. The KDP-based algorithms mostly outperform ZHH-based algorithms. The R(ZHH, ZDR) algorithm performs worst at C-band due to its higher sensitivity of ZDR to the WRE, and R(ZHH) has the highest values of NRMSE at S-band.  However, the R(K DP , Z DR ) algorithms are less affected by Z DR than R(Z HH , Z DR ). It can be explained by the more negative (more weighted) seasonal exponents of Z DR in the R(Z HH , Z DR ) relations, and the less negative (less weighted) seasonal exponents of Z DR in R(K DP , Z DR ). The sophisticated seasonal R(Z HH , Z DR ) algorithms are sensitive to the Z DR bias in the real case. The R(Z HH , Z DR ) algorithms using seasonal coefficients at S-band shows less deterioration due to the relative insensitivity of Z DR to the WRE. Overall, R(K DP ) shows the most improvements after using seasonal coefficients, consistent with the result from the theoretical verification in Section 3.2.

C-and S-Band Discrete QPE Comparison (D-QPE)
The C-and S-band D-QPEs are first compared individually at different rainfall intensities to identify the best algorithm. The NRMSE (or NBIAS) as a function of rainfall intensities are derived by gradually increasing rainfall intensity thresholds in Equations (12) and (13); namely, only the data of R t > rainfall intensity threshold are included for the calculation. In Figure 8, the R(K DP , Z DR ) algorithm shows the lowest NRMSE value over other algorithms consistently at different rainfall intensities at both C-and S-band radars. The K DP -based algorithms mostly outperform Z HH -based algorithms. The R(Z HH , Z DR ) algorithm performs worst at C-band due to its higher sensitivity of Z DR to the WRE, and R(Z HH ) has the highest values of NRMSE at S-band. to the all-season. It is noticed that both C-and S-band R(ZHH, ZDR) algorithms using the seasonal coefficients perform much worse. The biased ZDR measurement due to the uncorrected WRE (visually examined, not shown in the paper) is postulated as the main reason. However, the R(KDP, ZDR) algorithms are less affected by ZDR than R(ZHH, ZDR). It can be explained by the more negative (more weighted) seasonal exponents of ZDR in the R(ZHH, ZDR) relations, and the less negative (less weighted) seasonal exponents of ZDR in R(KDP, ZDR). The sophisticated seasonal R(ZHH, ZDR) algorithms are sensitive to the ZDR bias in the real case. The R(ZHH, ZDR) algorithms using seasonal coefficients at S-band shows less deterioration due to the relative insensitivity of ZDR to the WRE. Overall, R(KDP) shows the most improvements after using seasonal coefficients, consistent with the result from the theoretical verification in Section 3.2.

C-and S-Band Discrete QPE Comparison (D-QPE)
The C-and S-band D-QPEs are first compared individually at different rainfall intensities to identify the best algorithm. The NRMSE (or NBIAS) as a function of rainfall intensities are derived by gradually increasing rainfall intensity thresholds in Equations (12) and (13); namely, only the data of Rt > rainfall intensity threshold are included for the calculation. In Figure 8, the R(KDP, ZDR) algorithm shows the lowest NRMSE value over other algorithms consistently at different rainfall intensities at both C-and S-band radars. The KDP-based algorithms mostly outperform ZHH-based algorithms. The R(ZHH, ZDR) algorithm performs worst at C-band due to its higher sensitivity of ZDR to the WRE, and R(ZHH) has the highest values of NRMSE at S-band.  Subsequently, various D-QPEs from two radars are compared in Figure 9. Except for the R(Z HH , Z DR ) algorithm, the C-band D-QPEs are slightly better than S-band D-QPEs, which show smaller errors in heavy rain. Better results from the C-band radar can be concluded for two reasons. First, the C-band radar is located at a relatively lower altitude and provides radar measurements closer to the surface. Second, the K DP measurement is more sensitive to rainfall rate at C band. Beware that the C-band QPEs are obtained with a longer radar scan period, otherwise the advantages of the C-band radar would be more noticeable. As the comparable QPEs from S-and C-band radar have been obtained after the complete QC procedures and seasonal coefficients are applied, the integration method is investigated in the next section. Subsequently, various D-QPEs from two radars are compared in Figure 9. Except for the R(ZHH, ZDR) algorithm, the C-band D-QPEs are slightly better than S-band D-QPEs, which show smaller errors in heavy rain. Better results from the C-band radar can be concluded for two reasons. First, the C-band radar is located at a relatively lower altitude and provides radar measurements closer to the surface. Second, the KDP measurement is more sensitive to rainfall rate at C band. Beware that the C-band QPEs are obtained with a longer radar scan period, otherwise the advantages of the C-band radar would be more noticeable. As the comparable QPEs from S-and C-band radar have been obtained after the complete QC procedures and seasonal coefficients are applied, the integration method is investigated in the next section.

Discretely Combined C-and S-Band QPEs (DC-QPE)
The results of DC-QPEs ( Figure 10 black lines) show that both R(KDP) and R(KDP, ZDR), which are the best D-QPEs and thus chosen for further examination, have pronounced improvements. The DC-QPEs outperform both S-and C-band D-QPEs, especially in R(KDP, ZDR), with lower values of NRMSE in all rainfall intensities. The reductions of NRMSE from D-QPEs to DC-QPEs are about 1.5-7.0 % in R(KDP) and about 3.5-8.5 % in R(KDP, ZDR). The encouraging improvements confirm the fact that radar scanning strategy (i.e., temporal resolution) does play a crucial role in radar-based QPE. Integrating asynchronous D-QPE products can reduce the inaccuracy dramatically by increasing the radar sample number.

Discretely Combined C-and S-Band QPEs (DC-QPE)
The results of DC-QPEs ( Figure 10 black lines) show that both R(K DP ) and R(K DP , Z DR ), which are the best D-QPEs and thus chosen for further examination, have pronounced improvements. The DC-QPEs outperform both S-and C-band D-QPEs, especially in R(K DP , Z DR ), with lower values of NRMSE in all rainfall intensities. The reductions of NRMSE from D-QPEs to DC-QPEs are about 1.5-7.0% in R(K DP ) and about 3.5-8.5% in R(K DP , Z DR ). The encouraging improvements confirm the fact that radar scanning strategy (i.e., temporal resolution) does play a crucial role in radar-based QPE. Integrating asynchronous D-QPE products can reduce the inaccuracy dramatically by increasing the radar sample number. The temporal resolution (∆ ) in this case is 10 minutes. The convective core (R > 100 mm hr −1 ) and precipitation area (R > 10 mm hr −1 ) shifted northward noticeably within 10 minutes. It also clearly shows the precipitation system not only moved fast but also evolved vastly. The heavy rainfall area had expanded, and its intensity had been enhanced. An example of LEA-QPE of ∆ = 5 minutes is shown in Figure 11c. The convective core (blue ⨁) is located between the cores of and (white and black ⨁). The movement and evolution of the precipitation structure are also noticeable. There are nine additional LEA-QPEs obtained within these 10 minutes using the LEA technique. The C-band radar, which has larger values of ∆ than the S-band, shows 1-4% reductions of NRMSE after the LEA algorithm is applied (Figure 12). On the other hand, Sband LEA-QPEs have little improvement with the NRMSE values remaining similar to D-QPEs. Moreover, the C-band LEA-QPEs have consistently lower values of NRMSE than the S-band LEA-QPEs. These results indicate that the LEA algorithm has more positive feedback in the case of large ∆ . The most improvements are found in rainfall rates above 40 mm hr −1 in R(KDP, ZDR). It is postulated that the evolutions of the precipitation systems shifted northward noticeably within 10 min. It also clearly shows the precipitation system not only moved fast but also evolved vastly. The heavy rainfall area had expanded, and its intensity had been enhanced. An example of LEA-QPE of ∆t j = 5 min is shown in Figure 11c. The convective core (blue ) is located between the cores of R T i and R T i+1 (white and black ). The movement and evolution of the precipitation structure are also noticeable. There are nine additional LEA-QPEs obtained within these 10 min using the LEA technique.  Figure 11 demonstrates two C-band QPE maps derived from R(KDP, ZDR) at 06:54 UTC ( ) and 07:04 UTC ( ) on 19 August in 2014. The temporal resolution (∆ ) in this case is 10 minutes. The convective core (R > 100 mm hr −1 ) and precipitation area (R > 10 mm hr −1 ) shifted northward noticeably within 10 minutes. It also clearly shows the precipitation system not only moved fast but also evolved vastly. The heavy rainfall area had expanded, and its intensity had been enhanced. An example of LEA-QPE of ∆ = 5 minutes is shown in Figure 11c. The convective core (blue ⨁) is located between the cores of and (white and black ⨁). The movement and evolution of the precipitation structure are also noticeable. There are nine additional LEA-QPEs obtained within these 10 minutes using the LEA technique. The C-band radar, which has larger values of ∆ than the S-band, shows 1-4% reductions of NRMSE after the LEA algorithm is applied (Figure 12). On the other hand, Sband LEA-QPEs have little improvement with the NRMSE values remaining similar to D-QPEs. Moreover, the C-band LEA-QPEs have consistently lower values of NRMSE than the S-band LEA-QPEs. These results indicate that the LEA algorithm has more positive feedback in the case of large ∆ . The most improvements are found in rainfall rates above 40 mm hr −1 in R(KDP, ZDR). It is postulated that the evolutions of the precipitation systems The C-band radar, which has larger values of ∆T than the S-band, shows 1-4% reductions of NRMSE after the LEA algorithm is applied (Figure 12). On the other hand, S-band LEA-QPEs have little improvement with the NRMSE values remaining similar to D-QPEs. Moreover, the C-band LEA-QPEs have consistently lower values of NRMSE than the S-band LEA-QPEs. These results indicate that the LEA algorithm has more positive feedback in the case of large ∆T. The most improvements are found in rainfall rates above 40 mm h −1 in R(K DP , Z DR ). It is postulated that the evolutions of the precipitation systems can be mainly revealed by the RSD variations. Hence, the LEA algorithm can further improve Z DR -based QPEs by including the RSD evolutions from Z DR measurements.  As discussed in the previous section, the DC-QPE outperforms the D-QPE by combining the S-and C-band D-QPEs. Applying the LEA technique compensates for the disadvantage of relatively lower temporal resolution at the C-band radar. In Figure 13 (upper panel), the QPEs derived from R(KDP) show a consistent underestimation of the rainfall rate, and ones from R(KDP, ZDR) are less biased. When the LEA technique is applied to DC-QPE (LEAC-QPE), the LEAC-QPEs are slightly better than DC-QPEs for R > 0 mm hr −1 . The difference between LEAC-QPEs and DC-QPEs diminishes as the rainfall intensity increases. NRMSE in the lower panel of Figure 13 shows that the DC-QPEs outperform both the S-and C-band LEA-QPEs with lower NRMSE. LEAC-QPEs show nearly identical NRMSE values to DC-QPEs in both R(KDP) and R(KDP, ZDR). Overall, the LEAC-QPEs have less biased NBIAS than DC-QPEs and the lowest NRMSE as DC-QPEs.  As discussed in the previous section, the DC-QPE outperforms the D-QPE by combining the S-and C-band D-QPEs. Applying the LEA technique compensates for the disadvantage of relatively lower temporal resolution at the C-band radar. In Figure 13 (upper panel), the QPEs derived from R(K DP ) show a consistent underestimation of the rainfall rate, and ones from R(K DP , Z DR ) are less biased. When the LEA technique is applied to DC-QPE (LEAC-QPE), the LEAC-QPEs are slightly better than DC-QPEs for R > 0 mm h −1 . The difference between LEAC-QPEs and DC-QPEs diminishes as the rainfall intensity increases. NRMSE in the lower panel of Figure 13 shows that the DC-QPEs outperform both the S-and C-band LEA-QPEs with lower NRMSE. LEAC-QPEs show nearly identical NRMSE values to DC-QPEs in both R(K DP ) and R(K DP , Z DR ). Overall, the LEAC-QPEs have less biased NBIAS than DC-QPEs and the lowest NRMSE as DC-QPEs. can be mainly revealed by the RSD variations. Hence, the LEA algorithm can further improve ZDR-based QPEs by including the RSD evolutions from ZDR measurements.

Lagrangian-Evolution Adjustment (LEA) QPE
(a) (b) As discussed in the previous section, the DC-QPE outperforms the D-QPE by combining the S-and C-band D-QPEs. Applying the LEA technique compensates for the disadvantage of relatively lower temporal resolution at the C-band radar. In Figure 13 (upper panel), the QPEs derived from R(KDP) show a consistent underestimation of the rainfall rate, and ones from R(KDP, ZDR) are less biased. When the LEA technique is applied to DC-QPE (LEAC-QPE), the LEAC-QPEs are slightly better than DC-QPEs for R > 0 mm hr −1 . The difference between LEAC-QPEs and DC-QPEs diminishes as the rainfall intensity increases. NRMSE in the lower panel of Figure 13 shows that the DC-QPEs outperform both the S-and C-band LEA-QPEs with lower NRMSE. LEAC-QPEs show nearly identical NRMSE values to DC-QPEs in both R(KDP) and R(KDP, ZDR). Overall, the LEAC-QPEs have less biased NBIAS than DC-QPEs and the lowest NRMSE as DC-QPEs.

Summary
The dual-pol QPEs of RCWF and NCU C-POL radars have been investigated comprehensively in this study. Three key factors influencing the QPE accuracy, namely, the radar data quality, RSD variability, and the QPE integration method, were examined. Eighteen heavy rain events over northern Taiwan were selected for QPE validation in this work.
The QC procedures, including the corrections of attenuation, the systematic bias, and the WRE for S-and C-band radars over northern Taiwan, have been documented. Different levels of Z HH corrections were applied for QPEs for 18 heavy precipitation events. The results show that attenuation and the WRE play crucial roles in QPE, even for S-band radars. The proper QC procedures significantly reduce the QPE uncertainty. The C-band QPE, in the end, performs slightly better than the S-band partially due to the lower altitude of the radar-site. The R(K DP , Z DR ) algorithm outperforms other QPEs.
The all-season and seasonal coefficients in four power-law QPE relations derived from eight-year 2DVD disdrometer data were examined to investigate the impact of seasonal RSD variability on QPE. The results indicate that the seasonal coefficients pronouncedly reduce the error by diminishing the RSD variability. The R(Z HH , Z DR ) algorithm has higher values of NRMSE due to the WRE of Z DR measurements.
With the proper QC procedures and seasonal coefficients, the comparable QPEs from S-and C-band radars are thus ready for further composition. Even though these QPEs were from asynchronous S-and C-band radar scanning with different temporal resolutions, two QPE integration methods have been carried out to increase the radar sample number. The D-QPEs from C-and S-band radars were first combined discretely. DC-QPE has improved the QPE accuracy significantly with the reductions of NRMSE about 1.5-7.0% in R(K DP ) and about 3.5-8.5% in R(K DP , Z DR ) from D-QPE to DC-QPE. However, the D-QPE/DC-QPE may still miss the motion and evolution of the precipitation systems. A newly developed algorithm, namely Lagrangian-evolution adjustment (LEA), is proposed in this study to further improve the QPE performance. The advection of precipitation systems is estimated via a tracking technique, and the evolution is derived via time-weighted linear interpolation. The LEA-QPE has shown a noticeable improvement in R(K DP , Z DR ) at the C-band radar, which has larger scanning temporal gaps (up to 10 min). NRMSE reduction after the LEA algorithm is about 1-4%. Further combining the DC-QPE and LEA-QPE, namely LEAC-QPE, shows little improvement.

Conclusions
The individual dual-pol QPE can be significantly improved by two key factors: (1) improving the data quality by applying proper radar data quality procedures, including attenuation, the radar systematic bias and the WRE corrections, and (2) reducing the influence of the RSD variability on dual-pol QPE by applying seasonal coefficients. Consequently, the comparable QPEs from asynchronous S-and C-band radar scans can be composited using more sophisticated integration methods, such as discretely combined QPE and Lagrangian-Evolution Adjustment (LEA) proposed in this study. The synthetic LEA-QPEs by combining S-and C-band dual-pol radars have outperformed conventional QPEs.