# Performance of a Radar Mosaic Quantitative Precipitation Estimation Algorithm Based on a New Data Quality Index for the Chinese Polarimetric Radars

^{1}

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## Abstract

**:**

_{H}; the differential reflectivity factor, Z

_{DR}; the specific differential phase, K

_{DP}; and the correlation coefficient, ρ

_{HV}. A novel radar data quality index (RQI) is specifically developed for the Chinese polarimetric radars. Not only the influences of partial beam blockages and bright band upon radar data quality, but also those of bright band correction performance, signal-to-noise ratio, and non-precipitation echoes are considered in the index. RQI can quantitatively describe the quality of various polarimetric parameters. A new radar mosaic QPE algorithm based on RQI is presented in this study, which can be used in different regions with the default values adjusted according to the characteristics of local radar. RQI in this algorithm is widely used for high-quality polarimetric radar data screening and mosaic data merging. Bright band correction is also performed to errors of polarimetric parameters caused by melting ice particles for warm seasons in this algorithm. This algorithm is validated by using nine rainfall events in Guangdong province, China. Major conclusions are as follows. Z

_{H}, Z

_{DR}, and K

_{DP}in bright band become closer to those under bright band after correction than before. However, the influence of K

_{DP}correction upon QPE is not as good as that of Z

_{H}and Z

_{DR}correction in bright band. Only Z

_{H}and Z

_{DR}are used to estimate precipitation in the bright band affected area. The new mosaic QPE algorithm can improve QPE performances not only in the beam blocked areas and the bright band affected area, which are far from radars, but also in areas close to the two radars. The sensitivity tests show the new algorithm can perform well and stably for any type of precipitation occurred in warm seasons. This algorithm lays a foundation for regional polarimetric radar mosaic precipitation estimation in China.

## 1. Introduction

_{H}is used to calculate precipitation.

_{H}, differential reflectivity factor Z

_{DR}, specific differential phase K

_{DP}, and correlation coefficient ρ

_{HV}) in mosaics and to estimate precipitation. However, in the Multi-Radar Multi-Sensor (MRMS) system developed based on the NMQ system [11], Z-R relationships are used to calculate QPE at the first stage. The QPE algorithms of the MRMS system are largely based upon NMQ QPE components [11]. Recently, studies have focused on developing a seamless polarimetric synthetic QPE calculated via a combination of specific attenuation A, K

_{DP}, and Z

_{H}within the MRMS system. This new polarimetric radar QPE algorithm applies R(A) in areas where radar is observing pure rain, R(K

_{DP}) in regions potentially containing hail, and R(Z

_{H}) elsewhere [3]. Both systematic and random errors are reduced by using A, K

_{DP}, and Z

_{H}(rather than only Z

_{H}) to calculate QPE. However, the QPE product still needs further refinements in very light and sporadic rain where the attenuation signal is too weak, and in widespread light stratiform rain [3]. The estimator R(A) must be very carefully used in the above situations or else local adjustment will be needed. However, the performance of R(A) is unstable for Guangzhou radar when estimating precipitation during rainfall events with hourly accumulations below 50 mm [12]. Hence, the other polarimetric parameters (e.g., Z

_{H}, Z

_{DR}, and K

_{DP}) are chosen to estimate precipitation in this study. Therefore, the use of Z

_{H}, Z

_{DR}, and K

_{DP}to obtain accurate mosaic QPE products is the main focus of this study.

_{DR}in BB was also found to increase as the snow melted [25,26]. In the study of Mario et al., Z

_{DR}and K

_{DP}are found to sharply increase just above the freezing level and below it [27]. The vertical variations of Z

_{DR}and K

_{DP}in BB can cause more uncertainties in QPE; however, most studies do not take this into account when estimating precipitation. Therefore, they are considered in this study to improve the radar QPE performance.

_{DR}, ρ

_{HV}, and Φ

_{DP}. They use it to discriminate the nonmeteorological targets from weather returns [29]. This application is used for two C-band polarimetric radars in the mountainous areas of Italy and achieves encouraging results. It indicates that this quality index shows advantages of the application of the radar located in complex terrain. This characteristic of the quality index is very important in radar mosaic. Therefore, the quality index is also the core technical parameter in radar mosaic, especially when radars are located in the mountainous area. In French and American radar mosaic systems, these similar quality indexes are well used [30,31]. The quality indexes of the French system are used as weights to obtain the best rainfall estimation. They only depend upon the presence of ground clutter, the degree of blocking, and the altitude. The quality indexes of the American system (MRMS system) are used to choose high-quality Z

_{H}[31]. Only partial beam blockage and BB are considered in their quality index. Although all these above quality indexes are well used in different radars or radar systems, they still need to be improved, especially for the Chinese polarimetric radars. The influences of SNR upon radar data quality are not considered in their study, but SNR has obvious influence in data quality, especially for Z

_{DR}, K

_{DP}, and ρ

_{HV}of Chinese polarimetric radars [16,32]. Besides this, the BB correction performance influences the data quality after the correction is applied to these data. If this factor is not considered, the corrected data cannot be used in a correct way. Therefore, a new radar data quality index (RQI) must be proposed to accurately represent the quality of Z

_{H}, Z

_{DR}, K

_{DP}, and ρ

_{HV}of the Chinese polarimetric radars. This is a novel and core radar mosaic technical parameter that is proposed in this study.

## 2. Materials and Methods

#### 2.1. Polarimetric Radar Data Analysis

#### 2.1.1. Beam Blockage Situation of Polarimetric Radars

#### 2.1.2. Data and Quality Control Method

_{H}accuracy is better than 1 dB, meeting the requirements for QPE. Z

_{DR}is also calibrated with vertical pointed calibration method before the radar operation.

_{DR}is smoothly filtered along the radial direction to reduce random fluctuations. The smoothing range bin number M depends upon the Z

_{H}value. The value of M is as follows:

_{DR}based on Z

_{H}values. In this way, Z

_{DR}is smoothed to various degrees with various reflectivity factors to avoid non-complete smoothing for weak echoes and excessive smoothing for strong ones.

_{DP}, and K

_{DP}is calculated by a linear least squares fit using N samples of the Φ

_{DP}[14]. N is the number of consecutive radar bins for the piecewise linear fit, which is adjusted according to three reflectivity factor levels:

_{DP}in light precipitation regions [13]. Since the range resolution of the radar is 0.25 km, the estimation can tolerate small-scale variability up to 2.25 km under heavy rain and large-scale variability up to 4.25 km under light rain. Moreover, K

_{DP}is also smoothly filtered in the same way as Z

_{DR}to reduce random fluctuations. Besides this, the data influenced by radio frequency interference have been identified and eliminated with the method proposed by Wen et al. [34].

#### 2.1.3. Analysis of Polarimetric Radars Data Consistency

_{H}, Z

_{DR}, and K

_{DP}are shown in Figure 3. The diagonal lines are equal lines. It is apparent that the three polarimetric parameters are basically distributed near the diagonal lines. The average differences are 0.2555 dB (Z

_{H}), 0.0061 dB (Z

_{DR}), and 0.0058 °/km (K

_{DP}), respectively. The standard deviations of the differences are 4.4848 dB (Z

_{H}), 0.3527 dB (Z

_{DR}), and 0.2380 °/km (K

_{DP}), respectively. Considering that there are biases caused when calculating CAPPI (2 km), the two radars’ data are basically consistent, which satisfies the mosaic condition.

#### 2.2. The Key Methods in Polarimetric Radar Mosaic QPE Algorithm

#### 2.2.1. BB Correction

_{H}, Z

_{DR}, and K

_{DP}, and a decrease in ρ

_{HV}[25,26]. These changes can make QPE performances uncertain. It is necessary to correct these changing data; however, most previous studies have only corrected Z

_{H}to improve QPE performance. In fact, there are some other relations between polarimetric parameters and rain rate R for estimating precipitation in the polarimetric radar QPE algorithm. Besides Z

_{H}, some other radar data (such as Z

_{DR}and K

_{DP}) also need to be corrected. Although ρ

_{HV}is not directly used to calculate precipitation, it is very sensitive to mixed-phase precipitation particles and can be used to detect BB height. For BB correction, convective and stratiform precipitation echoes are first segregated, then the BB height range is identified, and finally the data are corrected after the vertical profile model is established.

^{−2}[23,35]. Otherwise, the precipitation is classified as being stratiform.

_{H}correction in several studies [23,24].

_{DR}, K

_{DP}, and ρ

_{HV}are unreliable when SNR of the polarimetric radars in Guangdong is below 20 dB [16,32], AVPDs are collected via the ZQ10 method [23] used for Z

_{H}with the added condition that the data collected here must have an SNR > 20 dB to ensure high-quality. The AVPD frequency distributions of Z

_{H}, Z

_{DR}, K

_{DP}, and ρ

_{HV}(shown in Figure 4) are obtained from the Guangzhou and Yangjiang radar data according to the nine rainfall events listed in Table 2. High frequencies indicate that data are concentrated, and show the same feature of most profiles. AVPDs of Z

_{H}and Z

_{DR}have the same obvious BB feature: the frequencies are very high in the peak-value region, meaning that a large number of data affected by BB become larger than the data near the ground. The same feature provides the basis for the AVPD model. Although the AVPDs of K

_{DP}also show that data affected by BB become larger than data near the ground, data points in the peak-value region are more dispersed than those of Z

_{H}and Z

_{DR}, which poses a challenge for K

_{DP}correction in BB. There is a strange profile in the high altitude of the ρ

_{HV}AVPDs because ρ

_{HV}does not go back close to unity in ice. There are two possible reasons for the strange profile of ρ

_{HV}in the high altitude. One reason is the ice mixed with rain. The other one is the SNR with too small value. The reflectivity of the ice in the high altitude is small, and its SNR is also small. The SNR has an obvious influence on ρ

_{HV}of the polarimetric radars in Guangdong. When the SNR becomes small, the quality of ρ

_{HV}becomes bad [16,32]. Although only data corresponding to SNR > 20 dB are collected to obtain AVPD of ρ

_{HV}, the SNR of the ice in the high altitude is smaller than that in the low altitude, and may be close to 20 dB. Therefore, it is the small SNR that makes the ρ

_{HV}profile strange in the high altitude where pure ice exists.

_{H}, Z

_{DR}, and K

_{DP}is established based on the same feature of frequency distributions, and it is shown in Figure 5. It can represent most AVPDs of Z

_{H}, Z

_{DR}, and K

_{DP}. The main height parameters include BB top height (h

_{t}), BB bottom height (h

_{b}), and BB peak height (h

_{p}).

_{b}. However, the bottom data of Z

_{H}, Z

_{DR}, and K

_{DP}are scattered, while the bottom data of ρ

_{HV}are very concentrated (see Figure 4). Most bottom ρ

_{HV}data are concentrated above 0.975, which is helpful for identifying h

_{b}. Therefore, the method used in the MRMS system that identifies h

_{b}by searching for the first inflection point of Z

_{H}is not used in this study [23,24]. Instead, ρ

_{HV}is used to identify h

_{b}. ρ

_{HV}is searched from h

_{p}down; when the value change rate of ρ

_{HV}is approximately zero, its height is h

_{b}, meaning that ρ

_{HV}is basically stable. When ρ

_{HV}is stable, the phase of the hydrometeors is basically unchanged. What’s more, it should be noted that most precipitation particles at the BB bottom height are liquid particles, so ρ

_{HV}must be larger than a threshold value, which is set to 0.975 in this study. A similar method proposed by Qi et al. [36] that uses ρ

_{HV}to detect h

_{b}proves to perform better than that using Z

_{H}(such as ZQ10) on tests for three heavy precipitation events from different geographical regions and seasons in the United States, which indicates the feasibility of the proposed method in this study.

_{t}, h

_{b}, and h

_{p}, are used to derive a parameterized, two-piece-linear AVPD model. One piece is between the BB top and the peak and another is between the BB bottom and the peak. The slope values α and β are fitted using two data sections according to a least squares method. The correction factor D

_{a}(h) is obtained based on the established AVPD model, which is shown as follows:

_{H}(dBZ), Z

_{DR}(dB), and K

_{DP}(°/km).

#### 2.2.2. Radar Data Quality Index and Polarimetric Radar Mosaic Algorithm

_{HV}> 0.7 are chosen as the hybrid scan data based on this principle, to avoid complex terrain influences.

_{DR}, K

_{DP}, and ρ

_{HV}are obviously influenced by SNR [16,32]. Therefore, SNR is a key factor which need be considered when Chinese radar data are used. All the above factors are reflected in RQI with four indexes. They are introduced as follows.

_{blk}is an index proposed in Z11 study. It is still used here, shown as follows:

_{blk}is the index affected by partial beam blockages and is calculated based on blk. At any given time, the quality of radar data is generally worse in complex terrains (large blockages) than in flatlands (no blockages). Therefore, when blk is large, the RQI

_{blk}is set to small, and vice versa. The model of RQI

_{blk}is shown in Figure 6a.

_{hgt}is the other part of RQI in the Z11 study, and this index is affected by BB. However, in the Z11 study, RQI

_{hgt}was calculated based on the assumptions that the thickness of BB is 700 m and that the data below h

_{0c}-700 (m) are not affect by BB. This is obviously not accurate, so RQI

_{hgt}is improved based on h

_{b}according to the observed BB. In addition to the thickness of BB, a height scale factor is also a fixed value in the Z11 study, meaning that the BB correction performance is not considered. In this study, H

_{sf}(m) is a height scale factor that changes with BB correction performance and is used in the new RQI

_{hgt}. It is shown as follows:

_{a}(m) is the height of the beam axis, ave

_{BB}is the average value of data in BB, ave

_{uBB}is the average value of data under BB, and ND is the normalized difference between ave

_{BB}and ave

_{uBB}. ND represents data quality in BB. When ND is 0, the data in BB and under BB show good consistency. When ND is larger (resp. smaller) than 0, the average value of data in BB is larger (resp. smaller) than that under BB. The smaller the absolute value of ND, the better the BB correction performance is. The average value of data in BB and under BB are used to calculate ND, because it makes the calculation of RQI

_{hgt}simple and feasible, and ND can basically reflect the performance of BB correction to make the RQI

_{hgt}more reasonable. However, computing an average value under the BB will mask signature of microphysical processes that influence precipitation rate. In fact, some data under BB are not invariable, and have different changing trends. The changing trends of data under BB are discussed in Section 4.1. ND

_{fix}is a fixed value of ND, which can stand for the average ND before BB correction. The default ND

_{fix}of Z

_{H}is 0.07, that of Z

_{DR}is 0.5, and that of K

_{DP}is 0.8. These are values derived from the nine rainfall events in this study. These values can be treated as the empirical values of radars in Guangdong. If the ND

_{fix}s are used for other radars, the values of them can be adjusted according to the characteristics of local radar. RND is the ratio of |ND| and ND

_{fix}, which can represent the BB correction performance. It is used to calculate H

_{sf}. The equation of H

_{sf}is established empirically to form the curves in Figure 6b. H

_{sf}is limited in the range (500–2500) to avoid the abnormal value. The black lines 1, 2, and 3 in Figure 6b represent RQI

_{hgt}with H

_{sf}values of 500 m, 1500 m, and 2500 m, respectively.

_{hgt}is also influenced by the position of the beam axis relative to the BB bottom height, h

_{b}. When the beam axis is below h

_{b}, rain drops cannot be frozen and the value of RQI

_{hgt}is 1; the higher the beam axis is relative to h

_{b}, the less accurate that the data are. In addition, when the ambient temperature is too low, h

_{0c}is very close to the ground and it is difficult to identify h

_{b}, which is denoted by h

_{b}< 0 in formula (6), and only h

_{a}is used to calculate RQI

_{hgt}. The greater the height, the less accurate the data.

_{blk}and RQI

_{hgt}can satisfy requirements. However, radar data quality is also influenced by SNR and the non-precipitation echoes, especially for the polarimetric parameters Z

_{DR}, K

_{DP}, and ρ

_{HV}. SNR and the non-precipitation echoes are represented by snr (in linear scale) and ρ

_{HV}, respectively. The index takes the form of a Gaussian function because it can represent the gradual change of radar data quality affected by snr or ρ

_{HV}. The snr and ρ

_{HV}are x-axis variables [38]. The value of the Gaussian function gradually decreases by controlling the threshold value. RQI

_{snr}and RQI

_{Ρ}

_{HV}are shown as follows:

_{HV}* are the threshold values of the Gaussian function. The SNR * (corresponding to snr *) of Z

_{H}is 0dB and those of Z

_{DR}, K

_{DP}, and ρ

_{HV}are 25 dB. The Δ ρ

_{HV}* values of Z

_{DR}and K

_{DP}are 0.1. RQI

_{snr}is the index affected by SNR, and is calculated based on snr. Some studies [16,32] have shown that when the SNR of the polarimetric radars in Guangdong falls below 20 dB, ρ

_{HV}, Z

_{DR}, and K

_{DP}become unreliable. Therefore, the index of RQI

_{snr}is set to 0 when the SNR is below 20 dB, as can be seen from the model shown in Figure 6c. RQI

_{Ρ}

_{HV}is the index affected by the non-precipitation echoes, which is calculated based on ρ

_{HV}. When precipitation echoes are mixed with the non-precipitation echoes, ρ

_{HV}becomes smaller, and the qualities of the other polarimetric parameters become worse. When ρ

_{HV}is under 0.7, the echoes are non-precipitation echoes [16], so the RQI

_{Ρ}

_{HV}of Z

_{DR}and K

_{DP}is set to 0. The RQI

_{Ρ}

_{HV}model of Z

_{DR}and K

_{DP}is shown in Figure 6d. Ground echo suppression has been made for Z

_{H}, and echoes corresponding to low ρ

_{HV}are treated in a certain way by the QPE algorithm, so the index of Z

_{H}is set to 1. ρ

_{HV}is the value reflecting non-precipitation echoes. Since it does not make sense to use ρ

_{HV}to evaluate ρ

_{HV}, the index of ρ

_{HV}is also 1.

_{lowest}) is used as a standard value for comparison with the RQI of the other data in the same grid. The data point with an RQI value under RQI

_{lowest}− 0.2 or equal to 0 are treated as low quality data and eliminated. The number of the data points remaining determines how the mosaic data are obtained. If no data are left, the mosaic data of this grid would be flagged as suspicious. If only one data point is left, then this data point is selected to be the mosaic data for this grid. If there are two data points left, they are merged to obtain the mosaic data. For three or more data points left, only the three with the largest RQI values are merged.

_{L}and w

_{H}are the horizontal and vertical weighting factors, respectively, d is the horizontal distance between the analysis point and the radar, h is the height of the radar bin, and L and H are the scaling factors with default values of 100 km and 2 km, respectively. Mosaic Data is the final mosaic radar data, and n is the mosaic radar number. In addition to the larger weighting given to the data that are closer to the ground and to the radar, the data with higher quality are also more heavily weighted in calculating the mosaic data, because RQI is considered as a weighting factor. This makes the mosaic data more reliable.

#### 2.2.3. Polarimetric Radar Mosaic QPE Algorithm

_{DR}and K

_{DP}values of high quality from those of low quality in Z18 algorithm. The Z-R relationship is used to estimate precipitation when Z

_{DR}and K

_{DP}have low quality. Although the same strategy is applied to the QPE algorithm, the RQIs of Z

_{H}, Z

_{DR}, and K

_{DP}are used to determine whether the Z-R relationship is suitable for estimating precipitation in the new QPE algorithm. This is because RQI can more accurately represent the quality of data than SNR. When RQI(Z

_{H}) − RQI(Z

_{DR}) > 0.5 and RQI(Z

_{H}) − RQI(K

_{DP}) > 0.5, the quality of Z

_{H}is much better than that of Z

_{DR}and K

_{DP}, thus the Z-R relationship is used to estimate precipitation.

_{H}, Z

_{DR}, and K

_{DP}upon the QPE in the BBA are studied. In order to study these influences, average raw and corrected data in the BB are used to estimate precipitation, and precipitation estimated based on data at the BB bottom height is treated as the “truth” value to evaluate them. As statistical indicators of the QPE performance in this study, the correlation coefficient (CC), root mean square error (RMSE), normalized relative bias (NB), normalized absolute error (NE), and bias ratio of radar-estimated rainfall to the “truth” value of rainfall are obtained:

_{i}

^{truth}– QPE

_{i}

^{radar}pairs, RMSE has the same units as QPE, and NE and NB are both percentages. A bias ratio value larger (resp. smaller) than one indicates overestimation (resp. underestimation).

_{H}and Z

_{DR}values are better than those derived from the corrected K

_{DP}in terms of NE and NB. This indicates that the corrected Z

_{H}and Z

_{DR}values are more suitable for estimating precipitation in the BBA than the corrected K

_{DP}. Therefore, only corrected Z

_{H}and Z

_{DR}are used to estimate precipitation in the BBA in this study.

_{DR}correction performance in BB is bad or much worse than the Z

_{H}correction performance in BB, the Z-R relationship becomes the only choice for estimating precipitation. When |ND(Z

_{DR})| > 0.2, the quality of Z

_{DR}is considered to be very low, and the Z

_{DR}correction performance in BB is bad. When RND(Z

_{H}) − RND(Z

_{DR}) < −0.2, the BB correction performance of Z

_{DR}is considered to be much worse than that of Z

_{H}. Therefore, when |ND(Z

_{DR})| > 0.2 or RND(Z

_{H}) − RND(Z

_{DR}) < −0.2, the Z-R relationship is used in the QPE algorithm. These values used in this study are also empirical values, which can be adjusted according to the characteristics of local radar.

_{H}< 20 dBZ and ρ

_{HV}< 0.8 are treated as the characteristics of the clear-air echo; there is no precipitation. The rest of the QPE algorithm flowchart follows the Z18 algorithm, which is not introduced in this study.

## 3. Results

#### 3.1. Performances of BB Correction

_{H}, Z

_{DR}, and K

_{DP}derived from the nine rainfall events listed in Table 2 are shown in Figure 9; the gray histograms are derived from corrected data in BB, and those with black lines outside are derived from raw data in BB. The NDs of Z

_{H}, Z

_{DR}, and K

_{DP}all approach zero after BB correction, indicating good correction performance for the whole dataset. The average NDs of the corrected Z

_{H}, Z

_{DR}, and K

_{DP}values are 0.013, −0.026, and −0.241, respectively. The average NDs of Z

_{H}and Z

_{DR}are all much closer to zero than that of K

_{DP}. The main ND frequency distributions of corrected Z

_{H}and Z

_{DR}are mostly Gaussian; however, that of the corrected K

_{DP}is not. These all indicate that the BB correction performance of K

_{DP}is not as good as that of Z

_{H}and Z

_{DR}. This is also why K

_{DP}is not suitable for estimating precipitation in the BBA.

_{H}, Z

_{DR}, and K

_{DP}. The original and corrected mosaic data at 20:54 on 15 June 2016 are shown in Figure 10. This is a squall line rainfall event. The small value of ρ

_{HV}in the stratiform region behind the convective echoes of the squall line is obviously caused by BB, which is marked with a black circle in Figure 10a–h. Blue in Figure 10h represents BBA. Most of the BBA is in the black circle. The values of the corrected mosaic Z

_{H}, Z

_{DR}, and K

_{DP}in the circles have been reduced compared with the original data.

_{H}, Z

_{DR}, K

_{DP}, and ρ

_{HV}, as derived from the Guangzhou radar, are shown in Figure 10. Black dots indicate original observations and red dots indicate corrected values. It can be seen that the original values of Z

_{H}, Z

_{DR}, and K

_{DP}show obvious enlargement at a height of around 5 km. The thickness of the BB is larger than the true value due to the beam broadening effect, especially at the BB top height, which may deviate from the true value. However, it does not affect the correction of polarimetric radar data. The large values of the original data at around 5 km become close to the ground data values after correction. However, the discontinuity of the original K

_{DP}vertical profile leads to discontinuity in the corrected K

_{DP}vertical profile. BB correction for Z

_{H}and Z

_{DR}performs better than that for K

_{DP}. Although the AVPD frequency distribution of K

_{DP}follows the ideal AVPD model, certain vertical profiles of K

_{DP}sometimes cannot follow the ideal AVPD model well; this is why the BB correction performance of K

_{DP}is not very good. This also influences the performances of estimators using the corrected K

_{DP}(Table 3). Therefore, K

_{DP}should not be used to estimate precipitation in the BBA even after correction.

_{H}is positively correlated with R while Z

_{DR}is negatively correlated with R in the rainfall estimators. Z

_{H}and Z

_{DR}in BB both increase before correction, but the change of R is related to the proportion of the two parameters used to estimate precipitation and the contributions of the two parameters to R. The QPE performances in the BBA are further analyzed in Section 3.3.

#### 3.2. Results of the Polarimetric Radar Data Mosaic

_{H}, Z

_{DR}, K

_{DP}, and ρ

_{HV}are obtained via the proposed mosaic algorithm using the data observed by the Guangzhou and Yangjiang radars at 5:00 on 20 May 2016. The mosaic data and their corresponding RQIs are shown in Figure 12.

_{H}) with a high value (e.g., >0.9) is the largest. It is mainly influenced by the height of the radar data, since when the height is larger than a given value, RQI

_{hgt}decreases rapidly. The distributions of RQI(Z

_{DR}) and RQI(K

_{DP}) behave similarly. The only difference between them is RQI

_{hgt}because of the different BB correction performances. The distributions of RQI(Z

_{DR}), RQI(K

_{DP}), and RQI(ρ

_{HV}) are all seriously influenced by SNR. The ranges of RQI(Z

_{DR}), RQI(K

_{DP}), and RQI(ρ

_{HV}) are almost the same as the range of SNR larger than 20 dB (shown in Figure 12i). In addition, RQI(Z

_{DR}) and RQI(K

_{DP}) are also influenced by ρ

_{HV}. Although the SNR is large in areas near the two radars, RQI(Z

_{DR}) and RQI(K

_{DP}) are small because of the small value of ρ

_{HV}, which corresponds to ground clutter.

_{DR}) and RQI(K

_{DP}) are larger than zero do Z

_{DR}and K

_{DP}have a chance to participate in estimating precipitation alongside Z

_{H}. In the other areas, Z

_{H}is the only reliable estimation parameter, especially in areas where RQI(Z

_{H}) is larger than 0.9. It seems that the red areas of RQI(Z

_{H}) can indicate effective QPE areas, and this will be analyzed via the QPE performance in Section 4.2.

#### 3.3. Results of Polarimetric Radar Mosaic QPE

^{2}. The rainfall accumulations measured at the rain gauge station are used as “true” accumulations. The rainfall accumulations from the radars are accumulated by using the data of every volume scan period on the assumption that the rain rate for the duration of the volume scan is continuous. The average radar-estimated precipitation of the nine grids nearest the rain gauge station is used to evaluate the QPE performance. Since the minimum rainfall measurement of the rain gauge is 0.1 mm, only rainfall measurements exceeding this value were used for evaluation. There are 51,985 sample pairs of QPE-gauge data used for evaluation in this region. The distributions of the bias ratios derived from the evaluation results of radar mosaic QPE and the two-radar QPE are shown in Figure 13.

^{2}. There are 12,694 sample pairs of QPE-gauge data used for evaluation in this region. The scores are listed in the Table 4. Although the NB of the radar mosaic QPE is not very good, it still falls within acceptable limits. The QPE performance of the radar mosaic is better than those of either single radar in terms of CC, RMSE, and NE. After the radar mosaic is constructed, the RMSE and NE of QPE are reduced by at least 5.29% and 5.59%, respectively. The main advantage of radar mosaic is that it can improve QPE performances in the blocked area and the area far from the radars compared to the single radar. However, without considering the error caused by partial beam blockages and the beam partially overshooting cloud top, the performance of polarimetric radar mosaic QPE is still better than that of single polarimetric radar QPE. This indicates that the polarimetric radar mosaic QPE algorithm proposed in this study can take advantage of all radars to obtain mosaic data which can be better used to estimate the ground precipitation.

_{H}, Z

_{DR}, and K

_{DP}in the polarimetric radar mosaic QPE algorithm. In order to analyze the effect of BB correction upon QPE, the algorithm without BB correction and the algorithm proposed in this study are respectively used to estimate precipitation. The evaluation results are shown in Figure 15.

_{H}and Z

_{DR}still overestimates precipitation in the BBA. BB is known to lead to a significant increase in Z

_{H}and Z

_{DR}. Although the increase in Z

_{DR}can reduce the QPE value, the overestimated results indicate that the increase of Z

_{H}has a larger effect upon QPE than does the increase of Z

_{DR}. According to the statistics, the percentage of precipitation estimated from Z

_{H}, Z

_{H}+ Z

_{DR}, K

_{DP}, and K

_{DP}+ Z

_{DR}are 90.45%, 7.92%, 0.29%, and 1.34%, respectively. This indicates the RQI of Z

_{H}is better than Z

_{DR}and K

_{DP}, and the rainfall estimators use Z

_{H}more often than they use Z

_{DR}. Therefore, the algorithm without BB correction still overestimates precipitation in BBA.

#### 3.4. Sensitivity Tests about the Precipitation Types

## 4. Discussion

#### 4.1. AVPD under BB

_{H}and Z

_{DR}caused by melting ice particles, causing the average values of Z

_{H}and Z

_{DR}in BB to approach those under the bottom of the BB. Therefore, the QPE bias in the BBA for all nine rainfall events becomes small, as described in Section 3.3. However, some phenomena still require examination, including the changing trend of data under BB, because they may exert obvious influences upon QPE performance.

_{H}and Z

_{DR}profiles under BB. The green lines in Figure 17a,d are perpendicular to the horizontal axis, meaning that the averages of Z

_{H}and Z

_{DR}are basically unchanged with height under the BB. In general, the profiles of Z

_{H}and Z

_{DR}are basically unchanged under BB, or at least have no discernible tendency to change. However, significant changes sometimes occur in the profiles of Z

_{H}and Z

_{DR}under BB, as shown in Figure 17b,c,e,f. These always cause some uncertainties in precipitation estimation.

_{H}and Z

_{DR}in Figure 17b,e, respectively. The changing rates under BB differ from those between the BB peak and bottom heights. This indicates that their changing mechanisms are different. The other changing tend is that the average values increase as the height decreases, as shown for Z

_{H}and Z

_{DR}in Figure 17c,f, respectively. The changing trends under BB are complex and their mechanisms are not clear. The precipitation particles change from the ice phase to the liquid phase in BB. The changing trends under BB are probably associated with changing drop size distribution (DSD). It is necessary to study the vertical change of DSD under BB in future work. This study can also be extended to different precipitation regions and different precipitation types to analyze the vertical changes in DSD and polarimetric parameters to obtain more accurate QPE.

#### 4.2. The Relationship between QPE Accuracy and RQI

_{H}to estimate precipitation, while more polarimetric parameters are used in this study and more factors are considered in our RQI. To study the relationship between QPE accuracy and RQI, the bias ratio and average RQIs of Z

_{H}, Z

_{DR}, and K

_{DP}for the nine rainfall events are shown in Figure 18.

_{DP}is almost the same as that of Z

_{DR}, because their values only differ in terms of the BB correction performances, and this difference is very small on average. The average RQI distributions of Z

_{H}, Z

_{DR}, and K

_{DP}show some similar characteristics. Their shapes with colors are all limited by the partial beam blockages and the distance from the radars. The average RQI values of Z

_{H}are larger than those of Z

_{DR}and K

_{DP}. This is because the low SNR and ρ

_{HV}decrease the RQIs of Z

_{DR}and K

_{DP}but have little influence upon the RQI of Z

_{H}.

_{H}from the distributions in Figure 18, as well as the RQIs of Z

_{DR}and K

_{DP}, despite the values of Z

_{H}and Z

_{DR}(or K

_{DP}) being so different. To quantify their correlation, a new bias ratio is proposed, which is shown as follows:

_{H}(Z

_{DR}and K

_{DP}) is 0.80 (0.71 and 0.70). This quantitatively verifies the view that there is good correlation between the QPE accuracy and the RQI of Z

_{H}(Z

_{DR}and K

_{DP}). Such correlation exists because the RQI partially models the uncertainties due to the partial beam blockages, BB, BB correction performance, SNR, and the non-precipitation echoes. However, the uncertainties associated with spatially varying drop size distributions still affect the correlation between QPE accuracy and the RQI of Z

_{H}(Z

_{DR}and K

_{DP}), because RQI cannot represent these uncertainties. Based on the good correlation found between QPE accuracy and the RQI of Z

_{H}, an effective QPE area can be defined with an RQI of Z

_{H}lager than 0.9. QPE performances are evaluated within the radars’ detection range. At the same time, only the QPEs corresponding to the RQIs of Z

_{H}larger than 0.9 are used for evaluation, and the performance is basically acceptable in terms of CC (0.83), RMSE (4.00 mm), NE (44.8%), and NB (−2.84%). Therefore, the effective QPE area defined here is reasonable. This area can help in obtaining accurate radar QPE information, which will be beneficial to the application of radar QPE products. Besides this, since there is good correlation between the QPE accuracy and the RQI, RQI can reflect the QPE accuracy to some extent. Therefore, RQI can be used in a weigh function when radar QPE is merged with other precipitation products derived from other different sensors. This is also beneficial to the application of radar QPE products.

## 5. Conclusions

_{H}, Z

_{DR}, K

_{DP}, and ρ

_{HV}, and is used in high-quality data screening and mosaic data merging. In this algorithm, BB correction is performed to mitigate the increase of Z

_{H}, Z

_{DR}, and K

_{DP}caused by the melting ice particles in the rainfall events of warm seasons. The new algorithm is evaluated based on nine rainfall events occurring in Guangdong province, China, and detected by the Guangzhou and Yangjiang polarimetric radars. Main conclusions are summarized as follows:

- After BB correction, the values of Z
_{H}, Z_{DR}, and K_{DP}in BB become closer to those under BB than before. However, the BB correction performance of K_{DP}is not as good as that of Z_{H}and Z_{DR}. Only the corrected Z_{H}and Z_{DR}are used to estimate precipitation in the BBA. Precipitation is overestimated even when using polarimetric parameters in the BBA prior to BB correction. BB correction in this new radar mosaic QPE algorithm obviously mitigates the overestimation of rainfall in the BBA. - The new polarimetric radar mosaic QPE algorithm based on RQI can combine the different radars’ advantages to improve QPE performances in the blocked area and the area far from the radars, thereby obtaining more accurate and wider range of mosaic data and QPE products. The new algorithm also performs better than the single radar QPE algorithm in the area close to the two radars. Within 180 km of the radars, the RMSE and NE decrease by at least 5.29% and 5.59%, respectively. The near real-time statistics of evaluated indicators show that there is a near real-time improvement when the radar mosaic QPE algorithm is applied. It is important for the operational application of this new algorithm.
- The sensitivity tests with the changing percentage of stratiform and convective precipitation show that NE and NB are basically stable when this percentage changes. The new polarimetric radar mosaic QPE algorithm can perform well and stably for any type of precipitation occurred in warm seasons.
- There is good correlation between QPE accuracy and the RQI of Z
_{H}(Z_{DR}and K_{DP}). An effective QPE area can be defined with an RQI of Z_{H}lager than 0.9, resulting in a small bias (NB = −2.84%) for rainfall events in this study.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Distributions of the Guangzhou and Yangjiang S-band polarimetric radar (GZ SPOL, and YJ SPOL, black triangles) in (

**a**,

**b**), and the gauge stations (gray circles) in (

**b**). The background color in (

**a**) indicates altitude, and the black circles (460-km radius) indicate the maximum range of radar observations. The gauge stations are less than 300 km from either radar in (

**b**). The gray rectangle in the lower right of (

**b**) shows the extent of the region in South China.

**Figure 2.**Beam blockages at 0.5° tilt of (

**a**) Guangzhou radar and (

**b**) Yangjiang radar. The triangles indicate radars and the narrow black area between the two radars indicates the common area for comparing data. The blockages are topped at the elevation angles of Guangzhou radar and Yangjiang radar which are shown in (

**c**,

**d**), respectively.

**Figure 3.**Frequency distributions of (

**a**) Z

_{H}, (

**b**) Z

_{DR}, and (

**c**) K

_{DP}from 2 km CAPPI. The horizontal axis indicates Guangzhou radar data and the vertical axis indicates Yangjiang radar data.

**Figure 4.**Apparent vertical profile of data (AVPD) frequency distributions of (

**a**) Z

_{H}, (

**b**) Z

_{DR}, (

**c**) K

_{DP}, and (

**d**) ρ

_{HV}derived from the nine rainfall events during May to June 2016.

**Figure 5.**The ideal AVPD model of Z

_{H}, Z

_{DR}, and K

_{DP}. h

_{t}indicates the bright band (BB) top height, h

_{b}indicates the BB bottom height, h

_{p}indicates the BB peak height, and h

_{0c}indicates the 0 °C height. α and β indicate the respective slopes of the two lines.

**Figure 6.**The models of (

**a**) RQI

_{blk}, (

**b**) RQI

_{hgt}, (

**c**) RQI

_{snr}, and (

**d**) RQI

_{Ρ}

_{HV}. h

_{b}in (

**b**) is the height of the BB bottom. Lines 1, 2, and 3 correspond to H

_{sf}values of 500 m, 1500 m, and 2500 m, respectively. The SNR * s (corresponding to snr * s) of the dotted and solid lines in (

**c**) are 0 dB and 25 dB, respectively.

**Figure 7.**Flowchart describing the polarimetric radar data mosaic algorithm. The “data points” are original resolution polar data of different radars corresponding to the same ground grid.

**Figure 9.**ND frequencies of (

**a**) Z

_{H}, (

**b**) Z

_{DR}, and (

**c**) K

_{DP}are shown with histograms. The gray ones are derived from corrected data, and those with black lines outside are derived from raw data in the BB.

**Figure 10.**The original mosaics for (

**a**) Z

_{H}, (

**b**) Z

_{DR}, (

**c**) K

_{DP}, and (

**d**) ρ

_{HV}at 20:54 UTC on 15 June, 2016. The corrected mosaics for (

**e**) Z

_{H}, (

**f**) Z

_{DR}, and (

**g**) K

_{DP}are also shown, respectively. The mosaic data are from the lowest hybrid scans in original polar coordinates. The colors in (

**h**) represent BBA (blue) and non-BBA (gray). The triangles indicate radars. The black circles in (

**a**–

**h**) indicate the main areas that are affected by BB. The AVPDs of (

**i**) Z

_{H}, (

**j**) Z

_{DR}, (

**k**) K

_{DP}, and (

**l**) ρ

_{HV}, as derived from Guangzhou radar, are also shown. Black dots indicate the original observations, and red dots indicate the corrected values. The corresponding feature heights are marked in the figures.

**Figure 11.**The ideal mosaic height. Three areas marked by boxes. Regions 1, 2, and 3 are mainly located at 3–5 km height, and are easily affected by BB.

**Figure 12.**Mosaics for (

**a**) Z

_{H}, (

**b**) Z

_{DR}, (

**c**) K

_{DP}, (

**g**) ρ

_{HV}, and (

**i**) SNR at 5:00 UTC on 20 May 2016. The corresponding RQIs of (

**d**) Z

_{H}, (

**e**) Z

_{DR}, (

**f**) K

_{DP}, and (

**h**) ρ

_{HV}are also shown next to the radar data. The triangles indicate radars.

**Figure 13.**Bias ratio distributions of (

**a**) radar mosaic QPE and (

**b**,

**c**) two single radars’ QPEs. A gauge corresponds to a bias ratio value. The bias ratio is computed with the pairs of radar-estimated precipitation and gauge-observed precipitation of this gauge. The evaluation area is less than 300 km from the two radars, and the evaluation results are based on all nine rainfall events. Bubbles indicate the bias ratio at the gauge stations. Different colors indicate different bias ratio values. Red indicates underestimation and purple indicates overestimation. Bubble size indicates the average hourly rainfall accumulation at each gauge. The inner distance of the spindle shape marked with a black line is less than 180 km from either radar.

**Figure 14.**(

**a**–

**i**) Time series of RMSEs derived from the nine rainfall events. QPE is also evaluated in the area less than 180 km from either radar. Green, blue, and red lines represent RMSEs derived from Guangzhou radar QPE, Yangjiang radar QPE, and radar mosaic QPE, respectively.

**Figure 15.**Bias ratio distributions of the QPEs estimated by the algorithm without (

**a**) and with (

**c**) BB correction. The color bubbles are the same as those in Figure 13. The associated scatterplots of the QPEs before (

**b**) and after (

**d**) improvements vs. gauge data in regions 1, 2, and 3 are also shown.

**Figure 16.**(

**a**) RMSEs, (

**b**) NEs, and (

**c**) NBs changing with the percentage of convective precipitation. The precipitation in these tests is only mixed with convective precipitation and stratiform precipitation. The percentages of stratiform precipitation are from 100% to 0% from left to right.

**Figure 17.**AVPDs of (

**a**–

**c**) Z

_{H}and (

**d**–

**f**) Z

_{DR}. Black dots indicate the original observations and red dots indicate the corrected values. Green lines represent the changing trends of the Z

_{H}and Z

_{DR}profiles under BB. The corresponding times and feature heights are marked in the figures. “GZ” means data are derived from the Guangzhou radar, and “YJ” means data are derived from the Yangjiang radar.

**Figure 18.**(

**a**) Bias ratio distribution of the radar mosaic QPE within almost the entire range that can be detected by the two radars. The color bubbles in (

**a**) are the same as those in Figure 13. (

**b**–

**d**) present the area distributions of the average RQI of Z

_{H}, Z

_{DR}, and K

_{DP}, as derived from nine rainfall events. The color bubbles in (

**b**–

**d**) indicate the average values of RQI at the gauge stations. Different colors indicate different RQI values. The bubble size indicates the average hourly rainfall accumulation at each gauge.

Parameter Type | Setting |
---|---|

The antenna diameter (m) | 8.54 |

The antenna gain (dB) | 45.31 |

The beam width (°) | <0.98 |

The first side lobe (dB) | <−30 |

The wave length (cm) | 10.3 |

The operating mode | simultaneous horizontal and |

vertical transmission and reception | |

The minimum detectable power (dBm) | −117.8 |

The volume scan mode | VCP21 (9 tilts) |

The range resolution (km) | 0.25 |

# | Date (UTC) | Total Time (h) | No. of Valued Gauges | Mean Gauge Accumulation (mm) | Max Gauge Accumulation (mm) | Precipitation Type |
---|---|---|---|---|---|---|

1 | 6 May 2016 | 12 | 730 | 19.04 | 118.5 | squall line |

2 | 9–10 May 2016 | 34 | 905 | 34.68 | 222.8 | convective |

3 | 15 May 2016 | 10 | 963 | 14.19 | 67.1 | squall line |

4 | 19–21 May 2016 | 43 | 1001 | 55.77 | 416.6 | stratocumulus |

5 | 27–28 May 2016 | 24 | 991 | 30.48 | 177.2 | squall line |

6 | 4–5 June 2016 | 24 | 935 | 29.20 | 109.4 | stratocumulus |

7 | 9 June 2016 | 8 | 269 | 9.56 | 80.2 | stratocumulus |

8 | 11–14 June 2016 | 86 | 1007 | 44.57 | 211.4 | stratocumulus |

9 | 15 June 2016 | 6 | 719 | 11.99 | 79 | squall line |

**Table 3.**Evaluated statistical scores of radar QPE based on raw/corrected data in the BB. Radar QPE based on data at the BB bottom height is treated as the “truth” value.

Method | Based on Raw Data in BB | Based on Corrected Data in BB | ||||
---|---|---|---|---|---|---|

CC | NE (%) | NB (%) | CC | NE (%) | NB (%) | |

R1(Z_{H}) | 0.39 | 41.66 | 37.55 | 0.80 | 11.79 | −1.24 |

R2(Z_{H}) | 0.39 | 40.42 | 36.42 | 0.80 | 11.50 | −1.22 |

R1(K_{DP}) | 0.15 | 100.2 | 73.30 | 0.26 | 60.28 | 16.96 |

R2(K_{DP}) | 0.15 | 97.52 | 71.14 | 0.26 | 59.02 | 16.41 |

R(Z_{H},Z_{DR}) | 0.52 | 38.38 | 31.06 | 0.87 | 13.81 | 1.53 |

R(K_{DP},Z_{DR}) | 0.16 | 93.39 | 66.61 | 0.26 | 59.30 | 16.17 |

**Table 4.**Evaluated statistical scores of radar mosaic QPE, as well as those of the two single radars.

Method | CC | RMSE (mm) | NE (%) | NB (%) |
---|---|---|---|---|

Radar mosaic QPE | 0.86 | 3.76 | 39.72 | −5.89 |

Guangzhou Radar QPE | 0.85 | 3.97 | 42.07 | −2.06 |

Yangjiang Radar QPE | 0.65 | 5.88 | 64.26 | −29.30 |

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**MDPI and ACS Style**

Zhang, Y.; Liu, L.; Wen, H.
Performance of a Radar Mosaic Quantitative Precipitation Estimation Algorithm Based on a New Data Quality Index for the Chinese Polarimetric Radars. *Remote Sens.* **2020**, *12*, 3557.
https://doi.org/10.3390/rs12213557

**AMA Style**

Zhang Y, Liu L, Wen H.
Performance of a Radar Mosaic Quantitative Precipitation Estimation Algorithm Based on a New Data Quality Index for the Chinese Polarimetric Radars. *Remote Sensing*. 2020; 12(21):3557.
https://doi.org/10.3390/rs12213557

**Chicago/Turabian Style**

Zhang, Yang, Liping Liu, and Hao Wen.
2020. "Performance of a Radar Mosaic Quantitative Precipitation Estimation Algorithm Based on a New Data Quality Index for the Chinese Polarimetric Radars" *Remote Sensing* 12, no. 21: 3557.
https://doi.org/10.3390/rs12213557