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The loss function (i.e., mean squared error) is an important indicator to measure the performance of GRU NN training. Figure 3 shows the variation of loss function of GRU_Z-ET with epoch (i.e., the number of iterations) for different batch sizes. Although there are large differences in loss function for different batch sizes at the beginning of the iteration, these loss functions converge rapidly. After 10 iterations, all loss functions (about 0.009) are less than 0.01, implying the stability and good fit of GRU_Z-ET. In the following sections, the batch size of 32 is selected in the GRU_Z-ET. To further test the performance of GRU_Z-ET training, the GRU_Z-ET model at epoch 10 was also applied to validation data (early June 2017), test data (May−July 2018), SRAO data (Shangrao radar and rainfall data in May−July 2019) and JDZ data (jingdezhen radar and rainfall data in May−July 2019). The corresponding loss functions are shown in Table 1. All the loss functions for different datasets are smaller than 0.01, further indicating the stability and good fitting of GRU_Z-ET.
Figure 3. The variation of loss functions of GRU_Z-ET training with epoch for different batch sizes.
Train data Validation data Test data SRAO data JDZ data 0.0090 0.0090 0.0098 0.0086 0.0096 Table 1. The loss function of the GRU_Z-ET model at 10 epochs for different data.
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To assess the performance of the method proposed in this study to produce radar QPE, two cases were selected in the study area representative of short-term heavy rainfall events with a rainfall intensity of more than 40 mm h−1: one at 2300 UTC 5 July and the other at 0300 UTC 20 June 2018. In addition, a case of scattered, isolated convective rainfall with a rainfall intensity of more than 20 mm h−1 was chosen: at 1000 UTC 19 June 2018.
For the case that occurred at 2300 UTC 5 July, 2018, the radar echoes mainly appear to the south of 28.5°N, and the maximum reflectivity in excess of 45 dBZ appears about 70 km to the southeast of the radar station (Fig. 4a). In addition, there are strong echoes with reflectivity > 40 dBZ to the south and southwest of the radar station (Fig. 4a). Correspondingly, the areas with reflectivity > 45 dBZ (or even 40 dBZ) have short-term heavy rainfall with a rainfall intensity of more than 40 mm h−1. The regions with reflectivity > 35 dBZ roughly coincide with the areas with a rainfall intensity of more than 10 mm h−1 (Figs. 4a–4b).
Figure 4. (a) The mean CR (dBZ), (b) the observed rainfall rate (mm h−1), and the radar QPE (mm h−1) obtained from (c) GRU_Z-ET, (d) GRU_Z, (e) ZR_OPT and (f) ZR_WSR at 2300 UTC 5 July 2018. The black plus sign represents the location of the Nanchang radar station.
The radar QPE results derived from the four methods (GRU_Z-ET, GRU_Z, ZR_WSR and ZR_OPT) are presented in Figs. 4c–4f. The results from these four methods can reproduce at least some aspects in the rainfall cases. However, the ZR_WSR remarkably underestimates the precipitation intensity of this case. The areas with a rainfall rate above 40 mm h−1 to the southeast of the radar station are markedly reduced, and the rainfall rate to the south and southwest of the radar station is also less than 30 mm h−1 (Fig. 4f). The radar QPE results derived from the ZR_OPT and GRU_Z have quite similar intensity and spatial distribution. Although the ZR_OPT and the GRU_Z improve the QPE accuracy compared with the ZR_WSR, they still underestimate the observed rainfall rate (Figs. 4d–4e). The GRU_Z-ET further improves the radar QPE, and its results are noticeably larger to the southeast, south and southwest of the radar station (Fig. 4c), in closer agreement with the observations (Fig. 4b). Overall, the radar QPE results from the GRU_Z-ET are the closest to the observations in both rainfall intensity and spatial distribution (Fig. 4c). Especially to the southwest of the radar station (dashed rectangle in Fig. 4c), the GRU_Z-ET is the only method that can simulate the observed rainfall rate of more than 40 mm h−1.
Regarding the case at 0300 UTC 20 June 2018, the radar echoes mainly appear in the southeast of the radar station and to the south of the Poyang Lake, with maximum reflectivity of more than 40 dBZ (Fig. 5a). Correspondingly, heavy precipitation of more than 30 mm h−1 appears in the vicinity of the strong echoes above 40 dBZ (Fig. 5b). Over the southern end of the Poyang Lake, there are radar echoes > 35 dBZ and heavy rainfall with the intensity exceeding 20 mm h−1 (Figs. 5a–5b), which may be associated with the air-lake interaction. Figures 5c–5f show the radar QPE results from the four methods. Similar to the case at 2300 UTC 5 July 2018, the ZR_WSR clearly underestimates the rainfall rate, where the rainfall rate exceeding 20 mm h−1 appears only in a small area, and the rainfall rate in the southern end of the Poyang Lake is smaller than 10 mm h−1 (Fig. 5f). The results of the ZR_OPT and GRU_Z are quite similar in estimating the intensity and spatial distribution of rainfall, and the rainfall rate obtained by these two methods is greater than that of the ZR_WSR (Figs. 5d–5e). At the southern end of the Poyang Lake, the rainfall rate from the ZR_OPT and GRU_Z is also more than 10 mm h−1. However, the maximum rainfall rate from the two methods is still less than 30 mm h−1 (Figs. 5d–5e). The QPE results from the GRU_Z-ET are larger than those of the three methods above, with the maximum rainfall rate exceeding 30 mm h−1 (Fig. 5c), which are the closest to the observations among the results of the four methods (Figs. 5c–5f).
For the scattered, isolated convective rainfall event at 1000 UTC 19 June 2018, the radar echoes are scattered around the Nanchang radar station, with the maximum reflectivity > 40 dBZ appearing to the southwest and southeast of the radar station (Fig. 6a). Note that the radar echoes of more than 10 dBZ
also appear over the west, south and east shores of the Poyang Lake (Fig. 6a), which may be related to the air-lake interaction. Correspondingly, the precipitation is also scattered around the radar station, and the maximum rainfall rate is more than 20 mm h−1, appearing to the south and east of the Poyang Lake and the southwest of the radar station (Fig. 6b). Since the meteorological stations observing precipitation are relatively few and scattered, the spatial distribution of rainfall rate is shown by the use of color dots at each of the stations instead of the interpolated two-dimensional filling map. The radar QPE results derived from the four methods are presented in Figs. 6c–6f. Similar to the above two cases, the ZR_WSR obviously underestimates the rainfall rate, and only one station has an estimate exceeding 10 mm h−1 (Fig. 6f). The ZR_OPT and GRU_Z improve the QPE, with two stations having estimated rainfall rates of above 10 mm h−1 (Figs. 6c–6d). The GRU_Z-ET further improves the QPE, with the estimated rainfall rates exceeding 20 mm h−1 appearing at two stations (Fig. 6c). Although the stations with rainfall rates greater than 10 mm h−1 or 20 mm h−1 in the GRU_Z-ET results (Fig. 6c) are still less than those of the observations, the GRU_Z-ET results are the closest to the observations among the four methods (Figs. 6c–6f). -
The estimates for the three cases above suggest that the GRU_Z-ET proposed in this study produces a more accurate QPE than the ZR_WSR, ZR_OPT and GRU_Z. To verify the generality of this finding, we collect 200 rainfall events with the total samples of 21 882 in the study area from May to July in 2018 for further assessment. In each rainfall event, the stations with rainfall rates of ≥1 mm h−1 are more than 30.
Figure 7 shows the frequency distribution of precipitation difference (observations minus QPE values) between the AWS observation and QPE values obtained from the four methods. For the ZR_WSR method, most of the difference values are more than 0 mm h−1, with the maximum frequency (about 28%) at difference values of 2 mm (Fig. 7d). The frequency of the differences between −10 mm h−1 and 10 mm h−1 is about 82.4%, which is the smallest among the results of the four methods, while the frequency of differences over 10 mm h−1 is about 17.3%, which is the largest (Table 2). In addition, the RMSE of the ZR_WSR results is about 8.6 mm h−1, which is also the largest among the four methods (Fig. 7). These statistics further demonstrate that the QPE accuracy of the ZR_WSR is the lowest among the four methods. In terms of the ZR_OPT estimates, the maximum frequency (about 22%) shifts to the differences of about 0 mm h−1, and the frequency of the differences less than 0 mm h−1 increases remarkably (Fig. 7c). As shown in Table 2, the frequency of the differences between −10 mm h−1 and 10 mm h−1 increases to 87.2%, and that of the differences exceeding 10 mm h−1 decreases to 12.0%. Moreover, the RMSE of the ZR_OPT estimates is reduced from 8.6 mm h−1 to 7.49 mm h−1. These statistics suggest that the ZR_OPT method obviously improves QPE accuracy compared with the ZR_WSR.
Regarding the GRU_Z estimates, the frequency distribution of the differences between the observations and QPE values is similar to that of the ZR_OPT estimates, except that the frequency increases somewhat at differences between −2 mm h−1 and 00 mm h−1 and decreases somewhat at 2 mm h−1 differences (Fig. 7b). The frequency of differences between −10 mm h−1 and 10 mm h−1 is about 87.8%, slightly more than that of the ZR_OPT, and the frequency of difference over 10 mm h−1 is about 11.8 mm h−1, slightly less than that of the ZR_OPT (Table 2). Additionally, the RMSE of the GRU_Z estimates is about 7.41 mm h−1, which is also slightly lower than that of the ZR_OPT (Figs. 7b–7c). These results suggest that the GRU_Z has a slight improvement in the radar QPE compared with the ZR_OPT.
After introducing the echo-top height, the frequency of precipitation differences between the observations and QPE values derived from the GRU_Z-ET is relatively uniformly distributed on both sides of 0 mm h−1 differences (Fig. 7a). The frequency of differences between −10 mm h−1 and 10 mm h−1 is about 89.3%, which is the largest among the results of the four methods, while the frequency of differences exceeding 10 mm h−1 is about 9.1%, which is the smallest (Table 2). Note that the RMSE reflecting the deviation degree is about 7.04 mm h−1, which is also the smallest among RMSE values of the four methods. Therefore, the GRU_Z-ET proposed in this study performs the best on the QPE compared with the other three methods, as in the case studies discussed above.
Figure 8 shows the RMSE and relative RMSE of radar QPE from different methods for different-intensity precipitation. The RMSE values for different methods increase gradually with the increase of rainfall rate (Fig. 8a), implying that the deviations of QPE from observed values also increase with increasing rainfall intensity. Among the four methods, the GRU_Z-ET have the largest RMSE for the rainfall rate less than 5 mm h−1, but have the lowest RMSE for all the other rainfall intensities, indicating the worst performance for rainfall rate less than 5 mm h−1 and the best performance for the other rainfall intensities. Zhang et al. (2021b) suggested that even if the polarization variables from dual-polarization radar are used, the radar QPE results from NN cannot be clearly better than the ZR_WSR for the rainfall rate less than 5 mm h−1. Figure 8b shows that the relative RMSE values of different methods are about 0.9 for the rainfall rate less than 5 mm h−1, and about 0.5 for the other rainfall intensity. This indicates that although the RMSE values are large for rainfall rate more than 20 mm h−1 or even 50 mm h−1, the deviation of radar QPE is about one-half of mean rainfall. Similar to RMSE, the relative RMSE of GRU_Z-ET is the largest for the rainfall rate less than 5 mm h−1, and the smallest for the other rainfall intensity. This further suggests that the GRU_Z-ET performs the best among the four methods to derive radar QPE for the rainfall intensity more than 5 mm h−1.
Previously, the RMSE and relative RMSE were used to perform an overall evaluation of the QPE derived from the four methods based on the 21882 precipitation samples in May–July of 2018. In order to further validate the spatial distribution of rainfall and the estimation skill for heavy rainfall, we also applied CORR, TS and POD to the individual rainfall events firstly, and then conducted statistical analysis upon the entire sample. Table 3 presents the average CORR between the observed rainfall rate and QPE values from the different methods for the 200 rainfall events in May-July of 2018. The average CORR value of the ZR_WSR estimates is only about 0.39, which is the smallest compared with that of the other three methods, indicating that the ZR_WSR performs the worst in estimating the spatial distribution of rainfall. Note that blocking radar beams at low elevation angles may contribute to the low CORR values. Using the Z-R relationship fitted by the optimal method (ZR_OPT) can remarkably improve the spatial distribution of the estimated precipitation, and the average CORR value increases to 0.53 (Table 3). The mean CORR of the GRU_Z estimates is 0.54, slightly higher than that of the ZR_OPT estimates. This result implies that the GRU_Z and ZR_OPT have comparable capability in estimating the spatial distribution of rainfall. The mean CORR value of the GRU_Z-ET estimates is 0.59, which is the largest among the estimates of the four methods and 0.05 higher than the second-highest mean CORR value of the GRU_Z (Table 3), indicating that the GRU method can obviously improve the spatial distribution of the estimated precipitation after introducing the echo-top height.
Figure 9 presents the box plots of the TS for the QPE from different methods. For the threshold of 10 mm h−1, the mean and median TS values of the ZR_WSR method are about 0.21 and 0.23, respectively, and they are the smallest among the TS values of the four methods, demonstrating that the performance of the ZR_WSR is the worst among the four methods on the QPE with the intensity more than 10 mm h−1. In terms of the ZR_OPT, the mean, median and box locations of the TS are obviously higher than those of the ZR_WSR (Fig. 9a), implying a substantial improvement in the QPE of hourly precipitation above 10 mm. The mean and median TS values of the GRU_Z are slightly smaller than those of the ZR_OPT (Fig. 9a), indicating that the ZR_OPT performs slightly better than the GRU_Z in estimating the hourly precipitation exceeding 10 mm. However, after introducing the echo-top height, the mean and median TS values of the GRU_Z-ET show the largest among the TS values of the four methods (Fig. 9a). Thus, the performance of the GRU_Z-ET is the best on the QPE with the rainfall rate exceeding 10 mm h−1. At the threshold of 20 mm h−1, although the TS values of different methods decrease somewhat, the mean and median TS values of the GRU_Z-ET are still the largest (Fig. 9b). This confirms that the GRU_Z-ET still performs the best in the QPE with the rainfall rate exceeding 20 mm h−1.
Figure 10 displays the box plots of the POD scores for QPE from different methods at the threshold of 10 mm h−1 and 20 mm h−1. At the threshold of 10 mm h−1, although the POD value of each method is larger than that of the corresponding TS value, the variations of the POD values of the four methods are quite similar to the TS variations. In addition, the POD of the GRU_Z-ET method is the largest, and that of the ZR_WSR method is the smallest (Fig. 10a). The POD of the ZR_OPT method is slightly larger than that of the GRU_Z method. At the threshold of 20 mm h−1, the POD values of different methods decrease compared with those at the threshold of 10 mm h−1. However, the variation characteristics of the POD values for different methods remain similar to the TS variations. The same, the POD of the GRU_Z-ET method is the largest, and that of the ZR_WSR method is the smallest (Fig. 10b). These analyses further support that the GRU_Z-ET method proposed in this study obviously improves the QPE accuracy for the heavy precipitation with rainfall rates above 10 mm h−1 and 20 mm h−1.
Figure 7. The frequency of precipitation difference between AWS observation and QPE obtained from (a) GRU_Z-ET, (b) GRU_Z, (c) ZR_OPT and (d) ZR_WSR during May−July 2018. The number of samples is 21882.
QPE Algorithm GRU_Z-ET GRU_Z ZR_WSR ZR_OPT −10 mm<Diff<10 mm 89.3% 87.8% 87.2% 82.4% Diff≥10 mm 9.1% 11.8% 12.0% 17.3% Table 2. The frequency statistics of precipitation difference (Diff) between AWS observation and QPE derived by different methods.
Figure 8. The (a) RMSE and (b) relative RMSE of radar QPE obtained from different methods for different intensities of precipitation.
QPE Algorithm GRU_Z-ET GRU_Z ZR_WSR ZR_OPT CORR 0.59 0.54 0.39 0.53 Table 3. The mean spatial correlation coefficient (CORR) between AWS observation and QPE derived by different methods in the 200 rainfall events.
Figure 9. Box plots of TS score for QPE produced by different methods at the threshold of (a) 10 mm h−1 and (b) 20 mm h−1. In each box, the top (bottom) of the box indicates the 75% (25%) quartile, and the middle line of the box presents the median value, while the triangle depicts the location mean value.
Train data | Validation data | Test data | SRAO data | JDZ data |
0.0090 | 0.0090 | 0.0098 | 0.0086 | 0.0096 |