Radar Reflectivity and Meteorological Factors Merging-Based Precipitation Estimation Neural Network

The meteorological factors are important determinants of the surface rainfall. However, in studies of quantitative precipitation estimation (QPE) based on Doppler radar data, meteorological elements are usually used as the weighting factors to correct precipitation, and the active role of meteorological factors in determining rainfall is neglected, which limits the improvement of radar QPE accuracy. In this study, the effectiveness of applying one-dimensional convolutional neural network together with radar data and meteorological factor data to estimate precipitation is explored. Various combinations of meteorological factors were tested for the set of input variables. The proposed model performance was evaluated over the Shijiazhuang area at the spatial resolution of 0.01° and at the 6-min time scale. The results indicates that the proposed model (RM-1DCNN) provides more accurate precipitation estimation compared to the Ordinary Kriging interpolation, two Z-R relationships, and Back Propagation Neural Network. The root mean square error of the RM-1DCNN with temperature was 0.642 mm per 6 min and the average Threat Score exceed 55%, which was the best among all schemes.

(exponential, spherical, gaussian, and linear). The experimental results reveal that the Exponential and Spherical functions are well adapted to the OK method in daily precipitation interpolation. Even with advanced spatial interpolation techniques, obtaining high-resolution rainfall estimates in sparse gauge areas is still a challenging task.
Weather radar provides large-scale quantitative precipitation estimation with high temporal and spatial resolution. The traditional method of converting radar reflectivity (dBZ) to rainfall relies on the Z-R relationship (Marshall & Palmer, 1948). Ryde (1946) predicted various weather systems based on dBZ of different sizes (5-10 cm). Based on China's New Generation Weather Radar (CINRAD) system data, the QPE in mainland China follows the fixed relationship of 1.4 300 E Z R   (Crosson et al., 1996). Nevertheless, the nature of radar precipitation measurements is influenced by numerous sources of error. Some of the known errors in reflectivity measurements are ground clutter, beam obstruction, abnormal propagation, bright bands, hail, and attenuation (Berne & Krajewski, 2013;Chumchean et al., 2003). Inevitably, these error factors affect precipitation and reflectivity measurements, making the Z-R relationship a physically difficult model to satisfy ideal conditions, and radar data are not extensively used for hydrological applications. Many studies have concentrated on minimizing the errors in the Z-R relationship and improving the accuracy of radar QPE (Abdella, 2016;Chumchean et al., 2006;Ciach et al., 2007;Villarini, Serinaldi, & Krajewski, 2008). In Huffman's et al. (1997) work, a single correction factor was obtained from the ratio of radar estimation value to rain gauge measurement value, and the spatial variation between ratios is not considered. The correction factor acquired was used to adjust radar data, which effectively reduces the error of the Z-R model. Ramli et al. (2011) used an optimization method to obtain the Z-R relationships of three different rainfall levels in Malaysia. Gou et al. (2018) improved Z-R relationships based on the reflectivity threshold (RT) algorithm and the storm cell identification and tracking (SCIT) algorithm using observations from 11 Doppler meteorological radars and 3,264 rain gauges on the eastern Tibetan Plateau, and formulated two Radar QPE program. Yuan et al. (2010) proposed an improved least squares method as a discriminant function to optimize the parameters in the fixed Z-R relationship. They summarized the Z-R relationship optimized by the optimization method, and both the average relative error at the station and the relative error of area rainfall are greatly reduced. The improved Z-R relationship, however, cannot be applied to all precipitation regions and does not significantly improve the accuracy (Hu et al., 2012;Villarini & Krajewski, 2010). Moreover, some of the underlying physical processes are still not understood well enough to allow significant advances (Villarini & Krajewski, 2010).
The precipitation processes are associated with the numerical changes of many meteorological factors, and surface precipitation is significantly influenced by meteorological factors (Pratap et al., 2020). Many studies have been conducted to consider meteorological factors in estimating precipitation (Auer, 1974;Fassnacht et al., 2001;Killingtveit, 1976;Rohrer, 1989). The Finnish Meteorological Institute used temperature and humidity observations from weather stations to estimate precipitation stages and utilized the information to formulate various rain or snow products (Koistinen et al., 2004;Saltikoff et al., 2015). The Nordic Precipitation Data Operation Correction Manual (Førland et al., 1996) classified precipitation phases according to temperature, and used the average of different solid and liquid precipitation equations for mixed precipitation estimation. The correction equation used the wind speed and air temperature at each weather station location to correct the standard precipitation for insufficient wind-induced capture. In previous studies, Koistinen et al. (2004) and Saltikoff et al. (2000Saltikoff et al. ( , 2015 used near-surface air temperature and relative humidity or wet bulb temperature to estimate the precipitation dominant stage in the selection of the Z-R relationship, and refined the description of different rainfall types in the Z-R relationship. Fassnacht et al. (1999) demonstrated the use of surface air temperature to estimate the fraction of snow content in mixed precipitation and used it to adjust radar estimates of mixed precipitation. According to reports, this adjustment has improved estimates of snow cover in Ontario, Canada. Further, Fassnacht et al. (2001) showed that the adjusted radar data provided a more realistic precipitation estimates for the precipitation-runoff model than the calibrated rain gauge precipitation data, which greatly improves the accuracy of the radar precipitation estimation in the cold season. Sivasubramaniam et al. (2018) indicated that using air temperature as the second covariate in the K-NN non-parametric model dramatically reduces the root mean square error (RMSE) and improved the radar precipitation estimation at colder temperatures. Although, the above method used meteorological factor data in the precipitation estimation method, and achieved good results. However, the methods in previous studies used meteorological factors as correction factors for precipitation estimation and lacked the consideration of meteorological factors as independent variables.
The wide applicability of machine learning (ML) algorithms to natural phenomena (Gagne et al., 2014;Ganguli & Reddy, 2014;Mosavi et al., 2018;Tao et al., 2017) provides new options for QPE based on radar data. Yu et al. (2017) attempted to develop quantitative precipitation forecast (QPF) models of rain radar data using random forest (RF) and support vector regression (SVR). Their proposed method focused on QPF models for typhoons in Taiwan and performed well. Shin et al. (2019) investigated the applicability of RF, stochastic gradient boosted (SGB), and extreme learning machine (ELM) in quantitative precipitation estimation models. The results demonstrated that the quantitative precipitation estimation model based on ML had better performance than the model based on the Z-R relationships, especially for heavy rain. The neural networks are one of the most popular and effective types in ML, and many meteorologists have started to experiment with the use of neural networks to fit the relationship between dBZ factors and precipitation (Mahdianpari et al., 2018). Shao et al. (2009) introduced backward propagate neural networks (BPNN) into the radar precipitation estimation work and achieved a great improvement over the Z-R relationship. Kusiak et al. (2012) used a multi-layer perceptron (MLP) to estimated rainfall intensity at multiple time scales and obtained more accurate estimation results than traditional methods. Kou et al. (2018) used the co-combination of ground-based and spaceborne radar data as the input of the neural network. The experimental results revealed that the fusion of radar data could estimate the rainfall intensity more accurately. However, the precipitation estimation methods that have been proposed, including conceptual models or neural networks, only consider the dBZ at a given location, which represented a point-to-point (PTP) framework (Chiang et al., 2006;Teschl et al., 2006;Trafalis et al., 2002;Xiao & Chandrasekar, 1997). The radar QPE method based on the PTP framework is limited to the further improvement of estimation accuracy. On the basis of the convolutional neural networks (CNN), some researchers (Tian et al., 2020;Yo et al., 2021) estimated the precipitation of ground stations by using two-dimensional radar echo as input. The CNNs can effectively extract the characteristics of precipitation from the reflectivity data, but the precision of the experimental results is not high due to the difference of reflectivity data size and the large-scale two-dimensional data contains many signals unrelated to precipitation. In this study, we propose a framework of real-time precipitation estimation based on a one-dimensional convolutional neural network by taking regional dBZ data and various meteorological factor data as dependent variables. The model will hereafter be referred to as RM (dBZ and meteorological factors) one-dimensional convolutional neural network (RM-1DCNN). The rest of the manuscript is structured as follows. Section 2 covers information regarding the study area and the utilized data. Section 3 describes the details of the model and evaluation metrics. Section 4 covers the evaluation of the proposed model and the comparison models at the 6-min time scale. The main conclusions of this study are summarized in Section 5.

Study Area and Weather Stations Data
All of the data used in this study were obtained from the Shijiazhuang Meteorological Observatory, including Z9311 Doppler dBZ, National Weather Stations (NWSs) data, and Automatic Weather Stations (AWSs) data from January to December 2018 (UTC+8). The study area is located in northern China (red area in the inset in Figure 1), with 37.3°-38.8°N and 113.3°-115.5°E. The climatic background of precipitation in the study area is complicated, and the flood season is mainly affected by summer monsoon activities, which makes precipitation estimation based on radar data a challenging task (Yang et al., 2011). The distribution of the radar station, 17 NWSs, and 260 AWSs (Figure 1), and are in Table 1.
This study focuses on the estimation of rainfall, so the precipitation does not involve the snowfall process. The start of each precipitation process was chosen such that there was significant rainfall over a spatially coherent area. The end of each precipitation process was determined to be the time at which there was no longer any significant rainfall occurring in the area. The weather radar takes 6 min to complete a volume scan and data from the NWSs and AWSs were calculated every minute. To match the precipitation with the reflectivity, the precipitation obtained by the weather station in the radar volume scanning recording time is added to the previous continuous 6-min precipitation as the precipitation at the time the radar volume scan was completed, the unit is mm/6 min. A total of 17 precipitation events were analyzed, with no less than 10,000 sets of radar measurements for each event. For four meteorological factors, the average of the six values during the radar volume scan time is taken as the meteorological factor value for time period.

Weather Radar Reflectivity (dBZ) Data
The weather radar has nine elevation angles (0.49°, 1.40°, 2.38°, 3.20°, 4.27°, 5. 93°, 9.79°, 14.50°, and 19.42°) at different height levels, completes a complete volume scan every 6 min, and has a detection radius of 460 km, and can work continuously in the rainy season. The study area is mainly alluvial plain and the terrain has no significant effect on the scanning of the lowest elevation angle scan. According to the principle of estimating surface precipitation using low elevation angle observations and ensuring that beam blocking does not occur (Li et al., 2014), we chose the maximum reflectivity of the radar at 0.49°, 1.40°, and 2.38°, also known as the combined reflectivity and a detection radius of 110 km radar data, which is enough to cover the entire area of Shijiazhuang. To associate the precipitation echo measured by the weather radar with the precipitation measured by the ground weather stations, a corresponding relationship between the radar spatial and the ground-based rainfall measurement units must be established, that is, the polar coordinates of the radar echo are converted into Cartesian coordinates with a 6-min scale and a spatial resolution of 0.01° ( Figure 2). According to the precipitation time and weather station coordinates in the precipitation samples, the dBZ units at the same location and time are taken out. The large-scale reflectance map contain information unrelated to ground rainfall, resulting in poor precipitation estimation accuracy. The nine (3 × 3) surrounding reflectivity factors centered on the cell location are used as input (Gao et al., 2019).

Meteorological Factor Data
The meteorological factor data obtained from 17 NWSs are only representative of conditions within 1 km of the site location and there are no reference values for areas outside the range. It is essential to interpolate the four meteorological factors of air pressure, temperature, relative humidity, and wind speed (L. Wang et al., 2015). There are numerous studies on the spatial interpolation of meteorological factors, all concluding that the best interpolation method is relative (Song et al., 2015;Xiao et al., 2010). The accuracy of OK interpolation outperforms Inverse Distance Weight (IDW) interpolation and tension spline interpolation method when considering both distance and spatial position of known sample points and spatial orientation relationship with interpolation points (Eldrandaly & Abu-Zaid, 2011). In this study, we used the OK interpolation algorithm for four meteorological factors. Kriging;s general formula (Oliver & Webster, 1990) is as follows: where E Z is the meteorological factor value of the estimated point, i E  is the weight of the meteorological factor of the estimated point by the NWSs participating in the interpolation, and i E X is the location of the NWSs.
The weight coefficient of OK interpolation is determined by the following two equations:  is the Lagrange multiplier for minimization. Kriging is based on the regional change of elements and uses a variogram to represent the spatial structure characteristics of variables (McBratney & Webster, 1986). The variation function expression is: The OK interpolation can be divided into the Spherical model, Circular model, Exponential model, and Gaussian model according to different fitting semivariance models (McBratney & Webster, 1986). In the interpolation of meteorological element field, spherical simulation is better (Chiu et al., 2009), and its mathematical model is as follows: The range of the interpolated meteorological factor data is the same as the radar reflectance for the same period ( Figure 3). The meteorological factor data were used as input data for the RM-1DCNN using the same method as for the radar data processing.

RM-1DCNN Architecture
Currently, QPE studies based on weather radar only consider the reflectivity factor at each point. The input data of radar QPE based on the Z-R relationship or ML is the reflectivity of multiple points or the average reflectivity of nine grid points at the minimum elevation above the rain gauge (Ciach et al., 2007). Precipitation is a weather system with a strong spatial correlation, and the reflectivity points can hardly reflect the actual precipitation process. By expanding the scale of the reflectivity data and applying the 2D-CNN networks as the QPE models, it is possible to learn the precipitation characteristics in reflectivity data. Nevertheless, the larger-scale reflectivity data contains many signals unrelated to precipitation, and the accuracy of the rain gauge data is difficult to encompass large areas of reflectivity (Tian et al., 2020;Yo et al., 2021). Therefore, we propose RM-1DCNN for weather radar QPE based on 1D-CNN. The architecture of the RM-1DCNN model is described below.
The RM-1DCNN includes convolution layers, pooling layers, and full connection layers. The function of the convolution layer is to convolute the input reflectivity data and meteorological factor data with the convolution kernel. Each convolution kernel extracts the local features of the local receptive region of the input data and constructs the output feature vector under the action of the activation function. The output feature vector of each layer is the convolution result of multiple input features. Assuming that   1 l i E a j E j -th neuron convolution operation in the i -th feature surface of the E j -th convolutional layer.
After the convolution operation, we use the linear rectification function (ReLU) activation function for nonlinear conversion. The expression is as follows: The pooling layer reduces the dimension of the input feature vector through pooling operation and continues to extract features. The mathematical expressions of maximum pooling and average pooling are as follows: where E w is the width of the pooling area,   l i E q t is the value of the t -th neuron in the i -th feature plane of the l -th layer, and   1 l i E p j  is the value corresponding to the 1 E l  -th layer of the neuron. It can be seen from Equations 8 and 9 that the maximum pooling is to output the maximum value of the receptive region of the feature surface, and the average pooling output is the average value of the elements in the receptive domain. The RM-1DCNN uses maximum pooling.

Model Setup
The architecture of the proposed RM-1DCNN model with details of input shape, filter size, stride size, and output is shown in Figure 4. The input is n (1 ≤ n ≤ 5) 3 × 3 matrices, with the first layer being the dBZ, and the other n-1 layers beng the meteorological factor data. The proposed model first combines n (1 ≤ n ≤ 5) mapping features using a concatenation function, and then performs a dimensional transformation from n × 3 × 3 to n × 9 (1 ≤ n ≤ 5). Then two consecutive one-dimensional convolution and maximum pooling operations are performed. Finally, three fully connected layers are used for down-sampling to obtain the estimated precipitation.
The precipitation data of 17 NWSs were divided into training and verification sets according to the ratio of 8:2. The precipitation data of 260 AWSs was used as the test set. The training data set is utilized to optimize the model parameters and prevent overfitting. To build a regression model using deep learning (DL) algorithm, the hyperparameters of the model should be tuned during the training phase. The initial values of the parameters are randomly selected from the standard normal distribution. In the training and verification phase, the MSE is defined as the minimum loss function to calculate the error between the estimated value and the true value. The error during the training phase is trained by the gradient descent method to update the parameters of the model and minimize the error for each epoch. Various combinations of hyperparameters are tested to optimize the learnable parameters of the model and obtain the lowest MSE. Finally, the learning rate of the model is 0.0001, a minibatch size of 15, and an epoch size of 150.

Performance Measurements
Three continuous indices were used to evaluate the estimated precipitation on the 6-min time scale. The three continuous indices are: root-mean-square error (RMSE), correlation coefficient (CC), and mean absolute error (MAE), which can reflect the total error of estimation results. The specific calculation equation is as follows: where i E y is the precipitation estimated by the model, i E y is the measured precipitation of the weather station; i E y and i E y are the average values of the corresponding variables; and i is the amount of data. In addition, we used the threat score (TS) to determine the quality of the estimated precipitation. According to the precipitation classification standard proposed by Zhang et al. (2020), the precipitation at the time scale of 6 min is divided into five degrees (  where the E k values ranged from 1 to 4, representing 6 min precipitation forecasts of ≥0.1, ≥0.7, ≥1.5, and ≥4 mm, respectively. NA, NB, and NC represent hit counts, false alarms, and miss times, respectively.

Precipitation Estimation Performance Using Different Models
To illustrate the priority of the proposed model, the OK interpolation based on Spherical variogram (Q. Wang et al., 2016), (Crosson et al., 1996), Z-R relationship based on the optimization algorithm (Z-R(2)) (Yuan et al., 2010), and BPNN model (Xiao & Chandrasekar, 1997) were selected for comparison with the proposed model based on dBZ data. From Figures 5 and 6 and Table 3, it can be seen that dBZ combined with DL technology to estimate precipitation is effective, and more accurate results can be obtained. The precipitation estimated by the two models based on DL has a strong correlation with the gauge values, which reflects the advantages of DL technology in QPE (Chen et al., 2019). Simultaneously, compared with OK, Z-R(1), Z-R(2), and BPNN, the estimated values of RM-1DCNN is closer to the gauge values, and the error is the smallest.   More specifically, the correlation of the OK interpolation based on the cross-validation method (Giraldo et al., 2011) is the lowest, the TSs of the four precipitation categories are the lowest, and the TSs of the rainstorm and downpour are less than 5%. The degree of precipitation stationarity decreases as the amount of precipitation increases, and the increase in precipitation sometimes leads to a decrease in the correlation described by the semivariogram, which affects the quality of the precipitation interpolation (Chen et al., 2010). The RMSE and MAE of Z-R(1) are larger than those of all DL methods, which indicates that the fixed Z-R relationship does not applicable to all regions of China. The Z-R(2) based on the optimization algorithm is more suitable for the study area than the fixed-relationship Z-R(1), with smaller errors than Z-R(1). In addition, the quality of the precipitation estimate of the Z-R(2) is better than that of the Z-R(1), and in particular, the estimate for the downpour increased by 68%. The TSs of the two Z-R relationships for light/moderate rain and heavy rain are all greater than 45%, which is one of the reasons that the Z-R Figure 6. Threat scores of the precipitation estimates for four categories of rainfall obtained using different models. relationship is an effective algorithm for radar QPE, which is consistent with the results of other researchers (Liu et al., 2001;G. Wang et al., 2012). The errors of BPNN are smaller than all non-DL methods, but only the TS values of light/moderate rain and downpour are higher than OK and the two Z-R relationships. This may be because the BPNN only fits the radar data and precipitation data nonlinearly, and it does not consider precipitation spatial correlation (Xia & Fang, 2016). Among all the evaluation results, the performance of the RM-1DCNN is slightly better than that of the BPNN, and only the TS of heavy rainfall is lower than the BPNN. The main reason for this result is that the 1-D convolution can learn information about adjacent data, which is not possible with BPNN based on MLP.
Further on the RM-1DCNN model, ablation experiments are carried out for the influence of meteorological factors on the estimation of precipitation. The evaluation results of the proposed model have changed after adding meteorological factors. When the input of the RM-1DCNN model includes P or W-speed, the evaluation results of the model turned out to be worse. The possible reasons for this result are that the measured air pressure varies very slightly in the horizontal direction and has very few correlations with surface precipitation; the low and mid-level wind speeds measured by the NWSs are too large or too small for cloud formation precipitation, and the wind speed has a strong influence on the distribution of liquid precipitation (F. X. Guo et al., 2014). The assessment became better when T and RH are added to the model inputs separately or in combination, which is consistent with the results of other researchers (Saltikoff et al., 2000(Saltikoff et al., , 2015. Comprehensive analysis shows that the model with the lowest RMSE is RM-1DCNN with temperature added in the input (RM-1DCNN (T) ), which is 7.76% lower than that of the RM-1DCNN. Compared with the evaluation results of other models, the precipitation estimated by RM-1DCNN (T) and the gauge value exhibit the strongest correlation and the smallest error rate. The TS values from RM-1DCNN (T) shows a significant improvement, particularly for rainstorm and downpour, with an increase of approximately 10% compared to RM-1DCNN. Moreover, the TSs of the other rainfall degrees increased by about 4.0% and 1.7% compared with those from RM-1DCNN. These results support the conclusion that the RM-1DCNN (T) is superior to the other precipitation estimation methods.
The above analysis is the average performance in the verification phase. Figures 7a-7g show the evaluation results of four representative models on the 6-min time scale of 17 NWSs. The Z-R(1) and BPNN are the most representative radar QPE models in terms of meteorology and DL, respectively. The abscissa of Figure 7 is the station number of NWSs. In Figure 7a, the RMSE of most NWSs with RM-1DCNN is between 0.5 and 1.0, while RMSE of NWSs using RM-1DCNN (T) is further reduced. Although all models at the site 54701 have high RMSE, RM-1DCNN (T) has relatively high QPE accuracy compared with other methods. Figure 7b presents the CC of estimated precipitation with the gauge rainfall, in which it can be that the CC of the RM-1DCNN does not fall below 60%, and the RM-1DCNN (T) does not fall below 70%, indicating a strong correlation between the estimated values and gauge values. The MAE curves illustrate the degrees of underestimation or overestimation. Figure 7c is consistent with the average MAE values analyzed above. From Figures 7d-7g, the TSs of RM-1DCNN (T) has been improved in the four categories, while the TS improvement is less significant for heavy rain and rainstorm. Compared with the Z-R(1), the TSs of RM-1DCNN and RM-1DCNN (T) are increased by 28% and 35% in light/moderate rain, and by 68% and 74% in the downpour. Similarly, the TSs of the four categories are consistent with the average TSs analyzed above. The air temperature determines the final characteristics and phase of the hydrometeor that reaches the ground, which is helpful for QPE based on radar data (Fassnacht et al., 2001). As a result, RM-1DCNN (T) is the best among all comparison models.

Spatial Distribution of the Metrics for the Different Models
The spatial distributions of metrics for Z-R(1), BPNN, RM-1DCNN, and RM-1DCNN (T) estimated precipitation over the study area are shown in Figure 8. Based on the observations of the 260 AWSs, the precipitation estimated by models was calculated for CC, MAE, and RMSE at each gauge, and the gauge values were interpolated into others using inverse distance weight (IDW) interpolation to obtain the spatial distribution of the metrics. As can be seen from Figure 8, the correlation coefficients of the Z-R(1) in the study area is the lowest, and the CC in most areas is lower than 0.4. The performances of BPNN and RM-1DCNN are similar in that both have the problem of low CC values in the center of the study area. The RM-1DCNN (T) has the highest CC in most parts of the region, but also suffers from a non-uniform CC distribution. Several possible factors: First, the distribution of AWSs is not uniform, and the error cannot be measured with actual precipitation. Second, the accuracy of the meteorological factor data obtained by interpolation for a small number of stations is not accurate. The MAE and RMSE of the Z-R(1) are the highest among all the models in the study area, which indicates the problem of overestimation. The performances of other models are similar, the smallest error values are obtained for RM-1DCNN (T) . Figure 9 demonstrates how the models perform in detecting and estimating the precipitation throughout the different evolution stages of the intense storm that occurred over the study area from 1,000 to 1559 UTC July 18, 2018. Time-series plots for the 6-min precipitation estimates by the AWSs, Z-R(1), BPNN, RM-1DCNN, and RM-1DCNN (T) are shown in Figure 9a. The Z-R(1) almost overestimates the rainfall of the whole precipitation event. The BPNN and RM-1DCNN performed similarly, underestimating rainfall  intensity at multiple points in time. The RM-1DCNN (T) has further reduced the estimation error at each time point compared with the RM-1DCNN, which effectively improves the estimation accuracy. The same situation is reflected in the time series diagram of positive bias (Figure 9b). The maximum positive bias ratios of the four models are 10.4, 6.28, 5.98, and 4.23, respectively. Meanwhile, the number of positive deviations less than 1 mm/6 min are 13, 50, 54, and 57, respectively.

Performance of the Models on Different Time Scales
Quantitative precipitation estimates on a longer time scale are of great significance for studying water resource changes during the prolonged precipitation event and for coping with secondary disasters caused by precipitation (Chen & Chandrasekar, 2015;Habib et al., 2001;Villarini, Mandapaka, et al., 2008). Figure 10 demonstrates how the proposed model and the comparison models perform in terms of detecting and estimating the hourly rainfall intensity in Shijiazhuang area during the flood season from 1800 July 18 to 1900 July 19, 2018. Similar to the quantitative 6-min time scale precipitation estimation, the Z-R(1) overestimates the amount of rainfall during the precipitation event. The precipitation estimated by the BPNN is lower than the measured values from the AWSs. The RM-1DCNN improves the accuracy of the precipitation estimation, but the results are not good during the period when the rainfall intensity changes suddenly. The estimated values of the RM-1DCNN (T) correspond well with the AWS observations although there is a slight overestimation when there is a sudden change in the rainfall intensity ( Figure 10a). During periods of heavy precipitation, the positive deviation of the model tends to increase, but the trend of the RM-1DCNN (T) is the least obvious. The maximum values of the positive bias for the Z-R(1), BPNN, RM-1DCNN, and RM-1DCN-N (T) models are about 6.86, 2.17, 0.95, and 0.50 mm/h, respectively (Figure 10b). The estimated precipitation time series of all models on the 6-min and hourly time scales indicate that the proposed model can estimate long-term precipitation events very well.

Conclusions
In this study, the application of convolutional neural networks (CNNs) in estimating precipitation from dBZ and meteorological factors was explored. A case study over the Shijiazhuang area was conducted to assess the effectiveness of the presented model at 0.01° spatial resolution for 6-min time scale. In the current study, we reach the following conclusions: 1. DL algorithm can be used to construct the QPE models of weather radar data. In general, the QPE models based on DL outperform models based on Z-R relationships. The DL algorithms can extract information from radar data more effectively than the Z-R relationships, thus improving the QPE of the radar data. 2. The evaluation results of the proposed RM-1DCNN model in the validation set suggest that it is superior to the two Z-R relationships and BPNN in estimating precipitation, both in the average performance and the performance on individual sites. 3. It is innovatively proposed to add four meteorological factors to the input of RM-1DCNN model in a single or combined form. The experimental results have shown that the scheme of temperature and relative humidity alone or combined can further improve the performance of RM-1DCNN. Among them, the RM-1DCNN (T) is the optimal with the RMSE of 0.642 mm per 6 min and the average TS could exceed 55%. Comparing the Z-R(1), Z-R(2), BPNN, and RM-1DCNN, RM-1DCNN (T) obtain the best spatial distribution of metrics and time series of precipitation.
In this study, the meteorological factors in the study area were not analyzed and verified, so the assessment results have considerable limitations. Besides, it is difficult to obtain meteorological factor surface data with larger areas and more accurate values, which poses a challenge to the implementation of the proposed scheme. However, the proposed RM-1DCNN model has high adaptability in QPE, so it provides a good option for the modeling function between weather radar data and QPE.