Radar Quantitative Precipitation Estimation Based on the Gated Recurrent Unit Neural Network and Echo-Top Data

Quantitative precipitation estimation (QPE) with high accuracy and high spatio-temporal resolution is crucial for agriculture, manufacturing, flash flood operations, hydrologic forecasting, long-term climate assessment and water resource management (Martinaitis et al., 2020; Zhang et al., 2020a, b). Ground-based rain gauges can provide direct measurements of precipitation at point locations. However, the sparse ground-based rain gauge network not only cannot satisfy the need for QPE applications, but also is not easy to cover special terrain surfaces such as lakes and high-altitude mountainous areas. The radar (active remote sensing) and satellite (passive remote sensing) can provide observational data for producing QPE over large areas. However, compared with satellite data, the radar (ground-based weather radar) data have a higher spatio-temporal resolution (Joyce et al., 2004; Wang and Chandrasekar, 2010). Therefore, radar data are often regarded as an important source to generate QPE products (Wu et al., 2018; Zhang et al., 2020c).

Due to the wide application of the QPE in agriculture, hydrologic forecasting and water resource management, the estimation of QPE has become one of the major objectives in radar meteorology (Zhang et al., 2016). An operational radar QPE method was proposed in the 1990s and has been used for the U.S. Weather Surveillance Radar-1988 Doppler (WSR-88D) system (Fulton et al., 1998). For conventional single-polarization Doppler weather radar, the QPE is usually achieved by the assumed nonlinear (power-law) relationship between radar reflectivity factor (Z) and rainfall rate (R), i.e., the Z-R relationship (Jorgensen and Willis, 1982; Fujiwara, 1965). The fixed Z-R relationship used in the U.S. WSR-88D system and the China New Generation Weather Radar (CINRAD) system is Z=300R^1.4 (Fulton et al., 1998; Wu et al., 2018). However, the Z-R relationship relies on the raindrop size distribution of precipitation and may vary for different precipitation types and in different regions (Fujiwara, 1965; Lee, 2006; Wu et al., 2018). Obviously, the uncertainty in raindrop size distribution is one of the primary error sources of the radar QPE (Lee, 2006; Huang et al., 2020).

In order to improve the radar QPE, He et al. (2007) employed a least square method to obtain the appropriate Z-R relationship for typhoon precipitation based on the rain-gauge observations and radar reflectivity in Zhejiang, China. Yang et al. (2015) utilized an optimization method to optimize the Z-R relationship of convective precipitation in Henan, China. These Z-R relationship methods are not suitable for all regions and seasons due to the differences in precipitation types. Therefore, several scholars developed and used a categorized Z-R relationship method to improve the radar QPE for different precipitation types (Liu et al., 1999; Ramli et al., 2011; Bracci et al., 2022). In this method, precipitation is firstly categorized into different types, and then a set of Z-R relationships for different precipitation types are derived based on an optimization method. Moreover, Alfieri et al. (2010) suggested that the Z-R relationship varies over time, and thus they proposed a time-dependent (dynamic) Z-R relationship. That is, they argued that the Z-R relationship in a short period should be redetermined by the observed precipitation and radar reflectivity during this period. Further, Wang et al. (2011) and Wu et al. (2018) proposed a dynamic classified Z-R relationship method. Although their method can obviously improve the radar QPE, it requires real-time feedback from the observed precipitation, which restricts its application.

In recent years, some Doppler weather radar systems have been upgraded to dual-polarization that can measure differential reflectivity factor (Z_DR), specific differential phase shift (K_DP) and differential phase shift (φ_DP) in addition to horizontal reflectivity factor (Z_H). The radar QPE is less sensitive to the raindrop size distributions of precipitation after introducing Z_DR or K_DP into the conventional power-law Z-R relationship, e.g., R(Z_H, Z_DR) = aZ_H^bZ_DR^c or R(K_DP) = aK_DP^b, where a, b and c denote coefficients (Ryzhkov et al., 2005; Bringi et al., 2011; Chen et al., 2017; Seo et al., 2020). On this basis, a specific attenuation parameter (A) is constructed according to Z_H and differential phase shift, which is also applied to perform the radar QPE (Wang et al., 2014; Diederich et al., 2015; Huang et al., 2020; Seo et al., 2020; Zhang et al., 2020a). The radar QPE based on A, namely R(A) = aA^b, is less sensitive to the raindrop size distribution of precipitation than that based on the Z_H, Z_DR and K_DP in S, C and X band radars (Diederich et al., 2015; Huang et al., 2020). Nevertheless, dual-polarization weather radars have not been deployed in many parts of the world (Zhang et al., 2021a).

In addition to the power-law relationship method, several statistical approaches, such as linear regression (Jung et al., 2008) and frequency analysis (Eldardiry et al., 2015), can be used to perform the radar QPE. However, the accuracy of these statistical approaches is relatively low (Zhang et al., 2020c). Recently, with the development of computing technology, data-driven methods for the radar QPE have become feasible, including the support vector machine (Sehad et al., 2017; Zhang et al., 2020c), random forest (Kuang et al., 2016; Wolfensberger et al., 2021) and neural networks (Kusiak et al., 2013; Kou et al., 2018; Zhang et al., 2021a). These methods attempt to identify the relationship between radar reflectivity and rain-gauge observed rainfall rate, having great potential in improving the radar QPE. Furthermore, in addition to radar reflectivity, radar echo-top height is a valuable indicator of rainfall rate and storm development because it essentially depends on the updraft velocity in storms (Adler and Mack, 1984; Atlas et al., 1990). Adler and Mack (1984) and Rosenfeld et al. (1990) demonstrated that the echo-top height correlates well with rainfall rate.

Due to the great potential of neural networks for the QPE and the indicative effect of radar echo-top height on rainfall rate, introducing echo-top height into neural networks is expected to further improve the single-polarization radar QPE. Therefore, we employ a Gated Recurrent Unit (GRU) neural network in this study, which is a variant of long short-term memory (LSTM) neural network and is quite suitable for the estimation and prediction of variables (Mirzaei et al., 2022). The basic principle of this method is to select the echo-top height and radar reflectivity as two independent variables to perform the radar QPE.

The remainder of this paper is organized as follows. Section 2 briefly introduces the study area and data used in this research. Section 3 describes the proposed method to conduct the radar QPE. Section 4 presents the study results. The conclusions are shown in section 5.

The study area is northern Jiangxi Province in China, located in the East Asian monsoon region and to the south of the Yangtze River (Fig. 1a). This area has a rather complex land surface, with the biggest freshwater lake in China (Poyang Lake), plains below 100 m in elevation and steep mountains as high as 800 m in maximum elevation (Lushan, Mufu Mountains and Wuyi Mountains), as shown in Fig. 1b. The Poyang Lake can induce local rainfall (i.e., lake-effect rainfall) and enhance the rainfall of storms crossing the Poyang Lake (Zou et al., 2020, 2022). Mountains also contribute to the occurrence and enhancement of local rainfall (Liao et al., 2007). Jointly affected by the East Asian monsoon and the complex surface, persistent heavy precipitation and short-term heavy precipitation occur quite frequently during the rainy season (May–July) in the study area (Zou et al., 2013; Zhang et al., 2018).

Figure 1.  (a) The location of the study area (orange rectangle) in China, with the JX representing Jiangxi Province, and the blue lines indicating the Yangtze River and the Yellow River. (b) The surrounding topography (color shading, m; see color bar on the right) and rain gauges (black dots) in the study area, the 35 km and 120 km range circles from the radar station at Nanchang, and the gray fan shadows indicating the blocking area of radar beam at 0.5° tilt.

The radar data used in this study were from the CINRAD single-polarization radar of S-band type A (CINRAD-SA radar) in Nanchang City, the capital of Jiangxi Province. This radar data comprises volume scan data in polar coordinates, with ~1-km range and ~ 1° resolutions (Zou et al., 2019). These volume scans are made from the Volume Coverage Pattern 21 (i.e., VCP 21), with a temporal resolution of about 6 min, including nine elevation angles (0.5°, 1.5°, 2.4°, 3.4°, 4.3°, 6.0°, 9.9°, 14.6° and 19.5°).

The hourly rainfall data at more than 600 automatic weather stations (AWSs) were used in this study (Fig. 1b). Moreover, the radar data detected by the CINRAD/SA single-polarization radar at Shangrao and Jingdezhen in Jiangxi Province, China, and the AWS hourly rainfall data within 120 km around the two radar stations were used to evaluate the performance of the machine learning model. The Shangrao and Jingdezhen radar stations are located at (28.42°N, 119.96°E) and (29.35°N, 117.22°E), respectively. The radar data and rainfall data during the rainy season (May–July) in 2017–2019 were provided by the Meteorological Information Center of Jiangxi Meteorological Bureau.

The radar data are often contaminated by non-meteorological echoes such as ground clutter and biological echoes, which is also an important source of errors in the radar QPE (Lee, 2006; Huang et al., 2020). Therefore, the quality control method of single-polarization radar reflectivity developed by Zou et al. (2018) was used to remove these non-meteorological echoes. Since the radar echo is affected not only by clouds and precipitation, but also by atmospheric refraction and the radar beam side lobes, its changing structure is quite complex. Any single quality control method is insufficient to completely remove non-meteorological echoes. In the operational monitoring of strong convection, some non-meteorological echoes with echo-top heights between 2.0 and 2.5 km usually appeared over the high-altitude areas to the south of Nanchang. However, the echo-top height of precipitation echoes often exceeds 2.5 km during the rainy season (Zhang et al., 2004; Zou et al., 2018). Therefore, the radar reflectivity at points with an echo-top height less than 2.5 km was eliminated. Since the radar data are volume scan data in polar coordinates, for convenience, the nearest neighbor interpolation method on the azimuth-range plane and the linear interpolation method on the vertical plane were applied to convert the radar data from polar coordinates to a Cartesian coordinate with the horizontal resolution of 0.01°×0.01°.

Neural networks are excellent non-linear fitters and can perform accurate estimations through training and learning existing data (Li et al., 2019). Convolutional neural networks and the recurrent neural networks are the two most widely used neural networks. Convolutional neural networks are mainly applied in computer vision, while recurrent neural networks are proposed and widely used to process the time series of signals such as natural language and voice (Yang et al., 2017). The greatest advantage of recurrent neural networks is that they can store previous information. However, recurrent neural networks have a fatal trouble in long-term dependence, i.e., these neural networks can result in partial deviations in the final training results when the training data is far from the current time (Li et al., 2019). The LSTM neural network was developed to remedy this problem. It is controlled by three “doors”, i.e., forgetting, updating and outputting doors (Greff et al., 2017). The GRU neural network is a variant of the LSTM, but it has only two doors, i.e., update and reset doors. Due to the small number of doors, the computational effort of the GRU neural network is less than that of the LSTM neural network (Yang et al., 2017). Since the precipitation signal is continuous, and each signal is related to the radar data, the GRU neural network is selected to process precipitation signals in this study.

The schematic of the GRU neural network is shown in Fig. 2a. The gating units of the GRU neural network adjust the information flow inside the units without separating memory cells. The update door (z_t in Fig. 2a) controls the influence of the output hidden layer on the current hidden layer in the preceding time step and the number of updated units. The reset door (r_t in Fig. 2a) mainly determines how to combine the previous statement with the current input information (Mirzaei et al., 2022). A more significant value for the update gate means that more information is transferred to the next state cell, while a more significant value for the reset gate means that more details of the prior cell may be ignored. The mathematical relations of the GRU network structure are as follows (Eqs. 1–4; Li et al., 2019; Mirzaei et al., 2022).

Figure 2.  (a) The structure of GRU model and (b) the variations of radar beam height at different angles with the distance from radar station.

where $ \sigma $ denotes the sigmoid function and tanh represents the tanh function, r the rest gate vector, z the update gate vector, X the input vector, $ \widetilde {\boldsymbol{h}} $ the candidate activation vector, and h the output of the memory cell (the hidden state vector). W, V and b represent the parameter matrices and vector, and t indicates the time.

Radar reflectivity reflects the content of hydrometeors in the atmosphere, which correlates well with rainfall rate. Therefore, radar reflectivity is often regarded as an input variable to estimate rainfall rate by using machine learning methods (Kusiak et al., 2013; Kuang et al., 2016; Sehad et al., 2017; Kou et al., 2018; Wolfensberger et al., 2021). Besides, the echo-top height is a useful indicator of storm intensity and rainfall rate (Adler and Mack, 1984; Atlas et al., 1990). Wu et al. (2018) indicated that the correlation coefficient between the AWS rainfall and echo-top height is comparable to that between the AWS rainfall and radar reflectivity in the middle and lower reaches of the Yangtze River. Therefore, both radar composite reflectivity (maximum reflectivity for nine elevation angles) and echo-top height are considered as the two independent input variables of the GRU to estimate precipitation in this study. The specific process includes the following four steps.

(1) Normalize the data of hourly radar composite reflectivity, echo-top height and AWS rainfall rate by the following formula (Eq. 5).

where $ {x}_{i} $ and $ {\tilde x_i} $ respectively represent the normalized and original data at ith rain gauge, and $ {x}_{\mathrm{m}\mathrm{a}\mathrm{x}} $ and $ {x}_{\mathrm{m}\mathrm{i}\mathrm{n}} $ denote the maximum and minimum values at all AWS stations during May–July in 2017–19. The normalized variables are all in the range from −1 to 1.

(2) Construct the GRU dataset $\text{D}=({(}{\varphi }_{\text{1}}{,}{Q}_{1}), ({\varphi }_{{2}}{,}{Q}_{2}), ({\varphi }_{\text{3}}{,}{Q}_{3}{), }\mathrm{...}{, (}{\varphi }_{N}{,}{Q}_{N}{))}$. Among them, $ {\phi _k} = [{\text{C}}{{\text{R}}_{i,j}},{\text{ E}}{{\text{T}}_{i,j}}] $ represents the input data of the GRU, where CR_i,j and ET_i,j indicate the hourly mean radar composite reflectivity and echo-top height at the ith (i=1, 2, 3, ..., n) rain gauge and jth (j=1, 2, 3, ..., m) time. Q_k=[R_i,j] denotes the hourly AWS cumulative rainfall (the observed precipitation) at the same location and time. $ N = n \times m $ depicts the total samples in the study area and time period. Note that the echo-top height is defined as the maximum height of echo exceeding 18 dBZ, and calculated by the improved method of Lakshmanan et al (2013). The composite reflectivity rather than reflectivity at a fixed angle/height is selected as the input variable because of its wide coverage and good ability to capture rain signals.

(3) Choose mean squared error loss function, 4 neurons and Adam optimization algorithm which is the update of the RMSprop optimizer; it can dynamically adjust the learning rate of each parameter by using first- and second-order moment estimations. The data in May–July of 2019 is used to train the GRU model, and the data in early June of 2017 is used as validation data in the training process. The data in May-July of 2019 rather than that in May-July of 2018 or 2017 as training data was chosen because there were more rainfall events in 2019 in the study area.

(4) Use the trained GRU model to produce the normalized values of the radar QPE from May to July in 2018 and 2019. These normalized values are inversely transformed to the results of the radar QPE by the following expression (Eq. 6).

The height of radar beam is jointly affected by elevation angle, earth curvature and atmospheric refraction. The expression of radar beam height in the standard atmosphere is given as (Zhang et al., 2005).

where L represents the distance of the radar beams, $ \theta $ the elevation angles and R_W (8500 km) the equivalent earth radius. The variation of the radar beam height with distance at different elevation angles is shown in Fig. 2b based on Eq. (7). Obviously, when the distance is less than about 35 km, the maximum height detected by radar is less than 12.5 km, indicating that the echo-top height is also less than 12.5 km. At a distance exceeding 120 km, only one elevation angle has an altitude below 4 km, and the height interval between two elevation angles is more than 2 km, resulting in a low resolution of echo-top data in the vertical direction. Therefore, the data (CR, ET and R) in the annular region with the distance between 35 km and 120 km from radar site (Fig. 1b) were used to train and test the GRU model.

With the development of urbanization, Nanchang City has witnessed an astonishing proliferation of high-rise buildings in recent years. Meanwhile, Meiling Mountains, with the maximum altitude exceeding 500 m, is about 30 km to the northwest of the Nanchang radar station. These tall buildings and Meiling Mountains often block the radar beams at 0.5° or even 1.5° elevation angles. The gray sector shaded areas in Fig. 1b represent the anomalous low-frequency regions with radar reflectivity above 20 dBZ at 0.5° elevation angle in May–July of 2019, which is mainly induced by the radar beam blocking. In these areas, the rainfall rate may not be correlated with radar reflectivity and echo-top height. Therefore, the data in these blocking areas are excluded before training the GRU model. After eliminating the data at the distance from radar less than 35 km and more than 120 km and the data in the blocking areas, a total of 21721 samples are selected to train the GRU model.

In section 3.1, we proposed a new method (GRU_Z-ET) based on the GRU neural network and two independent variables (radar reflectivity and echo-top height) to conduct the QPE. This method takes into account both the content of hydrometeors in the atmosphere (radar reflectivity) and the ascending motion in storms (echo-top height), which is expected to improve the accuracy of radar QPE. In order to evaluate the performance of this method, the QPE results derived by the GRU_Z-ET proposed in this research and three other methods are compared with the observed precipitation at AWSs in this section. The three other methods are listed below.

(1) WSR-88D system and CINRAD system. The Z-R relationship in the two systems is Z=300R^1.4 (ZR_WSR).

(2) A GRU neural network with only one independent input variable of radar reflectivity (GRU_Z), and setting GRU NN to be the same as that of GRU_Z-ET.

(3) Z-R relationship optimizing method (ZR_OPT). The Z-R relationship is obtained from the optimizing method based on the hourly radar reflectivity and AWS rainfall in the study area during May–July of 2019. The optimizing method is as follows.

where CTF indicates the goal function, Z the radar reflectivity (dBZ), O_i the observed rainfall at the ith AWS, and n the total sample number of precipitation stations in May–July of 2019. When CTF is at a minimum, the corresponding a and b are the solutions of the optimizing method. In order to obtain the minimum CTF, a is adjusted from 1 to 1200 at the interval of 1, and b is adjusted from 1 to 3 at an interval of 0.01. After calculation, we find that a = 79 and b = 1.68 are the solutions. Therefore, the Z-R relationship used by the ZR_OPT method is Z=79R^1.68.

To assess the performance of the above four methods to produce radar QPE, the AWS rainfall was taken as the reference, and pertinent performance metrics are required. The root mean square error (RMSE) and relative RMSE (RRMSE) were applied to evaluate the overall accuracy of radar QPE, and their expressions (Duan et al., 2013) are as follows (Eq. 9 and Eq.10) .

where n is the sample number, H_i denotes the QPE value at ith sample obtained from different methods. RMSE reflects the overall deviation of the QPE results from the observations. The smaller the RMSE values, the higher the QPE accuracy. Moreover, in order to further assess the spatial distribution and the heavy-rainfall estimation skill of radar QPE results from different methods, the spatial correlation coefficient (CORR), threat score (TS), and probability of detection (POD) were calculated for the individual rainfall events, according to (Zou et al., 2019; Zhang et al., 2020c):

where m denotes the number of stations with a rainfall rate of ≥1 mm h⁻¹ in a rainfall event, and n_s, n_f and n_m indicate the number of stations with successful, false and missing estimations, respectively. The thresholds for identifying the rainfall rate at a station to be correctly estimated are set as 10 mm h⁻¹ and 20 mm h⁻¹, respectively.

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.

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).

Figure 5.  As in Fig. 4, except for 0300 UTC 20 June 2018.

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 6.  As in Fig. 4, except for 1000 UTC 19 June 2018.

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.

Figure 8.  The (a) RMSE and (b) relative RMSE of radar QPE obtained from different methods for different intensities of precipitation.

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.

Figure 10.  As in Fig. 9 but for POD score.

A new method for the QPE of single-polarization radar, GRU_Z-ET, was proposed in this study. This method is based on the GRU neural network, which is a variant of the LSTM neural network. The radar reflectivity and echo-top height were selected as the two independent variables to feed the GRU model. After removing the data at distances from the radar station less than 35 km and greater than 120 km and the data in the blocking areas of the radar beam at 0.5° elevation angle, a total of 21721 samples in May–July of 2019 were applied to train the GRU model. In order to assess the performance of the GRU_Z-ET on the QPE, it was compared with the other three methods, namely the Z-R relationship of Z=300R^1.4 used in the WSR-88D and CINRAD systems (ZR_WSR), the Z-R relationship (i.e., Z=79R^1.68) obtained by the optimizing method based on the data in May–July of 2019 (ZR_OPT) and the GRU neural network with only radar reflectivity as the independent input variable (GRU_Z).

To test the four methods, we selected three cases, i.e., two short-term heavy rainfall events with rainfall rates of more than 40 mm h⁻¹ at 2300 UTC 5 July and 0300 UTC 20 June 2018 and one scattered and isolated convective rainfall event with a rainfall rate of more than 20 mm h⁻¹ at 1000 UTC 19 June 2018. The results show that the estimates from all four methods can reasonably reproduce the three rainfall events. However, the radar QPE values from the GRU_Z-ET are the largest and closest to the observed rainfall, while the ZR_WSR has the smallest QPE values and remarkably underestimates the rainfall. The radar QPE values from the GRU_Z and ZR_OPT are quite similar in spatial distribution and rainfall intensity, and the two methods also underestimate the rainfall.

Moreover, 200 rainfall events from May to July in 2018 with a total sample number of 21882 were collected to further evaluate the performance of the proposed GRU_Z-ET and the other three methods. Note that the number of stations with an hourly rainfall of ≥1 mm is more than 30 in each rainfall event. The results indicate that the RMSE values of the GRU_Z-ET, GRU_Z, ZR_OPT and ZR_WSR estimates are 7.04 mm h⁻¹, 7.41 mm h⁻¹, 7.49 mm h⁻¹ and 8.6 mm h⁻¹, respectively, suggesting that the performance of the GRU_Z-ET is the best for the QPE (especially for the rainfall intensity > 5 mm h⁻¹), while the ZR_WSR performs the worst. The CORR, TS and POD were calculated for individual rainfall events. The mean CORR values of 200 rainfall events are 0.59, 0.54, 0.53 and 0.39 for the GRU_Z-ET, GRU_Z, ZR_OPT and ZR_WSR, respectively, implying the best performance for GRU_Z-ET in estimating the spatial distribution of precipitation. The TS and POD of the GRU_Z-ET at thresholds of 10 mm h⁻¹ and 20 mm h⁻¹ are the largest, while those of the ZR_WSR are the smallest, and those of the ZR_OPT are slightly greater than those of the GRU_Z. This suggests that the GRU_Z-ET still performs the best in estimating heavy precipitation, and the performance of the ZR_OPT is comparable with that of the GRU_Z. Overall, the GRU_Z-ET has the best performance on the radar QPE among the four methods.

In summary, the GRU_Z-ET method proposed in this study can improve the accuracy of the radar QPE for rainfall intensity exceeding 5 mm h⁻¹. However, it is not suitable for use in areas close to the radar station due to the limitation of the detected echo-top height. Meanwhile, in areas far from the radar station, the method is also not applicable due to the low resolution of echo-top data in vertical direction. Fortunately, new CINRAD radars have been deployed in China recently. In most parts of eastern, southern and central China (e.g., the study area), the horizontal resolution of the radar station is about 100 km. Therefore, through the technique of multiple-radar reflectivity mosaics (Zhang et al., 2005), a 3D reflectivity mosaic data can be obtained. This can provide multiple layers of reflectivity data in areas close to a radar station and far from a radar station, which can solve the limitation of echo-top height in areas close to radar stations and improve the vertical resolution of echo-top data in areas far from radar stations. Moreover, the 3D reflectivity mosaic data can also provide the reflectivity in regions where the beam of some radars is blocked. Therefore, the single-radar data should be replaced by a multiple-radar mosaic data in future work. Additionally, the fusion of the radar QPE, satellite QPE and rain-gauge observations should be considered because the fusion QPE of multiple sources has better quality than any single-source data.

Acknowledgements. We thank two anonymous reviewers for insightful comments that guided the revision of the manuscript, Meteorological Information Center of Jiangxi Meteorological Bureau for collecting and providing the single-polarization radar and automatic weather station data, and Nanjing Hurricane Translation for reviewing the English language quality of this paper. This work was jointly supported by the National Science Foundation of China (Grant Nos. 42275007 and 41865003) and Jiangxi Provincial Department of science and technology project (Grant No. 20171BBG70004).