Study on Radar Echo-Filling in an Occlusion Area by a Deep Learning Algorithm

: Radar beam blockage is an important error source that affects the quality of weather radar data. An echo-ﬁlling network (EFnet) is proposed based on a deep learning algorithm to correct the echo intensity under the occlusion area in the Nanjing S-band new-generation weather radar (CINRAD/SA). The training dataset is constructed by the labels, which are the echo intensity at the 0.5 ◦ elevation in the unblocked area, and by the input features, which are the intensity in the cube including multiple elevations and gates corresponding to the location of bottom labels. Two loss functions are applied to compile the network: one is the common mean square error ( MSE ), and the other is a self-deﬁned loss function that increases the weight of strong echoes. Considering that the radar beam broadens with distance and height, the 0.5 ◦ elevation scan is divided into six range bands every 25 km to train different models. The models are evaluated by three indicators: explained variance ( EVar ), mean absolute error ( MAE ), and correlation coefﬁcient ( CC ). Two cases are demonstrated to compare the effect of the echo-ﬁlling model by different loss functions. The results suggest that EFnet can effectively correct the echo reﬂectivity and improve the data quality in the occlusion area, and there are better results for strong echoes when the self-deﬁned loss function is used.


Introduction
Weather radar is an important means of cloud precipitation physics research and precipitation monitoring and early warning. It is widely used in meteorological operational observations and research. Radar detection capability is affected not only by the radar hardware parameters but also by the topography and tall buildings around the radar station [1]. Terrain blockage results in a radar observation blind area, which causes a reduction in the radar beam power and further influences the multiradar mosaic and other radar secondary products, such as quantitative precipitation estimation (QPE), which depends on echo intensity [2,3]. Therefore, blocking correction is important to improve the accuracy of quantitative detection of weather radar.
At present, many beneficial studies have been performed on radar beam blocking. For example, beam blockage correction is based on a high-precision digital elevation model (DEM). The DEM is a kind of terrain model that expresses the spatial distribution of ground elevation. The DEM-based beam blockage correction method was based on the equations of radar beam propagation in a standard atmosphere proposed by Battan [4]. Some scholars correct reflectivity bias over the blockage zone by calculating the power loss of beam shielding in a standard atmosphere [5][6][7]. According to the occlusion rate calculated by the DEM, a filling method using the average value of gates is proposed, which can correct the echo data in the azimuth of a small blocking coefficient using the adjacent plan position indicator (PPI) in real time [8]. A correction method of partial beam blockage is discussed according to the valid data area calculated by the DEM in the constant altitude plan position indicator (CAPPI) [9]. Shakti et al. [10] proposed a modified DEM method by means of simply calculating the power loss of the received signal because of ground clutter, hardware calibration errors, etc. However, the above DEM-based beam blockage correction methods are mainly based on standard atmospheric conditions, which are not suitable for blockage correction of super-refraction. Furthermore, the emergence of new buildings and trees causes additional beam blocking, which makes it difficult to update DEM data in time. Therefore, some echo correction models that do not rely on DEMs have been addressed recently. Gou et al. [11] proposed a blocking region identification algorithm based on the echo probability features and not dependence on DEM, in which the partial occlusion echoes are removed first and then corrected with multiradar mosaic data to eliminate the discontinuity of echo. According to the spatial correlation in adjacent azimuths, the echo data in adjacent radial and upper elevations are used for occlusion correction and linear interpolation is performed for partial occlusion or complete occlusion in a small area [12].
In addition, the vertical profiles of reflectivity (VPR) are utilized in beam blockage correction [13,14]. The mesoscale VPR retrieved by rainfall data within 70 km and by radar reflectivity are performed to correct the blockage, and the correction scheme is verified by comparing radar QPE with gauge measurements [15]. An optimal match method is suggested on the basis of the echo uniformity to calculate the VPR in different areas. The VPR in the occlusion area is matched with the average VPR in multiple nonocclusion areas, and these average VPRs are further matched with rain gauges to obtain the optimal reflectivity, which is utilized to fill the blocking echo corresponding to the gauges [16]. There are other VPR correction methods according to the occlusion orientation and degree calculated by the DEM. Andrieu et al. [17] and Creutin et al. [18] divided radar volume scan data into blocked and unblocked areas by means of the DEM and corrected the reflectivity in the blocked area with VPR generated from the unblocked areas. The echoes in lowelevation, completely blocked areas are filled by the data in high-elevation, unblocked areas using the statistical analysis of VPR, and the filling effect is evaluated by contrasting the reflectivity factor and radar QPE values before and after filling [19]. However, most of the above VPR technology is focused on large-scale precipitation processes dominated by stratiform clouds, the VPR correction method has its shortage since there are poor relationship between upper and lower reflectivity in an isolated convective storm with uneven internal distribution.
In recent years, artificial intelligence (AI) has been developing rapidly. In contrast to the traditional meteorological analysis method, deep learning, as the main AI algorithm, has an obvious advantage in dealing with nonlinear problems. Many studies have been performed with deep learning in the meteorological field, such as cloudage nowcasting [20], cloud-type classification [21], tropical cyclone intensity estimation [22], etc. Moreover, weather radar is a major means to examine the intensity of precipitation and distribution of weather systems, and combining it with a deep learning algorithm to process it will effectively improve rain nowcasting [23]. Recurrent neural networks (RNNs) are employed to capture spatiotemporal correlations from radar echo spatiotemporal sequences to obtain extrapolation vectors and to further predict the development and movement of radar echoes [24,25]. Tran et al. [26] presented an investigation into the problem of 3D radar echo extrapolation in precipitation nowcasting with recent AI advances and computer vision technology. Two neural network-based architectures, namely, a radar mosaic-based convolutional neural network (RMCNN) and a radar mosaic-based multilayer perceptron (RMMLP), are proposed to estimate typhoon rainfall [27]. Bouget et al. [28] trained a deep learning model on a fusion of rainfall radar images and wind velocity produced by a weather forecast model to determine whether using other meteorological parameters such as wind would improve forecasts.
The paper is organized as follows. In Section 2 of this paper, the construction steps of the training dataset are introduced in detail, which include data sources, preprocessing, and range splitting skills. In Section 3, an echo-filling network (EFnet) is proposed, which includes model network architecture design, self-defined loss function improvement, and hyperparameter setting. Six models are built by means of a training dataset and EFnet network. Two cases are tested to verify the filling models in Section 4. Finally, a summary and discussion of radar applications based on deep learning algorithms are presented in Section 5.

Data Sources
The radar data are observed with the Nanjing S-band new-generation Doppler weather radar (CINRAD/SA). The radar operates with a spatial resolution of 1 km × 1 • , and maximum detection range of 460 km, and it works with the volume scan mode of VCP21, which is performed every 6 min and 9 elevation layers (0.5 • , 1.5 • , 2.5 • , 3.5 • , 4.5 • , 6.0 • , 10.0 • , 15.0 • , and 19.5 • ). As shown in Figure 1, due to the influence of the surrounding geographical environment, there is serious terrain blockage in azimuths from 132 • to 137 • and from 220 • to 233 • in the 0.5 • elevation. The maximum blockage rate is larger than 0.75, and beam occlusion disappears with radar antenna lifting. The paper is organized as follows. In the second section of this paper, the construction steps of the training dataset are introduced in detail, which include data sources, preprocessing, and range splitting skills. In the third section, an echo-filling network (EFnet) is proposed, which includes model network architecture design, self-defined loss function improvement, and hyperparameter setting. Six models are built by means of a training dataset and EFnet network. Two cases are tested to verify the filling models in the fourth section. Finally, a summary and discussion of radar applications based on deep learning algorithms are presented in the last section.

Data Sources
The radar data are observed with the Nanjing S-band new-generation Doppler weather radar (CINRAD/SA). The radar operates with a spatial resolution of 1 km × 1°, and maximum detection range of 460 km, and it works with the volume scan mode of VCP21, which is performed every 6 min and 9 elevation layers (0.5°, 1.5°, 2.5°, 3.5°, 4.5°, 6.0°, 10.0°, 15.0°, and 19.5°). As shown in Figure 1, due to the influence of the surrounding geographical environment, there is serious terrain blockage in azimuths from 132° to 137° and from 220° to 233° in the 0.5° elevation. The maximum blockage rate is larger than 0.75, and beam occlusion disappears with radar antenna lifting.

Data Preprocessing
Data cleaning is a key process to ensure model accuracy and effectiveness before the training dataset is constructed. The quality control of radar base data is implemented to eliminate the pollution of ground clutter and other non-meteorological echoes [29][30]. Some thresholds which include echo intensity, radial velocity, and the vertical gradient of echo intensity are used to reduce the misjudgment of the meteorological echo [31]. The deep learning training dataset consists of labels and feature data. The labels are the conclusion that needs to be obtained, in which are the echo intensity at 0.5° elevation, and the feature data are the evidence for correction, in which are the intensity at the upper elevation corresponding to the location of labels. Therefore, atmospheric refraction should be considered when the ranges at different elevation angles are calculated.
In the ideal state, the electromagnetic wave propagates along a straight line. However, the propagation path is curved because of the uneven distribution of the refractive index in the atmosphere, which is the results of variation in temperature, pressure, and humidity with the height (Figure 2). To simplify the calculation, an equivalent earth radius is applied to support radar beam propagation as a straight line [32]. The relationship between the equivalent earth radius R' and atmospheric refractive index n is:

Data Preprocessing
Data cleaning is a key process to ensure model accuracy and effectiveness before the training dataset is constructed. The quality control of radar base data is implemented to eliminate the pollution of ground clutter and other non-meteorological echoes [29,30]. Some thresholds which include echo intensity, radial velocity, and the vertical gradient of echo intensity are used to reduce the misjudgment of the meteorological echo [31]. The deep learning training dataset consists of labels and feature data. The labels are the conclusion that needs to be obtained, in which are the echo intensity at 0.5 • elevation, and the feature data are the evidence for correction, in which are the intensity at the upper elevation corresponding to the location of labels. Therefore, atmospheric refraction should be considered when the ranges at different elevation angles are calculated.
In the ideal state, the electromagnetic wave propagates along a straight line. However, the propagation path is curved because of the uneven distribution of the refractive index in the atmosphere, which is the results of variation in temperature, pressure, and humidity with the height (Figure 2). To simplify the calculation, an equivalent earth radius is applied to support radar beam propagation as a straight line [32]. The relationship between the equivalent earth radius R and atmospheric refractive index n is: where R is the radius of earth (R = 6371 km) and h is the height of the radar beam from the ground. In the standard atmosphere, dn/dh is taken as −4 × 10 −8 m −1 , and Equation (1) is simplified as R ≈ 4/3 R. Therefore, the number of radial gates corresponding to each scan layer can be calculated as: where G is the gate number, h 0 is the antenna height from the ground, α is the equivalent geocentric angle (α = 4/3 a, where a is the geocentric angle), β is the elevation angle, and r is the radial resolution (r = 1 km). Through Equation (2), the reflectivity values at 0.5 • elevation can be obtained as labels, and N × 3 × 3 values within 3 radials, 3 gates, and N scan layers corresponding to the location of labels are outputted as features of the training dataset.
where R is the radius of earth (R = 6371 km) and h is the height of the radar beam from the ground. In the standard atmosphere, dn/dh is taken as −4 × 10 −8 m −1 , and Equation (1) is simplified as R' ≈ 4/3R. Therefore, the number of radial gates corresponding to each scan layer can be calculated as: where G is the gate number, h0 is the antenna height from the ground, α is the equivalent geocentric angle (α = 4/3a, where a is the geocentric angle), β is the elevation angle, and r is the radial resolution (r = 1 km). Through Equation (2), the reflectivity values at 0.5° elevation can be obtained as labels, and N × 3 × 3 values within 3 radials, 3 gates, and N scan layers corresponding to the location of labels are outputted as features of the training dataset. The reflectivity value is set to −20 dBZ when it is less than the radar detection sensitivity of −5 dBZ. If the value of the tag is −20 dBZ, this gate is not outputted into the training dataset. On the other hand, the data are also not appended to the dataset when all feature values are −20 dBZ. Then, the data are normalized into [0,1] by the min-max standardization method: where y and y' are the true and normalized values, respectively; the value of min is set to −20 dBZ, and the value of max is set to 70 dBZ.

Building the Training Dataset
Considering that the radar beam broadens with distance and altitude, only data within 150 km are built as models. The range in 0.5° elevation is divided into six sections The reflectivity value is set to −20 dBZ when it is less than the radar detection sensitivity of −5 dBZ. If the value of the tag is −20 dBZ, this gate is not outputted into the training dataset. On the other hand, the data are also not appended to the dataset when all feature values are −20 dBZ. Then, the data are normalized into [0,1] by the min-max standardization method: where y and y are the true and normalized values, respectively; the value of min is set to −20 dBZ, and the value of max is set to 70 dBZ.

Building the Training Dataset
Considering that the radar beam broadens with distance and altitude, only data within 150 km are built as models. The range in 0.5 • elevation is divided into six sections each 25 km, i.e., from 1 to 25, 25 to 50, 50 to 75, 75 to 100, 100 to 125, and 125 to 150 km. It can be seen from Figure 1 that the unblocked areas include azimuths from 0 • to 90 • and 300 • to 360 • in the Nanjing radar, so the two nonocclusion areas are selected to construct a training dataset of deep learning, where the echo reflectivity at 0.5 • elevation is taken as the labels, the reflectivity of N × 3 × 3 points consisting of 3 radials, 3 gates, and N scan layers are the input features, and N equals to 7, 6, 5, 4, 3, or 2 according to the distance of the section to the radar. A total of 114 volume scan data from April to July, 2012-2017, was selected, which is the rainy season in Nanjing. The data sizes in the six sections are listed in Table 1, which are split into a training set and a test set of 80% and 20% to build and test the echo-filling models, respectively.

Model Network Architecture Design
Deep learning is also called a multilayer neural network. Its basic architecture includes an input layer, multiple hidden layers, and an output layer. Activation functions are invented to solve the problem of gradient disappearance or explosion caused by too many hidden layers. The common activation functions include the sigmoid function, tanh, softmax, and ReLU. By means of the activation function, hidden layers, and nodes in each hidden layer, the neural network can fit a very complex nonlinear model and can describe a more detailed mapping relationship.
Considering fitting speed and effect, an EFnet is designed with three linear hidden layers after many tests. To avoid overfitting and enhance the generalization ability of the model, a dropout layer is added in each hidden layer, in which 20% of neurons are randomly discarded in each linear layer during forward propagation. The active functions select ReLU and sigmoid. The architecture of EFnet is shown in Figure 3 and the modeling flow chart is shown in Figure 4.
300° to 360° in the Nanjing radar, so the two nonocclusion areas are selected to construc a training dataset of deep learning, where the echo reflectivity at 0.5° elevation is taken a the labels, the reflectivity of N × 3 × 3 points consisting of 3 radials, 3 gates, and N sca layers are the input features, and N equals to 7, 6, 5, 4, 3, or 2 according to the distance o the section to the radar.
A total of 114 volume scan data from April to July, 2012-2017, was selected, which the rainy season in Nanjing. The data sizes in the six sections are listed in Table 1, whic are split into a training set and a test set of 80% and 20% to build and test the echo-fillin models, respectively.

Model Network Architecture Design
Deep learning is also called a multilayer neural network. Its basic architecture in cludes an input layer, multiple hidden layers, and an output layer. Activation function are invented to solve the problem of gradient disappearance or explosion caused by to many hidden layers. The common activation functions include the sigmoid function, tanh softmax, and ReLU. By means of the activation function, hidden layers, and nodes in eac hidden layer, the neural network can fit a very complex nonlinear model and can describ a more detailed mapping relationship.
Considering fitting speed and effect, an EFnet is designed with three linear hidde layers after many tests. To avoid overfitting and enhance the generalization ability of th model, a dropout layer is added in each hidden layer, in which 20% of neurons are ran domly discarded in each linear layer during forward propagation. The active function select ReLU and sigmoid. The architecture of EFnet is shown in Figure 3 and the modelin flow chart is shown in Figure 4.

Self-defined Loss Function
In the process of model training, the error E between the prediction and true value is calculated with the loss function, and then, the weight coefficient wj,k at each node in each hidden layer is adjusted through the optimizer during back propagation (Equation (5)).
,, , where wj,k are the weight coefficients at the k th node in the j th hidden layer and μ is the learning rate.
In essence, training a deep learning model minimizes a loss function whose value indicates how far away from perfection is a given dataset. For the regression problem, the mean square error (MSE, Equation (6)) is often used as the loss function: where ypred is the predicted value and ytrue is the true value. For weather forecasting and analysis, a strong echo is more instructive to disaster weather events. However, the points of strong echo are generally fewer than those of weak echo. In the dataset of the six sections, the proportion of strong echo (>40 dBZ) from near to far are 11.9%, 9.8%, 6.3%, 3.7%, 4.6%, and 4.3%, respectively. Additionally, the model accuracy will depend on weak echo with the training process when MSE is used as the loss function. Therefore, a self-defined loss function is proposed by increasing the weight of the strong echo and weak echo, which can improve the filling effect to the strong echo and reduce the accumulated error of the weak echo (Equation (7)).

Model Hyperparameters Setting and Training
Hyperparameters that cannot be adjusted automatically during the training process have an obvious influence on model accuracy, which includes the learning rate, optimizer, and the number of nodes of the input layer, output layer, hidden layer, iteration epochs, etc.
According to the features in each range section explained in Section 2.3, the node number of the input layer in each range section from near to far can be calculated as 63,

Self-Defined Loss Function
In the process of model training, the error E between the prediction and true value is calculated with the loss function, and then, the weight coefficient w j,k at each node in each hidden layer is adjusted through the optimizer during back propagation (Equation (4)).
where w j,k are the weight coefficients at the kth node in the jth hidden layer and µ is the learning rate.
In essence, training a deep learning model minimizes a loss function whose value indicates how far away from perfection is a given dataset. For the regression problem, the mean square error (MSE, Equation (5)) is often used as the loss function: where y pred is the predicted value and y true is the true value. For weather forecasting and analysis, a strong echo is more instructive to disaster weather events. However, the points of strong echo are generally fewer than those of weak echo. In the dataset of the six sections, the proportion of strong echo (>40 dBZ) from near to far are 11.9%, 9.8%, 6.3%, 3.7%, 4.6%, and 4.3%, respectively. Additionally, the model accuracy will depend on weak echo with the training process when MSE is used as the loss function. Therefore, a self-defined loss function is proposed by increasing the weight of the strong echo and weak echo, which can improve the filling effect to the strong echo and reduce the accumulated error of the weak echo (Equation (6)).

Model Hyperparameters Setting and Training
Hyperparameters that cannot be adjusted automatically during the training process have an obvious influence on model accuracy, which includes the learning rate, optimizer, and the number of nodes of the input layer, output layer, hidden layer, iteration epochs, etc.
According to the features in each range section explained in Section 2.3, the node number of the input layer in each range section from near to far can be calculated as 63, 54, 45, 36, 27, and 18. Since echo correction is a regression problem that predicts the reflectivity at 0.5 • elevation, the node number of the output layer is one.
Accounting for the convergence speed and loss error, through many experiments, the hyperparameters in EFnet are set as follows: learning rate 0.01; iteration epochs 100; Adam gradient descent optimizer; number of hidden layers 3; and nodes in the three hidden layers as 258, 128, and 64.
Three evaluation indicators, i.e., explained variance (EVar), mean absolute error (MAE), and correlation coefficient (CC), are adopted to evaluate the accuracy of echo-filling (Equations (7)-(9)): (9) Figure 5 shows the six scatter plots of actual and predicted echo reflectivity with the test dataset of each section, where the loss function of MSE is used in the training process. The red line is a linear trend line of scattered points. The color mark represents the Gaussian kernel density estimation of the scatter point (Equations (10) and (11)). The larger the value is, the denser the scatter point.
where x i are sample points, s > 0 is a smoothing parameter called the bandwidth or window, K(x) is the kernel function, and it is a Gaussian curve. As shown in Figure 5, owing to the radar beam broadens with distance and altitude, the error in the long-distance section is larger than that in the close-distance section. In general, the six range section models perform well using the test set except for the section from 125 to 150 km, and most of the points are on the diagonal. Table 2 lists the values of three evaluation indicators when models are compiled with the MSE as the loss function. The values of EVar in the models of sections from 1 to 75 km are above 0.85, and the others are all above 0.80. The MAEs are all 3-4 dB. For CCs, the values are all above 0.90 except for 0.88 in the section from 125 to 150 km. Therefore, all six echo-filling models using the MSE as the loss function have good performance and high accuracy. In Figure 5, the predicted strong echo is slightly lower than the measured value. Therefore, a self-defined loss function is proposed in Section 3.2 to improve the model fitting effect in the strong echo region. Figure 6 shows the scatter plot corresponding to Figure 5 but using the self-defined loss function, in which the strong echo points have  Table 3,  and a column chart of the comparison between Tables 2 and 3 is shown in Figure 7. The performance of model compiled with the self-defined loss function is slightly worse than that with MSE, in which the average value of MAE increases by 0.0646 and EVar and CC decrease by 0.0067 and 0.0019, respectively, and it is mainly because the model with self-defined loss function highlights the strong echoes more but the proportion of strong echo is relatively small in the test dataset.  Table 2 lists the values of three evaluation indicators when models are compiled with the MSE as the loss function. The values of EVar in the models of sections from 1 to 75 km are above 0.85, and the others are all above 0.80. The MAEs are all 3-4 dB. For CCs, the values are all above 0.90 except for 0.88 in the section from 125 to 150 km. Therefore, all six echo-filling models using the MSE as the loss function have good performance and high accuracy. In Figure 5, the predicted strong echo is slightly lower than the measured value. Therefore, a self-defined loss function is proposed in Section 3.2 to improve the model fitting effect in the strong echo region. Figure 6 shows the scatter plot corresponding to Figure 5 but using the self-defined loss function, in which the strong echo points have been obviously improved. The values of the evaluation indicator are listed in Table 3, and a column chart of the comparison between Table 2 and Table 3 is shown in Figure 7. The performance of model compiled with the self-defined loss function is slightly worse than that with MSE, in which the average value of MAE increases by 0.0646 and EVar and CC decrease by 0.0067 and 0.0019, respectively, and it is mainly because the model with selfdefined loss function highlights the strong echoes more but the proportion of strong echo is relatively small in the test dataset.

Comparing with Multivariable Linear Regression Models
In order to verify the advantages of deep learning algorithm, six multivariable linear regression models are established based on the same dataset as the EFnet but only N × 1 point are used as feature data instead of N × 3 × 3 points. Figure 8 shows the six scatter Remote Sens. 2021, 13, 1779 9 of 16 plots of actual and fitting echo reflectivity with the test dataset, it is obviously that the fitting effect with linear models are obviously worse than that with EFnet.  Figure 6. Scatter plot corresponding to Figure 5 but using the self-defined loss function. . Column chart of comparison between Table 2 and Table 3.

Comparing with Multivariable Linear Regression Models
In order to verify the advantages of deep learning algorithm, six multivariable linear regression models are established based on the same dataset as the EFnet but only N × 1 point are used as feature data instead of N × 3 × 3 points. Figure 8 shows the six scatter plots of actual and fitting echo reflectivity with the test dataset, it is obviously that the fitting effect with linear models are obviously worse than that with EFnet.

Case Study
Two volume scan data points observed with Nanjing CINRAD/SA radar are selected to verify the six models in different sections, which are trained and tested in Section 3.

Case Study
Two volume scan data points observed with Nanjing CINRAD/SA radar are selected to verify the six models in different sections, which are trained and tested in Section 3. One of them demonstrated in Section 4.1 is dominated by the weak echoes at 0002 UTC on 2 July 2017, and the other in Section 4.2 is dominated by strong echoes at 1008 UTC on 3 July 2012. The outputs of the model are evaluated with the true value of reflectivity in the unblocked fan-shaped area, which is bounded by red lines in Figure 9 and Figure 13. are prediction images by means of models compiled with the MSE and the self-defined loss function, respectively, in which the distance circle is 25 km (the same below), the red ellipse is the serious occlusion area, and the blue ellipse is one of the strong echo areas. Table 4. Values of the evaluation indicator in the nonocclusion area of Figure 9 with weak echoesdominated volume data. As shown in Figure 9a, the case is dominated by weak echoes in which most echo intensity is less than 40 dBZ, and there is obvious terrain blockage in the third quadrant, which is marked with an ellipse of a red line in which the echoes are obviously weak and even disappear completely. Both the models with the MSE and the self-defined loss function can fill the echoes in the occlusion area well and effectively improve the echo structure to make it more accurate. Furthermore, the strong echoes area marked with the blue ellipse is more consistent between the raw data and the prediction with the self-defined loss function (Figure 9c) than with the MSE (Figure 9b). In other words, the model with the self-defined loss function is better than that with the MSE in fitting strong echoes.
In order to demonstrate the filling effect more clearly, three radial profiles at the blocked azimuth 215° in Figure 9 are shown in Figure 10, in which image (a) is the raw data and (b) and (c) are the corrected data with the MSE and the self-defined loss function, respectively. Both the models can correct the 0.5° occlusion well and make the vertical structure of cloud more complete. In the strong echoes area (red ellipse area), the filling echoes with the self-defined loss function are stronger than that with the MSE, which realizes the purpose of highlighting the strong echo.

Weak Echoes-Dominated Case
The weak echoes-dominated volume data are arranged in the input format of the models and put into the models, and then, the predicted values of reflectivity in each section of 0.5 • elevation are outputted by means of the model fitting. Figure 9 shows the plan position indicator (PPI) images of reflectivity at 0.5 • elevation, where Figure 9a shows the raw observed image and Figure 9b,c shows prediction images by means of models that are compiled with the MSE and the self-defined loss function, respectively. Table 4 lists the evaluation results of models with two loss functions in the nonocclusion fan-shaped area, which are bounded by red lines in Figure 9. Table 4. Values of the evaluation indicator in the nonocclusion area of Figure 9 with weak echoes-dominated volume data. As shown in Figure 9a, the case is dominated by weak echoes in which most echo intensity is less than 40 dBZ, and there is obvious terrain blockage in the third quadrant, which is marked with an ellipse of a red line in which the echoes are obviously weak and even disappear completely. Both the models with the MSE and the self-defined loss function can fill the echoes in the occlusion area well and effectively improve the echo structure to make it more accurate. Furthermore, the strong echoes area marked with the blue ellipse is more consistent between the raw data and the prediction with the selfdefined loss function (Figure 9c) than with the MSE (Figure 9b). In other words, the model with the self-defined loss function is better than that with the MSE in fitting strong echoes.

Range
In order to demonstrate the filling effect more clearly, three radial profiles at the blocked azimuth 215 • in Figure 9 are shown in Figure 10, in which image (a) is the raw data and (b) and (c) are the corrected data with the MSE and the self-defined loss function, respectively. Both the models can correct the 0.5 • occlusion well and make the vertical structure of cloud more complete. In the strong echoes area (red ellipse area), the filling echoes with the self-defined loss function are stronger than that with the MSE, which realizes the purpose of highlighting the strong echo. The values of the model evaluation indicator for the case are listed in Table 4. The EVars of the two models are all above 0.85, the MAEs are approximately 4 dB, and the CCs are above 0.9 and even greater than 0.97 when using the self-defined loss function in the range from 25 to 50 km, which illustrates the effectiveness of the models quantitatively. Comparing the values in Table 4, the performance of model compiled with the selfdefined loss function is slightly better than that with MSE, in which the average value of EVar increases by 0.0111, MAE and CC decrease by 0.2356 and 0.0087, respectively, and it is mainly because the proportion of strong echoes in the case is higher than that in the test dataset. Figures 11 and 12 show the scatter plots of the predicted and true reflectivity in the unblocked area in each section model compiled with the MSE and the self-defined loss function, respectively. Most of the points are near the diagonal, which illustrates that the models perform well. The values of the model evaluation indicator for the case are listed in Table 4. The EVars of the two models are all above 0.85, the MAEs are approximately 4 dB, and the CCs are above 0.9 and even greater than 0.97 when using the self-defined loss function in the range from 25 to 50 km, which illustrates the effectiveness of the models quantitatively.
Comparing the values in Table 4, the performance of model compiled with the self-defined loss function is slightly better than that with MSE, in which the average value of EVar increases by 0.0111, MAE and CC decrease by 0.2356 and 0.0087, respectively, and it is mainly because the proportion of strong echoes in the case is higher than that in the test dataset. Figures 11 and 12 show the scatter plots of the predicted and true reflectivity in the unblocked area in each section model compiled with the MSE and the self-defined loss function, respectively. Most of the points are near the diagonal, which illustrates that the models perform well.

Strong Echoes-Dominated Case
The strong echoes-dominated volume data are reshaped into the input format of each range section model, and then the values of reflectivity at 0.5 • elevation are fitted by means of the models. Figure 13 shows the PPI images corresponding to Figure 9 except for the strong echoes. Similarly, Table 5 lists the evaluation indicators in the nonocclusion fan-shaped area bounded by red lines in Figure 13. Table 5. Values of the evaluation indicator in the nonocclusion area of Figure 13 with strong echoes-dominated volume data. EVar increases by 0.0111, MAE and CC decrease by 0.2356 and 0.0087, respectively, and is mainly because the proportion of strong echoes in the case is higher than that in the t dataset. Figures 11 and 12 show the scatter plots of the predicted and true reflectivity in unblocked area in each section model compiled with the MSE and the self-defined l function, respectively. Most of the points are near the diagonal, which illustrates that models perform well.  Scatter plots corresponding to Figure 11 but using the self-defined loss function.

Strong Echoes-Dominated Case
The strong echoes-dominated volume data are reshaped into the input format of each range section model, and then the values of reflectivity at 0.5° elevation are fitted by means of the models. Figure 13 shows the PPI images corresponding to Figure 9 except for the strong echoes. Similarly, Table 5 lists the evaluation indicators in the nonocclusion fan-shaped area bounded by red lines in Figure 13. As shown in Figure 13, the shapes of the strong echo marked with the blue ellipse are basically consistent among the three PPIs, and the consistency between Figure 13a,c is better, which further illustrates that the self-defined loss function performs better on strong echo fitting. The points number of strong echo (>40 dBZ) in Figure 11 are counted. There are 1807 points (3.37%) in the actual PPI (Figure 13a), 1740 points (3.24%) in the PPI predicted with the MSE loss function model (Figure 13b) and 1841 points (3.43%) with the self-defined loss function model (Figure 13c), and the proportion of strong echo with the self-defined loss function is closer to that of raw observation.
In order to further verify the performance in strong echo area with the self-defined loss function, three radial profiles at the unblocked azimuth 48 • in Figure 13 are plotted in Figure 14. As shown in the red ellipse area in the 0.5 • elevation, comparing with the raw data (a), the strong echoes with the self-defined loss function (c) are more consistent than that with the MSE (b), which demonstrate that the model with the self-defined loss function is better than that with the MSE for fitting strong echoes.

Strong Echoes-Dominated Case
The strong echoes-dominated volume data are reshaped into the input format of each range section model, and then the values of reflectivity at 0.5° elevation are fitted by means of the models. Figure 13 shows the PPI images corresponding to Figure 9 except for the strong echoes. Similarly, Table 5 lists the evaluation indicators in the nonocclusion fan-shaped area bounded by red lines in Figure 13.  Table 5. Values of the evaluation indicator in the nonocclusion area of Figure 13 with strong echoes-dominated volume data. As shown in Figure 13, the shapes of the strong echo marked with the blue ellipse are basically consistent among the three PPIs, and the consistency between Figure 13a,c is better, which further illustrates that the self-defined loss function performs better on strong echo fitting. The points number of strong echo (>40 dBZ) in Figure 11 are counted. There are 1807 points (3.37%) in the actual PPI (Figure 13a), 1740 points (3.24%) in the PPI predicted with the MSE loss function model (Figure 13b) and 1841 points (3.43%) with the self-defined loss function model (Figure 13c), and the proportion of strong echo with the self-defined loss function is closer to that of raw observation. In order to further verify the performance in strong echo area with the self-defined loss function, three radial profiles at the unblocked azimuth 48° in Figure 13 are plotted in Figure 14. As shown in the red ellipse area in the 0.5° elevation, comparing with the raw data (a), the strong echoes with the self-defined loss function (c) are more consistent than that with the MSE (b), which demonstrate that the model with the self-defined loss function is better than that with the MSE for fitting strong echoes. However, for weak echoes in the northwest direction beyond 100 km, the reflectivity estimated by the model is obviously stronger than that measured by the Nanjing radar. It is well known that the beam broadens and the echo intensity weakens with increasing distance from the radar. To compare filling effect, the reflectivity observed simultaneously with the Bengbu SA radar, which is located at Nanjing SA radar azimuth 303.5° and distance of 142.5 km (the red triangle in Figure 15), is interpolated to the gates of the Nanjing radar ( Figure 15). It can be seen from the area marked with a rectangle of red lines in Figure 15 that the weak echoes observed with the Bengbu radar are obviously stronger than those observed with the Nanjing radar because of the distance. On the other hand, the echo predicted by the model is affected by the melting layer in far distance, so this strong echo area may be due to the insufficient melting layer data collected in the training dataset, which causes strong fitting results.
In Table 5, the EVars are all above 0.92 except for the models of the first range section from 1 to 25 km, the MAEs are less than 4.5 dB, and the CCs are greater than 0.96 except for the first section, which further verifies the effectiveness and stability of the deep learning algorithm applied to the echo correction. Comparing the values of the model evaluation indicator compiled with the self-defined loss function and MSE in Table 5, the average value of MAE decreases 0.1085 and EVar and CC increase 0.0023 and 0.0017, respectively, which suggests that the models with the self-defined loss function perform better. However, for weak echoes in the northwest direction beyond 100 km, the reflectivity estimated by the model is obviously stronger than that measured by the Nanjing radar. It is well known that the beam broadens and the echo intensity weakens with increasing distance from the radar. To compare filling effect, the reflectivity observed simultaneously with the Bengbu SA radar, which is located at Nanjing SA radar azimuth 303.5 • and distance of 142.5 km (the red triangle in Figure 15), is interpolated to the gates of the Nanjing radar ( Figure 15). It can be seen from the area marked with a rectangle of red lines in Figure 15 that the weak echoes observed with the Bengbu radar are obviously stronger than those observed with the Nanjing radar because of the distance. On the other hand, the echo predicted by the model is affected by the melting layer in far distance, so this strong echo area may be due to the insufficient melting layer data collected in the training dataset, which causes strong fitting results.
In Table 5, the EVars are all above 0.92 except for the models of the first range section from 1 to 25 km, the MAEs are less than 4.5 dB, and the CCs are greater than 0.96 except for the first section, which further verifies the effectiveness and stability of the deep learning algorithm applied to the echo correction. Comparing the values of the model evaluation indicator compiled with the self-defined loss function and MSE in Table 5, the average value of MAE decreases 0.1085 and EVar and CC increase 0.0023 and 0.0017, respectively, which suggests that the models with the self-defined loss function perform better.  Figure 13 observed with the Nanjing radar (a) and interpolated with the Bengbu radar (b), where the red triangle is the location of the Bengbu radar.

Discussion
An EFnet based on a deep learning algorithm is used to fill and correct the ra reflectivity in the occlusion area at the 0.5° elevation angle, and a self-defined loss func is proposed to improve the model fitting in strong echoes. The training dataset is structed with the data in unblocked areas in the Nanjing SA radar; six echo-filling mo are built according to the range, and three indicators are utilized to evaluate the mod Whether from the subjective impression of the PPI images or from the quantitative a ysis of the indicator tables, the results show that the low-level occlusion reflectivity been corrected very well. This shows that deep learning has broad prospects in wea radar applications.
In the process of model training, data preprocessing, namely, data quality con and normalization, is a critical step. Other superparameter settings, such as the loss f tion, optimizer, number of hidden layers, nodes, and iteration epochs, also have a sig cant impact on the fitting effect to models, which needs to be adjusted and tested rep edly.
Although the number of training datasets in this paper reaches approxima 200,000, it is still relatively small. In practical applications, the number of radar vol scan data can be greatly increased to make the training dataset reach more than sev million, and the models will achieve a better fitting effect. In addition, more data of st precipitation echo should be added into the training datasets to further improve the in ence of melting layer.
When multiple elevation angles are blocked, the echo-filling model can be simil established using deep learning. Compared with using only a single parameter of th flectivity factor as input, the polarimetric parameters can be added as input features the training data with the polarization upgrading of weather radar, which will effecti improve the effect of echo correction, and the polarization parameters can also be rected by a similar deep learning network. In addition, some features, such as terr underlying surface information, and weather background, can also be applied to const a multimodal model, which is a popular method for deep learning training at pres These means can achieve refined, intellectualized, and automatic echo correction for ra beam blockage.   Figure 13 observed with the Nanjing radar (a) and interpolated with the Bengbu radar (b), where the red triangle is the location of the Bengbu radar.

Discussion
An EFnet based on a deep learning algorithm is used to fill and correct the radar reflectivity in the occlusion area at the 0.5 • elevation angle, and a self-defined loss function is proposed to improve the model fitting in strong echoes. The training dataset is constructed with the data in unblocked areas in the Nanjing SA radar; six echo-filling models are built according to the range, and three indicators are utilized to evaluate the models. Whether from the subjective impression of the PPI images or from the quantitative analysis of the indicator tables, the results show that the low-level occlusion reflectivity has been corrected very well. This shows that deep learning has broad prospects in weather radar applications.
In the process of model training, data preprocessing, namely, data quality control and normalization, is a critical step. Other superparameter settings, such as the loss function, optimizer, number of hidden layers, nodes, and iteration epochs, also have a significant impact on the fitting effect to models, which needs to be adjusted and tested repeatedly.
Although the number of training datasets in this paper reaches approximately 200,000, it is still relatively small. In practical applications, the number of radar volume scan data can be greatly increased to make the training dataset reach more than several million, and the models will achieve a better fitting effect. In addition, more data of stable precipitation echo should be added into the training datasets to further improve the influence of melting layer.
When multiple elevation angles are blocked, the echo-filling model can be similarly established using deep learning. Compared with using only a single parameter of the reflectivity factor as input, the polarimetric parameters can be added as input features into the training data with the polarization upgrading of weather radar, which will effectively improve the effect of echo correction, and the polarization parameters can also be corrected by a similar deep learning network. In addition, some features, such as terrain, underlying surface information, and weather background, can also be applied to construct a multimodal model, which is a popular method for deep learning training at present. These means can achieve refined, intellectualized, and automatic echo correction for radar beam blockage.