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

remote sensing

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

Xiaoyan Yin 1, Zhiqun Hu 1,2,*, Jiafeng Zheng 1 , Boyong Li 1 and Yuanyuan Zuo 1

1 School of Atmospheric Sciences, Chengdu University of Information Technology, Chengdu 610225, China; [email protected] (X.Y.); [email protected] (J.Z.); [email protected] (B.L.); [email protected] (Y.Z.) 2 State Key Lab of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China * Correspondence: [email protected]

Abstract: 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 Citation: Yin, X.; Hu, Z.; Zheng, J.; the occlusion area, and there are better results for strong echoes when the self-defined loss function Li, B.; Zuo, Y. Study on Radar is used. Echo-Filling in an Occlusion Area by a Deep Learning Algorithm. Remote Keywords: deep learning; weather radar; beam blockage; echo-filling Sens. 2021, 13, 1779. https://doi.org/ 10.3390/rs13091779

Academic Editor: Andrzej Stateczny 1. Introduction Weather radar is an important means of cloud precipitation physics research and Received: 18 March 2021 precipitation monitoring and early warning. It is widely used in meteorological operational Accepted: 29 April 2021 Published: 2 May 2021 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

Publisher’s Note: MDPI stays neutral station [1]. Terrain blockage results in a radar observation blind area, which causes a with regard to jurisdictional claims in reduction in the radar beam power and further influences the multiradar mosaic and published maps and institutional affil- other radar secondary products, such as quantitative precipitation estimation (QPE), which iations. 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 Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. ground elevation. The DEM-based beam blockage correction method was based on the This article is an open access article equations of radar beam propagation in a standard atmosphere proposed by Battan [4]. distributed under the terms and Some scholars correct reflectivity bias over the blockage zone by calculating the power conditions of the Creative Commons loss of beam shielding in a standard atmosphere [5–7]. According to the occlusion rate Attribution (CC BY) license (https:// calculated by the DEM, a filling method using the average value of gates is proposed, which creativecommons.org/licenses/by/ can correct the echo data in the azimuth of a small blocking coefficient using the adjacent 4.0/). plan position indicator (PPI) in real time [8]. A correction method of partial beam blockage

Remote Sens. 2021, 13, 1779. https://doi.org/10.3390/rs13091779 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, 1779 2 of 16

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 low- elevation, 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 Section2 of this paper, the construction steps of the training dataset are introduced in detail, which include data sources, preprocessing, and range splitting skills. In Section3, an echo-filling network (EFnet) is proposed, which Remote Sens. 2021, 13, x FOR PEER REVIEW 3 of 17

Remote Sens. 2021, 13, 1779The paper is organized as follows. In the second section of this paper, the construc- 3 of 16 tion 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 includes model network architecture design, self-deﬁned loss function improvement, and improvement, and hyperparameter setting. Six models are built by means of a training hyperparameter setting. Six models are built by means of a training dataset and EFnet dataset and EFnetnetwork. network. Two Two cases cases are testedare tested to verify to verify the ﬁllingthe filling models models in Section in the4 fourth. Finally, a summary section. Finally,and a summary discussion and of radardiscussion applications of radar based applications on deep based learning on deep algorithms learning are presented in algorithms are Sectionpresented5. in the last section.

2. Construction2. of Construction the Training of D theataset Training Dataset 2.1. Data Sources2.1. Data Sources The radar dataThe are radar observed data are with observed the Nanjing with the NanjingS-band new S-band-generation new-generation Doppler Doppler weather weather radar radar(CINRAD/SA). (CINRAD/SA). The radar The operates radar operates with a spatial with a resolution spatial resolution of 1 km of× 1°, 1 km × 1◦, and and maximummaximum detection detectionrange of 460 range km, of and 460 km,it works and itwith works the with volume the volumescan mode scan of mode of VCP21, ◦ ◦ ◦ ◦ ◦ ◦ VCP21, which whichis performed is performed every 6 every min and 6 min 9 elevation and 9 elevation layers (0.5°, layers 1.5°, (0.5 2.5°,, 1.5 3.5°,, 2.5 4.5°,, 3.5 , 4.5 , 6.0 , ◦ ◦ ◦ 6.0°, 10.0°, 15.0°,10.0 and, 15.019.5°)., andAs shown 19.5 ). in As Figure shown 1, due in Figure to the1 influence, due to the of the inﬂuence surrounding of the surrounding ◦ ◦ geographical environment,geographical there environment, is serious there terrain is seriousblockage terrain in azimuths blockage from in azimuths 132° to 137° from 132 to 137 ◦ ◦ ◦ and from 220° toand 233° from in the 220 0.5°to 233elevation.in the The 0.5 maximumelevation. blockage The maximum rate is blockage larger than rate 0.75, is larger than 0.75, and beam occlusionand beam disappears occlusion with disappears radar antenna with radarlifting. antenna lifting.

(a) 1 (b) 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0

Figure 1. TransmittanceFigure 1. Transmittance of the Nanjing of the S-band Nanjing new-generation S-band new Doppler-generation weather Doppler radar weather (SA) at radar the elevation (SA) at anglethe of 0.5◦ (a) elevation angle of 0.5° (a) and 1.5° (b). and 1.5◦ (b).

2.2. Data Preprocessing2.2. Data Preprocessing Data cleaning isData a key cleaning process is to a keyensure process model to accuracy ensure model and effectiveness accuracy and before effectiveness the before the training datasettraining is constructed. dataset isThe constructed. quality control The of quality radar controlbase data of is radar implemented base data to is implemented eliminate the pollutionto eliminate of ground the pollution clutter of and ground other clutter non-meteorological and other non-meteorological echoes [29–30]. echoes [29,30]. Some thresholdsSome which thresholds include echo which intensity, include radial echo intensity,velocity, and radial the velocity, vertical gradient and the verticalof gradient echo intensity ofare echo used intensity to reduce are the used misjudgment to reduce of the the misjudgment meteorological of theecho meteorological [31]. The echo [31]. deep learning trainingThe deep dataset learning consists training of labels dataset and consists feature of data. labels The and labels feature are data. the con- The labels are the clusion that needsconclusion to be obtained, that needs in which to be obtained, are the echo in which intensity are at the 0.5° echo elevation, intensity and at 0.5 the◦ elevation, and feature data arethe the feature evidence data for are correctio the evidencen, in which for correction, are the intensity in which at the are upper the intensity eleva- at the upper tion correspondingelevation to the corresponding location of labels. to the Therefore, location of atmospheric labels. Therefore, refraction atmospheric should refractionbe should considered whenbe consideredthe ranges at when different the ranges elevation at different angles are elevation calculated. angles are calculated. In the ideal state,In the the ideal electromagnetic state, the electromagnetic wave propagates wave along propagates a straight along line. a straight How- line. However, ever, the propagationthe propagation path is curved path is because curved becauseof the uneven of the uneven distribution distribution of the refractive of the refractive index in index in the atmosphere,the atmosphere, which which is the isresults the results of variation of variation in temperature, in temperature, pressure, pressure, and and humidity humidity with withthe height the height (Figure (Figure 2). To2). simplify To simplify the calculation, the calculation, an equivalent an equivalent earth earth radius radius is applied is applied to supportto support radar radar beam beam propagation propagation as a straight as a straight line [32]. line [The32]. relationship The relationship be- between the tween the equivalentequivalent earth earth radius radius R’ andR0 andatmospheric atmospheric refractive refractive index index n is:n is:

R R0 = dn , (1) 1 + R dh

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R R  , Remote Sens. 2021, 13, 1779 dn 4 of(1 16) 1 R dh where R is the radius of earth (R = 6371 km) and h is the height of the radar beam from thewhere ground.R is the In the radius standard of earth atmosphere, (R = 6371 km) dn/ anddh is h taken is the as height −4 × of10− the8 m radar−1, and beam Equation from (1) the −8 −1 isground. simplified In the as R’ standard ≈ 4/3R. atmosphere,Therefore, thedn number/dh is taken of radial as − 4gates× 10 correspondingm , and Equation to each scan (1) is 0 ≈ layersimpliﬁed can be as calculatedR 4/3 Ras:. Therefore, the number of radial gates corresponding to each scan layer can be calculated as: 0 ((RRh+h00) )sinsinα GG= ,, (2) (2) rr·coscos((α+ β) )

where G is the gate number, h0 is the antenna height from the ground, α is the equivalent where G is the gate number, h0 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, geocentric angle (α = 4/3a, where a is the geocentric angle), β is the elevation angle, and r and r is the radial resolution (r = 1 km). Through Equation (2), the reﬂectivity values at is the radial resolution (r = 1 km). Through Equation (2), the reflectivity values at 0.5° 0.5◦ elevation can be obtained as labels, and N × 3 × 3 values within 3 radials, 3 gates, elevation can be obtained as labels, and N × 3 × 3 values within 3 radials, 3 gates, and N and N scan layers corresponding to the location of labels are outputted as features of the scan layers corresponding to the location of labels are outputted as features of the training training dataset. dataset.

β h

Figure 2. Sketch map of radar beam propagation in a standard atmosphere. The lower right corner Figure 2. Sketch map of radar beam propagation in a standard atmosphere. The lower right corner shows the 3 × 3 features, and the black point is the corresponding location of the label at the bottom. shows the 3 × 3 features, and the black point is the corresponding location of the label at the bottom. 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 The reflectivity value is set to −20 dBZ when it is less than the radar detection sensi- training dataset. On the other hand, the data are also not appended to the dataset when tivity of −5 dBZ. If the value of the tag is −20 dBZ, this gate is not outputted into the train- all feature values are −20 dBZ. Then, the data are normalized into [0,1] by the min-max ing dataset. On the other hand, the data are also not appended to the dataset when all standardization method: feature values are −20 dBZ. Then, the data arey0 −normalizedmin into [0,1] by the min-max stand- y = , (3) ardization method: max − min where y and y0 are the true and normalizedy values,  min respectively; the value of min is set to y  , (3) −20 dBZ, and the value of max is set to 70max dBZ. min where2.3. Building y and y’ the are Training the true Dataset and normalized values, respectively; the value of min is set to −20 dBZ,Considering and the value that the of radarmax is beam set to broadens 70 dBZ. 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 2.3.25 km,Building i.e., from the T 1raining to 25, 25Dataset to 50, 50 to 75, 75 to 100, 100 to 125, and 125 to 150 km. It can be seenConsidering from Figure 1 that that the the radar unblocked beam areas broadens include with azimuths distance from and 0 altitude,◦ to 90◦ and only 300 data◦ to within360◦ in 150 the km Nanjing are built radar, as somodels. the two The nonocclusion range in 0.5° areas elevation are selected is divided to construct into six a sections 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. Remote Sens. 2021, 13, x FOR PEER REVIEW 5 of 17

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 Remote Sens. 2021, 13, 1779 the section to the radar. 5 of 16 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 Asplit total into of 114a training volume set scan and data a fromtest set April of to80% July, and 2012–2017, 20% to build was selected, and test which the echo is -filling themodels, rainy seasonrespectively. in Nanjing. The data sizes in the six sections are listed in Table1, which are split into a training set and a test set of 80% and 20% to build and test the echo-ﬁlling models,Table 1. respectively. The data size in the six sections.

TableRange 1. The (km) data size in the six sections.1–25 25–50 50–75 75–100 100–125 125–150 Using elevation layer number 7 6 5 4 3 2 Range (km) 1–25Data size 25–50 (group) 50–75171,887 75–100 190,182 199,830 100–125 185,808125–150 201,990 182,676 Using elevation layer number 7Training set 6size (80%) 5137,510 4152,146 159,864 3 148,646 161,592 2 146,141 Data size (group) 171,887Test set 190,182 size (20%) 199,83034,377 185,808 38,036 39,966 201,990 37,162 182,67640,398 36,535 Training set size (80%) 137,510 152,146 159,864 148,646 161,592 146,141 Test set size (20%) 34,377 38,036 39,966 37,162 40,398 36,535 3. Building the Echo-Filling Model

3.3.1. Building Model theNetwork Echo-Filling Architecture Model Design 3.1. ModelDeep Network learning Architecture is also Designcalled a multilayer neural network. Its basic architecture in- cludesDeep an learning input layer, is also calledmultiple a multilayer hidden neurallayers, network. and an Itsoutput basic architecturelayer. Activation includes functions anare input invented layer, to multiple solve the hidden problem layers, of and gradient an output disappearance layer. Activation or explosion functions caused are by too inventedmany hidden to solve layers. the problem The common of gradient activation disappearance functions or explosion include causedthe sigmoid by too function, many tanh, hiddensoftmax, layers. and ReLU. The common By means activation of the activation functions includefunction, the hidden sigmoid layers, function, and tanh,nodes in each softmax,hidden andlayer, ReLU. the neural By means network of the activation can fit a very function, complex hidden nonlinear layers, and model nodes and in each can describe hidden layer, the neural network can fit a very complex nonlinear model and can describe a more detailed mapping relationship. a more detailed mapping relationship. ConsideringConsidering fitting fitting speed speed and and effect, effect, an EFnet an EFnet is designed is designed with three with linear three hidden linear hidden layerslayers after after many many tests. tests To. To avoid avoid overfitting overfitting and and enhance enhance the generalizationthe generalization ability ability of of the themodel, model, a dropout a dropout layer layer is is added added in eacheach hiddenhidden layer, layer, in in which which 20% 20% of neuronsof neurons are are ran- randomlydomly discarded discarded in eacheach linear linear layer layer during during forward forward propagation. propagation. The active The functions active functions selectselect ReLU ReLU and and sigmoid. sigmoid. The The architecture architecture of EFnet of EFnet is shown is sh inown Figure in3 Figure and the 3 modeling and the modeling flowflow chart chart is is shown shown in Figurein Figure4. 4.

Input Linear

Hidden layer1 Dropout 0.2

ReLU

Linear

Hidden layer2 Dropout 0.2

ReLU

Linear

Hidden layer3 Dropout 0.2

Sigmoid Ouput

FigureFigure 3. 3.Echo-ﬁlling Echo-filling network network (EFnet) (EFnet architecture.) architecture.

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Labels: the echo reflectivity in 0.5° Data preprocessing Spliting into six range elevation in the non-occlusion area Radar data Quality control sections each 25 km Features: the N×3×3 reflectivity in Normalization the corresponding upper layers

Modeling completed Evaluating the model loss Compiling EFnet and training models

Adjusting the loss function and hyper-parameters

Figure 4. ModelingFigure flow 4.chart.Modeling ﬂow chart.

3.2. Self Self-Deﬁned-defined L Lossoss F Functionunction 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 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(Equation (4)).(5)). E ()()ww ∂E (w )j,, k new= (w j) k old− µ ,, (4)(5) j,k new j,k old w ∂wj,kjk,

where wj,k are the weight coefficients at the kth node in the jth hidden layer and μ is the where wj,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 functionfunction whosewhose valuevalue indicates how far away from perfection is a given dataset. For the regression problem, the mean square error ((MSE,MSE, Equation (5))(6)) is often used as the lossloss function:function: n 1n 2 MSE1 () y y 2 , (6) MSE = (ypredpred− ytrue true) , (5) n∑i1 n i=1

where ypred is the predicted value and ytrue is the true value. where y is the predicted value and ytrue is the true value. Forpred weather forecasting and analysis, a strong echo is more instructive to disaster 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 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 echo. In the dataset of the six sections, the proportion of strong echo (>40 dBZ) from near to far are 11.9%,11.9%, 9.8%,9.8%, 6.3%,6.3%, 3.7%,3.7%, 4.6%,4.6%, and 4.3%, respectively. Additionally, thethe modelmodel accuracy willwill dependdepend onon weak weak echo echo with with the the training training process process when whenMSE MSEis used is used as the as lossthe lossfunction. function. Therefore, Therefore, a self-defined a self-defined loss loss function function is proposed is proposed by increasingby increasing the the weight weight of ofthe the strong strong echo echo and and weak weak echo, echo which, which can can improve improve the the filling filling effect effect to the to strongthe strong echo echo and andreduce reduce the accumulatedthe accumulated error error of the of weak the weak echo echo (Equation (Equation (6)). (7)). 1 n Ew1 n () y  y 2 , E = · (y pred− y true)2 (7) w n∑i1 pred true , (6) n i=1 where w equals [10, 5, 2, 5, 8, 10], which is a vector with different weight coefficients for where w equals [10, 5, 2, 5, 8, 10], which is a vector with different weight coefficients for different intervals of normalized echo reflectivity [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]. different intervals of normalized echo reflectivity [0.1, 0.2, 0.3, 0.4, 0.5, 0.6].

3.3. Model H Hyperparametersyperparameters S Settingetting and T Trainingraining Hyperparameters that cannot be adjusted automatically during the training process have an obvious influence inﬂuence on on model model accuracy, accuracy, which includes the the learning learning rate, rate, optimizer, optimizer, and the numbernumber ofof nodesnodes of of the the input input layer, layer, output output layer, layer, hidden hidden layer, layer, iteration iteration epochs, epochs, etc. etc. According to the features in each range section explained in Section 2.3, the node numberAccording of the input to the layer features in each in range each sectionrange section from near explained to far can in beSection calculated 2.3, the as 63,node 54, number of the input layer in each range section from near to far can be calculated as 63,

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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)): var(ypred − ytrue) EVar = 1 − (7) var(ytrue) n 1 MAE = ∑ ( ytrue − ypred ) (8) n i=1 n ∑ (ytrue − ytrue)(ypred − ypred) = CC = i 1 . (9) s n s n 2 2 ∑ (ytrue − ytrue) ∑ (ypred − ypred) i=1 i=1 Figure5 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.

n n ˆ 1 1 x − xi fs(x) = ∑ Ks(x − xi) = ∑ K( ) (10) n i=1 ns i=1 s

1 1 K(x) = √ exp(− x2), (11) 2π 2

where xi 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 Figure5, 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. Table2 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.

Table 2. Values of the evaluation indicator with the mean square error (MSE) as the loss function.

Range (km) 1–25 25–50 50–75 75–100 100–125 125–150 EVar 0.8717 0.8739 0.8555 0.8309 0.8256 0.7809 MAE 3.7340 3.3501 3.3028 3.1489 3.3989 3.7964 CC 0.9346 0.9340 0.9230 0.9142 0.9039 0.8846

In Figure5, 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. Figure6 shows the scatter plot corresponding to Figure5 but using the self-defined loss function, in which the strong echo points have Remote Sens. 2021, 13, 1779 8 of 16

been obviously improved. The values of the evaluation indicator are listed in Table3, and a column chart of the comparison between Tables2 and3 is shown in Figure7. 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 Remote Sens. 2021, 13, x FOR PEER REVIEW 8 of 17 self-deﬁned loss function highlights the strong echoes more but the proportion of strong echo is relatively small in the test dataset.

(a)1-25 (b)25-50 (c)50-75

(d)75-100 (e)100-125 (f)125-150

FigureFigure 5. ScatterScatter plots plots of ofthe the actual actual and andpredicted predicted echo echoreflectivity reﬂectivity with the with testthe dataset test of dataset each of each section,section, where where the the loss loss function function of mean of mean square square error error (MSE (MSE) is used) is during used during the training the training process. process. In Remote Sens. 2021,In which13, which x FOR the PEER thered redline REVIEW line denotes denotes a linear a linear trend trend line of line scattered of scattered points. points,, and color and mark color represents mark represents the the 9 of 17 Gaussian kernel density estimation of the scatter point. Gaussian kernel density estimation of the scatter point. Table 2 lists the values of three evaluation indicators when models are compiled with the MSE(a)1 as the-25 loss function. The values(b)25 of-50 EVar in the models of(c)50 sections-75 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.

Table 2. Values of the evaluation indicator with the mean square error (MSE) as the loss function.

Range (km) 1–25 25–50 50–75 75–100 100–125 125–150 EVar(d)75 -100 0.8717 0.8739(e)100 -1250.8555 0.8309 (f)1250.8256-150 0.7809 MAE 3.7340 3.3501 3.3028 3.1489 3.3989 3.7964 CC 0.9346 0.9340 0.9230 0.9142 0.9039 0.8846

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 FigureFigure 6. Scatter 6. Scatter plot correspondingplot corresponding to Figure to Figure5 but 5 usingbut using the self-deﬁnedthe self-defined loss loss function. function. performance of model compiled with the self-defined loss function is slightly worse than 3.4.that Comparingwith MSE, Table within which Multivariable3. Values the average of evaluation Linear value Regression indicator of MAE with increases Models the self by-defined 0.0646 loss and function EVar .and CC decrease by 0.0067 and 0.0019, respectively, and it is mainly because the model with self- In order to verify the advantages of deep learning algorithm, six multivariable linear defined loss functionRange highlights (km) the strong1–25 echoes 25 more–50 but 50the–75 proportion 75–100 of strong100 –echo125 125–150 × regressionis relatively models small in are theEVar established test dataset. based 0.8656 on the0.8677 same dataset0.8455 as the0.8241 EFnet but0.8210 only N 1 0.7740 point are used as featureMAE data instead3.8435 of N × 33.4084× 3 points. 3.3520 Figure 83.2592 shows the3.4112 six scatter 3.8445 CC 0.9314 0.9321 0.9199 0.9097 0.9092 0.8802

1.00 EVar-self EVar-MSE 4.0 MAE-self MAE-MSE CC-self CC-MSE 0.95 3.8

0.90 )

3.6 B (d

0.85

MAE

EVar/CC 3.4 0.80

3.2 0.75

0.70 3.0 1-25 25-50 50-75 75-100 100-125 125-150 Range (km)

Figure 7. Column chart of comparison between Table 2 and Table 3.

Remote Sens. 2021, 13, x FOR PEER REVIEW 9 of 17

(a)1-25 (b)25-50 (c)50-75

(d)75-100 (e)100-125 (f)125-150

Remote Sens. 2021, 13, 1779 9 of 16

plots of actual and fitting echo reflectivity with the test dataset, it is obviously that the Figure 6. Scatterfitting plot effect corresponding with linear to modelsFigure 5 arebut obviouslyusing the self worse-defined than loss that function. with EFnet.

Table 3. Values of evaluation indicator with the self-defined loss function. Table 3. Values of evaluation indicator with the self-deﬁned loss function. Range (km) 1–25 25–50 50–75 75–100 100–125 125–150 Range (km) 1–25 25–50 50–75 75–100 100–125 125–150 EVar 0.8656 0.8677 0.8455 0.8241 0.8210 0.7740 EVar 0.8656 0.8677 0.8455 0.8241 0.8210 0.7740 MAEMAE 3.84353.8435 3.4084 3.4084 3.3520 3.3520 3.2592 3.2592 3.4112 3.4112 3.8445 3.8445 CC 0.93140.9314 0.9321 0.9321 0.9199 0.9199 0.9097 0.9097 0.9092 0.9092 0.8802 0.8802

1.00 EVar-self EVar-MSE 4.0 MAE-self MAE-MSE CC-self CC-MSE 0.95 3.8

0.90 )

3.6 B (d

0.85

MAE

EVar/CC 3.4 0.80

Remote Sens. 2021, 13, x FOR PEER REVIEW 10 of 17 3.2 0.75

3.4. Comparing with Multivariable Linear Regression Models 0.70In order to verify the advantages of deep learning algorithm, six multivariable3.0 linear regression models1-25 are established25-50 based50-75 on the75-100 same dataset100-125 as the125-150 EFnet but only N × 1 point are used as feature data insteadRange of N (km)× 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 FigurefittingFigure 7. 7.effectColumnColumn with chart chart linear of of comparison models comparison are between obviously between Table Tables worse 2 2and and than Table3. that 3. with EFnet.

(a)1-25 (b)25-50 (c)50-75

(d)75-100 (e)100-125 (f)125-150

Figure 8. 8. TheThe six six scatter scatter plots plots of actual of actual and and fitting ﬁtting echo echo reflectivity reﬂectivity with withthe test the dataset test dataset of each of each section using using the the multivariable multivariable linear linear regression regression models models..

4. 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 Figures 9 and 13.

4.1. 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.

Remote Sens. 2021, 13, 1779 10 of 16

4. 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 Section3. 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 Remote Sens. 2021, 13, x FOR PEER REVIEW 11 of 17 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 Figure9 and Figure 13.

(a) (b) (c)

◦ FigureFigure 9.9. Plan position indicator ( (PPI)PPI) images images of of reflectivity reﬂectivity at at 0.5° 0.5 elevationelevation:: (a ()a )is is the the raw raw observed observed image image and and (b ()b and,c) are (c) predictionare prediction images images by means by means of models of models compiled compiled with thewithMSE the andMSE the and self-deﬁned the self-defined loss function, loss function, respectively, respectively, in which in thewhich distance the distance circle is circle 25 km is (the25 km same (the below), same below) the red, the ellipse red ellipse is the serious is the serious occlusion occlusion area, and area, the an blued the ellipse blue ellipse is one ofis one the strongof the strong echo areas. echo areas.

4.1.Table Weak 4. Values Echoes-Dominated of the evaluation Case indicator in the nonocclusion area of Figure 9 with weak echoes- dominated volume data. The weak echoes-dominated volume data are arranged in the input format of the models and putRange into (km) the models, and then,1–25 the25 predicted–50 50–75 values 75–100 of reflectivity100–125 125 in– each150 ◦ section of 0.5 elevation are outputtedEVar by0.9156 means 0.9481 of the 0.8652 model fitting.0.8373 Figure0.88099 shows0.9029 the ◦ plan positionMSE loss indicator function (PPI) imagesMAE of reflectivity4.2895 3.1031 at 0.5 3.2099elevation, 3.9277 where 3.9277 Figure 9a4.3006 shows the raw observed image and FigureCC9 b,c shows0.9610 prediction0.9735 0.9378 images 0.9415 by means 0.9415 of models 0.9505 that are compiled with the MSE andEVar the self-defined 0.9243 loss0.9486 function, 0.8685 respectively.0.8562 0.8696 Table 4 lists0.9496 the evaluationSelf-defined results loss function of models withMAE two loss4.0580 functions 2.9573 in the3.2546 nonocclusion 2.9447 3.9176 fan-shaped 4.2122 area, which are bounded by red linesCC in Figure 0.96359. 0.9749 0.9341 0.9375 0.9423 0.9012

Table 4. Values of the evaluation indicatorAs shown in thein Figure nonocclusion 9a, the area case of Figureis dominated9 with weak by echoes-dominatedweak echoes in volumewhich most data. echo intensity is less than 40 dBZ, and there is obvious terrain blockage in the third quadrant, Range (km) 1–25 25–50 50–75 75–100 100–125 125–150 which is marked with an ellipse of a red line in which the echoes are obviously weak and evenEVar disappear0.9156 completely. 0.9481 Both the models 0.8652 with the 0.8373MSE and the 0.8809 self-defined 0.9029loss func- MSE MAE 4.2895 3.1031 3.2099 3.9277 3.9277 4.3006 loss function tion can fill the echoes in the occlusion area well and effectively improve the echo struc- CC 0.9610 0.9735 0.9378 0.9415 0.9415 0.9505 ture to make it more accurate. Furthermore, the strong echoes area marked with the blue ellipseEVar is more0.9243 consistent between 0.9486 the raw 0.8685 data and 0.8562the prediction 0.8696 with the self 0.9496-defined Self-defined loss function MAE 4.0580 2.9573 3.2546 2.9447 3.9176 4.2122 losCCs function 0.9635(Figure 9c) than 0.9749 with the MSE 0.9341 (Figure 9 0.9375b). In other words, 0.9423 the model 0.9012 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 blockedAs shownazimuth in 215° Figure in 9Figurea, the case9 are is shown dominated in Figure by weak 10, in echoes which inimage which (a) most is the echo raw intensitydata and (b) is less and than (c) are 40 the dBZ, corrected and there data is with obvious the terrainMSE and blockage the self- indefined the third loss quadrant, function, whichrespectively. is marked Bothwith the models an ellipse can of correct a red linethe 0.5° in which occlusion the echoeswell and are m obviouslyake the vertical weak andstructure even of disappear cloud more completely. complete. Both In the strong models echoes with the areaMSE (redand ellipse the self-definedarea), the filling loss function can fill the echoes in the occlusion area well and effectively improve the echo echoes with the self-defined loss function are stronger than that with the MSE, which re- structure to make it more accurate. Furthermore, the strong echoes area marked with alizes the purpose of highlighting the strong echo. the blue ellipse is more consistent between the raw data and the prediction with the self- defined loss function (Figure9c) than with the MSE (Figure9b). In other words, the model with the self-defined loss function is better than that with the MSE in fitting strong echoes.

Remote Sens. 2021, 13, 1779 11 of 16

In order to demonstrate the filling effect more clearly, three radial profiles at the blocked azimuth 215◦ in Figure9 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 Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 17 echoes with the self-defined loss function are stronger than that with the MSE, which realizes the purpose of highlighting the strong echo.

180 ZH(dBZ) (a) (b) (c) 70 160 65 140 60 55 120 50 45 100 40 80 35 30 60 25 Height (100 m) (100 Height 20 40 15 20 10 5 0 0 0 25 50 75 100 125 150 0 25 50 75 100 125 150 0 25 50 75 100 125 150 Range (km) Range (km) Range (km)

Figure 10. Radial profiles at the blocked azimuth 215◦ in Figure9, in which image ( a) is the raw data and (b,c) are the Figure 10. Radial profiles at the blocked azimuth 215° in Figure 9, in which image (a) is the raw data and (b) and (c) are corrected data with the MSE and the self-defined loss function, respectively; the red ellipse areas are for comparison. the corrected data with the MSE and the self-defined loss function, respectively; the red ellipse areas are for comparison. The values of the model evaluation indicator for the case are listed in Table4. The EVarThes of thevalues two of models the model are all evaluation above 0.85, indicator the MAE fors are the approximately case are listed 4 dB,in Table and the 4. TheCCs EVarsare above of the 0.9 two and models even greater are all than above 0.97 0.85, when the using MAEs the are self-defined approximately loss function4 dB, and in the CCsrange are from above 25 0.9 to 50and km, even which greater illustrates than 0.97 the when effectiveness using the of self the-defined models loss quantitatively. function in theComparing range from the values25 to 50 in km, Table which4, the performanceillustrates the of effectiveness model compiled of the with models the self-defined quantitatively.loss function Comparing is slightly the values better in thanTable that 4, the with performanceMSE, in which of model the compiled average value with the of EVarself- definedincreases loss by function 0.0111, MAEis slightlyand CCbetterdecrease than that by with 0.2356 MSE, and in 0.0087, which respectively, the average andvalue it of is EVarmainly increases because by the 0.0111, proportion MAE and of CC strong decrease echoes byin 0.2356 the caseand 0.0087, is higher respectively, than that inand the it istest mainly dataset. 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 unblockedFigures area 11 and in each 12 show section the modelscattercompiled plots of the with predic the tedMSE andand true the reflectivity self-defined in lossthe unblockedfunction, respectively. area in each Most section of themodel points compiled are near with the diagonal,the MSE and which the illustrates self-defined that loss the function,models perform respectively. well. Most of the points are near the diagonal, which illustrates that the models perform well. 4.2. Strong Echoes-Dominated Case

(a)1-25 The strong echoes-dominated(b)25-50 volume data(c)50 are- reshaped75 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 Figure9 except for the strong echoes. Similarly, Table5 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.

Range (km) 1–25 25–50 50–75 75–100 100–125 125–150 (d)75-100EVar 0.8709(e)100- 0.9284125 0.9497(f)125 0.9488-150 0.9488 0.9354 MSE loss function MAE 4.4745 4.4930 3.8682 4.3950 3.9859 4.4552 CC 0.9333 0.9636 0.9745 0.9746 0.9743 0.9671 EVar 0.8763 0.9301 0.9535 0.9535 0.9483 0.9342 Self-deﬁned loss function MAE 4.3681 4.5081 3.6362 4.1202 3.8835 4.5047 CC 0.9374 0.9647 0.9767 0.9765 0.9756 0.9666

Figure 11. Scatter plots between true reflectivity and the model prediction in each section using the MSE loss function in this case with weak echoes-dominated volume data.

Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 17

Figure 10. Radial profiles at the blocked azimuth 215° in Figure 9, 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; the red ellipse areas are for comparison.

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 Remote Sens. 2021, 13, 1779 unblocked area in each section model compiled with the MSE and the12 self of 16-defined loss function, respectively. Most of the points are near the diagonal, which illustrates that the models perform well.

(a)1-25 (b)25-50 (c)50-75

(d)75-100 (e)100-125 (f)125-150

Remote Sens. 2021, 13, x FORFigure PEER 11. REVIEW FigureScatter 11.plotsScatter between plots true between reflectivity true and reﬂectivity the model and prediction the model in prediction each section in using each sectionthe MSE13 using of loss 17 function the in

this case withMSE weakloss echoes function-dominated in this case volume with data weak. echoes-dominated volume data.

(a)1-25 (b)25-50 (c)50-75

(d)75-100 (e)100-125 (f)125-150

Figure 12. Scatter plots corresponding to Figure 11 but using the self-defined loss function. Figure 12. Scatter plots corresponding to Figure 11 but using the self-deﬁned loss function.

4.2. StrongAs shown Echoes in-D Figureominated 13 C,ase the shapes of the strong echo marked with the blue ellipse are basicallyThe strong consistent echoes-dominated among the volume three data PPIs, are and reshaped the consistency into the input between format Figure of each 13 a,c isrange better, section which model, further and illustrates then the that values the of self-defined reflectivity lossat 0.5° function elevation performs are fitted better by on strongmeans echoof the fitting. models. The Figure points 13 numbershows the of PPI strong images echo corresponding (>40 dBZ) in Figureto Figure 11 are9 except counted. Therefor the are strong 1807 echoes points. Similarly, (3.37%) in Table theactual 5 lists PPIthe evaluation (Figure 13 a),indicators 1740 points in the (3.24%) nonocclusion in the PPI predictedfan-shaped with area the boundedMSE loss by red function lines in model Figure (Figure 13. 13b) and 1841 points (3.43%) with the self-defined loss function model (Figure 13c), and the proportion of strong echo with the (a) self-defined loss(b) function is closer to that of raw(c) 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.

Figure 13. PPI images of reflectivity at 0.5° elevation: (a) is the raw observed image and (b) and (c) are prediction images by means of models compiled with the MSE and the self-defined loss function, respectively, in which the blue ellipse mark the strong echo areas.

Table 5. Values of the evaluation indicator in the nonocclusion area of Figure 13 with strong echoes-dominated volume data.

Range (km) 1–25 25–50 50–75 75–100 100–125 125–150 EVar 0.8709 0.9284 0.9497 0.9488 0.9488 0.9354 MSE loss function MAE 4.4745 4.4930 3.8682 4.3950 3.9859 4.4552 CC 0.9333 0.9636 0.9745 0.9746 0.9743 0.9671 EVar 0.8763 0.9301 0.9535 0.9535 0.9483 0.9342 Self-defined loss function MAE 4.3681 4.5081 3.6362 4.1202 3.8835 4.5047 CC 0.9374 0.9647 0.9767 0.9765 0.9756 0.9666 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

Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 17

(a)1-25 (b)25-50 (c)50-75

(d)75-100 (e)100-125 (f)125-150

Figure 12. Scatter plots corresponding to Figure 11 but using the self-defined loss function.

4.2. 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 Remote Sens. 2021, 13, 1779 13 of 16 for the strong echoes. Similarly, Table 5 lists the evaluation indicators in the nonocclusion fan-shaped area bounded by red lines in Figure 13.

Remote Sens. 2021, 13, x FOR PEER REVIEW 14 of 17 (a) (b) (c)

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 ◦ Figure 13. PPI images images of of reflectivity reﬂectivityraw data at (a), at 0.5° 0.5 the elevatioelevation: strongn: echoes(a ()a is) isthe thewith raw raw theobserved observed self-defined image image and loss and (b function) ( band,c) are(c) are prediction(c) prediction are more images imagesconsistent by meansby means of modelsof models compiled compiledthan with with thethat theMSE with MSEand the and the MSE the self-deﬁned self (b),-defined which loss loss function,demonstrate function, respectively, respectively, that the in model which in which thewith bluethe the blue ellipse self ellipse- markdefined mark the loss strongthe strong echo echo areas. areas. function is better than that with the MSE for fitting strong echoes.

180 Table 5. Values of the evaluation indicator in the nonocclusion area of Figure 13 with strongZH(dBZ) ech- (a) oes-dominated volume(b) data. (c) 70 160 65 Range (km) 1–25 25–50 50–75 75–100 100–125 125–150 140 60 EVar 0.8709 0.9284 0.9497 0.9488 0.9488 0.935455 120 MSE loss function MAE 4.4745 4.4930 3.8682 4.3950 3.9859 4.455250 CC 0.9333 0.9636 0.9745 0.9746 0.9743 0.967145 100 40 EVar 0.8763 0.9301 0.9535 0.9535 0.9483 0.9342 80 35 Self-defined loss function MAE 4.3681 4.5081 3.6362 4.1202 3.8835 4.504730

60 CC 0.9374 0.9647 0.9767 0.9765 0.9756 0.966625 Height (100 m) (100Height As shown in Figure 13, the shapes of the strong echo marked with the blue ellipse20 are 40 15 basically consistent among the three PPIs, and the consistency between Figure 13a,c is 20 10 5 0 0 0 25 50 75 100 125 150 0 25 50 75 100 125 150 0 25 50 75 100 125 150

Range (km) Range (km) Range (km)

Figure 14. Radial profiles at the unblocked azimuth 48◦ in Figure 13, in which image (a) is the raw data and (b,c) are the Figure 14. Radial profiles at the unblocked azimuth 48° in Figure 13, in which image (a) is the raw data and (b) and (c) are thefilling filling data data with with the theMSE MSEand and the the self-defined self-defined loss loss function, function, respectively; respectively the; the red red ellipse ellipse areas areas are are for comparison.for comparison. However, for weak echoes in the northwest direction beyond 100 km, the reflectivity 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. estimated by the model is obviously stronger than that measured by the Nanjing radar. It It is well known that the beam broadens and the echo intensity weakens with increasing 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 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 with the Bengbu SA radar, which is located at Nanjing SA radar azimuth 303.5° and dis- distance of 142.5 km (the red triangle in Figure 15), is interpolated to the gates of the tance of 142.5 km (the red triangle in Figure 15), is interpolated to the gates of the Nanjing Nanjing radar (Figure 15). It can be seen from the area marked with a rectangle of red lines radar (Figure 15). It can be seen from the area marked with a rectangle of red lines in in Figure 15 that the weak echoes observed with the Bengbu radar are obviously stronger Figurethan those 15 that observed the weak with echoes the Nanjing observed radar with because the Bengbu of the distance. radar are On obviously the other hand,stronger the thanecho those predicted observed by the with model the isNanjing affected radar by the because melting oflayer the distance. in far distance, On the so other this hand, strong theecho echo area predicted may be due by tothe the model insufficient is affected melting by the layer melting data collected layer in in far the distance, training s dataset,o this strongwhich echo causes area strong may fittingbe due results. to the insufficient melting layer data collected in the training dataset,In which Table5 ,causes the EVar strongs are fitting all above results. 0.92 except for the models of the first range section fromIn 1 Table to 25 km,5, the the EVarsMAE ares are all less above than 0.92 4.5 except dB, and for the theCC modelss are greater of the thanfirst 0.96range except section for fromthe first 1 to section,25 km, the which MAEs further are less verifies than the 4.5 effectiveness dB, and the andCCs stabilityare greater of thethan deep 0.96 learning except foralgorithm the first appliedsection, which to the echofurther correction. verifies the Comparing effectiveness the valuesand stability of the of model the deep evaluation learn- ingindicator algorithm compiled applied with to the the echo self-defined correction. loss Comparing function and the MSEvaluesin of Table the model5, the averageevalua- tionvalue indicator of MAE compileddecreases with 0.1085 the self and-definedEVar and lossCC functionincrease and 0.0023 MSE and in Table 0.0017, 5, respectively,the average valuewhich of suggests MAE decreases that the 0.1085 models and with EVar the and self-defined CC increase loss 0.0023 function and perform 0.0017, better.respectively, which suggests that the models with the self-defined loss function perform better.

Remote Sens. 2021, 13, 1779 14 of 16 Remote Sens. 2021, 13, x FOR PEER REVIEW 15 of 17

ZH(dBZ) ZH(dBZ) 150 150 (a) 70 (b) 70 65 65 125 60 125 60 55 55 100 50 100 50 45 45 40 40 75 75 Bengbu 35 35 30 Bengbu 30 50 25 50 25 20 20 25 15 15 10 25 10 5 5 0 0 0 0 -150 -125 -100 -75 -50 -25 0 -150 -125 -100 -75 -50 -25 0

Figure 15. The weak echoes area in Figure 13 observed with the Nanjing radar (a) and interpolated Figure 15. The weak echoes area in Figure 13 observed with the Nanjing radar (a) and interpolated with the Bengbu radar (b), where thewith red the triangle Bengbu is radarthe location (b), where of the the Bengbu red triangle radar. is the location of the Bengbu radar.

5. Discussion 5. Discussion An EFnet based on a deep learning algorithm is used to fill and correct the radar An EFnet based on a◦ deep learning algorithm is used to fill and correct the radar reflectivity in thereflectivity occlusion in area the atocclusion the 0.5 areaelevation at the angle, 0.5° elevation and a self-defined angle, and loss a self function-defined is loss function proposed to improveis proposed the model to improve fitting inthe strong model echoes. fitting The in strong training echoes. dataset The isconstructed training dataset is con- with the data instructed unblocked with areasthe data inthe in unblocked Nanjing SA areas radar; in the six echo-fillingNanjing SA modelsradar; six are echo built-filling models according to theare range, built according and three to indicators the range, are and utilized three toindicators evaluate are the utilized models. to Whether evaluate the models. from the subjectiveWhether impression from the of subjective the PPI imagesimpression or from of the the PPI quantitative images or analysisfrom the of quantitative the anal- indicator tables,ysis the of results the indicator show that tables, the low-level the results occlusion show that reflectivity the low- haslevel been occlusion corrected reflectivity has very well. Thisbeen shows corrected that deep very learning well. This has broadshows prospects that deep in learning weather has radar broad applications. prospects in weather In the processradar of applications model training,. data preprocessing, namely, data quality control and normalization, is aIn critical the process step. Other of model superparameter training, data settings, preprocessing, such asthe namely, loss function, data quality control optimizer, numberand normalization, of hidden layers, is a critical nodes, step. and iterationOther superparameter epochs, also have settings, a significant such as the loss func- impact on thetion, fitting optimizer, effect to models,number whichof hidden needs layers, to be nodes, adjusted and and iteration tested epochs, repeatedly. also have a signifi- Althoughcant the numberimpact on of trainingthe fitting datasets effect to in models, this paper which reaches needs approximately to be adjusted 200,000, and tested repeat- it is still relativelyedly. small. In practical applications, the number of radar volume scan data can be greatly increasedAlthough to make the the training number dataset of training reach datasetsmore than in several this paper million, reaches and the approximately models will achieve200,000, a better it is still fitting relatively effect. Insmall. addition, In practical more data applications, of stable precipitation the number echoof radar volume should be addedscan into data the can training be greatly datasets increased to further to make improve the the training influence dataset of melting reach more layer. than several When multiplemillion, elevation and the models angles arewill blocked, achieve a the better echo-filling fitting effect. model In canaddition, be similarly more data of stable established usingprecipitation deep learning. echo should Compared be added with into using the training only a singledatasets parameter to furtherof improve the the influ- reflectivity factorence as of input,melting the layer. polarimetric parameters can be added as input features into the training dataWhen with multiple the polarization elevation upgradingangles are blocked, of weather the radar, echo-filling which model will effec- can be similarly tively improveestablished the effect ofusing echo deep correction, learning. and Compared the polarization with using parameters only a single can parameter also be of the re- corrected by aflectivity similar deep factor learning as input, network. the polarimetric In addition, parameters some features, can be added such as as terrain, input features into underlying surfacethe training information, data with and the weather polarization background, upgrading can also of weather be applied radar, to constructwhich will effectively a multimodalimprove model, whichthe effect is a of popular echo correction, method for and deep the learningpolarization training parameters at present. can also be cor- These means canrected achieve by arefined, similar intellectualized,deep learning network. and automatic In addition, echo correction some features, for radar such as terrain, beam blockage.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. Author Contributions: Conceptualization, X.Y. and Z.H.; methodology, Z.H.; software, B.L.; valida- These means can achieve refined, intellectualized, and automatic echo correction for radar tion, J.Z., B.L. and Y.Z.; formal analysis, J.Z.; investigation, B.L.; resources, J.Z.; data curation, Y.Z.; writing—originalbeam draft blockage preparation,. X.Y.; writing—review and editing, X.Y. and Z.H.; visualization, X.Y.; supervision, Z.H.; project administration, Z.H.; funding acquisition, Z.H. All authors have read Author Contributions: Conceptualization, X.Y. and Z.H.; methodology, Z.H.; software, B.L.; vali- and agreed to the published version of the manuscript. dation, J.Z., B.L. and Y.Z.; formal analysis, J.Z.; investigation, B.L.; resources, J.Z.; data curation, Funding: This researchY.Z.; writing was funded—original by thedraft “Key-Area preparation, Research X.Y.; writing and Development—review and Program editing, of X Guang-.Y. and Z.H.; visuali- dong Province (2020B1111200001)”,zation, X.Y.; supervision, the “Key Z.H.; project project of administration, monitoring, early Z.H warning.; funding and acquisition, prevention Z of.H. All authors major natural disastershave read of Chinaand agreed (2019YFC1510304)”, to the published and version the “Scientific of the manuscript. Research Projects of Weather Modification in Northwest China (RYSY201905)”.

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Data Availability Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: The authors would like to sincerely thanks Fen Xu of Nanjing Joint Institute for Atmospheric Sciences for providing technical guidance. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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