Estimation of Hourly Rainfall During Typhoons Using Radar Mosaic-Based Convolutional Neural Networks

remote sensing

Article Estimation of Hourly Rainfall during Typhoons Using Radar Mosaic-Based Convolutional Neural Networks

Chih-Chiang Wei * and Po-Yu Hsieh Department of Marine Environmental Informatics & Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan; [email protected] * Correspondence: [email protected]

Received: 7 February 2020; Accepted: 9 March 2020; Published: 10 March 2020

Abstract: Taiwan is located at the junction of the tropical and subtropical climate zones adjacent to the Eurasian continent and Pacific Ocean. The island frequently experiences typhoons that engender severe natural disasters and damage. Therefore, efficiently estimating typhoon rainfall in Taiwan is essential. This study examined the efficacy of typhoon rainfall estimation. Radar images released by the Central Weather Bureau were used to estimate instantaneous rainfall. Additionally, two proposed neural network-based architectures, namely a radar mosaic-based convolutional neural network (RMCNN) and a radar mosaic-based multilayer perceptron (RMMLP), were used to estimate typhoon rainfall, and the commonly applied Marshall–Palmer Z-R relationship (Z-R_MP) and a reformulated Z-R relationship at each site (Z-R_station) were adopted to construct benchmark models. Monitoring stations in Hualien, Sun Moon Lake, and Taichung were selected as the experimental stations in Eastern, Central, and Western Taiwan, respectively. This study compared the performance of the models in predicting rainfall at the three stations, and the results are outlined as follows: at the Hualien station, the estimations of the RMCNN, RMMLP, Z-R_MP, and Z-R_station models were mostly identical to the observed rainfall, and all models estimated an increase during peak rainfall on the hyetographs, but the peak values were underestimated. At the Sun Moon Lake and Taichung stations, however, the estimations of the four models were considerably inconsistent in terms of overall rainfall rates, peak rainfall, and peak rainfall arrival times on the hyetographs. The relative root mean squared error for overall rainfall rates of all stations was smallest when computed using RMCNN (0.713), followed by those computed using RMMLP (0.848), Z-R_MP (1.030), and Z-R_station (1.392). Moreover, RMCNN yielded the smallest relative error for peak rainfall (0.316), followed by RMMLP (0.379), Z-R_MP (0.402), and Z-R_station (0.688). RMCNN computed the smallest relative error for the peak rainfall arrival time (1.507 h), followed by RMMLP (2.673 h), Z-R_MP (2.917 h), and Z-R_station (3.250 h). The results revealed that the RMCNN model in combination with radar images could efficiently estimate typhoon rainfall.

Keywords: rainfall; modeling; radar image; typhoon; CNN; deep learning

1. Introduction Taiwan is situated at the junction of the tropical and subtropical climate zones, bordering the Eurasian continent and the Pacific Ocean. Natural disasters frequently occur each year because of typhoons—the strong winds and rainfall of which often lead to severe disasters. In addition, the northwest Pacific Ocean is commonly affected by typhoons; approximately four typhoons strike Taiwan every year and cause serious severe damage [1,2]. For example, typhoon Megi, a typical moderate-strength typhoon, made landfall on the east coast of Taiwan in 2016. The strong winds and heavy rain caused severe damage; buildings were buried by a mudslide down a river, and 650,000 households experienced power outages, which resulted in US$100 million in economic

Remote Sens. 2020, 12, 896; doi:10.3390/rs12050896 www.mdpi.com/journal/remotesensing Remote Sens. 2020, 12, x FOR PEER REVIEW 2 of 19 heavy rain caused severe damage; buildings were buried by a mudslide down a river, and 650,000 Remotehouseholds Sens. 2020 experienced, 12, 896 power outages, which resulted in US$100 million in economic losses2 of[3] 19. Improving quantitative precipitation estimation (QPE) for tropical storms is crucial for disaster lossesmitigation [3]. [4,5] Improving. quantitative precipitation estimation (QPE) for tropical storms is crucial for disasterTaiwan’s mitigation Central [4,5 Mountain]. Range (CMR) runs from the north to the south of the island, dividing it intoTaiwan’s eastern and Central western Mountain parts. Range The CMR (CMR) is situated runs from in the east north and to theis 340 south km oflong the and island, 80 km dividing wide, itwith into an eastern average and elevation western of parts.approximately The CMR 2500 is situatedm [6]. When in the a typhoon east and strikes is 340 Taiwan km long from and the 80 east, km wide,it exerts with its an most average severe elevation effects of on approximately the eastern regions, 2500 m [ which6]. When sustain a typhoon considerable strikes Taiwandamage. from By thecontrast, east, itthe exerts western its most regions severe sustain effects less on damage the eastern because regions, the typhoon which sustain structure considerable is often disrupted damage. Byand contrast, weakened the by western the CMR. regions Notably, sustain the less distribution damage because of major the rainfall typhoon during structure typhoons is often statistically disrupted andresembles weakened the contours by the CMR. of terrain Notably, height, the often distribution referred of to majoras the rainfall“phase- duringlocking” typhoons mechanism statistically [7]. The resemblesphase-locking the mechanism contours of can terrain provide height, a basic often explanation referred to of as the the topographic “phase-locking” rainfall mechanism in the CMR [7]. Theassociated phase-locking with typhoons mechanism impinging can provide from different a basic explanation directions [8]. ofthe Several topographic researchers rainfall have in discussed the CMR associatedthe effects withof the typhoons aforementioned impinging mechanism, from different such directions as [9–13]. [ 8These]. Several researchers researchers have have revealed discussed that thewhen eff ectstyphoons of the approach aforementioned Taiwan mechanism, from the east such before as [ 9passing–13]. These through researchers the CMR, have their revealed routes thatare whenmore easily typhoons estimated, approach and Taiwan early warning from thes eastcan beforebe provided passing for through precaution theCMR, against their the routescorresponding are more easilywind and estimated, rain. By and contrast, early warnings after typhoons can be pass provided through for precautionthe CMR, the against routes, the arrival corresponding times of wind andand rain. rain, By and contrast, delays after in rainfall typhoons become pass through unpredictable the CMR, [1 the4,15] routes,. Therefore, arrival times efficiently of wind estimating and rain, andtyphoon delays rainfall in rainfall is crucial become for unpredictableTaiwan. [14,15]. Therefore, efficiently estimating typhoon rainfall is crucialA radar for Taiwan.is commonly used for both weather surveillance and research to help meteorologists understandA radar the is commonly dynamics used and formicrophysical both weather processes surveillance of atmospheric and research phenomena to help meteorologists [16]. Radar understandreflectivity is thea measure dynamics of the andfraction microphysical of electromagnetic processes waves of reflected atmospheric by precipitation phenomena particles [16]. Radar(e.g., rain, reflectivity snow, or is hail). a measure Different of thecolors fraction are used of electromagnetic to create radar images waves reflectedaccording by to precipitationthe intensity particlesof the signal (e.g., reflected rain, snow, by precipitation or hail). Diff erentparticles colors [3]. areThe used intensity to create of reflection radar images is associated according with to the intensitysize, shape, of thestate signal of matter, reflected and by number precipitation of particles particles within [3]. The a unit intensity of precipitation. of reflection Stronger is associated reflected with thesignals size, generally shape, state indicate of matter, heavier and numberprecipitation of particles. Therefore, within radar a unit images of precipitation. can be used Stronger to examine reflected the signalsintensity generally of precipitation indicate and heavier distribution precipitation. of weather Therefore, systems radar [17] images. Currently, can be the used Central to examine Weather the intensityBureau (CWB of precipitation) of Taiwan and has distribution four S-band of (10 weather-cm wavelength) systems [17 weather]. Currently, surveillance the Central radar Weather (WSR) Bureausystems; (CWB) this new of Taiwan type of has radar four is S-bandalso referred (10-cm as wavelength) WSR-88D (Weather weather Surveillance surveillance Radarradar— (WSR)1988 systems;Doppler). this Of thenew four type WSR of radar systems, is also three referred are separately as WSR-88D located (Weather in Hualien Surveillance in Eastern Radar—1988 Taiwan, Doppler).Kenting in Of southern the four Taiwan, WSR systems, and Cigu three in are W separatelyestern Taiwan located (locations in Hualien displayed in Eastern in Taiwan,Figure 1); Kenting these inthree southern systems Taiwan, use a Doppler and Cigu radar. in Western The remaining Taiwan (locations system is displayedlocated in inWufenshan Figure1); thesein northern three systems Taiwan useand auses Doppler a dual radar.-polarized The remainingradar. The system scan range is located of the infour Wufenshan systems covers in northern Taiwan Taiwan and its and adjacent uses a dual-polarizedbodies of water radar. (i.e., the The Pacific scan range Ocean, of theEast four China systems Sea, coversTaiwan Taiwan Strait, andand itsLuzon adjacent Strait) bodies and ofform waters a (i.e.,WSR the network. Pacific Ocean, East China Sea, Taiwan Strait, and Luzon Strait) and forms a WSR network.

Figure 1. Geography of Taiwan and the locations of study sites and radar stations. Remote Sens. 2020, 12, 896 3 of 19

Numerous operational nowcasting systems use the relationship between static radar reflectivity (Z) and the rain rate (R), such as the commonly used Marshall–Palmer [18] formula of Z = 200 R1.6, to convert radar echo into rainfall estimates. Radar- and gauge-based rainfall estimates are typically consistent, particularly when the rainfall intensity is high [19–25]. Researchers have studied the QPE of tropical cyclones. For example, Ku and Yoo [26] analyzed the rainfall engendered by typhoon Nakri by using radar and rain gauge data. Libertino et al. [27] developed a quasi-real-time procedure to optimize the radar estimation of rainfall rates. Moreover, Tang and Matyas [28] developed a nowcasting model for tropical cyclone precipitation based on rain retrieval for a Doppler radar. Chen et al. [29] reported the vertical structures of the raindrop size distribution and QPE parameters of two main synoptic systems: typhoons and Meiyu (or Baiu) fronts. According to these researchers, radar reflectivity factors constitute a vital variable that can be used as a QPE model input. This study developed a model for estimating hourly rainfall during typhoons and analyzed the accuracy of typhoon rainfall estimation. As previously discussed, to address the problem of QPE, reflectivity measurements were employed. Radar imagery released by the CWB was used to estimate instantaneous rainfall, and a neural network-based model was employed to develop a precipitation estimation model. Specifically, multilayer perceptron (MLP) neural networks and convolutional neural networks (CNNs) were used to develop a typhoon precipitation estimation model. Numerous studies have discussed typhoon rainfall estimation using machine learning models. Such models are typically composed of an MLP network, a radial basis function network, a support vector machine, and random forests and Bayesian networks [30–35]. Studies have combined such machine learning models with radar reflectivity and satellite remotely sensed data [36,37]. For example, Wei [38] developed a fuzzy inference-based neural network and estimated overland precipitation by using ground climatological data and radar reflectivity. Tao et al. [39] extracted useful features from bispectral satellite information, infrared images, and water vapor channels to detect rain by using deep neural networks. Furthermore, studies have employed new deep learning models such as CNNs. CNNs are revolutionary in image analysis and are considered state-of-the-art for numerous tasks, including image classification, face recognition, and object detection [40–44]. CNNs are typically used in classification tasks in which the output of an image is a single-class label [45]. A standard CNN consists of alternating convolutional and pooling layers with fully connected layers above them [46]. A pretrained CNN such as VGG-16 [47] and its intermediate convolutional layer are used as an initial feature-map extractor. The convolutional layer is the core component of a CNN and outputs feature maps by computing the dot product between the local region in the input feature maps and a filter [48]. The pooling layer performs downsampling on feature maps by computing the maximum or average value of a subregion. Such newly developed models can be used to process radar images in atmospheric studies (e.g., rainfall inversion or typhoon intensity prediction). For example, Chen et al. [49] proposed a satellite imagery-based CNN for estimating the tropical cyclone intensity. Tran and Song [50] predicted multichannel radar image sequences by using deep neural network-based image processing techniques. Lee et al. [51] adopted CNNs using image patterns to estimate the tropical cyclone intensity by mimicking human cloud pattern recognition. Few studies have applied CNNs and remote sensing images to tropical cyclone rainfall estimation. Accordingly, the present study proposes a relevant methodology to fill this research gap. This study proposes two structures for radar mosaic-based neural networks, namely a radar mosaic-based convolutional neural network (RMCNN) and a radar mosaic-based multilayer perceptron (RMMLP), to estimate typhoon rainfall. The neural network-based models were compared with empirical formulas by using the formula Z = 200 R1.6 proposed by [18], which is referred to as the Marshall–Palmer model (Z-R_MP). In addition, the formula Z = a Rb was reformulated at each station for the investigated events (Z-R_station). Regarding rainfall rate estimations of the studied stations, the smallest relative root mean squared error was computed by the proposed RMCNN (0.713), followed by RMMLP (0.848), Z-R_MP (1.030), and Z-R_station (1.392). Remote Sens. 2020, 12, 896 4 of 19

2. Materials The geography of the research area is illustrated in Figure1. Typhoons generally move from east to west through Taiwan. Accordingly, this study used three experimental stations, namely Hualien station in the east (121.6051◦E, 23.9729◦N), Sun Moon Lake station in central Taiwan (120.9081◦E, 23.8813◦N), and Taichung station in the west (120.6841◦E, 24.1457◦N), to analyze the accuracy of rainfall forecasts in typhoon precipitation. This study considered 17 typhoons that affected the area between 2013 and 2017 (Figure2). As the typhoonsRemote Sens. landed2020, 12, x on FOR Taiwan, PEER REVIEW the CWB released radar images every hour and collected observatory4 of 19 data. The resolution and color appearance of earlier radar images (released by CWB before 2012) di2.ff Materialsers from those of recent images (released by CWB after 2013). Therefore, we collected radar images startingThe from geography 2013. Accordingof the research to the area CWB, is illustrated the maximum in Figure wind 1. Typhoons speeds of generally mild, moderate, move from and east severe typhoonsto west through are 17.2–32.6, Taiwan. 32.7–50.9, Accordingly, and this>51 study m/s, respectively. used three experimental The statistics stations, in Table namely1 demonstrate Hualien that fromstation 2013 in tothe 2017, east five(121.6051 severe° E, (29.4%), 23.9729 seven° N), Sun moderate Moon (41.2%),Lake station and fivein central mild typhoonsTaiwan (120.9081 passed through° E, the23.8813 research° N), area.and Taichung station in the west (120.6841° E, 24.1457° N), to analyze the accuracy of rainfallThe forecasts radar reflectivityin typhoon precipitation. images collected in this study were radar mosaics produced by the CWB.This The study CWB considered typically creates17 typhoons a mosaic that affected by using the the area reflectivity between fields2013 and of the2017 four (Figure WSR 2). systems. As Reflectivitythe typhoons is measuredlanded on in Taiwan, decibels relativethe CWB to Zreleased(dBZ), andradar higher images dBZ every values hour suggest and strongercollected echo signals.observatory Radar data. mosaics The resolution are created and as color follows: appearance The WSR of systemsearlier radar scan forimages a period (released of approximately by CWB 7before min. 2012) Approximately differs from 2.5those min of recent later, theimages data (released collected by byCWB the after four 2013). WSR Therefore, systems arewe collected delivered to theradar host images computer starting for datafrom processing, 2013. According and a compositeto the CWB, mosaic the maximum is produced. wind After speeds another of mild, 1–5 min, themoderate, mosaic and and severe relevant typhoons data are are sent 17.2 to–32.6, each 32.7 servo–50.9, host. and Accordingly, >51 m/s, respectively. a radar mosaic The statistics can be created in approximatelyTable 1 demonstrate 15 min that after from the 2013 WSRs to begin2017, scanning.five severe (29.4%), seven moderate (41.2%), and five mild typhoons passed through the research area.

FigureFigure 2. 2.HistoricalHistorical typhoon typhoon paths. paths.

Remote Sens. 2020, 12, 896 5 of 19

The radar mosaics collected during typhoons in the present study were composed of hourly radar images. The radar images of the typhoons that made landfall or approached Taiwan are depicted in Figure3. Most of the radar mosaics were complete because they comprised radar images delivered from several radar systems. Few mosaics included partial sea areas that were not covered by the radar systems. This study ﬁlled in the missing areas in the images by using the most recent images captured beforeRemote Sens. the time2020, 12 corresponding, x FOR PEER REVIEW to missing data. 6 of 19

FigureFigure 3. 3.Reﬂectivity Reflectivity imagesimages ofofanalyzed analyzedtyphoons. typhoons.

Step 3: Preprocess the data sets and categorize typhoon event data into training–validation and testing subsets. Of the analyzed typhoons, four approached the island from the east, made landfall on the east coast, passed through the CMR, and left the island from the west coast. The typhoon routes were near the three experimental stations in Hualien, Sun Moon Lake, and Taichung, and passed through the center of the island. This type of typhoon route results in the most severe damage. The four typhoons, namely Matmo in 2014 (Figure 2e), Soudelor in 2015 (Figure 2h), Dujuan in 2015 (Figure 2j), and Megi in 2016 (Figure 2m), constituted the testing set. The remaining 13 typhoons constituted the training–validation set. The training–validation set was used to train model parameters and to verify the applicability of models by using 10-fold cross-validation. In total, 4701 hourly data were obtained. Of these, 4146 were used for the training–validation set and 555 were used for testing; Step 4: Crop the reflectivity images. The latitudinal and longitudinal range of the original radar images was 117.32°–124.79° E, 21.70°–27.17° N. Because the original images had a wide geographical range, cropping was required to obtain the most suitable image size that included the rainfall data collected by ground-based observatories; Step 5: Conduct neural network-based estimation and identify optimal reflectivity image sizes and model parameters. This study developed an RMCNN model in accordance with the different image sizes after cropping and initially applied default mode parameter values to identify the most suitable image size. After selection, relevant parameters for the RMCNN and RMMLP models were analyzed. The number of neurons and learning rate were calibrated in the RMCNN and RMMLP models. The model inputs were the reflectivity images cropped in Step 4, and the outputs were the

Remote Sens. 2020, 12, 896 6 of 19

Table 1. Typhoons aﬀecting the research area, 2013–2017 (17 incidents).

Total rain (mm) Typhoon Period (UTC) Intensity Hualien Sun Moon Lake Taichung Cimaron 17–18 July 2013 Mild typhoon 29 1 13 Usagi 21–22 September 2013 Severe typhoon 303 25 5 Fitow 5–6 October 2013 Moderate typhoon 59 5 2 Hagibis 15–16 June 2014 Mild typhoon 10 16 5 Matmo 22–23 July 2014 Moderate typhoon 334 240 95 Fung-Wong 19–22 September 2014 Mild typhoon 169 64 31 Linfa 7–9 July 2015 Mild typhoon 9 2 12 Soudelor 7–8 August 2015 Moderate typhoon 219 133 66 Goni 22–23 August 2015 Severe typhoon 269 5 12 Dujuan 28–29 September 2015 Severe typhoon 168 129 87 Nepartak 7–9 July 2016 Severe typhoon 309 23 12 Meranti 13–14 September 2016 Severe typhoon 323 52 19 Megi 27–28 September 2016 Moderate typhoon 399 98 76 Nesat 28–29 July 2017 Moderate typhoon 55 209 42 Haitang 30–31 July 2017 Mild typhoon 90 79 153 Hato 22–23 August 2017 Moderate typhoon 115 6 8 Talim 13–13 September 2017 Moderate typhoon 33 0 0

3. Methodology This study designed a set of methods for estimating rainfall during typhoons by using the received instantaneous radar images. The procedures can be explained as follows: Step 1: Collect relevant data from the research area and select typhoons for analysis. Typhoon weather information was scanned to confirm whether the typhoons affected the research area, and the event data of all historical typhoons were then examined; Step 2: Refine the data collected from radar reflectivity images and gauge rainfall during the typhoons. After the relevant typhoon data were collected, data preprocessing was conducted. The preprocessed data were divided into radar images and observatory rainfall data. The observatory rainfall data obtained in this study were raw data. Parts of the observatory data were incomplete because of instrument malfunction or human error. Before data analysis, the missing values were supplied using interpolation. The method of radar image processing is explained in Section2; Step 3: Preprocess the data sets and categorize typhoon event data into training–validation and testing subsets. Of the analyzed typhoons, four approached the island from the east, made landfall on the east coast, passed through the CMR, and left the island from the west coast. The typhoon routes were near the three experimental stations in Hualien, Sun Moon Lake, and Taichung, and passed through the center of the island. This type of typhoon route results in the most severe damage. The four typhoons, namely Matmo in 2014 (Figure2e), Soudelor in 2015 (Figure2h), Dujuan in 2015 (Figure2j), and Megi in 2016 (Figure2m), constituted the testing set. The remaining 13 typhoons constituted the training–validation set. The training–validation set was used to train model parameters and to verify the applicability of models by using 10-fold cross-validation. In total, 4701 hourly data were obtained. Of these, 4146 were used for the training–validation set and 555 were used for testing; Step 4: Crop the reflectivity images. The latitudinal and longitudinal range of the original radar images was 117.32◦–124.79◦E, 21.70◦–27.17◦N. Because the original images had a wide geographical range, cropping was required to obtain the most suitable image size that included the rainfall data collected by ground-based observatories; Step 5: Conduct neural network-based estimation and identify optimal reflectivity image sizes and model parameters. This study developed an RMCNN model in accordance with the different image sizes after cropping and initially applied default mode parameter values to identify the most suitable image size. After selection, relevant parameters for the RMCNN and RMMLP models were analyzed. The number of neurons and learning rate were calibrated in the RMCNN and RMMLP Remote Sens. 2020, 12, 896 7 of 19 models. The model inputs were the reflectivity images cropped in Step 4, and the outputs were the rainfall rates at the stations. The RMCNN and RMMLP models were implemented using the Remoteopen-source Sens. 2020 scikit-learn, 12, x FOR PEER and REVIEW Keras libraries in Python 3.7 (Python Software Foundation, Wilmington,7 of 19 DE, USA) [52,53]; rainfallStep rate 6:s at Evaluate the stations. the accuracy The RMCNN of the and neural RMMLP network-based models were models implemented using the using testing the subset.open- sourceEach selected scikit-learn typhoon and wasKeras analyzed libraries using in Python the models 3.7 (Python to estimate Software typhoon Foundation, rainfall and Wilmington, compare model DE, USA)errors [ and52,53 effi]; ciency. This study used the root mean squared error (RMSE), mean absolute error (MAE), relativeStep RMSE 6: Evaluate (rRMSE), the relativeaccuracy MAE of the (rMAE), neural andnetwork efficiency-based coe modelsfficient using (CE) the as evaluation testing subset. measures. Each selectedTheir equations typhoon can was be analyzed defined as using follows: the models to estimate typhoon rainfall and compare model errors and efficiency. This study used the root mean squared error (RMSE), mean absolute error v t n (MAE), relative RMSE (rRMSE), relative MAE (rMAE),1 X and efficiency2 coefficient (CE) as evaluation RMSE = Rest Robs , (1) measures. Their equations can be defined as follows:n i − i i=1 푛 1 n 1 X est obs 2 RMSE = √ ∑( 푅푖est − 푅obs푖 ) , (1) MAE = 푛 Ri Ri , (2) n 푖=1 − i=1

1 푛 RMSEest obs MAErRMSE= ∑푖==1 |푅푖 − 푅,푖 |, (2 (3)) 푛 obs RMSER rRMSE = obs , (3) MAE푅 rMAE = , (4) 푀퐴퐸obs rMAE = Robs, 푅 (4) Pn obs est 2 i∑=푛1 ((R푅obs−푅estR)2 ) CECE= =1 1 − 푖=1 푖i − 푖 i , , (5) 푛 obs ̄ obs 2 2 (5) − ∑푖=1(푅푖 −푅 obs) Pn ( obs − ) est i=1 Riobs R where n represents the number of data; 푅푖 and 푅푖 − represent the ith estimated and observed obs est obs values,where n respectivelyrepresents the; and number 푅 represents of data; Ri theand averageRi represent observed the valueith estimated; and observed values, obs respectively;Step 7: Compare and R representsthe optimal the neural average network observed-based value; models with empirical formulas by using the ZStep-R_MP 7: Compareand Z-R_ thestation optimal formulas neural. W network-basede computed the models Z-R relationship with empirical at Hualien formulas station by using (Z- R_Hualien)the Z-R_MP as and Z = Z-R_station288 R1.195, that formulas. at Sun Moon We computedLake station the as Z-RZ = 378 relationship R1.0957, and at that Hualien at Taichung station station(Z-R_Hualien) (Z-R_Taic ashung)Z = 288 asR Z1.195 = 352, that R0.8376 at Sun. Moon Lake station as Z = 378 R1.0957, and that at Taichung station (Z-R_Taichung) as Z = 352 R0.8376. 3.1. Network Architecture Network Architecture The developed RMMLP and RMCNN models were based on two types of neural networks, namelyThe an developed MLP and RMMLPa CNN. The and framework RMCNN models of the proposed were based RMMLP on two (Figure types 4) of is neural a conventional networks, typenamely of ANN an MLP that and include a CNN.s input, The framework hidden, and of the output proposed layers. RMMLP The additional (Figure4) isfully a conventional connected layer type directlyof ANN receive that includess the cropped input, hidden, imagesand to be output flattened layers. (conversion The additional from fullya two connected-dimensional layer to directly a one- dimensionalreceives the croppedarray). Therefore, images to bethe ﬂattened RMMLP (conversion model can frombe used a two-dimensional when images serve to a one-dimensional as the network modelarray). input Therefore,s. the RMMLP model can be used when images serve as the network model inputs.

Figure 4. Architecture of the proposed radar mosaic-based multilayer perceptron (RMMLP). Figure 4. Architecture of the proposed radar mosaic-based multilayer perceptron (RMMLP).

Remote Sens. 2020, 12, 896 8 of 19

RMMLP model training involves learning and recall phases. In the learning phase, data training is conducted using known input and output values to obtain a set of connection weights in the hidden layer. The weights are used to calculate objective output results. In the recall phase, another input value (i.e., validation and test sets) is entered, and the estimated value is output using the weights Remote Sens. 2020, 12, x FOR PEER REVIEW 8 of 19 obtained in the learning phase. UnlikeUnlike thethe RMMLPRMMLP model, the the RM RMCNNCNN model model has has two two additional additional layers: layers: convolutional convolutional and and poolingpooling layerslayers (Figure(Figure 55)).. TheThe two additional additional layers layers enable enable the the RM RMCNNCNN to toefficiently e ﬃciently convert convert the the collectedcollected information information into applicable applicable data data for for extract extractinging features. features. Subsequently, Subsequently, the the features features are are combinedcombined byby thethe fully connected layer, layer, and and model model trainin trainingg is isconducted. conducted.

FigureFigure 5. ArchitectureArchitecture of of radar radar mosaic mosaic-based-based convolutional convolutional neural neural network network (RMCNN (RMCNN).).

TheThe convolutional convolutional layer layer of the of RM theCNN RMCNN model contains model containsseveral convolution several convolutionkernels. Different kernels. Diweightfferent combinations weight combinations assigned to assigned the convolution to the convolution kernels can kernels be used can to be sharpen used to images, sharpen detect images, detectedges, edges, and extract and extract features features for recognition for recognition purposes. purposes. The neurons The neurons in the in convolutional the convolutional layer layer are are featurefeature detectors. detectors. The input input end end first first corresponds corresponds to to a convolution a convolution kernel kernel and and defines defines its size. its size. In brief, In brief, thethe convolutional convolutional layer layer extracts extracts features features in in an an image. image. The The convolution convolution equation equation is expressed is expressed as follows: as follows: Z ∞ ∞ 푓(f휏()τ푔)(g푥(−x 휏)τ푑휏)dτ, (6) ∫−∞ − , (6) −∞ wherewhere ff((x) is the the original original pixels; pixels; the the original original image image is created is created after afterall pixels all pixels are superimposed. are superimposed. In Inaddition, addition, g(xg)( xdenotes) denotes the the point point of application. of application. ThroughThrough thethe convolution equation, equation, the the modeling modeling system system can can output output a result a result superimposed superimposed by by multiplemultiple inputsinputs at a a specific specific moment. moment. In Inimage image analysis, analysis, a convolution a convolution kernel kernel is the iscombination the combination of ofall all application application points. points. The The application application points points on onthe the convolution convolution kernel kernel affect aff theect the original original pixel pixel sequentially;sequentially; accordingly,accordingly, the output output of of the the linear linear superposition superposition is the is the final final output output of the of theconvolution convolution kernel.kernel. TheThe equation is is as as follows: follows: 1 1 푂(푖, 푗) = (퐼 ∗ 퐾)(푖, 푗) = ∑X1 ∑X1 퐼(푖 + 푚, 푗 + 푛) 퐾(푚, 푛), (7) O(i, j) = (I K)(i, j) = 푚=0 푛=0 I(i + m, j + n)K(m, n), (7) ∗ m=0 n=0 where O, I, and K are outputs, inputs, and convolution kernels, respectively, and m and n are defined whereby theO convolution, I, and K are kernel outputs, function. inputs, and convolution kernels, respectively, and m and n are defined by theIn convolution an RMCNN, kernel the function.fully connected layer performs a regression on the extracted features flattenedIn an in RMCNN, the convolution the fully and connected pooling layer layers. performs Data are a regressionprocessed onusing the a extracted dropout featuresfunction flattenedthat inenables the convolution the models andto shut pooling down layers. some of Data the neurons are processed to prevent using overfitting a dropout during function training. that enables the models to shut down some of the neurons to prevent overfitting during training. 4. Modeling 4. Modeling This study employed the training–validation set to train model parameters and verify model applicability.This study Two employed types of the neural training–validation network models set (i.e., to trainRMCNN model and parameters RMMLP and models) verify were model applicability.established to Two examine types ofthe neural most networksuitable modelssize and (i.e., hyperparameters RMCNN and RMMLP(e.g., number models) of neurons were established and tolearning examine rate) the concerning most suitable radar size images. and hyperparametersA trial-and-error approach (e.g., number was used of neuronsfor verification, and learning and the rate) concerningRMCNN architecture radar images. used in A this trial-and-error study is displayed approach in Figure was 5 used. The forsettings verification, of each RMCNN and the model RMCNN parameter are outlined as follows: filter weighting size = 3 × 3; padding method = same; max pooling size = 2 × 2. The activation function of the convolutional layer was a rectified linear unit (ReLU) function, the activation function of the hidden layer was a sigmoid function, and the dropout rate was 0.2.

Remote Sens. 2020, 12, 896 9 of 19 architecture used in this study is displayed in Figure5. The settings of each RMCNN model parameter are outlined as follows: ﬁlter weighting size = 3 3; padding method = same; max pooling size = × 2 2. The activation function of the convolutional layer was a rectiﬁed linear unit (ReLU) function, × the activation function of the hidden layer was a sigmoid function, and the dropout rate was 0.2.

4.1. Image Resizing and Selection The resolution of the original radar images was 1024 1024 pixels. This study ﬁrst located and × centered the experimental stations in the images and then cropped the sheet by sizes of 4 4, 6 6, × × ... , and 30 30 pixels. One pixel typically corresponds to an actual distance of 0.703 km. The cropped × images and observatory rainfall data were then used as inputs into the RMCNN model for rainfall estimation. In this phase, the number of neurons and the learning rate in the hidden layer were set to 10 and 0.0001, respectively. Tables2–4 present the RMSE results for di ﬀerent image sizes for the Hualien, Sun Moon Lake, and Taichung stations, respectively. The lowest RMSE values for the estimations at both experimental stations (3.449, 3.061, and 2.478 mm/h) were observed when the image size of 12 12 pixels was × used for Hualien and Taichung and the image size of 14 14 pixels was used for Sun Moon Lake. × Therefore, these were selected as the most suitable image sizes. Here, 12 pixels correspond to an actual distance of 8.44 km.

Table 2. Results for various image sizes (pixel pixel) at Hualien station. × Image size 4 4 6 6 8 8 10 10 12 12 14 14 16 16 × × × × × × × RMSE (mm/h) 3.776 3.773 3.659 4.285 3.449 4.263 4.813 Image size 18 18 20 20 22 22 24 24 26 26 28 28 30 30 × × × × × × × RMSE (mm/h) 3.886 3.639 4.344 4.014 3.854 4.461 4.114

Table 3. Results for various image sizes (pixel pixel) at Sun Moon Lake station. × Image size 4 4 6 6 8 8 10 10 12 12 14 14 16 16 × × × × × × × RMSE (mm/h) 3.473 3.787 3.273 3.447 3.343 3.061 3.330 Image size 18 18 20 20 22 22 24 24 26 26 28 28 30 30 × × × × × × × RMSE (mm/h) 3.182 3.280 3.172 3.158 3.446 3.706 4.002

Table 4. Results for various image sizes (pixel pixel) at Taichung station. × Image size 4 4 6 6 8 8 10 10 12 12 14 14 16 16 × × × × × × × RMSE (mm/h) 2.797 2.997 3.061 2.662 2.478 2.640 2.534 Image size 18 18 20 20 22 22 24 24 26 26 28 28 30 30 × × × × × × × RMSE (mm/h) 2.623 3.119 3.091 3.127 2.936 3.017 3.099

4.2. Parameter Calibration After the most suitable image size was selected, the RMCNN model hyperparameters were examined. First, the number of neurons in the hidden layer was calibrated. The number of neurons was set between 5 and 35. Figure6a,c,e present the RMSE values of the RMCNN and RMMLP models when applied at the Hualien, Sun Moon Lake, and Taichung stations, respectively. The lowest RMSE values (2.764 and 3.624 mm/h) were obtained when the RMCNN and RMMLP models applied at the Hualien station had 18 and 20 neurons, respectively; the lowest RMSE values (2.141 and 2.695 mm/h) for the estimations at the Sun Moon Lake station were obtained when the RMCNN and RMMLP models had 13 and 16 neurons, respectively; and the lowest RMSE values (1.542 and 1.756 mm/h) for Remote Sens. 2020, 12, 896 10 of 19 the estimations at the Taichung station were obtained when the RMCNN and RMMLP models had 20 andRemote 22 Sens. neurons, 2020, 12 respectively., x FOR PEER REVIEW 10 of 19

FigureFigure 6. 6.Parameter Parameter calibration calibration of of the the number number of of neuron neuron nodes nodes and and learning learning rate rate at Hualien at Hualien (a,b ),(a Sun, b), MoonSun Moon Lake Lake (c,d), ( andc, d), Taichung and Taichung (e,f). (e, f).

ThisThis studystudy usedused adaptiveadaptive momentmoment estimationestimation (Adam)(Adam) proposedproposed byby [[5454]]to to analyze analyze the the learning learning rate.rate. TheThe AdamAdam algorithmalgorithm waswas selectedselected becausebecause itit hashas anan adaptiveadaptive learninglearning raterate andand cancan adjustadjust thethe learninglearning raterate andand updateupdate neuralneural networknetwork weightsweights onon thethe basisbasis ofof ﬁrst-first- andand second-ordersecond-order momentmoment estimation,estimation, whichwhich increasesincreases thethe calculationcalculation eefficiency.ﬃciency. ToTo applyapply thethe AdamAdamalgorithm, algorithm, thisthis studystudy setset thethe initialinitial learninglearning rate to to between between 0.0001 0.0001 and and 0.00 0.002.2. Fig Figureures 66bb,d,f, d, and illustrate f illustrate theRMSE the RMSE values values of theof the RMCNN RMCNN and and RMMLP RMMLP models models applied applied at at the the three three stations. stations. For For the the estimations estimations at at the the Hualien Hualien station,station, the the RMCNNRMCNN and and RMMLPRMMLPmodels models hadhad minimumminimum RMSERMSE valuesvalues (2.690(2.690and and 3.2223.222 mmmm/h)/h) whenwhen thethe learninglearning raterate waswas 0.00080.0008 andand 0.0009,0.0009,respectively. respectively. ForFor SunSun MoonMoon LakeLake station, station, thethe RMCNNRMCNNand and RMMLPRMMLP modelsmodels hadhad minimumminimum RMSERMSE valuesvalues (2.031(2.031 andand 2.6062.606 mmmm/h)/h) whenwhen thethe learninglearning raterate waswas 0.00060.0006 and and 0.0008, 0.0008 respectively., respectively. For Taichung For Taichung station, station, the RMCNN the RMCNN and RMMLP and modelsRMMLP had models minimum had RMSEminimum values RMSE (1.437 values and 1.563 (1.437 mm and/h) when 1.563 themm/h) learning when rate the was learnin 0.0006g and rate 0.0007, was 0.000 respectively.6 and 0.0007, respectively. 5. Results and Discussion

5. ResultsTo examine and Discussion the applicability of the three models and estimation errors for typhoons passing through the CMR from east to west, this study selected data on four typhoons for evaluation and comparedTo examine the analysis the applicability results of the of RMCNN, the three RMMLP, models Z-R_MP,and estimation and Z-R_station errors for models. typhoons passing through the CMR from east to west, this study selected data on four typhoons for evaluation and compared the analysis results of the RMCNN, RMMLP, Z-R_MP, and Z-R_station models.

5.1. Simulation Results Four typhoons (Matmo, Soudelor, Dujuan, and Megi) were employed to identify the most suitable rainfall estimation model. Figure 7 presents hyetographs of observed rainfall and RMCNN, RMMLP, Z-R_MP, and Z-R_station model estimations at the Hualien, Sun Moon Lake, and Taichung stations.

Remote Sens. 2020, 12, 896 11 of 19

5.1. Simulation Results Four typhoons (Matmo, Soudelor, Dujuan, and Megi) were employed to identify the most suitable rainfall estimation model. Figure7 presents hyetographs of observed rainfall and RMCNN, RMMLP, Z-R_MP,Remote Sens. and 2020 Z-R_station, 12, x FOR PEER model REVIEW estimations at the Hualien, Sun Moon Lake, and Taichung stations.11 of 19

Figure 7. Rainfall hyetographs and model estimations for (a) Hualien, (b) Sun Moon Lake, and (c) Figure 7. Rainfall hyetographs and model estimations for (a) Hualien, (b) Sun Moon Lake, and (c) Taichung stations. Taichung stations. The rain duration of typhoon Matmo was 43 h (time series: t = 1–43 h; Figure7). The Hualien, Sun The rain duration of typhoon Matmo was 43 h (time series: t = 1–43 h; Figure 7). The Hualien, Moon Lake, and Taichung stations had the maximum observed rainfall at t = 20 h (41 mm/h), t = 24 h Sun Moon Lake, and Taichung stations had the maximum observed rainfall at t = 20 h (41 mm/h), t = (26 mm/h), and t = 24 h (20 mm/h), respectively. After the typhoon circulation structure was disturbed 24 h (26 mm/h), and t = 24 h (20 mm/h), respectively. After the typhoon circulation structure was by the CMR, the observed rainfalls at the Taichung and Sun Moon Lake stations were less than that at disturbed by the CMR, the observed rainfalls at the Taichung and Sun Moon Lake stations were less the Hualien station. The results for the remaining three typhoons were similar. Typhoon Soudelor than that at the Hualien station. The results for the remaining three typhoons were similar. Typhoon had a rain duration of 50 h (t = 44–93 h) and the Hualien station recorded the maximum rainfall at Soudelor had a rain duration of 50 h (t = 44–93 h) and the Hualien station recorded the maximum t = 66 h (54 mm/h), whereas the Sun Moon Lake station recorded the maximum rainfall with a 3-h delay rainfall at t = 66 h (54 mm/h), whereas the Sun Moon Lake station recorded the maximum rainfall (t = 69 h; 19 mm/h) and Taichung station recorded the maximum rainfall with a 7-h delay (t = 73 h; with a 3-h delay (t = 69 h; 19 mm/h) and Taichung station recorded the maximum rainfall with a 7-h 9 mm/h). The rain duration of typhoon Dujuan was 28 h (t = 94–121). The maximum rainfall at the delay (t = 73 h; 9 mm/h). The rain duration of typhoon Dujuan was 28 h (t = 94–121). The maximum Hualien station was reached at t = 109 h (35 mm/h); that at the Sun Moon Lake station was reached at rainfall at the Hualien station was reached at t = 109 h (35 mm/h); that at the Sun Moon Lake station t = 114 h (34 mm/h), with a 5-h delay; and at the Taichung station, it was reached at t = 114 h (15 mm/h), was reached at t = 114 h (34 mm/h), with a 5-h delay; and at the Taichung station, it was reached at t with a 5-h delay. Typhoon Megi had a rain duration of 63 h (t = 122–184 h). The maximum rainfall = 114 h (15 mm/h), with a 5-h delay. Typhoon Megi had a rain duration of 63 h (t = 122–184 h). The at the Hualien, Sun Moon Lake, and Taichung stations was reached at t = 140 h (61 mm/h), t = 143 h maximum rainfall at the Hualien, Sun Moon Lake, and Taichung stations was reached at t = 140 h (61 (8 mm/h), and t = 151 h (8 mm/h; 11-h delay), respectively. mm/h), t = 143 h (8 mm/h), and t = 151 h (8 mm/h; 11-h delay), respectively. Regarding the estimated rain pattern, the estimations of all models at the Hualien station (Figure7a) Regarding the estimated rain pattern, the estimations of all models at the Hualien station (Figure were mostly identical to the observed pattern. Concerning the peak rainfall on the hyetographs, all 7a) were mostly identical to the observed pattern. Concerning the peak rainfall on the hyetographs, models reﬂected an increase in rainfall. However, these models had larger diﬀerences in estimated all models reflected an increase in rainfall. However, these models had larger differences in estimated types of rain, peak rainfall on the hyetograph, and the arrival time of peak rainfall for data recorded at the Sun Moon Lake and Taichung stations. This may be because the rapidly changing typhoon circulation structure and the radar images detected and received at the Sun Moon Lake and Taichung stations increase forecast uncertainty. By contrast, before a typhoon reaches the island, its structure and circulation observed at the Hualien station tend to be more stable, which facilitates the estimation of intense rainfall. This study compared these models according to their performance for several evaluation measures.

Remote Sens. 2020, 12, 896 12 of 19 types of rain, peak rainfall on the hyetograph, and the arrival time of peak rainfall for data recorded at the Sun Moon Lake and Taichung stations. This may be because the rapidly changing typhoon circulation structure and the radar images detected and received at the Sun Moon Lake and Taichung stations increase forecast uncertainty. By contrast, before a typhoon reaches the island, its structure and circulation observed at the Hualien station tend to be more stable, which facilitates the estimation of intense rainfall. This study compared these models according to their performance for several evaluation measures.

Remote Sens. 2020, 12, x FOR PEER REVIEW 12 of 19 5.2. Evaluations 5.2. Evaluations Figure8 shows scatter plots comparing the observations obtained with the four model estimations. For bothFigure stations, 8 shows the scatter correlation plots comparing coeﬃcient the (r) observations indicated that obtained the RMCNN with the modelfour model was more accurate estimations. For both stations, the correlation coefficient (r) indicated that the RMCNN model was than the RMMLP, Z-R_MP, and Z-R_station models. The RMCNN model estimations at the Hualien more accurate than the RMMLP, Z-R_MP, and Z-R_station models. The RMCNN model estimations stationat the Hualien (r = 0.946) station and (r = Sun 0.946 Moon) and Sun Lake Moon station Lake(r station= 0.961) (r = 0. were961) were more more satisfactory satisfactory and and consistent with theconsistent observed with data the observed than those data atthan the those Taichung at the Taichung station (rstation= 0.878). (r = 0.878).

Figure 8. 8. ScatterplotsScatterplots of observations of observations versus versusestimations estimations using RMCNN using, RMMLP RMCNN,, Marshall RMMLP,–Palmer Marshall–Palmer Z-RZ-R relationship relationship (Z- (Z-R_MP),R_MP), and reformulated and reformulated Z-R relationship Z-R relationship at each site at(Z each-R_station site) (Z-R_station)models for models for Hualien (a–d), Sun Moon Lake (e–h), and Taichung (i–l). Hualien (a–d), Sun Moon Lake (e–h), and Taichung (i–l). Regarding absolute errors, this study assessed the MAE and RMSE for the four examined typhoons.Regarding For the absolute RMCNN errors,model, the this MAE study and assessed RMSE values the MAE for the and four RMSE typhoons for theobserved four examinedat the typhoons. ForHualien the RMCNNstation were model, higher than the MAEthose observed and RMSE at the values Sun Moon for Lake the fourand Taichung typhoons station observeds (Figure at the Hualien station9a, e). Similar were higherresults were than observed those observed for the RMMLP at the ( SunFigure Moon 9b, f), Lake Z-R_MP and (Figure Taichung 9c, g) stations, and Z- (Figure9a,e). SimilarR_station results (Figure were9d, h) observedmodels. According for the to RMMLP these results, (Figure the estimations9b,f), Z-R_MP at the Hualien (Figure station9c,g), andhad Z-R_station (Figurea larger9 errord,h) because models. of Accordingthe rainfall atto this these station. results, the estimations at the Hualien station had a larger error because of the rainfall at this station.

Remote Sens. 2020, 12, 896 13 of 19 Remote Sens. 2020, 12, x FOR PEER REVIEW 13 of 19

Figure 9. Absolute errors for RMCNN, RMMLP, Z-R_MP, and Z-R_station: (a–d) MAE and (e–h) RMSE. Figure 9. Absolute errors for RMCNN, RMMLP, Z-R_MP, and Z-R_station: (a–d) MAE and (e–h) ThisRMSE. study also used rMAE and rRMSE to evaluate the estimations for the four typhoons. For the RMCNN model, the rMAE and rRMSE values observed for the Taichung station were higher than those observedThis forstudy the also Hualien used andrMAE Sun and Moon rRMSE Lake to stations evaluate for the typhoons estimations Matmo, for the Soudelor, four typhoons. and Dujuan For (Figurethe RMCNN 10a,e). model, For the the RMMLP rMAE and and rRMSE Z-R_MP values models, observed the rMAE for the and Taichung rRMSE station values were observed higher for than the Taichungthose observed station for were the also Hualien higher and than Sun those Moon observed Lake for station the Hualiens for typhoons and Sun Matmo, Moon Lake Soudelor, stations and for typhoonsDujuan (Figure Matmo 10 anda, e). Soudelor For the RMMLP (Figure 10andb,c,f,g). Z-R_MP models, the rMAE and rRMSE values observed for the Taichung station were also higher than those observed for the Hualien and Sun Moon Lake stations for typhoons Matmo and Soudelor (Figure 10b, c, f, g).

RemoteRemote Sens.Sens. 20202020,, 1212,, 896x FOR PEER REVIEW 1414 ofof 1919

Figure 10. Relative errors for RMCNN, RMMLP, Z-R_MP, and Z-R_station: (a–d) rMAE and (Figuree–h) rRMSE. 10. Relative errors for RMCNN, RMMLP, Z-R_MP, and Z-R_station: (a–d) rMAE and (e–h) rRMSE. Table5 presents the overall performance levels obtained for the models for the four examined typhoonsTable at5 presents Hualien, the Sun overall Moon performance Lake, and Taichung levels obtained stations. for the The models RMCNN for modelthe four exhibited examined a superiortyphoons performance at Hualien, for Sun each Moon measure Lake compared, and Taichung with the stations. RMMLP, The Z-R_MP, RMCNN and Z-R_station model exhibited models. a Moreover,superior performance the absolute for errors each observed measure for compared the estimations with the at the RMMLP, Hualien Z station-R_MP, were and greater Z-R_station than thosemodels. observed Moreover, for the the estimations absolute errors at the Sun observed Moon Lakefor the and estimations Taichung stations, at the Hualien but the relative station errors were observedgreater than for thethose estimations observed atfor the the Hualien estimations station at werethe Sun lower Moon than Lake those and observed Taichung for stations, the estimations but the atrelative the Sun errors Moon observed Lake and for Taichung the estimations stations. at the Finally, Hualien the RMCNNstation were model lower had than the those highest observed CE (0.867) for forthe theestimations estimations at atthe the Sun Hualien Moon station,Lake and whereas Taichung the Z-R_station stations. Finally, model the had R theMCNN lowest model CE among had the all modelshighest atCE the (0.86 three7) for stations. the estimations at the Hualien station, whereas the Z-R_station model had the lowest CE among all models at the three stations.

Remote Sens. 2020, 12, 896 15 of 19

Table 5. Overall model performance levels for four typhoons.

Station Model RMCNN RMMLP Z-R_MP Z-R_ station MAE (mm/h) 1.870 2.218 2.670 4.206 RMSE (mm/h) 3.502 4.351 4.955 7.569 rMAE 0.309 0.366 0.441 0.695 Hualien rRMSE 0.579 0.719 0.818 1.250 r 0.946 0.930 0.868 0.854 CE 0.867 0.794 0.733 0.378 MAE (mm/h) 1.070 1.340 1.522 2.268 RMSE (mm/h) 2.124 2.672 3.155 4.458 rMAE 0.314 0.393 0.446 0.665 Sun Moon Lake rRMSE 0.623 0.783 0.925 1.307 r 0.961 0.939 0.835 0.852 CE 0.860 0.778 0.691 0.383 MAE (mm/h) 0.771 0.905 1.141 1.474 RMSE (mm/h) 1.641 1.828 2.361 2.836 rMAE 0.440 0.517 0.651 0.842 Taichung rRMSE 0.937 1.043 1.348 1.619 r 0.878 0.843 0.655 0.741 CE 0.727 0.661 0.416 0.185

5.3. Estimation Performance for Peak Rainfall This study examined the estimation performance of the four models for peak rainfall. The relative error of peak rainfall and the absolute time error of peak rainfall were derived as measures for comparison. First, the relative error of peak rainfall (REPeak), deﬁned as the average ratio of absolute errors, can be expressed as follows:

Pm ppre pobs k=1 O O RE = k − k , (8) peak Pm pobs k=1 Ok

ppre pobs where Ok is the estimated peak value in typhoon event k, Ok is the observed peak value in typhoon event k, and m is the total number of typhoon events. Second, the absolute time error of peak rainfall (ATPeak), deﬁned as the average of absolute time errors, can be expressed as follows:

Xm 1 ppre pobs ATpeak = T T , (9) m k=1 k − k

ppre pobs where Tk is the arrival time of estimated peak rainfall in typhoon event k and Tk is the arrival time of observed peak rainfall in typhoon event k. Lower REPeak and ATPeak values indicate higher performances. Figure 11 displays the REPeak and ATPeak values for the four typhoons. As illustrated by Figure 11a, the following results were observed: (1) For the estimations at the Hualien and Sun Moon Lake stations, the REPeak value for the RMCNN model was superior to those for the RMMLP, Z-R_MP, and Z-R_station models, but for the estimations at the Taichung station, the REPeak value for the Z-R_MP model was superior to those for the RMCNN, RMMLP, and Z-R_station models; (2) with relative error of the estimated peak rainfall on RMCNN, Hualien station computed the smallest REPeak (0.262), followed by Sun Moon Lake station (0.303), and then Taichung station (0.385). The peak rainfall estimated at the Hualien station was less than that at the Sun Moon Lake and Taichung stations because the typhoon routes were disturbed by the CMR. Hence, peak rainfall was diﬃcult to estimate at the Sun Moon Lake and Taichung stations. Remote Sens. 20202020, 1212,, 896x FOR PEER REVIEW 16 of 19

Figure 11. Performance levels for RMCNN, RMMLP, Z-R_MP, and Z-R_station in terms of (a) the Figure 11. Performance levels for RMCNN, RMMLP, Z-R_MP, and Z-R_station in terms of (a) the relative error of peak rainfall (REpeak) and (b) the absolute time error of peak rainfall (ATpeak). relative error of peak rainfall (REpeak) and (b) the absolute time error of peak rainfall (ATpeak).

Additionally, as shown in Figure 11b, the following results were observed: (1) The ATPeak values Additionally, as shown in Figure 11b, the following results were observed: (1) The ATPeak values observed for the RMCNN and RMMLP models for the estimations at Hualien station were 0, indicating observed for the RMCNN and RMMLP models for the estimations at Hualien station were 0, that the models accurately estimated the wind and rain arrival times. Although all models could not indicating that the models accurately estimated the wind and rain arrival times. Although all models accurately estimate the rain arrival times for the estimations at the Sun Moon Lake and Taichung could not accurately estimate the rain arrival times for the estimations at the Sun Moon Lake and stations, the ATPeak value obtained for the RMCNN model was smaller than those obtained for the Taichung stations, the ATPeak value obtained for the RMCNN model was smaller than those obtained RMMLP, Z-R_MP, and Z-R_station models; (2) the ATPeak values obtained for all models for the for the RMMLP, Z-R_MP, and Z-R_station models; (2) the ATPeak values obtained for all models for estimations at Hualien station were smaller than those obtained for the estimations at the Sun Moon the estimations at Hualien station were smaller than those obtained for the estimations at the Sun Lake and Taichung stations because the typhoon eye and structure were more stable before reaching Moon Lake and Taichung stations because the typhoon eye and structure were more stable before landforms. Therefore, the peak rainfall arrival time was more easily estimated in Hualien. reaching landforms. Therefore, the peak rainfall arrival time was more easily estimated in Hualien. 6. Conclusions 6. Conclusions This study examined the efficiency of typhoon precipitation estimation and evaluated the influence of theThis CMR study on rainfall examined during the typhoons. efficiency In of general, typhoon when precipitation a typhoon approaches estimation Taiwan and evaluated from east the to west,influence its route of the or CMR the wind on andrainfall rain during it carries typhoons. are more In easily general, predicted when before a typhoon it passes approaches through the Taiwan CMR. fromBy contrast, east to afterwest, the its typhoonroute or passesthe wind the and CMR, rain its it route carries and are delay more in easily rainfall predic becometed before unpredictable. it passes throughThis the study CMR. considered By contrast, 17 typhoons after the that typhoon affected passes the research the CMR, area from its route 2013 and to 2017 delay and in collected rainfall becomehourly radar unpredictable. images released by the CWB during the typhoons, as well as observatory data. Hualien stationThis in the study east, considered Sun Moon 17 Lake typhoons station in that Central affected Taiwan, the research and Taichung area from station 2013 in the to west 2017 were and collectedselected as hourly the three radar experimental images released sites, by and the RMCNN, CWB during RMMLP, the typhoons Z-R_MP, and, as well Z-R_station as observatory models data. were Hualienemployed. station The RMCNNin the east model, Sun wasMoon incorporated Lake station with in C theentral radar Taiwan, images and to estimate Taichung typhoon station rainfall. in the westUsing were the selected overall rainfallas the three rates experimental of all stations, sites, RMCNN and RMCNN computed, RMMLP the smallest, Z-R_MP, relative and Z root-R_station mean modelssquared were error (0.713),employed. followed The RMCNN by RMMLP model (0.848), was Z-R_MP incorporated (1.030), with and Z-R_stationthe radar images (1.392). to Moreover, estimate typhoonthe smallest rainfall. relative U errorsing the of peak overall rainfall rainfall was yielded rates of by all RMCNN stations, (0.316), RMCNN followed computed by RMMLP the smallest (0.379), relativeZ-R_MP root (0.402), mean and squared Z-R_station error (0.688). (0.713), The followed smallest by relative RMMLP error (0.8 of48), peak Z rainfall-R_MP arrival (1.030), time and was Z- R_stationcomputed (1.392) by RMCNN. Moreover, (1.507 the h), followed smallest byrelative RMMLP error (2.673 of peak h), Z-R_MP rainfall (2.917was yielded h), and by Z-R_station RMCNN (3.250(0.316), h). followed On the basisby RMMLP of relevant (0.379), evaluation Z-R_MP measures, (0.402), theand RMCNN Z-R_station model (0.688) outperformed. The smallest the RMMLP,relative errorZ-R_MP, of peak and Z-R_stationrainfall arrival models. time was computed by RMCNN (1.507 h), followed by RMMLP (2.673 h), ZThe-R_MP estimations (2.917 h), of and the fourZ-R_station models at(3.250 Hualien h). stationOn the werebasis mostly of relevant identical evaluation to the observed measures, rainfall the RMCNNdata. Although model all outperformed models estimated the RMMLP an increase, Z-R_MP, in rainfall and at Z the-R_station peak rainfall models. time on the hyetographs, the peakThe valueestimations was underestimated. of the four mo Thedels estimations at Hualien of station the four were models mostly concerning identical the to hyetograph the observed and peakrainfall rainfall data. arrivalAlthough time all at models the Sun estimated Moon Lake an and increase Taichung in rainfall stations at were the peak considerably rainfall inconsistenttime on the withhyetographs, the observed the peak data. value This was may underestimated. be because the rapidly The estimations changing of typhoon the four circulation models concernin structureg andthe hyetographthe radar images and peakincrease rainfall the uncertainty arrival time of atrainfall the Sun forecasting. Moon Lake By contrast,and Taichung peak rainfall station ands were the peakconsiderably rainfall arrivalinconsistent time werewith the easier observed to detect data. at HualienThis may station be because because the therapidly typhoon changing structure typhoon and circulation arestructure more stableand the before radar the images typhoon increase reaches the theuncer island.tainty In of conclusion, rainfall forecasting. this study By employed contrast, peak rainfall and the peak rainfall arrival time were easier to detect at Hualien station because the typhoon structure and circulation are more stable before the typhoon reaches the island. In conclusion, this study employed the RMCNN model integrated with radar imagers to estimate

Remote Sens. 2020, 12, 896 17 of 19 the RMCNN model integrated with radar imagers to estimate typhoon rainfall, and the results reveal that the model incorporating radar images can eﬀectively estimate precipitation during typhoons.

Author Contributions: C.-C.W. conceived and designed the experiments and wrote the manuscript; C.-C.W. and P.-Y.H. carried out this experiment and analysis of the data and discussed the results. All authors have read and agreed to the published version of the manuscript. Funding: This study was supported by the Ministry of Science and Technology, Taiwan, under Grant No. MOST108-2111-M-019-001. Acknowledgments: The authors acknowledge data provided by the Central Weather Bureau of Taiwan, which are available at https://rdc28.cwb.gov.tw/. This manuscript was edited by Wallace Academic Editing. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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