Real-Time Rainfall Forecasts Based on Radar Reflectivity during Typhoons: Case Study in Southeastern Taiwan

This study developed a real-time rainfall forecasting system that can predict rainfall in a particular area a few hours before a typhoon’s arrival. The reflectivity of nine elevation angles obtained from the volume coverage pattern 21 Doppler radar scanning strategy and ground-weather data of a specific area were used for accurate rainfall prediction. During rainfall prediction and analysis, rainfall retrievals were first performed to select the optimal radar scanning elevation angle for rainfall prediction at the current time. Subsequently, forecasting models were established using a single reflectivity and all elevation angles (10 prediction submodels in total) to jointly predict real-time rainfall and determine the optimal predicted values. This study was conducted in southeastern Taiwan and included three onshore weather stations (Chenggong, Taitung, and Dawu) and one offshore weather station (Lanyu). Radar reflectivities were collected from Hualien weather surveillance radar. The data for a total of 14 typhoons that affected the study area in 2008–2017 were collected. The gated recurrent unit (GRU) neural network was used to establish the forecasting model, and extreme gradient boosting and multiple linear regression were used as the benchmarks. Typhoons Nepartak, Meranti, and Megi were selected for simulation. The results revealed that the input data set merged with weather-station data, and radar reflectivity at the optimal elevation angle yielded optimal results for short-term rainfall forecasting. Moreover, the GRU neural network can obtain accurate predictions 1, 3, and 6 h before typhoon occurrence.


Introduction
Taiwan is located in the intertropical convergence zone in the western Pacific Ocean with a geographical location of approximately 22 • N-25 • N and 120 • E-122 • E. Taiwan is frequently affected by typhoons during summer and autumn that result in heavy precipitation. Although heavy precipitation causes disasters such as flooding, landslides, and debris flows, it is a main source of water [1,2]. Therefore, when typhoons approach, government agencies must make various cautious decisions regarding future strong winds and heavy precipitation, e.g., reservoir discharges. This study developed a system that can forecast future rainfall time patterns and then used them to enact timely typhoon-prevention measures.
Weather radar is an essential analysis tool for meteorological observations because it can be used to locate weather patterns, large-scale rainfall, and airflow characteristics [3][4][5][6]. Radar emits electromagnetic waves from an antenna. When contacting targets in the air (e.g., water vapor), the waves are scattered and partially reflected back to the radar direction [7,8]. Marshall et al. [9] calculated the reflectivity power and raindrop size distribution observed from a disdrometer at a distance of 8.8 km from the radar and demonstrated an excellent correlation with the calculated reflectivity factor (Z). Marshall and Palmer [10] proposed Z = 200 × R 1. 6 and explained the relationship between Z and rainfall intensity (R). Studies on convective systems have, however, underestimated quantitative precipitation (e.g., [11,12]). Therefore, these coefficients may not be the most suitable

Data Description
The study area (Figure 1) was southeastern Taiwan and included three onshore weather stations (Chenggong, Taitung, and Dawu stations) and one offshore station (Lanyu station). The selected experimental areas are located in typical typhoon paths and are affected by typhoons. Table 1 lists 14 typhoon events that affected the study area from 2008 to 2017 and their occurrence dates, total precipitation, and maximum wind speeds at the typhoon centers. Moreover, Figure 2 illustrates the spatial distribution of 24-h accumulated rainfall over the study area of each collected typhoon.
weather stations (Chenggong, Taitung, and Dawu stations) and one offshore statio (Lanyu station). The selected experimental areas are located in typical typhoon paths an are affected by typhoons. Table 1 lists 14 typhoon events that affected the study area from 2008 to 2017 and their occurrence dates, total precipitation, and maximum wind speeds a the typhoon centers. Moreover, Figure 2 illustrates the spatial distribution of 24-h accu mulated rainfall over the study area of each collected typhoon.    This study collected radar reflectivity and ground-weather data from the CWB of Taiwan. The CWB directly supervises four weather radar stations [38], which comprise a Doppler weather radar network in Taiwan. Hualien Weather Radar Station (Figure 1) was selected as the experimental radar station because Hualien Weather Radar Station covers the experimental area and is not directly blocked by Central Mountain Range (although slightly blocked by Coastal Mountain Range and East Rift Valley). The Hualien Weather Radar Station was established in 2001 and uses the METEOR 1000S radar model, which is an S-band (wavelength of 10 cm) Doppler weather radar. The radar can continually provide data of three high-precision and high-resolution measurements, namely reflectivity, mean radial velocity, and spectral width within 5-10 min [38]. Its geographical coordinates are 23.99 • N, 121.62 • E, and it has an elevation of 63 m and observation radius of 460 km. The radar can be used to observe weather systems such as typhoons and rainy seasons from the Pacific Ocean, South China Sea, and Bashi Channel. When scanning over eastern Taiwan, the Hualien WSR uses true north as the starting point to perform a 360-degree clockwise conical surface scan, and conical surface data at different elevation angles obtained from each observation can form a complete volume scan. The Hualien WSR uses VCP21 (nine elevation angles) for typhoon and precipitation observations, and a total volume scan can be completed in approximately 6 min [38].  This study collected radar reflectivity and ground-weather data from the CWB o Taiwan. The CWB directly supervises four weather radar stations [38], which comprise a Doppler weather radar network in Taiwan. Hualien Weather Radar Station (Figure 1) was selected as the experimental radar station because Hualien Weather Radar Station covers the experimental area and is not directly blocked by Central Mountain Range (although slightly blocked by Coastal Mountain Range and East Rift Valley). The Hualien Weather Radar Station was established in 2001 and uses the METEOR 1000S radar model, which is an S-band (wavelength of 10 cm) Doppler weather radar. The radar can continually pro vide data of three high-precision and high-resolution measurements, namely reflectivity mean radial velocity, and spectral width within 5-10 min [38]. Its geographical coordi nates are 23.99° N, 121.62° E, and it has an elevation of 63 m and observation radius of 460 km. The radar can be used to observe weather systems such as typhoons and rainy seasons Regarding meteorological data, this study collected ground-weather characteristics at four stations. Each station has 12 characteristics, including ground air pressure (hPa), air pressure at sea level (hPa), ground temperature ( • C), ground dew-point temperature ( • C), ground relative humidity (%), ground global solar radiation (MJ/m 2 ), ground vapor pressure (hPa), surface wind speed (m/s), surface wind direction (deg), maximum instantaneous wind speed (m/s), instantaneous wind direction (deg), and precipitation (mm/h). A single station can collect 2544 pieces of hourly records. This study used a correlation coefficient greater than 0.3 (i.e., at least a moderate correlation) between characteristics and precipitation as the characteristic screening threshold, and all four stations were screened simultaneously. In addition to the target precipitation characteristics, four other weather characteristics were selected (i.e., ground temperature, ground relative humidity, maximum instantaneous wind speed, and rainfall duration within 1 h) on the basis of the analysis results. The correlation coefficients of these characteristics at the four stations are presented in Figure 3. pressure (hPa), surface wind speed (m/s), surface wind direction (deg), maximum instan taneous wind speed (m/s), instantaneous wind direction (deg), and precipitation (mm/h) A single station can collect 2544 pieces of hourly records. This study used a correlation coefficient greater than 0.3 (i.e., at least a moderate correlation) between characteristic and precipitation as the characteristic screening threshold, and all four stations wer screened simultaneously. In addition to the target precipitation characteristics, four othe weather characteristics were selected (i.e., ground temperature, ground relative humidity maximum instantaneous wind speed, and rainfall duration within 1 h) on the basis of th analysis results. The correlation coefficients of these characteristics at the four stations ar presented in Figure 3.  Figure 4 presents a schematic of the real-time typhoon rainfall forecasting system developed in this study. After the CWB issued a typhoon warning over ocean and land the system collected radar reflectivity and ground-weather data in the area. This proces of rainfall prediction is performed in two steps, namely precipitation retrieval (step 1 dashed red box in Figure 4) and precipitation prediction (step 2, dashed blue box). Befor the precipitation forecast model is established, rainfall retrieval is performed to determin the optimal radar elevation angle for precipitation prediction at current time. Rainfall re trieval is performed using the reflectivity values {αi}i=1,9 of the nine elevation angles usin VCP21 scanning strategy to develop the retrieval values at the current time. This stud used the relationship Z = a × R b , and the parameters a and b were derived depending on the elevation angle because the nine elevation angles, nine Z-R relations were established at each station. Thus, the retrieval values of the individual radar elevation angles of th four stations could be inferred separately.

Prediction System and Models
The Z-R relations were used only to determine the optimal elevation angle α*. How ever, this relation may underestimate the quantitative precipitation estimation on convec tive systems [40]. The absolute values of the differences between the retrieval values and the observation values (assuming that the observed rainfall at the current time was ob tained in real time) at the current time are subsequently compared, and the angle corre sponding to the least absolute errors is the optimal scanning angle α* at the current time  Figure 4 presents a schematic of the real-time typhoon rainfall forecasting system developed in this study. After the CWB issued a typhoon warning over ocean and land, the system collected radar reflectivity and ground-weather data in the area. This process of rainfall prediction is performed in two steps, namely precipitation retrieval (step 1, dashed red box in Figure 4) and precipitation prediction (step 2, dashed blue box). Before the precipitation forecast model is established, rainfall retrieval is performed to determine the optimal radar elevation angle for precipitation prediction at current time. Rainfall retrieval is performed using the reflectivity values {α i } i=1,9 of the nine elevation angles using VCP21 scanning strategy to develop the retrieval values at the current time. This study used the relationship Z = a × R b , and the parameters a and b were derived depending on the elevation angle because the nine elevation angles, nine Z-R relations were established at each station. Thus, the retrieval values of the individual radar elevation angles of the four stations could be inferred separately.

Prediction System and Models
The Z-R relations were used only to determine the optimal elevation angle α*. However, this relation may underestimate the quantitative precipitation estimation on convective systems [40]. The absolute values of the differences between the retrieval values and the observation values (assuming that the observed rainfall at the current time was obtained in real time) at the current time are subsequently compared, and the angle corresponding to the least absolute errors is the optimal scanning angle α* at the current time.
The second step is precipitation prediction. The input data of the precipitation prediction model include data sets {Z}, {W}, and {R}. Here, the reflectivity characteristics of nine elevation angles in the VCP21 system were expressed as data set {Z} = {Z i } i=1,9 ; the four ground-weather characteristics are represented as data set {W}; and the precipitation characteristics are represented as data set {R}. Then, the precipitation prediction P t+∆t can be expressed as where t is the current time, and ∆t is the forecast horizon (the forecast horizons in this study were 1, 3, and 6 h).
To design the prediction scenarios, this study established a single reflectivity prediction model (scenarios 1-9) from the nine elevation angles of VCP21. For example, scenario 1 is P t+∆t = f ({Z 1 ,W,R}), and Z 1 = radar reflectivity at 0.5 • . In addition, this study added a scenario in which all elevation angles {α 1 , α 2 , . . . , α 9 } were the input characteristics The second step is precipitation prediction. The input data of the precipitation prediction model include data sets {Z}, {W}, and {R}. Here, the reflectivity characteristics of nine elevation angles in the VCP21 system were expressed as data set {Z} = {Zi}i=1,9; the four ground-weather characteristics are represented as data set {W}; and the precipitation characteristics are represented as data set {R}. Then, the precipitation prediction Pt+Δt can be expressed as where t is the current time, and Δt is the forecast horizon (the forecast horizons in this study were 1, 3, and 6 h).
To design the prediction scenarios, this study established a single reflectivity prediction model (scenarios 1-9) from the nine elevation angles of VCP21. For example, scenario 1 is Pt+Δt = f ({Z1,W,R}), and Z1 = radar reflectivity at 0.5°. In addition, this study added a scenario in which all elevation angles {α1, α2, …, α9} were the input characteristics (scenario 10). Therefore, when the system forecasts rainfall in real time, 10 sets of predicted values are generated. Of the 10 sets of generated prediction values, the scenario corresponding to the optimal elevation angle α* in rainfall retrieval at the current time was adopted as the optimal prediction (pred_opt). Moreover, all the maximal predictions (pred_max) and minimal predictions (pred_min) of the scenarios were used to obtain the possible range of pred_max and pred_min.
In this study, GRU and XGB were used to establish the rainfall forecasting model. The GRU model, a variant of the LSTM neural network, is composed of the input, forget, and output layers [63]. The input gate regulates the amount of information that enters the memory cell, the forget gate directs the memory cell and remains in the present memory cell through recurring connection, and the output gate determines the amount of data used to calculate the output activation of the memory cell and information flow to the rest of the neural network [60]. Similar to the LSTM unit, the GRU has gating units that modulate the flow of information inside the unit without having a separate memory cell [70]. The weights corresponding to these gates are updated through backpropagation through time stochastic gradient descent to minimize a loss function [62,71]. The GRU algorithm was derived by Cho et al. [65] and Chung et al. [71].
XGB is a type of tree-based boosting method that is a sequential ensemble learning model of a decision tree [72]. The principal feature of XGB is its ability to automatically use multithreading for parallel computing while improving algorithm accuracy. XGB can perform parallel tree boosting (also known as gradient-boosted decision trees), which rapidly and accurately solves numerous data problems [73]. XGB uses a second-order Taylor expansion for the loss function and uses both the first-and second-order derivatives. To avoid overfitting, the regularization term is added to help smooth the final learned weights. See Chen and Guestrin [55] and Jia et al. [74] for details on algorithm derivation in XGB.

Modeling and Verification
In this study, three typhoon events in 2016, namely Typhoons Nepartak, Meranti, and Megi, were selected to be test events. The remaining 11 typhoons were used as training and validation data sets. The rainfall forecasting model necessitated a test for optimal rainfall lag time because precipitation was the predicted target characteristic of the model. The test was also required to increase effective information input for improving precipitation prediction accuracy. The training and validation process involved 10-fold cross-validation in which 90% of the data were randomly selected each time as training data, and the remaining 10% were validation data that were not repeatedly selected until all data had been selected as the 10% test set.
This study used root mean squared error (RMSE) to evaluate the errors. RMSE is defined as follows: where n is the number of pieces of data; p pre i is the i th predicted value; and p obs i is the i th observed value. Figure 5 illustrates the validation results of lag time = 1-4 h. According to the figure, errors were minimal for the GRU model (by preset parameters) when the lag time was 1, 3, 1, and 2 h for Chenggong, Taitung, Dawu, and Lanyu stations, respectively. Therefore, increased inputs for testing the optimum rainfall lag time were used for the modeling process. The model hyperparameters were verified subsequently. For the GRU model, the hyperparameters of the number of the hidden layers and the number of neurons in a hidden layer were calibrated. The ReLU activation function, which is defined as the positive part of its argument, that is, f(x) = max (0, x), where x is the input to a neuron, was used in the hidden layers. In the optimization process, adaptive moment estimation (Adam) was used to learn the learning rate. Adam is a first-order optimization algorithm that can replace the traditional stochastic gradient descent algorithm, and it can adapt the learning rate to the parameters [75]. The number of hidden layers was set to 1-6 for validation, and the validation range of the number of neurons in a hidden layer was 10-100. First, the number The model hyperparameters were verified subsequently. For the GRU model, the hyperparameters of the number of the hidden layers and the number of neurons in a hidden layer were calibrated. The ReLU activation function, which is defined as the positive part of its argument, that is, f (x) = max (0, x), where x is the input to a neuron, was used in the hidden layers. In the optimization process, adaptive moment estimation (Adam) was used to learn the learning rate. Adam is a first-order optimization algorithm that can replace the traditional stochastic gradient descent algorithm, and it can adapt the learning rate to the parameters [75]. The number of hidden layers was set to 1-6 for validation, and the validation range of the number of neurons in a hidden layer was 10-100. First, the number of neurons in a hidden layer was fixed to obtain the number of hidden layers with a small RMSE. Next, the optimal parameter for the number of neurons in a hidden layer was validated.
For the XGB model, the hyperparameters were min_child_weight and max_depth. The min_child_weight refers to the minimum sum of the instance weight required in a child and max_depth to preventing overfitting to avoid tree growing very deep. Modeling was performed using preset parameters, namely min_child_weight = 1 and max_depth = 3 (these hyperparameters were tested in the subsequent section for optimal values). The min_child_weight was set to 1, 2, and 3 for validation, and the validation range of max_depth was 3-18. First, min_child_weight was fixed to obtain a parameter with a small RMSE. After obtaining the optimal min_child_weight parameter, the optimal parameter for max_depth was validated. Figure 6 illustrates the validation results of the GRU, XGB, and MLR forecasting models at Chenggong, Taitung, Dawu, and Lanyu stations. The figure plots the RMSE performance of scenarios 1-10 at lead time = 1, 3, and 6 h. For GRU models, Figure 6a-d indicates that the longer the forecast horizon is, the larger the prediction error is. In addition, performance data in each scenario at each station were organized. At lead time = 1, 3, and 6 h, Chenggong station obtained minimum errors in scenarios 7, 5, and 6, respectively. At the same lead times, Taitung station obtained minimum errors in scenarios 5, 5, and 6, and Dawu station obtained minimum errors in scenarios 5, 4, and 4, respectively. Lanyu station obtained the minimum error in scenario 5 for lead time = 1, 3, and 6 h. Compared with the onshore stations (Chenggong, Taitung, and Dawu), the offshore station (Lanyu) obtained optimal results for one scenario at all three lead times. This may have occurred because the offshore station does not have terrain blockage. Therefore, one radar elevation angle can be used to obtain optimal prediction results in different forecast horizons. Figure 6e-h illustrates the validation results of the XGB prediction model, and Figure 6i-l presents the validation results of the MLR prediction model. Among GRU, XGB, and MLR, the prediction errors obtained in XGB and MLR were generally higher than those obtained in the GRU.
For comparisons of GRU, XGB and MLR models, Figure 7 averages the results of the 10 scenarios at each station. The GRU prediction model was considerably more effective than the XGB and MLR models were at each station with lead times of 1, 3, and 6 h. Therefore, the GRU model was used in the subsequent analysis. In addition, Lanyu station had smaller RMSEs than Chenggong, Taitung, and Dawu stations did.
Sensors 2021, 21, x FOR PEER REVIEW 10 of 21 than the XGB and MLR models were at each station with lead times of 1, 3, and 6 h. Therefore, the GRU model was used in the subsequent analysis. In addition, Lanyu station had smaller RMSEs than Chenggong, Taitung, and Dawu stations did.   than the XGB and MLR models were at each station with lead times of 1, 3, and 6 h. Therefore, the GRU model was used in the subsequent analysis. In addition, Lanyu station had smaller RMSEs than Chenggong, Taitung, and Dawu stations did.

Simulation and Comparison
Typhoons Nepartak, Meranti, and Megi were simulated. Figures 8-10 plot the rainfall forecast results for the three typhoons (lead time = 1 and 3). In the figures, the solid gray line denotes observed rainfall (obs). The real-time forecasts included pred_opt (blue dashed line), pred_max (red dotted line), and pred_min (green dotted line). Hyetograph definitions for pred_opt, pred_max, and pred_min were discussed in Section 3.

Simulation and Comparison
Typhoons Nepartak, Meranti, and Megi were simulated. Figures 8-10 plot the rainfall forecast results for the three typhoons (lead time = 1 and 3). In the figures, the solid gray line denotes observed rainfall (obs). The real-time forecasts included pred_opt (blue dashed line), pred_max (red dotted line), and pred_min (green dotted line). Hyetograph definitions for pred_opt, pred_max, and pred_min were discussed in Section 3.  Regarding prediction performance, the graphs indicate that pred_opt was between pred_max and pred_min, as expected. The following comparisons between the three forecasts and obs can be drawn visually: (1) pred_opt predicted future rainfall trends with fluctuations in obs, (2) pred_max generally overestimated lighter rainfall, and (3)

Evaluation Indices of Each Typhoon
To understand the differences between the predicted values (i.e., pred_opt, pred_max, and pred_min) and obs, the RMSEs of each typhoon at lead time = 1, 3, and 6 h were analyzed. As illustrated in Figure 11, the prediction results of pred_opt of the three typhoons were more satisfactory than those of pred_max and pred_min were. Therefore, from a user's perspective, a theoretically favorable prediction value can be obtained using pred_opt because the 10 scenarios can be used in real-time prediction. In addition, pred_max and pred_min can be used to understand the maximum error that may occur when predicting high and low values and provide users with more prediction information.

Overall Evaluation Index
The averaged evaluation indices for all test typhoons were used to understand prediction errors among stations. Because Chenggong, Taitung, and Dawu stations experienced heavier rainfall than Lanyu station did, the model predictions had higher absolute errors. Regarding prediction performance, the graphs indicate that pred_opt was between pred_max and pred_min, as expected. The following comparisons between the three forecasts and obs can be drawn visually: (1) pred_opt predicted future rainfall trends with fluctuations in obs, (2) pred_max generally overestimated lighter rainfall, and 3) pred_min generally underestimated heavy rainfall.

Evaluation Indices of Each Typhoon
To understand the differences between the predicted values (i.e., pred_opt, pred_max, and pred_min) and obs, the RMSEs of each typhoon at lead time = 1, 3, and 6 h were analyzed. As illustrated in Figure 11, the prediction results of pred_opt of the three typhoons were more satisfactory than those of pred_max and pred_min were. Therefore, from a user's perspective, a theoretically favorable prediction value can be obtained using pred_opt because the 10 scenarios can be used in real-time prediction. In addition, pred_max and pred_min can be used to understand the maximum error that may occur when predicting high and low values and provide users with more prediction information.   Figure 12a plots the absolute RMSE performance of pred_opt at the four stations, indicating that (1) for onshore stations, Chenggong station exhibited higher performance than Taitung and Dawu stations did and (2) Lanyu station performed far lower than Chenggong, Taitung, and Dawu stations did. Figure 12b presents the rRMSE performance of pred_opt at the four stations, among which (1) for onshore stations, Chenggong station outperformed Taitung and Dawu stations, (2) Lanyu station outperformed Taitung and Dawu stations, and (3) Lanyu station performed more favorably at lead time = 1 h, but less favorably at lead time = 3 and 6 h than Chenggong station did.

Overall Evaluation Index
The averaged evaluation indices for all test typhoons were used to understand prediction errors among stations. Because Chenggong, Taitung, and Dawu stations experienced heavier rainfall than Lanyu station did, the model predictions had higher absolute errors. For prediction, this study used relative RMSE (rRMSE), the equation for which is where is the average of observations. Figure 12 plots the average RMSE and rRMSE for all test typhoons. Figure 12a plots the absolute RMSE performance of pred_opt at the four stations, indicating that (1) for onshore stations, Chenggong station exhibited higher performance than Taitung and Dawu stations did and (2) Lanyu station performed far lower than Chenggong, Taitung, and Dawu stations did. Figure 12b presents the rRMSE performance of pred_opt at the four stations, among which (1) for onshore stations, Chenggong station outperformed Taitung and Dawu stations, (2) Lanyu station outperformed Taitung and Dawu stations, and

Comparison of predicted and CWB values
Nowcasting data for Typhoons Nepartak, Meranti, and Megi released by CWB were compared with the prediction results of this research model to confirm the practicability of the developed conceptual system. Figure 13 plots total obs (solid black line), predicted

Comparison of Predicted and CWB Values
Nowcasting data for Typhoons Nepartak, Meranti, and Megi released by CWB were compared with the prediction results of this research model to confirm the practicability of the developed conceptual system. Figure 13 plots total obs (solid black line), predicted values (pred_opt, pred_min, and pred_max; histogram), and CWB nowcasting values (pred_CWB; orange dotted line) of the test typhoons at each station. The observations were between pred_min and pred_max. Furthermore, pred_opt was closer to the observation value than pred_CWB was. Therefore, the simulation results of pred_opt have reference value. This study used the error rate of cumulative rainfall (ERROR_RATE) to evaluate the percentage of the total rainfall prediction error. ERROR_RATE was used to evaluate an average ratio of the absolute errors of cumulative rainfall and was defined as where is the estimated cumulative rainfall for typhoon event k; is the observed cumulative rainfall for typhoon event k; and K is the number of test typhoons. Figure 14 compares the ERROR_RATE of pred_opt with that of pred_CWB. According to the figure, pred_CWB was more likely to be overestimated than pred_opt was. The average ERROR_RATE values of pred_opt and pred_CWB for the test typhoons were 17.8% and 49.7%, at Chenggong station, 11.2% and 54.8% at Taitung station, 6.3% and 12.4% at Dawu station, and 12.9% and 276.3% Lanyu station, respectively. ERROR_RATE for pred_opt was the lowest for Dawu station, followed by Taitung, Lanyu, and Chenggong stations; for pred_CWB, ERROR_RATE was lowest at Dawu station, followed by Chenggong, Taitung, and Lanyu stations. This study used the error rate of cumulative rainfall (ERROR_RATE) to evaluate the percentage of the total rainfall prediction error. ERROR_RATE was used to evaluate an average ratio of the absolute errors of cumulative rainfall and was defined as where R pre k is the estimated cumulative rainfall for typhoon event k; R obs k is the observed cumulative rainfall for typhoon event k; and K is the number of test typhoons. Figure 14 compares the ERROR_RATE of pred_opt with that of pred_CWB. According to the figure, pred_CWB was more likely to be overestimated than pred_opt was. The average ERROR_RATE values of pred_opt and pred_CWB for the test typhoons were 17.8% and 49.7%, at Chenggong station, 11.2% and 54.8% at Taitung station, 6.3% and 12.4% at Dawu station, and 12.9% and 276.3% Lanyu station, respectively. ERROR_RATE for pred_opt was the lowest for Dawu station, followed by Taitung, Lanyu, and Chenggong stations; for pred_CWB, ERROR_RATE was lowest at Dawu station, followed by Chenggong, Taitung, and Lanyu stations.

Discussion
This study was conducted in southeastern Taiwan and included three onshore weather stations (Chenggong, Taitung, and Dawu) and one offshore weather station (Lanyu). The Chenggong station exhibited superior prediction results to those of Taitung and Dawu stations. This may have occurred because Chenggong station is closer to the Hualien radar station and experienced less interference caused by topographic factors than Taitung and Dawu stations did. Therefore, Chenggong station may have obtained a higher-quality radar reflectivity signal. In addition, the rRMSE results indicated that although radar reflectivity signals at Lanyu station were less affected by topographic factors, reflectivity quality may have been slightly affected because the station was farthest from the Hualien radar station; however, it outperformed Taitung and Dawu stations.
Regarding the overshooting of the beam and blockage, the radar elevation angles derived from the model-induced results were examined. The Chenggong station is possibly sheltered by the Coastal Mountain Range (an average height of 1000 m; Figure 1). The theoretical elevation angles can be computed (Figure 1). The height of the cloud top in a typhoon is assumed to be 18 km according to [76]. The distance from the Hualien radar station to the Chenggong station is 102 km and to the northern tip of the Coastal Mountain Range is 15 km. The elevation of Hualien radar station is 53 m. Therefore, the range of radar elevation angles is from 3.61° to 10.01°. According to Section 4, the optimal results from the GRU model can be derived in scenarios 7, 5, and 6 at lead time = 1, 3, and 6 h, respectively. The corresponding elevation angles are 9.9°, 4.3°, and 6.0°, which reveal that the model results appear reasonable because they fall in the range of theoretical elevation angles.
The Taitung and Dawu stations seem mainly affected by the East Rift Valley (an average height of 250 m; Figure 1). The Hualien radar station is 146 and 196 km away from the Taitung and Dawu stations, respectively, and the northern tip of the East Rift Valley is 30 km away. Therefore, the range of radar elevation angles is 0.38° to 7.05°. The verification results revealed the optimal elevation angles are at 4.3°, 6.0°, and 6.0° (corresponding to scenarios 5, 5, and 6, respectively) at lead time = 1, 3, and 6 h for the Taitung station and 4.3°, 3.4° and 3.4° (scenarios 5, 4, and 4, respectively) for the Dawu station, which demonstrated these were reasonable results. Finally, the Lanyu station possibly is not affected by terrain blockage. The Hualien radar station is 218 km away from the Lanyu sta-

Discussion
This study was conducted in southeastern Taiwan and included three onshore weather stations (Chenggong, Taitung, and Dawu) and one offshore weather station (Lanyu). The Chenggong station exhibited superior prediction results to those of Taitung and Dawu stations. This may have occurred because Chenggong station is closer to the Hualien radar station and experienced less interference caused by topographic factors than Taitung and Dawu stations did. Therefore, Chenggong station may have obtained a higher-quality radar reflectivity signal. In addition, the rRMSE results indicated that although radar reflectivity signals at Lanyu station were less affected by topographic factors, reflectivity quality may have been slightly affected because the station was farthest from the Hualien radar station; however, it outperformed Taitung and Dawu stations.
Regarding the overshooting of the beam and blockage, the radar elevation angles derived from the model-induced results were examined. The Chenggong station is possibly sheltered by the Coastal Mountain Range (an average height of 1000 m; Figure 1). The theoretical elevation angles can be computed (Figure 1). The height of the cloud top in a typhoon is assumed to be 18 km according to [76]. The distance from the Hualien radar station to the Chenggong station is 102 km and to the northern tip of the Coastal Mountain Range is 15 km. The elevation of Hualien radar station is 53 m. Therefore, the range of radar elevation angles is from 3.61 • to 10.01 • . According to Section 4, the optimal results from the GRU model can be derived in scenarios 7, 5, and 6 at lead time = 1, 3, and 6 h, respectively. The corresponding elevation angles are 9.9 • , 4.3 • , and 6.0 • , which reveal that the model results appear reasonable because they fall in the range of theoretical elevation angles.
The Taitung and Dawu stations seem mainly affected by the East Rift Valley (an average height of 250 m; Figure 1). The Hualien radar station is 146 and 196 km away from the Taitung and Dawu stations, respectively, and the northern tip of the East Rift Valley is 30 km away. Therefore, the range of radar elevation angles is 0.38 • to 7.05 • . The verification results revealed the optimal elevation angles are at 4.3 • , 6.0 • , and 6.0 • (corresponding to scenarios 5, 5, and 6, respectively) at lead time = 1, 3, and 6 h for the Taitung station and 4.3 • , 3.4 • and 3.4 • (scenarios 5, 4, and 4, respectively) for the Dawu station, which demonstrated these were reasonable results. Finally, the Lanyu station possibly is not affected by terrain blockage. The Hualien radar station is 218 km away from the Lanyu station. The theoretical elevation angles can be from 0 • to 5.24 • . The verification results revealed the optimal elevation angles are all at 4.3 • at lead times 1, 3, and 6 h. Therefore, the most suitable elevation angles can be successfully identified.

Conclusions
This study developed a real-time rainfall forecasting system that can predict rainfall in an area a few hours before a typhoon arrives at Taiwan. To effectively predict rainfall data, this study used reflectivity data obtained from nine elevation angles in the Taiwan Doppler VCP21 system and ground-weather data in southeastern Taiwan. The area included three onshore weather stations (Chenggong, Taitung and Dawu) and one offshore station (Lanyu). Radar data were provided by the Hualien WSR. This study analyzed 14 typhoons that affected the study area from 2008 to 2017. GRU was used to establish the prediction model, and XGB and MLR were used as the benchmark. The GRU prediction model was substantially superior to the XGB and MLR model in forecasting rainfall at lead times of 1, 3, and 6 h at each station.
The simulation results for three test typhoons revealed that the predictive performance of pred_opt was more satisfactory than that of pred_max or pred_min was. Therefore, when developing a real-time prediction system, 10 scenarios can be used to select an optimal solution (i.e., pred_opt) to obtain a favorable prediction value. In addition, pred_max and pred_min can be obtained to provide the probable ranges of predicted values. Consequently, the overall results revealed that the input data set combined with weather-station data and radar reflectivity at the optimal elevation angle yielded optimal results for short-term rainfall forecasting. Moreover, nowcasting values released by the CWB were compared with the predicted values of this study, which demonstrated that pred_opt was closer to the observed values than pred_CWB was. Therefore, the simulation results of the system have practical reliability.

Data Availability Statement:
The related data were provided by Taiwan's CWB, which are available at https://rdc28.cwb.gov.tw/ (accessed on 1 August 2020).