Statistical prediction of typhoon‐induced accumulated rainfall over the Korean Peninsula based on storm and rainfall data

A statistical model for typhoon‐induced accumulated rainfall (TAR) prediction over the Korean Peninsula using track, intensity and rainfall data of 91 typhoons affecting the peninsula during the period 1977–2014 is developed. The statistical estimation of the TAR consists of three steps: (1) estimating the TAR at 56 observational weather stations for the 91 typhoons; (2) selecting typhoons whose tracks are similar to that of the target typhoon within the area of 32–40 ° N and 120–138 ° E using a fuzzy C‐mean clustering method; and (3) calculating the mean TAR for the 16 selected typhoons based on track similarity after an intensity correction of the TAR using a linear regression between the TAR and intensity anomaly. To validate the model, real case predictions were performed on typhoons Chan‐hom and Goni in 2015 and compared with the observed TARs as well as with those from local and global operational models. The result showed that when the best‐track data are used, the present statistical model can predict the TAR with the accuracy of mean root mean square errors (RMSEs) of 33 mm (Chan‐hom) and 29 mm (Goni) at the 56 stations, which were much less than the results of the local model. With the predicted track and intensity data for the two typhoons, the present model also showed an overall good performance with RMSEs of 30–34 mm (Chan‐hom) and 29–49 mm (Goni), depending on the accuracy of the predicted track and intensity, which were generally less than the results of the global model.


| INTRODUCTION
The Korean Peninsula (KP) is directly and/or indirectly affected by three or four typhoons per year on average. Heavy rainfall and strong winds associated with the typhoons result in disastrous damage, accounting for more than 60% of the natural hazards in Korea (Moon and Choi, 2011). In particular, the typhoon-induced rainfall causes associated landslides and floods that bring astronomical damage, affecting a geographical range of several hundred kilometres (Rogers et al., 2009;Kim and Jain, 2011;Lee and Choi, 2013). A statistical analysis showed that the extremes of typhoon-related heavy rainfall on the KP have increased remarkably since the 1970s, and the degree of damage has accordingly increased (Kim et al., 2006;Choi and Moon, 2008).
Most rainfall in Korea is concentrated during the rainy season from June to September. Typhoons cause widespread rainfall in Korea, mostly during late summer and early fall following the end of the summer rainy season (Moon and Kwon, 2012). Accurately predicting the amount of rainfall during the passage of a typhoon is crucial for securing sufficient water resources to prepare for the long dry seasons in Korea as well as for disaster prevention and mitigation. For example, when typhoons approach Korea, deciding whether to release or to maintain water in a reservoir is a very difficult but greatly important matter. The failure to manage water resources due to incorrect predictions of precipitation during a typhoon may result in serious flooding or water shortages (Kim, 2013), even if prior rainfall predictions and water management before typhoon season were on track.
Track and intensity-prediction techniques for typhoons have improved along with the development of satellite observations and numerical modelling skills (Bender et al., 2007;Lin et al., 2008). In particular, typhoon track prediction has continuously improved due to the development of ensemble techniques and data assimilation using a variety of observational data (Elsberry and Carr, 2000;Goerss, 2000). Despite the rapid development of observational technology and numerical modelling, accurate typhooninduced rainfall forecasting is still limited, especially in predicting the area coverage, intensity and spatial distribution of rainfall Tuleya et al., 2007;Wang et al., 2012;Ren et al., 2018). This is because the rainfall prediction model requires an accurate prediction of not only the storm track and intensity but also the intricate physical processes related to typhoon-land interactions that lead to rapid precipitation changes during typhoon landfall (Mackey and Krishnamurti, 2001;Kidder et al., 2005). Even if the track, strength and structure of a typhoon can be predicted well, rainfall predictions often fail due to unexpected localized heavy rainfall caused by a mixture of warm/humid air supplied by the typhoon and local cold air as well as topographical effects, and thus typhoon-induced rainfall prediction is a highly challenging task (Lin and Chen, 2005;Lonfat et al., 2007;Konrad and Perry, 2010). For example, 870 mm of rainfall in Gangwon-do province during the passage of Typhoon Rusa in 2002 is still difficult to simulate using the latest numerical models (Park and Lee, 2007).
Therefore, for typhoon-induced rainfall predictions, statistical or dynamic-statistical approaches (Marks et al., 2002;Ebert et al., 2011) are widely used in practice, which can provide consistent and basic information. Marks et al. (2002) developed an operational tropical cyclone (TC) rainfall climatology and persistence (R-CLIPER) model based on a climatological rain gauge and satellite microwave estimates in which the mean rainfall rate is defined as a function of radius (r) and time (t) after landfall along the forecast track. Lonfat et al. (2007) upgraded the R-CLIPER model by taking into account the effect of shear and topography on rainfall distribution. Kidder et al. (2005) and Liu (2009) suggested a satellite-based tropical rainfall potential (TraP) technique that accumulates rainfall rates obtained at the initial time along the predicted track, assuming constant rainfall rates during the landfall process. Ebert et al. (2011) showed that an ensemble TraP can further improve short-range forecasts of heavy rainfall in TCs. Lee et al. (2006) also suggested a climatology model for the typhoon-induced rainfall estimates that uses hourly rainfall data of meteorological stations and considers the topographical lifting and variations of rain rate with radius. Recently, Li et al. (2016) developed an operational non-parametric statistical scheme for estimating the maximum daily (R24) and three day accumulative rainfall (R72) based on the percentile box plot corresponding to the landfalling TC category using the forecast intensity from the numerical model.
On the other hand, Wei (2012a) used a neural network that combines the principal component analysis (PCA) technique and the radial basis function (RBF) network to predict accumulated precipitations for a reservoir watershed during typhoon passage. Wei (2012b) applied two support vector machine (SVM) models (the traditional Gaussian kernel SVM and advanced SVM) to forecast hourly precipitation during TC events. Recently, Ren et al. (2018) developed an innovative dynamic-statistical ensemble forecast scheme for landfall TC precipitation based on the TC track similarity index (TSAI) and ensemble members estimated using various parameters, such as initial times, seasonal similarities and similarity regions.
These statistical approaches have been mostly developed as optimized for specific regions because the characteristics of TCs and a rainfall-related environment vary from region to region. Therefore, state-of-the-art methods and techniques for predicting typhoon-induced rainfall with a proven high performance in one region may not guarantee similar results in other regions. For example, in Korea, which is located in the mid-latitudes, most typhoons experience a weakening stage, including an extratropical transition and a mixture of local cold air and TC-supplied warm air, while in tropical regions, such as Taiwan, most typhoons are affected by the tropical environment and maintain a strong strength.
In South Korea, the Korea Water Resources Corporation (K-Water) responsible for the nation's water management has used the rainfall records of the storms with tracks similar to a target typhoon approaching Korea as a complementary measure to compensate for the limitations of the numerical model of typhooninduced rainfall prediction. It is based on the assumption that typhoons with similar tracks tend to have a similar precipitation distribution, which is reasonable because heavy rain areas generally occur along the eye walls and spiral rain bands of the storm tracks. However, even if the tracks of two typhoons are highly similar, the distribution and amount of rainfall could differ completely due to differences in the environmental conditions and storm translation speeds as well as the intensities and structures of the storms (Ren et al., 2018).
The aim of the present study was to develop a new statistical model for estimating the typhoon-induced accumulated rainfall (TAR) optimized for the KP regions by applying various techniques, such as the clustering method, ensemble averaging (EA) and intensity correction, to the traditional method used by K-Water. Section 2 describes the data used in developing the statistical model. Section 3 explains how to calculate the TAR for each typhoon in the KP, how to select typhoons of a similar track as the target typhoon, how to correct the TAR when considering a typhoon's intensity and how to select the optimal number of tracks for EA. Section 4 shows the prediction results of the model after training with prior typhoon data. The model was tested with two typhoons that affected Korea in 2015. Finally, Section 5 presents the summary and conclusion, including discussions of how the present method differs from existing approaches.

| DATA
To develop a TAR prediction model, hourly rainfall and 6 hr typhoon best-track data during the period 1977-2014 were primarily used. The typhoon position and intensity information was obtained from the Regional Specialized Meteorological Center (RSMC)-Tokyo best-track data with date, time, latitude, longitude, intensity and minimum-central pressure every 6 hr along the storm's track. The positions and intensities of a typhoon are interpolated at 1 hr intervals. As typhoons transition to extratropical cyclones (ETs), their intensities rapidly weaken, but a considerable amount of rainfall still affects many regions, leading to flooding, associated property damage and loss of life (Matyas, 2017). For this reason, the present analysis includes the ET periods of all the storms.
To verify the performance of the TAR predictions, typhoon track and intensity as well as TAR data obtained from the operational typhoon prediction model of Jeju National University for typhoons Chan-hom and Goni in 2015 were used. The model is based on the Weather Research and Forecasting (WRF) model, which consists of a fixed domain of 27 km grid in the East Asia region and two moving-nested domains with the resolutions of 9 and 3 km, respectively. The initial field and the atmospheric boundary layer of this model use reanalysis and prediction data from the Global Forecast System (GFS) with a spatial resolution of 0.5 × 0.5 (https://www. ncdc.noaa.gov/data-access/model-data/model-datasets/ global-forcast-system-gfs). For additional verification, the F I G U R E 1 Tracks of 91 Korean Peninsula-influenced typhoons used in the present study (a) and the locations of 56 rainfall observation stations (b). The black box in (a) represents the region (32-40 N, 120-138 E) used to determine the similarity of tropical cyclone tracks. Symbols in (b) denote the five administrative districts in the Korean Peninsula, respectively TARs predicted by a global operational model, the European Centre for Medium-Range Weather Forecasts (ECMWF) model, were also used. The observed rainfall data were obtained from 56 weather stations of the Korea Meteorological Administration.

| Calculation of the observed TAR
The TAR model development began by calculating the observed TAR for each typhoon at the 56 stations in the KP, which requires determining the typhoon-affected period. The procedure used to calculate the TAR is as follows: • Typhoons are selected if the storm centre entered the KP regions from 20 N to 45 N and from 120 E to 145 E ( Figure 1a). • The 56 observational stations are divided into five administrative regions: Gyeonggi-do, Gangwon-do, Chungcheong-do, Gyeongsang-do and Jeolla-do ( Figure 1b). • Total rainfall duration is calculated by determining the times when the rainfall starts (ends) at the regions where a typhoon enters (leaves) the KP.
• Typhoon-affected periods are then determined using geostationary meteorological satellite (GMS) satellitederived data and a weather map. • The TAR at the 56 stations for each typhoon is calculated by summing the hourly rainfall for the determined period. Figure 2 shows two opposite examples for the TAR calculation. The first case was Typhoon Ewiniar in 2006. There were no rainfall events over the Jeolla-do region before Ewiniar made landfall at 1200 UTC July 9 and after it left the KP at 2000 UTC July 10. Based on the observational records, it was clear that the rainfall began in Jeolla-do and lasted until the typhoon passed through Gangwon-do at 2000 UTC July 10 ( Figure 2a). The clear start and end times of the rainfall allowed for the easy determination of the TAR period for Ewiniar. The second case was Typhoon Meari in 2011. Determination of the TAR period in this case was particularly difficult due to the rainfall resulting from the Changma (monsoon) fronts before and after the passage of Meari ( Figure 2b). For the analysis of typhoons with complex weather conditions, such as Meari, an additional weather map and satellite image data were used. When large uncertainty was expected in determining the TAR periods despite the use of various data, these cases were not used in the F I G U R E 2 Time series of hourly rainfall observed at the 56 stations before and after the passage of typhoons Ewiniar (a) and Meari (b) along with their tracks. Colours represent the five administrative districts. Arrow ranges represent the estimated period of the typhoon-induced accumulated rainfall (TAR). For Typhoon Meari, the two events of the typhoon and Changma fronts coexisted, which made the determination of the TAR period difficult T A B L E 1 Information (tropical cyclone (TC) number/name and period of the typhoon-induced accumulated rainfall (TAR)) on development of the present statistical model. In addition, when the total integrated TARs at the 56 stations were < 5 mm during the passage of the typhoons, these cases were also eliminated in the present study. Through both processes, six and 19 typhoons were excluded, respectively, and eventually a total of 91 of 118 typhoons during the period 1977-2014 were selected to develop the present statistical model (Table 1 and Figure 1a).

| Selection of typhoons with similar tracks
Typhoons with similar tracks were selected using the fuzzy C-means clustering method (FCM) (Bezdek et al., 1984) (based on . The FCM is the most popular algorithm in the fuzzy cluster theory, which suggests a possibility that an observation value (x i ) belongs to any group (K). The current FCM model calculates weights or membership co-efficients (W ik ), indicating the possibility that each typhoon (x i ) belongs to a target typhoon (c k ). The calculation of W ik is determined by the partial derivative of the existing method for the sum of squared error (SSE) given by the following: where d(x i , c k ) 2 is the track distance between each observed typhoon and target typhoon. To apply the FCM to the classification of similar tracks for storms, the points on the tracks of all typhoons must have the same number of points, which allows for the calculation of the distance along the storm track. In the present study, all typhoons were interpolated to 21 points, as suggested by . The constant parameter for weight value (p) is usually set to 2. Originally, the FCM in  was used to classify typhoon tracks, where the similarity among the typhoon tracks is determined using a membership coefficient. In the present study, typhoons with tracks similar to a target typhoon were selected using the FCM membership co-efficient: the larger the value, the higher the similarity. In addition, the similarity of the typhoon tracks was estimated only within the region of 32-40 N and 120-138 E (the box in Figure 1a). This is because the purpose was only to predict the TAR in the KP. If the entire track of a typhoon is used, the membership co-efficient would be less optimal for the KP region.
As an example, Figure 3 shows the selected top six typhoons with the greatest similarity to the two typhoons, Bolaven (1215) and Sanba (1216), that affected the KP during 2012. Bolaven moved along the west coast, while Sanba made landfall on the south coast. The results showed that Muifa (1109) in 2011 and Bolaven (0006) in 2000 were typhoons whose tracks were most similar to that of Bolaven (1215) and Sanba (1216), respectively. For each typhoon, the ranking based on track similarity was estimated from 1 to 90. F I G U R E 4 Scatter plot showing the relationship between mean intensity anomaly (ΔV, kn) and mean typhoon-induced accumulated rainfall (TAR) anomaly (ΔP, mm) using a typhoon with the greatest similarity for the total 91 typhoons. The mean TAR and intensity anomalies were averaged over 56 stations and during the passage of a typhoon, respectively. The black solid line represents the linear regression. The linear equation is denoted at the bottom F I G U R E 5 Accuracy in terms of root mean square error (RMSE) (a) and correlation co-efficient (b) of the typhoon-induced accumulated rainfall (TAR) by rank of track similarity and number of ensemble members used estimated using a single typhoon (solid line) and multiple typhoons (grey line). The symbol "X" indicates the optimal numbers for ensemble averaging (EA) that showed the lowest RMSE and the highest correlation, respectively 3.3 | Correction of the TAR when considering typhoon intensity Even if the tracks of two typhoons are alike, the TAR can differ due to the difference in typhoon intensity. Because stronger typhoons tend to have more rainfall (Cerveny and Newman, 2000), the correction of the TAR considering typhoon intensity is expected to reduce the errors in the statistical model. In the present study, to consider the effect of typhoon intensity on the TAR, a regression equation between the mean rainfall anomaly (ΔP, mm) at the 56 stations and mean intensity anomaly (ΔV, kn) during the passage of a typhoon was obtained using a typhoon of the greatest track similarity for each of the 91 typhoons ( Figure 4) as follows: Equation 3 implies that there is a positive correlation (r = 0.43) between typhoon intensity and TAR anomalies, which is statistically significant at the 99% confidence level. During the training process of the model, this linear equation was used to correct the TAR for all typhoons of a similar track.

| Effects of track similarity, ensemble averaging (EA) and intensity correction on the TAR predictions
To investigate the effect of track similarity on TAR predictions, we first predicted the TARs at the 56 stations for 91 typhoons during the period 1977-2014 using the rainfall data of a single typhoon with the greatest track similarity. The results show that the mean RMSE of the TARs for the 91 typhoons at the 56 stations was 77 mm (Figure 5a). If the rainfall data of a typhoon with the second greatest track similarity were used, the mean error was slightly reduced to 73 mm; however, in general, the error (correlation coefficient) decreased (increased) with the use of a typhoon of a higher (lower) track similarity, that is, of a higher rank (see the solid and dotted black lines in Figure 5). This result also shows that using a single typhoon during a TAR prediction has a limitation in reducing errors, even though the track is highly similar to a target typhoon.
EA can be a means to reduce errors further (Mackey and Krishnamurti, 2001;Qi et al., 2014). To test the EA effect on the TAR prediction, the TARs were averaged at each station by sequentially increasing the number of ensemble members from the typhoon of a higher track similarity, and they were then compared with the observations. The results indicated that the RMSE gradually decreased as the ensemble number increased (grey lines in Figure 5).
The RMSE was the lowest (54 mm) when 14 ensemble members (i.e., the top 14 similar typhoons) were used ( Figure 5a). As the number of ensembles further increased, F I G U R E 6 Comparison of root mean square error (RMSE) based on the number of ensemble members used before (grey line) and after (black line) intensity correction. The symbol "X" indicates the optimal number for ensemble averaging (EA) after intensity correction F I G U R E 7 Flowchart showing the procedure for predicting the typhoon-induced accumulated rainfall (TAR) at the 56 stations using the statistical model developed in the present study the error gradually increased. Similarly, in the analysis of correlation co-efficients, the highest values were found when 16-18 ensemble members were used (Figure 5b).
To investigate the effect of the intensity correction on the TAR prediction, the EA technique was applied to calculate the TAR after using Equation 1. The result showed that the mean RMSE decreased by 1 mm after the intensity correction ( Figure 6). Based on these experiments, the optimal number for the EA for the TAR estimation was 16.
The statistical TAR prediction model developed in the present study is operated as follows (Figure 7): • The model begins to run when the predicted typhoon track approaches the KP, especially when the centre of the typhoon is within the region of 32-40 N and 120-138 E. • The top 16 typhoons based on track similarity within the region are selected. • An intensity correction for the observed TARs of the 16 typhoons at the 56 stations using Equation 1 is applied. • The intensity-corrected TARs for the 16 typhoons at each station are averaged. Figure 8 shows the spatial distributions of RMSE and the correlation co-efficient at the 56 stations estimated using the present TAR model for 91 typhoons during the training period. Interesting features found in these figures are large errors and low correlations along the southern and eastern coastlines of the KP. This may be related to the fact that for the southern coasts, typhoons tend to maintain a stronger intensity during landfall (Moon and Kwon, 2012), leading to a large amount and a more variable TAR; for the eastern coastlines, it is difficult to predict the TAR due to the large amount of precipitation and high spatial variability related to the presence of the high mountain range.

| Performance using the besttrack data
The performance of the statistical TAR prediction model was verified with two typhoons, Chan-hom (1509) and Goni (1515), which affected the KP in 2015. These typhoons showed different track patterns and intensities when they passed near the KP. Goni quickly passed through the Korean Straits to the East Sea and rapidly transitioned into an ET, while Chan-hom passed the Yellow Sea along the west coast of the KP, maintaining tropical storm intensity (Figure 9). According to the procedure shown in Figure 7, the 16 typhoons that are most similar to the two typhoon tracks were first selected using the best-track data, and the intensity-corrected TAR at the 56 stations was then estimated for both typhoons using the intensity when the centre of the storm reached 32 N. Figure 10 shows the tracks of the 16 typhoons selected for the TAR prediction of Chan-hom and Goni, where typhoons Parapiroon (0012) and Shanshan (0613) were the storms with the most similar tracks, respectively. The TARs of Chan-hom and Goni at the 56 stations were predicted by averaging the past TAR records for these 16 typhoons after the intensity correction, and they were compared with the observations and WRF model simulations using reanalysis data (Figure 11). The results revealed that the mean RMSEs (correlation co-efficient) at the 56 stations were 33.3 mm (0.89) and 29.3 mm (0.77) for Chan-hom and Goni, respectively (Table 2). It is encouraging that these errors are lower than those (53 mm) obtained during the training period for the 91 typhoons as well as those (118.5 and 189.3 mm) from the WRF model (Table 3).
For Chan-hom, the overall TAR distribution is highly similar to the observed TAR spatial pattern, even though the predictions were underestimated for Jeolla-do province and overestimated for Gangwon-do province F I G U R E 1 0 As for Figure (1515)  Note: Errors of the predicted track were estimated using the best-track data. The predicted intensity was obtained at 32 N.
( Figure 11a,b). For Goni, partial underestimations occurred for Chungcheong-do and Gangwon-do provinces, but the spatial pattern was highly consistent with that of the observations (Figure 11d,e). The results of the WRF model simulation (Figure 11c,f) showed an overall overestimation for both typhoons, although there was an underestimation in some regions for Goni. The large error may be related to the deviated track and intensity simulations of the WRF model ( Figure 12 and Table 3).
Considering that the WRF model uses initial and boundary conditions based on the reanalysis data (not the predicted data) in these simulations, the current numerical model has limitations in realistically predicting the TARs for the two typhoons.
T A B L E 3 As for Table 2, but for the results of the WRF-simulated typhoon-induced accumulated rainfall (TAR) and track using the reanalysis data

| Performance using predicted tracks
In actual forecast situations, there is always an error in the track and intensity prediction of the target typhoon.
To test the impact of such errors on the TAR predictions, the TAR model was rerun for the two typhoons using the predicted track and intensity information instead of the best-track data. Figure 13 shows the comparison of the predicted tracks to the best-track data for three cases of Typhoon Chan-hom at 0000 UTC on July 10, 1200 UTC on July 10 and 0000 UTC on July 11, 2015. The predicted tracks are slightly different from the observations and have a mean error of 107.5 km ( Table 2). The intensity prediction data (55.5, 52.9 and 56.0 kn) used in the model were slightly lower than the observations (59.1 kn); however, the TAR predictions using the biased tracks and intensities did not increase the error for the case of Chanhom. The mean error (32.0 mm) for the three cases was actually lower than the result (33.3 mm) using the besttrack data ( Figure 14 and Table 2). For additional comparisons, the TARs predicted from the ECMWF and their errors are shown in Figure 15 and Table 4, respectively.
The results show that the mean RMSEs (32.0 mm) of the current statistical model are generally smaller than that F I G U R E 1 5 Spatial distribution of the typhoon-induced accumulated rainfall (TAR) predicted from the European Centre for Medium-Range Weather Forecasts (ECMWF) at the 56 stations for Typhoon Chan-hom at 0000 UTC July 10 (a), 1200 UTC July 10 (b) and 0000 UTC July 11 (c), 2015 F I G U R E 1 4 Spatial distribution of the typhoon-induced accumulated rainfall (TAR) predicted from the present statistical model at the 56 stations for Typhoon Chan-hom at 0000 UTC July 10 (a), 1200 UTC July 10 (b) and 0000UTC July 11 (c), 2015, in which real-timepredicted track data were used to find typhoons with a high track similarity (43.1 mm) of the ECMWF for Chan-hom. This can be partially explained by the fact that the track error (107.5 km) used in the statistical model is smaller than that (174.1 km) of the ECMWF for Chan-hom. For the eight cases of Typhoon Goni, the mean error (34.4 mm) was slightly larger than the result (29.3 mm) using the best-track data, which is likely due to the larger track error (158.5 km) compared with that (107.5 km) of Chan-hom (Table 2, and Figures 16  and 17); however, the overall differences between the results using the best and predicted tracks are not large for the two typhoons. These results suggest that the performance of the statistical TAR prediction model developed in the present study is less sensitive to the error of track and intensity predictions. This is mainly because the present model uses the average of 16 ensemble tracks that are already different from the observations; however, it should be noted that if the predicted track significantly deviates from the observations, the TAR error proportionally increases. The case of Goni at 0000 UTC August 23 is a good example with which to emphasize the importance of track accuracy. At that time, the track error of Goni reached 235 km, which is the highest among all the cases (Table 2), and F I G U R E 1 6 Comparison of tracks predicted from the WRF model (filled circles) using the predicted Global Forecast System (GFS) data for Goni (1515)  T A B L E 4 As for the predicted track was biased to the west from the actual track and approached nearer to the KP ( Figure 16e) compared with the real track. As a result, the predicted TARs are significantly overestimated at most stations (Figure 17e), resulting in the largest TAR error (48.6 mm). The TARs predicted from the ECMWF generally showed good performance, although the mean error (45.7 mm) was slightly larger than (34.4 mm) that of the statistical model for Goni (Figure 18). It should be noted that this result was obtained even with a larger mean track error in the statistical model (158.5 km) than the ECMWF (133.4 km) for Goni (Table 4), which again emphasizes that the current statistical model is less sensitive to track error than dynamic models.

| DISCUSSION AND CONCLUSIONS
A statistical model used for predicting typhoon-induced accumulated rainfall (TAR) in the Korean Peninsula (KP) was developed using track, intensity and rainfall data for 91 KP-influenced typhoons during the period 1977-2014. The present statistical model was based on the assumption that typhoons of a similar track tend to have a similar precipitation distribution and that using information from multiple typhoons of a similar trackrather than a single typhoon-can reduce errors. First, an observed TAR database for 91 typhoons was carefully constructed at the 56 stations on the KP using observed rainfall data. The top 16 typhoons similar to the track of a target typhoon were then selected using a fuzzy Cmeans clustering method (FCM). Finally, the TARs at the 56 stations were estimated by averaging the observed TARs for the selected top 16 typhoons at each station following an intensity correction. Using the developed model, as a training process, the TAR was estimated for the 91 typhoons that affected the KP during the period 1977-2014; the mean error at the 56 stations was 53 mm. For real-time predictions for two typhoons, Chan-hom and Goni, in 2015, which were not used during the training process, the present model was capable of simulating the TAR with an accuracy of a root mean square error (RMSE) of 33 mm (30-33 mm) and 29 mm (28-50 mm), respectively, when the best-track data (predicted tracks) were used. These errors were much less than the results of the Weather Research and Forecasting (WRF) model (119 and 189 mm, respectively). With the predicted track and intensity data for the two typhoons, the present statistical model also showed overall good performance with mean RMSEs of 32 mm (Chan-hom) and 34 mm (Goni), which were slightly less than those of the European Centre for Medium-Range Weather Forecasts (ECMWF) model (43 and 47 mm, respectively). It was also found that as the predicted track and intensity of the typhoon were more accurate, the error of the predicted TAR was smaller; however, the performance of the statistical model was not very sensitive to the error of track and intensity predictions because the present model uses the average of 16 ensemble tracks that themselves already include errors.
The current TAR prediction model has a limitation in that it cannot provide temporal variations in rainfall at all locations of the KP, while numerical models can provide such data. This implies that the results of the current model cannot predict where, when and how much rain will fall from a typhoon; however, it can be used as basic and additional data, particularly for water and flood control, by providing stable typhooninduced accumulated rainfall (TAR) predictions at major stations to supplement numerical models that are sensitive to the accuracy of the predicted track and intensity.
Storm translation speed and size can also be considered factors that affect the TAR; however, the correlation between these factors and the TAR is not statistically significant based on the analysis using typhoons of the greatest similarity for 91 typhoons, which is likely due to the insufficient number of samples and differences from the actual track included in the sample. If the sample size increases in future as more typhoon data are collected, it is expected that the correlations may be stronger, which will contribute to the further improvement of prediction skills by including the storm translation speed and size corrections.
Recently, Ren et al. (2018) proposed a new TAR prediction method very similar to the proposed approach in that both methods use indices to identify tropical cyclone (TC) track similarity and ensemble techniques, but there are also differences: (1) they used a more sophisticated TC track similarity index (TSAI); (2) they configured many ensemble members (15,552) using more parameters, such as initial time, similarity region, seasonal similarity, thresholds, number of the most similar TCs and prediction schemes; and (3) they did not consider the effect of intensity. The introduction of more sophisticated indices and parameters considering various conditions that were proposed by Ren et al., but which have not been used in the current model, can contribute to improving the performance of the current TAR model near the KP in future studies.