STORM SURGE PREDICTION USING ARTIFICIAL NEURAL NETWORK MODEL AND CLUSTER ANALYSIS

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1 STORM SURGE PREDICTION USING ARTIFICIAL NEURAL NETWORK MODEL AND CLUSTER ANALYSIS DA-UN LEE 1 ; JANG-WON SEO 1 1 Global Environment System Research Lab, National Institute of Meteorological Research, Korea Meteorological Administration 45 Gisangcheong-gil, Dongjak-gu, Seoul, Republic of Korea ; ddaung@metri.re.kr; jwseo@metri.re.kr In the present study, the artificial intelligence model of neural network methodology on the prediction of storm surge was constructed and validated. In order to find the optimal model and evaluate its performance, several individual artificial neural networks were experimented with identified parameters which could be adjusted before the training phase, and the results were compared with observed sea levels and forecasted values calculated by conventional harmonic analysis (HA). Based on these previous studies, the Artificial Neural Network (ANN) model with cluster analysis method was developed to predict storm surge in the whole Korean coastal regions with especial focuses on the regional extension. The model used in this study is ANN model for each cluster (CL- NN) with the cluster analysis. In order to find the optimal clustering of the twenty one stations, agglomerative clustering with centroid-linkage method among hierarchical clustering was used. Finally the CL-NN can be constructed for predicting storm surge in the cluster regions. To validate model results, predicted sea level value from CL-NN model was compared with that of conventional harmonic analysis (HA) and of the ANN model in each region (NN). The forecast values from NN and CL-NN models show more accuracy with observed data than that of HA. Especially the statistics such as RMSE (Root Mean Square Error) and correlation coefficient shows little differences between CL-NN and NN model results. These results show that cluster analysis and CL-NN model can be applied in the regional storm surge prediction and developed forecast system. Keywords: storm surge prediction, neural network model, cluster analysis INTRODUCTION To reduce crucial coastal damage caused by strong meteorological forces, such as typhoons and strong cold fronts, more accurate storm surge prediction modeling, as well as

2 production of rapid and accurate information about typhoons, has been needed. Until now, some numerical models were usually used for predicting storm surges. However, there are limits to these models; for example, they are hard to reflect fully regional properties, especially in the Korean complex coastal regions, and demand too much time to accomplish anything. So these models are less accurate, especially in the high sea level intervals than around the average values (Sztobryn, 2003). For a more accurate local storm surge prediction, we use artificial neural network (ANN) model which is one of the statistical models. And we also use cluster analysis for regional extension to the whole Korean coastal regions. The artificial neural network model has been recently applied to many areas because of its high accuracy (Tissot et al., 2003). MODEL DESCRIPTION ARTIFICIAL NEURAL NETWORK MODEL Neural network model, originating from human brain biology, can be represented by a network diagram which is composed of three components: input layer, hidden layer and output layer (Figure 1). This model contains many interconnected units (neurons) which can extract linear and nonlinear relationships in the data. The neural network applies to regression and classification. For regression, this model has one output unit, and, for k-class classification, there are k output units in the output layer. x 1 ω 11 x 2 ω 12 H 1 M ω 1 E(y) M ω N1 H N ω 1p ω N 2 ω Np ω N x p (Input layer) (Hidden layer) (Output layer) FIGURE 1 - MLP STRUCTURE WITH ONE HIDDEN LAYER, N HIDDEN UNITS Input units correspond to input variables and each variable is usually normalized. Combination functions combine input units or hidden units, and, in the MLP (multi-layer perceptron) structure, linear combination function is mainly used. Hidden units are created by linear combinations of the input units, and the output unit is modeled as a function of linear combinations of the hidden units. The activation functions are usually chosen to be the sigmoid functions such as logistic, hyperbolic tangent functions and so on. The output

3 function allows a final transformation of linear combinations of hidden units. For regression, we typically choose the identity function. In this study, we use feed-forward neural network architecture, which receives an input layer, one broadcasting output layer, and one or more hidden layers in betweens. In a feed-forward neural network model, the units in one layer are connected only to the units in the next layer. CLUSTER ANALYSIS In the cluster analysis, distances that can show similarities are calculated for unsupervised data when variables that are highly correlated with each cluster characteristics are given. Cluster analysis groups data objects based on these distance information found in the data that describes the objects and their relationships. That is, the objects within a group are similar to one another and different from the objects in other groups (Tan et al., 2006). We consider a lot of standards of distance for measuring similarities between object X i and X j, and one of the most commonly used methods is Euclidean distance. Euclidean distance between object X and X is given in this form: i j 1/ 2 p 2 D ij = ( X i X j )( X i X j ) = ( X ki X kj ), k = 1 where p is the number of variables which are used in the cluster analysis. Especially, in agglomerative method among hierarchical clustering these methods are used for calculating similarity between objects or clusters. There are many linkage methods, including single, complete, average, and centroid methods, and centroid method is used in this study. The process of the centroid linkage method is as follows. First, if the number of objects which belong to cluster is n, then the centroid CL j CL j X j of the CL j is calculated in this form: X j = X n i CL j CL j i Second, if the number of objects which belong to cluster CL and CL is and j k n CL j ncl k, and the centroids is X j and X k, then distance D jk of the centroids between two clusters is calculated in this form: D jk = X j X k 2 Lastly, centroid X of the newly composed cluster, which is formed when two clusters are combined, is calculated by weighted average like this.

4 n X = CL j n X j CL j + n + n CLk CLk X k By repetition of these processes, we can calculate distance between each cluster, after which we can make cluster analysis. NEURAL NETWORK OPTIMUM MODELING FOR EACH STATION The optimum structure of this neural network model should be determined from the data. Therefore this stage involves some problems (Hastie et al., 2001). 1) Starting values: The starting values for weights are chosen to be random values near zero. So the model starts out nearly linear, and becomes nonlinear as the weights increase. 2) Over-fitting: Neural network has often too many weights so that it has tendency to over-fit the training data. Hence we should train the model only for a while, and stop well before it approaches the global minimum of the training data. 3) The number of Hidden units and layers: With too many hidden units, the extra weights can be shrunk toward zero if appropriate regularization is used. It is most common to put down a reasonably large number of units and train them with regularization and choose the number of hidden units. 4) Selection of input variables: The appropriate lags and input variables of the model have to be selected. To choose the optimal model for station Jeju and Yeosu in the Korean Peninsula, many experiments were carried out using different training data sets, input variables (variable and lag selection of observed storm surge height, wind stress, and sea level pressure), model structure and model parameter (learning rate and momentum parameter) (Lee et al., 2005). TABLE 1 SUMMARY OF THE EXPERIMENTS FOR OPTIMUM NEURAL NETWORK MODEL STRUCTURE Training Data set (year) Lags included in input data Model structure Experiment1 2000/2001/ MLP 2003 Experiment2 2000/2001/ RBF 2003 Experiment3 1990~ MLP 2003 Experiment Experiment5 stormy situations (1990~2003) except Maemi case Storm surge:-6hr~-1hr Atmospheric elements :-3hr~-1hr Storm surge: -6hr~-1hr Atmospheric elements :-3hr~-1hr MLP MLP Period for validation Typhoon Maemi case (2003) Typhoon Maemi case (2003) In Experiment1, one year continuous data (2000, 2001, and 2002) is used for model training respectively and MLP structure which contained input units, 2~5 hidden units and one output unit is used. Input variables are observed east-west wind stress, north-south wind stress and pressure. Target variable is storm surge height. Experiment2 uses RBF (radial basis function) structure and other conditions are same as Experiment1. Experiment3 comprises thirteen year continuous data series (1990~2002) and MLP structure which shows better and

5 more stable performance in Experiment1 and Experiment2. Experiment4 uses one year (2002) continuous data series as training data and uses past lagged measurements as well as present east-west wind stress, north-south wind stress and pressure as input variables. Experiment5 uses thirty Typhoon cases from 1990 to 2003 as training data and other conditions are same as Experiment4. Table 1 shows the outline of experiments and Table2~Table5 show results of the Experiment1~Experiment5. One year (2003) continuous data is used for validation in Experiment1~Experiment3 and data during the passage of Typhoon Maemi is used for validation in Experiment4~Experiment5 and Figure 2 shows the results from Experiment5. Results indicate that neural network model forecasts are accurate. The root mean square error between MLP and RBF seemed to have little difference, but MLP was more stable than RBF. The best result reached, when MLP training with three hidden units and previous input data, to a RMSE of approximate 20 cm, which is about 5 % of tidal range at Jeju and Yeosu. TABLE 2 RMSE OF THE MODELS FROM EXPERIMENT1 AND HARMONIC FORECAST AT JEJU AND YEOSU STATION IN THE KOREAN PENINSULA (CM) Year for MLP MLP MLP MLP StationHarmonic forecast training (hidden=2)(hidden=3)(hidden=4)(hidden=5) Jeju Yeosu TABLE 3 RMSE OF THE MODELS FROM EXPERIMENT2 AND HARMONIC FORECAST AT JEJU AND YEOSU STATION IN THE KOREAN PENINSULA (CM) Station Harmonic Year for RBF RBF RBF RBF forecast training (hidden=2)(hidden=3)(hidden=4)(hidden=5) Jeju Yeosu TABLE 4 RMSE OF THE MODELS FROM EXPERIMENT1, EXPERIMENT3 AND HARMONIC FORECAST (CM)

6 Station Harmonic forecast Experiment1 Experiment3 Jeju Yeosu TABLE 5 RESULTS OF EXPERIMENT4 AND EXPERIMENT5: COMPARISON BETWEEN OBSERVED SEA LEVELS AND FORECASTS AT YEOSU STATION DURING TYPHOON MAEMI (CM) Model Harmonic 1h-forecast 24h-forecast performance forecast Experiment4 Experiment5 Experiment4 Experiment5 RMSE(cm) Correlation Sea level(cm) Sea level(cm) (a) Gladys(1991) 50 (b) Faye(1995) Datetime (mm-dd hh) Datetime (mm-dd hh) Sea level(cm) (c) Yanny(1998) Datetime (mm-dd hh) Seal level(cm) (d) Rusa(2002) Datetime (mm-dd hh) FIGURE 2 RESULTS OF EXPERIMEMT 5: SEA LEVEL OBSERVED (SOLID LINE), AND PREDICTED FROM HA (DASHED) AND ANN (DOTTED) AT YEOSU DURING THE PASSAGE OF (a) TYPHOON GLADYS IN 1991, (b) FAYE IN 1995, (c) YANNY IN 1998, (d) RUSA IN 2002 In many experiments' results, we finally choose MLP structure, one hidden layer of three units, hyperbolic tangent hidden activation function and identity output activation function. Next, we consider two models. These models deal with predicted data from numerical model as input data, whereas observed pressure and wind stress are used as input variables so far. Model1 uses the typhoon event data which was obtained from Yeosu, Busan

7 and Wando station in the Korean Peninsula from 1990 to Input variables are pressure, east-west wind stress, north-south wind stress and target variable is storm surge height. Model1 does not include past information. Model2 was trained by Yeosu, Busan and Wando data in The lags of pressure and wind stress as well as past surge height were used as input variables in the model. Figure 3 represents the results of Model1 for Busan using the predicted data from MM5-KMA (Mesoscale Model version 5 from Korea Meteorological Administration) on 12 and 13 September Neural network model predictions greatly improve on predicted sea level from Harmonic analysis. Also, performance of Model2 for Yeosu data is presented in Table 6 for forecasting times of 3, 6, 12 and 24 hours. For 24-hour forecasts, root mean square error improves from 13-39cm to 12-15cm. FIGURE 3 OBSERVED SEA LEVEL (BLACK), PREDICTED SEA LEVEL FROM HARMONIC ANALYSIS (GREEN) AND ARTIFICIAL NEURAL NETWORK (RED) FOR BUSAN STATION IN THE KOREAN PENINSULA - MODEL1 TABLE 6 MODEL PERFORMANCE (RMSE) FOR TYPHOONS AT YEOSU STATION IN THE KOREAN PENINSULA MODEL2 Forecast RMSE (cm) time Olga (1999) Saomai (2000) Rusa (2002) 3h h h h Harmonic forecast REGIONAL REAL-TIME STORM SURGE PREDICTION SYSTEM FOR THREE STATIONS OF THE KOREAN PENINSULA Regional real-time storm surge prediction systems are constructed based on the previous neural network model experiments in Busan, Yeosu and Wando stations of the Korean Peninsula. Neural network model results for three stations are showed in Figure 4. Plots on the left side represent sea level observed (dotted), sea level predicted (predicted storm surge

8 from neural network model plus predicted tide from harmonic analysis) by neural network (red) and tide predicted by harmonic analysis (blue). Vertical line represents present time when surge prediction starts. Plots on the right side represent observed surge (prior to the vertical line) and predicted surge from neural network model (posterior to the vertical line). Input values are updated in hourly and newly updated values are applied to the model continuously. FIGURE 4 REAL-TIME STORM SURGE PREDICTION USING NEURAL NETWORK MODEL: OBSERVED (DOTTED), PREDICTED (RED LINE) SEA LEVEL AND PREDICTED TIDE (BLUE LINE) (LEFT) AND OBSERVED AND PREDICTED SURGE (RIGHT) AT BUSAN, YEOSU, AND WANDO IN THE KOREAN PENINSULA CLUSTER ANALYSIS FOR STATION For regional extension to the whole Korean coastal regions of the ANN model, we use the clustering method. Variables for cluster analysis are maximum storm surge heights for each typhoon that passed through Korean peninsula from 2000 to 2004 and station information (latitude and longitude). Seven variables are used and all of the variables are normalized. Since the most part of correlation coefficients between variables is not high, we calculate similarities between objects using Euclidean distance. The object of the cluster analysis is twenty one stations which is capable of using sea level height from NORI (National Oceanographic Research Institute) in Korea and AWS (Automatic Weather System) data from KMA (Korea Meteorological Administration). The number of stations for clustering will be larger while the amount of available data increases. In the case of Masan and Wido, which has missing values, an average of maximum storm surges from the nearest two stations

9 is substituted. Agglomerative clustering method among hierarchical clustering methods is used and it merges objects which have a lot of similarities as a start. The centroid linkage clustering criterion is used and it has not seriously affected the outliers. In the first step, each object constitutes each cluster and there is only one cluster in the final step. TABLE 7 STATION CLUSTERING FOR EACH STAGE Stage Cluster name Clusters joined Normalized Centroid Distance Difference in distance 1 CL20 POHA, ULSN CL19 KSOT, BORG CL18 WAND, JEJU CL17 CL18(WAND, JEJU), SOGW CL16 ANHG, CL19(KSOT, BORG) CL15 CL20(POHA, ULSN), BUSN CL14 MUKH, SOKC CL13 MASN, TONY CL12 KOMU, YOSU CL11 CL16(ANHG, KSOT, BORG), DAEH CL10 CL11(ANHG, KSOT, BORG, DAEH), WIDO CL09 13 CL08 PYOT, CL10(ANHG, KSOT, BORG, DAEH, WIDO) CL12(KOMU, YOSU), CL17(WAND, JEJU, SOGW) CL07 ULEU, CL14(MUKH, SOKC) CL06 CL07(ULEU, MUKH, SOKC), CL15((POHA, ULSN, BUSN) CL05 INCH, MOKP CL9(PYOT, ANHG, KSOT, BORG, DAEH, 17 CL04 18 CL03 19 CL02 WIDO), CL06(ULEU, MUKH, SOKC, POHA, ULSN, BUSN) CL04(PYOT, ANHG, KSOT, BORG, DAEH, WIDO, ULEU, MUKH, SOKC, POHA, ULSN, BUSN), CL08(KOMU, YOSU, WAND, JEJU, SOGW) CL03(PYOT, ANHG, KSOT, BORG, DAEH, WIDO, ULEU, MUKH, SOKC, POHA, ULSN,

10 20 CL01 BUSN, KOMU, YOSU, WAND, JEJU, SOGW), CL05(INCH, MOKP) CL2(PYOT, ANHG, KSOT, BORG, DAEH, WIDO, ULEU, MUKH, SOKC, POHA, ULSN, BUSN, KOMU, YOSU, WAND, JEJU, SOGW, INCH, MOKP), CL13(MASN, TONY) Table 7 displays station clustering for each stage. It expresses stations clustered at each stage for Incheon(INCH), Pyongtaek(PYOT), Anhung(ANHG), Boryeong(BORG), Kunsan(KSOT), Wido(WIDO), Mokpo(MOKP), Daeheuksando(DAEH), Wando(WAND), Jeju(JEJU), Seogwipo(SOGW), Geomundo(KOMU), Yeosu(YOSU), Tongyoung(TONY), Masan(MASN), Busan(BUSN), Ulsan(ULSN), Pohang(POHA), Uleungdo(ULEU), Mukho(MUKH), and Sokcho(SOKC). In the first stage, Pohang and Ulsan, where the distance between them is the shortest, form the cluster first, which causes the distance from the centroid to become longer in process of time. FIGURE 5 DENDROGRAM OF STATION CLUSTERING USING CENTROID LINKAGE METHOD Figure 5 shows a dendrogram, which shows hierarchical clustering shape for twenty one stations. Despite Storm surge height information for each typhoon, as well as latitude and longitude variables that represent position information for each station that use variables, we notice that closer stations are comprised in the same cluster as a whole. This means that storm surge heights of each typhoon case for stations closer to each other express a similar pattern.

11 St b FIGURE 6 DISTANCES BETWEEN CLUSTER CENTROIDS FOR EACH STAGE FIGURE 7 CLUSTERS FROM RESLUTS OF THE CLUSTER ANALYSIS Figure 6 shows that distance between two objects or centroids of two clusters in each stage. Because the standard for optimum number of cluster does not exist, we may consider the conclusion that clustering stops when distances between the merged clusters from Figure 6 begin to become noticeably larger (Wilks, 1995). That is, the distance between centroids has increased steadily until stage 7 or 12 but distance for the centroids between clusters of the stage 7 and stage 8 or of the stage 12 and stage 13 has drastic increase. Therefore we may stop the process after stage 7 or 12. In this study, we stop the process after stage 12 for the appropriate number of clusters. But this method aside, there are diverse methods for decision

12 of the number of clusters. We also display clusters from results of the cluster analysis in Figure 7. NEURAL NETWORK MODELING FOR EACH CLUSTER We enforce storm surge prediction modeling for each cluster based on cluster analysis results. Neural network modeling for Cluster1 (composed of Busan, Ulsan and Pohang) and Cluster2 (composed of Wando, Jeju and Seogwipo) especially took effect and the results were compared with the results of the model using Busan or Jeju data only and the predicted tide from harmonic analysis. We use data of the hour for the typhoon prapiroon (2000), Saomai (2000), Rusa (2002), Maemi (2003), and Megi (2004) of each three stations. Input variables are predicted air pressure and wind stress from MM5-KMA. Neural network model structure selected from prior experiments for model capacity is used. That is, it is MLP structure which has one hidden layer constituting of three hidden units. Model validation is performed by cross-validation for five typhoons. Typhoons, except the typhoon for validation, are used for model learning and the ratio for training data versus validation data is 80 versus 20. We compare RMSE (Root Mean Square Error) and correlation coefficient for each validation data. The result of the cluster neural network (CL-NN) is compared with predicted tide by harmonic analysis and the results of each station s neural network (NN) model. Table 8 shows RMSE and correlation coefficient (CORR) of each typhoon for Busan and Jeju. In Busan s case, results of CL-NN and NN shows higher RMSE and less correlation coefficient than predicted tide for Typhoon prapiroon which maximum storm surge height is about only 20 cm. Performance of the Neural networks for Typhoon Saomai (2000) and Rusa (2002) which storm surge height records more than 60 cm is better than other typhoon case. CL-NN specifically trained to use the cluster in which Busan, Ulsan, and Pohang records RMSE 8.82 cm, correlation coefficient 0.99 in Saomai s case, and RMSE 8.25 cm, correlation coefficient 0.97 in Rusa s case. These results shows that performance of the CL-NN is better than NN that is trained with only Busan data (RMSE 9.32 cm, correlation coefficient 0.98 for Saomai case, and RMSE 8.80 cm, correlation coefficient 0.96 for Rusa case). TABLE 8 COMPARISON OF HARMONIC ANALYSIS AND NEURAL NETWORK (NN, CL-NN) MODEL PERFORMANCE FOR BUSAN AND JEJU Tide NN CL-NN Busan RMSE Prapiroon CORR Saomai RMSE CORR Rusa RMSE CORR Maemi RMSE CORR Megi RMSE

13 Jeju Prapiroon Saomai Rusa Maemi Megi CORR RMSE CORR RMSE CORR RMSE CORR RMSE CORR RMSE CORR Storm surge heights in the Typhoon Maemi (2003) and Megi (2004) cases are so high and in these cases, NN shows better performance than CL-NN. In Jeju s case, result of CL- NN shows better performance than other models for Typhoon prapiroon, Maemi, and Megi. For Typhoon Saomai and Rusa s cases, result of NN using Jeju data only shows better performance. TABLE 9 MAXIMUM OBSERVED SEA LEVEL, TIDE AND PREDICTED SEA LEVEL AT BUSAN AND JEJU DURING TYPHOONS Max. sea level (cm) station Typhoon OBS. TIDE NN CL-NN Prapiroon Saomai Busan Rusa Maemi Megi Prapiroon Saomai Jeju Rusa Maemi Megi Table 9 shows maximum sea level heights for each typhoon, predicted tide heights when sea level is maximum, and storm surge heights predicted from neural network (NN and CL-NN) plus tide. In Busan case, CL-NN shows good performance because it shows 2, 11, and 14 cm residuals for each Saomai, Rusa, and Maemi and the majority of the CL-NN have over-estimated tendency. In Jeju case, NN model shows under-estimated tendency and these results are counter to Busan case. These results reflect multiple characteristics of many stations used in the cluster training. On the whole, CL-NN shows better performance than NN in the typhoon cases which have high surge heights and there is opposite appearance in the typhoon cases which have low surge

14 heights. We display observed sea level height, predicted sea level height from neural network (CL-NN and NN) and predicted tide for each typhoon in Figure 8. And Figure 9 shows observed and predicted storm surge heights at Busan station during typhoon saomai, rusa, maemi and megi. FIGURE 8 OBSERVED (SOLID), PREDICTED (NN:DOTTED/SQUARES, CL-NN: DASHED /CIRCLES) SEA LEVEL AND PREDICTED TIDE(DASH-DOTTED) AT BUSAN (UPPER) AND JEJU(LOWER) DURING TYPHOON SAOMAI, RUSA, MAEMI FIGURE 9 OBSERVED (SOLID) AND PREDICTED (NN:DOTTED/SQUARES, CL- NN:DASHED/CIRCLES) STORM SURGE AT BUSAN DURING TYPHOON SAOMAI, RUSA, MAEMI, AND MEGI

15 SUMMARY AND CONCLUSION In this study, for more accurate storm surge prediction, artificial neural network models were developed and applied to predict storm surges at more than three stations (Wando, Yeosu, and Busan) of the Korean coast. Artificial neural network models provide significant improvements over harmonic forecasts. And we express the results of the cluster analysis for regional extension to cover entire Korean coastal regions of the neural network for storm surge prediction and the results of the neural network modeling for each cluster. First of all, we consider station information and storm surge height for each typhoon for objective standard establishment of the station clustering and establish cluster analysis. Based on the skill which measures similarity between clusters, the nearest objects gather first, clustering will be stopped when distances between merged clusters begin to become noticeably larger. As a result, we cluster stations into several clusters. We put in operation cluster modeling for Cluster 1 (Busan, Ulsan, and Pohang) and Cluster 2 (Wando, Jeju, and Seogwipo) so that we calculate performance of the neural network model for each cluster. And we compare these results with the results of the models used Busan or Jeju data only and predicted tide. We know that CL-NN model has similar RMSE or correlation coefficient to NN model for the past typhoon cases and especially in the Saomai and Rusa cases, in which storm surge height is very high, CL-NN model has less RMSE or higher correlation coefficient rather than NN. This results reflect that we train the cluster model used more and more typhoon information for many stations. That is, as a result of the neural network modeling, CL-NN and NN model predict storm surge height well and especially, better performance comes out in the prediction of high storm surge height. Hence for the extension of the regional storm surge forecasting system, regional clustering and neural network modeling for each cluster will be supposed to be significant. Based on the result of this study, neural network model for each cluster could be applied to regional storm surge forecasting system and the extension into all coastal regions will be possible. In the future for the stable extension into all coastal regions more and more information of the typhoon cases will be required. Moreover, for better model accuracy, correction of the predicted air pressure and wind stress, which uses model input variables, will be required, especially in the passage of the typhoon, wind stress seems to be underestimated or overestimated. And construction of the dynamic modeling system will be also performed and then present meteorological state or condition, as well as past typhoon information, will be included in the real-time training optimized model. ACKNOWLEDGEMENTS This research was carried out as a part of Development of storm surge and wind wave monitoring system supported by METRI/KMA.

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