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Article Using Adjacent Buoy Information to Predict Wave Heights of Typhoons Offshore of Northeastern

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

 Received: 2 November 2018; Accepted: 6 December 2018; Published: 7 December 2018 

Abstract: In the northeastern sea area of Taiwan, typhoon-induced long waves often cause rogue waves that endanger human lives. Therefore, having the ability to predict wave height during the typhoon period is critical. The maintains the Longdong and Guishandao buoys in the northeastern sea area of Taiwan to conduct long-term monitoring and collect oceanographic data. However, records have often become lost and the buoys have suffered other malfunctions, causing a lack of complete information concerning wind-generated waves. The goal of the present study was to determine the feasibility of using information collected from the adjacent buoy to predict waves. In addition, the effects of various factors such as the path of a typhoon on the prediction accuracy of data from both buoys are discussed herein. This study established a prediction model, and two scenarios were used to assess the performance: Scenario 1 included information from the adjacent buoy and Scenario 2 did not. An artificial neural network was used to establish the wave height prediction model. The research results demonstrated that (1) Scenario 1 achieved superior performance with respect to absolute errors, relative errors, and efficiency coefficient (CE) compared with Scenario 2; (2) the CE of Longdong (0.802) was higher than that of Guishandao (0.565); and (3) various types of typhoon paths were observed by examining each typhoon. The present study successfully determined the feasibility of using information from the adjacent buoy to predict waves. In addition, the effects of various factors such as the path of a typhoon on the prediction accuracy of both buoys were also discussed.

Keywords: wave height; typhoon; buoy; neural network; prediction

1. Introduction Taiwan is located at the border of the tropical and subtropical regions of the Pacific Ocean, where typhoons often occur during summer and autumn. Most typhoons gradually form above the sea surface southeast of Taiwan and produce torrential rains and strong winds that provide considerable water resources but also cause countrywide disasters [1]. When typhoons approach Taiwan from the Pacific Ocean, the northeastern sea and coastal area (Figure1) are the first to be threatened. Because violent storms strike the sea surface with extreme wind speed that persists for a long duration, the resultant waves exhibit long wave periods and great wave heights [2]. Moreover, the topography of seabed may cause wave height to increase to a severely dangerous extent near the shore; for example, seawater intrusion may occur in lowland areas and anchored fishing boats may be capsized or dismantled because of the sudden rise of the waves or a fierce wave impact. The waters near Taiwan are prone to enormous waves generated by strong winds. Such waves contain a massive amount of energy that can be transmitted to the coast of Taiwan from extremely far away, for which reason they are commonly called long waves. They can be transmitted over hundreds or thousands of kilometers, which is why in summer and autumn surface waves often

Water 2018, 10, 1800; doi:10.3390/w10121800 www.mdpi.com/journal/water Water 2018, 10, 1800 2 of 20 Water 2018, 10, 1800 2 of 20 far away, for which reason they are commonly called long waves. They can be transmitted over hundreds or thousands of kilometers, which is why in summer and autumn surface waves often suddenly occur at the east coast of Taiwan Taiwan before a typhoon comes. Usually, Usually, several big waves occur in a row, afterafter whichwhich thethe seasea surface becomes calm for a while, and then giant waves suddenly occur again. Such a pattern gives rise to the name “rogue waves”, and locals colloquially call them “mad dog waves” [[3].3]. Long waves move extremely fast and carry considerableconsiderable momentum; long waves generated by typhoons often carry a large quantity of sea water to the coast where people often get taken under by the waves because they are caught unprepared. According to the data of the Central Weather BureauBureau (CWB)(CWB) of Taiwan, atat leastleast 340 incidentsincidents of rogue waves were recorded between 2000 and 2018, causing injury or death to 568 persons.

Figure 1. NortheasternNortheastern coast coast of of Taiwan Taiwan and the location of the relevant test stations.

Because long waves generated by typhoons often occur in the northeastern sea of Taiwan and cause rogue waves that threaten the safety of people, it is critical to develop the ability to accurately predict wavewave heightsheights duringduring aa typhoon. typhoon. The The CWB CWB has has set set up up the the Longdong Longdong and and Guishandao Guishandao buoys buoys in inthe the northeastern northeastern sea areasea (Figurearea (Figure1) for long-term 1) for long-term monitoring monitoring and the collection and the of keycollection oceanographic of key oceanographicdata. The buoys data. record The up-to-date buoys record information up-to-date concerning information waves concerning in this area waves that can in this then area be subjected that can thento further be subjected analysis to and further used toanalysis make predictions;and used to moreover, make predictions; the information moreover, can informthe information public safety can preparationsinform publicthat safety prevent preparations adverse that outcomes. prevent However,adverse outcomes. performance However, records performance of the buoys records indicate of thethat buoys there areindicate often nothat wave there data are available often no owing wave to data data available loss or other owing malfunctions. to data loss The or present other malfunctions.study thus hypothesized The present thatstudy if wavethus hypothesized heights around that a particularif wave heights buoy around could be a predictedparticular usingbuoy coulddata from be predicted the adjacent using buoy data when from the the target adjacent buoy malfunctioned, buoy when the the target problems buoy associated malfunctioned, with buoy the problemsmalfunctioning associated could with be overcomebuoy malfunctioning and key information could be overcome regarding and the waveskey information in the target regarding area could the wavesstill be in collected the target [4]. area The could aim of still this be study collected was to[4]. evaluate The aim the of this feasibility study ofwas predicting to evaluate waves the feasibility using the ofdata predicting collected waves by the using adjacent the data buoy. collected Moreover, by th thise adjacent study assessed buoy. Moreover, the prediction this study accuracy assessed of buoy the predictiondata in light accuracy of the of influence buoy data of in various light of factors the infl suchuence as of the various path factors of typhoons. such as Thisthe path study of typhoons. used two Thisscenarios study to used develop two thescenarios prediction to develop model, the one predicti that usedon datamodel, from one the that adjacent used data buoy from and the one adjacent that did buoynot. The and study one alsothat evaluateddid not. The other study factors also that evalua mightted affect other wave factors height that predictions might affect such wave as the height path predictionsof typhoons, such the as location the path of of buoys, typhoons, and typhoonthe location intensity. of buoys, Artificial and typhoon neural intensity. networks Artificial (ANNs) neural were networksused to develop (ANNs) an were efficient used and to develop accurate an wave efficient prediction and accurate model. wave prediction model. Computation speed has increased considerably because of the rapid development of computer hardware andand software. software. Researchers Researchers have have thus thus been been able able to develop to develop numerous numerous wave predictionwave prediction models modelsfor typhoon for typhoon periods usingperiods wave using theories wave and theori complexes and computation. complex computation. Commonly usedCommonly computation used computationmodels include models numerical include models, numerical regression models, analysis, regression and analysis, ANNs. and Numerical ANNs. Numerical models use models wave usegoverning wave governing equations equations with correction with correction items generated items generated from local from differences local differences to conduct to complexconduct complexcomputations. computations. Because Because this method this method employs employs grid computing, grid computing, the conversion the conversion from afrom global a global scale scaleto a scaleto a scale suitable suitable for thefor the target target coast coast area, area, which which involves involves complicated complicated computations computations andand grid

Water 2018, 10, 1800 3 of 20 selection, is often extremely time-consuming [5–8]. Regression analysis uses typhoon or weather parameters that affect wind waves during typhoons to establish a simple statistical regression. Then, the coefficient and intercept of each parameter on the regression line are identified to simulate the waves during a typhoon. However, whether or not a particular parameter actually affects the wave during a typhoon cannot be determined, rendering it devoid of physical meaning or implication. Key research in this field has been reported in Asma et al. [9], Li et al. [10], Makarynskyy et al. [11], Sánchez-Arcilla et al. [12], Suzuki et al. [13], and Young [14]. ANNs use the input of parameters that affect waves during a typhoon to generate outputs after performing complex statistical computations in hidden layers. By continuously computing the errors between outputs and actual measurements, this method progressively corrects the weight where connects two neurons of two adjacent layers until the output value approaches the actual measurement. For example, Mandal [15] used a deep learning ANN to predict wave height on the basis of actual measurements of wave height, and demonstrated superior results to the use of a single-layered ANN. Tsai and Tsai [16] used ANN to convert pressure signals into the following parameters: the significant wave height, the wave period, the maximum wave height, and the peak of wave spectrum. Other relevant studies include Aminzadeh-Gohari et al. [17], Arena and Puca [18], Chang and Chien [19], Chang and Chien [20], Deo and Naidu [21], Lin-Ye et al. [22], Londhe [23], Ni and Ma [24], Salcedo-Sanz et al. [25], Stefanakos [26], Tseng et al. [27], and Tsai et al. [28]. Numerous studies have employed other artificial intelligence algorithms, such as support vector regression (SVR), which was used by Salcedo-Sanz et al. [25], and the adaptive neuro-fuzzy inference system (ANFIS), notably applied by Karimi et al. [29]. Other studies have compared the use of multiple artificial intelligence models for wave prediction analysis; for example, Malekmohamadi et al. [30] compared SVR, the multilayer perceptron (MLP) neural network, Bayesian networks, and ANFIS models, and Wei [31] compared k-nearest neighbors, linear regressions, model trees, MLP, and SVR models. The aforementioned studies demonstrated that ANN models generate rapid and accurate predictions; therefore, the present study also employed an ANN to establish a wave height prediction model.

2. Data Source The northeastern sea area of Taiwan was selected as the experimental location of this study (Figure1) and the buoys of Longdong and Guishandao were chosen as the experimental subjects for wave height prediction. This study compiled data from 2005 to 2015. During some typhoons in this period, the buoys malfunctioned, which resulted in incomplete data records. These typhoon incidents thus had to be disregarded by this study, but complete data existed for 53 typhoons that affected the target area, and they were used in this study. Table1 lists these typhoons and their dates.

Table 1. Typhoon incidents between 2005 and 2015.

Year Typhoon and Date Year Typhoon and Date Matsa (8/3–6), Sanvu (8/11–13), Aere (5/9–10), Songda (5/27–28), 2005 Damrey (9/21–23), 2011 Meari (6/23–25), Muifa (8/4–6), Longwang (9/30–10/3) Nanmadol (8/27–30) Talim (6/19–21), Doksuri Chanchu (5/16–18), Ewiniar (7/7–9), (6/28–29), Saola (7/30–8/3), Bilis (7/12–15), Kaemi (7/23–26), 2006 2012 Haikui (8/6–7), Kai-Tak (8/14–15), Saomai (8/9–10), Bopha (8/7–9), Tembin (8/21–28), Shanshan (9/14–16) Jelawat (9/27–28) Soulik (7/11–13), Trami (8/20–22), Pabuk (8/6–8), Wutip (8/8–9), 2007 2013 Kong-Rey (8/27–29), Sepat (8/16–19), Mitag (11/26–27) Usagi (9/19–22), Fitow (10/4–7) Water 2018, 10, 1800 4 of 20

Table 1. Cont.

Year Typhoon and Date Year Typhoon and Date Kalmaegi (7/16–18), Fung-Wong (7/26–29), Nuri (8/19–21), Hagibis (6/14–15), Matmo 2008 2014 Sinlaku (9/11–16), Hagupit (9/21–23), (7/21–23), Fung-Wong (9/19–22) Jangmi (9/26–29) Linfa (6/19–22), Molave (7/16–18), Noul (5/10–11), Linfa (7/6–9), 2009 2015 Morakot (8/5–10), Parma (10/3–6) Chan-Hom (7/9–11) Lionrock (8/31–9/2), 2010 Namtheun·(8/30–31), Meranti (9/9–10), Fanapi (9/17–20), Megi (10/21–23)

This study collected data concerning relevant attributes of the experimental area that might affect wave height. First, sea and land typhoon warnings issued by the CWB were compiled. The warnings contained data concerning the following four attributes of each typhoon: the at the typhoon center, the maximum wind speed at the typhoon center, the latitude of the typhoon center, and the longitude of the typhoon center. Data collected from observation stations included meteorological data and oceanographic data. Meteorological data were obtained by the land-based weather stations affiliated with the CWB located in Keelung, Pengjiayu, Suao, and Yilan. Data from the weather stations comprised the following four attributes: ground air pressure, average wind speed, maximum 10-min mean wind speed, and maximum instantaneous wind speed. Oceanographic data, including significant wave height, were obtained by the CWB Longdong and Guishandao buoys. All the wave heights mentioned in this study refer to the significant wave heights. The aforementioned data were organized and processed with interpolation and supplementing, which yielded 3052 entries of data recorded at hourly intervals. Table2 presents the attributes, their unit, and the statistical values (including maximal, minimal, and mean values) of the 53 typhoons.

Table 2. Statistical attributes of the typhoons, meteorological data, and buoy-obtained data.

Attribute (unit) Min–Max, Mean Attribute (unit) Min–Max, Mean Maximum instantaneous wind Pressure at the typhoon center (hPa) 910.0–998.0, 965.7 2.0–65.8, 19.2 speed at Pengjiayu (m/s) Iintensity of the typhoon (km/h) 54.0–198.0, 121.9 Ground air pressure at Suao (hPa) 966.7–1011.9, 998.3 Latitude of the typhoon center (degree) 15.9–29.1, 22.4 Average wind speed at Suao (m/s) 0–33.4, 4.7 Longitude of the typhoon Maximum 10-min mean wind speed 113.9–130.9, 122.1 0.3–37.2, 6.3 center (degree) at Suao (m/s) Maximum instantaneous wind Ground air pressure at Keelung (hPa) 934.6–1011.2, 997.2 1.7–62.4, 12.1 speed at Suao (m/s) Average wind speed at Keelung (m/s) 0–24.0, 5.0 Ground air pressure at Yilan (hPa) 968.6–1013.6, 1000.4 Maximum 10-min mean wind speed at 0–25.1, 6.3 Average wind speed at Yilan (m/s) 0.1–25.2, 3.8 Keelung (m/s) Maximum instantaneous wind speed at Maximum 10-min mean wind speed 0.1–39.6, 11.7 0.1–29.6, 5.0 Keelung (m/s) at Yilan (m/s) Maximum instantaneous wind Ground air pressure at Pengjiayu (hPa) 955.0–1003.8, 990.3 0.1–48.5, 8.8 speed at Yilan (m/s) Average wind speed at Pengjiayu (m/s) 0–44.3, 11.3 Wave height at Longdong (m) 0.2–11.2, 2.2 Maximum 10-min mean wind speed at 0.9–48.4, 12.7 Wave height at Guishandao (m) 0.2–16.4, 2.3 Pengjiayu (m/s)

3. Model Development

3.1. Artificial Neural Network (ANN) This study employed a well-developed ANN model to establish a wave height prediction model. The theoretical basis of the ANN model is as follows. An ANN simulates the neural transmissions of Water 2018, 10, 1800 5 of 20 human brains and performs parallel distributed computations using multiple nonlinear arithmetic units, or neurons, and their connections. Through a large amount of numerical data, a computer performs constant learning and convergence and adjusts weight value between units to train the ANN to generate the results and answers sought by researchers. McCulloch and Pitts [32] first proposed using a model—the ANN—based on mathematical and logical algorithms that functions similarly to the neural transmissions of a brain. After considerable research and failures, the development of computer science led to the proposal of the back propagation network (BPN) by Rumelhart and McClelland [33]. The BPN became the most frequently used neural network because it enabled model optimization and resolved numerous problems encountered by earlier research. The BPN is a supervised learning method with a feedforward framework and multilayered perception. The multiple layers are generally categorized as the input layer, hidden layer, and output layer. The computation equation in the hidden layer is as follows:

= ( + ) oh f ∑i whioi θh (1) where oh refers to the output signal of the hth processing unit (neuron) in the hidden layer, and f represents the activation function of the processing units. The term whi refers to the weight between the hth unit in the hidden layer and ith unit in the input layer, oi represents the output value of ith unit in the input layer, and θh represents the threshold of the hth unit in the hidden layer. The equation in the output layer is as follows:

= ( + ) ok f ∑k wkhoh θk (2) where ok refers to the output signal of the kth processing unit in the output layer, wkh refers to the weight between the kth unit in the output layer and hth unit in the hidden layer, and θk represents the threshold of the kth unit in the output layer. The BPN learning algorithm is divided into forward propagation and backward propagation. Forward propagation means the input enters through the input layer and undergoes weight processing in the hidden layer and then yields an output value after going through a conversion function. If the output value is critically different from the target output value, the steepest descent method is applied to solve for the correction value of the weight; this value is then used for backward propagation. Forward and backward propagations are continually performed until the error between the output value and target output value meets a certain standard. This generates the optimal weight and achieves BPN convergence. The equation for the error function E is as follows:

1 E = (d − o )2 (3) 2 ∑k k k where dk represents the target value of the kth unit in the output layer. The partial differential equation for the error function and weight is as follows:

∂E ∆w = −η (4) ∂w where ∆w represents the weight correction value between the processing units of each layer, and η represents the learning rate that controls the value of each weight correction. The weight correction ∆wkh between the hth unit in the hidden layer and the kth unit in the output layer is as follows:

∆wkh = η × δk × oh (5) where δk = (dk − ok)ok(1 − ok). Water 2018, 10, 1800 6 of 20

Water 2018, 10, 1800 6 of 20

The weight correction ∆whi between the ith unit in the input layer and the hth unit in the hidden The weight correction ∆𝑤hi between the ith unit in the input layer and the hth unit in the hidden layer is as follows: layer is as follows: ∆whi = η × δh × oi (6) ∆𝑤hi = 𝜂×𝛿h ×𝑜i (6) where δh = oh(1 − oh) ∑k(δkwkh). where 𝛿h =𝑜h(1 − 𝑜h)∑k(𝛿k𝑤kh). 3.2. Data Partitioning 3.2. Data Partitioning Numerous empirical methods are used for optimizing an ANN model. As indicated in Pasini [34], a training-validation-testNumerous empirical procedure methods are is used usually for optimizing adopted for an theANN optimization model. As indicated of an ANN in Pasini model. This[34], study a training-validation-test employed the procedure. procedure To establish is usually the adopted model, the for typhoonsthe optimization selected of for an use ANN in thismodel. study wereThis divided study employed into training, the procedure. validation, To and establish testing the sets. model, The the 30 typhoons typhoons selected that occurred for use in between this 2005–2010study were in divided the training into training, set were validation, used to and establish testing sets. the modelThe 30 typhoons structure that and occurred adjust between the model 2005–2010 in the training set were used to establish the model structure and adjust the model parameters for the ANN output to approach the target value. The BPN algorithm is applied on parameters for the ANN output to approach the target value. The BPN algorithm is applied on a a training set, then, at each step of iteration, the performance of the obtained input-output map is training set, then, at each step of iteration, the performance of the obtained input-output map is validated on the validation set (12 typhoons occurred at years 2011 and 2012). This procedure, called validated on the validation set (12 typhoons occurred at years 2011 and 2012). This procedure, called early stopping, is performed to avoid the overfitting due to a too much close reconstruction of the early stopping, is performed to avoid the overfitting due to a too much close reconstruction of the datadata in in the the training training set. set. The The typhoons typhoons (11(11 typhoonstyphoons occurred occurred between between 2013–2015) 2013–2015) in inthe the testing testing set, set, completelycompletely unknown unknown to to the the network, network, werewere usedused toto verify the selected selected models. models.

WaveWave Heights Heights in in the the Testing Testing Set Set TheThe typhoons typhoons in in the the testing testing setset werewere Soulik, Tram Trami,i, Kong-Rey, Kong-Rey, Usagi, Usagi, Fitow, Fitow, Hagibis, Hagibis, Matmo, Matmo, Fung-Wong,Fung-Wong, Noul, Noul, Linfa, Linfa, and and Chan-Hom. Chan-Hom. The paths paths of of these these 11 11 typhoons typhoons are are presented presented in Figure in Figure 2. 2. ThisThis section section discusses discusses the the wave wave heightheight changeschanges recorded at at Longdong Longdong and and Guishandao Guishandao (i.e., (i.e., the the observationobservation values) values) in in light light of of thethe variousvarious pathspaths of the typhoons, typhoons, which which are are discussed discussed further further with with respectrespect to to prediction prediction outcomes outcomes and and the the performanceperformance of the prediction prediction model. model.

FigureFigure 2. 2.Paths Paths of of the the 11 11 typhoons typhoons in in the the testing testing set: set: (a ()a Soulik) Soulik in in 2013; 2013; ( b(b)) Trami Trami in in 2013; 2013; ( c()c) Kong-Rey Kong- inRey 2013; in ( d2013;) Usagi (d) inUsagi 2013; in ( e2013;) Fitow (e) inFitow 2013; in ( f2013;) Hagibis (f) Hagibis in 2014; in (2014;g) Matmo (g) Matmo in 2014; in (2014;h) Fung-Wong (h) Fung- in 2014;Wong (i) Noulin 2014; in ( 2015;i) Noul (j) in Linfa 2015; in (j 2015;) Linfa and in 2015; (k) Chan-Hom and (k) Chan-Hom in 2015. in 2015.

Water 2018, 10, 1800 7 of 20

Figure3 presents the observation record of the significant wave height of all the typhoons in the testing set. The observed wave heights recorded by the Longdong and Guishandao buoys are both present to facilitate the comparison of wave height changes during the same typhoon. According to Figure3, the wave height varied considerably during typhoons Soulik, Usagi, Fitow, and Matmo. Figure4 presents the maximum wave height (shorten as MWH) and mean value of the wave height (AWH) of typhoons in the testing set to compare the wave heights of said typhoons. Here, the AWH is computed by averaging the measurements from the individual typhoon. The following observations can be made according to Figure4: (1) The MWH recorded at Longdong was 12.79 m during and the maximal AWH was 3.71 m during , and at Guishandao, the MWH of 9.72 m was also recorded during typhoon Soulik, but the maximal AWH of 3.27 m was recorded during . (2) The highest MWH values were both recorded during typhoon Soulik, and the recorded wave height at Longdong was 3.07 m higher than that at Guishandao. Among the typhoons for which the recorded wave height at Longdong was higher than that at Guishandao, typhoon Soulik is discussed first in this section. Typhoon Soulik was classified as a typhoon of intense intensity—an intensity level at which the wind intensity is greater than 51.0 m/s, as defined by the CWB—and the records indicate that the lowest pressure recorded at its center was 925 hPa, the maximum wind speed close to its center was 51 m/s, and the maximum instantaneous wind speed was 72 m/s. The path of Soulik was a generally westward path from east to west (Figure2a), and the typhoon made landfall on Taiwan after passing through the Longdong and Guishandao buoys. Consequently, it had a considerable effect on both buoys and caused severe wind waves that resulted in wave height records that were notably higher than during the other typhoons. Typhoon Fitow was classified as a typhoon of moderate intensity—an intensity level at which the wind intensity ranges from 32.7 to 50.9 m/s, as defined by the CWB—and the records indicated its lowest pressure at center was 960 hPa, its maximum wind speed close to the center was 38 m/s, and its maximum instantaneous wind speed was 54 m/s. Although typhoon Fitow caused a remarkable wave height at Longdong, the recorded wave height at Guishandao was only 3.92 m. The difference between the records of the two buoys was as much as 5.68 m. As depicted in Figure2e, the path of typhoon Fitow went from east to west and passed through the border of the research area without making landfall on Taiwan. Nevertheless, this typhoon caused remarkable wave heights at the Longdong buoy. However, the Guishandao buoy recorded less remarkable wave heights, which might have resulted from the fact that when the periphery of the typhoon touched the landmass of Taiwan, its structure was damaged and it became less powerful. Other typhoons with similar paths such as typhoons Trami (Figure2b) and Chan-Hom (Figure2k) also resulted in similar wave records. Conversely, several typhoons generated considerably higher records of maximum and average wave heights at Guishandao than at Longdong. These situations can be categorized into three types: (1) typhoons that passed through the east coast of Taiwan moving from south to north, including Kong-Rey, Fung-Wong, and Noul; (2) a typhoon that passed through the Central Mountain Range, namely typhoon Matmo; and (3) a typhoon that passed by the south of Taiwan through the Bashi Channel, namely typhoon Usagi. In these situations, the Guishandao buoy was directly affected by the typhoon, whereas the height of wind waves recorded at Longdong decreased under the protection of the Central Mountain Range that disrupted the peripheral structure of the typhoon. Water 2018, 10, 1800 8 of 20 Water 2018, 10, 1800 8 of 20 Water 2018, 10, 1800 8 of 20

Figure 3. Observation record of the significant wave height of the 11 typhoons in the testing set. FigureFigure 3. 3.Observation Observation record record of of the the significant significant wave wave height height of of the the 11 11 typhoons typhoons in in the the testing testing set. set.

FigureFigure 4.4. Observation record ofof (aa)) maximummaximum wavewave heightheight (MWH)(MWH) andand ((bb)) meanmean valuevalue ofof wavewave heightheight Figure 4. Observation record of (a) maximum wave height (MWH) and (b) mean value of wave height (AWH)(AWH) ofof thethe 1111 typhoonstyphoons inin the the testing testing set. set. (AWH) of the 11 typhoons in the testing set. 3.3. Case Modeling and Parameter Calibration 3.3. Case Modeling and Parameter Calibration 3.3. Case Modeling and Parameter Calibration TheThe inputinput attributesattributes forfor thethe modelmodel proposedproposed inin thisthis studystudy includedincluded thethe typhoontyphoon warningswarnings andand The input attributes for the model proposed in this study included the typhoon warnings and datadata collectedcollected byby weatherweather stationsstations andand buoysbuoys asas presentedpresented inin SectionSection2 2.. TheThe pressure pressure at at the the typhoon typhoon data collected by weather stations and buoys as presented in Section 2. The pressure at the typhoon center,center, maximummaximum wind wind speed speed at at the the typhoon typhoon center, center, latitude latitude of theof the typhoon typhoon center, center, and and longitude longitude of the of center, maximum wind speed at the typhoon center, latitude of the typhoon center, and longitude of typhoonthe typhoon center center were were the four the attributes four attributes collected colle fromcted the from warnings the warnings and were and represented were represented in sequence in the typhoon center were the four attributes collected from the warnings and were represented in from A1 to A4; the attributes obtained by the land-based weather stations were represented in sequence sequence from A1 to A4; the attributes obtained by the land-based weather stations were represented sequence from A1 to A4; the attributes obtained by the land-based weather stations were represented from B j to B j, which refer to the ground air pressure, average wind speed, maximum 10-min mean in sequence1, from4, B1,j to B4,j, which refer to the ground air pressure, average wind speed, maximum in sequence from B1,j to B4,j, which refer to the ground air pressure, average wind speed,j maximum wind10-min speed, mean and wind maximum speed, and instantaneous maximum windinstantane speed,ous respectively; wind speed, moreover, respectively; when moreover,= 1, 2, 3, when and 4, j 10-min mean wind speed, and maximum instantaneous wind speed, respectively; moreover, when j the= 1, numbers 2, 3, and refer 4, the to numbers Keelung, Pengjiayu,refer to Keelung, Suao, and Pengjiayu, Yilan, respectively. Suao, and Yilan, The wave respectively. heights observed The wave at = 1, 2, 3, and 4, the numbers refer to Keelung, Pengjiayu, Suao, and Yilan, respectively. The wave the buoys were represented by H1 and H2, which refer to Longdong and Guishandao, respectively. heights observed at the buoys were represented by H1 and H2, which refer to Longdong and heights observed at the buoys were represented by H1 and H2, which refer to Longdong and Guishandao, respectively. 3.3.1.Guishandao, Cases of respectively. the Length of Lag Times 3.3.1.This Cases study of the designed Length five of Lag variations Times of lag time to test and select the optimal prediction. Lag times 3.3.1. Cases of the Length of Lag Times varying from the current moment (∆t = 0) to 4 h ahead (∆t = 4) were tested and marked as Case 1 to This study designed five variations of lag time to test and select the optimal prediction. Lag Case 5.This This study study designed tested the five wave variations height predictionof lag time of to the test next and hour select to determinethe optimal the prediction. length of theLag times varying from the current moment (Δt = 0) to 4 h ahead (Δt = 4) were tested and marked as Case times varying from the current moment (Δt = 0) to 4 h ahead (Δt = 4) were tested and marked as Case 1 to Case 5. This study tested the wave height prediction of the next hour to determine the length of 1 to Case 5. This study tested the wave height prediction of the next hour to determine the length of

Water 2018, 10, 1800 9 of 20 lag time ∆t. In other words, Case 1 used all the attribute data of the current moment (∆t = 0), Case 2 applied the attribute data of the current moment (∆t = 0) and that of 1 h ahead (∆t = 1), and so on for Case 3 and the rest. Therefore, the prediction equation for the Longdong buoy is as follows:

H1,t+1 = f {(Ai,t−k)i=1,4;k=0,∆t,(Bi,j,t−k) i=1,4; j=1,4;k=0,∆t,(Hi,t−k)i=2;k=0,∆t} (7) where t represents the time index. Particularly, with respect to the prediction of wave height for the Longdong buoy, only the wave height attributes from Guishandao, rather than those from the Longdong buoy, were applied. This measure was used to ensure that even if the Longdong buoy malfunctioned, the data collected from the Guishandao buoy could still be used for Longdong buoy predictions. The prediction equation for the Guishandao buoy is as follows:

H2,t+1 = f {(Ai,t−k)i=1,4;k=0,∆t,(Bi,j,t−k) i=1,4; j=1,4;k=0,∆t,(Hi,t−k)i=1;k=0,∆t} (8)

Likewise, for the prediction of wave height at the Guishandao buoy, only attribute data from the Longdong buoy were applied for the same reason mentioned in the previous paragraph.

3.3.2. Definition of the Evaluation Indexes This study used the following indexes to determine the performance of the prediction model: mean absolute error (MAE), root mean square error (RMSE), relative MAE (rMAE), relative RMSE (rRMSE), correlation coefficient (CC), and CE. The calculations of each index are as follows:

n 1 MAE = ∑ Hi,pre − Hi,obs (9) n i=1

MAE rMAE = (10) Hi,obs s n 2 ∑ = Hi,pre − Hi,obs RMSE = i 1 (11) n RMSE rRMSE = (12) Hi,obs n   ∑ = Hi.pre − Hi,pre Hi.obs − Hi,obs CC = i 1 (13) n 2 n 2 ∑i=1 Hi,pre − Hi,pre ∑i=1 Hi,obs − Hi,obs 2 ∑n h − h = − i=1 i.obs i,pre CE 1 2 (14) n   ∑i=1 hi,obs − hi,obs where n represents the number of data entries, Hi,pre represents the predicted wave height at buoy i, and Hi,obs represents the observed wave height at buoy i. Moreover, Hi,pre represents the predicted average wave height at buoy i and Hi,obs represents the observed average wave height at buoy i.

3.3.3. Modeling and Parameter Calibration This study established an ANN-based prediction model using nntool toolbox in Matlab. The training set was used to establish the model structure and train the model parameters. With respect to the BPN framework design, the number of hidden layers was one and the number of neurons in the hidden layer was set to be solved from the following equation: (number of neurons in the input layer + number of neurons in the output layer − 1)/2, according to Trenn [35]. In addition, the activation function between the input layer and hidden layer was the log-sigmoid transfer function Water 2018, 10, 1800 10 of 20

Water 2018, 10, 1800 10 of 20 and the activation function between the hidden layer and output layer was a linear transfer function. TheThe Levenberg-Marquardt trainingtraining algorithmalgorithm was was used used for for the the training training function function and and the the learning learning rate ratewas was set atset default. at default. MomentumMomentum is is a a variable variable that that affects affects the weight of forward input. The The introduction introduction of of the the momentummomentum term term is is used used to to accelerate accelerate the the learni learningng process process by by triggering triggering the the weight weight changes changes to to continuecontinue in in the the same same direction direction with with larger step steps.s. Furthermore, Furthermore, the the momentum momentum term term prevents prevents the the learninglearning processprocess fromfrom settling settling in ain local a local minimum. minimum. Because Because the momentum the momentum parameter parameter ranged betweenranged between0 and 1, this0 and study 1, this conducted study conducted a test on this a test parameter on this and parameter set the interval and set at the 0.1. interval This parameter at 0.1. This was parameterthen substituted was then into substituted the five cases into described the five cases in Section described 3.3.1 in and Section the RMSE 3.3.1 and between the RMSE the prediction between theoutcome prediction and outcome observed and wave observed height wave was calculated.height was calculated. Figure5 presents Figure 5 the presents analyses the for analyses both thefor bothLongdong the Longdong and Guishandao and Guishandao buoys using buoys the using validation the validation set. With respect set. With to therespect Longdong to the buoy,Longdong when buoy,the momentum when the momentum was 1.0, 0.6, was 0.4, 0.4,1.0, and0.6, 0.80.4, for 0.4, Cases and 0.8 1 to for 5, minimalCases 1 to RMSE 5, minimal values RMSE of 1.597 values m, 1.552 of 1.597m, 1.562 m, 1.552 m, 1.564 m, m,1.562 and m, 1.578 1.564 m m, were and obtained, 1.578 m respectively.were obtained, For respectively. the Guishandao For buoy,the Guishandao Cases 1 to 5 buoy,obtained Cases minimal 1 to 5 obtained RMSE values minima of 1.023l RMSE m, 1.011values m, of 1.053 1.023 m, m, 1.080 1.011 m, m, and 1.053 1.115 m, m1.080 for m, momenta and 1.115 of 0.8,m for0.4, momenta 0.5, 0.8, and of 0.8, 0.5, 0.4, respectively. 0.5, 0.8, and According 0.5, respec totively. these According outcomes, applyingto these outcomes, Case 2 with applying a momentum Case 2 withof 0.6 a momentum would attain of the0.6 would optimal attain solution the optimal for the solution Longdong for buoy,the Longdong whereas buoy, applying whereas Case applying 2 with a Casemomentum 2 with a of momentum 0.4 would attainof 0.4 thewould optimal attain solution the optimal for the solution Guishandao for the buoy. Guishandao buoy.

FigureFigure 5. Parameter calibration results results for for momentum: momentum: (a (a) )Longdong Longdong buoy buoy and and (b) (b Guishandao) Guishandao buoy. buoy.

4. Analysis of Scenarios and Evaluations 4. Analysis of Scenarios and Evaluations 4.1. Designed Scenarios—Whether to Use Data from the Adjacent Buoy 4.1. Designed Scenarios—Whether to Use Data from the Adjacent Buoy This section discusses Scenarios 1 and 2, which were used to determine whether using data This section discusses Scenarios 1 and 2, which were used to determine whether using data collected by the adjacent buoy for modeling would affect the prediction outcomes. Scenario 1 model collected by the adjacent buoy for modeling would affect the prediction outcomes. Scenario 1 model input combined all three data sets, namely typhoon warnings, data from weather stations, and data input combined all three data sets, namely typhoon warnings, data from weather stations, and data from the adjacent buoy. Scenario 2 excluded the data from the adjacent buoy and used only the data from the adjacent buoy. Scenario 2 excluded the data from the adjacent buoy and used only the data sets concerning typhoon warnings and data from weather stations. Scenario 2 can be understood sets concerning typhoon warnings and data from weather stations. Scenario 2 can be understood to to represent the hypothetical situation in which the wave height data from both the Longdong represent the hypothetical situation in which the wave height data from both the Longdong and and Guishandao buoys were missing and the prediction could only be completed with data from Guishandao buoys were missing and the prediction could only be completed with data from weather weather stations. stations. On the basis of the analytic results detailed in the previous section, the Case 2 setting was applied On the basis of the analytic results detailed in the previous section, the Case 2 setting was applied for the model input. The attributes at the current moment (∆t = 0) and at a lag time of 1 h (∆t = 1) were for the model input. The attributes at the current moment (Δt = 0) and at a lag time of 1 h (Δt = 1) were used for input. The Case 2 setting was used for model input in the rest of this study. The prediction used for input. The Case 2 setting was used for model input in the rest of this study. The prediction models for both Scenarios 1 and 2 with the lead time of 1 h at the Longdong buoy are represented models for both Scenarios 1 and 2 with the lead time of 1 h at the Longdong buoy are represented as as follows: follows:

ScenarioScenario 1: H 1,1:t+1 H=1,t+1f {( =A fi{(,t−Aki),ti−=1,4;k)i=1,4;k=0,1k=0,1,(, B(Bi,ji,,tj,−t−k)i=1,4;=1,4; j=1,4;j=1,4;k=0,1k=0,1, (H,(iH,t−ki),ti−=2;kk)=0,1i=2;}k =0,1}(15) (15)

ScenarioScenario 2: H 2:1, tH+11,t=+1 f={( Af{(i,At−i,kt−)ki)=1,4;i=1,4;kk=0,1=0,1,,( (Bi,,jj,,tt−−k)ki=1,4;)i=1,4; j=1,4;j=1,4;k=0,1k}=0,1 }(16) (16) For the buoy at Guishandao, the prediction models for both Scenarios 1 and 2 with the lead time of 1 h are represented as follows:

Water 2018, 10, 1800 11 of 20

Scenario 1: H2,t+1 = f{(Ai,t−k)i=1,4;k=0,1, (Bi,j,t−k)i=1,4; j=1,4;k=0,1, (Hi,t−k)i=1;k=0,1} (17) Water 2018, 10, 1800 11 of 20 Scenario 2: H2,t+1 = f{(Ai,t−k)i=1,4;k=0,1, (Bi,j,t−k)i=1,4; j=1,4;k=0,1} (18)

For the buoy at Guishandao, the prediction models for both Scenarios 1 and 2 with the lead time 4.2. Prediction Outcomes of 1 h are represented as follows: Figure 6 presents the prediction outcomes of both buoys for all the typhoons in the testing set

with a leadScenario time of 1 1: h;H the2,t+1 black-edged= f {(Ai,t−k circles)i=1,4;k =0,1represent,(Bi,j,t −thek) iobserved=1,4; j=1,4;k data,=0,1,( solidHi,t− redk)i=1; linesk=0,1 represent} (17) Scenario 1, and blue dotted lines represent Scenario 2. The figure indicates that the results of Scenario 1 were closer to the observed data than those of Scenario 2. Scenario 2 notably underestimated wave Scenario 2: H2,t+1 = f {(Ai,t−k)i=1,4;k=0,1,(Bi,j,t−k)i=1,4; j=1,4;k=0,1} (18) height for various typhoons; for example, data for typhoons Soulik and Fitow at Longdong and 4.2. Predictiontyphoons Soulik, Outcomes Fitow, and Matmo at Guishandao. Scenario 1 achieved a satisfactory level of performance for Longdong, but underestimated the wave height for typhoons Usagi and Matmo at Guishandao.Figure6 presents Figure the 7a,c prediction depicts the outcomes distribution of of both observation buoys for values all the and typhoons prediction in values, the testing and the set with a leadresults time indicate of 1 h; the the black-edged following: (1) circles the CE represent of Scenario the 1 observedhad stronger data, agreement solid red than lines that represent of Scenario Scenario 1, and2 at blue both dotted Longdong lines and represent Guishandao, Scenario which 2.means The figurethat Scenario indicates 1 had that better the fitting results results; of Scenario however, 1 were closerthe to CE the of observedScenario 1 dataat Guishandao than those was of only Scenario slightly 2. higher Scenario than 2 that notably of Scenario underestimated 2; (2) in Scenario wave 1, height for variousthe gradients typhoons; were 0.8996 for example, and 0.5829 data for forthe typhoonsLongdong Soulikand Guishandao and Fitow buoys, at Longdong respectively, and which typhoons means that the prediction outcomes for Longdong presented less underestimation for wave height Soulik, Fitow, and Matmo at Guishandao. Scenario 1 achieved a satisfactory level of performance than Guishandao. for Longdong, but underestimated the wave height for typhoons Usagi and Matmo at Guishandao. To compare the accuracy achieved using ANNs of Scenario 1, a traditional multiple linear Figureregression7a,c depicts (MLR) the model distribution (namely, of Scenario observation 1-MLR) values was and applied prediction as a benchmark. values, and In the Figure results 6, the indicate the following:prediction (1)results the CEobtained of Scenario using 1the had ANN-based stronger agreementScenario 1 thanare satisfactorily that of Scenario consistent 2 at both with Longdong the andobserved Guishandao, data compared which means to Scenario that Scenario 1-MLR. Moreover 1 had better, the results fitting in results; Figure 7b,d however, show that the CEthe slopes of Scenario 1 atcalculated Guishandao are greater was only in the slightly case of Scenario higher than 1 than that in the of case Scenario of Scenario 2; (2) 1-MLR, in Scenario indicating 1, the that gradients the wereestimates 0.8996 and obtained 0.5829 using for the the LongdongANN models and were Guishandao closer to the buoys, observed respectively, results than which the meansestimates that the predictionobtained outcomes using the forMLR Longdong models. presented less underestimation for wave height than Guishandao.

Figure 6. Prediction outcomes for wave height at a lead time of 1 h: (a) Longdong buoy, and (b) Guishandao buoy.

To compare the accuracy achieved using ANNs of Scenario 1, a traditional multiple linear regression (MLR) model (namely, Scenario 1-MLR) was applied as a benchmark. In Figure6, the prediction results obtained using the ANN-based Scenario 1 are satisfactorily consistent with the observed data compared to Scenario 1-MLR. Moreover, the results in Figure7b,d show that the slopes Water 2018, 10, 1800 12 of 20 Water 2018, 10, 1800 12 of 20 calculatedFigure are 6. greater Prediction in theoutcomes case of for Scenario wave he 1ight than at ina lead the time case of of 1 Scenario h: (a) Longdong 1-MLR, buoy, indicating and (b that) the estimatesGuishandao obtained buoy. using the ANN models were closer to the observed results than the estimates obtained using the MLR models. Water 2018, 10, 1800 12 of 20 FigureFigure8 presents 8 presents the the calculation calculation results results of of the the prediction prediction error error using using several several evaluation evaluation indexes. indexes. TheThe absolute absoluteFigure errors 6. errors Prediction (i.e., (i.e., MAEoutcomes MAE an an for RMSE) RMSE) wave he of ofight ScenarioScenario at a lead 11 time werewere of generallygenerally1 h: (a) Longdong less than buoy, those and (ofb of) Scenario Scenario 1- 1-MLRMLR andGuishandao Scenario buoy. 2 2 for for both both buoys, buoys, indicating indicating that that Scenario Scenario 1 had 1 had overall overall superior superior performance performance with withrespect respect to toerrors. errors. With With respect respect to to relative relative errors errors (i.e., (i.e., rMAE and rRMSE)rRMSE) andand CE, CE, Scenario Scenario 1 also1 also outperformedoutperformedFigure Scenario8 presentsScenario 1-MLRthe 1-MLR calculation and and Scenario resultsScenario of 2. the 2. Moreover, predictionMoreover, theerror the CE usingCE of of Scenarioseveral Scenario evaluation 1 was1 was higher indexes. higher for for the the The absolute errors (i.e., MAE an RMSE) of Scenario 1 were generally less than those of Scenario 1- LongdongLongdong buoy buoy (CE (CE = 0.802)= 0.802) than than for for the the Guishandao Guishandao buoy buoy (CE (CE = 0.565).= 0.565). MLR and Scenario 2 for both buoys, indicating that Scenario 1 had overall superior performance with respect to errors. With respect to relative errors (i.e., rMAE and rRMSE) and CE, Scenario 1 also outperformed Scenario 1-MLR and Scenario 2. Moreover, the CE of Scenario 1 was higher for the Longdong buoy (CE = 0.802) than for the Guishandao buoy (CE = 0.565).

FigureFigure 7. 7.X–Y X–Y distribution distributiondiagram diagram ofof wavewave height at at a a lead lead time time of of 1: 1: (a, (ba,)b Longdong) Longdong buoy buoy and and (c,d) Figure 7. X–Y distribution diagram of wave height at a lead time of 1: (a,b) Longdong buoy and (c,d) (c,Guishandaod) Guishandao buoy. buoy. Guishandao buoy.

FigureFigure 8. Performance 8. Performance levels levels of of wave wave heightheight predictions at at a alead lead time time of 1 of h: 1 (a h:) Longdong (a) Longdong buoy buoyand and (b)Figure Guishandao(b) Guishandao 8. Performance buoy. buoy. levels of wave height predictions at a lead time of 1 h: (a) Longdong buoy and (b) Guishandao buoy.

Water 2018, 10, 1800 13 of 20

4.3. Evaluation and Discussion

4.3.1.Water Evaluation: 2018, 10, 1800 According to Wave Classification 13 of 20 In the previous section, the results indicated that Scenarios 1 and 2 performed differently when 4.3. Evaluation and Discussion wave height was high (Figure7); therefore, this study proceeded to calculate the predictive error for various4.3.1. wave Evaluation: classifications. According The to Wave wave Classification classification system of the CWB served as the reference for this study. Waves were classified into the following three types: waves with a height less than 1.5 m In the previous section, the results indicated that Scenarios 1 and 2 performed differently when werewave small height waves, was those high with (Figure a height 7); therefore, between this 1.5 study m and proceeded 2.5 m were to calculate moderate the predictive waves, and error those for with a heightvarious higher wave than classifications. 2.5 m were The high wave waves. classification system of the CWB served as the reference for Figurethis study.9 presents Waves were the valuesclassified of into the absolutethe followin errorg three (RMSE) types: andwaves relative with a errorheight (rRMSE) less than when1.5 m the waveswere were small classified waves, asthose small, with moderate, a height between or high. 1.5 According m and 2.5 to m Figure were 9moderatea,c, the results waves, of and the those absolute errorwith (RMSE) a height for higher both Longdongthan 2.5 m were and high Guishandao waves. exhibited the estimated pattern—the error was relativelyFigure low for 9 presents small waves the values and of relatively the absolute high error for (RMSE) high waves. and relative The results error (rRMSE) from comparing when the the outcomeswaves of were each classified wave classification as small, moderate, are as or follows: high. According to Figure 9a,c, the results of the absolute error (RMSE) for both Longdong and Guishandao exhibited the estimated pattern—the error was • Smallrelatively waves low resultedfor small waves in similar and outcomesrelatively high in Scenarios for high waves. 1 and The 2 at results the Longdong from comparing buoy, yieldingthe resultsoutcomes of of 0.378 each mwave and clas 0.380sification m, respectively. are as follows: However, at the Guishandao buoy, the value of absolute• Small error waves for resulted Scenario in similar 1 was 0.653outcomes m, which in Scenarios was higher 1 and 2 than at the that Longdong for the Scenariobuoy, yielding 2 value of 0.509results m. Thus, of 0.378 Scenario m and 1 0.380 was notm, respectively. advantageous However, for predicting at the Guishandao small waves. buoy, the value of • Resultsabsolute from error both for buoys Scenario for 1 both was moderate0.653 m, which and was high higher waves than demonstrated that for the Scenario that Scenario 2 value of 1 had 0.509 m. Thus, Scenario 1 was not advantageous for predicting small waves. a lower value of absolute error than Scenario 2. Particularly, the results for high waves at • Results from both buoys for both moderate and high waves demonstrated that Scenario 1 had a Longdong yielded a major difference of 0.445 m (RMSE with Scenario 1 = 1.101 m; RMSE with lower value of absolute error than Scenario 2. Particularly, the results for high waves at ScenarioLongdong 2 = 1.546 yielded m). a major difference of 0.445 m (RMSE with Scenario 1 = 1.101 m; RMSE with Scenario 2 = 1.546 m). With respect to rRMSE, the results for the Longdong buoy (Figure9b) indicated that (1) the rRMSE of ScenarioWith 1 decreasedrespect to rRMSE, progressively the results among for the the Long small,dong moderate,buoy (Figure and 9b) high indicated wave that classifications, (1) the suggestingrRMSE thatof Scenario Scenario 1 1 decreased mitigated progressively the relative erroramong better the assmall, the wavesmoderate, grew and higher; high andwave (2) the classifications, suggesting that Scenario 1 mitigated the relative error better as the waves grew higher; values of rRMSE in Scenario 2 for all three classifications of waves were between 0.36 and 0.38. and (2) the values of rRMSE in Scenario 2 for all three classifications of waves were between 0.36 and The results for the Guishandao buoy (Figure9d) indicated that the relative errors for small waves in 0.38. The results for the Guishandao buoy (Figure 9d) indicated that the relative errors for small Scenarioswaves 1 in and Scenarios 2 were 1 bothand 2 highwere (0.610both high and (0.610 0.476, and respectively), 0.476, respectively), whereas whereas the relative the relative errors errors for both moderatefor both and moderate high waves and high were waves lower were than lower 0.4. than 0.4.

FigureFigure 9. Values 9. Values of of RMSE RMSE ((aa,,c) and and rRMSE rRMSE (b, (db) ,ford) Longdong for Longdong and Guishandao and Guishandao according according to the wave to the waveclassification. classification.

Water 2018, 10, 1800 14 of 20

4.3.2. Evaluation: According to Each Typhoon

Water 2018, This10, 1800 section evaluates the error values for each typhoon in the testing set. Figure 10 presents the14 of 20 RMSE of each typhoon in the testing set for the Longdong buoy and Guishandao buoy. This figure also presents the prediction results of Scenarios 1 and 2. The results demonstrated that the typhoons 4.3.2.with Evaluation: relatively According high error to values, Each Typhoonindicated by an RMSE higher than 1, were typhoons Soulik (Scenario 2) and Fitow (Scenarios 1 and 2) at the Longdong buoy and typhoons Soulik (Scenarios 1 Thisand 2), section Trami evaluates(Scenario 1), the Usagi error (Scenarios values for 1 and each 2), typhoon Fitow (Scenario in the testing2), and Chan-Hom set. Figure (Scenario 10 presents 2) the RMSEat ofthe each Guishandao typhoon inbuoy. the Five testing typhoons set for thehad Longdonga high RMSE buoy at andGuishandao Guishandao compared buoy. with This two figure at also presentsLongdong, the prediction which suggested results ofthat Scenarios wave height 1 and predicti 2. Theon at results Guishandao demonstrated might be thatmore the complex. typhoons This with relativelystudy highdetermined error values, several indicatedpossible factors by an that RMSE may higherhave added than to 1, the were difficulty typhoons of wave Soulik prediction (Scenario 2) and Fitowat Guishandao, (Scenarios resulting 1 and in 2)a higher at the prediction Longdong error buoy at Guishandao—the and typhoons path Soulik of the (Scenarios typhoons, 1 the and 2), Tramilocation (Scenario of the 1), buoy, Usagi the (Scenarios geographical 1 and environment, 2), Fitow and (Scenario typhoon 2), intensity. and Chan-Hom (Scenario 2) at the This study determined that Scenario 1 did not always outperform Scenario 2 for all the typhoons Guishandao buoy. Five typhoons had a high RMSE at Guishandao compared with two at Longdong, in the testing set; thus, adding data from buoys did not guarantee prediction accuracy. Scenario 2 did which suggested that wave height prediction at Guishandao might be more complex. This study perform better, as is evident from the relatively low RMSEs, for typhoons Trami, Matmo, Fung- determinedWong, and several Noul possibleat Longdong factors and thatTrami, may Kong-Rey, have added Usagi, toHagibis, the difficulty and Matmo of waveat Guishandao. prediction at Guishandao,Differences resulting between inScenarios a higher 1 and prediction 2 attributable error atto Guishandao—thethe differences between path typhoon of the typhoons,paths are the locationdiscussed of the in buoy, the following the geographical section. environment, and typhoon intensity.

FigureFigure 10. The 10. The RMSE RMSE of eachof each typhoon typhoon in in the the testingtesting set: set: (a ()a Longdong) Longdong buoy buoy and and (b) Guishandao (b) Guishandao buoy. buoy.

This4.3.3. studyEvaluation: determined According that to Scenario Typhoon 1Path did not always outperform Scenario 2 for all the typhoons in the testing set; thus, adding data from buoys did not guarantee prediction accuracy. Scenario 2 did This study classified the paths of the 11 typhoons in the testing set into four general types. Path- perform1 refers better, to the as path is evident by which from typhoons the relatively pass throug lowh RMSEs,the north for end typhoons of Taiwan Trami, via the Matmo,northeastern Fung-Wong, sea and Noularea. Typhoons at Longdong that andtook Trami, this path Kong-Rey, were Soulik, Usagi, Trami, Hagibis, Fitow, and and Matmo Chan-Hom. at Guishandao. Path-2 refers Differencesto the betweenpath Scenariosby which 1typhoons and 2 attributable go from south to theto north differences along the between east coast typhoon of Taiwan; paths Kong-Rey, are discussed Fung- in the followingWong, section. and Noul took this path. Path-3 refers to the path that crosses the main island of Taiwan through the Central Mountain Range; typhoon Matmo took this path. Path-4 refers to the path by 4.3.3.which Evaluation: typhoons According pass through to Typhoon the south Pathend of Taiwan via the Bashi Channel or other situations such as when typhoons develop in the South Sea; such typhoons included Usagi, Hagibis, and Linfa. This study classified the paths of the 11 typhoons in the testing set into four general types. Path-1 Figure 11 presents the RMSE and rRMSE results for the various types of typhoon paths. The refersresults to the from path the by Longdong which typhoons buoy indicated pass through that Longdong the north was end superior of Taiwan when viaPath-1 the or northeastern Path-4 was sea area. Typhoons that took this path were Soulik, Trami, Fitow, and Chan-Hom. Path-2 refers to the path by which typhoons go from south to north along the east coast of Taiwan; Kong-Rey, Fung-Wong, and Noul took this path. Path-3 refers to the path that crosses the main island of Taiwan through the Central Mountain Range; typhoon Matmo took this path. Path-4 refers to the path by which typhoons pass through the south end of Taiwan via the Bashi Channel or other situations such as when typhoons develop in the South China Sea; such typhoons included Usagi, Hagibis, and Linfa. Figure 11 presents the RMSE and rRMSE results for the various types of typhoon paths. The results from the Longdong buoy indicated that Longdong was superior when Path-1 or Path-4 was taken under WaterWater 20182018,, 1010,, 1800 1800 1515 of of 20 20 taken under the Scenario 1 setting, or when Path-2 or Path-3 was taken under the Scenario 2 setting. Thethe Scenariofollowing 1 setting,conclusions or when were Path-2 made or on Path-3 the basis was of taken the underresults the from Scenario Longdong 2 setting. buoy: The (1) following a Path-1 classificationconclusions weremeant made that onthe the typhoon basis of passed the results by th frome research Longdong area buoy: going (1) east a Path-1to west; classification therefore, informationmeant that the from typhoon the adjacent passed bybuoy the could research largely area goingmitigate east the towest; prediction therefore, error information (the difference from theof RMSEadjacent between buoy couldthe two largely scenarios mitigate reached the 0.43 prediction m); (2) because error (the the difference storm area of of RMSE typhoons between with thea Path- two 4scenarios trajectory reached was not 0.43 part m); of (2)the because research the area, storm the areaoscillation of typhoons of waves with detected a Path-4 at trajectory the northeastern was not coastpart ofwere the researchlong waves area, generated the oscillation by the of energy waves transmitted detected at thefrom northeastern afar; therefore, coast information were long waves from thegenerated adjacent by buoy the energy enabled transmitted accurate prediction; from afar; therefore,and (3) the information storm areas from of typhoons the adjacent with buoy Path-2 enabled and Path-3accurate trajectories prediction; were and strongly (3) the stormdisrupted areas by of topography—the typhoons with Path-2Central and Mo Path-3untain trajectoriesRange, resulting were instrongly irregular disrupted disturbances by topography—the of offshore wind Central waves; Mountain thus, the Range, adjacent resulting buoy could in irregular not provide disturbances effective of informationoffshore wind for waves; wave height thus, the predictions. adjacent buoy The couldprediction not provide results effectiveat Guishandao information were similar, for wave but height the informationpredictions. Thefrom prediction the adjacent results buoy at Guishandao did not improve were similar, predictions, but the according information to from the thelong adjacent wave predictionbuoy did not results improve for Path-4. predictions, according to the long wave prediction results for Path-4.

FigureFigure 11. TheThe values values of of RMSE RMSE ( (aa,,cc)) and and rRMSE rRMSE ( (bb,,dd)) for for Longdong Longdong and and Guis Guishandaohandao according according to to typhoontyphoon path. path. 4.3.4. Evaluation: Prediction with Lead Time Varying from 1 to 6 H 4.3.4. Evaluation: Prediction with Lead Time Varying from 1 to 6 H Wave height predictions for a lead time of 1 to 6 h were evaluated. The Scenario 1 model was Wave height predictions for a lead time of 1 to 6 h were evaluated. The Scenario 1 model was applied to conduct the comparison for both the prediction simulation and evaluation of indexes. applied to conduct the comparison for both the prediction simulation and evaluation of indexes. The The equations used were as follows: equations used were as follows: H = f {(A ) ,(B ) ,(H ) } (19) 1,t+HL 1,t+L = fi{(,t−Ak i,it=1,4;−k)i=1,4;k=0,1k=0,1, (Bi,j,it,j−,t−kk) i=1,4; j=1,4;j=1,4;k=0,1k=0,1, (Hi,t−ki),ti−=2;kk=0,1i=2;}k =0,1 (19)

H2,t+HL =2,t+fL{( =A fi{(,t−Ak)i,it=1,4;−k)i=1,4;k=0,1k=0,1,(, B(Bi,j,it,j−,t−kk) i=1,4; j=1,4;j=1,4;k=0,1k=0,1, (H,(iH,t−ki),ti−=1;kk)=0,1i=1;}k =0,1}(20) (20) FiguresFigures 1212 andand 1313 presentpresent the the wave wave height height prediction prediction results results for for the the Longdong Longdong and and Guishandao Guishandao buoysbuoys with a lead time varying from 22 toto 66 h.h. TheThe resultsresults ofof aa leadlead time time of of 1 1 h h is is presented presented in in Figure Figure6. 6.As As the the lead lead time time lengthened, lengthened, the the prediction prediction accuracy accuracyworsened. worsened. FigureFigure 14 presents the calculation resultsresults ofof eacheach evaluation evaluation index index when when lead lead time time varied varied from from 1 to 6 h;1 to the 6 results h; the were results used were to determine used to determinethe diffusion the of diffusion prediction of prediction error. Figure error. 14a–d Figure indicates 14a–d that indicates the errors that atthe Longdong errors at wereLongdong lower were than lowerthose atthan Guishandao those at Guishandao when the lead when time the varied lead fromtime 1varied to 5 h, from whereas 1 to 5 at h, a leadwhereas time at of a 6 lead h, the time error of at6 h,Longdong the error surpassedat Longdong that surpassed at Guishandao. that at Guishandao. However, at However, a lead time at of a 6lead h, thetime absolute of 6 h, the and absolute relative anderrors relative for both errors buoys for were both considerably buoys were large, considerably which diminished large, which the reliabilitydiminished of predictionthe reliability values. of predictionGenerally, avalues. reasonable Generally, threshold a reasonable for the error threshol itemd is for set the up toerror determine item is leadset up time to lengthdetermine for wavelead time length for wave height forecast in practice. For example, when the acceptable threshold for wave

Water 2018, 10, 1800 16 of 20

Water 2018, 10, 1800 16 of 20 height forecast in practice. For example, when the acceptable threshold for wave height prediction was set atheight rMAE prediction = 0.3, the was lead set time at rMAE for Longdong = 0.3, the buoylead time was for 4 h,Longdong whereas buoy for Guishandao was 4 h, whereas it was for 2 h, as depictedGuishandao in Figure it was14b. 2 Finally, h, as depicted both the in CCFigure (Figure 14b. Finally,14e) and both CE the (Figure CC (Figure 14f) were 14e) higherand CE at (Figure Longdong than14f) at Guishandao were higher at Longdong a lead time than of fromat Guishandao 1 to 6 h. at a lead time of from 1 to 6 h.

Figure 12. Wave height prediction of lead time = 2 to 6 h at Longdong buoy: (a) lead time = 2 h; (b) 3 h; (c) 4 h; (d) 5 h; and (e) 6 h. Water 2018, 10, 1800 17 of 20

Water 2018, 10Figure, 1800 12. Wave height prediction of lead time = 2 to 6 h at Longdong buoy: (a) lead time = 2 h; 17 of 20 (b) 3 h; (c) 4 h; (d) 5 h; and (e) 6 h.

Figure 13. Wave height prediction of lead time = 2 to 6 h at Guishandao buoy: (a) lead time = 2 h; (b) 3 h; (c) 4 h; (d) 5 h; and (e) 6 h. Water 2018, 10, 1800 18 of 20

Water 2018,Figure10, 1800 13. Wave height prediction of lead time = 2 to 6 h at Guishandao buoy: (a) lead time = 2 h; (b) 18 of 20 3 h; (c) 4 h; (d) 5 h; and (e) 6 h.

FigureFigure 14. 14.Evaluation Evaluation indexes indexesfor for wavewave height prediction prediction of oflead lead time time = 1 =to 16 toh at 6 hLongdong at Longdong and and GuishandaoGuishandao buoys: buoys: (a )(a MAE;) MAE; ( b(b)) rMAE; rMAE; ((c) RMSE; (d (d) )rRMSE; rRMSE; (e) ( eCC;) CC; and and (f) CE. (f) CE.

5. Conclusions5. Conclusions TaiwanTaiwan is located is located in in the the area area through through which typhoons typhoons frequently frequently pass. pass. Because Because it is unprotected it is unprotected by the Central Mountain Range, the east of Taiwan often receives a direct impact. The area is affected by the Central Mountain Range, the east of Taiwan often receives a direct impact. The area is affected by typhoons earlier than the rest of the region and usually faces the brunt of remarkably powerful by typhoonswinds, rains, earlier and thanwind thewaves. rest The of theperiphery region of and a typhoon usually may faces cause the long brunt waves of remarkably even before powerfulthe winds,arrival rains, of its and center. wind Long waves. waves The with periphery longer waves of amay typhoon transmit may the causewaves longto a particularly waves even faraway before the arrivallocation. of its Moreover, center. Long when waves such withwaves longer reach the waves shor maye, topography transmit may the wavescause the to wave a particularly to swell into faraway location.exceptionally Moreover, high when waves such referred waves to as reach rogue the waves. shore, Rogue topography waves generally may cause occur the when wave typhoons to swell into exceptionallyoccur at an high outer waves sea area, referred and the to public as rogue often waves. neglects Rogue the danger waves of generallyseaside activities occur whenduring typhoons the occurtime at anbefore outer the sea typhoon area,and arrives. the public often neglects the danger of seaside activities during the time before theThe typhoon CWB of arrives. Taiwan has set up the Longdong and Guishandao buoys in the northeastern sea areaThe to CWB conduct of Taiwan long-term has monitoring set up the Longdongof relevant oceanographic and Guishandao data. buoys However, in the the northeastern loss of records sea area or other malfunctions have caused a lack of comprehensive information concerning wind waves. The to conduct long-term monitoring of relevant oceanographic data. However, the loss of records or other present study thus hypothesized that if wave heights around a particular buoy could be predicted malfunctionsusing data havefrom the caused adjacent a lack buoy of when comprehensive the target buoy information malfunctioned, concerning the problems wind associated waves. The with present studybuoy thus malfunctioning hypothesized could that be if overcome wave heights and key around information a particular regarding buoy the waves could in bethe predicted target area using datacould from still the be adjacent collected. buoy when the target buoy malfunctioned, the problems associated with buoy malfunctioningThe aim couldof this bestudy overcome was to evaluate and key the information feasibility of regarding predicting thewaves waves using in the the data target collected area could still beby the collected. adjacent buoy. This study applied an ANN to establish a wave height prediction model. After The aim of this study was to evaluate the feasibility of predicting waves using the data collected by the adjacent buoy. This study applied an ANN to establish a wave height prediction model. After the model was established, two scenarios were tested to assess performance. Scenario 1 included information from the adjacent buoy and Scenario 2 did not. Water 2018, 10, 1800 19 of 20

The present study successfully determined the feasibility of using information from the adjacent buoy to predict waves. Key findings concerning the overall error of predictions are as follows:

• Scenario 1 achieved superior performance to Scenario 2 with respect to absolute errors (MAE and RMSE), relative errors (rMAE and rRMSE), and CE. Moreover, the CE of Longdong (0.802) was higher than that of Guish andao (0.565); moreover, the results concerning Longdong in Scenario 1 exhibited less underestimation of high wave heights than those for Guishandao. • When the waves were classified as small, moderate, or high, the evaluation based on rRMSE yielded the following results. The values of rRMSE for each wave classification for Longdong in Scenario 1 progressively decreased in the order of small, moderate, and high waves; this phenomenon demonstrated that the Scenario 1 setting had the ability to reduce relative error when the wave height increased. The other finding demonstrated that the values of the relative error for small waves at Guishandao in Scenarios 1 and 2 were relatively higher at 0.610 and 0.476, respectively. • An examination of each typhoon indicated that they took various types of paths; for example, typhoons passed the northeastern sea area from east to west, passed from south to north along the east coast, passed through the Central Mountain Range, or passed by the south end of Taiwan through the Bashi Channel. Various types of typhoon paths caused the periphery of the typhoon to become disrupted by the topography or the Central Mountain Range, which increased the complexity of making wind wave predictions and caused prediction accuracy to vary between the Longdong and Guishandao buoys.

Author Contributions: C.-C.W. conceived and designed the experiments and wrote the manuscript; C.-J.H. and C.-C.W. carried out this experiment and analysis of the data and discussed the results. Funding: This research received no external funding. Acknowledgments: This study was supported by the Ministry of Science and Technology, Taiwan, under Grant No. MOST105-2221-E-019-041. The data used in this work are made available on request. The authors would like to express their sincere appreciation for this grant. Conflicts of Interest: The authors declare no conflict of interest.

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