Development of a warning model for coastal freak wave occurrences using an artificial neural network

Ocean Engineering 169 (2018) 270–280

Contents lists available at ScienceDirect

Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng

Development of a warning model for coastal freak wave occurrences using an artificial neural network

T

Dong-Jiing Doonga,∗, Jen-Ping Pengb, Ying-Chih Chena a b

Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan Leibniz Institute for Baltic Sea Research Warnemuende (IOW), Rostock, Germany

A R T I C LE I N FO

A B S T R A C T

Keywords: Coastal freak wave Artificial neural network Warning model Data buoy

The potential for coastal freak waves (CFWs) represents a threat to people living in coastal areas. CFWs are generated via the evolution of a wave and its interactions with coastal structures or rocks; however, the exact mechanism of their formation is not clear. Here, a data-driven warning model based on an artificial neural network (ANN) is proposed to predict the possibility of CFW occurrence. Seven parameters (significant wave height, peak period, wind speed, wave groupiness factor, Benjamin Feir Index (BFI), kurtosis, and wind-wave direction misalignment) collected prior to the occurrence of the CFW are used to develop the model. The buoy data associated with 40 known CFW events are used for model training, and the data associated with 23 such events are used for validation. The use of data obtained during the 6-h period prior to CFW occurrence combined with the same amount of non-CFW data is shown to produce the best model. Two validations using mediapublished and camera-recorded CFW events show that the accuracy rate (ACR) exceeds 90% and the recall rate (RCR) exceeds 87%, demonstrating the accuracy of the proposed model. This warning model has been implemented in operational runs since 2016.

1. Introduction An oceanic freak wave is a suddenly appearing, unexpected wave in the open sea. Such waves can cause shipwrecks. Hazardous waves of this type may also occur in coastal areas, where they can be disastrous for those on the shore, including individuals who may be fishing at breakwaters or along rocky shores. The coastal freak wave (CFW) is a phenomenon in which a large amount of splash water is generated due to the interaction between shoaling waves and coastal structures such as breakwaters, armor blocks and rocks. A CFW may occur even when the sea is calm and in the absence of significant preceding phenomena. In Taiwan, especially along its northeastern coast, people are frequently hit by these unpredictable CFWs. Local media and fishermen in Taiwan call this type of dangerous wave a “mad-dog wave”, a term that emphasizes its unpredictability. A photograph of a typical CFW is shown in Fig. 1. An oceanic freak wave is common defined by two quantitative criteria (H > 2Hs or ηc > 1.25Hs), where H is the individual wave height, Hs is the significant wave height, and ηc is the height from the mean sea level to the wave crest over a time series of finite duration 20 min. They were proposed by Dysthe et al. (2008) used for typical wave conditions for North Sea. Wave-wave interaction has been proven

∗

to be one of the mechanisms for the occurrence of oceanic freak waves (Janssen, 2003; Dysthe et al., 2008; Kharif et al., 2009). However, a quantitative definition of a CFW is still lacking because this type of wave involves complicated interactions among waves, structures and people. Academic articles on CFW are rare compared to studies of oceanic freak waves (Mori et al., 2002; Guedes Soares et al., 2004; Dysthe et al., 2008; Kharif et al., 2009; Veltcheva and Guedes Soares, 2012, 2016; Mori, 2012; Cavaleri et al., 2012; Fedele et al., 2016). One of the reasons for this is that CFWs are not easily recorded by scientific instruments. However, CFWs have been reported worldwide (Didenkulova et al., 2006; Kharif et al., 2009; Didenkulova and Andersen, 2010; Nikolkina and Didenkulova, 2011). Chien et al. (2002) assumed that the freak waves that occur in the coastal ocean and at the coast are both CFWs, which is not entirely consistent with the definition of CFW employed in this study. Those authors studied 140 accidents associated with CFWs reported in Taiwanese newspapers from 1949 to 1999. These events caused 35 shipwrecks and left more than 500 persons injured or dead. Tsai et al. (2004) suggested that the generation of CFWs is associated with typhoons and winter monsoons, and they found that the presence of grouping waves is highly correlated with the occurrence of CFWs. Moreover, they observed three successive waves

Corresponding author. Department of Hydraulic and Ocean Engineering, National Cheng Kung University, 1, University Rd., Tainan, 70101, Taiwan. E-mail address: [email protected] (D.-J. Doong).

https://doi.org/10.1016/j.oceaneng.2018.09.029 Received 8 April 2017; Received in revised form 13 September 2018; Accepted 15 September 2018 0029-8018/ © 2018 Elsevier Ltd. All rights reserved.

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

Fig. 1. An actual photo of a typical coastal freak wave.

warning system to personal communication devices to communicate flood warnings as rapidly as possible. These previous studies show that ANNs are widely used to establish warning systems, especially for potential natural disasters. This paper describes the development of an early warning model for CFWs using an artificial neural network; the physical mechanisms underlying CFWs are not discussed.

with similar periods when CFWs occur. Some researchers (Zhao et al., 2014; Deng et al., 2016; Tang et al., 2016; Qin et al., 2017) have begun to consider the impacts of these rare but extreme waves on coastal and ocean construction. The mechanism of CFW occurrence is still unclear, and human activities in coastal areas still carry inherent risks. This paper describes the development of an early warning model that can be used to mitigate threats due to such dangerous waves. Because the mechanism of CFWs is not yet understood, deterministic predictions are not possible in this phase; hence, a stochastic approach is employed in this study. An artificial neural network (ANN) is used to develop a CFW warning model. An ANN is a type of data mining technique that is designed to mimic biological structures and features. The greatest benefit of an ANN is its ability to organize fuzzy information associated with complicated interrelations or unclear functional relations. ANNs are frequently used to address complicated problems of coastal engineering such as tide level forecasting and compensation, storm surge forecasting, typhoon wave height prediction, etc. (Deo et al., 1999, 2001; Tsai and Lee, 1999; Lee, 2006; Makarynska and Makarynskyy, 2008; de Oliveira et al., 2009; Deo, 2010; Chang et al., 2011; Bernier and Thompson, 2015; Hashemi et al., 2016). Thus, the use of an ANN to develop an early warning model to mitigate the risks associated with natural hazards is not a novel concept. For example, an early warning system for earthquakes was developed by Böse et al. (2008); their results provided highly accurate predictions of real earthquake events. An early warning system for tsunamis has also been established using an ANN (Romano et al., 2009; Mase et al., 2011); this ANN-based warning system not only forecasts the occurrence of a tsunami but also predicts the tsunami's level and arrival time. In addition, Chang et al. (2007) and Kung et al. (2012) built an ANN-based warning system for debris flow; their results show a 70% accuracy rate for the debris flow warning system. Thirumalaiah and Deo (1998) and Sunkpho and Ootamakorn (2011) used an ANN to predict floods in urban areas. López et al. (2012) connected such a

2. ANN model 2.1. Artificial neural network ANNs were inspired by biological systems and are designed to mimic the structure and function of the human brain. Much like a human brain, an ANN is able to learn and generalize from experience. The structure of a typical ANN is shown in Fig. 2. An ANN is composed of a number of interconnected computational elements called neurons or nodes. Each node receives an input signal from an input layer, and this signal is then multiplied by a given weight, summed, and fed into the next node with this added bias. The signal is then passed on to the hidden-layer nodes, which provide an output signal through a (generally) nonlinear transfer function. The concept of artificial neurons was first introduced by McCulloch and Pitts (1943). However, the presentation of a back-propagation algorithm by Rumelhart et al. (1986) made possible numerous applications of this concept. Currently, a major application of ANNs is forecasting. Several distinctive features of ANNs make them valuable and attractive for forecasting tasks. Zhang et al. (1998) noted some advantages of ANNs. Compared with traditional statistical methods, an ANN is a data-driven self-adaptive method. Hence, ANNs are well suited for application to problems that involve abundant descriptive data or observations but whose solutions require knowledge that is difficult to quantify. An ANN can often correctly infer the unseen component of a problem after learning from the data even if the input data contain noisy information. In addition, ANNs 271

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

propagation faster. Therefore, this study employed the Tansig transfer function for model development, as shown in Eq. (3).

f (χ ) =

2 −1 1 + e−2χ

(3)

The back-propagation learning algorithm has been used in ANNs in many previous studies and textbooks (Schalkoff, 1997; Luger, 2002; Negnevitsky, 2002; Russell et al., 2003). Because the BPN is a supervised learning algorithm, the difference between the output Zk and the target value is amended by an error function. The error function is defined as follows (Widrow and Hoff, 1960):

E=

1 2

K

∑ ek2 = k=1

1 2

K

∑ (Tk − Zk )2 k=1

where Tk is the desired output or target value and is known in advance and ek is the error of each output node. To minimize the error function, the weight in each link is adjusted until the final output value matches the target value. To adjust the weights in the network, the gradient descent method is employed. In the link between the hidden and output layers, the partial derivative of E with respect to the weight Wjk is calculated as shown below (Haykin, 1999).

Fig. 2. Structure of a typical ANN model.

are nonlinear, like most natural systems. Because of the advantages of ANNs and the unclear physical mechanisms underlying CFWs, this method appears to be appropriate for CFW forecasting. Many different learning algorithms are used for ANN model training, and a single algorithm cannot be used to solve all problems (Zhang et al., 1998). The most popular algorithm for ANN training is the back-propagation algorithm, which is essentially a method that involves the gradient of steepest descent. In this paper, an ANN with a back-propagation network (BPN) is used to build an early warning model for CFW forecasting.

∂E ∂E ∂Zk ∂Yk = = −δk Yj ∂Wkj ∂Zk ∂Yk ∂Wkj

ΔWkj = r Yj δk

K ∂E ∂Zk ∂Yk ⎤ ∂Yj ∂Xj ∂E ⎡ = −δj Xi = ⎢∑ ∂ ∂Wji Z ∂Yk ∂Yj ⎥ ∂Xj ∂Wji ⎦ ⎣ k=1 k

K

δj = f '(Yj )

Yk =

(9)

The new weights in the input and hidden layers are calculated as follows:

(1)

∑ Wjk Yj − θk j=1

∑ δk Wkj k=1

J

Zk = f (Yk ),

(8)

The function δj can be derived as follows:

I i=1

(7)

In Eq. (7), n is the number of iterations. Correspondingly, the E value in the links between the input and hidden layers can be obtained using the partial derivative with respect to the weight Wij , as follows:

A single hidden-layer feed-forward network with a back-propagation learning algorithm is employed in this study because one hidden layer is sufficient for most forecasting problems. As shown in Fig. 2, the ANN model is characterized by a network of three layers; each layer contains I, J and K nodes, which are also called neurons. There are weights between the different nodes of each layer. The relationships between the input layer and the hidden layer and those between the hidden layer and the output layer are described by Eq. (1) and Eq. (2), respectively. Each input factor in the input layer is denoted by Xi; the outputs in the hidden layer and the output layer are denoted by Yj and Zk, respectively.

∑ Wij Xi − θj

(6)

where δj= ej f ′ (Yj) = (Tj − Zj ) f ′ (Yj) and r is the learning rate with a value between 0 and 1.

2.2. ANN architecture and a BPN algorithm

Xj =

(5)

The weight adjustment in the link between the hidden and output layers is calculated as follows:

Wkj (n+1) = Wkj (n) + ΔWkj (n)

Yj = f (Xj ),

(4)

ΔWji = r Xi δj

(10)

Wji (n+1) = Wji (n) + ΔWji (n)

(11)

Choosing the number of nodes in each layer is a crucial task in ANN modeling. The most common methods of determining the number of hidden nodes are experimentation and trial and error. In cases involving a single hidden layer, several rules have been proposed for determining the number of hidden nodes; these include the use of “2n+1” (Lippmann, 1987; Hecht-Nielsen, 1990), “2n” (Wong, 1991), “n” (Tang and Fishwick, 1993) and “n/2” (Kang, 1991), where n is the number of input nodes. Although none of these rules works well for all problems (Zhang et al., 1998), networks with the same numbers of hidden and input nodes have been reported in several studies to yield better forecasting performance (de Groot and Wurtz, 1991; Chakraborty et al., 1992; Sharda and Patil, 1992; Tang and Fishwick, 1993). The number of input nodes depends on the number of factors that influence the CFW occurrence, which will be discussed in section 3.3. The number of output nodes is easier to specify because it is directly proportional to the problem being studied.

(2)

In Eqs. (1) and (2), I is the number of input nodes, J is the number of hidden nodes. In this study, the output node is set to one, ie. k = 1. In addition, Wij is the numerical weight between the input and hidden layers, and Wjk , the numerical weight between the hidden and output layers, is the same; θj and θk are the biases; f is the transfer function, which is used in both the hidden and the output layers; and Xj and Yk are the results, which were calculated before applying f. Three types of activation functions are included; these are also called “transfer functions”. These functions are the tangent sigmoid (Tansig), the logistic sigmoid (Logsig) and the linear transfer functions. Fig. 3 shows the patterns of these transfer functions. Sibi et al. (2013) concluded that only a trivial difference is found in the training results obtained using systems configured with different transfer functions. Kriesel (2007) suggested that use of the Transig function makes neural network 272

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

Fig. 3. Transfer functions in the ANN model.

the data into the first quartile statistics with respect to the past 17 years of data. The data were preprocessed before they were used for model development to eliminate errors associated with the characteristics and magnitudes of the data. The data were normalized to values between 0 and 1 using Eq. (12), in which Xnew and Xraw are the normalized data and the raw data, respectively; min. and max. are the data minima and maxima.

3. Data preparation for model setup 3.1. Study area From 2000 to 2016, 301 accidents induced by CFWs were recorded along the Taiwanese coast, especially along its northeastern portion. Longdong, which is shown in Fig. 4, is a well-known area for coastal fishing and is therefore the location most likely to experience accidents due to CFWs. During the past 17 years, 76 such events have been recorded at the Longdong coast. Therefore, Longdong was chosen as the study area for this research. Longdong is characterized by its irregular coastline and rapidly changing bathymetry. The water depth reaches 1000 m just a few kilometers offshore. The monsoon period from November to February always brings strong NE winds and generates severe seas over and around northeastern Taiwan; these conditions are especially prevalent in the Longdong area due to the NW-SE orientation of its coastline.

Xnew =

Xraw − min.(x ) max.(x ) − min. (x )

(12)

3.3. Data used for model training The data used in model development are crucial for forecasting future CFW occurrence. Data mining models such as ANN require a large amount of training data to produce good forecasting results, even when the physics of the chosen parameters are not considered. However, the dependence of the parameters on the target, i.e., the occurrence of coastal freak waves, is considered. This study chose data that correspond to potential causes of CFWs that have been reported in the literature. Sea state, swell occurrence, wave groupiness and wave nonlinearity are the factors most likely to be associated with CFW generation (Tsai et al., 2004; Chien et al., 2002). We also suggest that the effects of directionality of waves and winds and wind speed on CFW generation cannot be neglected. Table 1 summarizes these factors, and they are described further below.

3.2. Data source and preprocessing The field data used in this study were collected from the Longdong Data Buoy, which has been in use by the Central Weather Bureau of Taiwan since 1998. The buoy is located 1 km off the Longdong coast at a location with a water depth of 23 m, as shown in Fig. 4. The buoy automatically measures the surface waves and the corresponding meteorological parameters such as wind speed, wind direction, wind gusts, barometric pressure, air temperature and surface water temperature at 1-h intervals. A rigorous data quality verification system was applied to the buoy-measured data (Doong et al., 2007). In this study, meteorological and oceanographic data recorded at the Longdong Buoy during 63 CFW events were used as the input data for ANN model training. In addition to these field data, data were also collected during periods in which no CFWs occurred (i.e., ordinary days) for model training purposes. These “ordinary day” data were collected at times that satisfied the “slight sea state” criteria, for which the significant wave height, mean wind speed and wave peak periods were less than 0.6 m, 2.6 m/s, and 6.9 s, respectively, thereby placing

3.3.1. Sea state Severe sea states produce large waves with a higher probability of becoming CFWs when they break along the coast. The sea state can be indicated by sea surface roughness, wave steepness and significant wave height. The significant wave heights (Hs) measured from buoy data were selected as an input parameter for ANN model development in consideration of future warning applications. 273

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

Taipei

Longdong buoy

Fig. 4. Study area along the Longdong coast located in northeastern Taiwan.

employed in this study. GF is estimated from the smoothed instantaneous wave energy history (SIWEH) as shown in Eq. (13):

3.3.2. Swell occurrence Swell has a longer wave period and a higher propagation speed than wind waves. The momentum of a swell is higher than that of a wind wave; thus, a potentially larger splash of water can be created when it breaks at the coast. Some researchers (Chien et al., 2002; Tamura et al., 2009) have proposed that there is a strong relationship between swell and CFW occurrences. Swell characteristics can be represented by various parameters, including swell height/period, wave age, and peak wave period. For ease of input in future applications, here the peak wave period (Tp) is used to represent swell in the model training process.

GF =

1 S

1 TN

TN

∫ [S (t ) − S ]2 dt

(13)

0

where TN is the total length of the wave record, S(t) is the smoothed instantaneous wave energy history, which is expressed by Eq. (14), and S is the mean of S(t), which indicates the mean power of the spectrum. In Eq. (14), Tp is the wave period at the spectral peak, η (t ) is the surface elevation, and Q (τ ) is the Bartlett window smoothing function, as shown in Eq. (15).

3.3.3. Wave grouping High waves often seem to be grouped together. Tsai et al. (2004) and Chien et al. (2002) reported significant relationships between wave groupiness and CFW occurrence. When the first wave breaks at the coast, it may interact with the next grouping wave to generate a freak wave. There are several ways to quantify wave grouping. The groupiness factor (GF), which was proposed by Mansard and Funke (1980), is

S (t ) =

1 Tp

∞

∫ η2 (t + τ ) Q (τ ) dτ

(14)

−∞

1 − τ / Tp τ ≤ Tp Q(τ ) = ⎧ 0 τ > Tp ⎨ ⎩

(15)

Table 1 Categories of influencing factors in coastal freak wave occurrence and the corresponding parameters adopted for the ANN model development. Category

Parameter and abbreviation

Influences

References

Sea state Swell occurrence

Significant wave height (Hs) Peak period (Tp)

Severe sea states have large breaking waves. Strong relationship between swell and CFW occurrence

Wave grouping

Groupiness factor (GF)

Coastal freak waves are associated with groups of waves.

Wave nonlinearity

Benjamin-Feir Index (BFI) Kurtosis (KT) Onshore wind speed (OSW) Difference of wind and wave directions (Duw)

When wave nonlinearity increases, wave coalescence may occur.

Generally understood Chien et al. (2002); Tamura et al. (2009) Tsai et al. (2001, 2004); Chien et al. (2002); Janssen (2003);

Wind Speed Directionality

When strong winds blow perpendicular to the coast, a larger wave is expected. When the directions of the waves and winds are the same, wave superposition is expected.

274

This paper This paper

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

algorithm. There are seven input parameters for the model; two of these parameters (kurtosis and BFI) are associated with the nonlinearity of the data. The number of neurons in the hidden layer is the same as the number of input neurons suggested by Zhang et al. (1998). The model is designed to output a value between 1 and 0; this value represents a “high possibility” or a “low possibility” of CFW occurrence when it approaches 1 or 0, respectively.

3.3.4. Wave nonlinearity When wave nonlinearity increases, wave coalescence may occur, resulting in a freak wave. In this study, the kurtosis (KT) (Mori et al., 2011) and the Benjamin Feir Index (BFI) (Onorato et al., 2001; Janssen, 2003) are used as input parameters to represent the wave's nonlinearity. The distribution of the surface displacement is assumed to be Gaussian; however, it may deviate from a Gaussian distribution due to the effect of nonlinearity. Kurtosis is a parameter that is sensitive to this deviation and is therefore adopted. In addition, BFI is a quantitative measure of wave instability (Janssen, 2003; Mori and Janssen, 2006). The dimensionless parameter BFI, defined in Eq. (16), is correlated with wave steepness (ε) and relative bandwidth of the spectrum (Δ). The wave steepness is the ratio of wave height to wavelength. The relative spectral bandwidth is the ratio between the spectral bandwidth (σω ) and peak frequency (fp). Janssen (2003) and Serio et al. (2005) used the standard deviation as the measure of spectral bandwidth when assuming the spectrum is a Gaussian shape.

BFI =

2

ε where Δ = σω/fp Δ

4.2. Model training 4.2.1. Effect of data length and training data ratio Because the ANN-based model is a data-driven model, the training data significantly influence the model performance. The model is designed to forecast the possibility of a CFW occurrence with a 12-h lead time; therefore, input data are collected prior to each run. The model can be trained using a short time series such as the previous 2 h of data or data from a longer time series such as the previous 12 h of data. In this study, we examine input data lengths ranging from 2 to 8 h preceding the operation time. Another factor influencing the performance of the model is the training data ratio. In total, sixty-three datasets (including the seven input parameters described earlier) were collected from known CFW events at Longdong from 2000 to 2016. Two-thirds of these (40 events) are used for model training, and the remainder (23 events) are used for model verification. For model training purposes, data for the seven parameters in non-CFW circumstances are collected and mixed with the 40 CFW data. In fact, approximately 130 thousand datasets obtained during non-CFW conditions are available for the period from 2000 to 2016. This study designed 7 models using various combinations of data length and training data ratios, evaluated the results, and identified the best model. Data from 2, 4, 6 and 8 h prior to the operation time are used in conjunction with CFW:non-CFW data ratios of 1:1, 1:5, 1:10 and 1:50, respectively. The 7 candidate models are listed in Table 2.

(16)

3.3.5. Wind speed The Longdong coast lies to the windward side of the northeasterly monsoon. When strong winds blow perpendicular to the coast, they may trigger large waves and increase the probability of CFW occurrence. In this paper, the onshore wind speed (OSW) obtained from wind measurements from the data buoy is used to calibrate the ANN model. 3.3.6. Wave and wind directions Local wind generates wind waves. The coexistence of local wind waves with swell increases the probability of occurrence of a freak wave by 5–20% (Gramstad and Trulsen, 2010). The interaction of short-crest wind waves with long-period swell will increase this probability even if they propagate in similar directions. Therefore, we think that consideration of the correlation of wind and wave directions is necessary. This study uses the misalignment between wind direction and wave direction (Duw) as one of the input parameters for model training.

4.2.2. Training process and assessment parameters The maximum values of the 7 parameters during the 2–8 h prior to the occurrence of the CFW are the inputs for the model. Model training is an iterative process. The goal of the training is to obtain the best weighting values between nodes according to the lowest bias of the forecast and real values. In this study, the initial weighting values are randomly assigned. Adjustment values are added to each weight if the bias is still not smaller than the assigned value. The maximum number of iterations is set to 500. To assess the prediction accuracy of the warning model, two indicators are proposed: the accuracy rate (ACR) and the recall rate (RCR). The ACR is an integrated index that is used to assess the performance of the forecast; it is defined as the proportion of events that are correctly predicted by the proposed model, as shown in Eq. (17). The RCR is defined as the proportion of events that are accurately captured according to the real occurrence events, as shown in

4. Model development 4.1. Design and flow of the operational model The warning model is designed to be run twice daily for the purpose of forecasting the occurrence of a CFW with a lead time of 12 h relative to the operation time. The operational flow is shown in Fig. 5. The first warning is designed to be announced at UTC 00. Data observed by the buoy prior to this run are preprocessed and input into an ANN model. The second run is designed to be conducted 12 h later. The architecture of the ANN-based CFW warning model is shown in Fig. 6. It contains three layers and a back-propagation learning

Fig. 5. Operational flow of the warning model for CFWs. 275

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

Fig. 6. Architecture for one of the proposed warning models for coastal freak waves.

Note: DL represents data length; Suc. represents success; Fail. represents failure; ACR represents the accuracy rate and RCR represents the recall rate.

understand the effect of the length of time over which the data are collected, whereas the fifth to seventh models are used to demonstrate the effect of the training data ratio. The training results show that the rate of successful forecasts of CFW occurrences is close to 100%; this indicates that the models are well trained via the back-propagation learning algorithm and that they have low sensitivity to the input data combinations. Relatively low successful forecast rates (85%) are achieved when only 2 h of data are used with the same number of nonCFW datasets. Thus, input of short-term data facilitates running of the model but may introduce higher uncertainty, whereas input of longterm data may reduce the uncertainty of the model without generating higher accuracy. To eliminate the bias and error caused by imbalances in the training data, the same number of non-CFW datasets are employed in this study, i.e., model no. 3 is best.

Eq. (18).

4.3. Model verification

Table 2 Results of the proposed models. 7-inputs-models

Training

Verification

No.

DL

Ratio

Suc.

Fail.

Suc. rate

Suc.

Fail.

ACR

RCR

1 2 3 4 5 6 7

2h 4h 6h 8h 6h 6h 6h

1 1 1 1 5 10 50

68 78 77 80 237 435 2017

12 2 3 0 3 5 23

85% 98% 97% 100% 99% 99% 99%

34 41 43 39 132 245 1153

12 5 3 7 6 8 20

75% 89% 94% 85% 96% 97% 99%

74% 78% 87% 74% 74% 69% 61%

ACR = (A + D)/(A + B + C + D)

(17)

RCR = D /(B + D)

(18)

The data obtained from twenty-three known occurrences of CFWs within sixty-three events are employed to verify the proposed model. In addition to showing the validation result for the best model no. 3, Table 2 also shows the validation results for the other models. The ACR (accuracy rate) and the RCR (recall rate) are used to evaluate each model's performance. The best model, no. 3, displays 94% (43 of 46 validation cases) accuracy in forecasting the occurrence or non-occurrence of CFWs, and it only produces 3 forecast errors; the RCR for model no. 3 is 87%. The results are shown in Fig. 7(b). The validation results enhance the confidence in applying the model. When the training data ratio is fixed (models no. 1–4), model no. 3, which uses input data from the past 6 h, is the best, as indicated by its highest ACR and RCR values. Comparison of model no. 3 with models no. 5–7, which have the same data collection lengths but different training data ratios, shows that the ACR increases from 94% to 99% but the RCR decreases from 87% to 61% when the latter models are employed. For prediction purposes, the RCR is more important than the ACR. By definition, RCR (Eq. 18) represents the percentage of correct prediction. The reason for the high ACR (for example, 99% in the case of model no. 7) might be that a large denominator was obtained from the correct prediction of non-CFW events, which is not the main concern of this study. On the other hand, the RCR indicates the rate of

The variables A to D in Eqs. (17) and (18) are all conditional numbers. A is the number of CFWs that do not occur during periods in which the model predicts that they will not occur; B is the number of CFWs that occur although the model predicts that they will not occur; C is the number of CFWs that do not occur although the model predicts that they will occur; and D is the number of the CFWs that occur when the model predicts that they will occur. Higher values for the two indices correspond to increased accuracy of the warning model. 4.2.3. Model training results Since the datasets were normalized and the Tansig transfer function was employed, the output values are expected to range from 0 to 1. The training result of candidate model no. 3 is shown in Fig. 7(a). A threshold of 0.5 is used to divide the results into higher and lower occurrence probabilities of CFWs. A result that is greater than 0.5 and close to 1.0 indicates good consistency with the circumstances preceding the actual occurrence of CFWs. A CFW is unlikely to occur if the model output approaches 0. The quantitative results are shown in Table 2. The first to the fourth models listed in Table 2 are used to 276

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

(a)

(b) Fig. 7. Output results of the best ANN-based warning model (No. 3 in Table 2) for (a) model training and (b) model verification.

fall when the splash height is higher than half the person's height and the wave has a speed of 0.4 m/s. We applied these conditions to identify CFWs. Because wave speed is usually greater than 0.4 m/s, the speed criterion is ignored in our study, and only the splash height is used to identify a CFW. An image-processing algorithm is applied to identify the splash height. When the splash height is greater than 0.9 m (an average person's height is assumed to be 1.8 m), we count the wave as a CFW. The forecast results obtained using the proposed warning model and the observational results from the image analysis are shown in Fig. 8. The gray areas in the figure show the typhoon alarm periods; the red and green lines show the occurrence or non-occurrence of CFWs, respectively, based on the camera images. Fig. 8 shows the consistency between the forecast results and the observations. The ACR and RCR are 90% and 91%, respectively; this represents a strong outcome and validates the ability of the ANN-based warning model to forecast CFWs. In addition, the time series of 7 input parameters are shown in Fig. 9 for comparison with the results shown in Fig. 8. It is found from the figures that the occurrence of coastal freak waves is not due to a dominant influence of just a few of these quantities. An example of a CFW is shown in Fig. 10. This event was recorded on September 5, 2016. The model predicted that a CFW might occur that day, and the camera observations verified that one occurred. Fig. 10(a) shows that the sea state was not severe at 09:31:20 on the day of the CFW. Fishermen can be observed standing on the coastal rock. Six seconds later (09:31:26), a large wave occurred with a splash height greater than a person's height. In this case, the fishermen were not harmed by the CFW because they

correct prediction of CFW events, which is what this study is most concerned with. The RCR of model no. 3 is the highest, and its ACR (94%) is not low. This again indicates that model no. 3 is the best model. In addition, model no. 3 yields superior results when the same amounts of CFW and non-CFW data are used. The bias from the sampling uncertainty is smaller than that for the models with large training data ratios.

4.4. Advanced model validation The data used in the proposed model development and validation were obtained mainly from media reports. Although all cases were validated as real CFW events, the data are still uncertain and incomplete. For example, an event will not be identified as a CFW if a person is not swept away by the wave. Thus, more accurate records and the data associated with those records are needed for model training and validation. The Central Weather Bureau of Taiwan established a video camera station at Longdong in 2016. This high-resolution camera can record successive waves in the daytime, including CFWs. The sea state videos are used for validation in this study. The videos span the period from September 1st to September 27th, 2016. Although the video record covers only one month, it recorded a significant month because 2 typhoons approached Taiwan during this period. We expect the performance of the proposed warning model to be clearly demonstrated during this period of ordinary and typhoon conditions. The first step in the validation is to identify the CFWs in the images. Murata et al. (2010) proposed that a CFW will cause a person to 277

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

Fig. 8. Results of the warning model (blue circles) and observational images (lines). The typhoon periods are shown in gray. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

mitigated in the future by the availability of a warning alarm.

were not standing close to the sea. This case was not reported in the media because an accident did not occur. However, a CFW did occur as forecast by the warning model, and it was observed by the camera. The proposed warning model is doubly validated using the camerarecoded events. The results presented in Fig. 8 show that the warning model is capable of forecasting CFW occurrences both during severe sea states (such as during typhoons) and on ordinary days. The CFWs that occur on ordinary days are associated with higher risk to persons on the shore than those that occur on typhoon days. The proposed model is now being operationally tested by the Central Weather Bureau of Taiwan, and the risk of CFW-related accidents is expected to be

5. Conclusions Coastal freak waves (CFWs) pose a risk to people in coastal areas, especially in countries such as Taiwan where fishing is a popular activity. To mitigate the risk associated with coastal activities, development of a model that can provide a warning before CFWs occur is essential. The mechanisms associated with CFW generation are not understood. As such, deterministic forecasting is not currently possible; therefore, this study adopts a stochastic approach to model

Fig. 9. Time series of the seven parameters used for the model from September 1 to September 27, 2016. 278

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

(a)

better results. The results show that using the 6 h of data prior to the CFW occurrence results in the best model performance. ANN model training requires both occurrence data and non-occurrence data. The ratio of these datasets influences the forecast performance. The results in this study show that a 1:1 dataset generates the best model performance, i.e., it is suggested that similar amounts of data from non-CFW circumstances and CFW circumstances be used. When the Tansig transfer function was used, the model outputs had a value between 1 and 0. When the result is 1, the model forecasts that a CFW will occur. However, the model output is unlikely to be exactly 1 and is more likely to approach 1, thereby representing the uncertainty of nature. Thus, a perfect model does not exist, and when the model output approaches 1.0 or is exactly 1.0, a high possibility of CFW occurrence is assumed. However, a CFW may also have a low probability of occurrence. We suggest using 0.5 as the boundary between high and low likelihood of CFW occurrence based on the developed ANN CFW forecast model. The proposed warning model was validated using two different sources of CFW events: media-published events and camera-recorded events. These validations yielded ACR/RCR values of 94%/87% and 90%/91%, respectively. These results indicate that the proposed warning model is accurate and reliable for CFW forecasting and confirm that an ANN is useful for natural hazard warnings.

(b)

Acknowledgments The authors thank the anonymous reviewers for their careful reading of the manuscript and their many insightful and constructive comments and suggestions to improve this paper. This research was supported by the Ministry of Science and Technology (Grant No: MOST 106-2628-E-006-008-MY3) and the Central Weather Bureau (Grant No: MOTC-CWB-107-O-02) of Taiwan. The buoy data used in this study were measured and qualified by the Coastal Ocean Monitoring Center of National Cheng Kung University. The authors would like to express their great thanks for all the supports. Thanks are also extended to Prof. Cheng-Han Tsai of the National Taiwan Ocean University, Prof. JenChih Tsai of the Chungyu University of Film and Arts and Prof. ShienTsung Chen of the Feng Chia University of Taiwan for their constructive comments and suggestions during this research.

(c) Fig. 10. (a)(b)(c) Consecutive images captured at Longdong in northeastern Taiwan. The photographs were taken on September 5, 2016.

References development. An artificial neural network (ANN)-based forecast model for CFW occurrence is developed in this study. The proposed ANN-based warning model is a data-driven model with a three-layered architecture; it uses a back-propagation learning algorithm that is designed to forecast the likelihood of a CFW twice a day. The Longdong area in northeastern Taiwan was chosen as the study area due to the frequent occurrence of CFWs in that area. This study collected datasets from 63 known CFW events; data from twothirds of these events (40 events) were used for model training, and data from one-third of these events (23 events) were used for model verification. Although ANN is a data mining technique that requires a large amount of data for model training, this study prioritizes the physical representation of CFWs and the simplicity of application of the model. Six factors (sea state, swell occurrence, wave nonlinearity, wave grouping, wind speed, and wind/wave direction) are considered to indicate the possibility of CFW occurrence. Seven parameters corresponding to these six factors are used as input for model training; they are the significant wave heights (Hs), the peak wave period (Tp), the Benjamin Feir Index (BFI), the onshore wind speed (OSW), the kurtosis (KT) of sea surface elevation, the groupiness factor (GF) and the misalignment between wind and wave directions (Duw). In addition to these model input parameters, the data length and the ratio of CFW to non-CFW data are two critical factors in the model development. Collection of data for longer periods of time does not necessarily yield

Böse, M., Wenzel, F., Erdik, M., 2008. A neural network-based approach to earthquake early warning for finite faults. Bull. Seismol. Soc. Am. 98, 366–382. Bernier, N.B., Thompson, K.R., 2015. Deterministic and ensemble storm surge prediction for Atlantic Canada with lead times of hours to ten days. Ocean Model. 86, 114–127. Cavaleri, L., Bertotti, L., Torrisi, L., Bitner-Gregersen, E., Serio, M., Onorato, M., 2012. Rogue waves in crossing seas: the louis majesty accident. J. Geophys. Res. 117, C00J10. https://doi.org/10.1029/2012JC007923. Chakraborty, K., Mehrotra, K., Mohan, C.K., Ranka, S., 1992. Forecasting the behavior of multivariate time series using neural networks. Neural Network. 5, 961–970. Chang, F.J., Tseng, K.Y., Chaves, P., 2007. Shared near neighbours neural network model: a debris flow warning system. Hydrol. Process. 21, 1968–1976. Chang, H.K., Liou, J.C., Liu, S.J., Liaw, S.R., 2011. Simulated wave-driven ANN model for typhoon waves. Adv. Eng. Software 42, 25–34. Chien, H., Kao, C.C., Chuang, L.Z.H., 2002. On the characteristics of observed freak waves. Coast Eng. J. 44, 301–319. de Groot, C., Wurtz, D., 1991. Analysis of univariate time series with connectionist nets: a case study of two classical examples. Neurocomputing 3, 177–192. de Oliveira, M.M., Ebecken, N.F.F., de Oliveira, J.L.F., de Azevedo Santos, I., 2009. Neural network model to predict a storm surge. J. Appl. Meteorol. Climatol. 48, 143–155. Deng, Y., Yang, J., Zhao, W., Li, X., Xiao, L., 2016. Freak wave forces on a vertical cylinder. Coast Eng. 114, 9–18. Deo, M.C., Sridhar Naidu, C., 1999. Real time wave forecasting using neural network. Ocean Eng. 26, 191–203. Deo, M.C., Jha, A., Chaphekar, A.S., Ravikant, K., 2001. Neural networks for wave forecasting. Ocean Eng. 28, 889–898. Deo, M.C., 2010. Artificial neural networks in coastal and ocean engineering. Ind. J. GeoMarine Sci. 39, 589–596. Didenkulova, I., Anderson, C., 2010. Freak waves of different types in the coastal zone of the Baltic Sea. Nat. Hazards Earth Syst. Sci. 10, 2021–2029. Didenkulova, I., Slunyaev, A.V., Pelinovsky, E.N., Kharif, C., 2006. Freak waves in 2005. Nat. Hazards Earth Syst. Sci. 6, 1007–1015.

279

Ocean Engineering 169 (2018) 270–280

D.-J. Doong et al.

Tsunami: to Survive from Tsunami. World Scientific Publishing, New Jersey. Negnevitsky, M., 2002. Artificial Intelligence: a Guide to Intelligent Systems. Addison Wesley, Harlow, England. Nikolkina, I., Didenkulova, I., 2011. Rogue waves in 2006-2010. Nat. Hazards Earth Syst. Sci. 11, 2913–2924. Onorato, M., Osborne, A.R., Serio, M., Bertone, S., 2001. Freak waves in random oceanic sea states. Phys. Rev. Lett. 86, 5831–5834. Qin, H., Tang, W., Xue, H., Hu, Z., Guo, J., 2017. Numerical study of wave impact on the deck-house caused by freak waves. Ocean Eng. 133, 151–169. Rumelhart, D.E., Hinton, G.E., Williams, R.J., 1986. Learning internal representations by back-propagating errors. Nature 323, 533–536. Russell, S., Norvig, P., 2003. Artificial Intelligence - a Modern Approach, second ed. Prentice Hall. Romano, M., Liong, S.Y., Vu, M.T., Zemskyy, P., Doan, C.D., Dao, M.H., Tkalich, P., 2009. Artificial neural network for tsunami forecasting. J. Asian Earth Sci. 36, 29–37. Schalkoff, R.J., 1997. Artificial Neural Networks. McGraw-Hill. Serio, M., Onorato, M., Osborne, A.R., Janssen, P.A.E.M., 2005. On the computation of the benjamin-feir index. Il Nuovo Cimento 28, 893–903. https://doi.org/10.1393/ncc/ i2005-10134-1. Sharda, R., Patil, R.B., 1992. Connectionist approach to time series prediction: an empirical test. J. Intell. Manuf. 3, 317–323. Sibi, P., Jones, S.A., Siddarth, P., 2013. Analysis of different activation functions using back propagation neural networks. J. Theor. Appl. Inf. Technol. 47, 1264–1268. Sunkpho, J., Ootamakorn, C., 2011. Real-time flood monitoring and warning system. J. Sci. Technol. 33, 227–235. Tamura, H., Waseda, T., Miyazawa, Y., 2009. Freakish sea state and well-windsea coupling: numerical study of the Suwa-Maru incident. Heographical Res. Lett. 36, L01607. Tang, Y., Li, Y., Wang, B., Liu, S., Zhu, L., 2016. Dynamic analysis of turret-moored FPSO system in freak wave. China Ocean Eng. 30, 521–534. Tang, Z., Fishwick, P.A., 1993. Feedforward neural nets as models for time series forecasting. ORSA J. Comput. 5, 374–385. Tsai, C.H., Su, M.Y., Huang, S.J., 2004. Observations and conditions for occurrence of dangerous coastal waves. Ocean Eng. 31, 745–760. Tsai, C.P., Lee, T.L., 1999. Back-propagation neural network in tidal-level forecasting. J. Waterw. Port, Coast. Ocean Eng. 125, 195–202 ASCE. Thirumalaiah, K., Deo, M.C., 1998. Real-time flood forecasting using neural networks. Comput. Aided Civ. Infrastruct. Eng. 13, 101–111. Veltcheva, A.D., Guedes Soares, C., 2012. Analysis of abnormal wave groups in hurricane camille by the hilbert huang transform method. Ocean Eng. 42, 102–111. Veltcheva, A.D., Guedes Soares, C., 2016. Nonlinearity of abnormal waves by the hilbert–huang transform method. Ocean Eng. 115, 30–38. Widrow, B., Hoff, M.E., 1960. Adaptive Switching Circuits. 1960 IRE WESCON Convention Record. pp. 96–104. Wong, F.S., 1991. Time series forecasting using backpropagation neural networks. Neurocomputing 2, 147–159. Zhang, G., Patuwo, B.E., Hu, M.Y., 1998. Forecasting with artificial neural networks: the state of the art. Int. J. Forecast. 14, 35–62. Zhao, X., Ye, Z., Fu, Y., Cao, F., 2014. A CIP-based numerical simulation of freak wave impact on a floating body. Ocean Eng. 87, 50–63.

Doong, D.J., Chen, C.C., Kao, C.C., Lee, B.C., Yeh, S.P., 2007. Data quality check procedures of an operational coastal ocean monitoring network. Ocean Eng. 34, 234–246. Dysthe, K., Krogstad, H.E., Müller, P., 2008. Oceanic rogue waves. Annu. Rev. Fluid Mech. 40, 287–310. Fedele, F., Brennan, J., de Leon, S.P., Dudley, J., Dias, F., 2016. Real world ocean rogue waves explained without the modulational instability. Sci. Rep. 6, 27715. https://doi. org/10.1038/srep27715. Gramstad, O., Trulsen, K., 2010. Can swell increase the number of freak waves in a windsea? J. Fluid Mech. 650, 57–79. Guedes Soares, C., Cherneva, Z., Antão, E.M., 2004. Abnormal waves during hurricane camille. J. Geophys. Res. 109, C08008. https://doi.org/10.1029/2003JC002244. Hashemi, M.R., Spaulding, M.L., Shaw, A., Farhadi, H., Lewis, M., 2016. An efficient artificial intelligence model for prediction of tropical storm surge. Nat. Hazards 82, 471–491. Haykin, S., 1999. Neural Network: a Comprehensive Foundation. Prentice Hall. Hecht-Nielsen, R., 1990. Neurocomputing. Addison-Wesley, Menlo Park, CA. Janssen, P.A., 2003. Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr. 33, 863–884. Kang, S., 1991. An Investigation of the Use of Feedforward Neural Networks for Forecasting. Ph.D. Thesis. Kent State University. Kharif, C., Pelinovsky, E., Slunyaev, A., 2009. Rogue Waves in the Ocean. Springer. Kung, H.Y., Chen, C.H., Ku, H.H., 2012. Designing intelligent disaster prediction models and systems for debris-flow disasters in Taiwan. Expert Syst. Appl. 39, 5838–5856. Kriesel, D., 2007. A Brief Introduction to Neural Networks. available at: http://www. dkriesel.com. Lee, T.L., 2006. Neural network prediction of a storm surge. Ocean Eng. 33, 483–494. Lippmann, R.P., 1987. An introduction to computing with neural nets. In: IEEE ASSP Magazine, April, 4–22. López, V.F., Medina, S.L., Paz, J.F.d., 2012. Taranis: neural networks and intelligent agents in the early warning against floods. Expert Syst. Appl. 39, 10031–10037. Luger, G.F., 2002. Artificial Intelligence–structures and Strategies for Complex Problem Solving, fourth ed. Addison Wesley, USA. Makarynska, D., Makarynskyy, O., 2008. Predicting sea-level variations at the Cocos (Keeling) Islands with artificial neural networks. Comput. Geosci. 34, 1910–1917. Mansard, E.P., Funke, E.R., 1980. The Measurement of Incident and Reflected Spectra Using a Least Squares Method, Hydraulics Laboratory Technical Report LTR-hy-72. National Research Council of Canada. Mase, H., Yasuda, T., Mori, N., 2011. Real-time prediction of tsunami magnitudes in osaka bay, Japan, using an artificial neural network. J. Waterw. Port, Coast. Ocean Eng. 137, 263–268 ASCE. McCulloch, W., Pitts, W., 1943. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115–133. Mori, N., 2012. Freak waves under typhoon conditions. J. Geophys. Res. 117, C00J07. https://doi.org/10.1029/2011JC007788. Mori, N., Janssen, P.A., 2006. On kurtosis and occurrence probability of freak waves. J. Phys. Oceanogr. 36, 1471–1483. Mori, N., Liu, P.C., Yasuda, T., 2002. Analysis of freak wave measurement. Ocean Eng. 29, 1399–1414. Mori, N., Onorato, M., Janssen, P.A.E.M., 2011. On the estimation of the kurtosis in directional sea states for freak wave forecasting. J. Phys. Oceanogr. 41, 1484–1497. Murata, S., Imamura, F., Katoh, K., Kawata, Y., Takahashi, S., Takayama, T., 2010.

280