Adaptive neuro-fuzzy inference system for the prediction of monthly shoreline changes in northeastern Taiwan

Ocean Engineering 84 (2014) 145–156

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

Adaptive neuro-fuzzy inference system for the prediction of monthly shoreline changes in northeastern Taiwan Fi-John Chang n, Horng-Cherng Lai Department of Bioenvironmental Systems Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Da-An District, Taipei 10617, Taiwan, ROC

art ic l e i nf o

a b s t r a c t

Article history: Received 6 September 2013 Accepted 15 March 2014

This study intends to model the shoreline change by investigating monthly shoreline position data collected from seven sandy beaches located at the Yilan County in Taiwan during 2004–2011. The harmonic analysis results indicate shorelines appear significantly periodic with great variation. The adaptive neuro-fuzzy inference system network (ANFIS) is configured with two scenarios, namely lumped and site-specific ones, to extract significant features of shoreline changes for making shoreline position predictions in the next year. The lumped models for all stations are first investigated based on a number of possible input information, such as month, location, and the maximum and mean wave heights. The results, however, are not as favorable as expected, and wave heights do not contribute to modeling due to their high variability. Consequently, a site-specific model is constructed for each station, with its current position and nearby stations' positions as model inputs, to predict its shoreline position in the next year. Compared with the harmonic analysis and the autoregressive exogenous (ARX) model, the ANFIS model produces more accurate prediction results. The results indicate that the constructed ANFIS models can accurately predict shoreline changes and can serve as a valuable tool for future coastline erosion warning and management. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Shoreline change Shoreline erosion Adaptive neuro-fuzzy inference system (ANFIS)

1. Introduction Shoreline erosion is a worldwide problem that causes a major concern to the socio-economic developments in coastal cities for many countries (Chen and Zong, 1998; Genz et al., 2007). Bird (1985) indicated that about 70% of the world's sandy beaches retreated at a rate of 0.5–1.0 m per year. The increasingly intensive human activities in river basins and/or along coasts enlarge coastal erosion areas and aggravate erosion processes, and thus cause land losses; moreover the global climate change in the past decades results in rising sea levels (IPCC, 2007; Church et al., 2008) and accelerates the sand losses of beaches (Bruun, 1962; DavidsonArnott, 2005). Such threat is particularly severe in Taiwan, an island bearing intense shoreline changes. Recent surveys indicate that more than 80% of the island's sandy beaches have undergone erosion over the past three decades and coastal erosion has occurred along most of sandy shores at an alarming rate, which becomes an island-wide problem in Taiwan (Hsu et al., 2007). Therefore, the environmental protection against beach loss, disaster warning systems for coastal zones and appropriate land

n

Corresponding author. Tel.: þ 886 2 23639461; fax: þ 886 2 23635854. E-mail address: [email protected] (F.-J. Chang).

http://dx.doi.org/10.1016/j.oceaneng.2014.03.020 0029-8018/& 2014 Elsevier Ltd. All rights reserved.

management along the coasts are critical issues that need to be carefully studied and adequately developed. Shorelines are known to be unstable and vary over time. Short-term changes occur over decadal time scales, more or less, and are related to daily, monthly and seasonal variations in tides, currents, wave climate, episodic events and anthropogenic factors. Shoreline movement is a complex phenomenon and involves distinguishing long-term shoreline movement (signal) from short-term changes (noise). Analysis of shoreline variability and erosion–accretion trend is elementally important to coastal scientists, engineers and managers (Douglas and Crowell, 2000). Both coastal management and engineering design requires information of the past, current and future shoreline positions. Successful coastal management requires long-term shoreline erosion rates to be determined and forecasts made of future shoreline positions along with the estimates of their uncertainty (Douglas and Crowell, 2000). Shoreline erosion–accretion is driven by both natural and human factors in response to the complexity of coastal hydrodynamics. Natural factors involve sea levels, tidal waves, crust changes, typhoons, and sand particle size as well as sediment transport in nearby rivers while human factors involve land subsidence induced by groundwater overpumping, illegal sand and gravel mining in river basins, a series of dams on rivers for reducing sediment transport to costal

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zones, and flow conditions varied by local terrains rendered from coastal structures, which could significantly alter coastal landforms (Hsu et al., 2007). Although great efforts have been devoted to quantifying the rates of shoreline movement and obtaining the empirical relationships between shoreline changes and the variables affecting the change process (Hsu, 1999), a definite solution, if impossible, is still far away and has not yet been found. Shoreline change prediction has gained considerable attention; nevertheless, little consensus has been made on the best predictive methodology due to the complex heterogeneity of coastal geomorphology and sediment-transport processes. In general, the study of coastal hydrodynamic processes can be divided into: (1) numerical models; (2) physical (hydraulic) models; and (3) field measurement data analysis (Hughes, 1993). Numerical simulation methods are frequently used to simulate and predict the influence of coastal engineering works on coastal hydrodynamics. For instance, Zhong (2003) applied the two-dimensional SBEACH numerical analysis method to establishing a beach section variation model for predicting the beach section change effect under monsoon- and typhoon-induced waves. The Water Resources Agency, Taiwan (2008) adopted numerical methods to assess coastal changes around Taiwan and found that the sediment transportation in the Lanyang River played an important role in the shoreline shape along the Yilan Coast. However, due to the dynamics and complexity of costal environment, simulation results commonly bear great uncertainty and/or vagueness, and thus could not well represent actual phenomena. Moreover, with limited observational data related to a large number of parameters, model validation in general could not be fully conducted and measured. Hydraulic models are usually adopted in large-scale development projects for investigating the behavioral characteristics of erosion profiles. Because of scale effects, the profile changes in small-scale laboratory experiments, however, cannot be transferred directly to field situations. Besides, hydraulic models are not recommended for long-term prediction because data collection and model verification processes are laborious, time consuming and costly. Alternatively, empirical equations have been developed to predict beach profiles based on simple environmental parameters such as wave height, wave period, grain-size or sediment fall speed (Kriebel, 1987). Field data analysis can be used to judge shoreline change rates as well as predict future shoreline changes. It has been recently considered as a more effective reflection of the shoreline change process and a more reliable estimation approach than numerical simulation and physical models (Dolan et al., 1991; Douglas et al., 1998). The shoreline position change of the US East Coast in the 19th century indicated that the linear regression model was appropriate in certain cases, namely shorelines were unaffected by inlets or engineering changes (Douglas and Crowell, 2000). The problem with linear regression models is that they work well only when the assumptions of underlying linearity and normal distribution are fulfilled. However, in some cases with poor quality data, linear regression assumptions may be violated. Uncertainties in the extracted shoreline data need to be appropriately addressed if those data are to be used to predict future shoreline positions for sustainable coastal management (Appeaning Addo et al., 2008). Honeycutt et al. (2001) proposed that long-term prediction of shoreline change could be more accurate without the use of storm data after investigating the prediction results of shoreline change rates with and without the use of storm data, respectively. Özö lçer (2008) considered that there was a strong correlation between coastal topography changes and wave heights. Kerh et al. (2009) extracted beach locations from aerial photographs and configured artificial neural networks to predict long-term shoreline changes. These approaches were mainly developed for

estimating long-term shoreline changes. Taiwan is located on the main track of western North Pacific typhoons. Rapid erosion and the recovery of beach width after ordinary storms is well known, consequently shoreline positions can have a highly irregular temporal pattern. A total of 187 typhoons invaded Taiwan during 1958 and 2012, i.e., 3.4 typhoons per year in average. Shoreline changes in Taiwan can be quick and dramatic, and thus easily bring disasters (Yan, 2005). Consequently developing accurate prediction models of coastal erosion is vitally important and critical to coastal managers for protecting resident safety, public investments and private properties in the coastal zones. Artificial neural networks (ANNs) mimic human nervous system to effectively learn and wisely provide human-like activities. They can efficiently handle large amounts of high dimensional data and process messages with excellent nonlinear mapping ability and fault tolerance property. ANNs have been extensively used in hydrological forecasting with great satisfaction for decades (Maier and Dandy, 2000; Dawson and Wilby, 2001; Chang and Chen, 2003; Wang et al., 2009; Tiwari and Chatterjee, 2010; Abrahart et al., 2012). Various types of neural networks have been developed, such as multi-layer feedforward neural network, recurrent neural networks, and the adaptive network fuzzy inference system (ANFIS) (Haykin, 1999; Ham and Kostanic, 2000). We notice that choosing a suitable neural network for a given problem is however still more of an art than a science. The ANFIS, proposed by Jang (1993), fuses the fuzzy inference system into the neural network to simultaneously possess the selflearning and self-organizing capabilities. It increases the learning and memory capacity that the fuzzy theory lacks for and provides the flexibility to deal with uncertainty and imprecision (Sauty, 1980; Çelikyilmaz and Türksen, 2009). The ANFIS succeeds in various applications of different fields, such as motor fault detection systems (Ertunc et al., 2012), dynamic power load systems (Singh and Chandra, 2011), reservoir operating systems (Chang et al., 2005; Chang and Chang, 2006), and sea level forecasts (Huang et al., 2003; Sztobryn, 2003; Makarynskyy, 2004; Makarynskyy et al., 2004; Lin and Chang, 2008; Ghorbani et al., 2010). Talebizadeh and Moridnejad (2011) discussed further about the estimation of the uncertainty caused by the error in measuring variables, the uncertainty in the outputs of ANN and ANFIS models, and initial configurations prior to training. The complex coastal change process mainly links between hydrodynamic forcing and the morphological response of the beach to sediment transport through waves (Cowell et al., 1999; Omhoog Masselink and Huges, 2003). Many modeling efforts, particularly conceptual and/or physical models based on available pre-knowledge, have provided further evidences and/or gained more solid interactive mechanisms, which greatly enhance the understanding of the underlying study process. Nevertheless, there is still no clear consensus on the subject, partly because related parameters (bedload, waves, sediment, etc.) are very difficult to measure under field conditions. Despite considerable researches on describing the past shoreline changes and/or predicting future ones (Cowell et al., 1995; Boak and Turner, 2005; Quartel et al., 2008; Davidson and Turner, 2009; Davidson et al., 2010; Alegria-Arzaburu et al., 2010; Del Río et al., 2013; Long and Plant, 2012; Osorio et al., 2012; Liu et al., 2013), to our best knowledge, only a few studies attempted to use ANNs for predicting shoreline variations (Muslim et al., 2006; Alizadeh et al., 2011; Goncalves et al., 2012). Therefore a consensus has emerged on the use of ANNs for forecasting future shoreline positions. Based on the best of our knowledge and previous research references regarding the coastal change modeling and available measurements in the study area, this study discusses the possibility of developing a short-term prediction model using different sources of temporal geodetic data with three different shoreline prediction

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models. The purpose of this study is to solve the temporal variability of shoreline changes through constructing a reliable prediction model by using artificial intelligence techniques, and consequently a useful reference can be provided to coastal managers for future early warning and management of shoreline changes. The ANFIS is implemented to investigate its applicability and suitability for predicting monthly shoreline changes in the next year. The eight-year monthly shoreline positions measured in the Yilan County of northeastern Taiwan are used to depict and model their shoreline erosion–accretion trends. The modeling process can offer a reliable approach for solving shoreline change problems, and the results obtained can be a valuable reference to the authorities of the study area.

2. Study area 2.1. Status of the Yilan Coast Taiwan is frequently attacked by typhoons, particularly serious in the Yilan County of northeastern Taiwan (Fig. 1), and shoreline erosion is a major concern to local residents. There always exists a panic among residents whenever a typhoon strikes because typhoons inevitably cause a threat to their safety and property. The Yilan County is an alluvial plain surrounded by mountains on three sides, and its east coast borders the Pacific Ocean with a coast length of about 103 km from north to south. The shoreline of the Yilan County can be divided into three coastal types: Jiaosi fault; Lanyang alluvial; and Suhua fault. The topographical change of the Jiaosi and Suhua faults is little because the geological structures of both faults compose of sea rocks and coastal cliffs. Therefore, this study focuses mainly on the 33-km sandy beach along the coast between Toucheng and Suao (Fig. 2). The 73-km Lanyang River originates from the northern part of the Nanhu Mountain at 3740 m above sea level and winds through the Yilan County from west to east. Its upstream is very steep with rapid flow coupled with a great deal of sand grains. Torrential rains as well as earthquakes make the river more susceptible to collapse and erosion at the rock base, and thus create an alluvial fan in the midstream region. In the downstream region, the flowing speed of the river turns slow gradually and gravels in various sizes are deposited in the river bed. The river carries mass eroded materials

Fig. 2. Locations of shoreline observation stations along the Yilan coast.

such as mud, sand and gravels, which is one of the main sources that form sandy beaches. Besides, sands drifting with tides result in shoreline changes. The estuary sand source is determined by the river sediment transport capacity and sand source supply amount (Sun, 2003). Beach stabilization along the Yilan Coast must rely on the sand source from the Lanyang River (Lee et al., 2004). Beach erosion makes direct impacts on the tourism economy of the Yilan County because the tourism economy depends highly on beautiful sandy beaches. Due to its particular geographic location, the Yilan County suffers from not only northeastern monsoons in winter but frequent typhoon invasions in summer. Shoreline recession occurs after each typhoon attacks Taiwan. Nevertheless, typhoon-induced torrential rains bring abundant sediments to replenish beach losses and continuous beach nourishment works carries out for several months after typhoon seasons, which consequently lead to a cyclical dynamic equilibrium. Fig. 3 shows the monthly shoreline changes in 2005 at Touchen (near Waiao) of the Yilan County, and such phenomenon has gained great attention on the shoreline change over this area. Yo (1993) compared the topographic maps of the Yilan County in the years of 1919–1987 and divided this area into three regions to discuss the shoreline erosion status. Based on the topographic data measured four times during June 1992 and June 1994, Xu (1995) estimated that the shoreline retreat was about 50 m along the coast between the south of the Wushi Port and the north of the Lanyang River. A mixture of shoreline recession and accretion is found in the coast located south of the Lanyang River. Nevertheless, the entire shoreline of the Yilan County still retains a stable morphology. In sum, the shoreline change along the Yilan County shows great spatial and temporal variations and it is essential to develop a site-specific model for predicting the shoreline change of the Yilan Coast. 2.2. Data collection

Fig. 1. Location of the Yilan coast.

When developing a prediction model for shoreline change based on highly variable shoreline data, data reliability is a

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Fig. 3. Typical shoreline changes in Touchen (near Waiao) of the Yilan County during 2005.

fundamental and important issue. Land surveying is considered as the most accurate method, however it is the most labor and cost intensive relative to remote sensing and photogrammetry. Remote sensing data can delineate shorelines over large areas, but accuracy achieved can sometimes be less than that of land surveying. The first step for calculating shoreline change is to measure shoreline positions as accurately as possible. The First River Management Office of Water Resources Agency in Taiwan set up seven shoreline observation stations along the Yilan Coast, which are located at Waiao, Dafu, Yongzhen, Buhou, Qingsnui, Lize and Xincheng (from north to south, Fig. 2). A reference point was established at each observation station to measure the distance of the shoreline position to the reference point. The distance measured in January 2004 is used as a baseline for shoreline change. A positive change indicates a shoreline accretion while a negative one indicates a shoreline recession. A total of 672 monthly data sets of shoreline change were collected from January 2004 to December 2011. The 672 data sets (8yrs  12 months  7 stations) are divided into three independent subsets for use in the training (2004–2009), validation (2010) and testing (2011) phases of modeling process.

3. Methods Data analysis begins with an attempt to find the associations between variables. To analyze shoreline variability and trends, a functional definition of the shoreline dynamic feature is commonly conducted. The definition must consider the shoreline changes in both a temporal and spatial sense and its variability on the time scale. Time series models constitute one of the most important groups to modeling and forecasting. We first conduct a harmonic analysis to learn their annual periodic behavior and then construct neural-fuzzy networks to estimate their variability at seven observation stations along the Yi-lan Coast. For the purpose of comparison, a common approach through the autoregressive exogenous (ARX) model is also performed. 3.1. Harmonic analysis Based on the long-term observations on shoreline change along the Yilan Coast, eminent annual cyclic behavior with seasonal variations for shoreline change is detected. This study utilizes the harmonic analysis to properly formulate the annual periodic

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behavior of shoreline change. The harmonic analysis is purely computational (i.e., requires no priori analysis) and is used to analyze whether a periodic behavior occurs over time. The harmonic analysis is commonly conducted based on a Fourier series, which expands a periodic function into the sum of a set of simple oscillating functions, i.e., sines and cosines, shown as follows: Assuming X^ τ is the fitness value obtained from the harmonic analysis of X τ X^ τ ¼ X τ ετ p=2

¼ μ þ ∑ αi sin i¼1




 p=2
 2iπ 2iπ τ þ ∑ βi cos τ P P i¼1

τ ¼ 1; 2; ⋯; P

ð1Þ

where μ is the average value; αi and βi are Fourier coefficients in each month; τ is the current month; and P ¼12 months. 2 p  L ¼ ∑ X τ  X^ τ τ¼1 p

¼ ∑

τ¼1

"

p=2

X τ μ  ∑ αi sin i¼1




 p=2
#2 2iπ 2iπ τ þ ∑ βi cos τ P P i¼1

ð2Þ

By the principle of the least mean square error (LMSE) estimation, the unknown μ, αi and βi can be obtained by setting their corresponding partial differentiation equal to zero, shown as follows: μ¼

1 p ∑ Xτ pτ¼1

ð3Þ

α^ i ¼


 p  2 p 2iπ τ f or i ¼ 1; 2; …; 1 ∑ X i sin pi¼1 p 2

ð4Þ


 p  2 p 2iπ τ f or i ¼ 1; 2; …; 1 β^ i ¼ ∑ X i cos pi¼1 p 2

ð5Þ

The F distribution test is used to identify whether the harmonic component is significant. If f ZF(1 α, k, N  k 1), the harmonic component is significant, where f is the statistical test value and F (1  α, k, N  k  1) is the threshold value. The degree of freedom for the numerator is k, while for the denominator is N  k  1. α is the threshold value for the significance level of the test (Özö lçer, 2008). 3.2. ARX model In the statistical analysis of time series, autoregressive-movingaverage (ARMA) models provide a parsimonious description of a weak stationary stochastic process. Apart from basic ARMA specifications, a whole range of alternative models have been proposed (Box et al., 1994). For the purpose of comparison, autoregressive (AR) models with exogenous (fundamental) variables (‘dynamic regression’, or ARX) might be an alternative way of modeling shoreline change. The basic model structure is given by the following formula (denoted ARX hereinafter): ARX(p, b) refers to the model with p autoregressive terms and b exogenous inputs terms, where p ¼1 and b¼3 in our case corresponding to the inputs of the ANFIS model. This monthly forecast model contains AR(1) and a linear combination of the last 3 terms of a known and external time series dt  12 . It is given by X t ¼ εt þ φX t  12 þ η1 d1; t  12 þ η2 d2; t  12 þ η3 d3; t  12

ð6Þ

where φ is the parameter of autoregressive term; ηi , i ¼1–3 are the parameters of the exogenous input di; t  12 , i¼ 1–3; and the random variable εt is white noise. There are various methods to

149

estimate the parameters and in the ARX model structure, and the least squares method is adopted in this study. 3.3. Adaptive network fuzzy inference system (ANFIS) The ANFIS has great capability in dealing with the imprecision and uncertainty of nonlinear systems and is frequently implemented to build the fuzzy IF-THEN rules of logical inference through its powerful and effective data mining techniques. Data mining techniques are used to extract the main features inside the data sets and self-configure their interactive relations. The Sugeno fuzzy model is used to establish IF-THEN rules. Regarding the learning procedure and parameter adjustment, a feedforward neural network coupled with a supervised learning algorithm is implemented, which effectively and appropriately adjusts all parameters of the fuzzy inference system so that the model can possess the self-learning and generalization capacity. For a clear explanation of the ANFIS model, a system with an input vector of 4 dimensions, one output value and a five-layer network is taken as an example, as shown in Fig. 4. Layer 1 (Input layer): map the input variables onto the fuzzy set (each input is mapped onto two clusters); Layer 2 (Rule layer): conduct the fuzzy logic calculation (a total of sixteen rules in this example); Layer 3 (Normalization layer): normalize the results obtained from Layer 2; Layer 4 (Consequence layer): multiply the results obtained from Layer 3 by the parameters of the Sugeno fuzzy model; and Layer 5 (Output layer): summarize the output results of Layer 4. The ANFIS model has a flexible architecture. For example, when mapping a set of input variables in the first layer, it can pre-set the number of sets for each input variable and then utilizes the method of permutation and combination to establish all possible rules. The input variables can also be merged to obtain a parsimony number of cluster centroids for producing an effective representation of a system's behavior. There are many clustering methods, such as k-means, fuzzy c-means and fuzzy subtractive clustering. In this study, the subtractive fuzzy clustering method is applied, and a number of clustering combinations with different radii are evaluated (a detailed explanation can be found in Chang and Chang (2001)). We find two clustering rules with Gaussian membership function can produce suitable results. Because there are only two clusters, the inference system becomes quite simple. Moreover, due to the combination of the self-learning and generalization capacity of the neural network, the ANFIS model can appropriately and effectively adjust model parameters. The ANFIS is implemented by using the software package “MATLAB R2012a”. More details of the ANFIS can be found in Chang and Chang (2006). 3.4. Modeling shoreline changes In this study, the harmonic analysis coupled with the F distribution test is first utilized to evaluate the annual periodic behavior of shoreline change, and then the ANFIS model is configured for predicting the shoreline change in the coming year. To build a prediction model, we need to identify the important factors that affect shoreline changes. From the input and output data sets, input variables in different combinations are incorporated into the prediction model to identify the input combination with the best output result for ensuring that the prediction model can effectively depict the characteristics of the observed data. The possible input information consists of month, station location, current shoreline position, nearby shoreline positions, and the

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Fig. 4. Architecture of the ANFIS model.

maximum and mean wave heights in the current month, whereas the output is the shoreline position in the same month of the next year. In brief, for modeling the ANFIS, the data are commonly divided into 3 sets for the purpose of training, validating and testing the constructed models: the training set is used to construct and train models; the validation set is used to select the best trained model; and the testing set is used to re-validate the best selected model. In the harmonic analysis (so as the ARX model – a linear model), the data are commonly divided into two sets for the purpose of training and testing. This is mainly because we can have only one best model in the training process of the linear model while we might have several optimal models in the training process of an ANN model.

Root Mean Square Error (RMSE) " #1=2 ∑ðX obs  X est Þ2 RMSE ¼ N

ð8Þ

where Yobs is the observed value, Yest is the estimated value, and i¼1 to the number of samples. As RMSE becomes smaller, the accuracy of the predicted values becomes higher. Correlation Coefficient (CC)    ∑ X obs  X obs X est  X est ð9Þ CC ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2ffi ∑ X obs  X obs X est  X est where Yobs is the observed value, Yest is the estimated value, Y obs is the average of observed values, Y est is the average of estimated values, and i¼1 to the number of samples. As CC is closer to 1, the accuracy of the model becomes higher.

3.5. Performance evaluation criteria 4. Results and discussion Three statistics are chosen to assess the accuracy and applicability of the prediction model: the coefficient of efficiency (CE) (Nash and Sutcliffe, 1970); the root-mean-square error (RMSE); and the correlation coefficient (CC). All of these indices are widely used for estimating the fitness to the hydrological models and for facilitating the comparison of estimated results. These three criteria are defined as follows: Coefficient of Efficiency (CE) CE ¼ 1 

∑ðX obs X est Þ2  2 ∑ X obs  X obs

ð7Þ

where Yobs is the observed value, Yest is the estimated value, Y obs is the average of observed values, and i¼ 1 to the number of samples. As CE is closer to 1, the accuracy of the model becomes higher.

Measurements of beach profiles spanning over an 8-year period (2004–2011) are examined for the spatial and temporal changes in beach nourishments. Table 1 shows the basic statistics of the observed data of shoreline change in the 8-year period (2004– 2011) at seven shoreline observation stations along the Yilan Coast. The results indicate that the shorelines at Dafu and Yungjen retreated 5.04 m and 6 m, respectively; while, in contrast, the shorelines at Buhou and Chingshuei moved toward the ocean in 34.79 m and 24.53 m, respectively. The shorelines of Dafu and Yungjen bear increasing trends induced by typhoons. Although the shoreline of Waiao moved outward, the shoreline change reached its maximum at 101.3 m with the highest standard deviation at 21.72 m. Such uniqueness of this location should be taken into consideration during model construction. The statistic results indicate that the shoreline

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Table 1 Basic statistics of shoreline changes at seven shoreline observation stations in the Yilan County (2004–2011). Unit: meter

Waiao

Dafu

Yungjen

Buhou

Chingshuei

Lize

Xincheng

Mean SDa Position range Minimum Maximum

9.84 21.72 101.30  42.00 59.30

 5.04 9.85 42.10  29.40 12.70

 6.00 9.13 40.30  29.00 11.30

34.79 13.67 67.40  5.00 62.40

24.53 11.53 69.00  8.00 61.00

4.05 12.02 59.20  19.20 40.00

13.26 12.99 65.30  21.00 44.30

a

Standard deviation.

change in the Yilan Coast is complex and has great variations in both spatial and temporal distribution, and therefore it is desired to develop a site-specific model for predicting the shoreline change of the Yilan Coast. 4.1. Results obtained from harmonic analysis – Fourier series models To conduct the harmonic analysis, we first obtain the average of monthly observation data of shoreline change at each station during 2004–2011 and then calculate the fitness value through the harmonic analysis of X τ . The F distribution test with the significance level threshold value α¼ 0.05 is set to determine whether the annual periodic behavior of the analyzed series is significant. According to the six-year (2004–2009) monthly observation data of shoreline change at seven observation stations along the Yilan Coast, the shoreline change shows an annual periodic behavior with eminent seasonal variations (Table 2). The results of the Fourier analysis indicate that the harmonic components at six of the seven stations are significant, where their f values are greater than the threshold value, F(1  α, k, N  k  1) ¼F(0.95, 2, 69) ¼3.13. The only station that fails to produce any significant homonic component is station Lize. Table 2 and Fig. 5 clearly present the harmonic component for the analyzed series at each station. In an annual time scale, because of the cyclical dynamic equilibrium the results suggest two distinct seasonal pivotal points that separate beach erosion from accretion: the beaches experienced the largest accretion during March and June due to continuous beach nourishment works for several months after typhoon seasons; and the most serious shoreline recession in general happened during September to November (after typhoons attacked). 4.2. Results obtained from ANFIS models As previous analysis results, shoreline changes clearly present the harmonic component for the observation series at shoreline observation stations; nevertheless we also notice that the fitted Fourier series fails to fully describe the variability of the observation series. Consequently, we implement the ANFIS model to construct and predict monthly shoreline changes along the Yilan Coast for the next year based on monthly shoreline change information collected at seven observation stations. A number of previous studies suggested that the main factors that significantly influence shoreline changes consist of wave heights and the amount of sediment transported from the river estuary (Ruggiero et al., 2010). The amount of sediment, however, cannot be obtained in this study case because the measurement of the transported sediment amount is not regularly conducted. It is difficult to assess the reliability and accuracy of the measures. Consequently, we have to abandon this important factor. Wave heights, on the other hand, could be measured and obtained by the Central Weather Bureau, Taiwan. Three kinds of wave height information are used as potential inputs: the monthly maximum

Table 2 Results of the F distribution test at shoreline observation stations during 2004–2009. Location

Test statistics value (f)

Test threshold value F (0.95, 2, 69)

Notes

Waiao Dafu Yungjen Buhou Chingshuei Lize Xincheng

38.44 16.51 7.78 3.24 4.14 1.09 4.60

3.13 3.13 3.13 3.13 3.13 3.13 3.13

Significant Significant Significant Significant Significant Insignificant Significant

wave height, the mean wave height, and the mean wave height with the standard deviation. For the lumped scenario, a great number of models with various input combinations are investigated through trial and error processes to identify the best input combination such that the constructed models can better describe the characteristics of observed data. Four input combinations for building ANFIS models are explored, and their reliability are examined. The variables of four input combinations are shown as follows: Model 1 (4 inputs): current month, station location, monthly shoreline position, and the monthly maximum wave height (73–1505 cm); Model 2 (4 inputs): current month, station location, monthly shoreline position, and the mean wave height (54–335 cm); Model 3 (4 inputs): current month, station location, monthly shoreline position, and the standard deviation of wave height (54–335 cm); and Model 4 (3 inputs): current month, station location and monthly shoreline position. The wave height information is calculated from the continuous hourly data collected at only one wave height monitoring station, and the wave height information is adopted as an input for all the seven shoreline monitoring stations. Monthly maximum wave height data are hourly data; mean wave height data are the average of hourly data collected in each month; and the standard deviation of wave height is associated with mean wave height data. The 672 data sets are divided into three independent subsets for use in the training (2004–2009), validation (2010) and testing (2011) phases of the ANFIS models. Only one ANFIS model is configured for all seven stations, consequently the three inputs, in addition to “current month”, are site-specific information and are not the same for all seven stations. The model performance in terms of CE, RMSE and CC in all the three phases is shown in Table 3. It appears that the results are inconsistent in three phases for Models 1, 2 and 3. For instance, their CE and CC values in validation and testing phases are much smaller than those in training phases, and their RMSE values are much greater in testing phases than in training phases. Nevertheless, Model 4,

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Fig. 5. Monthly observed seashore changes and the simulated harmonic functions at five selected shoreline observation stations during 2004–2011.

which excludes wave height information from its input combination, produces relatively consistent results in all three phases, and thus Model 4 is superior to Models 1–3. The results suggest that even though various kinds of wave height data may provide extra information when building the prediction models for shoreline change, wave height information, however, does not contribute extra values to establishing reliable models. We notice that only one wave height monitoring station is adopted, and the wave height information is used as an input for all the seven shoreline

monitoring stations. Therefore less wave height effect is expected for the prediction models. Moreover, the variability of hourly wave height data of storm events becomes ultimately high, and thus wave height is regarded as noise to the prediction models. Besides, compared with the measurement of shoreline change, the measurement of wave heights is more difficult to conduct and might involve large system errors (e.g., the monthly mean value is used). After carefully examining Table 3, we find the results of these constructed models are inconsistent for estimating seashore

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classified into both groups after a great number of trial and error identification processes. This is mainly because Buhou is a sand dune in the estuary of the Lanyang River (the largest river in the Yilan County), which makes significant impacts on the modeling processes of both groups. For each group, a similar ANFIS-based model (i.e., the same input variables but different output station) is then independently built for each station to predict its monthly shoreline change in the next year based on the current month information of all four related stations. The ARX model has the same inputs as the ANFIS model for each station. Table 4 gives a detailed inspection of predictions obtained from the ANFIS-based model associated with each station, in terms of CE, RMSE and CC values in the training (2004–2009), validation (2010) and testing (2011) phases at all seven stations. In the training phases, very high CE values (0.96– 0.99) and CC values (0.98–0.99) and relatively small RMSE values (0.99–3.88 m) are obtained. In the validation phases, CE values fall within 0.89–0.95; CC values belong to 0.96–0.99; and RMSE values range within 1.1–3.27 m. In the testing phases, CE values fall within 0.83–0.98; CC values belong to 0.92–0.99; and RMSE values range between 1.12–5.37 m. The results obtained from training phases are consistent with those of validation and testing phases, which indicate that the ANFIS models are well trained without over-fitting. It appears that the constructed models based on nearby station information coupled with periodic features of shoreline changes can provide much better performance than the previous Models 1–4, in term of much higher CE and CC values and smaller RMSE values. It clearly demonstrates that the ANFIS is capable to effectively depict the input–output patterns and produces reliable and accurate yearly forecasts of shoreline changes. Regarding the prediction accuracy of the ANFIS models, neither the Fourier analysis nor the ARX models can properly capture the trend of shoreline changes and thus results in an error (the ratio of RMSE to position change) about 15–30% of variation ranges at each station. Whereas, the ANFIS models produce more precise predictions than Fourier series and ARX models, in terms

changes, for instance, the RMSE values of Model 4 are larger than 10 m in all three phases, which is not accurate enough. To solve this problem, site-specific models are further investigated to construct suitable models through another great number of trial and error procedures (i.e., site-specific scenario). In the sitespecific model, the seven stations are divided into two groups. In each group, the same input variables (current month information of all four related stations) but different output (the shoreline of a selected station in the next year) are used to individually build an ANFIS-based model for each station. Because the same input variables are used, a similar ANFIS structure (two rules) is obtained, while the corresponding parameters are different for all four stations. The results suggest that the persistent characteristics of shoreline change and the shoreline change information of nearby stations could be the most important information for modeling reliable and accurate seashore changes. Consequently, two groups are established: Waiao, Dafu, Yongzhen and Buhou belong to one group (along the northern coast); and Buhou, QingSnui, Lize and Xincheng belong to the other group (along the southern coast). Each group has four input variables (monthly shoreline position at the four observation stations) and one output variable (shoreline position at each station in the same month of the next year). The architectures of the models are similar, as shown in Fig. 4. We would like to note that station Buhou is Table 3 Performance of the ANFIS models for the lumped scenario. Model Training (2004–2009) CE

1 2 3 4

RMSE (meter)

0.76 9.97 0.75 9.94 0.75 10.04 0.81 8.65

Validation (2010)

CC

CE

RMSE (meter)

0.87 0.86 0.86 0.90

0.59 10.87 0.60 10.71 0.59 10.85 0.73 8.75

Testing (2011) CC

CE

RMSE (meter)

0.78 0.79 0.79 0.87

0.66 9.80 0.61 10.48 0.65 9.89 0.71 9.07

153

CC

0.82 0.79 0.81 0.85

Table 4 Comparison between the ANFIS model and the harmonic analysis and the ARX model for the site-specific scenario. Method

ANFIS (2 rules)

Data sets

Training (2004–2009)

Validation (2010)

Testing (2011)

Harmonic analysis

Training (2004–2009)

Validation (2010)

Testing (2011)

ARX

Training (2004–2009)

Validation (2010)

Testing (2011)

Index

CE CC RMSE CE CC RMSE CE CC RMSE CE CC RMSE CE CC RMSE CE CC RMSE CE CC RMSE CE CC RMSE CE CC RMSE

Location Waiao

Dafu

Yungjen

Buhou

Chingshuei

Lize

Xincheng

0.97 0.98 3.89 0.92 0.96 3.27 0.83 0.92 5.37 0.53 0.73 16.01  0.85 0.44 15.75  1.11 0.73 18.67 0.25 0.50 19.86 0.21 0.59 10.29  1.37  0.10 19.77

0.97 0.99 1.49 0.89 0.96 2.27 0.90 0.96 1.69 0.32 0.57 7.65  1.85 0.46 11.70  4.17 0.70 12.30 0.28 0.55 7.43  1.28 0.61 10.47  0.86 0.69 7.37

0.98 0.99 0.99 0.98 0.99 1.10 0.96 0.98 1.48 0.18 0.43 7.89  0.53 0.44 10.74 0.02 0.89 7.54 0.04 0.29 8.22  0.10 0.33 9.12 0.03 0.27 7.49

0.99 0.99 1.10 0.92 0.97 1.67 0.98 0.99 1.12 0.09 0.29 14.03  1.87 0.10 9.93  1.12 0.58 10.74  0.17 0.50 11.39  1.22  0.36 8.72  2.47  0.25 13.73

0.96 0.98 2.12 0.93 0.97 1.86 0.86 0.93 3.69 0.11 0.33 11.02 0.27 0.60 6.09  0.83 0.32 13.35  0.87 0.23 13.16  0.20 0.54 7.80  1.34 0.08 15.10

0.99 0.99 1.12 0.95 0.98 1.57 0.95 0.98 1.59 0.03 0.18 12.64  0.30 0.18 7.90  0.66 0.72 9.45  0.10  0.08 13.20  0.17 0.12 7.49  10.88 0.49 25.30

0.98 0.99 1.93 0.94 0.98 3.21 0.96 0.98 2.23 0.08 0.28 11.57  0.97 0.57 18.29  0.11 0.58 11.19 0.23 0.48 11.03  0.98  0.05 18.32 0.05 0.50 10.37

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Training Phase Testing Phase

Fig. 6. Monthly observed and predicted shoreline changes in training (2004–2009) and testing (2011) phases at five selected shoreline observation stations.

of high CC and CE values and lower RMSE values. Apparently, the ANFIS-based prediction models of shoreline changes are more effective than the Fourier series-based and ARX-based models, and the results of ANFIS models are more stable than those of the two comparative models. Such performance can be due to the nonlinear characteristics of shoreline change. Fig. 6 presents the comparison results between the predictions obtained from the ANFIS models and actual measurements. Obviously, the ANFIS-based models demonstrate its excellent capability for predicting shoreline changes. It is evident that the predictions obtained from the ANFIS well fit the observations without the occurrence of significant overestimation or underestimation.

5. Conclusion Taiwan is located in a monsoon area where typhoons strike frequently, and a large percent of the island's sandy beaches has undergone erosion to an alarming rate over the past decades. This study investigates the monthly observation data of shoreline changes collected during 2004–2011 at seven sandy beaches of the Yilan County. The shorelines of these beaches appeared to have significantly periodic variations, i.e., the beach areas would expand to the largest during March and July due to continuous beach nourishment works after typhoon seasons but decrease seriously in September and November (in general, right after typhoon attacks). For this reason, seasonal shoreline changes are taken into consideration. The results of the Fourier analysis indicate that

the harmonic components at six of the seven observation stations are significant; however, the Fourier series-based models fail to properly capture the trend of shoreline changes and thus results in an error of 15–30% of variation ranges at each station. The ANFIS-based models are then constructed in two different scenarios to predict the monthly shoreline change in the next year at seven stations. In the first scenario (the lumped scenario), four ANFIS models with various input combinations including wave height information, current month, station location and shoreline position are first utilized to predict shoreline changes. The results of three models, whose inputs consist of wave height information, are inconsistent in training, validation and testing phases. Nevertheless, Model 4, whose inputs do not involve any wave height information, produces relatively consistent results in all three phases. The results suggest that even though wave height data can provide extra information for building the prediction models, such information, however, does not contribute extra values to establishing reliable prediction models for shoreline changes due to the high variability and/or uncertainty of the monthly mean wave height measurements. Besides, the constructed models at this stage are unreliable and inaccurate, where the estimated RMSE values are larger than 10 m in all three phases. In the second scenario (the site-specific scenario), the ANFIS-based model is further explored with various input combinations. A great number of possible input combinations are investigated, and two groups of stations are identified: Waiao, Dafu, Yungjen and Buhou belong to one group (along the northern coast); and Buhou, Chingshuei, Lize and Xincheng belong the other group (along the southern coast).

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A similar ANFIS-based model is then independently built for each station in each group to predict its monthly shoreline change of the next year based on the current monthly information of the group that the station belongs to. The results clearly demonstrate that the constructed ANFIS-based models can provide much better performance than the Fourier series-based models and the ARXbased models, in term of much higher CE and CC values and much smaller RMSE values. The constructed ANFIS-based models, indeed, maintain consistent performance in all three phases and can be effectively applied to shoreline change predictions in practice. Based on the comprehensive comparison, it is convincing that the constructed ANFIS-based models in the second stage are reliable and their results can serve as a valuable reference to the authorities for future shoreline erosion warnings and management.

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