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 The interannual shoreline variation during a 22-year period from 1987 to 2008 at the Hasaki coast located in eastern Japan was found to be induced by the fluctuation of the deep water wave energy flux using an empirical shoreline prediction model. The correlation coefficients between the deep water wave energy flux and climate indices showed that the wave energy flux has a positive correlation with the Arctic Oscillation (AO) index during the period from January to April, and negative correlations with the Nino-West Sea Surface Temperature (SST) anomaly and the Southern Oscillation Index (SOI) during the period from September to December. The shoreline prediction model using the correlations between the wave energy flux and climate indices indicated that the large-scale variations in climate represented by the AO index, the SOI, and the Nino-West SST anomaly accounted for 45% of the interannual shoreline variation.
 Sandy beaches prevent wave-related disasters by dissipating wave energy, offer attractive amenity to visitors, and nurture rich ecosystems. Hence, maintenance of those valuable sandy beaches is quite important from the viewpoints of disaster prevention, recreation, and environment.
 Beach profiles vary according to sediment movements induced by waves and currents in the nearshore zone. Over time scales of several days to several weeks, the shoreline retreats during storms, but advances during mild wave conditions. Even at interannual and interdecadal scales, sediment movement and beach profile change, and some of the variations were investigated with consideration of large-scale atmospheric patterns, such as the El Niño-Southern Oscillation or Pacific Decadal Oscillation (PDO).
 Despite the investigations shown above, the influences of waves and large-scale variations in climate on interannual shoreline movements are not fully understood, at least quantitatively, although understanding these influences is essential for long-term maintenance of sufficient beach width for wave energy dissipation and recreational use. The objective of this study was to investigate the linkages among interannual variations of shoreline, wave and climate at Hasaki, Japan, using beach profile and wave data obtained for a period of about 22 years and climate indices, such as the PDO index.
2. Data Description
 The shoreline positions at the high water level were detected from beach profiles measured along a 427-m-long pier of the Hazaki Oceanographical Research Station (HORS), located on the Hasaki coast of Japan facing the Pacific Ocean (Figure 1), at 5-m intervals every weekday during the period from October 1986 to January 2009. The seaward direction is defined to be positive. Deep water waves were measured at a water depth of about 24 m with an ultrasonic wave gage for 20 minutes every 2 hours throughout the investigation period (see location inFigure 1). The bathymetry around HORS is nearly uniform alongshore. The mean beach slope near the shore is about 1/40. Based on the datum level at Hasaki, the high, mean, and low water levels are 1.25 m, 0.65 m, and −0.20 m, respectively.
 The temporal variations of the monthly averaged values of the shoreline position, the shoreline change rate, and the deep water significant wave height (Figure 2) show that the shoreline retreats from September to October owing to high waves generated by typhoons (tropical cyclones). From May to June, on the other hand, relatively small waves induce shoreline advance. From January to March, although the wave height is relatively high owing to extratropical cyclones, the absolute value of the shoreline change rate is small. The shoreline change is assumed to be mainly caused by cross-shore sediment transport.
 To investigate the interannual variation of shoreline position, the measured shoreline positions were averaged over four-month periods. Considering the seasonal shoreline variation shown inFigure 2, the four-month periods were set to be from 1 November to 28 February (NDJF period), from 1 March to 30 June (MAMJ period), and from 1 July to 31 October (JASO period). Because the shoreline positions averaged during the NDJF, MAMJ, and JASO periods are assumed to be the values on 1 January, 1 May and 1 September, respectively, the wave parameters and climate indices, which represent driving forces of shoreline change, were averaged for the four-month periods from 1 January to 30 April, from 1 May to 31 August, and from 1 September to 31 December. The comparison between the shoreline positions at the high and mean water levels is shown in the auxiliary material.
3.1. Relationships Between Shoreline Position and Wave Parameters
 The relationships between the shoreline position and wave parameters are not linear—not only the instantaneous parameter value but also the cumulative value influences the shoreline variation. This indicates that a correlation coefficient does not fully represent the relationship between the shoreline position and the wave parameter. Hence, the relationship was investigated by examining the performances of shoreline prediction models expressed by equations (1) and (2).
where y is the shoreline position, t is the time, Δt is the time interval, P is the value of the wave parameter, and a0, a1, a2 and a3are coefficients. The second and third terms of the right-hand side ofequation (2) are based on Sunamura , who assumed that the shoreline change rate was expressed by a quadratic function of wave height in which the shoreline advances under calm wave conditions but retreats under severe conditions. The fourth term represents the assumption that the shoreline change rate is negatively proportional to the shoreline position [e.g., Katoh and Yanagishima, 1988; Miller and Dean, 2004]. The seaward shoreline change rate is enhanced by a more retreated shoreline position but suppressed by a more advanced one.
 The wave parameters investigated were the deep water wave energy flux Ef (=ρgHs,02cg,s,0/16), Hs,0/Ts,0, and Hs,02/Ts,0, where Hs is the significant wave height, ρ is the sea water density, g is the gravitational acceleration, and cg,s is the group velocity corresponding to the significant wave period Ts. The subscript 0 denotes the deep water value.
 The values of Hs,0/Ts,0 and Hs,02/Ts,0 were obtained from the Dean number H0/(ωT) [Dean, 1973] and the Dalrymple parameter gH02/(ω3T) [Dalrymple, 1992], respectively, both of which were developed for predicting the occurrence of storm and normal beach profiles. H0 is the deep water wave height, ω is the sediment fall velocity, and Tis the wave period. The fall velocity is a function of the sediment diameter and the water temperature. The sediment diameter is constant, and the water temperature is also assumed to be constant during a four-month period. Accordingly, the fall velocity and the gravitational acceleration were omitted from the original parameters, andH0 and T were replaced by Hs,0 and Ts,0, respectively.
 The coefficients of equation (2)were determined so that the error between the measured and predicted shoreline positions was minimal using the SCE-UA algorithm (Shuffled Complex Evolution-University of Arizona) [Duan et al., 1993].
 The model performance was investigated using the root-mean-square error, the coefficient of determinationr2, and the Brier skill score BSS [Murphy and Epstein, 1989], which is defined by equation (3).
where m and p denote the measured and predicted values, respectively. The value of yref is for the reference prediction, which is mostly the initial value and sometimes the mean measured value. The value of BSS is equal to 1 when the prediction perfectly matches the measurement and falls below 0 when the model performance is poorer than the reference model, which assumes no change from the initial or from the mean. van Rijn et al.  qualified model predictions of beach profile change with BSS > 0.8, 0.6–0.8, 0.3–0.6, 0–0.3 and <0 as Excellent, Good, Reasonable, Poor and Bad.
3.2. Relationships Among Shoreline Position, Wave Parameters and Climate Indices
 To examine the causes of the interannual variation of a wave parameter, the relationships between the wave parameter and climate indices shown below during the periods from January to April, from May to August, and from September to December were investigated. The indices used in the investigations were the PDO index [Mantua et al., 1997], the Southern Oscillation Index (SOI) [Ropelewski and Jones, 1987], the Nino-West Sea Surface Temperature (SST) anomaly, and the Arctic Oscillation (AO) index [Thompson and Wallace, 1998]. The Nino-West area, located 0°–15°N and 130°E–150°E, is set for El Niño monitoring by the Japan Meteorological Agency.
4. Results and Discussion
4.1. Relationships Between Shoreline Position and Wave Parameters
 The shoreline positions predicted using the deep water wave energy flux Efand the coefficients obtained with the SCE-UA algorithm [a0 = 0.1984 (m/day), a1 = 5.293 × 10−10 (s2m)/(N2day), a2 = −2.354 × 10−5 (s m)/(N day), and a3 = −1.173 × 10−3(1/day)] agree well with the measured values, and express the interannual shoreline variation (Figure 3). The root-mean-square errorε was 8.15 m, and the coefficient of determination r2 was 0.51. The BSS values using the initial and mean shoreline positions for the reference prediction were 0.90 (Excellent) and 0.51 (Reasonable), respectively. These results indicated that the interannual shoreline variation at Hasaki was caused by the fluctuation of the deep water wave energy flux.
 Although models using the other wave parameters were examined, the model performances were slightly poorer than that of the model using the deep water wave energy flux (ε = 9.02 m for Hs,0/Ts,0 and 8.67 m for Hs,02/Ts,0).
 Furthermore, other models using shoreline positions averaged for different four-month periods (ONDJ-FMAM-JJAS, DJFM-AMJJ-ASON) and three-month periods (NDJ-FMA-MJJ-ASO, DJF-MAM-JJA-SON, JFM-AMJ-JAS-OND) and the corresponding deep water wave energy flux were examined, but the model performances were poorer than that of the above model;ε ranged from 8.46 to 9.44 m.
4.2. Relationships Among Shoreline Position, Wave Parameters and Climate Indices
 The deep water wave energy flux Ef showed a positive correlation with the AO index (r = 0.44) during the JFMA period (Table 1). During the MJJA period, there were no significant correlations between Ef and the climate indices. However, Efshowed negative correlations with the Nino-West SST anomaly (r = −0.48) and the SOI (r = −0.41) during the SOND period. The relationships between Ef and the AO index during the JFMA period and between Efand the Nino-WEST SST anomaly during the SOND period are shown in the auxiliary material.
Table 1. Correlation Coefficients Between Deep Water Energy Flux and Climate Indices
 When the AO index is below zero, an atmospheric pressure pattern in which the high and low pressure areas are to the west and the east, respectively, develops around Japan in winter [e.g., Gong et al., 2001]. When such a pressure pattern develops, extratropical cyclones are less developed [Nakamura et al., 2004], which probably results in relatively low wave heights along coasts facing the Pacific Ocean, including Hasaki. This would be responsible for the positive correlation between Ef and the AO index during the JFMA period.
 When the Nino-West SST anomaly and the SOI are negative, an El Ninõ event tends to develop. During an El Ninõ event, traces of tropical cyclones shift south-eastward in fall [Wang and Chang, 2002], and the shift is likely to induce an increase in Ef. As a result, Efduring the SOND period at Hasaki showed negative correlations with the Nino-West SST anomaly and the SOI. AlthoughWang and Chang showed that the Nino-3.4 SST anomaly is correlated with the location of tropical cyclone formation over the western North Pacific during the JAS period, there was no significant correlation betweenEfand the Nino-3.4 SST anomaly at Hasaki.
 Using the linear regression models for the strongest correlations between the deep water wave energy flux and the climate indices during the three periods, the deep water wave energy fluxes were estimated for the shoreline prediction. Although no significant correlation was found during the MJJA period as mentioned above, the relationship between Ef and the SOI index, which had the highest correlation coefficient (r = 0.34) during this period, was used.
 The shoreline prediction using the deep water wave energy flux estimated from climate indices showed that the shoreline variation predicted with the estimated wave energy flux was smaller than that with the measured flux (Figure 3). The root-mean-square error was 9.26 m, and theBSSvalues using the initial and mean values for the reference prediction were 0.87 (Excellent) and 0.37 (Reasonable), respectively. The coefficient of determination was 0.45, which indicated that 45% of the interannual shoreline variation was attributable to the large-scale variations in climate represented by the AO index, the SOI, and the Nino-West SST anomaly.
 The results of this study were derived from the field data obtained at one particular beach (Hasaki beach), but the findings mentioned above are considered to be applicable to beaches that consist of fine sand and face the Pacific Ocean similar to Hasaki beach.
 The empirical shoreline prediction model assuming the seaward shoreline change rate is proportional to the deep water wave energy flux and negatively proportional to the shoreline position demonstrated that the interannual shoreline variation during the 22-year period from 1987 to 2008 at the Hasaki coast located in eastern Japan was caused by the fluctuation of the deep water wave energy flux.
 The deep water wave energy flux showed a positive correlation with the AO index (r= 0.44) during the period from January to April, and negative correlations with the Nino-West SST anomaly (r = −0.48) and the SOI (r= −0.41) during the period from September to December. The shoreline prediction using the correlations between the deep water wave energy flux and climate indices indicated that 45% of the interannual shoreline variation resulted from large-scale variations in climate represented by the AO index, SOI, and Nino-West SST anomaly.
 We would like to thank Meric Srokosz, the Editor, Robert Dean and two anonymous reviewers for their useful and informative comments to improve the original manuscript. The Nino-West SST anomaly data were provided by the Japan Meteorological Agency from their web site athttp://threadic.com/sora/translate.cgi/ds.data.jma.go.jp/tcc/tcc/products/elnino/index/ and data for the other climate indices were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their web site at http://www.esrl.noaa.gov/psd/. The deep water wave data at Hasaki were provided by the Ministry of Land, Infrastructure, Transport and Tourism. We are grateful to all the staff members of HORS for their contributions to the field measurements.
 The Editor thanks Robert Dean and an anonymous reviewer for their assistance in evaluating this paper.