Transaction A: Civil Engineering Vol. 16, No. 2, pp. 156{164 c Sharif University of Technology, April 2009 Wave Parameter Hindcasting in a Lake Using the SWAN Model M.H. Moeini1 and A. Etemad-Shahidi1 Abstract. Wind-induced wave characteristics are one of the most important factors in the design of coastal and marine structures. Therefore, accurate estimation of wave parameters is of considerable importance. The wave climate study can be conducted by eld measurements, empirical studies, physical modeling and numerical simulations. In this paper, the skill of a third-generation spectral model called SWAN has been evaluated in the prediction of wave parameters. The varying wind and wave climate of Lake Erie in the year 2002 has been used for evaluation of the model. The signicant wave height (Hs) and the peak spectral wave period (Tp) were the parameters employed in the study and the model has been executed in a nonstationary mode. The linear and exponential growth from wind input, four-wave nonlinear interaction, whitecapping and bottom friction have been considered in the simulation. The results of this study show that in the investigated case, the average scatter index of SWAN is about 19 percent for signicant wave height and 23 percent for the peak period. The error of the SWAN model in prediction of the wave height and period reduced about 3 percent after elimination of wave heights less than 0.5 meters. It was also found that using the cumulative steepness method for whitecapping dissipation yields worse results for signicant wave height and better results for peak spectral period estimation. After using this method, the average scatter index for the prediction of Hs increased about 5 percent and decreased more than 4 percent for Tp. It should be mentioned that the computational time required by using this method is approximately more than twice that of the Komen option. Keywords: Wave prediction Numerical model Third generation Lake Erie. INTRODUCTION In the marine environment, the planning of sustainable development of economic activities requires long term information about environmental conditions such as waves. Accordingly, the knowledge of wind wave statistical characteristics is necessary in a variety of applications including the design of coastal structures, studies of sediment transport, coastal erosion and pollution processes. Due to the lack of such information in many regions, the wave characteristics are estimated using dierent methods. Generally, wave climate sim- ulation is conducted by numerical models or empirical methods. Until now, dierent empirical methods have been developed for wave hindcasting and forecasting such 1. Department of Civil Engineering, Iran University of Science and Technology, Tehran, P.O. Box 16765-163, Iran. *. Corresponding author. E-mail: etemad@iust.ac.ir Received 31 January 2007 received in revised form 20 January 2008 accepted 26 May 2008 as [1-7]. Since introduction of the rst empirical formulation for the estimation of wave parameters by Bretschneider [1], the modeling of wind induced waves has been greatly improved. In recent years, with the development of high speed processors, several sophisti- cated numerical models have been developed for wave prediction. These models are usually phase-averaged spectral wave models developed in three generations, consisting of various physical processes. At present, SWAN [8,9] is one of the most widely applied spectral wave models in coastal engineering studies and is freely available for both research and consultancy studies. This model is specially designed for coastal applications and can be used both under laboratory conditions and at ocean scale. Such a nu- merical model is more time consuming than empirical methods and is believed to have more accuracy and resolution. Lin et al. [10] have used the SWAN model for wave simulation in the Chesapeake Bay. Their results show that the SWAN model overestimates signicant

Wave Parameter Hindcasting Using the SWAN Model 157 wave height and underestimates the peak spectral wave period. In their simulation, all wave heights were less than 1 meter. The SWAN model also has been used for simulating typhoon waves in the coastal waters of Taiwan [11]. Results show that simulations of typhoons are in relatively good agreement with measurements, but with delayed peak wave heights and periods. The aim of this study is to evaluate the SWAN numerical model and its newly developed method for whitecapping dissipation in a complex and varying wind climate by comparing results with eld observa- tions in a lake. For this purpose, the wave records of Lake Erie of the Great Lakes in the year 2002 have been used. For evaluation of the model accu- racy, the signicant wave height (Hs) and the peak wave period (Tp) were the parameters employed in the study and the BIAS parameter and scatter index were used for a quantitative inter comparison of the results. STUDY AREA AND FIELD DATA Lake Erie has a laterally-prolonged scale of about 400 km in a west-east direction between 79 000 W and 83 300 W (Figure 1). Its width is about 100 km in the north-south direction between 41 300 N and 44 000 N. This lake has an average depth of about 19 meters and the deepest water depth is only 58 m at latitude 42 north and longitude 80 west. The data collected by three buoys have been used in this study. The ID numbers of the buoys (and their water depths) are: 45005 (14.6 m), 45132 (22.0 m) and 45142 (27.0 m), respectively. The height of the anemometers attached to each buoy were 5 m over the lake surface. Figure 1 illustrates the Lake Erie bathymetry and the location of the 3 buoys deployed for wind and wave measurement. Measurement data of winds and waves were obtained from the National Data Buoy Center (for B45005) and from the Marine Environmental Data Service (for B45132 and B45142). The used data consists of hourly measured wind (speed and direction) Figure 1. Bathymetry of Lake Erie and location of buoys. and wave (signicant height and peak spectral period). For evaluating the SWAN model, the subset of data recorded in 2002 has been used. THE SWAN MODEL The SWAN model [8,9] is a third generation spectral model, suitable for the simulation of wind generated waves from the nearshore to the surf-zone. The spec- trum that is considered in SWAN is the action density spectrum rather than the energy density spectrum because, in the presence of currents, energy density is not conserved. The action density is equal to the energy density divided by the relative frequency: N ( ) = E( )=: (1) The independent variables are the relative frequency, (as observed in a frame of reference moving with cur- rent velocity), and the wave direction, (the direction normal to the wave crest of each spectral component). In the SWAN wave model, the evolution of the wave spectrum in position (x y) and time (t) is described by the spectral action balance equation, which for Cartesian coordinates is [3]: @ @t N + @ @x CxN + @ @y Cy N + @ @ C N + @ @ C N = S : (2) The rst term in the left-hand side of this equation represents the local rate of change of action density in time the second and third terms represent propagation of action in geographical space (with propagation velocities Cx and Cy in x and y space, respectively). The fourth term represents a shifting of the relative frequency due to variations in depths and currents (with propagation velocity C in space). The fth term represents depth-induced and current-induced refraction and propagation in directional space (with propagation velocity C in space). The term S = S( ) at the right hand side of the action balance equation is the source term in terms of energy density, representing the eects of generation, dissipation and nonlinear wave-wave interaction. This term consists of linear and exponential growth by wind, dissipation due to whitecapping, bottom friction, depth-induced wave breaking and energy transfer due to quadruplet and triad wave-wave interaction. Wave growth by wind is described by a combina- tion of linear and exponential terms: Sin( ) = A + BE( ): (3) Two optional expressions for exponential growth B are used in the model. The rst term is based on the linear expression of Snyder et al. [12], rescaled by Komen et al. [13], in terms of friction velocity U ,