## 3 Methodology
### Model Settings of the Numerical Wave Models  
Traditionally, wave research mainly uses on-scene observations, theoretical solutions, and statistical analyses. However, these methods are difficult to apply to wave forecasting and hindcasting predictions. Numerical simulation provides strong technical support for solving this problem. Since the 1960s, wave numerical models have gradually been developed, and their difficulties have been overcome by using the third-generation WAM model, i.e., nonlinear wave energy transmission and fragmentation, which was released in the 1980s. In recent years, based on the theoretical achievements in ocean waves, the third-generation wave models represented by WW3 and SWAN have also been continuously developed, and they follow the basic principles of the WAM. The scheme of the computational grid is different for the WW3 and SWAN models, i.e., a rectangle grid is employed in the WW3 and an unstructured grid is employed in the SWAN. Therefore, WW3 is suitable for wave simulation in large-scale oceans and has high computational efficiency, while SWAN has a good performance in regional seas due to its ability to meet indented coastlines. The key of WAM Is Its solution to the wave propagation balance equation, which illustrates changes in wave energy in space and time, as follows:  
\[\frac{D}{Dt}[N(k,\theta;x,t)]=\frac{E_{\text{in}}+E_{\text{bot}}+E_{\text{db}} +E_{\text{nl}}}{\sigma}, \tag{6}\]  
where \(N\) represents the wave action density spectrum in terms of the wave number, \(k\); the polar direction, \(\theta\); the space, \(x\); and the time, \(t\); \(\sigma\) is the intrinsic frequency; and the matrix, \(E\), represents the change in the energy intensity, i.e., the wind input, \(E_{in}\); the bottom fraction, \(E_{bot}\); the wave decay term associated with wave-breaking (\(E_{db}\)); and the nonlinear dissipation caused by wave\(-\)wave interactions (\(E_{nl}\)). The details of these sources are delicately described in the technical manuals for WW3 [48] and SWAN [49] users. According to [30], it has been found that sea surface currents and sea levels have an influence on wave simulations. Here, \(0.125^{\circ}\) gridded fusion wind at intervals of 12 h and daily average Copernicus Marine Environment Monitoring Service (CMEMS) sea currents and sea levels, with a spatial resolution of a \(0.08^{\circ}\) grid, were treated as the forcing fields. The water depths were derived from the General Bathymetry Chart of the Oceans (GEBCO). Figure 3 illustrates the water depths of the United States coastal waters overlaid by the geographic locations and identification numbers of the buoys used in this study. As a case study, Figure 4a,b depict the daily average CMEMS sea currents and sea levels map for 7 September 2020. The parameterization scheme for the WW3 model [30; 50] included the switch ST6 package for the input/dissipation source terms, the switch TR1 package, the switch GMD2 package for the wave\(-\)wave interactions, and the switch FLD2 and BT1 packages for the wave breaking and bottom friction, respectively. The parameterization scheme for the SWAN model [32] included WESTHupsen, that is, the propagation scheme that combines the wind and non-linear dissipation, and the switches QUADrupl, TRIad, and BREAinge for the wave\(-\)wave interactions and the wave bottom friction. In addition, other settings were default-employed, i.e., a directional resolution of 24 regular azimuthal directions  
Figure 4: The daily average Copernicus Marine Environment Monitoring Service (CMEMS) data maps for 7 September 2020 between (10\({}^{\circ}\)N, 100\({}^{\circ}\)E) and (60\({}^{\circ}\)N, 180\({}^{\circ}\)E): (a) sea current speed and (b) sea level map. Figure 3: The water depths derived from the General Bathymetry Chart of the Oceans (GEBCO) for the United States coastal waters overlaid by the geographic locations and identification numbers of the NDBC buoys of the National Oceanic and Atmospheric Administration (NOAA).