*2.2. Information on Offshore Wave Buoys*

Three wave buoys, namely, Fuguijiao, Longdong and Suao, located in the northern and northeastern offshore waters of Taiwan, were selected for model validation because they are closest to the tracks of Super Typhoons Maria in 2018 and Lekima in 2019 (as shown in Figure 1). The sampling frequency of wave buoys is 2 Hz for 10 min at the beginning of each hour with an accuracy of ±10 cm for the SWH measurements according to the annual buoy observation data report from the CWB. Information on the coordinates of the three wave buoys and their corresponding water depths is listed in Table 1.

**Table 1.** Information on wave buoys.


Data source: The Central Weather Bureau and Water Resource Agency of Taiwan.

### *2.3. Direct Modification of Typhoon Winds from ERA5*

Since the mid-1960s, many parametric cyclone wind models have been proposed [14,15] and widely used to mimic the wind distribution of typhoons [16–19] because of their simplicity. Parametric cyclone wind models could be used to accurately reconstruct the wind distributions near the center of the typhoon; however, they are unable to accurately reproduce wind speeds in regions far from the center of the typhoon. In contrast, reanalysis wind data obtained from the dynamical model with data assimilation show a superior performance for hindcasting the winds outside of the typhoon's center but are generally inferior for the hindcasts of maximum typhoon wind speed [20–24]. A direct modification technique recommended by Pan et al. [20] was applied in the present study to take advantage of combining the parametric cyclone wind model and reanalysis wind data and maintain a reliable structure for the entire typhoon wind field.

$$\mathcal{W}\_{DM} = \begin{cases} \mathcal{W}\_{ERA5} \left[ \frac{r}{R\_{\text{max}}} \left( \frac{W\_{\text{max}}}{W\_{E\text{max}}} - 1 \right) + 1 \right] & r < R\_{\text{max}}\\ \mathcal{W}\_{ERA5} \left[ \frac{R\_{\text{tr}} - r}{R\_{\text{tr}} - R\_{\text{max}}} \left( \frac{W\_{\text{max}}}{W\_{E\text{max}}} - 1 \right) + 1 \right] & R\_{\text{max}} \le r \le R\_{\text{tr}s}\\ \mathcal{W}\_{ERA5} & r > R\_{\text{tr}s} \end{cases} \tag{1}$$

where *WDM* is the wind speed at an arbitrary grid within the model domain through direct modification, *WERA*5 is the wind speed extracted from ERA5 (the fifth-generation reanalysis of the European Centre for Medium-Range Weather Forecasts for the global climate and weather) at an arbitrary point in the computational grid, *WBmax* is the maximum wind speed of the best track typhoon issued by the Regional Specialized Meteorological Center (RSMC) Tokyo-Typhoon Center, *WEmax* is the maximum wind speed of the typhoon among the hourly ERA5 wind fields, *r* is the radial distance from an arbitrary grid within the model domain to the eye of the typhoon, *Rtrs* is the radius of the modified scale (also known as the radius of the transitional zone) and *R*max is the radius at the maximum typhoon wind speed. *R*max can be expressed as a function of *WBmax* and the latitude of the typhoon's center:

$$R\_{\text{max}} = m\_0 + m\_1 \times \mathcal{W}\_{B\text{max}} + m\_2(\phi - 25) \tag{2}$$

where *φ* is the latitude of the typhoon's center. In Equation (2), *m*0, *m*1 and *m*2 were set to 38.0 (in <sup>n</sup>·mi), −0.1167 (in <sup>n</sup>·mi·kt−1) and −0.0040 (in <sup>n</sup>·mio−1), respectively, according to the results derived from Knaff et al. [25] for the Western Pacific typhoon basin. *Rtrs* is considered to be a key factor in determining the accuracy of wind fields; therefore, various *Rtrs* will be employed to create hybrid typhoon wind fields to better understand their effect on wind wave hindcasting.

### *2.4. Configuration of the Wave-Circulation Modeling System*

A seamless cross-scale hydrodynamic model based on an unstructured grid and triangular mesh served as the ocean circulation model in the wave-circulation modeling system. The hydrodynamic model is called SCHISM (semi-implicit cross-scale hydroscience integrated system model), which has been implemented by Zhang et al. [26] and other developers around the world. Similar to the SELFE (semi-implicit Eulerian-Lagrangian finite element/volume model, the predecessor of the SCHISM developed by Zhang and Baptista [27]), the SCHISM also avoids the severest stability constraints in the numerical model by means of a highly efficient semi-implicit scheme [28]. Hence, the high-performance calculations can be performed even when a very high spatial resolution mesh is used in the SCHISM. The splitting between internal and external modes could derive a numerical error [29], which is eliminated through the no-mode-splitting technique implemented in the SCHISM. A depth-averaged (two-dimensional (2D)) ocean circulation model is sufficient for simulating typhoon-driven hydrodynamics. Additionally, fewer computing resources and execution times are required for a 2D model. Therefore, a 2D model, i.e., SCHISM-2D, is selected for wind wave modeling in the present study. The SCHISM and its predecessor SELFE are multipurpose models that have been widely applied to the simulation of hydrodynamics and water quality transportation in coastal and estuarine environments in Taiwan, e.g., evaluation of storm tide-induced coastal inundation [30,31], assessment of tidal stream energy [32,33], transport of suspended sediment and fecal coliform [34,35]. The Manning coefficient and time step were set as 0.025 and 120 s for the barotropic ocean model, respectively, according to the geological characteristics of the seafloor in the waters surrounding Taiwan and the numerical stability of the SCHISM-2D.

The WWM-III is a derivative work from the original WWM-II (wind wave model version III, developed by Roland [36]). The WWM-III is a third-generation spectral wave model that is able to simulate and predict the ocean surface sea state [37]. The wave action balance equation governing the WWM-III is solved by the fractional step method on an unstructured grid. The number of directional bins is 36 with a minimum of 0◦ and a maximum direction of 360◦. The number of frequency bins is 36, the lowest limit of the discrete wave frequency is 0.04 Hz and a highest frequency limit of the discrete wave period is 1.0 Hz. The peak enhancement factor is specified as 3.3 for the JONSWAP (Joint North Sea Wave Project, [38]) spectra, while the wave breaking coefficients for the constant and bottom friction coefficients are 0.78 and 0.067, respectively, in WWM-III.

To enhance the information exchange efficiency between the ocean circulation and wind wave models and to eliminate the interpolation errors from the two models, SCHISM-2D and WWM-III take advantage of sharing the same subdomains and parallelization through the same domain decomposition scheme. Additionally, time steps of 120 s and 600 s were used in the SCHISM-2D and WWM-III models, respectively, to improve the computational performance of the coupled model, SCHISM-WWM-III. The fully coupled SCHISM-WWM-III modeling system has been applied to predict, simulate and hindcast typhoon-driven storm tides and waves [21–24,39], as well as long-term wave energy resources in the offshore waters of Taiwan [40–42].

For a successful storm surge, tide and wave modeling, the size of the computational domain must be large enough to accommodate the full typhoon; otherwise, the simulations would be affected by the boundary conditions [43,44]. The present study developed a computational domain spanning east longitudes from 105◦ to 140◦ and north latitudes from 15◦ to 31◦ (as shown in Figure 2). This large domain is composed of 540,510 nonoverlapping triangular elements and 276,639 unstructured grid points. A local-scale bathymetric dataset covering the area from east longitude 100◦ to 128◦ and north latitude from 4◦ to 29◦ with a spatial resolution of 200 m was provided by the Department of Land Administration and the Ministry of the Interior, Taiwan. The latest global-scale bathymetric product released from the General Bathymetric Chart of the Oceans (GEBCO), GEBCO\_2020 Grid, was employed to incorporate a local-scale bathymetric dataset (as mentioned above) to construct the gridded bathymetric data in the SCHISM-WWM-III modeling system.

Eight main tidal constituents (M2, S2, N2, K2, K1, O1, P1 and Q1) extracted from a regional inverse tidal model (China Seas and Indonesia [45]) were utilized to generate the tidal elevation and horizontal velocity at the ocean boundaries of the SCHISM-WWM-III. The inverse barometric effect for tidal elevation at the boundary nodes was also considered. Since wave-generating typhoons were completely within the computational domain in the present study, open boundary conditions for the waves were not always required [42,46].

**Figure 2.** Coverage of the computational domain for the wave-circulation modeling system.
