**3. Results**

The wind fields during Super Typhoon Maria from 1–15 July in 2018 and Super Typhoon Lekima from 1–15 August in 2019 were extracted from the ERA5 reanalysis and were corrected by the direct modification method expressed in Equation (1). The hybrid typhoon winds derived from Equation (1) with various *Rtrs* values were imposed in the SCHISM-WWM-III modeling system to compare the performance of the resulting storm wave hindcast. The effect of the wave-breaking formulation and wave-breaking criterion on the simulation of the SWH in the shallow nearshore waters off northern Taiwan during the passage of Super Typhoons Maria and Lekima was investigated by conducting several designed model experiments, as listed in Table 2.

**Table 2.** Designed numerical experiments in the present study.


### *3.1. Validation for Typhoon-Driven SWHs with Various Rtrs*

The inverse distance weighting method was employed to convert the hourly ERA5 and hybrid typhoon winds from the structured grid (at a horizontal resolution of 31 km) to the unstructured grid for the SCHISM-WWM-III modeling system. Comparisons of the SWH time series between model hindcasts using the different radii of the modified scale (*Rtrs*) and the corresponding measurements are depicted in Figure 3a–c for the Fuguijiao (Figure 3a), Longdong (Figure 3b) and Suao (Figure 3c) buoys during the passage of Super Typhoon Maria in 2018. The hindcasted peak wave heights are underestimated by 1.5 m and 2.0 m for the Fuguijiao and Longdong wave buoys, respectively, when the original ERA5 winds are used in the SCHISM-WWM-III modeling system but slightly overestimate the peak wave height within 0.5 m for the Suao buoy. Modified ERA5 winds with various *Rtrs* were imposed on the SCHISM-WWM-III modeling system to improve the

performance of typhoon wave hindcasts. The hybrid winds with *Rtrs* = 3 *Rmax*, *Rtrs* = 4 *Rmax*, *Rtrs* = 5 *Rmax*, *Rtrs* = 6 *Rmax* and *Rtrs* = 7 *Rmax* are called the H\_3Rmax, H\_4Rmax, H\_6Rmax, H\_6Rmax and H\_7Rmax winds, respectively. As shown in Figure 3a–c, the hindcasted peak wave heights for all three wave buoys increased when using a larger *Rtrs* value. For instance, the hindcasted peak wave height was raised to 7.5 m for the Fuguijiao wave buoy by exerting H\_4Rmax winds on the SCHISM-WWM-III modeling system (as shown in Figure 3a). Similar phenomena can be found in Figure 3b (for the Longdong wave buoy) and Figure 3c (for the Suao wave buoy). The hindcasted peak wave heights were always underestimated for the Fuguijiao wave buoy even though H\_7Rmax winds were utilized. However, the SCHISM-WWM-III modeling system overestimated the peak wave height for the Suao wave buoy once the hybrid typhoon winds were used for the meteorological boundary conditions. Figure 4 illustrates the spatial distribution of the difference in the maximum hindcasted SWH between adopting the winds from H\_4Rmax and the original ERA5 for Super Typhoon Maria in 2018. Significant differences can be detected along the track of Super Typhoon Maria, and the extents with differences exceeding 3.0 m occurred in the deep ocean. The spatial distributions of the difference in maximum hindcasted SWH between employing the winds from H\_5Rmax and H\_4Rmax, H\_6Rmax and H\_4Rmax and H\_7Rmax and H\_4Rmax are demonstrated in Figure 5a–c, respectively. The difference in maximum hindcasted SWH using different winds increased when *Rmax* was enlarged. The maximal differences were always distributed over the right side of Super Typhoon Maria in 2018, where the wind speed was highest (as shown in Figure 5a–c). The same validation process was conducted to verify the SWH hindcasts for Super Typhoon Lekima in 2019. Figure 6 presents the comparisons of the SWH time series between model hindcasts using the different *Rtrs* values and the corresponding measurements or the Fuguijiao (Figure 6a), Longdong (Figure 6b) and Suao (Figure 6c) buoys during the period of Super Typhoon Lekima in 2019. The hindcasts from the use of the H\_3Rmax and H\_4Rmax winds are more satisfactory for all three wave buoys. The improvements in the hindcasted peak SWH for Super Typhoon Lekima in 2019 are obvious; for example, the difference in the maximum hindcasted SWH between inputting the winds from H\_4Rmax and the original ERA5 were up to 5 m in the deep ocean (as shown in Figure 7). The spatial distributions of the difference in maximum hindcasted SWH between applying the winds from H\_5Rmax and H\_4Rmax, H\_6Rmax and H\_4Rmax and H\_7Rmax and H\_4Rmax for Super Typhoon Lekima in 2019 are shown in Figure 8a,c, respectively. Similar to the hindcasts of Super Typhoon Maria in 2018, maximal differences were also detected on the right side of Super Typhoon Lekima in 2019, where the wind speed was strongest and increased with the increase in *Rtrs*. According to the resulting storm wave hindcasts of Super Typhoons Maria in 2018 and Lekima in 2019, the hybrid wind field with *Rtrs* = 4 *Rmax*, i.e., H\_4Rmax winds, was adopted as the atmospheric forcing for the SCHISM-WWM-III modeling system to conduct a series of numerical experiments.

**Figure 3.** Comparison of the time series of the SWH between the wave simulation that used the winds from the original ERA5, from the hybrid winds with various *Rtrs* and the corresponding observations for the (**a**) Fuguijiao, (**b**) Longdong and (**c**) Suao wave buoys during the passage of Super Typhoon Maria in 2018.

**Figure 4.** Spatial distribution of the difference in maximum SWH using the winds from H\_4Rmax and the original ERA5 during the passage of Super Typhoon Maria in 2018.

**Figure 5.** Spatial distribution of the difference in maximum SWH using the winds from (**a**) H\_5Rmax and H\_4Rmax, (**b**) H\_6Rmax and H\_4Rmax and (**c**) H\_7Rmax and H\_4Rmax during the passage of Super Typhoon Maria in 2018.

**Figure 6.** Comparison of the time series of the SWH between the wave simulation that used the winds from the original ERA5, from the hybrid winds with various *Rtrs*, and the corresponding observations for the (**a**) Fuguijiao, (**b**) Longdong and (**c**) Suao wave buoys during the passage of Super Typhoon Lekima in 2019.

**Figure 7.** Spatial distribution of the difference in maximum SWH using the winds from H\_4Rmax and the original ERA5 during the passage of Super Typhoon Lekima in 2019.

**Figure 8.** Spatial distribution of the difference in maximum SWH using the winds from (**a**) H\_5Rmax and H\_4Rmax, (**b**) H\_6Rmax and H\_4Rmax and (**c**) H\_7Rmax and H\_4Rmax during the passage of Super Typhoon Lekima in 2019.

### *3.2. Effect of the Wave-Breaking Formulation on the Typhoon-Driven SWH Simulation in the Surf Zone*

To assess the effects of different wave-breaking formulations on the wave hydrodynamics in shallow nearshore waters, three depth-induced wave-breaking parameterizations, introduced in Section 2.5, were applied to hindcast the typhoon waves with the constant wave breaking criterion ( *γ*) and same wind forcing ( *Rtrs* = 4 *Rmax* winds). As listed in Table 2, the designed numerical experiments refer to S\_NO1 and S\_NO3 for the BJ87 and CT93 wave-breaking models, respectively, with a constant *γ* of 0.78. A wave-breaking index of 0.42, namely, *γGT*, is specified for the TG83 model in the present study, which is labeled S\_NO2 in Table 2. The spatial distribution of the difference in the maximum SWH between the scenarios of S\_NO1 and S\_NO2 and S\_NO1 and S\_NO3 during passage Super Typhoon Maria in 2018 are depicted in Figure 9. Figure 9a,b illustrate the differences in S\_NO1 and S\_NO2 and S\_NO1 and S\_NO2, respectively. Large storm waves were generated in the deep ocean and subsequently dissipated due to the decrease in water depth across a surf zone toward the shore. Although the surf zone usually lies in a shallow area where the water depth ranges from 5 to 10 m below sea level, nearshore areas with water depths greater than −20 m are shown in Figure 9 to effectively distinguish among the difference in hindcasted SWHs by different wave-breaking models. The surf zones along the north and northeast coasts of Taiwan are quite narrow because these areas are characterized by a very steep sloping seafloor. The differences in the maximum SWH between the S\_NO1 and S\_NO3 scenarios (Figure 9b) are more significant than those between the S\_NO1 and S\_NO2 (Figure 9a) scenarios. Two points, namely, P1 and P2, located in the north and northeastern shallow nearshore waters, were selected to compare the time series of hindcasted SWHs for the S\_NO1, S\_NO2 and S\_NO3 scenarios. The comparison results are presented in Figure 10a for P1 and Figure 10b for P2. The differences between the three scenarios can only be found during the passage of Super Typhoon Maria in 2018, i.e., from midday on 10 July to midday on 11 July in 2018. The maximal difference in the hindcasted SWH is approximately 2.5 m between the S\_NO1 and S\_NO3 scenarios for P2 (as shown in Figure 10b). However, the maximal difference in hindcasted SWH is within 1.0 m between the S\_NO2 and S\_NO3 scenarios for both P1 and P2 (as shown in Figure 10a,b). Similar results are also shown in Figure 11 (spatial distribution) and Figure 12 (time series comparison) for Super Typhoon Lekima in 2019. The maximal differences in hindcasted SWH in the shallow nearshore waters were smaller for Super Typhoon Lekima in 2019 than those for Super Typhoon Maria in 2018. The maximal difference in hindcasted SWH is approximately 1.5 m at P2 during the passage of Super Typhoon Lekima in 2019 (as shown in Figure 12b).

**Figure 9.** Spatial distribution of the difference in maximum SWH between the scenarios of (**a**) S\_NO1 and S\_NO2 and (**b**) S\_NO1 and S\_NO3 during the passage of Super Typhoon Maria in 2018. The areas with water depths greater than −20 m are shown.

**Figure 10.** Time series of hindcasted SWHs for (**a**) P1 and (**b**) P2 using the S\_NO1, S\_NO2 and S\_NO3 scenarios during the passage of Super Typhoon Maria in 2018.

**Figure 11.** Spatial distribution of the difference in the maximum SWH between the scenarios of (**a**) S\_NO1 and S\_NO2 and (**b**) S\_NO1 and S\_NO3 during the passage of Super Typhoon Lekima in 2019. The areas with water depths greater than −20 m are shown.

**Figure 12.** Time series of hindcasted SWHs for (**a**) P1 and (**b**) P2 using the S\_NO1, S\_NO2 and S\_NO3 scenarios during the passage of Super Typhoon Lekima in 2019.

### *3.3. Effect of the Wave-Breaking Criterion on the Typhoon-Driven SWH Simulation in the Surf Zone*

Many parameterizations of the wave-breaking criterion have been implemented within wind wave spectral models to yield substantial improvements in model hindcasts, simulations and forecasts. Hence, three scenarios, called S\_NO1, S\_NO4 and S\_NO5, exploiting the BJ87 wave-breaking model with *Rtrs* = 4*Rmax* wind forcing and different wave-breaking criteria (*γ*), were applied to hindcast storm waves in the shallow nearshore waters of northern Taiwan during the passage of Super Typhoon Maria in 2018 and Lekima in 2019. The spatial distributions of the difference in the maximum SWH hindcasted by S\_NO1 and S\_NO4 and S\_NO1 and S\_NO5 during the passage of Super Typhoon Maria in 2018 are illustrated in Figure 13a,b, respectively. The differences caused by different wavebreaking criteria *γ* are smaller than those caused by different wave-breaking formulations. Figure 14a,b demonstrate the time series of hindcasted SWHs for P1 and P2 using the S\_NO1, S\_NO4 and S\_NO5 scenarios during the passage of Super Typhoon Maria in 2018. The maximal difference is within 1.0 m at P2 (as shown in Figure 14b) but is less than 0.5 m at P1 (Figure 14a). The same phenomena were also detected in both the spatial distribution (as shown in Figure 15a,b) and time series of the hindcasted SWHs (as shown in Figure 16a,b) during the passage of Super Typhoon Lekima in 2019. Interestingly, the SWHs hindcasted by a constant *γ* (S\_NO1 scenario) are usually smaller than those hindcasted by *γ* based on local steepness (S\_NO4 scenario) and peak steepness (S\_NO5 scenario).

**Figure 13.** Spatial distribution of the difference in the maximum SWH between the scenarios of (**a**) S\_NO1 and S\_NO4 and (**b**) S\_NO1 and S\_NO5 during the passage of Super Typhoon Maria in 2018. The areas with water depths greater than −20 m are shown.

**Figure 14.** Time series of hindcasted SWHs for (**a**) P1 and (**b**) P2 using the S\_NO1, S\_NO4 and S\_NO5 scenarios during the passage of Super Typhoon Maria in 2018.

**Figure 15.** Spatial distribution of the difference in the maximum SWH between the scenarios of (**a**) S\_NO1 and S\_NO4 and (**b**) S\_NO1 and S\_NO5 during the passage of Super Typhoon Lekima in 2019. The areas with water depths greater than −20 m are shown.

**Figure 16.** Time series of hindcasted SWHs for (**a**) P1 and (**b**) P2 using the S\_NO1, S\_NO4 and S\_NO5 scenarios during the passage of Super Typhoon Lekima in 2019.
