**5. Summary and Conclusions**

In this paper, the effects of wave breaking formulations and wave breaking criteria in hindcasting typhoon-driven storm waves are investigated for shallow nearshore waters off northern Taiwan. A fully coupled high-resolution, unstructured grid wave-circulation modeling system, SCHISM-WWM-III, with a large computational domain was applied to hindcast the wind waves caused by the passages of Super Typhoon Maria in 2018 and Super Typhoon Lekima in 2019. The ERA5 reanalysis product were merged with the maximum wind from the best track dataset, and the hybrid typhoon wind created and served as the meteorological conditions for the SCHISM-WWM-III modeling system through a direct modification technique. The hindcasted SWHs during the typhoon period were more sensitive to the radius of the modified scale, *Rtrs* and this phenomenon was more pronounced at the peak SWH. *Rtrs* equal to four times *Rmax* (the radius at the maximum typhoon wind speed) is an adequate radius of the modified scale for simulating the storm waves induced by Super Typhoon Maria in 2018 and Super Typhoon Lekima in 2019 via model validations. A series of numerical experiments were conducted using the SCHISM-WWM-III modeling system incorporated with modified typhoon winds to better understand the wave hydrodynamics in the shallow nearshore waters off northern Taiwan. The results derived from the designed numerical experiments reveal that the wave breaking formulations influence the hindcast of storm waves in the surf zone of northern Taiwan. The maximum difference in peak SWH could reach 2.5 m and 1.2 m for Super Typhoons Maria (2018) and Lekima (2019), respectively, when the wave-breaking formulations of BJ78 and CT93 were introduced to the SCHISM-WWM-III modeling system. Regarding the wavebreaking criterion on the hindcast of typhoon waves in the surf zone of northern Taiwan, compared with the wave-breaking formulation, the maximum difference in peak SWHs was relatively non-sensitive to the wave-breaking criterion. The maximum difference in peak SWH is only 0.5 m using the constant breaking criterion, the breaking criterion based on local steepness or the breaking criterion based on peak steepness. Another important finding is that the utilization of the BJ78 wave-breaking formulation usually underpredicts the typhoon-generated SWHs in shallow nearshore waters than other parametrizations (i.e., TG83 and CT93). In future research, it will be important to acquire measurements in the surf zone where wave hydrodynamics are more sensitive to wave-breaking formulations and criteria during the passage or landfall of typhoons.

**Author Contributions:** Conceptualization, S.-C.H. and W.-B.C.; data curation, H.-L.W. and W.-D.G.; formal analysis, W.-D.G.; investigation, W.-B.C.; methodology, H.-L.W. and W.-B.C.; software, C.-H.C. and W.-R.S.; supervision, S.-C.H.; writing–original draft, W.-B.C.; Writing–review and editing, S.-C.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Ministry of Science and Technology (MOST), Taiwan, gran<sup>t</sup> No. MOST 109-2221-E-865-001.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Publicly available datasets were analyzed in the present study. The data can be found here: https://ocean.cwb.gov.tw/V2/ (accessed date on 26 June 2021).

**Acknowledgments:** The authors thank the Central Weather Bureau, Ministry of Transportation and Communications, Taiwan, for providing the survey data and Joseph Zhang at the Virginia Institute of Marine Science, College of William and Mary, for kindly sharing his experiences using the numerical model.

**Conflicts of Interest:** The authors declare no conflict of interest.
