**1. Introduction**

Ocean surface wind waves are a dominant process in coastal, nearshore and offshore regions worldwide. Understanding the characteristics of cyclone-driven extreme waves, their variability and historical and projected future changes are important considerations for the sustainable development of coastal and offshore infrastructures and the managemen<sup>t</sup> of coastal resources and ecosystems. The energy in ocean surface waves is transmitted from the wind. The wind patterns above the ocean surface have been affected as the upper ocean has warmed, consequently resulting in stronger ocean waves. According to the report from Reguero et al. [1], the energy of ocean waves, i.e., wave height, has grown over the past seven decades, which could have significant implications for coastal communities and ecosystems. Since the contributions of ocean surface waves to extreme total water levels are substantial at open coasts, they have mostly been considered in many local studies [2–5].

Predicting wave heights accurately in coastal and nearshore areas is essential for a number of human activities there, such as renewable energy applications, aquaculture, maritime transport and infrastructure; furthermore, information on both swells and wind seas is important to coastal applications. For example, the prediction of locally generated

**Citation:** Hsiao, S.-C.; Wu, H.-L.; Chen, W.-B.; Guo, W.-D.; Chang, C.-H.; Su, W.-R. Effect of Depth-Induced Breaking on Wind Wave Simulations in Shallow Nearshore Waters off Northern Taiwan during the Passage of Two Super Typhoons. *J. Mar. Sci. Eng.* **2021**, *9*, 706. https://doi.org/ 10.3390/jmse9070706

Academic Editor: Christos Stefanakos

Received: 20 April 2021 Accepted: 24 June 2021 Published: 26 June 2021

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wind seas is essential for high-speed passenger ferries, whereas information about the propagation of low-frequency swells in coastal areas and fjords is critical for the design of coastal structures or in the planning of marine operations.

Depth-induced wave breaking is one of the most dominant hydrodynamic processes occurring in coastal regions. This wave breaking not only controls the amount of wave energy impacting our coastlines and coastal defenses but also plays a crucial role in driving many nearshore processes, such as sediment transport, bottom morphology [6] and turbulence, which has been shown to be very important for local ecology [7]. Wave breaking also induces radiation stresses that drive wave-induced setup and currents [8], both of which are important for coastal engineering design and management. However, despite the importance and relevance toward our knowledge of wave hydrodynamics, depth-induced wave breaking is still poorly understood, which is partially due to its highly nonlinear nature; therefore, it is heavily parameterized in most wind wave models.

Many parameterizations for the wave-breaking index have been proposed and reported in previous studies. These parameterizations include dependencies of the wavebreaking index on the offshore wave steepness [9,10], a dissipation rate based on a normalized surf zone width [11], the offshore wave height and the inverse Iribarren number [12]. Ruessink et al. [13] also introduced a parameterization of the wave-breaking index that linearly increases with the local nondimensional depth based on the peak period.

This study provides a critical and objective assessment of three specialized depthinduced wave-breaking models and wave-breaking criteria, which are based on state-ofthe-art breaking wave formulations. The aim of this paper is to study the effect of the depth-induced wave-breaking formulation and wave-breaking criteria on the hindcasts of SWH in shallow nearshore waters off northern Taiwan during the passage of Super Typhoons Maria in 2018 and Lekima in 2019, as well as to better understand which hindcast is more influential in wave height hindcasting inside the surf zone. The details of the materials and methods are presented in the following section, and the results of model validation and a series of designed model experiments are described in Section 3. A discussion and uncertainties of the present study are given in Section 4. Finally, Section 5 summarizes and concludes the paper.
