*2.5. Parameterization of Depth-Induced Wave Breaking*

Three widely used parameterizations for characterizing depth-induced wave breaking in nearshore shallow waters were adopted in the present study and are briefly reviewed in this section. Battjes and Beji [47] proposed that the total energy dissipation can be distributed over the wave spectrum in proportion to the spectral density based on extensive laboratory experiments; hence, the wave-induced wave breaking (*Sbreak*) in the wave action density function is calculated as follows:

$$S\_{brck}(\sigma,\theta) = D\_{total} \frac{E(\sigma,\theta)}{E\_{total}} \tag{3}$$

where *Sbreak(<sup>σ</sup>*,*θ)* is the wave-induced wave breaking in spectral space (*<sup>σ</sup>*, *θ*), *Dtotal* is the total energy dissipation rate due to depth-induced wave breaking, *E(<sup>σ</sup>*,*θ)* is the wave energy in spectral space (*<sup>σ</sup>*, *θ*) and *Etotal* is the total wave energy.
