2.5.1. BJ78 Model

In the BJ78 model (proposed by Battjes and Janssen [48]), the total energy dissipation due to depth-induced wave breaking, *Dtot*\_*B J*78 is given as follows:

$$D\_{\text{tot\\_Bf78}} = -\frac{1}{4} \kappa\_{Bf} Q\_b \overline{f} H\_{\text{max}}^2 \tag{4}$$

where *αB J* is the proportionality parameter, *Qb* represents the fraction of breaking waves, *f* is the averaged frequency and *H*max represents the maximum individual wave height and is defined as a proportion of the water depth in the local area (*d*):

$$H\_{\text{max}} = \gamma d \tag{5}$$

where *γ* is the wave-breaking index. The fraction of breaking waves, *Qb* is determined by the Rayleigh distribution truncated at an upper limit with *H*max (maximum wave height). Therefore, the fraction of breaking waves is implicitly expressed as follows:

$$\frac{1 - Q\_b}{1 - \ln Q\_b} = \left(\frac{H\_{\text{rms}}}{H\_{\text{max}}}\right)^2 \tag{6}$$

where *Hrms* is the root-mean-square wave height.
