2.5.2. TG83 Model

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The TG83 model can be considered a variant of BJ78, and the total energy dissipation due to depth-induced wave breaking in the TG83 model (proposed by Thornton and Guza [49]), *Dtot TG*83 is formulated as follows:

$$D\_{\text{tot}\\_T\text{G83}} = -\frac{B^3}{4} \overline{\frac{f}{d}} \int\_0^\infty H^3 p\_b(H) dH \tag{7}$$

where *B* is the proportionality coefficient, *H* is the wave height and *pb*(*H*) is the fraction of breaking waves at each wave height. In which, *pb*(*H*) can be given as follows:

$$p\_b(H) = \mathcal{W}(H)p(H) \tag{8}$$

where *p*(*H*) is the Rayleigh wave height probability density function and can be expressed as follows: 

$$p(H) = \frac{2H}{H\_{rms}^2} \exp\left[-\left(\frac{H}{H\_{rms}}\right)^2\right] \tag{9}$$

The weighting function, *W*(*H*) is defined as in the TG83 model:

$$\mathcal{W}(H) = \left(\frac{H\_{rms}}{\gamma\_{TG}d}\right)^n \tag{10}$$

where the calibration parameter *n* = 4, *γTG* is the wave-breaking index for the TG83 model and is set to 0.42 according to Thornton and Guza [49,50].
