General description

For the fully spectral formulation the wind input source term is parameterized following Janssen’s formulation and implemented as in WAM cycle 4, see Komen et al. (1994). For a given wind speed and direction, the growth rate of waves of a given frequency and direction depends on the friction velocity, u_*, and sea roughness z₀. In principle, if the sea roughness is known or assumed (e.g. the Charnock parameter z_ch = g^.z₀/u_*², may be assumed), the wind fric­tion speed can be estimated using the logarithmic wind profile. Thus, the growth rate of waves due to wind input can be calculated. Assuming a dimen­sionless sea roughness (z_ch = g^.z₀/u_*²) of 0.0144, this formulation was shown in Komen et al. (1994) to fit the observations compiled by Plant (1982). Note that the use of a constant Charnock parameter implies that sea roughness is not coupled with the wave spectrum in the comparison with observations shown in Komen et al.

In addition to the parameterization of the wind input source term, Janssen (1991) parameterized the sea roughness in terms of wave induced stress, t_w which depends on the wave spectrum.