A parameterization with wave saturation adjustment of subgrid-scale average wave stress over three-dimensional topography

A parameterization of subgrid-scale wave stress over three-dimensional topography is described and applied to regions of low, moderate, and high-relief terrain. The scheme explicitly calculates the wave stress using linear theory and the two-dimensional Fourier transform of the subgrid-scale topography. It is shown that in the presence of wind direction shear, critical levels exist. Wave saturation (breaking), which occurs below a critical level, is parameterized using the so-called terrain-height adjustment scheme. Wave breaking produces a vertical divergence in the wave stress resulting in the generation of turbulence in the stable planetary boundary layer (PBL) and the residual layer even though the Richardson numbers there are greater than the critical value for the suppression of turbulence. In the case of general topography, terrain features can be spatially organized such that the magnitude of the wave stress is strongly dependent on the direction of the surface wind. Stress profiles are estimated for real terrains and meteorology. Unlike current wave stress parameterization schemes that assume the wave stress always acts in opposition to the surface wind, our scheme more accurately accounts for the effects of wind direction shear in the PBL