The inclusion of SGS slopes of topography into the model equations in the framework of a second order turbulence closure

If we want to describe the atmosphere close to the rigid surface of the earth within the so called roughness layer, this part of the atmosphere has to be resolved vertically by the simulating numerical model. In that case the sub grid scale (SGS) structures of that surface can no longer be neglected when filtering the budget equations according to the numerical grid. Rather, the filter procedure generates additional correlation terms describing the interaction of the mean flow with roughness layer elements in each model layer inside the roughness layer, and thus this interaction is not only part of the surface transfer scheme expressing the whole effect by a single roughness length value.

Using a topographic approximation, these terms are related to SGS slopes of an equivalent topography being representative for the real surface.

In this talk the generation of that kind of roughness layer terms is being showed. Thereafter I am going to present a possibility, how to parameterize these terms using a modified boundary layer approximation in the framework of a second order turbulence closure being applicable for grid scale slopes of topography as well.