Using Similarity Theory to Parameterize Mesoscale Heat Fluxes Generated by Subgrid-Scale Landscape Discontinuities in GCMs

Similarity theory was used to develop a parameterization of mesoscale heat fluxes induced by landscape discontinuities for large-scale atmospheric models (e.g., general circulation models). For this purpose, Buckingham Pi theory, a systematic method for performing dimensional analysis, was used to derive a set of dimensionless groups, which describes the large-scale atmospheric background conditions, the spatial variability of surface sensible heat flux, and the characteristic structure of the landscape. These dimensionless groups were used to calculate the coefficients of a fourth-order Chebyshev polynomial, which represents the vertical profiles of dimensionless mesoscale heat fluxes obtained for a broad range of large-scale atmospheric conditions and different landscapes. The numerous three-dimensional numerical experiments performed to evaluate this similarity relationship suggest that the parameterization is quite robust.