Stability analysis of turbulent heat exchange over the heterogeneous environmental interface in climate models

Based on a short review of the different parameterization schemes for sub-grid scale surface fluxes in climate and other atmospheric models of different scales, the flux aggregation effect over a heterogeneous grid-box leading to the occurrence of Schmidt’s paradox is considered. To investigate this effect in the sub-grid scale parameterization, we have introduced a dynamical system approach, where the horizontal energy exchange is taken into account and is represented by a matrix of coupling parameters. Since it is, in general, very difficult to specify the quantities in that matrix, a sufficient condition for the asymptotic stability that can be applied for any coupling matrix is derived. Two theorems that consider the flux aggregation effect over a heterogeneous grid-box are proved. Finally, we have showed how, by their application, Schmidt’s paradox can be overcome. It is demonstrated through a numerical example of turbulent energy exchange over the grid-box including the part of the Prospect park, New York, USA.