Parameterization of the albedo over the heterogeneous surfaces for different geometries in a land surface scheme by the Monte Carlo Ray-tracing method

The parameterization of physical processes over the heterogeneous environmental interfaces has become one of the basic tasks in environmental modeling from large to small scales. Previously introduced new approach for calculating the aggregated albedo of the heterogeneous grid cell with regions of different heights is analyzed in the case of different geometries (“rectangular prism,” “trilateral prism,” “slope” and “canyon”) in a grid cell commonly met in the environmental models. In order to determine the loss coefficient, relative flux that is lost due to the absorption on the vertical lateral boundaries of the patches lying on a higher level, rather complex analytical expression for this flux is derived wherever it was possible. For the situations when the analytical solution for the loss coefficient is not accessible, the Monte Carlo ray tracing (MCRT) method is highly efficient approach for calculating the aggregated albedo. Finally, the differences in albedo obtained in a conventional way and by the MCRT method were emphasized by the calculation of the effective surface temperature of the grid cell, for all considered geometries, using the land surface scheme LAPS. In all cases the temperature obtained by present method is higher.