Monte Carlo ray-tracing method for use in the calculation of the albedo for different geometries

Abstract

Environmental modeling at various scales demands the parameterization of physical processes over heterogeneous environmental interfaces. A previously introduced novel approach to calculating the aggregated albedo of a heterogeneous grid-cell with regions of different heights is analyzed using different geometries ("trilateral prism", "slope" and "canyon") in a grid-cell commonly encountered in environmental models. The loss coefficient, which describes the relative flux lost due to absorption on the vertical lateral boundaries of patches lying on the higher levels, can sometimes be derived as a rather complex analytical expression. In most situations, the analytical form of the loss coefficient is not accessible, and the Monte Carlo ray tracing (MCRT) method has been determined to be the most reliable approach for calculating the aggregated albedo. As the dimensions of the problems increase, this method becomes highly efficient and less time-consuming than deterministic methods. The albedo was calculated over a grid-cell consisting of the aforementioned geometries on a horizontal surface, leading to some extremely interesting results. Finally, the differences in albedo obtained by conventional techniques and by the MCRT method were emphasized by using the Land Air Parameterization Scheme (LAPS) to calculate the effective surface temperatures of the grid-cells of all considered geometries. © 2012 by Nova Science Publishers, Inc. All rights reserved.