Parameterization of Albedo over Heterogeneous Surfaces in Coupled Land-Atmosphere Schemes for Environmental Modeling. Part I: Theoretical Background

In grid-based environmental models, the underlying surface consists of patches of solid and liquid parts and different plant communities, creating a very heterogeneous picture in the grid cell. In these cases, numerical modelers usually use a simple arithmetic average to determine the grid-cell albedo, a key variable in the parameterization of the land-surface radiative transfer over the grid cell. The object of this paper is to consider the assumptions for aggregating the albedo over a very heterogeneous surface where various surfaces occur at different heights, and, then propose a method for deriving a general expression for it. The suggested expression for the albedo is compared with the conventional approach, for the two-patches grid-cell with a simple geometrical distribution and different heights of its components. A numerical test is performed to compare the two approaches by numerical simulation of the evolution of the surface temperature over the particular grid-cell. Specifically, a one-dimensional land-surface model was applied to an isolated rocky grid-cell with a hole in the center; the model was forced with meteorological observations taken on July 17, 1999 in Philadelphia, PA.