Geometrical constraint on shadowing in rough surfaces

摘要

In modeling the thermal emissivity of a rough surface, such as wind-driven waves on a lake or ocean, it is customary to treat the surface as a collection of individual facets, each of which is flat but tilted with respect to the horizontal. By considering a one-dimensional cross-section through the rough surface, the authors derive a purely geometrical constraint on the statistical distribution of shadowed facet slopes that should be satisfied by any model of surface emissivity that includes the effect of self-shadowing. The purpose is not to develop a single shadowing model, but to provide a condition that any valid shadowing model should satisfy. Although the emphasis of the presentation is theoretical, some practical ramifications are also discussed.