A MODIFIED HAPKE MODEL FOR SOIL BIDIRECTIONAL REFLECTANCE

The Hapke bidirectional reflectance model has been widely used for soi l modeling, but gives significant errors when the soil scatters very s trongly and anisotropically. In our new model, we decompose the radiat ion field into three components instead of two: single-scattering radi ance, double-scattering radiance, and multiple-scattering radiance. Th e first two components can be exactly calculated and multiple scatteri ng is equivalently approximated by the original Hapke formula. Compari sons with the numerical code-DISORT based on the discrete ordinate alg orithm indicate that this modified model significantly improves the ac curacy of the bidirectional reflectance. A numerical calculation for a clay soil using the Mie theory gives reasonable variation in the rang es of the single-scattering albedo and the asymmetry parameter of the phase function where the original Hapke model generally works poorly. An inversion experiment shows that the modified model also improves th e inversion accuracy.