A modified hapke model for soil bidirectional reflectance

The Hapke bidirectional reflectance model has been widely used for soil modeling, but gives significant errors when the soil scatters very strongly and anisotropically. In our new model, we decompose the radiation field into three components instead of two: single-scattering radiance, double-scattering radiance, and multiple-scattering radiance. The first two components can be exactly calculated and multiple scattering is equivalently approximated by the original Hapke formula. Comparisons with the numerical code-DISORT based on the discrete ordinate algorithm indicate that this modified model significantly improves the accuracy of the bidirectional reflectance. A numerical calculation for a clay soil using the Mie theory gives reasonable variation in the ranges 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 the inversion accuracy.