Analytical derivation of the vegetation optical depth from the microwave polarization difference index

A numerical solution for the canopy optical depth in an existing microwave-based land surface parameter retrieval model is presented. The optical depth is derived from the microwave polarization difference index and the dielectric constant of the soil. The original procedure used an approximation in the form of a logarithmic decay function to define this relationship and was derived through a series of lengthy polynomials. These polynomials had to be recalculated when the scattering albedo or antenna incidence angle changes. The new procedure is computationally more efficient and accurate.