Semi-empirical model of the ensemble-averaged differential Mueller matrix for microwave backscattering from bare soil surfaces

A semi-empirical model of the ensemble-averaged differential Mueller matrix for microwave backscattering from bare soil surfaces is presented. Based on existing scattering models and data sets measured by polarimetric scatterometers and the JPL AirSAR, the parameters of the co-polarized phase-difference probability density function, namely the degree of correlation α and the co-polarized phase-difference ς, in addition to the backscattering coefficients σ_νν⁰,σ_hh⁰ and σ_νh⁰, are modeled empirically in terms of the volumetric soil moisture content m_ν and the surface roughness parameters ks and kl, where k=2πf/c, s is the rms height and l is the correlation length. Consequently, the ensemble-averaged differential Mueller matrix (or the differential Stokes scattering operator) is specified completely by σ_νν⁰,σ_hh⁰,σ_νh⁰,α, and ζ.