Modeling active microwave remote sensing of snow using dense media radiative transfer (DMRT) theory with multiple-scattering effects

Dense media radiative transfer (DMRT) theory is used to study the multiple-scattering effects in active microwave remote sensing. Simplified DMRT phase matrices are obtained in the 1-2 frame. The simplified expressions facilitate solutions of the DMRT equations and comparisons with other phase matrices. First-order, second-order, and full multiple-scattering solutions of the DMRT equations are obtained. To solve the DMRT equation, we decompose the diffuse intensities into Fourier series in the azimuthal direction. Each harmonic is solved by the eigen-quadrature approach. The model is applied to the active microwave remote sensing of terrestrial snow. Full multiple-scattering effects are important as the optical thickness for snow at frequencies above 10 GHz often exceed unity. The results are illustrated as a function of frequency, incidence angle, and snow depth. The results show that cross polarization for the case of densely packed spheres can be significant and can be merely 6 to 8 dB below copolarization. The magnitudes of the cross polarization are consistent with the experimental observations. The results show that the active 13.5-GHz backscattering coefficients still have significant sensitivity to snow thickness even for snow thickness exceeding 1 m.