Microwave Signatures of Snow Cover Using Numerical Maxwell Equations Based on Discrete Dipole Approximation in Bicontinuous Media and Half-Space Dyadic Green's Function

A three-dimensional snowpack scattering and emission model is developed by numerically solving Maxwell's equations (NMM3D) over the entire snowpack on an underlying half-space. The solutions are crucial to microwave remote sensing that requires the preservation of coherent phase information. The heterogeneous snowpack is represented as a bicontinuous medium. Effects of the underlying half-space are included through a half-space Green's function in a volume integral equation formulation. The volume integral equation is then solved using the discrete dipole approximation. The fast Fourier transform is effectuated for all three dimensions with half-space Green's function rather than the conventional free space Green's function. To overcome the snow volume truncation in the finite numerical calculations, periodic boundary conditions are applied in the lateral extent. Thus, in NMM3D, the physical microwave scattering and emission problem is solved without using any radiative transfer equations. In this formulation, the scattering matrix of the snowpack accounts for both the magnitude and phase. The NMM3D simulations are demonstrated at Ku-band frequency for a snow cover up to 25-cm thick. The results are applicable to remote sensing of snow over sea ice, and thin layers of terrestrial snow. Quantitative values of backscattering and bistatic scattering coefficients are derived for active microwave remote sensing, and brightness temperatures for passive microwave remote sensing. The full wave simulation results are compared with those of the partially coherent approach of the dense media radiative transfer (DMRT). The NMM3D results capture effects of backscattering enhancement and coherent layering that are missed in DMRT. The full wave solution to Maxwell equations is important to advance radar polarimetry, interferometry, and tomography that require the preservation of the full phase information and all interface interactions for applications to radar remote sensing of snow cover on land and on sea ice.