Numerical simulation of Maxwell's equation in 3D (NMM3D) applied to active and passive remote sensing of terrestrial snow and snow on sea ice

Summary form only given. The partially coherent approach of dense media radiative transfer (DMRT) has been extensively applied to study the wave propagation and scattering inside dense media such as terrestrial snow [1-5]. In the DMRT partially coherent approach, the coherent part is obtained by solving Maxwell's equations over several cubic wavelengths of statistically homogeneous snow volume to compute the phase matrix, the extinction coefficient, the effective propagation constants and the effective permittivity. Solving Maxwell's equations accounts for the coherent near field and intermediate field interactions within several cubic wavelengths. The phase matrix is then substituted into the radiative transfer equation which constitutes the incoherent part of DMRT. The DMRT equation is then solved to include incoherent interactions and volume/surface interactions. This approach is appropriate when the snow layers are electrically thick such that the coherent far field interaction cancels out over statistical average. This is true for many applications in terrestrial snow remote sensing where the wavelength is 1 ~ 3 cm and the snow depth can be several decimeters to meters. On the other hand, snow on sea ice is typically thin of 10 ~ 20cm with a decreasing trend over the western Arctic [6]. The local wave interaction arising from these thin layers are largely coherent. And in the backscattering direction of the active remote sensing, the coherent wave interaction can extend to far field giving rise to backscattering enhancement phenomena [1]. These short-range and long-range coherent wave effects are not captured by DMRT. In [7], a fully coherent snowpack scattering model is developed by solving the Maxwell's equation directly over the entire domain of snowpack on top of a dielectric half-space. The half-space represents the soil ground under the terrestrial snow or the sea ice below the snow cover across the Arctic Ocean. This is applicable when the sea ice thickness is larger than the penetration depth, depending on the wave frequency of the incidence waves. Effects of the half-space are included in the volume integral equation by the half-space dyadic Green's function. The snow volume is represented by bicontinuous media [8] and discretized into cubes. The method of moments (MoM) is then used to solve the volume integral equation with a pulse basis function and point matching, leading to discrete dipole approximation (DDA). The fast Fourier transform (FFT) is adapted for the kernel of the half-space dyadic Green's function to accelerate the matrix-vector multiplication in the iterative linear system solver [9]. For the first time, the scattering matrix of the snowpack is computed using this fully coherent approach of NMM3D, including both magnitude and phase. This allows the modeling of the coherence matrix and speckle statistics. Backscattering enhancement effects are also exhibited, and for a homogeneous snowpack of moderate optical thickness, the overall trend of the bistatic scattering pattern from the fully coherent approach agrees with the results of DMRT. In this paper, the fully coherent approach is improved by implementing the periodic boundary condition. The periodic Green's function in half space is used. The incorporation of the periodic boundary condition removes the edge diffraction artifacts from the finite computational domain and produces more physically plausible results. We also extend the fully coherent approach to compute the brightness temperatures of the snowpack following the reciprocity principle. This approach accounts for an arbitrary temperature profile of the snowpack and includes coherent effects in the thin layer together with fully coherent volume-surface interactions. This new method circumvents the unrealistic isothermal condition incorrectly assumed in the Kirchhoff approximation approach. The brightness temperatures and backscatters from the fully coherent model are compared with the results of DMRT for various snowpack configurations to understand and to determine the applicability regime of DMRT.