Backscattering Coefficients, Coherent Reflectivities, and Emissivities of Randomly Rough Soil Surfaces at L-Band for SMAP Applications Based on Numerical Solutions of Maxwell Equations in Three-Dimensional Simulations

Abstract

We used Numerical Maxwell Model in 3-D Simulations (NMM3D) to study the backscattering coefficients, coherent reflectivities, and emissivities of soil surfaces using Gaussian random rough surfaces with exponential correlation functions. The surface area used is 8 by 8 square wavelengths. A total of close to 200 cases are computed by varying rms height, correlation length, and soil permittivity. We consider a 40° incidence angle. For each case, 15 realizations of rough surface profiles are generated, and 30 solutions of Maxwell equations are computed because of two polarizations. The method for solving the Maxwell equations is based on the Method of Moments (MoM) with Rao-Wilton-Glisson (RWG) basis functions. The solutions are accelerated by the sparse matrix canonical grid method implemented on parallel computing. The rms height varies up to 0.126 wavelength. The results are compared with the Dubois formulation, Small Perturbation Method (SPM), Kirchhoff Approximation (KA), and Advanced Integral Equation Model (AIEM). The NMM3D results are also compared with VV and HH backscatter data of soil surfaces where ground truth rms heights and correlation lengths were both measured. Good agreement is found between the NMM3D results and experimental measurement data. Based on the computed cases, interpolation tables are derived that can be directly applied to L-band active and passive microwave remote sensing of soil moisture, such as for the upcoming Soil Moisture Active and Passive (SMAP) mission.