Full-Wave Simulations of Electromagnetic Scattering by Vegetation for Microwave Remote Sensing Based on Numerical 3 D Solutions of Maxwell Equations

The electromagnetic scattering by vegetation is an important problem for microwave remote sensing of vegetation and vegetated surfaces. For example, whether the radar can sense the soil moisture of vegetated soils depends strongly on the transmission through vegetation. The scattering parameters and transmission of microwaves through vegetation and forests are also important in Polarimetric and Interferometric SAR. For more than two decades, two methods have been used to calculate the scattering from vegetation: the vector radiative transfer theory (VRT) and the distorted Born approximation (DBA). In this paper, we implement a new approach using Numerical Maxwell Model in 3D Simulations (NMM3D) for full-wave simulations of electromagnetic wave scattering from a vegetation layer consisting of many thin cylindrical scatterers. The full-wave approach for solving Maxwell’s equations is based on the Foldy-Lax multiple scattering equations (FL) combined with the Method of Moments for bodies of revolution (BOR). In BOR formulations, the basis functions for the surface currents are expanded in Fourier series in the azimuthal dimension because of the rotational symmetry. Thus, a merit of FL-BOR is the much smaller number of surface unknowns involving only 1-dimensional discretization than using Rao-Wilton-Glisson (RWG) 2-dimensional basis functions in the usual MoM codes. In DBA and VRT, there is an effective attenuation/extinction rate 〈 〉 which is a result of assuming that the probability density functions of positions of scatterers are statistical homogeneous in 3D. The results of this assumption of statistical homogenization give effective permittivity, effective extinction rates and effective phase matrix. In DBA and VRT models, Foldy’s approximation is used to compute the effective attenuation rate 〈 〉 which is calculated as the single scatterer extinction cross section multiplied by the number of scatterers per m3. is the sum of absorption and scattering cross sections and is further averaged over sizes and orientations of the scatterers. However, in NMM3D full-wave simulations, an effective attenuation rate 〈 〉 is not needed nor defined in Maxwell equations. Numerical solutions of Maxwell equations for a layer of vegetation scatterers give the scattering parameters and the transmission of that layer without calculating an attenuation rate 〈 〉.