Electromagnetic Scattering of Randomly Rough Soil Surfaces Based on Numerical Solutions of Maxwell Equations in Three-Dimensional Simulations Using a Hybrid UV/PBTG/SMCG Method

Abstract

A hybrid UV/PBTG/SMCG method is developed to accelerate the solution of NMM3D for 3-D electromagnetic wave scattering by random rough soil surfaces. It takes only 1.5 min using 16 processors on a cluster of NSF TeraGrid to compute 3-D solution of Maxwell equations of 8 by 8 square wavelengths. With the improved computational efficiency, we computed results using areas up to 32 by 32 square wavelengths. With the larger surface area, we were able to compute cases with larger rms heights up to 8 cm at SMAP radar frequency of 1.26 GHz that corresponds to kh = 2.28. New results computed include the cross-polarization. The five tests on the accuracy of results were performed: convergence with realizations, convergence with discrete samplings, convergence with sample surface sizes, energy conservation for each realization, and reciprocity for each realization. The numerical results show that for a single realization V H = HV within 0.5 dB in the backscattering direction showing that reciprocity is obeyed. Results were compared with experimental data, and both co-polarization and cross-polarization were in good agreements with experimental data.Index Terms-Microwave remote sensing, random rough surface, SMCG, soil moisture.

Spatial Variability of L-Band Brightness Temperature during Freeze/Thaw Events over a Prairie Environment

“…Furthermore, ice lenses formed during the ephemeral F/T events in winter can lead to important dielectric discontinuities in the snowpack, causing also possible coherence effects that can have a notable impact on T B [37][38][39]. Further evaluation using multi-layer snow radiative transfer models [40,41] need to better quantify and understand these variations.…”

Modelling and Validation of Combined Active and Passive Microwave Remote Sensing of Agricultural Vegetation at L-Band

“…The convergence of the integration with regard to the number of points used has been checked. To calculate the bistatic scattering coefficient γ we use the distorted Born approximation for the vegetation volume scattering and NMM3D [11] for coherent reflectivity and bistatic rough surface scattering of the soil surface. In the derivations below, the crucial assumptions are: (1) the vegetation scatterers are uniformly distributed in the vegetation layer; (2) each type of vegetation scatterer, such as stalks or leaves, is statistically identical in terms of the size, shape and permittivity; (3) there is no correlation between the scattered fields of different vegetation scatterers, hence the incoherent model can be used; and (4) the first-order scattering contributions are significantly larger than the high-order scattering contributions in the vegetation, such that a single scattering approximation is applicable.…”

“…Thus, empirical "best-fit" parameters rather than physical parameters are used in the tau-omega model. For active remote sensing modelling, we previously used the distorted Born approximation (DBA) [10] and the numerical solutions of the Maxwell equations (NMM3D) [11] (this method is called NMM3D-DBA for short), where the coherent reflectivity and rough surface scattering are calculated by NMM3D [12]. This model was used to calculate the V V and HH backscatter at L-band for pasture [13], wheat, winter wheat and canola fields.…”

“…The attenuation through the vegetation layer is accounted for by the imaginary part of the effective propagation constant calculated by Foldy's approximation [8]. NMM3D results are based on the Method of Moments (MoM) with the Rao-Wilton-Glisson (RWG) basis function using Gaussian random rough surfaces with exponential correlation functions, which have been shown to agree well with experimental data for various root mean square (RMS ) height values and soil moisture conditions [11]. The total bistatic scattering is expressed as the incoherent sum of three scattering mechanisms: volume scattering, double bounce scattering and surface scattering.…”

Scattering and Transmission of Waves in Multiple Random Rough Surfaces: Energy Conservation Studies With the Second Order Small Perturbation Method

“…To extend the validity region, numerical methods including the Method of Moments (MoM), 3D Numerical Method of Maxwell's equations (NMM3D) [22], Advanced Integral Equation Method (AIEM) [23,24], and Extended Boundary Condition Method (EBCM) [25][26][27][28], etc. have been developed.…”