Computational Electromagnetic Scattering Models for Microwave Remote Sensing
Authors: Ding Kung-Hau , Tsang Leung , Li Qin 
Published: April 2005

Modeling of electromagnetic wave propagation and scattering in random media play an important role in geoscience and remote sensing research. Considerable efforts have been made to elucidate and understand the wave interaction processes involved in such problems, and various models have been developed for microwave active and passive remote sensing applications. With the rapid advances in computer technology and fast computational electromagnetic algorithms, numerical simulations of scattering by random media allow us to solve Maxwell's equations exactly without the limitations of approximate analytical models. The numerical models can provide a valuable means for evaluating the validity regimes of analytical scattering theories; in addition, they can potentially aid in the future development of extended analytical models. In this article, updated developments in the numerical scattering models for discrete random scatterers are presented, with emphasis on the applications of microwave remote sensing in snowcover, seafoam, and vegetation canopy.

The frequency dependence of scattering by dense media at microwave frequencies is the first numerical model described, which is an important topic because multifrequency measurements are usually used in remote sensing applications. The approach used is based on the Monte Carlo simulations where the three‐dimensional solutions of Maxwell's equations are solved. The properties of absorption, scattering, and extinction are calculated for dense media consisting of sticky and nonsticky particles. Numerical solutions of Maxwell's equations indicate that the frequency dependence of densely packed sticky small particles is much weaker than that of independent scattering. Numerical results are illustrated using parameters of snow in microwave remote sensing. Comparisons are made with extinction measurements as a function of frequency.

Polarimetric microwave emissions form foam‐covered ocean surfaces are studied by modeling foam as densely packed air bubbles coated with thin seawater. The absorption, scattering, and extinction coefficients are computed from the Monte Carlo solutions of Maxwell's equations for a collection of coated particles. These quantities are then applied in the dense media radiative transfer theory to calculate the polarimetric microwave emissivities of ocean surfaces with foam cover. The theoretical results of Stokes brightness temperatures with typical parameters of foam in passive remote sensing at 10.8 and 36.5 GHz are illustrated and compared with experimental measurements.

It follows by describing an efficient computational model based on the sparse matrix iterative approach (SMIA) for tree scattering at VHF/UHF frequencies. The method of moments is applied to solve the volume integral equation for the tree scattering signatures. The SMIA decomposes the impedance matrix into a sparse matrix for the near interactions, and a complementary matrix for the far interactions of the tree structure. Solutions obtained from the SMIA method agree very well with the solutions obtained using extract matrix inversion and the conjugate gradient method (CGM). The key feature of the SMIA approach is that very little iteration is required to obtain convergent solutions; compared to the CGM, the SMIA approach may reduce the number of iterations by a factor of >100.

The UV multilevel partitioning (UV‐MLP) method is also presented for solving the general volume scattering problems. The method consists of setting up a rank table of transmitting and receiving block sizes and their separations. The table can be set up speedily using coarse–coarse sampling. For a specific scattering problem with given geometry, the scattering structure is partitioned into multilevel blocks. By looking up the rank in the pre‐determined table, the impedance matrix for a given transmitting and receiving block is expressed by a product ofUandVmatrices. We demonstrate the method for two‐dimensional volume scattering by discrete scatterers. Multiple scattering is cast into the Foldy–Lax equations of partial waves. We show that the UV decomposition can be applied directly to the impedance matrix of partial waves of higher order than the usual lowest‐order Green function. Numerical results are illustrated for randomly distributed cylinders with a diameter of 1 wavelength. For scattering by 1024 cylinders on a single PC processor with 2.6 GHz CPU and 2 GB memory, only 14  CPU minutes is needed to obtain the numerical solution and for 4096 cylinders, only 7.34 s is needed for one matrix–vector multiplication.