Computational Electromagnetic Scattering Models for Microwave Remote Sensing

Modeling of electromagnetic wave scatterings by random discrete scatterers and rough surfaces play an important role in geoscience and remote sensing research. Since the 1970s, considerable theoretical efforts have been made to elucidate and understand the scattering processes involved in such problems, and various models have been developed for microwave active and passive remote sensing applications [1–7]. With the rapid advances in computer technology and fast computational electromagnetics algorithms, numerical simulations of scattering by random media allow us to solve Maxwell’s equations exactly without the limitations of analytical approximate 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. These theoretical and numerical models, which are commonly used for tackling electromagnetic wave scattering problems and for remote sensing applications, have been presented in three volumes of books [5–7]. In this article, we will update the development in the numerical scattering models for discrete random scatterers, with emphasis on the applications of microwave remote sensing in snowcover, seafoam, and vegetation canopy. The frequency dependence of scattering by geophysical media at microwave frequencies is an important topic because multifrequency measurements are used in remote sensing applications. In Section 2, we investigate rigorously the frequency dependence of scattering by dense media [7–9]. The approach used is based on the Monte Carlo simulations where the three-dimensional solutions of Maxwell’s equations are pursued [6]. The particle positions are generated by deposition and bonding techniques. 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. In Section 3, polarimetric microwave emissions from foam-covered ocean surfaces are studied. The foam is treated as densely packed air bubbles coated with thin seawater coating [10–12]. 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 (DMRT) theory [2,7] 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 [10–12]. We present an efficient computational model for computing tree scattering at VHF/UHF frequencies in Section 4. A structure model with dielectric cylinders is used to simulate trees with bare branches. The method of moments (MoM) is applied to solve the volume integral equation for the tree scattering signatures. An efficient numerical algorithm based on the sparse matrix iterative approach (SMIA) is applied in solving the matrix equation iteratively [13–15]. The SMIA decomposes the impedance matrix into a sparse matrix for the near interactions, and a complementary matrix for the far interactions among the cylindrical subcells of the tree structure. The SMIA tree scattering model is applied to calculate scattering from various simulated trees with up to several hundreds of branches using a laptop computer. Solutions obtained from the SMIA method agree very well with the solutions obtained using exact 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 4100 [16]. In Section 5, a UV multilevel partitioning (UV-MLP) method is presented for solving the volume scattering problem [17–20]. 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 of U and V matrices. We demonstrate the method for twodimensional volume scattering by discrete scatterers. Multiple scattering is cast into the Foldy–Lax equations of partial waves [2,5–7]. 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 diameter of 1 wavelength. For scattering by 1024 cylinders on a single PC processor with 2.6-GHz CPU and 2 GB (gigabytes) of 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.