Kyung Pak

Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method

Scattering of a TE incident wave from a perfectly conducting one-dimensional random rough surface is studied with the banded matrix iterative approach/canonical grid (BMIA/CAG) method. The BMIA/CAG is an improvement over the previous BMIA. The key idea of BMIA/CAG is that outside the near-field interaction, the rest of the interactions can be translated to a canonical grid by Taylor series expansion. The use of a flat surface as a canonical grid for a rough surface facilitates the use of the fast Fourier transform for nonnear field interaction. The method can be used for Monte-Carlo simulations of random rough surface problems with a large surface length including all the coherent wave interactions within the entire surface. We illustrate results up to a surface length of 2500 wavelengths with 25000 surface unknowns. The method is also applied to study scattering from random rough surfaces at near-grazing incidence. The numerical examples illustrate the importance of using a large surface length for some backscattering problems. >

Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations

Backscattering enhancement of electromagnetic wave scattering from a perfectly conducting two-dimensional random rough surface (three-dimensional scattering problem) is studied with Monte Carlo simulations. The magnetic-field integral equation formulation is used with the method of moments. The solution of the matrix equation is calculated exactly with an efficient method known as the sparse-matrix flat-surface iterative approach. Numerical examples are illustrated with 32,768 surface unknowns, surface areas between 256 and 1024 square wavelengths, rms heights of 0.5 and 1 wavelength, and as many as 1000 realizations. The bistatic scattering simulations show backscattering enhancement for both copolarized and cross-polarized components. Comparisons are made with controlled laboratory experimental data for which the random rough surfaces are fabricated with prescribed properties of a rms height of 1 wavelength and a correlation length equal to 2 wavelengths. Comparisons are made between simulations and experimental data for the absolute value of the bistatic scattering coefficient. The copolarized scattering coefficient is in good agreement, and the cross-polarized scattering coefficient is in excellent agreement.

Numerical simulations and backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces with the sparse-matrix canonical grid method

Numerical simulations exhibiting backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces (three-dimensional scattering problem) are presented. The Stratton–Chu surface integral equation formulation is used with the method of moments to solve for the tangential and normal components of surface fields. The solution of the matrix equation is calculated efficiently by using the sparse-matrix canonical grid (SMCG) method. The accuracy of the solution is assessed by comparing the bistatic scattering coefficients obtained from the SMCG and the matrix inversion method. Also, a sufficient sampling rate is established with respect to the dielectric constant below the rough-surface boundary. Numerical simulations are illustrated for moderate rms heights of 0.2 and 0.5 electromagnetic wavelengths with rms slopes of 0.5 and 0.7. The magnitude of the relative permittivity ranges from 3 to 7. With use of the SMCG method, scattered fields from a surface area of 256 square wavelengths (98,304 surface unknowns) are found. For a rms height of 0.5 wavelength and a correlation length of 1.0 wavelength, backscattering enhancement is observed in both co-polarization and cross polarization. However, in the case in which the rms height is 0.2 wavelength and the correlation length is 0.6 wavelength, backscattering enhancement is observed in cross polarization only.

Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations

The exact solution of scattering by a two-dimensional random rough surface (three-dimensional scattering problem) of an area of 80 square wavelengths with 4096 surface unknowns is computed, and the results show backscattering enhancement. The computation is based on a new numerical method called the sparse-matrix flat-surface iterative approach. The approach decomposes the matrix of the integral equation as a sum of a sparse matrix, a flat-surface block Toeplitz matrix, and a weak remainder that is followed by an iterative solution until convergence is achieved.

A numerical study of the composite surface model for ocean backscattering

A numerical study of 14-GHz backscattering from ocean-like surfaces, described by a Pierson-Moskowitz spectrum, is presented. Surfaces rough in one and two dimensions are investigated, with Monte Carlo simulations performed efficiently through the use of the canonical-grid expansion in an iterative method of moments. Backscattering cross sections are illustrated for perfectly conducting surfaces at angles from 0 to 60/spl deg/ from normal incidence, and the efficiency of the numerical model enables the composite surface theory to be studied in the microwave frequency range for realistic one-dimensional (1D) surface profiles at low wind speeds (3 m/s). Variations with surface spectrum low-frequency cutoff (ranging over spatial lengths from 21.9 to 4.29 cm) are investigated to obtain an assessment of composite surface model accuracy. The 1D surface results show an increase in hh backscatter returns as surface low-frequency content is increased for incidence angles larger than 30/spl deg/, while /spl nu//spl nu/ returns remain relatively constant, all as predicted by the composite surface model. Similar results are obtained for surfaces rough in two dimensions, although the increased computational complexity allows maximum surface sizes of only 1.37 m to be considered. In addition, cross-polarized cross sections are studied in the two-dimensional (2D) surface case and again found to increase as surface low-frequency content is increased. For both 1D and 2D surfaces, backscattering cross sections within 20/spl deg/ of normal incidence are found to be well matched by both Monte Carlo and analytical physical optics (PO) methods for all low-frequency cutoffs considered, and a comparison of analytical PO and geometrical optics (GO) results indicates an appropriate choice of the cutoff wavenumber in the composite surface model to insure an accurate slope variance for use in GO predictions. This choice of cutoff wavenumber is then applied in the composite surface theory for more realistic ocean spectra and compared with available experimental data.

A numerical study of the composite surface model for ocean scattering

A numerical study of ocean backscattering for surfaces rough in two dimensions is presented. The numerical model is based on Monte Carlo simulation using the sparse matrix-flat surface iterative approach with canonical grid (SMFSIA/CAG), which is a more efficient version of the method of moments that allows large two dimensional surfaces to be treated. Backscattering cross sections are illustrated for perfectly conducting power law spectrum ocean surface models at angles from 0 to 60 degrees from normal incidence. Variations with surface spectrum low frequency cutoff (ranging over spatial lengths from 64 /spl lambda/ to 2 /spl lambda/) are investigated, and demonstrate the accuracy of the composite surface model.

A numerical study of ocean polarimetric thermal emission

A numerical model for polarimetric thermal emission from penetrable ocean surfaces rough in two directions is presented. The numerical model is based on Monte Carlo simulation with an iterative version of the method of moments (MOM) known as the sparse matrix flat surface iterative approach (SMFSIA), extended to the penetrable surface case through a numerical impedance boundary condition (NIBC) method. Since the small U/sub B/ brightnesses obtained from ocean surfaces (usually less than 1.5 K, or 0.5% of a 300-K physical temperature) require extremely accurate simulations to avoid large errors, a parallel version of the algorithm is developed to allow matrix elements to be integrated accurately and stored. The high accuracy required also limits simulations to near flat surface profiles, so that only high-frequency components of the ocean spectrum are modeled. Variations in nadir polarimetric brightness temperatures with spectrum low- and high-frequency cutoffs show the Bragg (or shortwave) portion of the spectrum to contribute significantly to emission azimuthal signatures, as predicted by the small perturbation or composite surface approximate theories. Quantitative comparisons with approximate methods show perturbation theory to slightly overestimate linear brightness temperatures, but accurately predict their azimuthal variations, while physical optics (PO) significantly underestimates both linear brightness temperatures and their azimuthal variations. Further simulations with the numerical model allow sensitivities to ocean spectrum models to be investigated and demonstrate the importance of an accurate azimuthal description for the ocean spectrum.

Monte Carlo simulations of large-scale composite random rough-surface scattering based on the banded-matrix iterative approach

Scattering of a TE incident wave from a perfectly conducting one-dimensional composite random rough surface is studied. A composite random surface contains roughness of more than one scale. With the recently developed efficient numerical technique known as the banded-matrix iterative approach, we are able to study large-scale composite roughness with two correlation lengths that are many times different from each other. It is shown that small-scale roughness, with its large rms slope, rather than large-scale roughness, with its small rms slope, can dominate bistatic scattering. It is also shown that backscattering enhancement can also exist in a composite rough surface.

Surface roughness, radar backscatter, and visible and near‐infrared reflectance in Death Valley, California

The vast alluvial fans of Death Valley, California, provide an ideal environment to examine the remote sensing measurement of geologic surfaces. One of the objectives of the shuttle imaging radar C (SIR-C) program in Death Valley is detection of the variation in surface microtopography with age of the surface. We present results of extensive field measurements of surface roughness together with an analysis of the effects of the surface microtopography on radar backscatter and visible and near-infrared (VNIR) reflectance as measured by aircraft and satellite sensors. This subject is addressed in both the forward and inverse sense: surface simulation and forward modeling are used to determine expected roughness effects, while a method of inverse analysis that uses finite impulse response (FIR) filters is used to assess the potential for inversion of multifrequency, polarimetric, synthetic aperture radar (SAR), and multispectral VNIR imagery for surface roughness. The interaction of radar and VNIR radiation with the Death Valley surfaces is complicated. Simple roughness parameters such as rms height, and slope and offset of surface power spectra, do not represent a sufficiently complete description of surface roughness to predict the radar or VNIR signature uniquely. Multiple scattering, which is controlled to a large extent by aspects of the phase of the surface Fourier transform, also exerts a controlling influence on the observed signal. The phase aspect of surface roughness has not been considered in existing roughness characterization. Our inversions demonstrate retrieval of roughness parameters with almost equal success from both SAR data and Landsat thematic mapper (TM) data and indicate much potential for joint SAR/VNIR data analysis. The solutions are not, however, very stable and include effects of additional parameters such as intermediate-scale topography and vegetation cover which masquerade as roughness variation. In designing a stable inversion of more general applicability, the multifrequency and polarimetric aspect of SIR C data is important. Nevertheless, high-resolution roughness recovery will probably require hierarchical analysis of radar and optical images, and also SAR acquisition at multiple look angles and directions.

Bistatic scattering and emissivities of random rough dielectric lossy surfaces with the physics-based two-grid method in conjunction with the sparse-matrix canonical grid method

Bistatic EM wave scattering from 2-D lossy dielectric random rough surfaces (3-D scattering problem) with large permittivity is studied. For media with large permittivities, the fields can vary rapidly on the surface. Thus, a dense discretization of the surface is required to implement the method of moments (MoM) for the surface integral equations. Such a dense discretization is also required to ensure that the emissivity can be calculated to the required accuracy of 0.01 for passive remote sensing applications. We have developed a physics-based two-grid method (PBTG) that can give the accurate results of the surface fields on the dense grid and also the emissivities. The PBTG consists of using two grids on the surface, the coarse grid and the required dense grid. The PBTG only requires moderate increase in central processing unit (CPU) and memory. In this paper, the numerical results are calculated by using the PBTG in conjunction with the sparse-matrix canonical grid (SMCG) method. The computational complexity and memory requirement for the present algorithm are O(N/sub scg/log(N/sub scg/)) and O(N/sub scg/), respectively, where N/sub scg/ is the number of grid points on the coarse grid. Numerical simulations are illustrated for root mean square (rms) height of 0.3 wavelengths and correlation length of 1.0 wavelength. The relative permittivity used is as high as (17+2i). The numerical results are compared with that of the second-order small perturbation method (SPM). The comparisons show that a large difference in brightness temperature exists between the SPM and numerical simulation results for cases with moderate rms slope.