Effect of shadowing on electromagnetic scattering from rough oceanwavelike surfaces at small grazing angles

A hybrid moment-method/geometrical-theory-of-diffraction technique (MM/GTD) has been implemented to numerically calculate the electromagnetic scattering from one-dimensionally rough surfaces at extreme illumination angles (down to 0° grazing). The hybrid approach allows the extension of the modeled scattering surface to infinity, avoiding the artificial edge diffraction that prevents use of the standard moment method at the smallest grazing angles, Numerical calculation of the backscattering from slightly rough large-scale surfaces approximating ocean wave features shows that roughness in strongly shadowed regions can contribute significantly to the total backscatter at vertical polarization. This is observed when the shadowing obstacle is several wavelengths high, and the magnitude of the shadow-region contribution does not depend on the radius-of-curvature of the shadowing feature. Strongly shadowed roughness does not significantly contribute to the backscatter at horizontal polarization, although weakly shadowed roughness near the incidence shadow boundary does. The calculations indicate that a shadowing-corrected two-scale model may be able to predict the distributed-surface portion of the sea-surface scattering from the ocean surface at grazing angles down to about 15°, but at lower grazing the shadowing and large-scale curvature of the surface prevent the establishment of a Bragg resonance and invalidate the model     

Monte Carlo simulations of large-scale one-dimensional randomrough-surface scattering at near-grazing incidence: Penetrable case

Scattering from dielectric one-dimensional (1-D) random rough surfaces at near grazing incidence is studied for both TE and TM cases. To obtain accurate results at incidence angles of 80°-85°, we use long surface lengths of up to 1000 wavelengths. Numerical results are illustrated for dielectric surfaces corresponding to soil surfaces with various moisture contents. Results indicate that TM backscattering is much larger than that of TE backscattering. The ratio of TM to TE backscattering increases as a function of soil moisture and can be used as an indicator of soil moisture in remote sensing applications. However, the ratio of TM to TE backscattering is much lower than that predicted by the small perturbation method. To facilitate computation of scattering by such long surfaces, the previously developed banded-matrix iteration approach/canonical grid method (BMIA/CG) has been extended to dielectric surfaces. The numerical algorithm consists of translating the nonnear-field interaction to a flat surface and the interaction subsequently calculated by fast Fourier transform (FFT)     

A numerical study of low-grazing-angle backscatter from ocean-likeimpedance surfaces with the canonical grid method

A numerical study of 14-GHz low-grazing-angle (LGA) backscattering from ocean-like surfaces described by a Pierson-Moskowitz spectrum is presented. Surfaces rough in one dimension are investigated with Monte Carlo simulations performed efficiently through use of the canonical grid expansion in an iterative method of moments. Backscattering cross sections are illustrated at angles from 81° to 89° from normal incidence under the impedance boundary condition (IBC) approximation with the efficiency of the numerical model enabling sufficiently large profiles (8192 λ) to be considered so that angular resolution problems can be avoided. Variations with surface spectrum low-frequency cutoff (ranging over spatial lengths from 175.5 m to 4.29 cm) at 3 m/s wind speed are investigated and initial assessments of the small perturbation method (SPM), composite surface theory, operator expansion method (OEM), small slope approximation (SSA), and curvature corrected SPM predictions are performed. Numerical results show an increase in horizontal (HH) backscatter returns as surface low-frequency content is increased while vertical (VV) returns remain relatively constant, as expected, but none of the approximate models considered are found to produce accurate predictions for the entire range of grazing angles. For the cases considered, HH scattering is always observed to be below VV, further demonstrating the importance of improved hydrodynamical models if “super-event” phenomena are to be modeled     

Fully polarimetric bistatic radar scattering behavior of forestedhills

The bistatic radar scattering measurements of forested hills were performed at grazing incidence and at azimuth scattering angles from 28° to 66° from the forward scatter plane. Using pulse-to-pulse switching between orthogonal transmitted polarizations, the radar simultaneously measures two orthogonally polarized components of the scattered wave to obtain full polarimetric information about the scattering process. These are the first fully polarimetric terrain clutter measurements to be conducted at large bistatic angles. The complete Stokes matrix, computed by averaging successive realizations of the polarization scattering matrix, is used to examine the polarization sensitivity of the bistatic clutter. It is found that the polarization state of the EM wave scattered out of the plane of incidence strongly depends on the polarization orientation of the incident electric field. Unlike the monostatic case, these two incident wave polarization states are found to produce substantially different scattered wave behavior when trees are viewed at large bistatic angles. Scattered fields resulting from vertically oriented incident fields are found to be highly polarized and to produce bistatic clutter power levels that are strongly dependent on the polarization of the receiving antenna. In contrast, horizontally oriented incident fields are found to produce weakly polarized scattered waves with bistatic clutter power levels that are insensitive to the polarization of the receiving antenna     

C-band backscatter signatures of old sea ice in thecentral Arctic during freeze-up

Radar backscatter signatures of old sea ice in the central Arctic have been measured and analyzed. A ship-mounted scatterometer was used to acquire backscattering coefficients at 5.4 GHz in the four linear polarization states and at incidence angles between 20° and 60°. Detailed in situ characterizations of the snow and ice were also made to enable comparison with theoretical backscatter models. Freeze-up conditions were prevalent during the experiment. The average backscattering coefficient was found to increase when the temperature of the ice surface layer decreased. The semi-empirical backscatter model is used to evaluate the measurements and shows that the backscatter increase is due to an increasing penetration depth, causing the volume scattering to increase. Model predictions also show that both surface and volume scattering contribute significantly at incidence angles of 20° to 26°. At these incidence angles, the dominating scattering mechanism changes from surface to volume scattering as the ice surface temperature decreases     

Propagation and depolarization of an arbitrarily polarized waveobliquely incident on a slab of random medium

The problem of how a slab of random medium affects the propagation and polarization of an arbitrarily polarized obliquely incident electromagnetic wave is investigated. The general formulation is given by using vector radiative transfer theory. The multiple scattering solution is compared with the analytical first-order solution when the optical distance is small and the comparison shows that the results are consistent with each other. The multiple scattering results for a left-handed circularly polarized incident wave show that the transmitted wave is still right-handed near the backscattering direction. The scattering signature obtained shows that for normal incidence one can obtain a maximum backscattered power if an arbitrarily oriented linearly polarized incident wave is chosen and that for an incident angle of 30°, a minimum backscattered power can be obtained if a linearly polarized incident wave is oriented at 45° or 135°     

Electromagnetic modeling of multipath scattering from breakingwater waves with rough faces

The low-grazing-angle (LGA) backscattering from one-dimensionally rough surface profiles approximating breaking water waves with roughened front faces has been numerically examined. The added front-face roughness approximates that expected from wind generation. The reference "exact" backscattering was found using a numerical technique based on the moment method. A model-based approach to predict the backscattering was also implemented. In this, the crest scattering was found directly using the moment method, the multipath scattering was modeled using physical optics, and the distributed-surface scattering from the small-scale roughness was found from the two-scale model. The calculations show that the roughness adds incoherent components to both the vertically (VV) and horizontally (HH) polarized scattering cross sections. At VV, this is due to the random scattering from the small-scale roughness, while at HH it results from random changes in the multipath interference due to the large-scale roughness. As the mechanisms for the incoherent scattering are independent, it is difficult to predict the magnitude of the HH-to-VV backscattering ratio that will occur with specific realizations of the roughness from the underlying breaking-wave shape alone, particularly with large rms roughness added. Overall, the model-based calculations give a good prediction of both the coherent and incoherent scattering coefficients     

95-GHz scattering by terrain at near-grazing incidence

This study, consisting of three complimentary topics, examines the millimeter-wave backscattering behavior of terrain at incidence angles extending between 70 and 90°, corresponding to grazing angles of 20° to 0°. The first topic addresses the character of the statistical variability of the radar backscattering cross section per unit area σ_A. Based on an evaluation of an extensive data set acquired at 95 GHz, it was determined that the Rayleigh fading model (which predicts that σ_A is exponentially distributed) provides an excellent fit to the measured data for various types of terrain covers, including bare surfaces, grasses, trees, dry snow, and wet snow. The second topic relates to the angular variability and dynamic range of the backscattering coefficient σ⁰, particularly near grazing incidence. We provide a summary of data reported to date for each of several types of terrain covers. The last topic focuses on bare surfaces. A semi-empirical model for σ⁰ is presented for vertical (VV), horizontal (HH), and cross (HV) polarizations. The model parameters include the incidence angle &thetas;, the surface relative dielectric constant ϵ, and the surface roughness ks, where k=2π/λ and s is the surface root mean square (RMS) height     

Low-grazing scattering from breaking water waves using an impedanceboundary MM/GTD approach

The radar backscattering from water waves of various degrees of breaking Is numerically examined. A hybrid moment method geometrical theory of diffraction (MM/GTD) technique previously used for small-grazing scattering from perfectly conducting surfaces is reformulated using impedance boundary conditions, allowing the treatment of large (but finite) conductivity scattering media such as sea water. This hybrid MM/GTD approach avoids the artificial edge effects that limit the standard moment method when applied to rough surfaces, allowing the calculation of the scattering at arbitrarily small grazing angles. Sample surfaces are obtained through the edge-detection of video stills of breaking waves generated in a wave tank. The numerical calculations show that the strength of the backscatter is closely associated with the size of the plume on the breaking wave. Strong interference appears in the both horizontal (HH) and vertical (VV) backscatter when the surfaces are treated as perfectly conducting. The VV interference is dramatically reduced when a sea water surface is used, but the HH interference is unaffected. The interference leads to HH/VV ratios of up to 10 dB. The behavior of the scattering is consistent with the multipath theory of sea-spike scattering     

A theory of wave scattering from an inhomogeneous layer with an irregular interface

Bistatic wave scattering from a layer of Rayleigh scatterers with an irregular interface is investigated by combining the doubling method in volume scattering with the Kirchhoff method in rough surface scattering. Theoretical results are shown illustrating the effect of the rough interface. It is found that for scattered and incident angles near the vertical, the rough interface causes a substantial increase relative to the plane interface in both the like and cross-scattering coefficients over all azimuth angles. However, for large scattered and incident angles, the reverse is true except for azimuth angles around the specular direction. It is interesting to note that while one dominant peak of the like polarized scattering coefficient occurs along the specular direction, two dominant peaks of the cross-polarized scattering coefficient may appear symmetrically with respect to the specular direction. In backscattering, the surface roughness causes a peak to appear in both the like and cross-scattering coefficients at near vertical incidence and also a decrease of these coefficients at large incidence angles.     

A numerical study of backscattering from time-evolving seasurfaces: comparison of hydrodynamic models

Results from a Monte Carlo simulation of backscattering from one-dimensional (1-D) time-evolving sea surface models are reported. A numerical electromagnetic method based on an accelerated forward-backward approach is used to calculate backscattered returns from impedance surface profiles at incidence angles of 0° (normal), 40°, and 80°. Surfaces are initialized as realizations of a Pierson-Moskowitz spectrum and then stepped in time through a numerical hydrodynamic method. Results from three distinct hydrodynamic methods are compared: a linear evolution, the "improved linear representation" of Creamer et al. (1989), and the "Watson-West" approach of West et al. (1987). Instabilities in the West model due to formation of steep wave features limit the study to L-band backscattering for wind speeds less than 2 m/s, so that the surfaces considered are only slightly rough on an electromagnetic scale. The small slope approximation for electromagnetic scattering is shown to provide reasonable predictions in this limit. Statistics of the resulting surface profiles and backscattered fields are compared for the three models and are found to be similar in most respects. Backscattered field Doppler spectra, however, show differences, with the West model apparently capturing more nonlinear interactions in the surface evolution     

Ku-band backscatter from the Cowlitz River: Bragg scattering with and without rain

Ku-band backscatter from the Cowlitz River in southwestern Washington State was measured for incidence angles from 0/spl deg/ to 80/spl deg/. The measurements were made for light-wind conditions with and without rain. In rain-free conditions, Bragg scattering was the dominant scattering mechanism for both horizontal (HH) and vertical (VV) polarizations out to 75/spl deg/, beyond which the SNR dropped very low at HH. When a light rain was falling on the river, the cross section increased substantially at moderate incidence angles. Doppler spectra taken during rain showed that VV polarized backscatter is primarily from Bragg scattering from ring waves, while HH polarization scatters from both ring waves and stationary splash products, depending on the incidence angle. From the VV polarized measurements, surface wave height spectrum for ring waves is inferred for light rains. Finally, a change in spectral properties was observed when rain changed to hail.     

Ray analysis of low-grazing scattering from a breaking water wave

Low-grazing-angle backscattering from a modeled breaking-wave surface profile has been calculated using a ray-optical approach and compared with reference scattering found using an extended moment method. The calculations show that interference between the direct backscatter from the breaking plume and multipath scattering between the plume and wave face can lead to the HH-to-VV polarization-backscattering ratios of greater than 9 dB that characterize sea-spike events. The multipath effects can be accurately predicted from simple reflection from the front face at the smallest grazing angles. At higher angles, diffraction from rapid changes in the surface curvature must also be considered     

Polarimetric scattering indexes and information entropy of the SAR imagery for surface monitoring

The Mueller matrix solution and eigenanalysis of the coherency matrix for completely polarimetric scattering have been applied to the analysis of synthetic aperture radar (SAR) imagery. Copolarized and cross-polarized backscattering for any polarized incidence can be obtained. The polarization index is usually defined as a parameter to classify the difference between polarized scattering signatures from the terrain surfaces. The eigenvalues of the coherency matrix and information entropy are derived to directly relate with measurements of the copolarized and cross-polarized indexes. Thus, it combines the Mueller matrix simulation, the information entropy of the coherence matrix, and two polarization indexes together and yields a quantitative evaluation for surface classification in the SAR imagery. This theory is applied to analysis of the AirSAR images and field measurements.     

Low-grazing-angle scattering from 3-D breaking water wave crests

The low-grazing-angle (high incidence angle) microwave back scattering from three-dimensional (3-D) surfaces approximating the crests of plunging-breaker water waves has been numerically found using the multilevel fast multipole algorithm. The test profiles were synthesized from a series of two-dimensional (2-D) profiles that represent the time evolution of a breaker. The results show that the strong cancellation of the vertically polarized backscattering (VV) midway through breaking that was previously identified with the 2-D profiles is maintained when the azimuthal variation of the 3-D wave is included. An optical-based model confirms that this is due to interference between back reflection from points on the forming jet and cavity of the wave. This is matched by constructive interference at horizontal polarization (HH), leading to HH-to-VV backscattering ratios that are much larger than unity. This effect remains when the azimuthal look angle is moved from directly upwave. When looking upwave, the interference disappears later in breaking when the fully formed jet shadows the cavity region. However, it returns when looking sufficiently away from directly upwave so that the cavity again becomes visible. The HH-to-VV ratios are typically greater than unity at this time, although HH cancellation can appear very late in the breaking when the round-trip distances to the jet and cavity specular points are sufficiently different.     

高斯粗糙表面低掠入射散射特性研究

该文针对传统解析法不能有效求解低掠入射下粗糙表面散射特性的问题,提出了一种高阶解析法,该算法基于表面散射场的高阶分量和表面轮廓函数的高阶Taylor级数展开。利用该算法,定量比较了同极化的高、低阶散射系数,讨论了低掠入射下不同粗糙度的散射特性,分析了低掠入射下高阶微扰法和高阶基尔霍夫法求解高斯粗糙面的修正效应,得出了高阶解析法可以很好求解低掠入射问题的结论。最后,还研究了同极化散射指数与掠入射角幂函数的拟合问题,修正了极化散射指数的经典表达式。     

Experimental studies of bistatic scattering from two-dimensionalconducting random rough surfaces

Despite the recent development of analytical and numerical techniques for problems of scattering from two-dimensional rough surfaces, very few experimental studies were available for verification. The authors present the results of millimeter-wave experiments on scattering from two-dimensional conducting random rough surfaces with Gaussian surface roughness statistics. Machine-fabricated rough surfaces with controlled roughness statistics were examined. Special attention was paid to surfaces with large rms slopes (ranging from 0.35 to 1.00) for which enhanced backscattering is expected to take place. Experimentally, such enhancement was indeed observed in both the copolarized and cross-polarized returns. In addition, it was noticed that at moderate angles of incidence, the scattering profile as a function of observation angle is fairly independent of the incident polarization and operating frequency. This independence justifies the use of the geometric optics approximation embodied in the Kirchhoff formulation for surfaces with large surface radius of curvature. When compared with the experimental data, this analytical technique demonstrates good agreement with the experimental data     

Radar scattering behavior of estuarine outflow plumes

We present results of dual-polarized radar scattering measurements of the Chesapeake Bay outflow plume. Near-unity polarization ratios (ratios of horizontally polarized radar echoes over vertically polarized ones) are observed in large incidence angle (60/spl deg/ to 80/spl deg/) radar echoes from the outflow plume and its frontal boundary (normally referred to as a front) under strong surface current convergence (0.008-0.02 S/sup -1/), suggesting the existence of steepened and breaking waves in the regions. Cumulative distribution functions of the horizontally polarized radar returns from the front show approximately 90% of the radar echoes are from steepened and breaking waves. Vertically polarized echoes do not show this effect. These experimental results substantiate early modeling investigators' speculation of featured scattering contributing to horizontally polarized radar signatures of oceanic fronts. Our results also suggest that horizontal radar polarization can be used to remotely sense additional hydrodynamic processes such as wave trapping, blocking, and breaking near oceanic fronts better than what is possible with only vertical polarization.     

Multiple scattering and depolarization by a randomly rough Kirchhoff surface

A matrix approach has been developed to compute bistatic scattering coefficients which include shadowing and multiple scattering effects for a randomly rough Kirchhoff surface. The method permits the computation of these coefficients in terms of the existing single-scatter bistatic scattering coefficients. Thus the effects of multiple scattering are readily recognized from the expressions obtained. The bistatic scattering coefficients are shown to satisfy energy conservation to at least two significant figures. It is observed that while polarized backscattering is dominated by the single-scattering process, the depolarized backscattering is due to multiple scattering. Unlike depolarization by slightly rough surfaces or volume scattering, the angular behavior of the depolarized backscattering is similar to that of the polarized backscattering. The transitional behavior of the relative dominance between single and multiple scattering for the polarized and depolarized scattering coefficient as a function of the azimuth angle is illustrated.     

A numerical model for electromagnetic scattering from sea ice

A numerical model for scattering from sea ice based on the finite difference time domain (FDTD) technique is presented. The sea ice medium is modeled as consisting of randomly located spherical brine scatterers with a specified fractional volume, and the medium is modeled both with and without a randomly rough boundary to study the relative effects of volume and surface scattering. A Monte Carlo simulation is used to obtain numerical results for incoherent υυ backscattered normalized radar cross sections (RCSs) in the frequency range from 3 to 9 GHz and for incidence angles from 10° to 50° from normal incidence. The computational intensity of the study necessitates an effective permittivity approach to modeling brine pocket effects and a nonuniform grid for small scale surface roughness. However, comparisons with analytical models show that these approximations should introduce errors no larger than approximately 3 dB. Incoherent υυ cross sections backscattered from sea ice models with a smooth surface show only a small dependence on incidence angle, while results for sea ice models with slightly rough surfaces are found to be dominated by surface scattering at incidence angles less than 30° and by scattering from brine pockets at angles greater than 30°. As the surface roughness increases, surface scattering tends to dominate at all incidence angles. Initial comparisons with measurements taken with artificially grown sea ice are made, and even the simplified sea ice model used in the FDTD simulation is found to provide reasonable agreement with measured data trends. The numerical model developed ran be useful in interpreting measurements when parameters such as surface roughness and scatterer distributions lie outside ranges where analytical models are valid