Laboratory backscatter measurements over urea ice with a snow coverat Ku band

Indoor laboratory facilities were used to measure radar backscatter at Ku band (13.9 GHz) over urea ice, which has been shown to be structurally similar to sea ice. Data were collected at angles of incidence from normal to 55°, over very thin (0 to 9 cm) ice, snow-covered ice, and ice with a hooded snow cover. The laboratory proved to be useful in creating and controlling specific physical properties of ice while keeping all other variables constant, a difficulty with measurements collected in the field. It was found that surface scattering and the dielectric constant are the dominant factors that cause variations (up to 15 dB) in the measured backscatter. The addition of a snow cover increased the surface roughness of the smooth ice, increasing the backscatter at 20° incidence angle by about 11 dB and decreasing the backscatter at normal incidence by about 6 dB. The subsequent flooding of this snow layer increased the backscatter at all angles of incidence due to the increased dielectric constant of the wet slush layer. These results indicate the importance of the snow layer in influencing the surface characteristics of the ice sheet, which in turn modifies the backscattered signal     

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     

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     

Tilt modulation of high resolution radar backscatter crosssections: unified full wave approach

The unified full wave approach is used to determine the tilt modulation of the like- and cross-polarized (high-resolution) radar backscatter cross sections for the rough sea surface. Real or synthetic aperture radars (SARs) with small effective footprints (resolution cells) are considered. Since the unified full-wave approach accounts for Bragg scattering as well as specular point scattering in a self-consistent manner, it is not necessary to adopt a two-scale model for the rough sea surface. The sea surface slope probability density function is assumed to be Gaussian. The backscattering cross sections are evaluated for all angles of incidence (normal to grazing). For tilts in the plane of incidence, the modulation of all the cross sections is largest at angles of incidence of 10°. The cross-section modulation due to tilts perpendicular to the plane of incidence critically depends on the incident and scattered polarizations. The effective filtering of the large-scale spectral components of the rough sea surface by the high-resolution radar is accounted for, and the dependence of the cross-section tilt modulation on the size of the effective footprint is determined     

Springtime C-band SAR backscatter signatures of LabradorSea marginal ice: measurements versus modeling predictions

During the March 1987 Labrador Ice Margin Experiment (LIMEX '87) two independent investigations were conducted to determine the C-band backscattering cross section of the marginal pack ice along the Newfoundland coast. In one experiment, data from a recently calibrated C-band airborne scatterometer were combined with C-band synthetic aperture radar (SAR) data to measure the normalized scattering cross section of the ice at incidence angles from 10° to 74° to within ±2 dB. In the other experiment, detailed measurements of ice surface roughness and surface properties were made and the radar cross sections were predicted from a scattering model. In the present study, measured and model results are combined and shown to be fully compatible. By extension, the results are expected to apply to any rubbled sea-ice surface when surface scattering dominates     

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     

A Monte-Carlo FDTD Technique for Rough Surface Scattering

A Monte-Carlo finite-difference time-domain (FDTD) technique is developed for wave scattering from randomly rough, one-dimensional surfaces satisfying the Dirichlet boundary condition. Both single-scale Gaussian and multiscale Pierson-Moskowitz surface roughness spectra are considered. Bistatic radar cross sections are calculated as a function of scattering angle for incident angles of 0, 45, 70, and 80 degrees measured from the vertical. The contour path FDTD method is shown to improve accuracy for incident angles greater than 45 degrees. Results compare well with those obtained using a Monte-Carlo integral equation technique     

Unified full wave solutions to interpret Apollo lunar surface data

Bistatic radar experiments carried out by Tyler and Howard during the Apollo 14, 15, and 16 missions provide a very useful dataset with which to compare theoretical models and experimental data. Vesecky et al. (1988) report that their model for near grazing angles compares favorably to experimental data. However, for angles of incidence around 80°, all the analytical models considered by Vesecky et al. predict values for the quasi-specular cross sections that are about half the corresponding values taken from the Apollo 16 data. In this work, questions raised by this discrepancy between the reported analytical and experimental results are addressed. The unified full wave solutions are shown to be in good agreement with the bistatic radar data taken during Apollo 14 and 16 missions. Using the full wave approach, the quasi-specular contributions to the scattered field from the large scale surface roughness as well as the diffuse Bragg-like scattering from the small scale surface roughness are accounted for in a unified self-consistent manner. Since the full wave computer codes for the scattering cross sections contain ground truth data only, it is shown how it can be readily used to predict the rough surface parameters, based on the measured data     

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     

Determination of volume and surface scattering from saline iceusing ice sheets with precisely controlled roughness parameters

Experiments were performed at the U.S. Army Cold Regions Research and Engineering Laboratory (CRREL) in Hanover, NH, to precisely determine the relative contributions of surface and volume scattering from saline ice that has well-known surface roughness characteristics. The ice growth phase of the experiment made use of two 6-ft diameter tanks and a 6-ft diameter mold with known roughness statistical parameters of rms height=0.25 cm and Gaussian correlation (correlation length=2.0 cm). One tank was used for growing a moderately thick saline ice sheet with very smooth surface, and the other was used for growing a thin layer of freshwater ice over the surface mold. The latter resulted in a layer with one statistically known rough boundary and one smooth boundary. Wide-bandwidth, multiple incidence angle backscattering measurements were performed, first on the bare saline ice sheet and then on the same sheet after the thin freshwater ice sheet was placed on top of it. Results indicate that the surface scattering dominates over saline ice volume scattering at all frequencies for low incidence angles for both the very smooth and Gaussian rough surfaces. The significance of volume scattering depends strongly on angle of incidence, frequency, volume scattering albedo, surface roughness, and surface correlation function     

On the use of finite surfaces in the numerical prediction of roughsurface scattering

Method of moments (MOM)-based Monte Carlo calculations are widely used in determining the average radar cross section of randomly rough surfaces. It is desirable in these numerical calculations to truncate the scattering surface into as short a length as possible to minimize the solution time. However, truncating the surface tends to change the solution for the surface fields near the truncation points and may alter the scattered far fields. In this paper, these end effect errors are examined for one-dimensional (i.e., grooved or corduroy) surfaces which are Gaussian distributed in height and have either a Gaussian or a Pierson-Moskowitz spectra. In the case of the Pierson-Moskowitz type surface, it is shown that a relatively short surface of 80-120 wavelengths can be used to obtain the average backscattered radar cross section for backscattering angles as large as 60° from normal. For a comparatively smooth Gaussian surface, on the other hand, its is shown that the truncation effects can be very significant at moderate backscattering angles. Also, great care should be taken when examining the scattering from Gaussian surfaces which are dominated by specular scattering. It is shown that in this situation, a very large number of calculations may be needed to obtain a good numerical average     

Analysis of scattering from rough surfaces at large incidenceangles using a periodic-surface moment method

The moment method is used to calculate electromagnetic backscattering from one-dimensionally rough surfaces at near-grazing incidence (angles of incidence up to 89°). A periodic representation of the scattering surface is used to prevent edge effects in the calculated scattering without the use of an artificial illumination weighting function. A set of universal series common to all elements of the moment interaction matrix are derived that allow the efficient application of the moment method to the periodic surface. Comparison with other moment method implementations demonstrates the efficiency of this approach. The scattering from surfaces with Gaussian roughness spectra is calculated at both horizontal and vertical polarizations, and the results are compared with the theoretical predictions of the small-perturbation method (SPM) and Kirchhoff approximation (KA). SPM shows the expected loss of accuracy in predicting the vertically polarized backscattering from small-roughness, short-correlation-length surfaces at large incidence angles. SPM accurately predicts the backscattering from the same type of surface at incidence up to 89° at horizontal polarization, KA provides accurate estimates of the scattering from long correlation-length surfaces as long as the incidence angle is small enough that surface self-shadowing does not occur. When shadowing occurs, KA severely underpredicts vertically polarized backscattering and less severely overpredicts backscattering at horizontal polarization     

Bistatic specular scattering from rough dielectric surfaces

An experimental investigation was conducted to determine the nature of bistatic scattering from rough dielectric surfaces at 10 GHz. This paper focusses specifically on the dependence of coherent and incoherent scattered fields on surface roughness for the specular direction. The measurements, which were conducted for a smooth surface with ks<0.2 (where k=2π/λ and s is the RMS surface height) and for three rough surfaces with ks=0.5, 1.39, and 1.94, included observations over the range of incidence angles from 20° to 65° for both horizontal and vertical polarizations. For the coherent component, the reflectivity was found to behave in accordance with the prediction of the physical optics model, although it was observed that the Brewster angle exhibited a small negative shift with increasing roughness. The first-order solution of physical optics also provided good agreement with observations for hh-polarized incoherent scattering coefficient, but it failed to predict the behavior of the vv-polarized scattering coefficient in the angular range around the Brewster angle. A second-order solution is proposed which appears to partially address the deficiency of the physical optics model     

Incoherent bistatic scattering from the sea surface at L-band

A bistatic electromagnetic wave scattering model for the sea surface is developed to examine its wind dependence property over a wide range of incident angles along the specular direction. This is done by combining an existing scattering model with a sea spectrum recently reported in the literature. In general, electromagnetic wave scattering from a rough surface is dependent on the Fourier transform of the nth power of its height correlation function which can be computed numerically from the surface spectrum. This transform relation indicates that scattering is sensitive not only to the surface spectrum but also to its convoluted properties. Generally, surface scattering is sensitive only to a portion of the surface correlation measured from the origin. The size of this portion is a function of three variables (the incident angle, the surface height standard deviation, and the exploring wavelength) and the rate of decay of the correlation function. The decay rate near the origin of the sea surface correlation is very small, so much so that at L-band this portion is too wide for a two-term approximation of the correlation function. This is true in spite of the fact that the sea surface has a very large rms height. Thus, a scattering model based on geometric optics is generally not applicable at L-band especially at large angles of incidence. An additional finding is that in specular scattering wind dependence is stronger at larger angles of incidence for incident angles between 0 and 70° over the wind speed range of 4 m/s-20 m/s     

Modeling of wind direction signals in polarimetric sea surfacebrightness temperatures

There has been an increasing interest in the applications of polarimetric microwave radiometers for ocean wind remote sensing. Aircraft and spaceborne radiometers have found a few Kelvins wind direction signals in sea surface brightness temperatures, in addition to their sensitivities to wind speeds. However, it was not clear what physical scattering mechanisms produced the observed brightness dependence on wind direction. To this end, polarimetric microwave emissions from wind-generated sea surfaces are investigated with a polarimetric two-scale scattering model, which relates the directional wind-wave spectrum to passive microwave signatures of sea surfaces. Theoretical azimuthal modulations are found to agree well with experimental observations for all Stokes parameters from near nadir to 65° incidence angles. The upwind and downwind asymmetries of brightness temperatures were interpreted using the hydrodynamic modulation. The contributions of Bragg scattering by short waves, geometric optics scattering by long waves and sea foam are examined. The geometric optics scattering mechanism underestimates the directional signals in the first three Stokes parameters, and predicts no signals in the fourth Stokes parameter (V). In contrast, the Bragg scattering was found to dominate the wind direction signals from the two-scale model and correctly predicted the phase changes of the upwind and crosswind asymmetries in T_υ and U from middle to high incidence angles. The phase changes predicted by the Bragg scattering theory for radiometric emission from water ripples is corroborated by the numerical Monte Carlo simulation of rough surface scattering. This theoretical interpretation indicates the potential use of polarimetric brightness temperatures for retrieving the directional wave spectrum of short gravity and capillary waves     

一维粗糙介质分形海面电磁散射的扩展边界条件法

在采用经典扩展边界条件法处理导体分形粗糙面散射的基础上,将此方法推广到了一维粗糙介质分形海面的电磁散射.通过与传统的基尔霍夫近似法计算结果进行比较,验证了本文所给的方法,分析了不同入射角,不同分维和空间波数时海面双站散射振幅角分布的特点.     

Electromagnetic scattering by pyramidal and wedge absorber

Electromagnetic scattering from pyramidal and wedge absorbers used to line the walls of modern anechoic chambers is measured and compared with theoretically predicted values. The theoretical performance for various angles of incidence is studied. It is shown that a pyramidal absorber scatters electromagnetic energy more as a random rough surface does. The apparent reflection coefficient from an absorber wall illuminated by a plane wave can be much less than the normal absorber specifications quoted by the manufacturer. For angles near grazing incidence, pyramidal absorbers give a large backscattered field from the pyramid side-faces or edges. The wedge absorber was found to give small backscattered fields for nuclear-grazing incidence. Based on this study, some new guidelines for the design of anechoic chambers are advocated because the specular scattering models used at present do not appear valid for pyramids that are large compared to the wavelength     

A Numerical Study of the Retrieval of Sea Surface Height Profiles From Low Grazing Angle Radar Data

A numerical study of the retrieval of sea surface height profiles from low grazing angle radar observations is described. The study is based on a numerical method for electromagnetic scattering from 1-D rough sea profiles, combined with the “improved linear representation” of Creamer for simulating weakly nonlinear sea surface hydrodynamics. Numerical computations are performed for frequencies from 2975 to 3025 MHz so that simulated radar pulse returns are achieved. The geometry utilized models a radar with an antenna height of 14 m, observing the sea surface at ranges from 520 to 1720 m. The low grazing angles of this configuration produce significant shadowing of the sea surface, and standard analytical theories of sea scattering are not directly applicable. Three approaches for retrieving sea height profile information are compared. The first method uses a statistical relationship between the surface height and the computed radar cross sections versus range (an incoherent measurement). A second method uses the phase difference between scattering measurements in two vertically separated antennas (“vertical interferometry) in the retrieval. The final technique retrieves height profiles from variations in the apparent Doppler frequency (coherent measurements) versus range and requires that time-stepped simulations be performed. The relative advantages and disadvantages of each of the three approaches are examined and discussed.