Backscattering Radar Cross Section Research Articles

RECONSTRUCTION PERMITTIVITY TENSOR AND PRINCIPAL AXIS FOR UNIAXIAL MEDIUM IN MICROWAVE BAND

The relationship of permittivity tensor of anisotropic medium in principal coordinate system and laboratory coordinate system is given. The characteristic of permittivity tensor of uniaxial anisotropic medium in the laboratory coordinate system is discussed. The transverse permittivity of an anisotropic plate is reconstructed in laboratory coordinate system based on the resonance and polarization characteristics of backscattering radar cross section (RCS) in wide band. Then, a new scheme of reconstructing the principal axis direction for a uniaxial sample plate is proposed, subject to the principal axis is unknown. The backscattering characteristics of a sample plate are discussed when the electromagnetic (EM) wave of different polarization is incident perpendicular to the sample plate. Three sample plates, which are cut perpendicularly to the x � , y � ,a nd zaxes in the laboratory coordinate system, are required. A numerical reconstruction example is given to demonstrate the availability of presented scheme.

The Effect of Sea Surface Slicks on the Doppler Spectrum Width of a Backscattered Microwave Signal.

The influence of a surface-active substance (SAS) film on the Doppler spectrum width at small incidence angles is theoretically investigated for the first time for microwave radars with narrow-beam and knife-beam antenna patterns. It is shown that the requirements specified for the antenna system depend on the radar motion velocity. A narrow-beam antenna pattern should be used to detect slicks by an immobile radar, whereas radar with a knife-beam antenna pattern is needed for diagnostics from a moving platform. The study has revealed that the slick contrast in the Doppler spectrum width increases as the radar wavelength diminishes, thus it is preferable to utilize wavelengths not larger than 2 cm for solving diagnostic problems. The contrast in the Doppler spectrum width is generally weaker than that in the radar backscattering cross section; however, spatial and temporal fluctuations of the Doppler spectrum width are much weaker than those of the reflected signal power. This enables one to consider the Doppler spectrum as a promising indicator of slicks on water surface.

Monostatic lidar/radar invisibility using coated spheres

The Lorenz-Mie theory is revisited to explicitly include materials whose permeability is different from unity. The expansion coefficients of the scattered field are given for light scattering by both homogeneous and coated spheres. It is shown that the backscatter is exactly zero if the impedance of the spherical particles is equal to the intrinsic impedance of the surrounding medium. If spherical particles are sufficiently large, the zero backscatter can be explained as impedance matching using the asymptotic expression for the radar backscattering cross section. In the case of a coated sphere, the shell can be regarded as a cloak if the product of the thickness and the imaginary part of the refractive index of the outer shell is large.

Radar Backscattering Computations for Fractal-Shaped Snowflakes

We propose a model for large snowflakes based on the fractal nature of their particle shapes. Monte Carlo simulations were conducted to make particles with a fractal dimension of 1.8 to 2.4. The roundness parameter for the projected images of the modeled particles was derived, and an average roundness of approximately 0.4 for particles with fractal dimension 2.1 was indicated; this average roundness matched reported values measured for large ice aggregates. The finite difference time domain method was used to calculate the backscattering cross-sections of ice particles with a fractal dimension of 2.1 and a particle diameter of up to ∼20 mm at microwave frequencies of 95 GHz, 35 GHz, and 9.8 GHz. The results were compared with those of equivalent-volume spheres and randomly oriented equivalent-volume hexagonal columns. Our snowflake model had smaller values of radar backscattering cross-sections than did the equivalent-volume spheres in the size range out of the Rayleigh regime. Furthermore, large differences in backscattering cross-sections between the snowflake model and the equivalent-volume hexagonal column were confirmed, in particular at a frequency of 35GHz.

Radar backscattering properties of nonspherical ice crystals at 94 GHz

The millimeter wavelength radar backscattering properties at 94 GHz for six nonspherical ice crystals, which include hexagonal column, hollow, plate, bullet rosette, aggregate, and droxtal with 46 maximum dimensions ranging from 2 to 10,500 μm, are investigated using the discrete dipole approximation (DDA) method and Lorenz‐Mie theory. It is found that the radar backscattering cross sections are sensitive to ice crystal habits and their representations, which use spherical particles with equivalent maximum dimension, volume, projected area, or the ratio of volume to projected area to model nonspherical ice crystals for the Lorenz‐Mie theory. The radar backscattering cross sections of the six nonspherical ice crystals from the DDA method are further parameterized as functions of maximum dimensions of ice crystals. The results from the parameterizations agree well with those computed from the DDA method. Moreover, the mean radar backscattering cross sections derived by averaging the results from the parameterizations over gamma distributions for ice clouds are consistent with those from the DDA method. The parameterizations are applied to derive the coefficients for the relationships between equivalent radar reflectivity factor and ice water content for ice clouds consisting of the six nonspherical ice crystal habits or a mixture of habits. The coefficients from the parameterizations are close to those from the DDA method. Both of them are sensitive to ice crystal habits. The pronounced differences among the relationship between equivalent radar reflectivity factor and ice water content for an ice cloud with a mixture of ice crystal habits, which has been extensively used for solar and infrared retrievals of ice cloud properties, and several previous relationships further confirm their sensitivity to microphysical properties of ice clouds.

Application of rational function approximation technique to hybrid FE/BI/MLFMA for 3D scattering

In this article, the rational function approximation technique (RFAT) is applied to the hybrid finite-element/boundary-integral/multilevel fast multipole algorithm (FE/BI/MLFMA) to acquire wide-band and wide-angle backscatter radar-cross-section (RCS) by complex targets. The two approaches of using the rational function approximation technique, asymptotic waveform evaluation (AWE) and model-based parameter estimation (MBPE), both have been investigated and compared by theoretical analysis and numerical experiments. The numerical results acquired by the developed computing algorithm of integrating the hybrid FE/BI/MLFMA with the RFAT are presented in the article, demonstrating that the rational function approximation technique can greatly speed up the hybrid FE/BI/MLFMA to acquire wide-band and wide-angle backscatter RCS by complex targets. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.

Analyses of internal solitary waves generated at the Columbia River plume front using SAR imagery

Internal solitons generated at the Columbia River plume front during ebb tide are displayed on a synthetic aperture radar (SAR) image taken on 26 July 2004 at 14:24:22 UTC. Scale analyses suggest that these internal solitons belong to the finite‐depth category. A theoretical model, relating the radar backscatter cross section to dynamic parameters of internal solitons in the continuous stratification, is developed. Using the model and background stratification data collected by the River Influences on Shelf Ecosystem (RISE) project in July 2004, we extract the soliton dynamic parameters of the half‐width, amplitude, phase speed, and average energy flux per crest length along a typical section across the internal solitons. The observed stratification is simulated by using a theoretical model parameterized by pycnocline depth, thickness, and maximum buoyancy frequency. The half‐width, amplitude, phase speed, and energy flux of the leading soliton at the section are 119.3 m, 9.3 m, 0.69 m s−1, and 417.4 W m−1 with the uncertainty ranges of ±14.7 m, ±2.6 m, ±0.10 m s−1, and ±281.6 W m−1, respectively. Sensitivity analyses reveal that the extraction of the soliton half‐width from the SAR image is not affected by the stratification. The amplitude is less influenced by the pycnocline thickness than the depth and is independent of the maximum buoyancy frequency.

Suppression of Surface Clutter Interference With Precipitation Measurements by Spaceborne Precipitation Radar

The sidelobe surface clutter along the nadir direction severely interferes with the rain echo in the off-nadir angle observations made using a spaceborne Precipitation Radar (PR). A new method to suppress this sidelobe clutter interference is introduced. A characteristic of the 1-D phased array antenna system is that high sidelobes arise along the beam scan plane. The proposed method tilts the antenna beam scan plane from the nadir such that these high sidelobes would not be directed along the nadir direction, along which a specular component of the backscattering radar cross section of the Earth's surface is dominant. The simulation results using the designed parameters of a Ka-band spaceborne PR indicate the validity of this method, which is also quantitatively confirmed using Tropical Rainfall Measuring Mission/PR observation data sets

A method for retrieving high-resolution surface soil moisture from hydros L-band radiometer and Radar observations

NASA's Earth System Science Pathfinder Hydrospheric States (Hydros) mission will provide the first global scale space-borne observations of Earth's soil moisture using both L-band microwave radiometer and radar technologies. In preparation for the Hydros mission, an observation system simulation experiment (OSSE) has been conducted. As a part of this OSSE, the potential for retrieving useful surface soil moisture at spatial resolutions of 9 and 3 km was explored. The approach involved optimally merging relatively accurate 36-km radiometer brightness temperature and relatively noisy 3-km radar backscatter cross section observations using a Bayesian method. Based on the Hydros OSSE data sets with low and high noises added to the simulated observations or model parameters, the Bayesian method performed better than direct inversion of either the brightness temperature or radar backscatter observations alone. The root-mean-square errors of 9-km soil moisture retrievals from the Bayesian merging method were reduced by 0.5 %vol/vol and 1.4 %vol/vol from the errors of direct radar inversions for the entire OSSE domain of all 34 consecutive days for the low and high noise data sets, respectively. Improvement in soil moisture estimates using the Bayesian merging method over the direct inversions of radar or radiometer data were even more significant for soil moisture retrieval at 3-km resolution. However, to address the representativeness of these results at the global and multiyear scales, further performance comparison studies are needed, particularly with actual field data.

Radar Observations of Comet Nuclei and Comae

Nine comets have been detected with either the Arecibo (12.6 cm wavelength) or Goldstone (3.5 cm) radar systems. Included are six nucleus detections and five detections of echoes from coma grains. The radar backscatter cross sections measured for the nuclei correlate well with independent estimates of their sizes and are indicative of surface densities in the range of 0.5 to 1.0 g cm-3. Like most asteroids, comets appear to have surfaces that are very rough at scales much larger than the radar wavelength. Coma echo models can explain the radar cross sections using grain size distributions that include a substantial population of cm-sized grains. A long term goal of the cometary radar program has been the high resolution imaging of a cometary nucleus. Eleven short period comets are potentially detectable over the next two decades a few of which may be suitable for imaging. We are always waiting for the arrival of a new comet with an orbit that brings it within 0.1 AU of the earth.

Diffraction by a rectangular groove with resistive walls

The plane wave diffraction from a rectangular groove having resistive vertical walls with material loading is analyzed for E polarization by using the Fourier transform technique. The problem is formulated into a modified Wiener–Hopf equation applying boundary conditions. The modified Wiener–Hopf equation is solved via the factorization and decomposition procedure. The scattered field is evaluated by taking the inverse Fourier transform and applying the saddle point method. Numerical results on the backscatter radar cross-section (RCS) patterns are presented for various physical parameters.

Azimuthal harmonic coefficients of the microwave backscattering from a non-Gaussian ocean surface with the first-order SSA model

In this paper, the first-order small slope approximation is applied to a rough sea surface with non-Gaussian statistics, for which the third- and the fourth-order statistics are taken into account in the calculation of the radar cross section. From the Cox and Munk slope distribution, the higher order statistic moments are derived, and behaviors of the corresponding correlation functions are assumed. We show that the fourth order (related to the peakedness or kurtosis) is isotropic, whereas the third order (related to the skewness) has a behavior as cos(/spl psi/), where /spl psi/ is the wave direction along the wind direction. Thus, using the Elfouhaily et al. sea height spectrum, related to the second-order statistics, we show that the normalized radar backscattering cross section (NRBCS) can be expanded as an even Fourier series in cos(n/spl phi/) (where n is a positive integer), for which the harmonic coefficients require only a single integration over the radial distance. This result is consistent with experimental data done for microwave frequencies. In addition, we show for microwave frequencies (like C- and Ku-bands) that the Fourier series can be truncated up to the second order, since the higher order harmonic coefficients vanish. The NRBCS is also compared with empirical backscattering models CMOD2-I3 and SASS-II, valid in C- and Ku-bands, according to the scattering angle and the wind direction. The first-order harmonic coefficient predicts the surface asymmetry along the upwind and downwind directions, whereas the second-order harmonic coefficient describes the surface asymmetry along the upwind and crosswind directions.

Calibration/Validation of an Altimeter Wave Period Model and Application to TOPEX/Poseidon and Jason-1 Altimeters

The altimeter radar backscatter cross-section is known to be related to the ocean surface wave mean square slope statistics, linked to the mean surface acceleration variance according to the surface wave dispersion relationship. Since altimeter measurements also provide significant wave height estimates, the precedent reasoning was used to derive empirical altimeter wave period models by combining both significant wave height and radar backscatter cross-section measurements. This article follows such attempts to propose new algorithms to derive an altimeter mean wave period parameter using neural networks method. Two versions depending on the required inputs are presented. The first one makes use of Ku-band measurements only as done in previous studies, and the second one exploits the dual-frequency capability of modern altimeters to better account for local environmental conditions. Comparison with in situ measurements show high correlations which give confidence in the derived altimeter wave period parameter. It is further shown that improved mean wave characteristics can be obtained at global and local scales by using an objective interpolation scheme to handle relatively coarse altimeter sampling and that TOPEX/Poseidon and Jason-1 altimeters can be merged to provide altimeter mean wave period fields with a better resolution. Finally, altimeter mean wave period estimates are compared with the WaveWatch-III numerical wave model to illustrate their usefulness for wave models tuning and validation.

Simultaneous wind and rain retrieval using SeaWinds data

The SeaWinds scatterometers onboard the QuikSCAT and the Advanced Earth Observing Satellite 2 measure ocean winds on a global scale via the relationship between the normalized radar backscattering cross section of the ocean and the vector wind. The current wind retrieval method ignores scattering and attenuation of ocean rain, which alter backscatter measurements and corrupt retrieved winds. Using a simple rain backscatter and attenuation model, two methods of improving wind estimation in the presence of rain are evaluated. First, if no suitable prior knowledge of the rain rate is available, a maximum-likelihood estimation technique is used to simultaneously retrieve the wind velocity and rain rate. Second, when a suitable outside estimate of the rain rate is available, wind retrieval is performed by correcting the wind geophysical model function for the known rain via the rain backscatter model. The new retrieval techniques are evaluated via simulation and validation with data from the National Centers for Environmental Prediction and the Tropical Rainfall Measuring Mission Precipitation Radar. The simultaneous wind/rain estimation method yields most accurate winds in the sweet spot of SeaWinds' swath. On the outer-beam edges of the swath, simultaneous wind/rain estimation is not usable. Wind speeds from simultaneous wind/rain retrieval are nearly unbiased for all rain rates and wind speeds, while conventionally retrieved wind speeds become increasingly biased with rain rate. A synoptic example demonstrates that the new method is capable of reducing the rain-induced wind vector error while producing a consistent (yet noisy) estimate of the rain rate.

Calibrating the quikscat/seawinds radar for measuring rainrate over the oceans

This effort continues a study of the effects of rain, over the oceans, on the signal retrieved by the SeaWinds scatterometer. It is determined that the backscatter radar cross section can be used to estimate the volumetric rain rate, averaged horizontally, across the surface resolution cells of the scatterometer. The dual polarization of the radar has a key role in developing this capability. The relative magnitudes of the radar backscatter depends on the volumetric rain rate, the rain column height and surface wind velocity, the viewing angle, as well as the polarization (due to the oblateness of raindrops at the higher rain rates). The approach to calibrating the SeaWinds normalized radar cross section (NRCS) is to collect National Weather Service Next Generation Weather Radar (NEXRAD) radar-derived rain rate measurements (4-km spatial resolution and 6-min rotating cycles) colocated in space (offshore) and time with scatterometer observations. These calibration functions lead to a Z-R relationship, which is then used at mid-ocean locations to estimate the rain rate in 0.25/spl deg/ or larger resolution cells, which are compared with Tropical Rainfall Mapping Mission (TRMM) Microwave Imager (TMI) rain estimates. Experimental results to date are in general agreement with simplified theoretical models of backscatter from rain, for this frequency, 14 GHz. These comparisons show very good agreement on a cell-by-cell basis with the TMI estimates for both wide areas (1000 km) and smaller area rain events.

The determination of the three-dimensional distribution of rain from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar

This paper describes a recent development in rainfall estimation using satellite-flown and ground-based radars. The Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR), its algorithms and data processing are discussed. The ground validation algorithms and processing of the ground-based radar reflectivity data are explained. The estimates of attenuation-corrected radar reflectivity factor and rainfall rate are given at each resolution cell of the PR. The estimated near-surface rainfall rate and average rainfall rate at the altitudes of 2 km are calculated for each beam position. The TRMM PR profiling algorithm and processing of the PR reflectivity for rain distribution are explained. The TRMM rain products and their geophysical parameters are derived from the measurements from the satellite and ground-based radar. The derived geophysical parameters include vertical rain and hydrometeor profile, rain type, radar back-scatter cross-section, raindrop size distribution, rain gauge rain rates and 5-day and monthly average rain rates. For validation purposes the instantaneous and climatological comparison of the rain estimates from both the Precipitation Radar and ground-based radar at Melbourne, Florida, was carried out on the basis of rain type; i.e. convective/stratiform, vertical structure and rain maps. The error sources in rain profile retrieval from space-borne radar; i.e. the PR and ground-based radar with their algorithm limitations are discussed. A second set of data, this time for an area where no simultaneous ground data are available has also been analysed; the data were chosen for the three-dimensional rain distribution over some parts of India. The issues such as discrimination of rain from surface clutter, calibration accuracy and sensitivity of precipitation radar and discrimination of rain echo from noise are discussed.

Soil water-content and surface roughness retrieval using ERS-2 SAR data in the Negev Desert, Israel

A study was conducted to explore the use of ERS-2 synthetic aperture radar (SAR) data to assess the soil water-content of agricultural farmlands in the Negev Desert, Israel. The ERS-2 data were acquired using the Israel Space Agency (ISA) receiving station operated by Israel Aircraft Industries. Field measurements of volumetric and gravimetric soil water-content and surface roughness were conducted, concurrent with the deployment of well-measured corner reflectors in the field for calibration and geo-rectification of the radar data. Results show that for individual fields, where surface roughness is homogeneous, the radar backscatter cross-section correlates well with the soil water-content component. For mapping water-content over several fields, the surface roughness must be incorporated into any model that correlates radar backscatter with soil water-content. To solve for roughness and soil water-content, two ERS images with different look directions were acquired, providing two different radar signatures. An empirical model was derived to assess water-content conditions, explainingca. 90% of the backscatter variation using water-content, roughness, and incidence angle. Because it is empirical, the model holds locally and would not be universally true. Therefore, the approach should be tested elsewhere.

Theoretical model for scattering of radar signals in K u - and C-bands from a rough sea surface with breaking waves

A small-slope approximation (SSA) is used for numerical calculations of a radar backscattering cross section of the ocean surface for both K u - and C-bands for various wind speeds and incident angles. Both the lowest order of the SSA and the one that includes the next-order correction to it are considered. The calculations were made by assuming the surface-height spectrum of Elfouhaily et al for fully developed seas. Empirical scattering models CMOD2-I3 and SASS-II are used for comparison. Theoretical calculations are in good overall agreement with the experimental data represented by the empirical models, with the exception of HH-polarization in the upwind direction. It was assumed that steep breaking waves are responsible for this effect, and the probability density function of large slopes was calculated based on this assumption. The logarithm of this function in the upwind direction can be approximated by a linear combination of wind speed and the appropriate slope. The resulting backscattering cross section for upwind, downwind and cross-wind directions, for winds ranging between 5 and 15 m s−1, and for both polarizations in both wave bands corresponds to experimental results within 1–2 dB accuracy.

Kelvin and V-like Ship Wakes Affected by Surfactants

Synthetic aperture radar (SAR) ship wake images in light wind and calm sea conditions frequently appear in the form of a bright V with a half-angle of 2 to 3 deg. Sophisticated and conflicting explanations of this phenomenon, based on the Bragg scattering mechanism, have been proposed. There is a belief that the narrow V-wake is not a part of the Kelvin wake. An alternative approach, which is not generally accepted, suggests that short divergent Kelvin waves may contribute to the V-wake imaging although these waves are mixed with unsteady surface waves generated by the ship-induced turbulence. Ship-generated divergent waves contaminated by surfactants and their radar backscattering cross section are studied. The hull of the ship is represented by a single layer of hydrodynamic singularities. The Green function of a point source moving below a free surface covered by surfactants is derived. A closed-form asymptotic solution for the far ship wave wake is obtained. It is used to calculate analytically the corresponding radar backscattering cross section. The radiative, viscous, and surfactant-induced decay of the V-wake brightness along the V-arms is discussed. The theoretical results are compared against available experimental data.

A Modified Perturbation Method of Electromagnetic Scatteringfrom a Rough Surface by Considering the Effect of the Curvature

A modified perturbation method of electromagnetic scattering from a roughsurface is presented, in which the effect of the curvature of thesurface is taken into account based on the conventional small perturbation method.The problem of scattering error by the conventional small perturbationmethod at grazing angle is solved. Compared with a set of measured data,the numerical results of the backscattering radar cross section show thatthis modified perturbation method is validity for small, moderate andgrazing angle incidence.