Radar backscattering model for multilayer mixed-species forests

A multilayer canopy scattering model is developed for mixed-species forests. The multilayer model provides a significantly enhanced representation of actual complex forest structures compared to the conventional canopy-trunk layer models. Multilayer Michigan Microwave Canopy Scattering model (Multi-MIMICS) allows overlapping layer configuration and a tapered trunk model applicable to forests of mixed species and/or mixed growth stages. The model is the first-order solution to a set of radiative transfer equations and includes layer interactions between overlapping layers. It simulates SAR backscattering coefficients based on input dimensional, geometrical, and dielectric variables of forest canopies. The Multi-MIMICS is an efficient realization of actual forest structures and can be shaped for specific interest of forest parameters. We present the model's application and validation in the paper. The model is parameterized using data collected from a 220,000-ha area of forests in central Queensland, Australia. Fifteen 50/spl times/50 m test sites representing the general forest diversity and growth stages are chosen as ground truth. Polarimetric backscattering airborne SAR (AIRSAR) data of the same area are acquired to validate the model simulations. The model predicts SAR backscattering coefficients of the test areas. Simulation results show a good agreement with AIRSAR data at most frequencies and polarizations. The simulated backscattering coefficient from the multilayer model and the standard MIMICS are also compared and significant improvements are observed.     

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     

Radiative transfer model for microwave bistatic scattering from forest canopies

A bistatic forest scattering model is developed to simulate scattering coefficients from forest canopies. The model is based on the Michigan Microwave Canopy Scattering (MIMICS) model (hence called Bi-MIMICS) and uses radiative transfer theory, where the first-order fully polarimetric transformation matrix is used. Bistatic radar systems offer advantages over monostatic radar systems because of the additional information provided by the diversity of the geometry. By simulating the forest canopy scattering from multiple viewpoints, we can better understand how the forest scatterers' shape, orientation, density, and permittivity affect the canopy scattering. Bi-MIMICS is parametrized using selected forest stands with different canopy compositions and structure. The simulation results show that bistatic scattering is more sensitive to forest biomass changes than backscattering. Analyzing scattering contributions from different parts of the canopy gives us a better understanding of the microwave's interaction with the tree components. The ground effects can also be studied. Knowledge of the canopy's bistatic scattering behavior combined with additional synthetic aperture radar measurements can be used to improve forest parameter retrievals. The simulation results of the model provide the required information for the design of future bistatic radar systems for forest sensing applications.     

Polarimetric scattering from a layer of random clusters of smallspheroids

Employing the volume integral equation formulation with self-interaction term for internal fields, the Jones scattering matrix and phase matrix for random clusters of small spheroids are derived. The mutual coherent wave interactions among clustered spheroids are included. Clustering enhances the internal fields and the scattering amplitude function. Substituting the newly derived phase matrix into the Mueller matrix in the approach of vector radiative transfer for a layer of random clusters of small spheroids, fully polarimetric copolarized and cross-polarized backscattering are numerically calculated. Clustering effects of a layer of random spheroids are quantitatively illustrated, and the backscattering enhancement of several dB order and its functional dependence on parameters are discussed     

Backscattering from a randomly rough dielectric surface

A backscattering model for scattering from a randomly rough dielectric surface is developed. Both like- and cross-polarized scattering coefficients are obtained. The like-polarized scattering coefficients contain single scattering terms and multiple scattering terms. The single scattering terms are shown to reduce to the first-order solutions derived from the small perturbation method when the roughness parameters satisfy the slightly rough conditions. When surface roughnesses are large but the surface slope is small, only a single scattering term corresponding to the standard Kirchhoff model is significant. If the surface slope is large, the multiple scattering term will also be significant. The cross-polarized backscattering coefficients satisfy reciprocity and contain only multiple scattering terms. The difference between vertical and horizontal scattering coefficients increases with the dielectric constant and is generally smaller than that predicted by the first-order small perturbation model. Good agreements are obtained between this model and measurements from statistically known surfaces     

粗糙面上混杂非球形粒子层全极化散射数值模拟

推导了随机取向有限细长圆柱的散射振幅函数,构造了粗糙面上非球形粒子层的矢量辐射传输方程的一阶Mueller矩阵解,包含了粗糙面面散射和粒子层体散射的五种散射机制.建立了粗糙面上混杂非球形粒子层的植被模型,其中垂直地面的有限长圆柱模拟树干,随机取向的有限细长圆柱模拟树枝,针状盘状粒子模拟针叶阔叶等.数值计算了粗糙面上混杂非球形粒子层的全极化散射,分析了各种散射机制的贡献,并与植被层散射的实验数据作了对比和分析.     

Numerical eigenanalysis of the coherency matrix for a layer ofrandom nonspherical scatterers

By using the first-order iterative solution of vector radiative transfer in small albedo for a layer of nonuniformly-oriented, random, nonspherical scatterers, the Mueller matrix and coherency matrix are obtained. Eigenanalysis of the coherency matrix is numerically calculated. The eigenanalysis of the coherency matrix is proposed as a better method for identifying physical scattering mechanisms than direct inspection of the Mueller matrix. The functional dependence of polarimetric scattering is also discussed     

Coupled canonical grid/discrete dipole approach for computingscattering from objects above or below a rough interface

A numerical model for computing scattering from a three-dimensional (3D) dielectric object above or below a rough interface is described. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. To improve computational efficiency, the canonical grid method and the discrete dipole approach (DDA) are used to compute surface to surface and object to object point couplings, respectively, in O(N log N), where N is the number of surface or object sampling points. Two distinct iterative approaches and a preconditioning method for the resulting matrix equation are discussed, and the solution is verified through comparison with a Sommerfeld integral-based solution in the flat surface limit. Results are illustrated for a sample landmine detection problem and show that a slight surface roughness can modify object backscattering returns     

A three-dimensional radar backscatter model of forest canopies

A three-dimensional forest backscatter model, which takes full account of spatial position of trees in a forest stand is described. A forest stand was divided into cells according to arbitrary spatial resolution. The cells may include “crown”, “trunk”, and “gap” components, determined by the shape, size and position of the trees. The forest floor is represented by a layer of “ground” cells. A ray tracing method was used to calculate backscattering components of 1) direct crown backscatter, 2) direct backscattering from ground, 3) direct backscattering from trunk, 4) crown-ground scattering, and 5) trunk-ground scattering. Both the attenuation and time-delay of microwave signals within cells other than “gap” were also calculated from ray tracing. The backscattering Mueller matrices of these components within the same range intervals were incoherently added to yield the total backscattering of an image pixel. By assuming a zero-mean, multiplicative Gaussian noise for image speckle, the high-resolution images were aggregated to simulate a SAR image with a given spatial resolution and number of independent samples (looks). A well-characterized 150 m×200 m forest stand in Maine, USA, was used to parameterize the model. The simulated radar backscatter coefficients were compared with actual JPL SAR data. The model gives reasonable prediction of backscattering coefficients averaged over the entire stand with agreement between model and data within 1.35 dB for all channels. The correlations between simulated images and SAR data (10 by 15 pixels) were positive and significant at the 0.001 level for all frequencies (P, L, and C bands) and polarizations (HH, HV, and VV)     

海面上方运动目标和人造箔条云干扰的多普勒频移仿真

计算空间取向偶极子箔条的极化散射,利用矢量辐射传输方程的一阶迭代解得到箔条云的双站散射截面.建立箔条云的扩散和箔条取向变化的模型,研究了半主动雷达制导过程中,导弹接收到的目标回波、海面杂波和人造箔条云干扰杂波的多普勒频移,得到数值仿真结果.     

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.     

高阶基尔霍夫法求解导体粗糙表面的散射特性

在分析粗糙表面电磁散射特性的基础上,提出了一种考虑粗糙表面协方差函数Taylor展开的高阶基尔霍夫近似(KA)法,解决了经典KA近似的大逼近误差问题.应用9阶高度的KA和传统的KA,对比研究了不同照射频率和均方根高度下的后向散射系数,并比较了遮挡函数的修正效应.同时应用高、低阶KA计算了典型粗糙面的后向散射系数,并分别与测量值和矩量法的数值解进行了比较.结果表明,9阶表面高度展开的切平面KA不仅拓宽了KA的适用条件,还具有更高的精度范围,从而证明了高阶均方根高度展开的KA近似的有效性.     

A coherent scattering model to determine forest backscattering inthe VHF-band

A coherent scattering model to determine the forest radar backscattering at VHF frequencies (20-90 MHz) has been developed. The motivation for studying this frequency band is the recent development of the CARABAS Synthetic Aperture Radar (SAR). In order to model the scattering from branches and trunks, homogeneous dielectric cylinders placed above a semi-infinite di-electric ground have been analyzed. An analytical approach, where the theoretically exact currents induced in an infinite cylinder are truncated, has been compared to a numerical solution using the finite difference time domain (FDTD) method. If the first-order coherent ray tracing is included in the analytical approach, the results match well with the numerically exact FDTD solution. The results show that, in order to determine the VHF-backscattering from a forest stand, the coherent ground interaction is an important part and has to be considered. In this paper, modeling results are in good agreement with CARABAS measurements     

Low-grazing angle scattering from rough surfaces in a duct formedby a linear-square refractive index profile

The problem of rough surface scattering and propagation over rough terrain in a ducting environment has been receiving considerable attention in the literature. One popular method of modeling this problem is the parabolic wave equation (PWE) method. An alternative method is the boundary integral equation (BIE) method. The implementation of the BIE in inhomogeneous media (ducting environments) is not straightforward, however, since the Green's function for such a medium is not usually known. In this paper, a closed-form approximation of the Green's function for a two-dimensional (2-D) ducting environment formed by a linear-square refractive index profile is derived using asymptotic techniques. This Green's function greatly facilitates the use of the BIE approach to study low-grazing angle (LGA) rough surface scattering and propagation over rough surfaces in the aforementioned ducting environment. This paper demonstrates how the BIE method can model the combined effects of surface roughness and medium inhomogeneity in a very rigorous fashion. Furthermore, it illustrates its capability of accurately predicting scattering in all directions including backscattering. The boundary integral equation of interest is solved via the method of ordered multiple interactions (MOMI), which eliminates the requirements of matrix storage and inversion and, hence, allows the application of the BIE method to very long rough surfaces     

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     

A comparison of integral equations with unique solution in theresonance region for scattering by conducting bodies

A comparison of integral equations, for problems involving scattering by arbitrary-shape conducting bodies, having a unique solution in the resonance region is presented. The augmented electric and magnetic field integral equations and the combined field integral equation, in their exact and approximate versions, are considered. The integral equations and the basis and test functions used in the method of moments to solve them are reviewed. Their implementation in a computer code is analyzed, mainly the relation between the matrix properties and the CPU time and memory. Numerical results (condition number and backscattering cross section) are presented for the cube. It is shown that the combined field integral equation, and the approximate (symmetric) combined field integral equation, are the most efficient equations to use in the neighborhood of resonant frequencies, because the overdetermined augmented integral equations require an extra matrix multiplication     

Polarimetric signatures of a layer of random nonspherical discretescatterers overlying a homogeneous half-space based on first- andsecond-order vector radiative transfer theory [geophysical radar remotesensing]

Complete polarimetric signatures of a layer of random, nonspherical discrete scatterers overlying a homogeneous half space are studied with the first- and second-order solutions of the vector radiative transfer theory. The vector radiative transfer equation contains a general nondiagonal extinction matrix and a phase matrix that are averaged over particle orientations. The nondiagonal extinction matrix accounts for the difference in propagation constants and the difference in attenuation rates between the two characteristic polarisations. The Mueller matrix based on the first-order and second-order multiple scattering solutions of the vector radiative transfer equation is calculated. The copolarized and depolarized returns are also calculated     

采用离散植被散射模型分析玉米冠层

基于修正的Born近似解得到离散植被散射模型,说明该模型中的植被散射机理,给出圆柱、椭圆片的散射幅度函数,以及植被、土壤的介电常数模型;在L波段下模型应用于玉米植被,得出HH,VV极化情况下的后向散射系数,同时与AIRSAR实验获得的数据比较,验证了同极化HH情况下模型的准确性。     

A microwave scattering model for layered vegetation

A microwave scattering model was developed for layered vegetation based on an iterative solution of the radiative transfer equation up to the second order to account for multiple scattering within the canopy and between the ground and the canopy. The model is designed to operate over a wide frequency range for both deciduous and coniferous forest and to account for the branch size distribution, leaf orientation distribution, and branch orientation distribution for each size. The canopy is modeled as a two-layered medium above a rough interface. The upper layer is the crown, containing leaves, stems, and branches. The lower layer is the trunk region, modeled as randomly positioned cylinders with a preferred orientation distribution above an irregular soil surface. Comparisons of results obtained using this model with measurements from deciduous and coniferous forests show good agreement at several frequencies for both like and cross polarizations     

Depolarization, Scattering, and Attenuation of Circularly Polarized Radio Waves by Spherically Asymmetric Melting Ice Particles

The eccentric spheres model and an extended Mie solution are used to formulate scattering of a plane, electromagnetic wave by a single melting ice particle as well as by a horizontal layer of such particles. The incident wave is left-hand circularly polarized, whereas the scattered wave, as a result of depolarization by the spherically asymmetric particles, comprises left-hand and right-hand circularly polarized components. The Stokes parameters of the scattered wave are calculated throughout the melting process. Furthermore, radar observables of backscattering and depolarization, as well as the specific attenuation, across the melting layer are calculated. The numerical application manifests how the internal spherical asymmetry of melting ice particles is imprinted on backscattering, forward scattering, and depolarization. Moreover, it is shown how each part of the melting layer contributes to the attenuation and depolarization of the radio waves crossing that layer