Tzong-Dar Wu

Emission of rough surfaces calculated by the integral equation method with comparison to three-dimensional moment method simulations

This paper presents a model of microwave emissions from rough surfaces. We derive a more complete expression of the single-scattering terms in the integral equation method (IEM) surface scattering model. The complementary components for the scattered fields are rederived, based on the removal of a simplifying assumption in the spectral representation of Greens function. In addition, new but compact expressions for the complementary field coefficients can be obtained after quite lengthy mathematical manipulations. Three-dimensional Monte Carlo simulations of surface emission from Gaussian rough surfaces were used to examine the validity of the model. The results based on the new version (advanced IEM) indicate that significant improvements for emissivity prediction may be obtained for a wide range of roughness scales, in particular in the intermediate roughness regions. It is also shown that the original IEM produces larger errors that lead to tens of Kelvins in brightness temperature, which are unacceptable for passive remote sensing.

A transition model for the reflection coefficient in surface scattering

In the development of wave scattering models for randomly dielectric rough surfaces, it is usually assumed that the Fresnel reflection coefficients could be approximately evaluated at either the incident angle or the specular angle. However, these two considerations are only applicable to their respective regions of validity. A common question to ask is what are the conditions under which we would choose one or the other of these two approximations? Since these approximations are basically roughness-dependent, how can we handle the in-between cases where neither is appropriate? In this paper, a physical-based transition function that naturally connects these two approximations is proposed. The like-polarized backscattering coefficients are evaluated with the model and are compared with those calculated with a moment method simulation for both Gaussian and non-Gaussian correlated surfaces. It is found that the proposed transition function provides an excellent prediction for the backscattering coefficient in the frequency and angle trends.

A reappraisal of the validity of the IEM model for backscattering from rough surfaces

An integral equation method (IEM) surface scattering model was examined in terms of its applicability to laboratory measurement and numerical simulations. New expressions for both single scattering and multiple scattering were obtained by rederiving the scattering coefficient to keep all the phase terms in the spectral representation of the Greens function. After quite intricate mathematical manipulations, a fairly compact form is obtained for the scattering coefficients. In addition, the Fresnel reflection coefficients used in the model were replaced by a transition function that takes surface roughness and permittivity into account. The results of comparisons with both the numerical simulations and measurements for the backscattering case indicate that the IEM is improved, becoming more accurate and practical to use.

Note on the multiple scattering in an IEM model

The authors derive the multiple scattering expression within the framework of an IEM model for rough surface scattering. The complementary field coefficients are rederived based on a new surface slope expressions which are dependent on spatial variables. This leads to a more complete expression of the multiple scattering terms, thus allowing the authors to account for multiple effects more accurately. Numerical calculations and comparisons with numerical simulation are provided to demonstrate the results.

A Model-Based Inversion of Rough Soil Surface Parameters From Radar Measurements

In this paper, a model-based retrieval algorithm is developed for the remote sensing of rough surfaces. The probabilistic and sensitive issues of parameter estimation for soil surfaces are discussed and modeled. A geophysical model function (GMF) that relates the input (observation space) and output vectors (parameter space) includes both an electromagnetic scattering model and a dielectric model; the electromagnetic scattering model describes the relationship between the radar echoes and the target parameters (geometrical and electrical), while the dielectric model connects the electrical parameter (permittivity) to the geophysical parameter of interest (soil moisture). Within the framework of an integral equation model, a scattering model is devised and used as part of the GMF. To estimate the parameters from finite sets of measurements, a good approximation of an GMF inverse function of GMF is required. We apply a neural technique to do this, by exploring its many merits, including not needing an explicit function. The necessary training data sets are generated using the GMF within a pre-defined domain. In order to alleviate an ill-posed problem, in which more than one set of parameters may be mapped onto a single backscattering coefficient, (i.e, non-unique), the range of parameters must be properly selected through a sensitivity analysis. In practice, the measured data are unavoidably contaminated by inherent noise. It turns out that the measurement uncertainty becomes quite large making the inversion accuracy even worse. By properly taking the noise components into account in the training data, the noise-tolerant capability of the inversion system can be increased. A reasonably good estimation of the surface correlation length, the roughness, and the soil moisture parameters may be obtained from laboratory-controlled measurements and AIRSAR data in this study.

Reanalysis of L-band brightness predicted by the LSP/R model-for prairie grassland: incorporation of rough surface scattering

L-band brightness predicted by the land surface process/radiobrightness (LSP/R) model for prairie grassland appears to be somewhat lower than expected. A crucial reason for the underestimate of the L-band brightness is that the soil surface was treated as smooth. In this paper, surface scattering of the soil determined by the IEM model is incorporated into the LSP/R model to examine its impact on the predicted L-band brightness. Eight sets of surface parameters, two correlation lengths (L) of 3 and 6 cm/spl times/4 root mean squared (RMS) heights (/spl sigma/) of 0.3, 0.6, 0.8, and 1.0 cm, are utilized to characterize the emission of the soil surface. It is found that H-polarized, L-band brightness is expectedly increased by different levels for all of the eight rough surface cases compared to the smooth surface case. The increase in the average of the H-polarized, L-band brightness is by as much as 13.2 K for the case with L=3 cm and /spl sigma/=1.0 cm. In addition, L-bands sensitivity to soil moisture is found to be approximately equal with and without the scattering effects. An increase in H-polarized, L-band brightness by about 12 K at the end of a 14-day simulation by the LSP/R model is in response to a decrease in soil moisture by 7% for all of the nine cases of concern (eight rough plus one smooth soil surfaces).

A Study of Backscattering From Multiscale Rough Surface

Most of the rough surfaces are generally multiscale in nature as observed by radar even at narrow-band. In this paper, we apply the modulation concept to study the characteristics of backscattering from such a multiscale surface, using the IEM scattering model. The modulated surface is special kind of multiscale surface in that a random surface is superimposed upon a periodic type surface. The modulation is rationed from the fact the measured correlation function usually exhibits zero-crossing which equally states the fact that the maxima of surface spectra is shifted toward the higher wavenumber. The amount of the frequency shift depends on the modulation wavenumber. It changes the spectral decay rates behind the peak valued. The normal incidence angle can be significantly shifted as well. It is also found the maximum modulation wavenumber is related by the inverse of base-band correlation length. In all cases studied, it was found that the modulation effects significantly changes the backscattering beha...

A re‐examination of the IEM model for microwave scattering from randomly rough boundary

Abstract An IEM surface scattering model was examined in terms of its applicability to simulations and laboratory measurements. New expressions for both single scattering and multiple scattering were obtained by re‐deriving the scattering coefficient to keep all the phase terms in the spectral representation of Greens function. After quite intricate mathematical manipulations, a fairly compact form for an advanced IEM model (AIEM) is obtained for the scattering coefficients. In addition, the Fresnel reflection coefficients used in the model were replaced by a transition function. The comparisons in this paper were concentrated in the case of backscattering with both numerical simulations and measurement data. The results indicate that the IEM is improved, becoming more accurate and practical to use.

Characterization of non-Gaussian rough surface scattering

Abstract In this paper, we examine the scattering properties of rough differently correlated surfaces using the IEM model. The effective correlation length of such a surface is pointed out and its effect on the backscattering behavior is discussed. It may be found from the cases considered here that the non‐Gaussian effects are very significant even with the same correlation length and height variance. This can be seen from the surface spectra where the roughness scales are distributed. Among the non‐Gaussian correlated surfaces, the exponential correlated has more small scale roughness at the high frequency components.

A reappraisal of the validity of IEM model

A surface scattering model based on the integral equation method is examined in terms of its applicability to laboratory measurements. The Fresnel reflection coefficients used in the model have been approximated as a function of the incidence angle at low frequency and as a function of the specular angle at high frequency. Based on a limited set of experimental measurements, a transition function is suggested for estimating the Fresnel reflection coefficients in the intermediate regions. Results of comparison indicate that the IEM is accurate and practical to use. Issues raised from dielectric information are also addressed.