Scale-Dependent Surface Roughness Behavior and Its Impact on Empirical Models for Radar Backscatter

The currently available backscatter inversion models often do not yield satisfactory results when applied to natural surfaces due to an inaccurate characterization of the soil roughness properties. This is caused by inadequacy of the applied soil roughness measuring techniques and by the high variation on soil roughness parameters within one agricultural field. From a theoretical study it was found that long profiles are necessary to obtain an accurate estimation of the roughness parameters. Short profiles, which are generally measured, tend to underestimate the roughness parameters. Soil roughness data were collected over three different tillages with the ESA laser profiler, which allows measurements of profiles up to 25 m, and a 4 m wide meshboard. This research compares the two measuring techniques and studies the possibility of compensating for the underestimation of short profiles. Analysis of the 25 m laser profiles confirmed the theoretical study that the rms height and the correlation length increase as profile length increases. The rms height reached a constant value for all three tillages whereas the correlation length only reached a constant value for the roughest tillages. The dependency on profile length of both rms height and correlation length could be quite accurately modeled which allowed the extrapolation from short profile data to rms height and correlation length values at higher profile lengths. Additionally, it was found that it is possible to convert the less accurate meshboard derived rms values to those obtained from the laser profiler. This conversion greatly improves when the parameter values of at least six, 4 m profiles are averaged. For the correlation length this conversion is not possible due to the high variance on this parameter

We present experimental results on the scattering of electromagnetic waves at millimeter‐wave frequencies from one‐dimensional very rough conducting surfaces with controlled surface roughness statistics. Very rough surfaces are defined as surfaces with rms height and correlation length of the order of a wavelength such that the rms slope is at least unity. It is expected that scattering experiments using these surfaces can provide useful insights since their statistics lie outside the range of validity of the present theories, namely, the Kirchhoff and perturbation theories. Strong backscattering enhancement at different incident angles, both in the transverse electric and transverse magnetic polarizations, are observed experimentally. Numerical calculations based on the exact integral equation method for cylindrical beam wave illumination compare favorably with the experimental results. The agreement between measurements and numerical calculations is good over a wide range of incident angles and for all scattering angles. The close agreement between the experimental results and numerical simulations indicates that this controlled experimental setup can be used to study scattering phenomena from one‐dimensional very rough surfaces with different roughness statistics as well as from two‐dimensional rough surfaces.

Stochastic surface models are useful for analyzing in situ roughness profiles and synthetic aperture radar (SAR) images of geological terrain. In this paper, two different surface models are discussed: surfaces with a stationary random roughness (conventional model) and surfaces with a power-law roughness spectrum (fractal model). In the former case, it must be considered that for short profiles (L<200l/sub 0/), the measured values of rms-height s and correlation length l may be significantly smaller than the intrinsic values s/sub 0/ and l/sub 0/. In the latter case, rms-height and correlation length depend on the profile length L, and the surface is better characterized by slope and offset of the roughness spectrum (which are independent of L), The sensitivity of the SAR signature to variations in surface roughness parameters is evaluated by means of theoretical scattering models. For smoother geological surfaces such as most arid terrain types, single scattering is dominant, which means that the roughness parameters can be determined from SAR data using comparatively simple algorithms. Multiple scattering processes on rough surfaces such as a'a lava and variations of the local incidence angle due to large-scale terrain undulations make the retrieval of roughness parameters by means of inverse modeling much more complex. Field data of surface roughness indicate that rougher geological surfaces may be in the diffractal regime at higher radar frequencies, in which the scattering characteristics deviate significantly from the patterns observed for stationary surfaces. On the basis of surface and scattering models, recently published observations of roughness data and radar signatures from volcanic, alluvial, and arid surfaces are examined.

Numerous analytical radar-scattering laws have been published through the past decades to interpret planetary radar observations, such as Hagfors’ law, which has been commonly used for the Moon, and the cosine law, which is commonly used in the shape modeling of asteroids. Many of the laws have not been numerically validated in terms of their interpretation and limitations. This paper evaluates radar-scattering laws for self-affine fractal surfaces using a numerical approach. Traditionally, the autocorrelation function and, more recently, the Hurst exponent, which describes the self-affinity, have been used to quantify the height correlation. Here, hundreds of three-dimensional synthetic surfaces parameterized using a root-mean-square (rms) height and a Hurst exponent were generated, and their backscattering coefficient functions were computed to evaluate their consistency with selected analytical models. The numerical results were also compared to empirical models for roughness and radar-scattering measurements of Hawaii lava flows and found consistent. The Gaussian law performed best at predicting the rms slope regardless of the Hurst exponent. Consistent with the literature, it was found to be the most reliable radar-scattering law for the inverse modeling of the rms slopes and the Fresnel reflection coefficient from the quasi-specular backscattering peak, when homogeneous statistical properties and a ray-optics approach can be assumed. The contribution of multiple scattering in the backscattered power increases as a function of rms slope up to about 20% of the backscattered power at normal incidence when the rms slope angle is 46°.

SummaryDisplacement‐based seismic assessment of buildings containing unreinforced masonry (URM) walls requires as input, among others, estimates of the in‐plane drift capacity at the considered limit states. Current codes assess the drift capacity of URM walls by means of empirical models with most codes relating the drift capacity to the failure mode and wall slenderness. Comparisons with experimental results show that such relationships result in large scatter and usually do not provide satisfactory predictions. The objective of this paper is to determine trends in drift capacities of modern URM walls from 61 experimental tests and to investigate whether analytical models could lead to more reliable estimates of the displacement capacity than the currently used empirical models. A recently developed analytical model for the prediction of the ultimate drift capacity for both shear and flexure controlled URM walls is introduced and simplified into an equation that is suitable for code implementation. The approach follows the idea of plastic hinge models for reinforced concrete or steel structures. It explicitly considers the influence of crushing due to flexural or shear failure in URM walls and takes into account the effect of kinematic and static boundary conditions on the drift capacity. Finally, the performance of the analytical model is benchmarked against the test data and other empirical formulations. It shows that it yields significantly better estimates than empirical models in current codes. The paper concludes with an investigation of the sensitivity of the ultimate drift capacity to the wall geometry, static, and kinematic boundary conditions.

Soil roughness greatly affects the scattering process of microwaves to the soil surface. Previous studies showed that the values of roughness parameters increase asymptotically with increasing profile length. In this paper, 25-m profiles are used to study the influence of profile length on the roughness parameters and on the shape of the autocorrelation function. It is further investigated whether correct soil roughness parameters, as obtained from long surface roughness profiles, can be determined from 4-m-long profiles. Therefore, the extrapolation of an empirical relationship between roughness parameters and profile length is investigated, for three different roughness classes. The technique yields parameter values which are comparable to the 25-m roughness parameters.

The Fresnel corrected Kirchhoff approximation is applied to drive expressions for the temporal response and spatial coherence of high-frequency acoustic signals forward scattered from random rough surfaces. With the assumption of a Gaussian distribution of heights, the results depend only on the rms height and slope of the scattering surface. The expressions obtained are numerically evaluated for comparison with representative Arctic acoustic data. It is found that relatively low values of the rms height and slope must be assumed to match high-frequency temporal response data. These same slope and height values yield predictions of the transverse horizontal spatial coherence consistent with acoustic measurement for closely spaced receivers. [Work supported by NOARL.]

In this paper we propose an efficient and accurate iterative numerical approach to analyze EM scattering from 1-D dielectric rough surfaces. It is based on a new splitting of the impedance matrix Z to improve the asymptotic convergence rate of the resultant iterative system. The structure of split matrix is then fully explored, in combination with the application of an identity for inverse of block matrix, to further reduce the computational and storage complexity. The embedded matrix-vector product is computed using the spectral acceleration technique. Extensive numerical simulations demonstrate a couple of appealing features of this proposed method for Gaussian surface with Gaussian spectrum: (1) It converges faster than both forward-backward method (FBM) and FBM with spectral acceleration (FBM-SA); (2) For HH polarization, the proposed method is about twice as fast as FBM-SA. For VV polarization, the proposed method is better when the rms slope is not larger than 16° or interestingly when rms height is beyond 2.0 wavelengths. Moreover, it converges for cases where FBM-SA fails for both polarizations. These features indicate that the proposed method can be effectively used to analyze EM scattering from 1-D dielectric Gaussian surface with Gaussian spectrum.

A theory of scattering from very rough surfaces is presented. Both the surface rms height and the correlation distance are close to a wavelength and the rms slope is close to unity. The theory is based on the first- and modified second-order Kirchhoff approximations. The second-order scattering includes the incident and scattering shadowing and the angular and propagation tapering shadowing. The angular shadowing limits the angular spectrum of the second-order scattering within those intercepted by the surface, while the propagation shadowing limits the propagation distance within those intercepted by the surface. The calculations are made for the rms height equal to 1.5, 1.0, and 0.5 wavelengths and the correlation distance equal to 1.8 wavelengths and show close agreement with the Monte Carlo simulation of the exact integral equation. The results show that the first-order Kirchhoff scattering is dominant for rms height equal to 0.5 wavelengths, but for rms heights equal to 1.0 and 1.5 wavelengths, the second-order scattering becomes comparable to the first-order and produces the enhanced backscattering. Therefore, this theory provides a possible physical explanation for the enhancement. The range of validity of the theory is also discussed. [Work supported by ARO and NSF.]

This paper presents a theory of scattering from very rough metallic and dielectric surfaces using the first- and second-order Kirchhoff approximations (KA) modified with the angular and propagation shadowing. The shadowing functions limit the single and double scattered waves which are illuminated and not shadowed by the surface. The theoretical results are compared with the Monte Carlo simulations showing the range of validity of the theory. The theory is applicable to the range where the RMS height is close to a wavelength and the RMS slope is close to unity, and the second medium is lossy. The second-order scattering includes two waves travelling in opposite directions on the surface, giving a physical explanation of the enhanced backscattering.

This paper aims to establish the joint roughness statistics for rms height s and correlation length l for agricultural bare soil fields and a variety of tillage conditions. To do so, we make use of a unique pan-European database of profile measurements covering five different sites and containing approximately 1.5 km of profile data. A preliminary assessment of the validity of the derived roughness statistics for electromagnetic scattering models is also carried out by comparing /spl sigma//sup 0/ predictions obtained using the integral equation model with derived roughness statistics and European Remote Sensing 1 and 2 (ERS 1/2) synthetic aperture radar observations. The results are then summarized within the overall context of roughness description and we discuss the implications in terms of forward modeling and inversion. The limitations of s and l parameters as roughness descriptors are also underlined.

Presents results for full three-dimensional simulations of numerical solutions of Maxwell equations for random rough surfaces. Emissivities and back-scattering coefficients are calculated for soil surfaces and ocean surfaces at microwave frequencies. This is unlike analytical methods or empirical models in that different roughness parameters are used for different microwave frequencies and for active and passive remote sensing. With advances in computational electromagnetics and available computer resources, we calculate 3-dimensional Maxwell equation solutions with a 2-D rough surface for practical remote sensing applications. Highlights of our numerical approach are: (i) the sparse-matrix canonical grid method (SMCG) and the physics-based two-grid method (PBTG) are used. (ii) An algorithm has been implemented for parallel computing. Dense discretization of the surfaces is used because of high permittivity and the energy conservation check is verified. We present results for soil surfaces in L- and C-bands, and for ocean surfaces at 19 GHz.

Summary Analysis of the experimental data for liquid-entrainment rate, forces exerted on liquid droplet, and secondary flow occurring in the gas core show that the liquid is mainly carried in the form of film in the inclined annular flow. Therefore, it is more reasonable to establish a mathematical model from the bottom-film reversal than from the droplet reversal. In this study, a new analytical model is developed from force balance of the bottom film of the inclined tubing after studying the bottom-film thickness and gas/liquid interfacial friction factor to reveal the liquid-loading mechanism. Furthermore, a new Belfroid-like empirical model is proposed that is based on the calculation results of a wide range of flowing parameters from the new analytical model to predict the liquid-loading status of gas wells. The new empirical model introduces a coefficient Cd,p,uSL,T to consider how the fluid properties under downhole flow condition affect the critical gas velocity. Cd,p,uSL,T in the new empirical model increases with the pipe diameter, liquid velocity, and flowing pressure, and decreases with the flowing temperature. The new analytical model, having an average error of 8.45%, agrees well with the published experimental data, and it also performs well in predicting the pressure gradient at liquid unloading condition. The new empirical model could be applied for the prediction of real field operations and has been validated with an accuracy rate of 95% against data newly collected from 60 horizontal wells. The new work can accurately and easily judge the liquid-loading status, and it also reveals how the fluid properties under downhole flowing condition affect the liquid loading.

A numerical study of performance for tight gas and shale gas reservoir systems

An analytical propagation model has previously been developed to predict radio signal attenuation in urban and suburban environments. Most of the traditional models commonly used for macrocellular system design are empirical, which account for radio signal attenuation between base and mobile stations using a simple slope-intercept approach. Unlike the empirical models, the analytical model explicates the path loss in urban and suburban environments as a result of signal reduction due to free space wave front spreading, multiple diffraction past rows of buildings, as well as building shadowing. Since the dependence on frequency, base station antenna height, mobile station antenna height, building height and street width are analytically explicit, this model is applicable for cellular as well as PCS applications in both macro and micro cellular environments. Good accuracy was found for this analytical model by comparing the predictions with numerous measurements made in various propagation environments. However, since the analytical model involves multiple dimension integration to calculate the signal attenuation due to multiple diffraction past rows of buildings, the model in its original format does not lend itself to be easily implemented into a radio system planning tool. To meet the needs of fast assessment of cell coverage, co-channel/adjacent channel interference, and system capacity, a simplified version of the analytical model is developed in this paper, which can be used for three different propagation scenarios with base station antenna above, below and near the average rooftop level.