High-frequency forward scattering in the Arctic

The global distribution of the reflectivity of the surface of Venus as determined by the Pioneer Venus orbital radar instrument has been analyzed in a geological context and statistically correlated with elevation. In addition, a comparison between the reflectivity and rms slope (roughness) correlations with elevation permits radar‐geologic topographic zones to be identified. The radar reflectivity ρ at normal incidence and at a wavelength of 17 cm (1.76 GHz) is a model‐dependent measure of the bulk dielectric constant κ of surfaces dominated by dry rocks and soils and depends on surface material properties such as porosity and conductivity. Only the quasi‐specular component of the radar echo was used in determining the reflectivity values analyzed in this study, and for very rough surfaces the absolute magnitude of ρ may be underestimated by 10–15%. Empirically derived relationships between ρ, κ, and bulk density γ are used to interpret geologically the ρ distribution. The global mean ρ of 0.13 is significantly greater than the average lunar and typical martian values of ∼0.07, suggesting the absence of a continuous soil mantle on Venus. The ρ distribution is well described by a two‐stage Gaussian distribution with modes at 0.11 and 0.14. The close proximity of these modes suggests that there is no fundamental dichotomy of surfaces on Venus insofar as their ρ properties, in contrast with roughness. Less than 15% of Venus has ρ values low enough to indicate a major soil component on the surface. Approximately 27% of the surface is dominated by low‐porosity materials such as bedrock, and less than 15% is enriched in high dielectrics. The rest of the surface (43%) is most simply envisioned as partially mantled bedrock, perhaps an extension of the types of terrain viewed by the Venera 10 and 13 landers. The most plausible model for the highest ρ (and thus highest κ) materials requires enrichment in Ti and Fe (e.g., minerals such as rutile, ilmenite, and magnetite). High‐titanium basalts such as those found on the moon would produce the required enrichment, as would pyrites. Since surface geochemical measurements demonstrate that there are basalts in the Venusian plains, a model in which high‐titanium basalts are exposed at the highest elevations (Maxwell, Theia, Atla, Ovda) is favored. Possible weathering of ilmenite in such basalts to produce rutile could explain the high‐κ materials in less elevated regions. When correlated with elevation, κ exhibits a complex nonmonotonic trend in which both decreases and increases are observed. A major decrease in ρ of ∼0.02 km−1 in the upper plains contrasts with the almost 1° rms km−1 increase in surface roughness over the same interval and may be an expression of increased soil production, perhaps due to enhanced breakdown of silicates into carbonates in the lower highlands. Alternately, the decrease could be due to increased centimeter scale roughening, perhaps caused by the increase in regional slope in the highlands. A major increase in ρ (0.05 km−1) in the middle highlands correlates with a rapid rise in rms slope. Unlike rms slope, however, there is no overall correlation of ρ with either elevation or regional slope, suggesting that it may be a more locally controlled parameter. Hierarchical clustering analysis of the ρ, roughness, and regional slope properties of Venus demonstrates that distinct subregions are best defined on the basis of topographic zones in which the radar parameters follow well‐defined trends. The lowland plains are extremely smooth at scales from centimeters to 100 km. In general, no single radar parameter (e.g., ρ) serves to subdivide the surface into distinct geologic regions, but taken together, the radar parameters can be statistically correlated to define meaningful radar geologic units. Such units appear to correlate with the kinds of surfaces that can be seen on Venus at kilometer resolution.

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.

High spectral components contained in surfaces with non-Gaussian correlation functions are believed to increase the magnitude of backscattering enhancement. In this paper, we present experimental and numerical studies of bistatic scattering from one-dimensional surfaces with Gaussian and power-law roughness spectral densities. Rough surfaces with an rms height of σ = 3 mm and correlation lengths of l = 3, 6 and 9 mm were fabricated and measured with a millimetre-wave scatterometer. The corresponding rms slopes were m = 1.41, 0.707 and 0.47, respectively. Both experimental and numerical simulation data show that surfaces obeying the power-law roughness spectral density have stronger backscattering enhancement than those with a Gaussian roughness spectral density for the same surface rms slope. Good agreement between experiments and numerical simulations was obtained. In addition, the numerical studies were conducted to obtain the scattering characteristics of surfaces with Gaussian and power-law roughness ...

The problem of mutually irradiating conducting fins is considered in this paper. The problem is analyzed under two types of surface models, namely, diffuse-specular (D-S) model and a directional (Dir) radiative surface property model, for various surface roughnesses and RMS slopes. Metal (aluminum) coated and dielectric (Aluminum oxide) coated surfaces are considered as the two extreme cases. Analysis indicates that dielectric coated surfaces are sensitive to the radiative surface property model while metal coated surfaces are insensitive to the surface property model. Irrespective of the surface property model used metal coated surface show a drastic drop in heat flux for even a slight increase in surface roughness.

One dimension band-limited fractal surfaces with different fractal dimension and different rms slope are created by Monte Carlo simulation. The curves of the single scattering shadowing function of the band-limited fractal surface with varying of the incident angle are obtained by utilizing a ray-tracing algorithm, the influence of different fractal dimension and different rms slope on the fractal surface shadowing function is analyzed. The curve of the shadowing function with varying of the incident angle for the fractal surface and Gaussian rough surface is compared with same rms slope. The results show that the curves of the shadowing function for the fractal surface with different fractal dimension and three Gaussian rough surface are basically same.

In bistatic radar observations, reflected echoes from the surface of a target planet can be analyzed to infer its surface statistics and near-surface constituents. In this work, a preliminary inspection of two X-band bistatic radar observations gathered by the Cassini spacecraft about Titan’s polar regions is presented. Profiles of relative dielectric constant and root-mean-square (rms) surface slope are provided as outputs of the analysis, discussed, and compared with the present knowledge of Titan geomorphology. For the assessment of the rms slope, proportional to the spectral broadening of reflected echoes, a basic fitting procedure was applied to the received spectra using a Gaussian template, to later evaluate the full-width half-maximum of the fitting curve. The dielectric constant was computed from the power ratio between orthogonally circularly polarized components of signal reflections from Titan. Dielectric constant estimates are, on average, consistent with the expected materials covering the dry surfaces of the planet, while slightly low values were found over the seas. The rms slopes are generally low compared to past bistatic observations of other targets. Titan’s north polar seas are revealed to feature an unprecedented smoothness, with 0.01^circ of slope as an upper bound. Similar values were inferred for isolated spots in the southern pole, hinting at the possible presence of basins filled with liquid hydrocarbons. The main issues with the analysis are emphasized throughout the document, and some ideas for future work are presented in the conclusions.

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.]

Scattering of a TE incident wave from a perfectly conducting one-dimensional composite random rough surface is studied. A composite random surface contains roughness of more than one scale. With the recently developed efficient numerical technique known as the banded-matrix iterative approach, we are able to study large-scale composite roughness with two correlation lengths that are many times different from each other. It is shown that small-scale roughness, with its large rms slope, rather than large-scale roughness, with its small rms slope, can dominate bistatic scattering. It is also shown that backscattering enhancement can also exist in a composite rough surface.

This work focuses on the application of a multivariable model predictive controller that regulates thin film surface roughness and mean slope to a two-dimensional kinetic Monte-Carlo thin film growth model using both substrate temperature and deposition rate as manipulated inputs. The description of the thin film growth involving both adsorption and surface migration is first given. Surface roughness and surface slope are defined as the root-mean-squares of the surface height profile and the surface slope profile, respectively. The dynamics of the evolution of the thin film surface height profile are assumed to be described by an Edwards-Wilkinson-type equation (a second-order stochastic partial differential equation) in two spatial dimensions. Analytical solutions of the expected surface roughness and surface slope are obtained on the basis of the Edwards-Wilkinson equation and are used in the controller design. The model parameters of the Edwards-Wilkinson equation depend on the substrate temperature and deposition rate. This dependence is used in the formulation of the predictive controller to predict the influence of the control action on the surface roughness and slope at the end of the growth process. The model predictive controller involves constraints on the magnitude and rate of change of the control action and optimizes a cost that involves penalty on both surface roughness and mean slope from the set-point values. The controller is applied to the two-dimensional kinetic Monte-Carlo thin film growth model and is shown to successfully regulate surface roughness and mean slope to set-point values at the end of the deposition.

Dynamics and control of aggregate thin film surface morphology for improved light trapping: Implementation on a large-lattice kinetic Monte Carlo model

For supersmooth optical surfaces, the equation relating diffusely scattered light to roughness and slope parameters assumes a simple form. Measurements of rms roughness and slope for such surfaces can be made with an instrument which accepts a solid angle much smaller than 2π steradian. Measurements made on fused silica surfaces yield values as low as 0·23 nm and 3·8 × 10−4 rad.

The cooling of the Ex-vessel in Light-Water-Reactors has been proposed to maintain reactor vessel integrity during severe accident. The critical heat flux — CHF — from the underside of down-facing convex surfaces, like hemispheres, is important to the assessment of the cooling. The authors examined CHFs on inclined plates under saturated boiling experimentally, focusing on the effect of the inclination angle on the CHF and characteristic length and velocity of coalesced bubbles near the heater at the CHF. In this study, the critical heat fluxes on the inclined plates in saturated boiling were investigated analytically by using the macrolayer model and the Kelvin-Helmholtz instability, based on our previous experimental report. Furthermore, the present model was developed for the CHF on a hemispheric surface. In the present model, the most dangerous wavelength and propagative velocity of the wave in the Kelvin-Helmholtz instability for ideal fluid with vapor flow of finite thickness and surface tension on liquid-vapor interface were calculated to determine the length and the velocity of the coalesced bubble on the heating surface at CHF. The time covered over the heater with the bubble was estimated as the calculated value with the length divided by the velocity. The predictions of the present CHF model by using the macrolayer model for CHF and the Kelvin-Helmholtz instability for the characteristic values of the coalesced bubble agree well with previous experimental data for CHF on inclined plates with 30 to 180 degree in orientation. Furthermore, the present model given as a function of the inclination angle relative to the horizontal downward plate was extended to CHF on a hemispheric surface. The CHFs obtained by the present model are in qualitative agreement with experimental data on hemispheres reported by some investigators.

One goal of radar remote sensing is the extraction of terrain statistics and surface dielectric properties from backscatter data for some range of wavelengths, incidence angles, and polarizations. This paper addresses empirical approaches used to estimate terrain properties from radar data over a wider range of roughness than permitted by analytical models. Many empirical models assume, at least implicitly, that roughness parameters like rms height or correlation length are independent of the horizontal length scale over which they are measured, in contrast to recent surveys of natural terrain, which show that self-affine, or power-law scaling, between horizontal scale and roughness statistics is very common. The rms slope at the horizontal scale of the illuminating wavelength s(lambda) is directly related to the variogram or structure function of a self-affine surface, can be readily obtained from field-measured topography, and, when used in an empirical model, avoids the need for arbitrary wavelength-dependent terms. To facilitate comparison with earlier approaches, an expression that links the rms height at some profile length with the rms (Allan) deviation at an equivalent horizontal sampling interval is obtained from numerical simulations. An empirical model for polarimetric scattering as a function of s(lambda) at 35deg-60deg incidence from smooth to rugged lava surfaces is derived and compared with earlier models for backscatter from modestly rough soil surfaces. The asymptotic behavior of polarization ratios for the lava flows suggests that the depolarization of linear-polarized illuminating signals occurs as a first-order process, likely through single scattering by rock edges or other discontinuities, rather than as the solely multiple-scattering effect predicted by some analytical models. Efforts to fully understand radar scattering from geological surfaces need to incorporate wavelength-scale roughness, perhaps through computational simulations.

This paper presents radar-altimeter scattering models for each of the diagenetic zones of the Greenland ice sheet. AAFE radar-altimeter waveforms obtained during the 1991 and 1993 NASA multi-sensor airborne altimetry experiments over Greenland reveal that the Ku-band return pulse changes significantly with the different diagenetic zones. These changes are due to varying amounts of surface and volume scattering in the return waveform.In the ablation and soaked zones, where surface scattering dominates the AAFE return, geophysical parameters such as rms surface height and rms surface slope are obtained by fitting the waveforms to a surface-scattering model. Waveforms from the percolation zone show that sub-sruface ice features have a much more significant effect on the return pulse than the surrounding snowpack. Model percolation waveforms, created using a combined surface- and volume-scattering model and an ice-feature distribution obtained during the 1993 field season, agree well with actual AAFE waveforms taken in the same time period. Using a combined surface- and volume-scattering model for the dry-snow-zone return waveforms, the rms surface height and slope and the attenuation coefficient of the snowpack are obtained. These scattering models not only allow geophysical parameters of the ice sheet to he measured but also help in the understanding of satellite radar-altimeter data.

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.]