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

Abstract

Abstract-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 powerlaw scaling, between horizontal scale and roughness statistics is very common. The rms slope at the horizontal scale of the illuminating wavelength s(A) 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 6'(A) at 35°-60° 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.

Earth-based 12.6-cm wavelength radar mapping of the Moon: New views of impact melt distribution and mare physical properties

“…Nearside Maria 45 deg Incidence The mean circular polarization ratios for Mare Imbrium flows of low TiO 2 content are similar to or greater than those of rough terrestrial lava surfaces, which have a maximum CPR value of about 0.6 at 60°incidence angle (Campbell, 2009). These relatively high values are partly a result of the sensitivity of the 12.6-cm radar signal to few-centimeter scale, near-surface rocks associated with even small impact craters in the mare regolith.…”

Selection of the InSight Landing Site

“…The radar images have a best spatial resolution of ∼3 km, but the echoes are sensitive to small-scale (0.1-1 m) surface roughness and to rocks larger than a few cm within the signal's penetration depth (1-3 m). Arecibo image data provide a strong constraint on surface roughness by comparison with well-calibrated observations of terrestrial-analog surfaces (e.g., Campbell 2001;2009;. Low-power returns may indicate a fine-grained mantling material, which can be further investigated by other means.…”

Initial observations of lunar impact melts and ejecta flows with the Mini‐RF radar

“…A double‐bounce geometry occurs when the radar wave reflects from two surfaces before returning to the receiver, thereby causing the received circular polarization state to be the same as that transmitted. Extremely rugged terrain can sometimes produce circular polarization ratios greater than one [e.g., Campbell and Campbell , 1992; Campbell , 2009]. These high CPR values cannot be caused by Bragg scattering from wavelength scale roughness [e.g., Ulaby et al , 1986] and require that a significant amount of the backscatter come from double‐bounce geometries.…”