Michael K. Shepard

The roughness of natural terrain: A planetary and remote sensing perspective

We examine the various methods and parameters in common use for quantifying and reporting surface topographic “roughness.” It is shown that scale-dependent roughness parameters are almost always required, though not widely used. We suggest a method of standardizing the parameters that are computed and reported so that topographic data gathered by different workers using different field techniques can be directly and easily intercompared. We illustrate the proposed method by analyzing topographic data from 60 different surfaces gathered by five different groups and examine the information for common features. We briefly discuss the implications of our analysis for studies of planetary surface roughness, lander safety, and radar remote sensing modeling and analysis.

Viking Lander image analysis of Martian atmospheric dust

We have reanalyzed three sets of Viking Lander 1 and 2 (VL1 and VL2) images of the Martian atmosphere to better evaluate the radiative properties of the atmospheric dust particles. The properties of interest are the first two moments of the size distribution, the single-scattering albedo, the dust single-scattering phase function, and the imaginary index of refraction. These properties provide a good definition of the influence that the atmospheric dust has on heating of the atmosphere. Our analysis represents a significant improvement over past analyses (Pollack et al. 1977, 1979) by deriving more accurate brightnesses closer to the sun, by carrying out more precise analyses of the data to acquire the quantities of interest, and by using a better representation of scattering by nonspherical particles. The improvements allow us to better define the diffraction peak and hence the size distribution of the particles. For a lognormal particle size distribution, the first two moments of the size distribution, weighted by the geometric cross section, are found. The geometric cross-section weighted mean radius (reff) is found to be 1.85±0.3 μm at VL2 during northern summer when dust loading was low and 1.52±0.3 μm at VL1 during the first dust storm. In both cases the best cross-section weighted mean variance (νeff) of the size distribution is equal to 0.5±0.2 μm. The changes in size distribution, and thus radiative properties, do not represent a substantial change in solar energy deposition in the atmosphere over the Pollack et al. (1977, 1979) estimates.

Surface modification of Venus as inferred from Magellan observations of plains

In Sedna Planitia, clear stratigraphic relations can be discerned among volcanic flow units. Young flows exhibit SAR specific cross section values similar to fresh terrestrial basalt flows, whereas older flows exhibit backscatter signatures similar to degraded terrestrial basalt flows. Total degradation of ∼1 m depth over ∼0.6 b.y. is inferred for the Sedna area from radar signatures, impact crater abundances, and ejecta superposition relations with respect to volcanic flow units. Analyses of parabolic ejecta deposits associated with the crater Stuart imply that the material is typically centimeters in thickness. A relatively small fraction (∼10%) of Venusian impact craters exhibit prominent parabolic ejecta deposits. These craters are interpreted to be relatively young and parabolic deposits are interpreted to be dispersed by aeolian activity over at least tens of millions of years. The inferred dispersal rate (<10−3 μm/yr) is too low to produce the degradation of flows at Sedna Planitia, and it is concluded that the dominant flow modification process is in situ weathering. In addition, elevation dependent weathering is inferred in western Ovda Regio, where plains above 6054 km radius have enhanced reflection coefficients as compared to adjacent plains at lower elevations. The inferred rate of generation of high reflection coefficient materials is no more than ∼10−2μm/yr, based on the inability of aeolian activity to cover high-reflectivity surfaces with normal reflection coefficient materials and the ubiquitous nature of high-reflectivity surfaces at high elevations. Surface modification rates on Venus are orders of magnitude lower than on Earth. Venusian rates are also much lower than the inferred rate of aeolian dispersal of friable materials on Mars but are comparable to the estimated rate of weathering and erosion of Martian bedrock. Low surface modification rates imply that it will be possible to determine regional-scale age variations on Venus based on the degree of preservation of volcanic landforms and microwave signatures.

Self-affine (fractal) topography: Surface parameterization and radar scattering

Starting with the assumption that planetary surfaces are self-affine (fractal) over the scales applicable to radar scattering, we derive various surface parameters, e.g., rms slopes and autocorrelation functions, and examine the implications for radar scattering models. The results of this work provide several new insights of interest to planetary geologists and others using radar to study surface features. First, the unidirectional slope histograms of self-affine surfaces are Gaussian, and the adirectional slope histograms are Rayleigh. Normalization of the adirectional histogram by solid angle results in a Gaussian adirectional slope density function and therefore a Gaussian quasi-specular angular scattering function. Next, the wavelength dependent behavior of surface roughness inferred from lunar radar observations is consistent with self-affine topography. Finally, surface rms height measurements are functions of profile length. Therefore, when determining the applicability of the small perturbation model to a surface based on those measurements, it is necessary to consider the length of the profile with respect to the sampling wavelength.

Lava flow surface roughness and depolarized radar scattering

Surface roughness has a strong controlling influence on radar scattering and other types of remote sensing observations. We compare field measurements of surface topography and dielectric constant for a range of lava flow textures to aircraft multipolarization radar observations at 5.7, 24, and 68 cm (C, L, and P band) wavelengths. The roughness is found to vary with scale in a self-affine (fractal) manner for scale lengths between 25 cm (the smallest horizontal step size) and 3–5 m. This result is used to demonstrate that a two-component surface description, consisting of the fractal dimension and rms height or slope at some reference scale, can resolve some of the ambiguities in previous efforts to quantify roughness. At all three radar wavelengths, the HV backscatter cross section is found to vary in an approximately exponential fashion with the rms height or Allan deviation at some reference scale, up to a saturation point, where the surface appears entirely diffusely scattering to the radar. Based on these observations, we use a parameter, γ, defined as the ratio of rms height to the particular scale of measurement. Backscatter values at 24-cm wavelength and the topographic profile data were used to derive expressions which link the HV radar cross section to γ or to the analogous wavelength-scale rms slope. These equations provide a reasonable fit to 24- and 68-cm echoes and for rough surfaces at 5.7 cm, but yield poor results for 5.7-cm echoes on smooth terrain. We conclude that the roughness at the two larger scales is well described by a single fractal dimension and rms height, but that texture at very small scales is characterized by different statistics. This inference is supported by analysis of 5-cm horizontal spacing topographic profiles. The relationships defined here allow determination of the surface rms height or slope at the scale of the radar wavelength. Given radar data at additional wavelengths, a more complete view of the statistical properties of the surface can be developed. Such techniques may be useful in analyses of synthetic aperture radar images for terrestrial volcanic areas, Magellan data for Venus, and other planetary radar observations.

Optical scattering properties of terrestrial varnished basalts compared with rocks and soils at the Viking Lander sites

Basalt flows at the Pisgah Volcanic Field, California, are mantled by aeolian silt-sized deposits. The bright mantle is overlain by a dense pavement of basalt cobbles smoothed by aeolian abrasion and coated with glossy dark gray and red desert varnishes. In contrast, the two Viking landing sites on Mars lack desert pavements, and rocks have glossy surfaces that in some cases are brighter than soils. To pursue further the scattering characteristics of varnished basalt cobbles for comparison to Mars rocks, laboratory measurements of bidirectional reflectance (0.69 μm center wavelength) were made as a function of incidence and emission angle along the principal plane for varnished and fresh basalt surfaces. The reflectance data, fit with a scattering model that includes specular reflections from rough surfaces and volume penetration and reflection, show that the red varnished surfaces have higher single scattering albedoes and higher surface roughness values than the dark gray varnished surfaces (0.56 and 0.42; 21° and 17°, respectively). Fresh cut surfaces have lowest values (0.40 and 6°). Results are consistent with observations made from thin sections for these surfaces and with field observations that show dark gray varnished surfaces are smoothed by exposure to wind abrasion. Dark red varnished surfaces tend to be rougher because they are embedded in the aeolian mantle and develop in a protected environment. Application of the model to atmospherically corrected, radiometrically calibrated Viking Lander images (0.60 to 0.74 μm) shows that many rocks are smoother and have single scattering albedoes higher than soils (9° versus 27°; 0.71 versus 0.63, respectively). Results are consistent with a model in which rocks at the surface of Mars become smoothed by aeolian abrasion and coated with atmospheric dust. Lack of desert pavement on Mars is probably associated with a scarcity of cobbles and a lack of soil forming processes. Similar bright, smooth coatings are expected at other locations on Mars, including the Pathfinder Ares Vallis site.

RADAR POLARIZATION PROPERTIES OF VOLCANIC AND PLAYA SURFACES : APPLICATIONS TO TERRESTRIAL REMOTE SENSING AND VENUS DATA INTERPRETATION

The radar polarization properties of lava flows in Hawaii (Kilauea) and Arizona (SP flow), and two play a surfaces (Lunar Lake, Nevada and Lavic Lake, California), are compared to the predicted behaviors of theoretical scattering models. At 5.7 cm and 24 cm wavelengths, Kilauea lava flows can be modeled by a combination of facet and diffuse (dipole-like) scattering. Scattering by rock faces on the scale of the radar wavelength is proposed to account for much of the facet return. The radar echoes at 24-cm wavelength from SP flow are, on average, consistent with entirely diffuse scattering, but there are regions within the flow where circular polarization ratios exceed unity, suggesting a coherent scattering effect. 68 cm data for the lava flows show evidence of radar penetration and volume scattering. The playa surfaces are characterized by polarization properties which in some cases are qualitatively consistent with the first-order small-perturbation model, but the echoes do not closely match the predictions of this model for any reasonable dielectric constant value. These results show that it may be difficult to construct invertible models for the polarization behavior of some surfaces (the playas), whereas for others (the Kilauea lava flows) the scattering properties can be successfully modeled. The first-order small-perturbation model is not appropriate for inverse modeling of most terrestrial lava flows, though very smooth surfaces on Venus may be amenable to the use of this model. High circular polarization ratios observed for SP flow, tentatively attributed here to coherent backscatter, may be analogous to Arecibo observations of high-reflectivity areas on Venus.

Cosmogenic exposure ages of basalt flows: Lunar Crater volcanic field, Nevada

[sup 36]Cl and [sup 10]Be cosmogenic exposure age data for the Black Rock basaltic lava flow, Lunar Crater volcanic field, Nevada, imply an emplacement age of [approximately] 38 [+-] 10 ka. [sup 36]Cl data for the 600 ka flow north of the Lunar Crater maar are consistent with (1) an apparent erosion rate of [approximately] 3 m/m.y., (2) a model of desert pavement formation in which basalt clasts eroded from the flow remain on the surface of the eolian-derived sediments that mantle the flow, and (3) the early formation of the eolian-derived sediment mantle. 20 refs., 3 figs., 2 tabs.

Characterization of lava-flow degradation in the Pisgah and Cima volcanic fields, California, using Landsat Thematic Mapper and AIRSAR data

Digital Landsat Thematic Mapper (TM) observations, multi-frequency polarimetric AIRSAR radar data, microtopographic profiles derived from helicopter-borne photography, and field measurements were analyzed over the Pisgah and Cima volcanic fields, and Lavic Lake playa, Mojave Desert, California. Surface radiance factors were extracted from TM data using radiative transfer procedures to model the atmosphere and surface simultaneously. AIRSAR data were calibrated to backscatter specific cross sections using corner reflectors deployed at a number of locations. Analyses focused on the use of key field sites to understand compositional and textural controls on TM band-5 (1.55 to 1.75 μm) radiance factors and C- (5.6 cm), L- (24 cm), and P- (68 cm) band specific cross sections. For the Pisgah and Lavic Lake sites, the TM data are explained using a linear mixing model of basalt and fine-grained sediment (clay to sand-sized grains of clay minerals, quartz, feldspar, carbonate, and lithic fragments) radiance factors, with the addition of shadows for the rough a9a flow. On the other hand, AIRSAR data are shown to be primarily controlled by surface roughness, as there is a strong correlation between specific cross section and surface height standard deviation. For the elongate flows at the Cima volcanic field, which exhibit a mix of pahoehoe and a9a properties, we find a positive linear relationship between TM band-5 radiance factors and flow ages for the 3 m.y. age range represented. Specific cross sections remain constant until about 0.14 Ma and then decrease with age up to about 0.56 Ma. On the other hand, data for the two older flows (0.70 and 0.85 Ma) show increasing specific cross sections with increasing age. We interpret the increase in TM band-5 radiance factors (from 0.05 to 0.25) with increasing flow age and the decrease in specific cross sections (8 dB change at 35° incidence angle for L band) for flows up to 0.56 Ma in age as due to smoothing by mass wasting and infill by fine-grained aeolian deposits. The increased specific cross sections for older flows are interpreted to be a consequence of surface roughness generated by fluvial dissection.

Specular scattering on a terrestrial playa and implications for planetary surface studies

Multiangle Advanced Solid State Array Spectroradiometer and Portable Apparatus for Rapid Acquisition of Bidirectional Observations of Land and Atmosphere visible and near infrared reflectance data covering the Lunar Lake playa, Nevada, were modeled using specular and volume scattering theory. The volume component used to model the data was based on the Hapke (1986) model and the specular scattering component was based on Fresnel reflection from surface facets with a distribution of tilts. Specular scattering was needed to explain the several-fold increase in reflectance observed at high phase angles in the solar principal plane. Results imply single scattering albedos of approximately 0.93 to 0.95, a real index of refraction value of approximately 1.52 (at a wavelength of 0.66 μm), a small imaginary index of refraction and an exponential facet tilt probability function for the playa. Electron micrographs showed the playa surface to consist of ensembles of smooth, micrometer-scale ellipsoidal particles on gently undulating topography at the millimeter to centimeter scale. The exponential probability function is consistent with this observation. Mars and the icy satellites are discussed as possible places to look for a significant specular scattering component.