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.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JE001429

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

Surface temperatures of a 1989 andesite lava flow at Volcan Lonquimay, Chile, derived from an analysis of Landsat Thematic Mapper (TM) infrared data, show a progressive cooling of crusted lava from 250°C to 170°C down a 1.5 km segment of the flow. These results are obtained by solving “dual-band” equations for the two short-wavelength infrared TM bands, assuming that the lava surface can be represented by two thermal components, exposed core and chilled crust, and unlike previous investigations, by predetermining the temperature of the hot component rather than the cool component. This approach is consistent with both observational data and theoretical models, and shows that any exposed core of the flow occupies tiny fractions, possibly less than 0.03%, of the surface area. As a result, the crust made by far the greatest contribution to radiative heat losses, estimated at between 1 and 3 MW per 30×30 m pixel, along most of the flow's length. Convective heat transfer into the air above the flow is about two thirds the corresponding radiative flux. These estimated surface heat losses suggest thicknesses of less than 1 m for a conductive thermal boundary layer component of the crust. Radiance values in the thermal infrared band 6 of the TM image are consistent with temperatures derived from the short-wavelength infrared data and reveal the thermal manifestation of a topographic step beneath the flow.

Lava flow cooling estimated from Landsat Thematic Mapper infrared data: The Lonquimay Eruption (Chile, 1989)

Full disk images of Mars have been obtained with the use of the Very Large Array (VLA) to map the radar reflected flux density. The transmitter system was the 70-m antenna of the Deep Space Network at Goldstone, California. The surface of Mars was illuminated with continuous wave radiation at a wavelength of 3,5 cm. The reflected energy was mapped in individual 12-minute snapshots with the VLA in its largest configuration; fringe spacings as small as 67 km were obtained. The images reveal near-surface features including a region in the Tharsis volcano area, over 2000 km in east-west extent, that displayed no echo to the very low level of the radar system noise. The feature, called Stealth, is interpreted as a deposit of dust or ash with a density less than about 0.5 gram per cubic centimeter and free of rocks larger than 1 cm across. The deposit must be several meters thick and may be much deeper. The strongest reflecting geological feature was the south polar ice cap, which was reduced in size to the residual south polar ice cap at the season of observation. The cap image is interpreted as arising from nearly pure CO_2 or H_2O ice with a small amount of martian dust (less than 2 percent by volume) and a depth greater than 2 to 5 m. Only one anomalous reflecting feature was identified outside of the Tharsis region, although the Elysium region was poorly sampled in this experiment and the north pole was not visible from Earth.

https://science.sciencemag.org/content/sci/253/5027/1508.full.pdf

Radar Images of Mars

Volcanology: lessons learned from synthetic aperture radar imagery

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.

/pdf/quantitative-roughness-characterization-of-geological-50qtzalrej.pdf

Quantitative roughness characterization of geological surfaces and implications for radar signature analysis

Analyses of imaging radar data of volcanic terranes on Earth and Venus have emphasized the need for a clearer understanding of how these data can be most effectively used to accomplish important volcanological goals, including the interpretation of eruptive styles and the characterization of the geologic history of volcanic centers. The second Shuttle Imaging Radar experiment (SIR-B) obtained two digital images over the summit caldera and the Southwest Rift Zone of Kilauea Volcano in 1984. Our geologic analyses of these images indicate that SIR-B data are particularly useful for delineating the distribution and surface textural variations of a9a lava flows, for mapping large-scale topographic features with radar-facing slopes, and for identifying an areally extensive pyroclastic deposit. Analyses of the SIR-B data of Kilauea, however, do not permit unambiguous identification of landforms such as pahoehoe lava flows, cinder cones, and fissures. Although separation of low-return units such as pahoehoe lava flows and adjacent pyroclastic ash is not greatly improved using standard image-enhancement techniques, the texture-analysis technique applied here did facilitate discrimination of such smooth-surfaced volcanic deposits. Although analyses of the SIR-B data permit a generally accurate interpretation of the eruptive history of Kilauea, the inability to distinguish low-return pahoehoe flows results in misinterpretation of several aspects of Kilauea volcanism, suggesting that caution should be exercised in the interpretation of SAR data of volcanic terranes.

Geologic analyses of Shuttle Imaging Radar (SIR-B) data of Kilauea Volcano, Hawaii

SIR-B images, field observations, and small-scale (cm) terrain measurements are used to study lave flow surface textures related to emplacement processes of a single Hawaiian lava flow. Although smooth pahoehoe textures are poorly characterized on the SIR-B data, rougher pahoehoe types and the a'a flow portion show image textures attributed to spatial variations in surface roughness. Field observations of six distinct lava flow textural units are described and used to interpret modes of emplacement. The radar smooth/rough boundary between pahoehoe and a'a occurs at a vertical relief of about 10 cm on this lava flow. While direct observation and measurement most readily yield information related to lava eruption and emplacement processes, analyses of remote sensing data such as those acquired by imaging radars and altimeters can provide a means of quantifying surface texture, identifying the size and distribution of flow components, and delineating textural unit boundaries.

Lisa R. Gaddis

Papers

Geologic analyses of Shuttle Imaging Radar (SIR-B) data of Kilauea Volcano, Hawaii

Lava flow surface textures - SIR-B radar image texture, field observations, and terrain measurements

Preliminary analyses of SIR-B radar data for recent Hawaii lava flows