Roughness of Hawaiian volcanic terrains

Abstract

[1] We performed analyses of topographic variation (surface roughness) using a new 2-D mapping method which shows that understanding the relationship between data resolution, Hurst exponent, y intercept, RMS deviation, and cell size is important for assessing surface processes. We use this new method to assess flows at six field sites in Kilauea caldera, Hawaii, using three data sets at different resolutions, TOPSAR (10 m/pixel), airborne lidar (1 m/pixel), and tripod-mounted lidar (0.02-0.03 m/pixel). The flows studied include ponded pahoehoe flows, compound pahoehoe flows, and jumbled, slabby pahoehoe. The 2-D quantification of surface roughness for the Kilauea lava flows indicates that features formed during emplacement and modification of the flows exhibit statistically distinct roughness signatures. The 2-D method provides a tool for unit mapping based on surface roughness. Key findings indicate that the new 2-D method provides more robust results than 1-D methods for surface roughness because of larger 2-D sample sizes and the removal of 1-D directional bias leading to a reduction in error. Furthermore, data set resolution relative to the scale of the features under study is important to consider when designing a 2-D surface roughness study. Future applications to topographic data sets from Mars will provide information on flow emplacement conditions and spatial and temporal evolution of volcanic provinces on Mars.

Self-affine subglacial roughness: consequences for radar scattering and basal water discrimination in northern Greenland

“…Self-affine scaling corresponds to when the vertical roughness increases at a fixed slower rate than the horizontal length scale, following a power-law relationship that is parameterised by the Hurst exponent (Malinverno, 1990;Shepard et al, 2001). It is observed for a wide variety of natural terrain (Smith, 2014), including the surface of Mars (Orosei et al, 2003), volcanic lava (Morris et al, 2008), and alluvial channels (Robert, 1988). If widely present, the self-affinity of subglacial roughness poses a challenge for integrating topographic roughness with existing glacial radar scattering models (Berry, 1973;Peters et al, 2005;MacGregor et al, 2013;Schroeder et al, 2015).…”

A laboratory study of the effects of roughness on the thermal infrared spectra of rock surfaces

“…The shoulder marks the transition from abrasive roughening at shorter length scales to pre-existing roughness at longer lengths scales. This type of change in slope (or break in Hurst exponent) has been observed in field and lab-based investigations (Chauvy et al, 1998;Shepard et al, 2001;Morris et al, 2008), which have demonstrated that the Hurst exponent correlates with the physical processes at a particular horizontal scale (Shepard et al, 2001). Shoulder ''points'' are located by linearly fitting the last several data points on either end of the log-log plot and calculating the point on the curve where there is equal variance from both lines.…”

“…The profile shapes compare well to the fine and coarse particle sandblasted titanium surfaces of Chauvy et al (1998). Many natural surfaces (e.g., lava flows, weathered surfaces) are fractal in nature (Mandelbrot, 1982;Shepard et al, 1995;Morris et al, 2008). For a surface to be considered fractal, the data on a log-log plot must be linear over a measurement of length scale of at least an order of magnitude (Stemp and Stemp, 2003).…”

Dispersion index of topographic surfaces

“…1). Surfaces can also be characterized through statistical descriptors such as roughness and the Hurst exponent (Shepard et al, 2001;Orosei et al, 2003;Morris et al, 2008). The latter properties are not local, and characterize the morphology at each point based on an increasingly wider neighborhood as the considered wavelength increases.…”