Multi-scale analysis of surface roughness

Abstract

Different approaches have been made concerning the definition, calculation and application of surface roughness in the Earth and Planetary Sciences. A single definition of surface roughness may not be possible, due to different types of analysis in different contexts. In this article, we use surface roughness as a expression of the variability of a topographic surface at a given scale, where the scale of analysis is determined by the size of the landforms or geomorphic features of interest. Three approaches to surface roughness determination (area ratio, vector dispersion and standard deviation of elevation) were selected for an analysis of the variable's behaviour at different scales and dataset resolutions, and applied as sequences of moving-window and raster algebra steps to a test area in Scotland. Area ratio operated independently of scale, providing consistent results across different spatial resolutions, although steep, smooth, slopes appear as rough terrain. Vector dispersion produced results with increasing roughness and homogenisation of terrain at coarser resolutions and larger window sizes. Whilst steep, smooth, slopes had low roughness values, breaks-of-slope were not readily identified and regional relief more difficult to identify. Standard deviation of elevation correctly identified breaks-of-slope and was good at detecting regional relief, although standard image processing techniques (such as contrast stretches) may be required to emphasise small features at fine resolutions and small window sizes. In addition to good performance at a variety of scales, the simplicity of calculation is perhaps its single greatest benefit, easily achievable in any raster based software. The final scale of analysis, that is, which geomorphic features can be identified, will be determined by an interaction between neighbourhood size and spatial resolution of the DEM.