Hyper-scale analysis of surface roughness

Surface roughness is frequently measured using DEMs to characterize the ruggedness and topographic complexity of landscapes. Roughness maps have been applied in geological mapping, ecological modeling, and other environmental applications. These maps are typically derived using a roving-window approach, where kernel size dictates the scale at which roughness is assessed. The pattern of roughness is strongly scale dependent and this roughness-scaling relation can reveal useful information about the geomorphologic character of landscapes. This study applied hyper-scale analysis of a normal-vector based roughness metric for a LiDAR DEM of Rondeau Bay, Canada. The use of integral images, a data structure for computationally efficient filtering operations, allowed for the fine scale resolution of the analysis. The unique roughness scale signature of each grid cell in the DEM was derived for all spatial scales ranging from 3 to 5000 cells (7.5 m to 12,502.5 m). Maps of maximum roughness and the scale of maximum roughness were created for the study site. This cell-specific scaling approach to the characterization of surface roughness is in contrast to the use of single, often arbitrarily selected, kernel sizes to map topographic attributes. The additional information provided by the scale map was found to provide valuable ancillary data for landscape interpretation.