Scale-Optimized Surface Roughness for Topographic Analysis

Abstract

Surface roughness is a terrain parameter that has been widely applied to the study of geomorphological processes. One of the main challenges in studying roughness is its highly scale-dependent nature. Determining appropriate mapping scales in topographically heterogenous landscapes can be difficult. A method is presented for estimating multiscale surface roughness based on the standard deviation of surface normals. This method utilizes scale partitioning and integral image processing to isolate scales of surface complexity. The computational efficiency of the method enables high scale sampling density and identification of maximum roughness for each grid cell in a digital elevation model (DEM). The approach was applied to a 0.5 m resolution LiDAR DEM of a 210 km2 area near Brantford, Canada. The case study demonstrated substantial heterogeneity in roughness properties. At shorter scales, tillage patterns and other micro-topography associated with ground beneath forest cover dominated roughness scale signatures. Extensive agricultural land-use resulted in 35.6% of the site exhibiting maximum roughness at micro-topographic scales. At larger spatial scales, rolling morainal topography and fluvial landforms, including incised channels and meander cut banks, were associated with maximum surface roughness. This method allowed for roughness mapping at spatial scales that are locally adapted to the topographic context of each individual grid cell within a DEM. Furthermore, the analysis revealed significant differences in roughness characteristics among soil texture categories, demonstrating the practical utility of locally adaptive, scale-optimized roughness.