Quantification of terrain plan concavity and convexity using aspect vectors from digital elevation models

Abstract

Terrain plan concave and convex parts are important topographical shapes that affect the convergence and divergence of flow. The plan concavity and convexity are generally calculated through the curvature method, which is limited by the serious sensitivity to digital elevation model (DEM) errors and scale dependence. In this study, we propose an aspect vector method to quantify the terrain plan concavity and convexity. This method considers different aspect changes of the plan concavity and convexity, which reduces the scale effect on the curve bending quantification. The proposed method is applied to a mathematical Gaussian surface and two different case studies using a DEM with resolution of 5 m. A comparative analysis is conducted between the proposed and existing curvature-based methods to assess the capability of the former. The results show that the proposed method achieves more realistic and accurate terrain plan concavity and convexity than does the existing method. Moreover, the aspect vector approach is less strongly affected by the spatial resolution of the DEM than is the existing curvature-based method, which demonstrates the application potential of the former to other studies. Furthermore, the concept of aspect vector can be expanded to quantify the terrain concavity and convexity from other directions and promote the development of existing curvature-based terrain quantification methods in geomorphometry.