Mathematical vector framework for gravity-specific land surface curvatures calculation from triangulated irregular networks

Abstract

Land surface curvature (LSC) is a basic attribute of topography and influences local effects of gravitational energy and surface material transport. However, the calculation of LSCs based on triangulated irregular networks (TINs) has not been fully studied, which restricts further geoscience studies based on TIN digital elevation models (DEMs). The triangular facets and vertices of a TIN are both expressions of the land surface; therefore, based on their adjacency relationship, the LSCs can be calculated. In this study, we propose a mathematical vector framework for LSC calculation based on TINs. We define LSCs from the perspectives of the curvature tensor, slope and normal contour direction vectors, and then provide the calculation operators for LSCs based on both TIN triangular facets and vertices. Next, based on a mathematically simulated surface, we find that the TIN-based method exhibits similar effects on the scale as the grid-based methods and very low error sensitivity. In addition, based on different real landform cases with various data sources, we perform experiments involving land surface concavity–convexity and hillslope unit classification by using the TIN-based method. The results show that the TIN-based method can enhance the performance of TINs in landform classification over grid-based DEM methods. The proposed mathematical vector framework for LSC calculation can improve other geoscience studies based on TINs.

Keywords

• land surface curvature
• triangulated irregular network
• digital elevation model
• mathematical vector operation
• digital terrain analysis