Comparison of polynomial models for land surface curvature calculation

Curvature is a fundamental surface property whose application, for example in geomorphology and hydrology, has long been recognised. Its measurement from Digital Terrain Models (DTMs) has received less attention than that of slope, and there is even disagreement about which definitions of curvature are most applicable. Here these problems are related to semantic problems in the definition of the land surface, and three distinct algorithms for the three main gravity-related components of curvature are compared for both artificial and real surfaces. Quadratic-based algorithms are shown to give more stable results. Higher-order local surfaces (e.g. partial quartic) can fit more complex landform features, but are reliable only for very accurate data.