Models of topography

Abstract

Models of topography, such as smooth and non-smooth, single-sided and double-sided, appear to be of value in choosing algorithms to calculate topographic attributes, and assist in predicting and understanding paradoxes in topography, such as statistically predictable or terrain-specific behaviour of landforms. This results in a new vision of how to use geomorphometry in digital terrain analysis: for example, the dependence of topographic attributes on scale creates results in problems of comparing observations obtained from different scales, while the use of predictable landforms may lead to unrealistic expectations of predictable properties of soil or vegetation patterns. The purpose of this chapter is to study models of topography. To achieve this purpose, direct studies on the dependence of topographic attributes on scale are considered, based on a theoretical background, such as two concepts of scale, Gibbs-like phenomena, an internal smoothing in algorithms, and sub-dividing of topographic attributes into non-intersecting classes. Results include a new approach to the comparison of algorithms, some artefacts from Gibbs-like phenomena, and a method to evaluate a minimal grid mesh from contour DEMs. Based on these results and concepts, methodological issues are discussed of both geomorphometry itself, and of its applications in digital terrain analysis.