Topographic Surface and Its Characterization

This chapter discusses the basic physical and mathematical concepts of digital terrain analysis. First, we introduce the notion of the topographic surface and its limitations. Second, we discuss contour lines, special and nonspecial points, slope lines, and flow lines. Third, we present definitions, formulae, and physical meanings for five main groups of morphometric variables, such as local, nonlocal, solar, and combined attributes, as well as structural lines. In particular, we present the derivation of formulae for slope gradient, aspect, plan curvature, horizontal curvature, vertical curvature, unsphericity curvature, rotor, difference curvature, ring curvature, accumulation curvature, the generating function, and insolation. Finally, we discuss three key types of landform classifications: the Gaussian classification, the Efremov-Krcho classification, and the Shary classification.