Morphometric Variables

Publisher Summary This chapter describes the topographic surface and landform classifications. The Earth's surface is too complex for rigorous mathematical treatment because it is not smooth and regular. However, for many practically important problems, it is sufficient to approximate the Earth's surface by the topographic surface. Here, the topographic surface as a closed, oriented, continuously differentiable, two-dimensional manifold S in the three-dimensional Euclidean space E3 are described. Three key restrictions are true for the topographic surface. The planar size of the topographic surface is essentially less than the Earth's radius. It is generally assumed that the curvature of the planet may be ignored if the size of the surface portion is less than 0.1 of the average radius of the planet. Landform classifications based on local morphometric attributes are of fundamental importance to the theory of geomorphometry and digital terrain modeling. There are three main quantitative approaches to classifying landforms using information on the local geometry of the surface: the Gaussian classification based on the signs of the Gaussian and mean curvatures, the EfremovKrcho classification using the signs of the horizontal and vertical curvatures, and the Shary classification based on the signs of the Gaussian, mean, difference, horizontal, and vertical curvatures.