On an application of cluster analysis for classification of valley cross profiles using special orthonormal functions

Morphometric approaches deal with obtaining quantitative parameters of relief forms. In particular, such parameters can be used for the classification of diverse relief forms. There is a noticeable demand for such approaches in geosciences. For example, the differentiation of valley forms belongs to the research field of geomorphology. A valley form includes important information with respect to the valley genesis. It is assumed that the U-shape probably corresponds to a glacier-induced valley, but the V-shape reflects the fluvial genesis of a valley. A prior generalisation of valley cross-profiles is necessary in order to obtain their morphometric parameters. These parameters contribute to the valley differentiation. The conventional generalisation approaches are based on the approximation of such cross-profiles using a special function. This function can be a catenary curve, a special polynomial or a set of polynomials. An alternative model is the GPL model. In this paper we propose a new generalisation approach, which uses special orthonormal functions. Based on these functions, form coefficients can be obtained for use in cluster analysis, resulting in the shape classification of valley cross profiles. An application of our approach for a real data set is presented.