Elementary forms for land surface segmentation: The theoretical basis of terrain analysis and geomorphological mapping

Land surface morphology is fundamental to geomorphological mapping and many GIS applications. Review and comparison of various approaches to segmentation of the land surface reveals common features, and permits development of a broad theoretical basis for segmentation and for characterization of segments and their boundaries. Within the context of defining landform units that maximise internal homogeneity and external differences, this paper introduces the concept of elementary forms (segments, units) defined by constant values of fundamental morphometric properties and limited by discontinuities of the properties. The basic system of form-defining properties represents altitude and its derivatives, constant values of which provide elementary forms with various types of homogeneity. Every geometric type of elementary form can be characterized by a defining function, which is a specific case of the general polynomial fitted function. Various types of boundary discontinuity and their connections and transformations into other types of morphological unit boundaries are analysed.The wealth of types of elementary forms and their boundaries is potentially unbounded and thus is sufficient to cover the real variety of landforms. Elementary forms in the basic set proposed here have clear potential for genetic and dynamic interpretation. A brief worked example documents the possibility of analytical computation of various models of ideal elementary forms for particular segments of landform. Ideal elementary forms can be considered as attractors, to which the affinity of surface segments can be measured by multivariate statistical methods. The use of the concept of elementary forms in landscape segmentation is promising and it could be adapted for elementary segmentation of various other spatial fields.