Fundamental quantitative methods of land surface analysis

Abstract

Effective quantitative land surface analyses in soil science need scale-free land surface attributes (morphometric variables, MVs) to be introduced for making comparable results obtained at different scales. To investigate the problem in more detail, a conceptual scheme and curvatures studied earlier in Shary (1995) [Math. Geol. 27 (1995) 373] are further developed in this paper, formulae for a complete system of 12 curvatures and some other MVs are given, and modified Evans–Young algorithm for curvature calculation is described that does not emphasize grid directions. The conceptual scheme is based on that MVs often describe not the land surface itself, but rather the system “land surface+vector field”, where vector fields of common interest are gravitational field and solar irradiation. Correspondingly, morphometric variables and concepts may (1) refer to this system description (field-specific), or (2) be invariant with respect to any vector field (field-invariant), that is, describing the land surface itself, its geometrical form. From the other side, MVs and concepts may be (1) local, (2) regional, which need extended portions of a restricted part of land surface for their determination at a given point, or (3) global (planetary), when elevations of all the Earth are needed for their determination at a given point. Global MVs do not consist subject of this paper; so, the four classes of MVs are considered here: class A (local field-specific MVs), class B (regional field-specific), class C (local field-invariant), and class D (regional field-invariant). MVs of these classes permit description of geometrical land form, pre-requisits of surface runoff, thermal regime of slopes, and altitude zonality. Class A contains three independent MVs expressed by first derivatives of elevation Z by plan coordinates (slope steepness, slope direction, solar insolation) and seven curvatures expressed by second derivatives of Z; class C contains five curvatures; class B contains two variables (catchment and dispersal areas); MVs of class D are not introduced yet. Also, some non-system MVs of class A are described, sense of all MVs is described, and interrelationships between MVs are shown. Three curvatures are independent, not two, as this is often implied. It is experimentally shown that average depth of a depression defined in class B may not depend upon scale, while local MVs may not have limit values for large scales. Scale-free morphometric variables are defined here as those that have limit values for large scales. It is experimentally shown that maximal catchment area (class B) is a scale-free variable for thalwegs. These results show that local MVs are scale-specific (except elevation), but scale-free regional MVs might be introduced as a generalization of curvature concept. Two surface runoff accumulation mechanisms are considered in their relation to local and regional field-specific MVs; although the first one is generalized to a regional MV (catchment area), there is no regional MV for the second one description, although it is of great importance in soil science as describing slow profile changes. Geometrical forms were little studied in soil science; arguments are given that they may be useful for studying memory in soils, which is determined by temporal shifts between land surface formation and soil formation processes. The following topics are discussed: the current state of morphometry, an ambiguity in land form definitions, and a possibility to generalize curvature concept for regional scale-free MVs. The consideration is restricted by methods of the general geomorphometry; partial approaches are considered only by selection.