Variability of the morphometric characteristics of valley networks caused by variations in a scale

Abstract

According to their shape, the valley networks are divided into six basic types (Howard 1967; Fairbridge 1968; Demek 1987; Babar 2005; Hugget 2007). Relevance to the given shape tends to be determined only based on the visual similarity to the pattern of the given network shape. The valley networks have a fractal character (Turcotte 1997, 2007a, 2007b; Baas 2002; Mandelbrot 2003) and their analysis is influenced by the scale selection (sensu Bendix 1994). This article indicates the quantitative tools, with assistance of which it is possible to characterize the morphology (shape) of the valley network and determine their variability caused by the scale change. The monitored morphometric characteristics (quantitative tools) are: 1) “number of various order valleys” according to the Gravelius order system; 2) “valley networks’ density”; 3) “bifurcation ratio of various order valleys”; 4) “total lengths of various order valleys”; 5) “total length-order ratio of various order valleys”; 6) “average lengths of various order valleys”; 7) “average length-order ratio of various order valleys”; 8) “fractal dimension of various order valleys”; 9) “relative fractal dimension of various order valleys”; 10) “valley junction angles”; 11) “homogeneity of various order valleys”. These characteristics have been applied to the paradigmatic examples of the schematic valley networks and have been analyzed in three scales. In order to analyze the valley networks, the most suitable are “valley junction angles” and “homogeneity of various order valleys”, i.e. morphometric characteristics resistant to any increase in the scale, “number of various order valleys” and “total lengths of various order valleys”, where the relevant values dropped while increasing the scale, but the normal (Gauss) distribution of values was preserved.