Representation of Process Development Laws in Morphological Pattern Laws: Approach of the Mathematical Morphology of Landscape

Abstract

The research is aimed at showing interrelations between quantitative parameters of the landscape morphological pattern and those of landscape forming processes based on the mathematical morphology of landscape. Landscape of thermokarst plains with fluvial erosion is a typical example of an area under a unidirectional process. We obtained the general expressions for morphological patterns describing interrelations of thermokarst and fluvial erosion processes with regularities of morphological patterns. Thermokarst lake radii obey the chi-distribution, areas obey the gamma distribution. Khasyrei radii obey the Rayleigh distribution, areas obey the exponential distribution. Landscapes with the broad development of landslides is an example of an area in a dynamic balance state. The mechanism of the relationship among dynamic parameters of geomorphological processes and the morphological pattern at any time was theoretically substantiated for a wide class of geomorphological processes which can be named the complex cyclic processes. The mathematical model of geomorphological processes, called the complex cyclic processes, was developed based on Markov chain technique. We obtained the expressions allowing us to estimate dynamic parameters of the current process with the help of quantitative characteristics of the morphological pattern from a single time slice.