Remote assessment of natural hazards on the base of the mathematical morphology of landscape

Abstract

The aim of this paper is to show approaches for the quantitative evaluation of natural hazards using the remote sensing data and basing on the results of the mathematical morphology of landscape. The mathematical model of the morphological pattern for lacustrine thermokarst plains with fluvial erosion was taken for the decision of the problem in case of an asynchronous start of the thermokarst process with the continuous generation of new thermokarst depressions. The mathematical analysis of assumptions taken in the model gives us the regularities of the morphological pattern for the thermokarst plains with fluvial erosion including exponential distribution for khasyrei areas, integral-exponential distribution for lake areas, and the Poisson distribution for a quantity of either khasyreis or lakes within the key sites. Besides, analyzing the development of the territory in question by the approaches used in mathematical morphology of landscape we found out that in case of asynchronous start under very general conditions a dynamic equilibrium is established in generating thermokarst lakes and turning them into khasyreis after a long time. At the same time, the distribution density of thermokarst foci and their sizes, as well as process damage and the dimensions of khasyreis tend to some final levels specified by the expressions described above. The results obtained were empirically tested at 17 key sites. Generally, the empirical testing shows that the asynchronous start takes place within thermokarst plains with fluvial erosion at a sufficient number of sites, and the theoretically obtained regulations are valid. The regulations obtained were used for the mathematical solution of the probabilistic task for damage of a linear structure crossing the thermokarst plain with fluvial erosion.