Modeling of the Morphological Pattern Development for Thermokarst Plains with Fluvial Erosion Based on Remote Sensing Data

The purpose of this work is to present the results of mathematical modeling of the morphological pattern development for thermokarst plains with fluvial erosion based on the approaches of the mathematical morphology of landscapes and using remote sensing data. The theoretical analysis has resulted in the model of the morphological pattern development for thermokarst plains with fluvial erosion, which has been empirically tested at a few key sites. The analysis has allowed us to conclude that the theoretical results on the exponential distribution of khasyrei areas are confirmed empirically in different physicogeographical, geological, and geocryological environments and that the distribution of the areas of thermokarst lakes within thermokarst plains with fluvial erosion obey both gamma- and lognormal distributions. It is shown that the distribution of average radii and diameters of the khasyreis should be the Rayleigh distribution. This analysis indicates that the variant of the synchronous start of thermokarst processes is the most common at the sites under consideration. The model also allows us to assess dynamic parameters of the processes using the landscape metrics of a single time slice.