Stochastic Modeling of Natural Lacustrine Thermokarst Under Stable and Unstable Climate

Many researches are devoted to the problem of lacustrine-thermokarst plain development. The purpose of this study is a stochastic modeling of the thermokarst plains’ pattern and development, primarily the morphological pattern of their landscapes. The bases of model creation are the approaches of mathematical morphology of landscape with wide use of random process theory. Studying territory type represents a slightly wavy subhorizontal surface with a predominance of different tundra or forest vegetation with the sprinkled lakes, without significant development of the erosion network. Several types of stochastic models were developed. These models were empirically verified at 16 sites all over cryolythozone. Theoretical statistical distributions of the lakes’ number on the randomly chosen site within lacustrine-thermokarst plains correspond to the Poisson distribution on the plots relatively homogenous by the geomorphological, geocryological, and landscape conditions and under various assumptions about the nature of development of the lacustrine-thermokarst plains; this is largely confirmed by empirical data. Theoretical statistical distributions of the thermokarst lake sizes within the lacustrine-thermokarst plains are different under various assumptions about the nature of development of the lacustrine-thermokarst plains on the plots relatively homogenous by the geomorphological, geocryological, and landscape conditions. The analysis of the empirical data shows that the observed distributions of the lakes’ number at randomly chosen site correspond to the Poisson distribution and the distributions of the thermokarst lake sizes in the overwhelming majority correspond to the lognormal distribution and do not agree with other types of distributions being investigated. The analysis leads to a conclusion in favor of a model based on the proportionality of the growth rate of the thermokarst lake size to the average heat loss density through the side surface in case of the synchronous start of the processes of thermokarst lake appearance for every plot.