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The purpose of this study was to identify relationships between the quantitative parameters of lake areas and khasyrei areas on erosion thermokarst plains. According to the previously developed model describing the morphological pattern of thermokarst plains with fluvial erosion, these areas reach a dynamic equilibrium state subject to the asynchronous start of thermokarst processes and a protracted development period amid slight climatic changes; in such situations, the distribution of lake areas must follow an integral-exponential distribution. From here it can be derived analytically that the ratio between the mean-square area of thermokarst lakes and their average area is equal to the average khasyrei area. Eleven key sites located in different regions and featuring various geocryological and physiographical conditions were selected to test experimentally the theoretically justified relationship on the basis of high-resolution satellite imagery. The collected empirical data have proven the analytical relationship for the vast majority of the homogeneous sites studied within thermokarst plains with fluvial erosion residing in a dynamic equilibrium state. [ABSTRACT FROM AUTHOR]

The regularities of the distribution of lake sizes on thermokarst plains with fluvial erosion are studied in order to evaluate the risk of dangerous natural processes. According to the previously elaborated model of landscape morphological patterns, thermokarst plains with fluvial erosion reach the status of dynamic balance in case of an asynchronous start of thermokarst processes under conditions of slight climate change and a long evolution period; the distribution pattern of lake areas should follow the integral exponential law. Test plots laid for empirical testing in different regions are characterized by various geocryological and physical–geographical parameters. We tested the conformity of the pattern of lake areas to different types of distribution, using air and space images of high resolution. The results show that the integral exponential law is mainly valid for homogenous parts of thermokarst plains with fluvial erosion. This confirms the model used and proves that the morphological pattern of the thermokarst plains with fluvial erosion is characterized by the status of the dynamic balance. [ABSTRACT FROM AUTHOR]