Relationships between Quantitative Parameters of Lake Areas and Khasyrei Areas on Thermokarst Plains with Fluvial Erosion

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.