Comparative analysis of lake area distributions for lacustrine thermokarst plains and thermokarst plains with fluvial erosion

A comparative analysis of lake area distributions for lacustrine thermokarst plains and thermokarst plains with fluvial erosion has been performed using he mathematical morphology of landscapes and remote sensing. We applied mathematical models of landscape patterns for lacustrine thermokarst plains and thermokarst plains with fluvial erosion under the “synchronous start” of the thermokarst conditions. Twenty-two key sites were included in the empirical testing. The empirical testing involves 22 key sites. These sites have different geomorphological environments within the areas of either continuous and discontinuous permafrost or sporadic permafrost. We have theoretically revealed and validated it empirically that in different natural environments, the lake area distribution within lacustrine thermokarst plains generally corresponds to the lognormal distribution while the gamma-distribution is almost absent. On the contrary, the model shows that lake area distribution within thermokarst plains with fluvial erosion generally corresponds to both the lognormal and gamma-distributions. This result does not exclude different scenarios of lake area distribution patterns for the plains with fluvial erosion under an asynchronous start of the thermokarst. The empirical testing proves the validity of the mathematical models of that the morphological patterns for the lacustrine thermokarst plains and thermokarst plains with fluvial erosion under the synchronous start of thermokarst processes. Therefore, different techniques should be used for the quantitative assessment of the impact probability of the thermokarst processes on engineering structures for the lacustrine thermokarst plains and thermokarst plains with fluvial erosion. The mathematical model used in this study proved to be a good instrument for such assessment.

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