Dynamic modeling for the morphological pattern of thermokarst plains with fluvial erosion on the base of remote sensing data

The paper deals with the results of the analysis of the dynamic mathematical model for the morphological pattern of thermokarst plains with fluvial erosion basing on the mathematical morphology of landscape approach and remote sensing data. The theoretical analysis resulted in the dynamic mathematical model for the morphological pattern of thermokarst plains with fluvial erosion, which was empirically tested at a set of the key sites. The empirical testing confirms the theoretical results about the exponential distribution of khasyrei areas in different natural environments with a broad geological and geocryological spectrums. Moreover, the area distribution of thermokarst lakes obeys both gamma and lognormal distributions. We have found that the average radius and diameter distributions should be the Raleigh one. The analysis shows that the variant of the thermokarst synchronous start is the most common for the taken key sites. Besides, the model allows us to assess certain dynamic parameters of the processes using landscape metrics from a single time slice.