Study of dynamics regularities for morphological pattern of abrasion shores of cryolithozone based on complexing mathematical modeling and space imagery

The article is devoted to the study of dynamics regularities of abrasion shores of the cryolithozone based on complex mathematical modeling and space imagery and their significance for obtaining information on dynamic parameters of ongoing processes based on remote sensing data. The studied landscape of abrasion shores is a combination of thermal cirques of different ages and preservation, it develops under the action of processes of both the appearance of new thermal cirques and partial or complete erasure of existing ones due to the formation of new ones. The characteristic feature of thermal cirques is a clear arc-shaped boundary with the adjacent watershed surface, which is well detected on remote sensing data. The technique includes creating and analyzinga mathematical model of the morphological pattern changes of abrasion shores within the cryolithozone. The model uses the approach of the random process theory and empirical measurement of thermal cirques in different physiographic conditions on space imagery. The combination of mathematical modeling with space imagery interpretation allowed us to show that in different physiographic and geocryological conditions, a stable stationary distribution of thermal cirque sizes of abrasion shores of the Arctic cryolithozone is formed with a significant development time in homogeneous areas. The physiographic and geocryological variety of different sites does not prevent the existence of the limiting stationary distribution. Thus, the morphological pattern of the abrasion shore, being in constant change, nevertheless has a stationary distribution of thermal cirque sizes, their average size, and average location density, i.e., it is in a state of dynamic balance. The research gave a mathematical dependence between the limiting thermal cirque size distribution for abrasion shores and the size distribution for forming young thermal cirques. The sites’ physical-geographical, geological-geomorphological, and geocryological conditions influence the character of the stationary limit distribution through the size distribution of forming young thermal cirques. The results obtained allow us to predict quantitative characteristics of the thermal cirques (and consequently landslides) formation process, namely, the size distribution of emerging new thermal cirques and landslides, based on measurements of the observed thermal cirque sizes using high-resolution single-shot remote sensing data. This is essential in predicting the development, in particular, of shore retreat.