Abstract <p>This paper is devoted to the study of regularities in the dynamics of abrasion shores of the cryolithozone based on a complex of mathematical modeling and space imagery and their significance for obtaining information on dynamic parameters of ongoing processes from remote sensing data. The landscape of abrasion shores with the development of thermocirques is a&#xa0;combination of thermocirques, it is affected by the action of processes of both the appearance of new thermocirques and partial or full erasure of existing ones due to the formation of new ones. The characteristic feature of thermocirques is a clear arc-shaped boundary with the adjacent water-dividing surface which is well identified on materials of satellite photography. The technique includes creation and analysis of a mathematical model of changes in the morphological structure of abrasion shores within the cryolithozone. The&#xa0;model uses the approach of the random process theory and empirical measurement of thermocirque sizes in different physiographic conditions by materials of 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 size distribution of thermocirques 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 structure of the abrasion shore, being in constant change, nevertheless has a stationary distribution of thermocirque sizes, average size, and average location density, i.e., it is in a state of dynamic equilibrium. The research yields a mathematical dependence between the limiting thermocirque size distribution for abrasion shores and the size distribution for forming young thermocirques. The physiographical, geological-geomorphological, and geocryological conditions of sites affect the character of the stationary limit distribution through the size distribution of forming young thermocirques. The results obtained allow us to predict quantitative characteristics of the thermocirque (and, consequently, landslide) formation process; namely, the size distribution of emerging new thermocirques and landslides, based on measurements of the observed thermocirque sizes using high-resolution single-shot remote sensing data. This is essential in predicting the evolution of shores, in particular, of their recession.</p>