# Application of mathematical morphology of landscape for studying thermokarst processes

Category Geomorphology GSI.IR International Geological Congress,oslo 2008 Kapralova, Veronika 21 September 2008

Climatic and technogenic changes have diverse effect on the environment, which reflects on economic activities. The area of development of permafrost rocks is one of the most sensitive to changes. More than 60 % of Russia is a zone of distribution of permafrost. And problems of permafrost rocks and integrated with them exogenous geological processes are very actual for our country. Many researches study thermokarst processes, but statistical methods are less studied, in particular we may tell it about analysis of quantitative aspects of thermokarst processes.
The purpose of this work is to study regularity of structure and development of the morphological structures associated with thermokarst process.
Within the framework of this work an attempt has been made to solve 2 problems:
- analyze regularity of space construction of the morphological structures associated with thermokarst;
- analyze regularity of dynamics of the morphological structures associated with thermokarst.
In our work we use a method of mathematical morphology of a landscape - a branch of landscape science, investigating quantitative laws of landscape mosaics and methods of the mathematical analysis of these mosaics. Theoretical basis of mathematical morphology of a landscape is formed by mathematical models of morphological structures — the quantitative dependences describing basic properties of morphological structures. Canonical initial mathematical models play a special role in mathematical morphology of a landscape. They deal with the patterns developed in uniform conditions at constancy of major factors of landscape differentiation and should develop under unique process.
The further combination of such models, in view of interaction of processes allows us to describe all variety of the morphological patterns developed in the diversified combinations of natural conditions. Also basic equations do not depend on a lot of particular conditions, for example, a material structure of surface sediments, climate, etc. Thus, the model allows us to examine the problems in general, i.e., obtaining a solution fair for a broad spectrum of natural geographical conditions. The equations of the mathematical model of a morphological pattern for thermokarst lake plains were used for the analysis of data and forecast constructions. They represent combination of the probabilistic mathematical relations reflecting the most essential geometrical features of the pattern. The equations include:
- Probabilistic distribution of a number of thermokarst lakes, which have appeared within a specified site during the given time interval
- Probabilistic distribution of changes of thermokarst lake areas The analysis has shown that a number of deductions of proposed mathematical model for thermokarst lake plains, in general are being corroborated by empirical data. The specified deviations, probably, are due to some non-uniformity of terrain.