ABSTRACT. The paper describes a non-linear d ynamic thermomechanical model or the snow-firn development in the high mounta in environm ent during the cold sea son. The model allows the estimation of the thermal and m echanical development of snow in a n inhomogeneous stratifi ed snowpack and in the upper part of the firn layer, th e development of the snow-firn structure and transformation of snow into firn . The non-linear m athematical model consists of a heat problem, water-vapor diffusion problem, densificati on of the snow-firn laye r, structural equ ations a nd strength conditions of th e metamorphosed snow-firn depending on its temperature, structura l parameters, density and rate of sublimation. Th e model includes conditions of snow transformation into firn a nd its structural ch anges. These equations are non-linear and coupled. The iterative finite-d ifference numerical method was used for the calculations and involved a full mathematica l model. Numerical experim ents we re implemented using the complete model as well as real. Th e numerical computations were made for various meteorological data, temperature g radients and in the wide range of structural para meters. Th e calculation res u lts were found to be in good agreement with the results of obse rvati ons.

The paper describes a non-linear dynamic thermomechanical model of the snow–firn development in the high mountain environment during the cold season. The model allows the estimation of the thermal and mechanical development of snow in an inhomogeneous stratified snowpack and in the upper part of the firn layer, the development of the snow–firn structure and transformation of snow into firn. The non-linear mathematical model consists of a heat problem, water-vapor diffusion problem, densification of the snow–firn layer, structural equations and strength conditions of the metamorphosed snow–firn depending on its temperature, structural parameters, density and rate of sublimation. The model includes conditions of snow transformation into firn and its structural changes. These equations are non-linear and coupled. The iterative finite-difference numerical method was used for the calculations and involved a full mathematical model. Numerical experiments were implemented using the complete model as well as real. The numerical computations were made for various meteorological data, temperature gradients and in the wide range of structural parameters. The calculation results were found to be in good agreement with the results of observations.

Studying the structure inside an inhomogeneous stratified snowpack is very important for modelling of the snowpack stability on mountain slopes, and to approximate surfaces of weak zones, and boundaries with different properties These surfaces are often the sliding surfaces of avalanches. Weather conditions" windpumping, snow densification and mechanical and complex heat- and mass-transfer processes define the structural variations of snow and the strength characteristics. The main ventilation components in the snowpack during the snowstorm are the heat and mass exchange between the snow grains and bonds, vapor and heat transfer. The vapor diffusion due to windpumping through snowpack intensifies the metamorphic process We propose the current mathematical model using meteorological data to simulate the snowpack characteristics in order to clarify the changes of the structural and physical-mechanical properties in the stratified snowpack under changing weather conditions. The system of equations allows calculation of the temperature variation in the snowpack, as well as in melted or frozen soil, the snow density, the structural parameters and the snowpack strength on the mountain slope as a function of the heat- and mass-transfer parameters. A numerical finite-difference model for simulations has been used. This allows prediction of the disposition of the depth-hoar layers and the physical-mechanical snow properties. The model has potential to estimate the potential avalanche volume.

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A mathematical model makes it possible to estimate the stability of soils in permafrost, the origin of different forms of underground ice, and pingo formation in several parts of the surface in the permafrost. The cryogenic formation of pingos, which is very widespread in permafrost areas, is investigated in the paper. The velocity and height of pingo growth depend on the total moisture content in soil, the type of soil, the initial salinity and the climate conditions. This problem is addressed using equations of Stefan’s heat problem, filtration and salt diffusion and equations for water pressure, with water moving to the phase boundary under different hydrostatic and osmotic pressures.