Mathematical modeling of temporal changes in snow-firn properties in the cold season

Abstract

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.

The effect of wind on the snow cover

“…Such density profiles lead us to conclude that in the equations of snow densification (Guseva-Lozinski, 1997), dependent on the type of snow and its mechanical properties, the influence of the mechanical wind pressure must be considered only for the near-surface part of the snowpack, and can be excluded from considerations below a certain depth. For the snow used in the present experiments, this depth was approximately 0.07 m.…”

Modelling thermomechanical properties of the snowpack

“…The current paper is based on a revised version of the mathematical model describing the non-uniform stratified snow cover (Golubev and Guseva, 1987; Guseva and Golubev, 1989, 1990; Guseva-Lozinski, 1997, 1998, 1999; Golubev and Frolov, 1998). The main difference between this approach and other work is that the equations include macro- and micro-diffusion and describe ice-matrix element changes.…”