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

Abstract

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 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.…”