Macroscopic Modeling for Heat and Water Vapor Transfer in Dry Snow by Homogenization

TLDR

Dry snow metamorphism, a key topic in cryospheric science, is primarily driven by heat and water vapor transfer through snow, including sublimation and deposition at the ice‑pore interface. This study derives a macroscopic equivalent model for heat and water vapor transfer in dry snow by homogenizing pore‑scale physics. The model homogenizes heat conduction, vapor diffusion, sublimation, and deposition, yielding two coupled transient diffusion equations with a phase‑change source term, and computes the effective vapor diffusion tensor from 3D snow images. Dimensional analysis and 2D simulations demonstrate that phase‑change source terms cannot be neglected except under small temperature gradients, and the self‑consistent formula estimates the effective diffusion coefficient within about 10% error, confirming that effective vapor diffusion is not enhanced in snow.

Abstract

Dry snow metamorphism, involved in several topics related to cryospheric sciences, is mainly linked to heat and water vapor transfers through snow including sublimation and deposition at the ice-pore interface. In this paper, the macroscopic equivalent modeling of heat and water vapor transfers through a snow layer was derived from the physics at the pore scale using the homogenization of multiple scale expansions. The microscopic phenomena under consideration are heat conduction, vapor diffusion, sublimation, and deposition. The obtained macroscopic equivalent model is described by two coupled transient diffusion equations including a source term arising from phase change at the pore scale. By dimensional analysis, it was shown that the influence of such source terms on the overall transfers can generally not be neglected, except typically under small temperature gradients. The precision and the robustness of the proposed macroscopic modeling were illustrated through 2D numerical simulations. Finally, the effective vapor diffusion tensor arising in the macroscopic modeling was computed on 3D images of snow. The self-consistent formula offers a good estimate of the effective diffusion coefficient with respect to the snow density, within an average relative error of 10%. Our results confirm recent work that the effective vapor diffusion is not enhanced in snow.