Model for Coupled Liquid Water Flow and Heat Transport with Phase Change in a Snowpack

Abstract

The flow of liquid water in a snowpack is complex because of the coupled processes involved, including the phase change between liquid and solid, and the latent and sensible heat transfer processes. To properly describe the details of spatial and temporal changes in a snowpack it is necessary to include these coupled processes. This paper presents a numerical model of coupled liquid water flow and heat transport in a snowpack. The model is intended to quantify infiltration into a snowpack, and evaluate the potential for the formation of distinct heterogeneities in liquid water and heat transport properties in a snowpack. The numerical model solves the two-dimensional form of the governing coupled equations using a finite difference scheme. The governing equations assume thermodynamic equilibrium between the solid and liquid phases in the snowpack. Equations describing the metamorphosis of ice grains during liquid water flow are applied within the model, and the heat and liquid water transport properties of the snow are treated with relations identical to those used for mineral porous media. Sample solution results for an alternative formulation taken from the literature are used to test the present solution, and it is found that the present model yields similar results but with some distinct differences. The effect of direct coupling of the temperature with the liquid water pressure is presented in a simple horizontal freezing simulation, which is compared with the Stefan problem where liquid water is not redistributed. Overall the direct coupling and water redistribution is found to lead to greater front penetration in comparison to the Stefan formulation. For infiltration with gravity it is shown that grain size growth during infiltration leads to increased wetting front penetration.