A Thermodynamic Nonequilibrium Model for Preferential Infiltration and Refreezing of Melt in Snow

Abstract

The transport of meltwater through porous snow is a fundamental process in hydrology that remains poorly understood but essential for more robust predictions of how the cryosphere will respond under climate change. Here, we propose a continuum model that resolves the nonlinear coupling of preferential melt flow and the nonequilibrium thermodynamics of ice-melt phase change at the Darcy scale. We assume that the commonly observed unstable melt infiltration is due to the gravity fingering instability and capture it using the modified Richards equation, which is extended with a higher-order term in saturation. Our model accounts for changes in porosity and the thermal budget of the snowpack caused by melt refreezing at the continuum scale, based on a mechanistic estimate of the ice-water phase change kinetics formulated at the pore scale. We validate the model in 1D against field data and laboratory experiments of infiltration in snow and find generally good agreement. Compared to existing theory of stable melt infiltration, our 2D simulation results show that preferential infiltration delivers melt faster to deeper depths, and as a result, changes in porosity and temperature can occur at deeper parts of the snow. The simulations also capture the formation of vertical low porosity annulus known as ice pipes, which have been observed in the field but lack mechanistic understanding to date. Our results demonstrate how melt refreezing and unstable infiltration reshape the porosity structure of snow and impacts thermal and mass transport in highly nonlinear ways that are not captured by simpler models.