Theory of water transport in melting snow with a moving surface

Abstract

A model is presented for the transport of water in melting snow where the snow surface and percolation front are treated as propagating singular surfaces. It is based on Colbeck's theory of water transport in bulk snow supplemented with boundary conditions that explicitly include the production of water by snow melting at the surface due to a surface heat supply. The consequent motion of the snow surface leads to a free boundary problem, where the snow surface must be determined as part of the solution, which itself depends on the motion of the snow surface. Explicit relations are obtained for the propagation of the melt surface and percolation front. Numerical examples are given of the propagation of one dimensional meltwater waves in deep snowpacks due to periodic heating of the snow surface. It is shown that, for commonly reported parameter values of deep, homogeneous snow packs, small motions of the snow surface generally lead to small corrections in the water saturation and flux.