Theory of water transport in melting snow with a moving surface

A model is presented for the transport of water in melting snow where the s now surface and percolation front are treated as propagating singular surfa ces. It is based on Colbeck's theory of water transport in bulk snow supple mented with boundary conditions that explicitly include the production of w ater by snow melting at the surface due to a surface heat supply. The conse quent motion of the snow surface leads to a free boundary problem, where th e snow surface must be determined as part of the solution, which itself dep ends on the motion of the snow surface. Explicit relations are obtained for the propagation of the melt surface and percolation front. Numerical examp les 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, f or commonly reported parameter values of deep, homogeneous snow packs, smal l motions of the snow surface generally lead to small corrections in the wa ter saturation and flux. (C) 2000 Elsevier Science B.V. All rights reserved .