A Theory of Water Percolation in Snow

Abstract A theory is developed to describe the vertical percolation of water in isothermal snow. The general theory of Darcian flow is reviewed to establish a reasonable physical basis for the construction of a model. It is shown that in simple gravity drainage, capillarity is negligible compared with gravity since values of water saturation are generally in the “mid-range”. It is postulated that the permeability to the water phase increases as a certain function of the water saturation, and porosity is assumed to decrease linearly with depth. Ice layers and other inhomogeneities are treated in the theory by considering the permeability of the snow with the inhomogeneities included. A method by which this value of permeability can be calculated is presented using the method of characteristics. The theory is applied to the Seward Glacier firn where Sharp measured water fluxes at various depths. A periodic surface flux is assumed and the particular solution for water flux at any depth is given. From this solution the wave forms passing each depth are constructed and compared with the measured ones. Although the experimental data are affected by the presence of ice layers, the comparison between theory and experiment is favorable and the theory is thought to be essentially correct.