A continuum model for meltwater flow through compacting snow

Meltwater is produced on the surface of glaciers and ice sheets when the seasonal energy forcing warms the snow to its melting temperature. This meltwater percolates into the snow and subsequently either runs off laterally in streams, is stored as liquid water, or refreezes, hence warming the subsurface through the release of latent heat. We present a continuum model for the percolation process that includes heat conduction, meltwater percolation and refreezing, as well as mechanical compaction. The model is forced by surface mass and energy balances, and the percolation process is described using Darcy’s law, allowing for both partially and fully saturated pore space. Water is allowed to runoff from the surface if the snow is fully saturated. The model outputs include the temperature, density, and water-content profiles as well as the surface runoff and water storage. We compare the propagation of freezing fronts that occur in the model to observations from the Greenland ice sheet. We show that the model applies to both accumulation and ablation areas and allows for a transition between the two as the surface energy forcing varies. The largest average firn temperatures occur at intermediate values of the surface forcing when perennial water storage is predicted.