A continuum model for meltwater flow through compacting snow

Meltwater is produced on the surface of glaciers and ice sheets when the seasonal surface energy forcing warms the snow to its melting temperature. This meltwater can run off the surface in streams or percolate through the porous snow and refreeze, which warms the subsurface through the release of latent heat. We model the percolation process from first principles using a continuum model that includes heat conduction, meltwater percolation and refreezing, as well as mechanical compaction. The model is forced by surface mass and energy balances. When the surface temperature reaches the melting point, we compute the amount of meltwater produced and allow it to percolate through the snow according to Darcy's law, or to run off the surface if the snow is already saturated. The model outputs 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. 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 firn temperatures occur at intermediate values of the surface forcing when perennial water storage is predicted.