Articles | Volume 11, issue 6
The Cryosphere, 11, 2799–2813, 2017
The Cryosphere, 11, 2799–2813, 2017

Research article 11 Dec 2017

Research article | 11 Dec 2017

A continuum model for meltwater flow through compacting snow

Colin R. Meyer1 and Ian J. Hewitt2 Colin R. Meyer and Ian J. Hewitt
  • 1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
  • 2Mathematical Institute, Woodstock Road, Oxford, OX2 6GG, UK

Abstract. 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 runs off laterally in streams, is stored as liquid water, or refreezes, thus 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 run off from the surface if the snow is fully saturated. The model outputs include the temperature, density, and water-content profiles and 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.

Short summary
We describe a new model for the evolution of snow temperature, density, and water content on the surface of glaciers and ice sheets. The model encompasses the surface hydrology of accumulation and ablation areas, allowing us to explore the transition from one to the other as thermal forcing varies. We predict year-round liquid water storage for intermediate values of the surface forcing. We also compare our model to data for the vertical percolation of meltwater in Greenland.