The Cryosphere, 11, 2799–2813, 2017 https://doi.org/10.5194/tc-11-2799-2017 © Author(s) 2017. This work is distributed under the Creative Commons Attribution 4.0 License. A continuum model for meltwater flow through compacting snow Colin R. Meyer1 and Ian J. Hewitt2 1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA 2Mathematical Institute, Woodstock Road, Oxford, OX2 6GG, UK Correspondence to: Colin R. Meyer (
[email protected]) Received: 2 July 2017 – Discussion started: 19 July 2017 Revised: 13 October 2017 – Accepted: 23 October 2017 – Published: 11 December 2017 Abstract. Meltwater is produced on the surface of glaciers health of glaciers and ice sheets under atmospheric warming and ice sheets when the seasonal energy forcing warms the (Harper et al., 2012; Enderlin et al., 2014; Forster et al., 2014; snow to its melting temperature. This meltwater percolates Koenig et al., 2014; Machguth et al., 2016). The balance be- into the snow and subsequently runs off laterally in streams, tween runoff, refreezing, and storage is controlled by the me- is stored as liquid water, or refreezes, thus warming the sub- chanics and thermodynamics of the porous snow. These pro- surface through the release of latent heat. We present a con- cesses also underlie the rate of compaction of firn into ice and tinuum model for the percolation process that includes heat therefore control the average temperature and accumulation conduction, meltwater percolation and refreezing, as well as rate that provide surface boundary conditions to numerical mechanical compaction. The model is forced by surface mass ice-sheet models (which typically do not include the com- and energy balances, and the percolation process is described pacting firn layer explicitly).