An enthalpy formulation for glaciers and ice sheets

Polythermal conditions are ubiquitous among glaciers, from small valley glaciers to ice sheets. Conventional temperature-based 'cold-ice' models of such ice masses cannot account for that portion of the internal energy which is latent heat of liquid water within temperate ice, so such schemes are not energy-conserving when temperate ice is present. Temperature and liquid water fraction are, however, functions of a single enthalpy variable: a small enthalpy change in cold ice is a change in temperature, while a small enthalpy change in temperate ice is a change in liquid water fraction. The unified enthalpy formulation described here models the mass and energy balance for the three-dimensional ice fluid, for the surface runoff layer and for the subglacial hydrology layer, together in a single energy-conserving theoretical framework. It is implemented in the Parallel Ice Sheet Model. Results for the Greenland ice sheet are compared with those from a cold-ice scheme. This paper is intended to be an accessible foundation for enthalpy formulations in glaciology.