An enthalpy formulation for glaciers and ice sheets

TLDR

Polythermal conditions are ubiquitous in glaciers, but conventional cold‑ice models fail to conserve energy because they ignore latent heat, whereas a single enthalpy variable simultaneously represents temperature and liquid‑water fraction. The paper introduces a unified enthalpy formulation that models mass and energy balance for three‑dimensional ice, surface runoff, and subglacial hydrology in a single energy‑conserving framework, aiming to provide an accessible foundation for glaciological studies. The formulation treats temperature and liquid‑water fraction as functions of enthalpy and is implemented in the Parallel Ice Sheet Model to simulate the coupled ice, runoff, and subglacial systems. When applied to the Greenland ice sheet, the enthalpy model’s results differ from those of a cold‑ice scheme, demonstrating the impact of accounting for latent heat.

Abstract

Abstract 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 threedimensional 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.