Models for polythermal ice sheets and glaciers

Polythermal ice sheets and glaciers contain both cold ice and temperate ice. We present two new models to describe the temperature and water-content of such ice masses, accounting for the possibility of gravity- and pressure-driven water drainage according to Darcy's law. Both models are based on the principle of energy conservation; one additionally invokes the theory of viscous compaction to calculate pore water pressure, and the other involves a modification of existing enthalpy gradient methods to include gravity-driven drainage. The models consistently predict the evolution of temperature in cold ice, and of water content in temperate ice. Numerical solutions are described, and a number of illustrative test problems are presented, allowing comparison with existing methods. The suggested models are simple enough to be incorporated in existing ice-sheet models with little modification.