A temperature only formulation for ice sheets

Abstract

Temperature plays an important role in the dynamics of large flowing ice masses like glaciers and ice sheets. Because of this role many models for ice sheets model temperature in some form. One type of model for polythermal glaciers (glaciers which contain both ice below, and at the pressure-melting temperature) explicitly separates the ice into distinct cold and temperate regimes, and tracks the interface between them as a surface. Other models track the enthalpy (internal energy) across both domains, with temperature being a function of enthalpy. We present an alternative mathematical formulation for polythermal glaciers and ice-sheets, in the form of a variational inequality for the temperature field only. Using the calculus of variations, we establish some sufficient conditions under which our formulation is well-posed. We then present some numerical approximations of solutions obtained via the Finite Element Method.