Enthalpy balance methods versus temperature models in ice sheets

In this paper we propose and numerically solve an original enthalpy formulation for the problem governing the thermal behaviour of polythermal ice sheets. Although the modelling follows some ideas introduced in Aschwanden and Blatter (2009), nonlinear basal boundary conditions in both cold and temperate regions are also considered, thus including the sliding effects in the frame of a fully coupled shallow ice approximation (SIA) model. One of the main novelties of this work comes from the introduction of the Heaviside multivalued operator to take into account the discontinuity of the thermal diffusion function at the cold-temperate transition surface (CTS) free boundary. Moreover, we propose a duality method for maximal monotone operators to solve simultaneously the nonlinear diffusive term and the free boundary. Some numerical simulation examples with real data from Antarctica are presented and illustrate the small differences between the computed results from the enthalpy formulation here proposed and the alternative formulation in terms of the temperature (Calvo et al., 2001).