We present an implicit three-dimensional thermal solver for polythermal ice based on the enthalpy formulation proposed by Aschwanden et. al. (2012), with the addition of the gravity-driven moisture drainage model proposed by Schoof and Hewitt (2016). The thermal solver is implicitly coupled with the Blatter-Pattyn ice sheet flow model allowing ice velocity and temperature to be solved together directly, either transiently or at steady state.

We show results on simplified geometries as well as for large-scale ice sheet problems, and compare them with results from the literature or obtained with other formulations. In particular we use the model to produce a steady-state initial condition and compare it with initial conditions obtained by “spinning-up” the temperature using explicit thermal solvers.
We investigate the effects of single features of the presented model. In particular we study the differences on the temperature computed with our fully 3D implementation vs the more traditional approach where diffusion and advection operators are split into a 2D horizontal advection and a 1d vertical diffusion.