Extended enthalpy formulations in the ice flow model ISSM version 4.17: discontinuous conductivity and anisotropic SUPG.

The thermal state of an ice sheet is an important control on its past and future evolution. Some parts of the ice sheets may be polythermal, leading to discontinuous properties at the cold–temperate transition surface (CTS). These discontinuities require a careful treatment in ice sheet models (ISMs). Additionally, the highly anisotropic geometry of the 3D elements in ice sheet modelling poses a problem for stabilization approaches in advection dominated problems. Here, we present extended enthalpy formulations within the finite-element Ice Sheet System Model (ISSM) that show a better performance to earlier implementations. In a first polythermal-slab experiment, we found that the treatment of the discontinuous conductivities at the CTS with a geometric mean produce more accurate results compared to the arithmetic or harmonic mean. This improvement is particularly efficient when applied to coarse vertical resolutions. In a second ice dome experiment, we find that the numerical solution is sensitive to the choice of stabilization parameters in the well-established Streamline Upwind Petrov–Galerkin (SUPG) method. As standard literature values for the SUPG stabilization parameter are not accounting for the highly anisotropic geometry of the 3D elements in ice sheet modelling, we propose a novel Anisotropic SUPG (ASUPG) formulation. This formulation circumvents the problem of high aspect-ratio by treating the horizontal and vertical directions separately in the stabilization coefficients. The ASUPG method provides accurate results for the thermodynamic equation on geometries with very small aspect ratios like ice sheets. [ABSTRACT FROM AUTHOR]