Abstract
Abstract. The thermal state of an ice sheet is an important control on its past and future evolution. Some parts of the ice sheet 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 and Sea-Level System model (ISSM) that show a better performance than earlier implementations. In a first polythermal-slab experiment, we found that the treatment of the discontinuous conductivities at the CTS with a geometric mean produces 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 do not account 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.
Highlights
Ice sheets and glaciers are important components of the climate system
With decreasing K0/Kc, the temperate ice layer thickness consistently decreases for the harmonic and geometric mean models and is almost halved for the lowest conductivity ratio K0/Kc = 10−5; the solution converges to the analytical cold–temperate transition surface (CTS) elevation for the high mesh resolution
For the harmonic mean, we detect a larger spread over the grid resolutions at low K0/Kc compared to the geometric mean
Summary
Ice sheets and glaciers are important components of the climate system. Their evolution is one of the primary sources of sea-level change (Church et al, 2013). Besides the interactions of the ice sheet with the environment, changes in ice flow can alter the internal thermal state of the ice, which in turn can affect ice dynamics The heat generated by viscous deformation leads to a change in phase (Fowler, 1984; Blatter and Hutter, 1991); temperate ice contains liquid water. The decrease in the ice viscosity with increasing content of liquid water in temperate ice in turn enhances ice flow (Duval, 1977), especially if the temperate ice is present in basal layers, where shear deformation is largest
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