An empirical anisotropic flow relation for ice-sheet modeling: development and implementation

The largest source of uncertainty in predictions of future sea levels is the contribution arising from the discharge of grounded ice from the polar ice sheets. A key factor in reducing this uncertainty is to improve the numerical models used to predict ice-sheet evolution. One important development is improving the description of the ice-flow physics used in ice-sheet models. Primary considerations in the specification of a realistic flow relation for ice are that it includes the effect of the anisotropy of polycrystalline ice on deformation in a realistic manner without dramatically degrading the computational efficiency of the model. We describe the key features of an empirical flow relation for ice that is based on tertiary creep rates from experiments conducted in simple shear, confined compression and a combination of these. We refer to this flow relation as ESTAR (empirical scalar tertiary anisotropic rheology). In ESTAR the anisotropic flow enhancement, which is typical of polycrystalline ice during steady tertiary creep, is described by a simple function of the stress configuration that reflects the presence of simple shear. ESTAR also maintains a collinear relationship between components of the strain rate and deviatoric stress tensors; aiding its incorporation into existing ice-sheet models. ESTAR has been implemented in the model ISSM (Ice Sheet System Model) and, in a simplified form termed ESTAR-MFL (MFL: minimal flow law), in the model SICOPOLIS (SImulation COde for POlythermal Ice Sheets). We present a preliminary assessment of the flow relation based on a series of idealized simulations, including tests developed previously for the intercomparison of ice-sheet models. In each case the ESTAR results are compared to corresponding simulations in which the prevailing isotropic rheology prescribed by the Glen flow relation is used. We demonstrate that ESTAR provides a noticeably different description of ice dynamics, particularly in situations where the flow regime is characterized by spatial variations or greater complexity in the proportions of shear and normal stresses.