A user-friendly anisotropic flow law for ice-sheet modeling

For accurate ice-sheet flow modelling, the anisotropic behaviour of ice must be taken fully into account. However, physically based micro-macro (μ-M) models for the behaviour of an anisotropic ice polycrystal are too complex to be implemented easily in large-scale ice-sheet flow models. An easy and efficient method to remedy this is presented. Polar ice is assumed to behave as a linearly viscous orthotropic material whose general flow law (GOLF) depends on six parameters, and its orthotropic fabric is described by an ‘orientation distribution function’ (ODF) depending on two parameters. A method to pass from the ODF to a discrete description of the fabric, and vice versa, is presented. Considering any available μ-M model, the parameters of the GOLF that fit the response obtained by running this μ-M model are calculated for any set of ODF parameters. It is thus possible to tabulate the GOLF over a grid in the space of the ODF parameters. This step is performed once and for all. Ice-sheet flow models need the general form of the GOLF to be implemented in the available code (once), then, during each individual run, to retrieve the GOLF parameters from the table by interpolation. As an application example, the GOLF is tabulated using three different μ-M models and used to derive the rheological properties of ice along the Greenland Icecore Project (GRIP) ice core.