A unified framework for large-scale fabric evolution models and anisotropic rheologies

Ice is anisotropic, with its viscosity varying by an order of magnitude in different directions when ice crystals align. However, how this variation affects ice flow is not well understood. This is because of a lack of a) models for fabric (the collective distribution of crystal orientations) evolution accurate enough to reproduce observations, and b) knowledge of which anisotropic rheology is most appropriate. Here we address both these problems. First, we review a range of previous models for fabric evolution and show they can be combined into a common differential equation. This incorporates a handful of parameters and an anisotropic rheology, which can be freely chosen. We apply this model, with a range of different anisotropic rheologies, to both an ice stream and an ice divide. For each rheology we choose the parameters to give the best possible fit to observations. We find these parameters are significantly different from those used previously. Best results come from assuming the grains rotate due to stress rather than deformation, with the stress calculated through an anisotropic rheology. By including grain rotation primarily due to stress, combined with a diffusion of the fabric, we can reproduce observations at both an ice divide and, for the first time, at an ice stream. We also compare and rank a range of anisotropic rheologies based on the accuracy of their fabric predictions. The rheologies which give the closest fit to observations have a tensor description of the anisotropy and assume that neighbouring ice grains experience approximately the same stress.