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

Abstract

ABSTRACT. For accurate ice-sheet flow modelling, the anisotropic behaviour of ice must be taken fully into account. However, physically based micro-macro (m-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 m-M model, the parameters of the GOLF that fit the response obtained by running this m-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 m-M models and used to derive the rheological properties of ice along the Greenland Icecore Project (GRIP) ice core.

Change in ice rheology during climate variations – implications for ice flow modelling and dating of the EPICA Dome C core

“…It is made up of a constitutive equation for the anisotropic behaviour of the ice polycrystal as a function of its fabric, an equation for the evolution of the fabric as a function of the strain-rates and deviatoric stresses experienced by ice, and a finite element code to solve the equations that govern the anisotropic ice flow. Details on the model and its applications can be found in Gillet-Chaulet et al (2005, 2006.…”

“…To relate the deviatoric stressesS to the strain-ratesD we use the General Orthotropic Linear Flow law (GOLF) (Gillet-Chaulet et al, 2005, 2006:…”

Modelling Dynamics of Valley Glaciers

“…Wang & Warner, 1999) and through physically-based parameterizations (e.g. Gillet-Chaulet et al, 2005;Morland & Staroszczyk, 2003).…”

Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic Flow Enhancement factor

“…which results from the CAFFE flow law (17) by settingÊ(S) ≡ 1, is isotropic and collinear with respect to the tensors D and S. On the other hand, many anisotropic flow laws published so far relate D and S by tensor quantities [1,16,19,26,27,31,52,53], thus giving up the collinearity between D and S. This often leads to the misconception (at least in the glaciological community) that isotropic flow laws must be collinear and anisotropic flow laws must be non-collinear with respect to D and S. However, this is not the case. As, we have seen above, the CAFFE flow law is anisotropic, but collinear.…”