Ice Sheet Dynamics

When modelling large ice sheets, local equilibrium of a vertical column with the size of the horizontal mesh (~ 100 km) can be assumed. The transit time of temperature disturbances from surface to bottom is ~ 60 ka. Thus, in general, actual and ice ages ice sheets are not in a steady state. If they were, a rule of thumb for the thickness, H ~ (2b/πk)(Ts/G0)2, would be more realistic than the usual assumption of a constant bottom shear stress. Less crude calculations assume uniform vertical strain rates. Still better ones consider a bottom boundary layer (BBL) whose temperatures get locally steady within a time step. In general, sliding demands that the temperature reach melting point not only at the ice-bed interface, but within a temperate BBL. The slight permeability of rocks at large scale should impede the accumulation of subglacial water, put forward by some authors to predict ice sheet surges. Polar ices are often very anisotropic, and we lack quantitative models for predicting their fabrics and behavior. The full rheological law of anisotropic ice with rotational symmetry, to be used in 3-D modelling, is given. A theory allows us to simplify it in the case of c-axes clustered near the z-axis, with two unknown parameters only, instead of ten.