Large-scale ice-sheet modeling with horizontal stress gradients

The increased understanding of the specific roles played by longitudinal/membrane stresses in ice-sheets mean that an ice-sheet model which includes such stresses can now be specified. It must contain sufficient physics to be able to represent (i) grounding line motion and the grounding line boundary layer; (ii) the role of longitudinal stresses in propagating ice-stream transients; and (iii) the role of longitudinal/membrane stresses in delocalizing dissipative heating. Numerical computations using spectral methods comparing the results of 3D higher order approximations (i.e. Blatter-type models) and 2D vertically integrated equivalents (super-MacAyeal models) are presented, as well as full Stokes solutions. Vertically integrated works very well for flat bottomed ice-streams, but is less accurate in the presence of high-relief topography. The vertically integrated solutions require much computation. Spectral methods are inappropriate for models of the current and former ice-sheets. A finite difference implementation of the vertically integrated model is presented and applied to the issues listed above as well as to a specific case study of the post-glacial retreat of the Antarctic ice-sheet.