Stability of ice rises and uncoupled marine ice sheets

Abstract

An analysis of the linear stability of marine ice sheets uncoupled from associated ice shelves is presented. The principal feature is a zero eigenvalue associated with infinitesimal shifts along the line of neutral equilibrium in phase space, termed the “equilibrium manifold”. A finite-difference scheme is constructed which respects this stability properly. The zero eigenvalue appears to allow modelling errors to accumulate rather than dissipate as occurs in land-based ice sheets. The practical significance of this is that even rather fine spatial grids may allow substantial numerical error to accumulate.