Studying ice sheet stability using the method of separation of variables

Abstract

Stability of two-dimensional stationary continental and marine ice sheets is studied using perturbations of ice sheet surface elevation and the margin position about a steady-state solution. Ice accumulation rate at the upper surface is specified as a function of elevation and span. Ice is considered as a Newtonian fluid. Linearisation and separation of variables yield a non-homogeneous eigenvalue problem. In case when the margin moves, a necessary condition for the existence of a solution is very restrictive on the functions of the bed profile and accumulation rate. The method of separation of variables is applicable when the margin is assumed to be stationary. Singularity of the perturbation at the margin is treated using the method of matched asymptotic expansions. Numerical experiments show that dependence of accumulation rate on elevation contributes strongly towards ice sheet instability. Bed slope, ice thickness at the grounding line of a marine ice sheet and equilibrium line inclination are the main parameters determining the ice sheet reaction to a surface perturbation.