Influence of ice accumulation distribution on ice sheet stability

The stability of a two-dimensional isothermal ice sheet with stationary margin is studied when the ice flow is described by Glen's flow law. The ice accumulation rate is assumed to depend on the elevation and the span. Surface perturbation is searched for as a normal mode, which determines a singular eigenvalue problem. The singularity of the perturbation at the margin can be treated by application of the method of matched asymptotic expansions. Numerical solution of the eigenvalue problem shows that the dependence of the accumulation rate on the elevation contributes strongly to the ice sheet instability. Positive downstream slope prevents stable solutions. Negative downstream inclination of the equilibrium line often equally leads to instability.