Marine ice sheet stability

• Published in: Journal of Fluid Mechanics
• Main Author: Schoof, Christian
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 2012
• Subjects: Ice Sheet
• Online Access: http://dx.doi.org/10.1017/jfm.2012.43; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112012000432

Abstract We examine the stability of two-dimensional marine ice sheets in steady state. The dynamics of marine ice sheets is described by a viscous thin-film model with two Stefan-type boundary conditions at the moving boundary or ‘grounding line’ that marks the transition from grounded to floating ice. One of these boundary conditions constrains ice thickness to be at a local critical value for flotation, which depends on depth to bedrock at the grounding line. The other condition sets ice flux as a function of ice thickness at the grounding line. Depending on the shape of the bedrock, multiple equilibria may be possible. Using a linear stability analysis, we confirm a long-standing heuristic argument that asserts that the stability of these equilibria is determined by a simple mass balance consideration. If an advance in the grounding line away from its steady-state position leads to a net mass gain, the steady state is unstable, and stable otherwise. This also confirms that grounding lines can only be stable in positions where bedrock slopes downwards sufficiently steeply.