Mass conservation in free-boundary ice dynamics models

Abstract:

Cryospheric modeling often requires solution of a conservation equation for a layer of ice (or liquid water) with a free/moving boundary. Problems of this type include ice sheet grounded margins, ice shelf calving fronts, subglacial hydrology, and supraglacial runoff, among other applications. Finding the boundary in a way that respects the physics is part of the problem, but additionally exact discrete mass (or energy) conservation is a goal, especially when the cyrospheric layer appears as a component in a climate or earth system model. I'll review the small existing free-boundary mass conservation literature for the continuum and discrete cases. Then I'll describe an abstracted view of the mass conservation equation with free boundary. This view suggests what degree of mass conservation is possible in such models, and what is needed for a time-stepping model to conserve mass as well as it can. I'll give examples.