A new approach to model the grounding line based on mass conservation principles

The sensitivity of ice sheet dynamics to grounding line processes remains a primary source of uncertainty in sea-level rise projections. In current numerical models based on the Stokes equations, the grounding line is treated as a free boundary solved through an explicit dynamic contact formulation. This approach is highly sensitive to mesh resolution, often requiring grid spacing finer than ~200 m to ensure numerical convergence, making Stokes-based grounding line calculations computationally prohibitive for continental-scale simulations.

We present an alternative formulation for modelling the grounding line position based on the mass conservation of ice and sea water. This framework provides a physically consistent description of the ice sheet and ice shelf systems without requiring high mesh resolutions. We compare our results against existing test case suggested by Schoof (2007), show the resolutions necessary for mesh convergence and demonstrate the computational efficiency of the method.

References

1. Schoof, C. (2007). Ice sheet grounding line dynamics: Steady states, stability, and hysteresis. Journal of Geophysical Research: Earth Surface, 112(F3).