Grounding-line dynamics in a Stokes ice-flow model (Elmer/Ice v9.0): improved numerical stability allows larger time steps

The efficient and accurate simulation of grounding line dynamics in marine ice-sheet models remains a challenge, largely due to restrictive time-step limitations. The restrictive time step size of ice-sheet simulations ( years) is one of the reasons for the routine use of approximate models that compromise physical complexity compared to full Stokes models. To address the time-step restriction and enhance the applicability of full Stokes simulations, we implement a numerical stabilisation scheme at the ice–ocean interface, namely the Free-Surface Stabilisation Algorithm (FSSA). The FSSA acts by predicting the surface elevation at the next time step, resulting in a reduction in surface oscillations and an increase in the largest numerically stable time step. When applied to the ice–ocean interface, FSSA acts in combination with the sea spring numerical stabilisation scheme, allowing larger time steps to be taken.

In order to test the capabilities of the FSSA when applied to the ice–ocean interface, we perform the benchmark simulation of Experiment 3a from the Marine Ice Sheet Model Intercomparison Project (MISMIP). These simulations demonstrate the ability of the model to capture grounding line migration on both prograde slopes (oceanward sloping) and retrograde slopes (inland sloping). We find a time step size of Δt=10 years to be numerically stable and accurate in the MISMIP experiment, which is more than an order of magnitude larger than the small time steps traditionally used. In comparison, a time-step size of Δt=50 years can maintain numerical stability, but is not capable of capturing the full range of grounding-line motion in the MISMIP experiments. We further demonstrate the applicability of the FSSA to a 3D marine terminating model domain of Ekström Ice Shelf, finding that a time-step size of Δt=10 years is numerically stable. However, these results are obtained for relatively slowly evolving grounding-line dynamics, and caution is required for more rapidly evolving systems driven by ocean melting (e.g., Thwaites Glacier). The increase in the largest numerically stable time step by greater than an order of magnitude in marine-terminating Stokes ice-flow problems through the inclusion of FSSA broadens the applicability of Stokes models, which have otherwise been deemed too computationally expensive for large-scale applications.