A numerical stabilisation scheme for the Shallow Shelf Approximation

Ice-flow modelling continues to be challenging due to the need to balance computational efficiency with physical complexity, a choice that directly affects the accuracy of sea-level projections. Several studies have successfully introduced numerical stabilisation schemes to Stokes models that reduce the stiffness of the system of equations by predicting the ice geometry at the next time step, allowing for larger time-step sizes without loss of accuracy (Durand et al., 2009, Löfgren et al., 2022, Henry et al., 2025). However, the high physical complexity of Stokes models nonetheless renders them infeasible in large-scale simulations, in part due to memory restrictions.

To address this, we introduce the Thickness Stabilisation Scheme (TSS) for the Shallow Shelf Approximation (SSA). This numerical stabilisation scheme is constructed by modifying the momentum equations with terms that predict the ice thickness at the next time step, thereby also reducing the stiffness of the problem. In order to investigate the accuracy and efficiency of TSS, we perform numerical experiments of idealised ice shelves. The results show that the inclusion of the TSS allows for a significantly larger time-step size. The improved efficiency of SSA simulations through the inclusion of the TSS enables the reallocation of computational resources towards increased spatial resolution and greater physical complexity.

Durand, O. Gagliardini, B. de Fleurian, T. Zwinger, and E. Le Meur. Marine ice sheet dynamics: Hysteresis and neutral equilibrium. Journal of Geophysical Research, 114(F3):F03009, 2009.

Löfgren, J. Ahlkrona, and C. Helanow. Increasing stable time-step sizes of the free-surface problem arising in ice-sheet simulations. Journal of Computational Physics: X, 16:100114, 2022.

A.C.J. Henry, T. Zwinger, and J. Ahlkrona. Grounding-line dynamics in a Stokes ice-flow model: Improved numerical stability allows larger time steps. EGUsphere, 2025.