A numerical stabilization scheme for the shallow shelf approximation

We present the Thickness Stabilization Scheme (TSS), a numerical stabilization scheme suitable for the Shallow Shelf Approximation (SSA), one of the most widely-used models for large-scale Antarctic and Greenland ice sheet simulations. The TSS is constructed by inserting adapted, explicit Euler thickness evolution equations into the driving stress, thereby treating terms implicitly. We investigate the applicability of TSS in idealized ice shelf experiments and grounded ice stream experiments. In a high-shear ice-shelf experiment, a threshold time step size is crossed between Δ t = 5 and Δ t = 10 years, beyond which errors are significantly lower in simulations with TSS. In grounded ice-stream experiments, simulations without TSS become unstable for time steps of Δ t ≥ 5 years. In contrast, simulations with TSS remain stable and exhibit errors well below 1% even for time steps exceeding 10 years. The improvement in simulation efficiency due to the includion of TSS offers greater flexibility for ice-sheet modeling by allowing the re-allocation of computational resources. This method is applicable not only to ice-sheet modeling, including in coupled frameworks, but also to other vertically integrated computational fluid dynamics problems that couple momentum and geometry evolution equations.