Ice flow forced by gravity is governed by the Full Stokes (FS) equations, which are computationally expensive to solve due to their non-linearity introduced by the rheology. Therefore, approximations to the FS equations are used, especially when modelling an ice sheet complex (ice sheet, ice shelf and/or ice stream) on the order of 1000 years or longer. The Shallow Ice Approximation (SIA) and Shallow Shelf Approximation (SSA) are commonly used but are accurate only in certain parts of an ice sheet. Here, we report on a novel way of iteratively coupling FS and SSA that has been implemented in Elmer/Ice and applied to conceptual marine ice sheets. The FS-SSA coupling appears to be very accurate; the relative error in velocity compared to FS is below 0.5&thinsp;% for diagnostic and below 5&thinsp;% for prognostic runs. Results for grounding line dynamics obtained with the FS-SSA coupling are similar to results obtained from a FS model in an experiment with a periodical temperature forcing over 3000 years inducing grounding line advance and retreat. The rapid convergence of the FS-SSA coupling shows a large potential in reducing computation time, such that modelling an ice sheet complex for thousands of years should become feasible in the near future. Despite inefficient matrix assembly in the current implementation, computation time is reduced significantly, i.e. by 32&thinsp;%, when the coupling is applied to a 3D ice shelf. In the future, the FS-SSA coupling can be extended to include a SIA-FS coupling of ISCAL (Ice Sheet Coupled Approximation Level)-type.
Van Dongen, E. C. H., Kirchner, N., Van Gijzen, M. B., Van De Wal, R. S. W., Zwinger, T., Cheng, G., … Von Sydow, L. (2018). Dynamically coupling full Stokes and shallow shelf approximation for marine ice sheet flow using Elmer/Ice (v8.3). Geoscientific Model Development, 11(11), 4563–4576. https://doi.org/10.5194/gmd-11-4563-2018