Dynamically coupling full Stokes and shallow shelf approximation for marine ice sheet flow using Elmer/Ice (v8.3)

Abstract

Abstract. Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve due to the nonlinearity introduced by the rheology. Therefore, approximations to the FS equations are commonly used, especially when modeling a marine ice sheet (ice sheet, ice shelf, and/or ice stream) for 103 years or longer. The shallow ice approximation (SIA) and shallow shelf approximation (SSA) are commonly used but are accurate only for certain parts of an ice sheet. Here, we report 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 % for diagnostic runs and below 5 % for prognostic runs. Results for grounding line dynamics obtained with the FS–SSA coupling are similar to those obtained from an FS model in an experiment with a periodical temperature forcing over 3000 years that induces grounding line advance and retreat. The rapid convergence of the FS–SSA coupling shows a large potential for reducing computation time, such that modeling a marine ice sheet for thousands of years should become feasible in the near future. Despite inefficient matrix assembly in the current implementation, computation time is reduced by 32 %, when the coupling is applied to a 3-D ice shelf.

A full Stokes subgrid scheme in two dimensions for simulation of grounding line migration in ice sheets using Elmer/ICE (v8.3)

“…For x < x GL we have H bw /H < ρ/ρ w since H bw decreases and H increases. The conclusion from numerical experiments in van Dongen et al (2018) is that the hydrostatic assumption and the SSA equations approximate the FS equations well for the floating ice beginning at a short distance away from the GL.…”

“…A simplification of the FS equations by integrating the depth of the ice is the shallow shelf (or shelfy stream) approximation (SSA) (MacAyeal, 1989), which is often used for simulation of the coupling between a grounded ice sheet and a marine ice shelf. In the zone between the grounded ice and the floating ice, it is necessary to use the FS equations (Wilchinsky and Chugunov, 2000;Schoof and Hindmarsh, 2010;Docquier et al, 2011;Schoof, 2011) unless the ice is moving rapidly on the ground with low basal friction, when the SSA equations are accurate both upstream and downstream of the GL.…”

Review of &quot;The impact of model resolution on the simulated Holocene retreat of the Southwestern Greenland Ice Sheet using the Ice Sheet System Model (ISSM)&quot;

“…7). Comparative studies on multi-millenial time scales have also been published by Bernales et al (2017); van Dongen et al (2018).…”

A full Stokes subgrid model for simulation of grounding line migration in ice sheets using Elmer/ICE(v8.3)

“…For x < x GL we have that H bw /H < ρ/ρ w since H bw decreases and H increases. The conclusion from numerical experiments inVan Dongen et al (2018) is that the hydrostatic assumption and the SSA equations approximate the FS equations well…”