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

Eef C H Van Dongen,Martin B Van Gijzen,Per Lötstedt,Gong Cheng,Lina Von Sydow,Roderik S W Van De Wal,Thomas Zwinger,Nina Kirchner

doi:10.5194/gmd-11-4563-2018

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.

Highlights

Dynamical changes in both the Greenland and Antarctic ice sheets are, with medium confidence, projected to contribute 0.03 to 0.20 m of sea level rise by 2081–2100 (IPCC, 2014)
The presented coupling is dynamic, since the coupling interface xc changes with grounding line changes, but the distance dGL that defines xc has to be chosen such that the full Stokes (FS) velocity at the interface is almost independent of z
We have presented a novel FS–shallow shelf approximation (SSA) coupling in Elmer/Ice, showing a large potential for reducing the computation time without losing accuracy

Summary

Introduction

Dynamical changes in both the Greenland and Antarctic ice sheets are, with medium confidence, projected to contribute 0.03 to 0.20 m of sea level rise by 2081–2100 (IPCC, 2014). Model validation is required over centennial to millennial timescales to capture the long response time of an ice sheet to external forcing (Alley et al, 2005; Phillips et al, 2010; Stokes et al, 2015). The computation time and memory required for an FS model to be applied to ice sheets restricts simulations to sub-millennial timescales (Gillet-Chaulet et al, 2012; Gladstone et al, 2012a; Nowicki et al, 2013; Seddik et al, 2012, 2017; Joughin et al, 2014). Approximations of the FS equations are employed for simulations over long timescales, such as the shallow ice approximation (SIA; Hutter, 1983), the shallow shelf approximation (SSA; Morland, 1987; MacAyeal, 1989), Blatter–Pattyn (Pattyn, 2003), and hybrid models (Hindmarsh, 2004; Bernales et al, 2017)

Methods

Findings

Discussion

Conclusion