Grounding line migration in an adaptive mesh ice sheet model

[1] Grounding line migration is a key process affecting the stability of marine ice sheets such as the West Antarctic ice sheet. Recent studies have shown that ice sheet models employing a fixed spatial grid (such as are commonly used for whole ice sheet simulations) cannot be used to solve this problem in a robust manner. We have developed a one-dimensional (vertically integrated) “shelfy stream” ice sheet model that employs the adaptive mesh refinement (AMR) technique to bring higher resolution to spatially and temporally evolving subregions of the model domain. A higher-order solver, the piecewise parabolic method (PPM), is used to compute the thickness evolution. Both AMR and PPM extend readily to greater than one dimension and could be used in full ice sheet simulations. We demonstrate that this approach can bring improvements in terms of accuracy and consistency in both grounded ice sheet and ice stream/ice shelf simulations, given the appropriate choice of refinement criteria. In particular, we demonstrate that AMR, in conjunction with a parameterization for subgrid scale grounding line position, can produce predictions of grounding line migration.

[1]  K. Hutter Theoretical Glaciology: Material Science of Ice and the Mechanics of Glaciers and Ice Sheets , 1983 .

[2]  J. H. Mercer West Antarctic ice sheet and CO2 greenhouse effect: a threat of disaster , 1978, Nature.

[3]  Gaël Durand,et al.  Full Stokes modeling of marine ice sheets: influence of the grid size , 2009, Annals of Glaciology.

[4]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[5]  T. Zwinger,et al.  Marine ice sheet dynamics: Hysteresis and neutral equilibrium , 2009 .

[6]  C. Schoof Ice sheet grounding line dynamics: Steady states, stability, and hysteresis , 2007 .

[7]  I. D. James,et al.  Advection schemes for shelf sea models , 1996 .

[8]  Antony J. Payne,et al.  Assessing the ability of numerical ice sheet models to simulate grounding line migration , 2005 .

[9]  Richard F. Katz,et al.  Stability of ice-sheet grounding lines , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[10]  Shian‐Jiann Lin,et al.  Multidimensional Flux-Form Semi-Lagrangian Transport Schemes , 1996 .

[11]  D. Goldberg Numerical and theoretical treatment of grounding line movement and ice shelf buttressing in marine ice sheets , 2009 .

[12]  David Pollard,et al.  Modelling West Antarctic ice sheet growth and collapse through the past five million years , 2009, Nature.

[13]  M. Norman,et al.  Turbulent Motions and Shocks Waves in Galaxy Clusters simulated with AMR , 2009, 0905.3169.

[14]  David G. Vaughan,et al.  West Antarctic Ice Sheet collapse – the fall and rise of a paradigm , 2008 .

[15]  Scott R. Kohn,et al.  Managing application complexity in the SAMRAI object‐oriented framework , 2002, Concurr. Comput. Pract. Exp..

[16]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[17]  B. O’Shea,et al.  Cosmological Shocks in Adaptive Mesh Refinement Simulations and the Acceleration of Cosmic Rays , 2008, 0806.1522.

[18]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[19]  P. Woodward,et al.  Application of the Piecewise Parabolic Method (PPM) to meteorological modeling , 1990 .

[20]  Bert De Smedt,et al.  Role of transition zones in marine ice sheet dynamics , 2006 .

[21]  Boyana Norris,et al.  Multigrid FDTD with Chombo , 2007, Comput. Phys. Commun..

[22]  A. Payne,et al.  Time-step limits for stable solutions of the ice-sheet equation , 1996 .

[23]  A. Payne,et al.  The Glimmer community ice sheet model , 2009 .