TC The Cryosphere TC 1994-0424 Copernicus GmbH Göttingen, Germany 10.5194/tc-6-1497-2012 The stability of grounding lines on retrograde slopes Gudmundsson G. H. 1 Krug J. 2 Durand G. 2 Favier L. 2 Gagliardini O. 2 3 British Antarctic Survey, High Cross, Madingley Rd., Cambridge, CB3 0ET, UK Laboratoire de Glaciologie et Géophysique de l'Environnement, UJF-Grenoble, CNRS, Saint-Martin-d'Hères, France Institut Universitaire de France, 103, BD Saint-Michel, 75005 Paris, France 12 12 2012 6 6 1497 1505 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.the-cryosphere.net/6/1497/2012/tc-6-1497-2012.html The full text article is available as a PDF file from http://www.the-cryosphere.net/6/1497/2012/tc-6-1497-2012.pdf

The stability of marine ice sheets grounded on beds that slope upwards in the overall direction of flow is investigated numerically in two horizontal dimensions. We give examples of stable grounding lines on such retrograde slopes illustrating that marine ice sheets are not unconditionally unstable in two horizontal dimensions. Retrograde bed slopes at the grounding lines of marine ice sheets, such as the West Antarctic Ice Sheet (WAIS), do not per se imply an instability, nor do they imply that these regions are close to a threshold of instability. We therefore question those estimates of the potential near-future contribution of WAIS to global sea level change based solely on the notion that WAIS, resting on a retrograde slope, must be inherently unstable.

 References Bamber,~J L., Riva,~R E M., Vermeersen,~B L A., and LeBrocq,~A M.: Reassessment of the potential sea-level rise from a~collapse of the West Antarctic ice sheet, Science, 324, 901–903, doi:http://dx.doi.org/10.1126/science.116933510.1126/science.1169335, available at: http://www.sciencemag.org/content/324/5929/901.abstract, 2009. Baral,~D R. and Hutter,~C.: Asymptotic theories of ice sheets and ice shelves, in: Geomorphological Fluid Mechanics, edited by: Balmforth,~N J. and Provenzale,~A., Lecture Notes in Physics, chap 11, Springer, 227–278, 2001. Dupont,~T K. and Alley,~R B.: Assessment of the importance of ice-shelf buttressing to ice-sheet flow, Geophys. Res. Lett., 32, L04503, doi:http://dx.doi.org/10.1029/2004GL02202410.1029/2004GL022024, 2005. Durand,~G., Gagliardini,~O., de~Fleurian,~D., Zwinger,~T., and Meur,~E L.: Marine ice sheet dynamics: hysteresis and neutral equilibrium, J. Geophys. Res., 114, F03009, doi:http://dx.doi.org/10.1029/2008JF00117010.1029/2008JF001170, 2009a. Durand,~G., Gagliardini,~O., Zwinger,~T., Meur,~E L., and Hindmarsh,~R.: Full-Stokes modeling of marine ice-sheets: influence of the grid size, Ann. Glaciol., 50, 109–114, 2009b. Favier,~L., Gagliardini,~O., Durand,~G., and Zwinger,~T.: A three-dimensional full Stokes model of the grounding line dynamics: effect of a pinning point beneath the ice shelf, The Cryosphere, 6, 101–112, doi:http://dx.doi.org/10.5194/tc-6-101-201210.5194/tc-6-101-2012, 2012. Gagliardini,~O., Durand,~G., Zwinger,~T., Hindmarsh,~R C A., and Meur,~E L.: Coupling of ice-shelf melting and buttressing is a~key process in ice-sheets dynamics, Geophys. Res. Lett., 37, L14501, doi:http://dx.doi.org/10.1029/2010GL04333410.1029/2010GL043334, 2010. Gladstone,~R M., Payne,~A J., and Cornford,~S,~L.: Resolution requirements for grounding-line modelling: sensitivity to basal drage and ice-shelf buttressing. Ann. Glaciol., 53, 97–105, doi:http://dx.doi.org/10.3189/2012AoG60A14810.3189/2012AoG60A148, 2012. Goldberg,~D., Holland,~D M., and Schoof,~C.: Grounding line movement and ice shelf buttressing in marine ice sheets, J. Geophys. Res., 114, F04026, doi:http://dx.doi.org/10.1029/2008JF00122710.1029/2008JF001227, 2009. Gudmundsson,~G H.: Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation, The Cryosphere, 2, 77–93, doi:http://dx.doi.org/10.5194/tc-2-77-200810.5194/tc-2-77-2008, 2008. Hindmarsh,~R C A.: Qualitative dynamics of marine ice sheets, in: Ice in the Climate System, edited by: Peltier,~W R., no 12 in NATO ASI Series I, Springer, 66–99, 1993. Hindmarsh,~R C A.: Stability of ice rises and uncoupled marine ice sheets, Ann. Glaciol., 23, 94–104, 1996. Hutter,~K.: Theoretical Glaciology; Material Science of Ice and the Mechanics of Glaciers and Ice Sheets, D. Reidel Publishing Company/Tokyo, Terra Scientific Publishing Company, 1983. Jamieson,~S S R., Vieli,~A., Livingstone,S J., Cofaigh,~C Ó, Stokes,~S., Hillenbrand,~C.-D., and Dowdeswell,~J D.: Ice-stream stability on a reverse bed slope, Nat. Geosci., 5, 799–802, 2012. Katz,~R F. and Worster,~M G.: Stability of ice-sheet grounding lines, P. Roy. Soc. A. Math., Phys., 466, 1597–1620, doi:http://dx.doi.org/10.1098/rspa.2009.043410.1098/rspa.2009.0434, 2010. MacAyeal,~D R.: Large-scale ice flow over a~viscous basal sediment: theory and application to ice stream B, Antarctica, J. Geophys. Res., 94, 4071–4078, 1989. Morland,~L W.: Thermomechanical balances of ice-sheet flows, Geophys. Astro. Fluid, 29, 237–266, 1984. Muszynski,~I. and Birchfield,~G E.: A~coupled marine ice-stream-ice – shelf model, J. Glaciol., 33, 3–14, 1987. Pattyn,~F., Schoof,~C., Perichon,~L., Hindmarsh,~R C A., Bueler,~E., de Fleurian,~B., Durand,~G., Gagliardini,~O., Gladstone,~R., Goldberg,~D., Gudmundsson,~G H., Huybrechts,~P., Lee,~V., Nick,~F M., Payne,~A J., Pollard,~D., Rybak,~O., Saito,~F., and Vieli,~A.: Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP, The Cryosphere, 6, 573–588, doi:http://dx.doi.org/10.5194/tc-6-573-201210.5194/tc-6-573-2012, 2012. Ross,~N., Bingham,~R G., Corr,~H F J., Ferraccioli,~F., Jordan,~T A., Brocq,~A L., Rippin,~D M., Young,~D., Blankenship,~D D., and Siegert,~M J.: Steep reverse bed slope at the grounding line of the Weddell Sea sector in West Antarctica, Nat. Geosci., 5, 393–396, doi:http://dx.doi.org/10.1038/ngeo146810.1038/ngeo1468, 2012. Schoof,~C.: Ice sheet grounding line dynamics: steady states, stability, and hysteresis, J. Geophys. Res., 112, F03S28, doi:http://dx.doi.org/10.1029/2006JF00066410.1029/2006JF000664, 2007a. Schoof,~C.: Marine ice-sheet dynamics, part 1, The case of rapid sliding, J. Fluid. Mech., 573, 27–55, doi:http://dx.doi.org/10.1017/S002211200600357010.1017/S0022112006003570, 2007b. Thomas,~R H. and Bentley,~C R.: A~model for Holocene retreat of the West Antarctic ice sheet, Quaternary Res., 10, 150–170, doi:http://dx.doi.org/10.1016/0033-5894(78)90098-410.1016/0033-5894(78)90098-4, available at: http://www.sciencedirect.com/science/article/pii/0033589478900984, 1978. Vieli,~A. and Payne,~A J.: Assessing the ability of numerical ice sheet models to simulate grounding line migration, J. Geophys. Res., 110, F01003, doi:http://dx.doi.org/10.1029/2004JF00020210.1029/2004JF000202, 2005. Walker, R. T., Dupont, T. K., Parizek, B. R., and Alley, R. B.: Effects of basal-melting distribution on the retreat of ice-shelf grounding lines, Geophys. Res. Lett., 35, L17503, doi:10.1029/2008GL034947, 2008. Weertman,~J.: Stability of the junction of an ice sheet and ice shelf, J. Glaciol., 13, 3–11, 1974.