Grounding line treatments

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This presentation aims at providing a wide overview of grounding line treatments and the concept of marine ice sheet instability. Not all existing methods will be covered, the focus is on 2-D treatment of marine ice sheet that flow into unconfined ice shelves (Ie: ignore the topic of back pressure). A word of warning: new work on grounding line migration appear regularly, so keep your eyes open…

Required reading:

Vieli, A. and A. Payne (2005). Assessing the ability of numerical ice sheet models to simulate grounding line migration. Journal of Geophysical Research 110, F01003.

Schoof, C. (2007). Ice sheet grounding line dynamics: Steady states, stability, and hysteresis. Journal of Geophysical Research 112, F03528. pdf

Some references:

Barcilon,V., MacAyeal, D.R., (1993). Steady flow of a viscous ice stream across a no-slip/free-slip transition at the bed. J. Glaciol. 39 (131), 167–185. [pdf][1]

Burnett, D. (1987). Finite element analysis: from concepts to applications. Addison-Wesley.

Chugunov, V.A., Wilchinsky, A.V., (1996). Modelling of a marine glacier and ice-sheet-ice-shelf transition zone based on asymptotic analysis. Ann. Glaciol. 23, 59–67.

Dupont, T. and R. Alley (2005). Assessment of the importance of ice-shelf buttressing to ice-sheet flow. Geophysical Research Letters 32, L04503

Durand, G., O. Gagliardini, T. Zwinger and E. Le Meur (2009). Full-Stokes modeling of marine ice-sheets: influence of the grid size, Annals of Glaciology.

Durand, G., O. Gagliardini, B. de Fleurian, T. Zwinger,2 and E. Le Meur (2009). Marine ice sheet dynamics: Hysteresis and neutral equilibrium, Journal of Geophysical Research, VOL. 114, F03009, doi:10.1029/2008JF001170

Gagliardini, O., D. Cohen, P. R°aback, and T. Zwinger (2007). Finite-element modeling of subglacial cavities and related friction law. Journal of Geophysical Research 112, F02027.

Herterich, K. (1987). On the flow within the transition zone between ice sheet and ice shelf. In van der Veen C.J. and J. Oerlemans (Eds.), Dynamics of the West Antarctic Ice Sheet, pp. 185–202. D. Reidel Publishing Company.

Hindmarsh, R. (1993). Qualitative dynamics of marine ice sheets. In W. Peltier (Ed.), Ice in the Climate System, Volume I 12, pp. 67–199. NATO ASI Series, Springer-Verlag Berlin Heidelberg.

Hindmarsh, R. (2006). The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, 1733–1767.

Huybrechts, P. (1997), Report of the third EISMINT workshop on model intercomparison report, EISMINT Intercomparison Group, Grindelwald, Switzerland.

Iken, A. (1981). The effect of the subglacial water pressure on the sliding velocity of a glacier in an idealized numerical model. Journal of Glaciology 27, 407–421.

Lestringant, R., (1994). A two-dimensional finite element study of flow in the transition zone between an ice sheet and an ice shelf. Ann. Glaciol. 20, 67–72.

Lliboutry, L. (1968). General theory of subglacial cavitation and sliding of temperate glaciers. Journal of Glaciology 7, 21–58.

Nowicki S.M.J. (2007). Modelling the transition zone of marine ice sheets, Phd thesis, University College London, UK

Nowicki S. M. J., D. J. Wingham (2008). Conditions for a steady ice sheet – ice shelf junction, Earth and Planetary Science Letters, doi 10.1016/j.epsl.2007.10.018

Pattyn, F., A. Huyghe, S. De Brabander, and B. De Smedt (2006). Role of transition zones in marine ice sheet dynamics. Journal of Geophysical Research 111, 2004–2014.

Pollard D., R. M. DeConto (2009). Modelling West Antarctic ice sheet growth and collapse through the past five million years, Nature, doi 0.1037/nature07809

Rignot, E. (1998). Fast recession of a west antarctic glacier. Science 281, 549–551.

Schoof, C. (2005). The effect of cavitation on glacier sliding. Proceedings of the Royal Society: Mathematical, Physical and Engineering Sciences 461, 609–627.

Schoof, C. (2007a). Ice sheet grounding line dynamics: Steady states, stability, and hysteresis. Journal of Geophysical Research 112, F03528.

Schoof, C. (2007b). Marine ice-sheet dynamics. Part 1. The case of rapid sliding. Journal of Fluid Mechanics 573, 27–55.

van der Veen, C. (1986). Numerical modelling of ice shelves and ice tongues. Annales Geophysicae 4B, 45–54.

Weertman, J. (1974). Stability of the junction of an ice sheet and an ice shelf. Journal of Glaciology 3, 3–11.

Wilchinsky, A. and V. Chugunov (2000). Ice-stream-ice-shelf transition: theoretical analysis of two-dimensional flow. Annals of Glaciology 30, 153–162.

Wilchinsky, A. and V. Chugunov (2001). Modelling ice flow in various glacier zones. Journal of Applied Mathematics and Mechanics 65, 479–493.