The Cryosphere Discussions www.the-cryosphere-discuss.net 1994-0432 1994-0440 4 3 2010 10.5194/tcd-4-1063-2010 http://www.the-cryosphere-discuss.net/4/1063/2010/ http://www.the-cryosphere-discuss.net/4/1063/2010/tcd-4-1063-2010.html http://www.the-cryosphere-discuss.net/4/1063/2010/tcd-4-1063-2010.pdf 1063 1105 2010-07-19 Parameterising the grounding line in ice sheet models R. M. Gladstone A. J. Payne S. L. Cornford School of Geographical Sciences, University of Bristol, University Road, Bristol BS8 1SS, UK Realistic predictions of the behaviour of marine ice sheets require that models are able to robustly simulate grounding line migration. Fixed grid ice sheet models have been shown to exhibit inconsistent and hence unreliable grounding line migration behaviour, except at very high resolution not achievable in whole ice sheet simulations. In this study we present several different approaches to parameterising the grounding line. These are distinguished by choices regarding the ice thickness profile from the last grounded to the first floating grid point, and how this profile is allowed to impact on the gravitational driving stress and basal drag. We demonstrate that the most obvious choice of thickness parameterisation, linear interpolation from the last grounded to the first floating grid point, is not the most effective. We show that use of a grounding line parameterisation greatly improves performance, and that choice of a better grounding line parameterisation over a simpler one can bring further improvements, in terms of both accuracy and more self consistent behaviour, comparable to halving the grid resolution. The approach presented here to parameterising the grounding line does not in itself completely solve the grounding line problem, however it reduces requirements in terms of grid resolution. The parameterisations are presented in the context of a 1-D "shelfy-stream" flow-line model, but could be extended to cope with more than one dimension and other model formulations. Durand, G., Gagliardini, O., de~Fleurian, B., Zwinger, T., and Le~Meur, E.: Marine ice sheet dynamics: hysteresis and neutral equilibrium, J. Geophys. Res.-Earth, 114, F03009 , \doi10.1029/2008JF001170, 2009. Gladstone, R., Lee, V., Vieli, A., and Payne, A.: Grounding line migration in an adaptive mesh ice sheet model, J. Geophys. Res.-Earth, submitted, 2010. Goldberg, D., Holland, D M., and Schoof, C.: Grounding line movement and ice shelf buttressing in marine ice sheets, J. Geophys. Res.-Earth, 114, F04026, \doi10.1029/2008JF001227, 2009. Katz, R F. and Worster, M G.: Stability of ice-sheet grounding lines, P. Roy. Soc. A-Math. Phy., 466, 1597–1620, \doi10.1098/rspa.2009.0434, 2010. Mercer, J.: West Antarctic ice sheet and \chemCO_2 greenhouse effect – threat of disaster, Nature, 271, 321–325, 1978. Patankar, S.: Numerical Heat Transfer and Fluid Flow, Taylor & Francis, Abingdon, UK, 1980. Pattyn, F., Huyghe, A., De~Brabander, S., and De~Smedt, B.: Role of transition zones in marine ice sheet dynamics, J. Geophys. Res.-Earth, 111, F02004, \doi10.1029/2005JF000394, 2006. Pollard, D. and DeConto, R M.: Modelling West Antarctic ice sheet growth and collapse through the past five million years, Nature, 458, 329–332, \doi10.1038/nature07809, 2009. Schoof, C.: Ice sheet grounding line dynamics: steady states, stability, and hysteresis, J. Geophys. Res.-Earth, 112, F03S28, \doi10.1029/2006JF000664, 2007a. Schoof, C.: Marine ice-sheet dynamics. Part 1. The case of rapid sliding, J. Fluid Mech., 573, 27–55, \doi10.1017/S0022112006003570, 2007b. Schoof, C., Pattyn, F., and Hindmarsh, R.: MISMIP: Marine Ice Sheet Model Intercomparison Project, http://homepages.ulb.ac.be/~fpattyn/mismip/, 2009. Tuma, J. and Walsh, R.: Engineering Mathematics Handbook, McGraw Hill, 1998. Vieli, A. and Payne, A.: Assessing the ability of numerical ice sheet models to simulate grounding line migration, J. Geophys. Res.-Earth, 110, F01003, \doi10.1029/2004JF000202, 2005.