The Cryosphere Discussions www.the-cryosphere-discuss.net 1994-0432 1994-0440 2 4 2008 10.5194/tcd-2-557-2008 http://www.the-cryosphere-discuss.net/2/557/2008/ http://www.the-cryosphere-discuss.net/2/557/2008/tcd-2-557-2008.html http://www.the-cryosphere-discuss.net/2/557/2008/tcd-2-557-2008.pdf 557 599 2008-07-14 Applicability of the Shallow Ice Approximation inferred from model inter-comparison using various glacier geometries M. Schäfer smartina@gmx.de O. Gagliardini F. Pattyn E. Le Meur LGGE, CNRS, UJF-Grenoble, BP 96, 38402 Saint-Martin d'Hères Cedex, France Laboratoire de Glaciologie, ULB, Bruxelles, Belgium This paper presents an inter-comparison of three different models applied to various glacier geometries. The three models are built on different approximations of the Stokes equations, from the well known Shallow Ice Approximation (SIA) to the full-Stokes (FS) solution with an intermediate higher-order (HO) model which incorporates longitudinal stresses. The studied glaciers are synthetic geometries, but two of them are constructed so as to mimic a valley glacier and a volcano glacier. For each class of glacier, the bedrock slope and/or the aspect ratio are varied. First, the models are compared in a diagnostic way for a fixed and given geometry. Here the SIA surface velocity can overestimate the FS velocity by a factor of 5 to a factor of 10. Then, the free surface is allowed to evolve and the time-dependent evolution of the glacier is studied. As a result, the difference between the models decreases, but can still be as large as a factor of 1.5 to 2. This decrease can be explained by a negative feedback for the SIA which overestimates velocities. Baiocchi, C., Brezzi, F., and Franca, L P.: Virtual bubbles and the Galerkin least squares method, Comp. Meths. Appl. Mech. Engrg., 105, 125–141, 1993. Baral, D R., Hutter, K., and Greve, R.: Asymptotic theories of large-scale motion, temperature, and moisture distribution in land-based polythermal ice sheets: A critical review and new developments, Appl. Mech. Rev., 54, 2001. Elmer Manuals, CSC: http://www.csc.fi/elmer/, 2006. Franca, L P. and Frey, S L.: Stabilized finite element methods: II. the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng., 99, 209–233, 1992. Franca, L P., Frey, S L., and Hughes, T. J R.: Stabilized finite element methods: I. application to the advective-diffusive model, Comput. Methods Appl. Mech. Eng., 95, 253–276, 1992. Gagliardini, O. and Zwinger, T.: The ISMIP-HOM benchmark experiments performed using the Finite-Element code Elmer, The Cryosphere, 2, 67–76, 2008. Greuell, W.: Hintereisferner, Austria: mass-balance reconstruction and numerical modelling of the historical lenght variation, J. Glaciol., 38, 233–244, 1992. Gudmundsson, G. H.: Transmission of basal variability to a glacier surface, J. Geophys. Res., 108, 2253, doi:10.1029/2002JB002107, 2003. Greve, R.: A Continuum-Mechanical Formulation for Shallow Polythermal Ice Sheets, Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 355, 921–974, 1997. Hindmarsh, R.: Notes on basic glaciological computational methods and algorithms, Continuum mechanics and applications in geophysics and the environment (A 02-10739 01-46), Berlin, Heidelberg and New York, Springer-Verlag, pp. 222–249, 2001. Hindmarsh, R.: A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modeling, J. Geophys. Res., 109, 1–15, 2004. Hubbard, A.: The Verification and Significance of Three Approaches to Longitudinal Stresses in High-Resolution Models of Glacier Flow, Geografiska Annaler. Series A, Physical Geography, 82, 471–487, 2000. Hutter, K.: Theoretical Glaciology: material science of ice and the mechanics of glaciers and ice sheets., D. Reidel Publishing Company, Terra Scientific Publishing Company (ISBN$90 277 1473 8$), 1983. Le Meur, E. and Vincent, C.: A two-dimensional shallow ice flow model of glacier de Saint Sorlin, France, J. Glaciol., 49, 527–538, 2003. Le Meur, E., Gagliardini, O., Zwinger, T., and Ruokolainen, J.: Glacier flow modelling: a comparison of the Shallow Ice Approximation and the full-Stokes solution, CRAS Physique, 5, 709–422, 2004. Leysinger Vieli, G. J.-M C. and Gudmundsson, G H.: On estimating length fluctuations of glaciers caused by changes in climatic forcing, J. Geophys. Res., 109, F01007, doi:10.1029/2003JF000027, 2004. Lliboutry, L.: Traité de glaciologie, Glaciers – Variations du climat – Sols gelés, Masson & Cie Editeurs, 1965. Morland, L W.: Thermomechanical balance of ice sheet flows, Geophys. Astrophys. Fluid Dynam., 29, 237–266, 1984. Pattyn, F.: A new three-dimensional higher-order thermomechanical ice sheet model: Basic sensitivity, ice stream development, and ice flow across subglacial lakes, J. Geophys. Res., 108, 2382, doi:10.1029/2002JB002329, 2003. Pattyn, F. and Payne, T.: Ice Sheet Model Intercomparison Project: Benchmark experiments for numerical Higher-Order ice-sheet Models, prefixhttp://homepages.ulb.ac.be/~fpattyn/ismip/, 2006. Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de~Smedt, B., Gagliardini, O., Gudmundsson, G H., Hindmarsh, R., Hubbard, A., Johnson, J V., Kleiner, T., Konovalov, Y., Martin, C., Payne, A J., Pollard, D., Price, S., Rückamp, M., Saito, F., Souček, O., Sugiyama, S., and Zwinger, T.: Benchmark experiments for higher-order and full Stokes ice sheet models (ISMIP-HOM), The Crysosphere Discuss., 2, 111–151, 2008. Schäfer, M. and Le Meur, E.: Improvements of a 2D-SIA ice flow model; application to the Saint Sorlin glacier, France, J. Glaciol., 53, 713–722, 2007. Weertman, J.: The theory of glacier sliding, J. Glaciol., 39, 287–303, 1964. Zwinger, T., Greve, R., Gagliardini, O., Shiraiwa, T., and Lyly, M.: A full Stokes-flow thermo-mechanical model for firn and ice applied to the Gorshkov crater glacier, Kamchatka, Ann. Glaciol., 45, 29–37, 2007.