GMD Geoscientific Model Development GMD Geosci. Model Dev. 1991-9603 Copernicus Publications Göttingen, Germany 10.5194/gmd-6-1299-2013 Capabilities and performance of Elmer/Ice, a new-generation ice sheet model Gagliardini O. https://orcid.org/0000-0001-9162-3518 1 2 Zwinger T. https://orcid.org/0000-0003-3360-4401 3 Gillet-Chaulet F. 1 Durand G. 1 Favier L. 1 de Fleurian B. https://orcid.org/0000-0001-8700-9822 1 Greve R. https://orcid.org/0000-0002-1341-4777 4 Malinen M. 3 Martín C. https://orcid.org/0000-0002-2661-169X 5 Råback P. 3 Ruokolainen J. 3 Sacchettini M. 1 Schäfer M. 6 Seddik H. 4 Thies J. 7 Laboratoire de Glaciologie et Géophysique de l'Environnement, UJF-Grenoble, CNRS – UMR5183, Saint-Martin-d'Hères, France Institut Universitaire de France, Paris, France CSC-IT Center for Science Ltd., Espoo, Finland Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan British Antarctic Survey, Cambridge, UK Arctic Centre, University of Lapland, Rovaniemi, Finland Uppsala University, Uppsala, Sweden European Commission ICE2SEA - Ice2sea - estimating the future contribution of continental ice to sea-level rise (226375) 22 08 2013 6 4 1299 1318 Copyright: © 2013 O. Gagliardini et al. 2013 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://gmd.copernicus.org/articles/6/1299/2013/gmd-6-1299-2013.html The full text article is available as a PDF file from https://gmd.copernicus.org/articles/6/1299/2013/gmd-6-1299-2013.pdf

The Fourth IPCC Assessment Report concluded that ice sheet flow models, in their current state, were unable to provide accurate forecast for the increase of polar ice sheet discharge and the associated contribution to sea level rise. Since then, the glaciological community has undertaken a huge effort to develop and improve a new generation of ice flow models, and as a result a significant number of new ice sheet models have emerged. Among them is the parallel finite-element model Elmer/Ice, based on the open-source multi-physics code Elmer. It was one of the first full-Stokes models used to make projections for the evolution of the whole Greenland ice sheet for the coming two centuries. Originally developed to solve local ice flow problems of high mechanical and physical complexity, Elmer/Ice has today reached the maturity to solve larger-scale problems, earning the status of an ice sheet model. Here, we summarise almost 10 yr of development performed by different groups. Elmer/Ice solves the full-Stokes equations, for isotropic but also anisotropic ice rheology, resolves the grounding line dynamics as a contact problem, and contains various basal friction laws. Derived fields, like the age of the ice, the strain rate or stress, can also be computed. Elmer/Ice includes two recently proposed inverse methods to infer badly known parameters. Elmer is a highly parallelised code thanks to recent developments and the implementation of a block preconditioned solver for the Stokes system. In this paper, all these components are presented in detail, as well as the numerical performance of the Stokes solver and developments planned for the future.

 References Alley, R. B. and Joughin, I.: Modeling Ice-Sheet Flow, Science, 336, 551–552, <a href="http://dx.doi.org/10.1126/science.1220530">https://doi.org/10.1126/science.1220530</a>, 2012. Amestoy, P., Duff, I., and L'Excellent, J.: MUMPS MUltifrontal Massively Parallel Solver, Tech. rep., Version 2.0. Technical Report TR/PA/98/02. CERFACS, 42 Ave G. Coriolis, 31057 Toulouse Cedex, France, 1998. Arthern, R. and Gudmundsson, G.: Initialization of ice-sheet forecasts viewed as an inverse Robin problem, J. Glaciol., 56, 527–533, 2010. Aschwanden, A., A\dhalgeirsdóttir, G., and Khroulev, C.: Hindcasting to measure ice sheet model sensitivity to initial states, The Cryosphere, 7, 1083–1093, <a href="http://dx.doi.org/10.5194/tc-7-1083-2013">https://doi.org/10.5194/tc-7-1083-2013</a>, 2013. 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. Benn, D. I., Warren, C. R., and Mottram, R. H.: Calving processes and the dynamics of calving glaciers, Earth-Sci. Rev., 82, 143–179, 2007. Blatter, H., Greve, R., and Abe-Ouchi, A.: Present State and Prospects of Ice Sheet and Glacier Modelling, Surveys Geophys., 32, 555–583, <a href="http://dx.doi.org/10.1007/s10712-011-9128-0">https://doi.org/10.1007/s10712-011-9128-0</a>, 2011. Brezzi, F., Marini, L. D., and Sli, E.: Discontinuous Galerkin methods for first-order hyperbolic problems, Math. Models. Meth. Appl. Sci., 14, 1893–1903, 2004. Bueler, E. and Brown, J.: Shallow shelf approximation as a 'sliding law' in a thermomechanically coupled ice sheet model, J. Geophys. Res. Earth Surf., 114, F03008, <a href="http://dx.doi.org/10.1029/2008JF001179">https://doi.org/10.1029/2008JF001179</a>, 2009. Burstedde, C., Ghattas, O., Stadler, G., Tu, T., and Wilcox, L.: Parallel scalable adjoint-based adaptive solution of variable-viscosity Stokes flow problems, Comput. Methods Appl. Mech. Eng., 198, 1691–1700, 2009. Calov, R. and Greve, R.: Correspondence. A semi-analytical solution for the positive degree-day model with stochastic temperature variations., J. Glaciol., 51, 173–175, 2005. Castelnau, O., Duval, P., Lebensohn, R. A., and Canova, G.: Viscoplastic modeling of texture development in polycrystalline ice with a self-consistent approach : Comparison with bound estimates, J. Geophys. Res., 101, 13851–13868, 1996. Castelnau, O., Shoji, H., Mangeney, A., Milsch, H., Duval, P., Miyamoto, A., Kawada, K., and Watanabe, O.: Anisotropic Behavior of GRIP Ices and Flow in Central Greenland, Earth Planet. Sci. Lett., 154, 307–322, 1998. Chung, D. H. and Kwon, T. H.: Invariant-based optimal fitting closure approximation for the numerical prediction of flow-induced fiber orientation, J. Rheol., 46, 169–194, 2002. Cornford, S., Martin, D., Graves, D., Ranken, D., Le Brocq, A., Gladstone, R., Payne, A., Ng, E., and Lipscomb, W.: Adaptive mesh, finite volume modeling of marine ice sheets, J. Comput. Phys., 232, 529–549, 2013a. Cornford, S. L., Martin, D. F., Graves, D. T., Ranken, D. F., Brocq, A. M. L., Gladstone, R. M., Payne, A. J., Ng, E. G., and Lipscomb, W. H.: Adaptive mesh, finite volume modeling of marine ice sheets, J. Computat. Phys., 232, 529–549, <a href="http://dx.doi.org/10.1016/j.jcp.2012.08.037">https://doi.org/10.1016/j.jcp.2012.08.037</a>, 2013b. de Fleurian, B., Gagliardini, O., Zwinger, T., Durand, G., Le Meur, E., Mair, D., and Råback, P.: A subglacial hydrological model dedicated to glacier sliding, The Cryosphere Discuss., 7, 3449–3496, <a href="http://dx.doi.org/10.5194/tcd-7-3449-2013">https://doi.org/10.5194/tcd-7-3449-2013</a>, 2013. Dupont, T. and Alley, R.: Assessment of the importance of ice-shelf buttressing to ice-sheet flow, Geophys. Res. Lett., 32, L04503, <a href="http://dx.doi.org/10.1029/2004GL022024">https://doi.org/10.1029/2004GL022024</a>, 2005. Durand, G., Gillet-Chaulet, F., Svensson, A., Gagliardini, O., Kipfstuhl, S., Meyssonnier, J., Parrenin, F., Duval, P., and Dahl-Jensen, D.: Change in ice rheology during climate variations – implications for ice flow modelling and dating of the EPICA Dome C core, Clim. Past, 3, 155–167, <a href="http://dx.doi.org/10.5194/cp-3-155-2007">https://doi.org/10.5194/cp-3-155-2007</a>, 2007. Durand, G., Gagliardini, O., Zwinger, T., Meur, E. L., and Hindmarsh, R. C. A.: Full-Stokes modeling of marine ice-sheets: influence of the grid size, Ann. Glaciol., 52, 109–114, 2009. Edwards, T. L., Fettweis, X., Gagliardini, O., Gillet-Chaulet, F., Goelzer, H., Gregory, J. M., Hoffman, M., Huybrechts, P., Payne, A. J., Perego, M., Price, S., Quiquet, A., and Ritz, C.: Effect of uncertainty in surface mass balance elevation feedback on projections of the future sea level contribution of the Greenland ice sheet – Part 2: Projections, The Cryosphere Discuss., 7, 675–708, <a href="http://dx.doi.org/10.5194/tcd-7-675-2013">https://doi.org/10.5194/tcd-7-675-2013</a>, 2013. Ern, A. and Guermond, J.: Theory and practice of finite elements, vol. 159, Springer, 2004. 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 Discuss., 5, 1995–2033, <a href="http://dx.doi.org/10.5194/tcd-5-1995-2011">https://doi.org/10.5194/tcd-5-1995-2011</a>, 2011. 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. Frey, P. and Alauzet, F.: Anisotropic mesh adaptation for CFD computations, Comput. Methods Appl. Mech. Eng., 194, 5068–5082, 2005. Gagliardini, O. and Meyssonnier, J.: Flow simulation of a firn-covered cold glacier, Ann. Glaciol., 24, 242–247, 1997. Gagliardini, O. and Zwinger, T.: The ISMIP-HOM benchmark experiments performed using the Finite-Element code Elmer, The Cryosphere, 2, 67–76, <a href="http://dx.doi.org/10.5194/tc-2-67-2008">https://doi.org/10.5194/tc-2-67-2008</a>, 2008. Gagliardini, O., Cohen, D., Råback, P., and Zwinger, T.: Finite-element modeling of subglacial cavities and related friction law, J. Geophys. Res., 112, F02027, <a href="http://dx.doi.org/10.1029/2006JF000576">https://doi.org/10.1029/2006JF000576</a>, 2007. Gagliardini, O., Gillet-Chaulet, F., and Montagnat, M.: A review of anisotropic polar ice models: from crystal to ice-sheet flow models, in: Physics of Ice Core Records II, edited by: Hondoh, T., Supplement Issue of Low Temperature Science, Hokkaido University, vol. 68, 149–166, 2009. Gagliardini, O., Durand, G., Zwinger, T., Hindmarsh, R., and Le Meur, E.: Coupling of ice-shelf melting and buttressing is a key process in ice-sheets dynamics, Geophys. Res. Lett., 37, L14501, <a href="http://dx.doi.org/10.1029/2010GL043334">https://doi.org/10.1029/2010GL043334</a>, 2010. Geenen, T., ur Rehman, M., MacLachlan, S., Segal, G., Vuik, C., van den Berg, A., and Spakman, W.: Scalable robust solvers for unstructured FE geodynamic modeling applications: Solving the Stokes equation for models with large localized viscosity contrasts, Geochem. Geophys. Geosys., 10, Q09002, <a href="http://dx.doi.org/10.1029/2009GC002526">https://doi.org/10.1029/2009GC002526</a>, 2009. Gilbert, J. C. and Lemaréchal, C.: Some numerical experiments with variable-storage quasi-Newton algorithms, Mathemat. Program., 45, 407–435, 1989. Gillet-Chaulet, F. and Durand, G.: Glaciology: Ice-sheet advance in Antarctica, Nature, 467, 794–795, 2010. Gillet-Chaulet, F., Gagliardini, O., Meyssonnier, J., Montagnat, M., and Castelnau, O.: A user-friendly anisotropic flow law for ice-sheet modelling, J. Glaciol., 41, 3–14, 2005. Gillet-Chaulet, F., Gagliardini, O., Meyssonnier, J., Zwinger, T., and Ruokolainen, J.: Flow-induced anisotropy in polar ice and related ice-sheet flow modelling, J. Non-Newtonian Fluid Mech., 134, 33–43, 2006. Gillet-Chaulet, F., Gagliardini, O., Seddik, H., Nodet, M., Durand, G., Ritz, C., Zwinger, T., Greve, R., and Vaughan, D. G.: Greenland ice sheet contribution to sea-level rise from a new-generation ice-sheet model, The Cryosphere, 6, 1561–1576, <a href="http://dx.doi.org/10.5194/tc-6-1561-2012">https://doi.org/10.5194/tc-6-1561-2012</a>, 2012. Greve, R. and Blatter, H.: Dynamics of ice sheets and glaciers, Springer, 2009. Grinevich, P. and Olshanskii, M.: An iterative method for the Stokes-type problem with variable viscosity, SIAM J. Sci. Comput., 31, 3959–3978, 2009. Heimbach, P. and Bugnion, V.: Greenland ice-sheet volume sensitivity to basal, surface and initial conditions derived from an adjoint model, Ann. Glaciol., 50, 67–80, 2009. Holland, P. and Feltham, D.: The effects of rotation and ice shelf topography on frazil-laden ice shelf water plumes, J. Phys. Oceanogr., 36, 2312–2327, 2006. Iken, A.: The effect of the subglacial water pressure on the sliding velocity of a glacier in an idealized numerical model, J. Glaciol., 27, 407–421, 1981. Jay-Allemand, M., Gillet-Chaulet, F., Gagliardini, O., and Nodet, M.: Investigating changes in basal conditions of Variegated Glacier prior to and during its 1982–1983 surge, The Cryosphere, 5, 659–672, <a href="http://dx.doi.org/10.5194/tc-5-659-2011">https://doi.org/10.5194/tc-5-659-2011</a>, 2011. Jouvet, G., Picasso, M., Rappaz, J., Huss, M., and Funk, M.: Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects, Math. Model. Nat. Phenomena, 6, 263–280, 2011. Kirchner, N., Hutter, K., Jakobsson, M., and Gyllencreutz, R.: Capabilities and limitations of numerical ice sheet models: a discussion for Earth-scientists and modelers, Quaternary Sci. Rev., 30, 3691–3704, <a href="http://dx.doi.org/10.1016/j.quascirev.2011.09.012">https://doi.org/10.1016/j.quascirev.2011.09.012</a>, 2011. Larour, E., Seroussi, H., Morlighem, M., and Rignot, E.: Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM), J. Geophys. Res., 117, F01022, <a href="http://dx.doi.org/10.1029/2011JF002140">https://doi.org/10.1029/2011JF002140</a>, 2012. 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. Leng, W., Ju, L., Gunzburger, M., and Ringler, T.: A parallel high-order accurate finite element nonlinear Stokes ice sheet model and benchmark experiments, J. of Geophys. Res., 117, F01001, <a href="http://dx.doi.org/10.1029/2011JF001962">https://doi.org/10.1029/2011JF001962</a>, 2012. Leng, W., Ju, L., Gunzburger, M., and Price, S.: Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models, The Cryosphere, 7, 19-29, <a href="http://dx.doi.org/10.5194/tc-7-19-2013">https://doi.org/10.5194/tc-7-19-2013</a>, 2013. Lliboutry, L.: General theory of subglacial cavitation and sliding of temperate glaciers, J. Glaciol., 7, 21–58, 1968. Ma, Y., Gagliardini, O., Ritz, C., Gillet-Chaulet, F., Durand, G., and Montagnat, M.: Enhancement factors for grounded ice and ice shelves inferred from an anisotropic ice-flow model, J. Glaciol., 56, 805–812, 2010. Malinen, M.: Boundary Conditions in the Schur Complement Preconditioning of Dissipative Acoustic Equations, SIAM J. Sci. Comput., 29, 1567–1592, <a href="http://dx.doi.org/10.1137/050629720">https://doi.org/10.1137/050629720</a>, 2007. Mart\'in, C. and Gudmundsson, G. H.: Effects of nonlinear rheology, temperature and anisotropy on the relationship between age and depth at ice divides, The Cryosphere, 6, 1221–1229, <a href="http://dx.doi.org/10.5194/tc-6-1221-2012">https://doi.org/10.5194/tc-6-1221-2012</a>, 2012. Mart\'in, C., Gudmundsson, G., Pritchard, H., and Gagliardini, O.: On the effects of anisotropic rheology on ice flow, internal structure, and the age-depth relationship at ice divides, J. Geophys. Res., 114, F04001, <a href="http://dx.doi.org/10.1029/2008JF001204">https://doi.org/10.1029/2008JF001204</a>, 2009. Moon, T., Joughin, I., Smith, B., and Howat, I.: 21st-Century Evolution of Greenland Outlet Glacier Velocities, Science, 336, 576–578, <a href="http://dx.doi.org/10.1126/science.1219985">https://doi.org/10.1126/science.1219985</a>, 2012. Morlighem, M., Rignot, E., Seroussi, H., Larour, E., Dhia, H., and Aubry, D.: Spatial patterns of basal drag inferred using control methods from a full-Stokes and simpler models for Pine Island Glacier, West Antarctica, Geophys. Res. Lett., 37, L14502, <a href="http://dx.doi.org/10.1029/2010GL043853">https://doi.org/10.1029/2010GL043853</a>, 2010. O'Leary, M. and Christoffersen, P.: Calving on tidewater glaciers amplified by submarine frontal melting, The Cryosphere, 7, 119-128, <a href="http://dx.doi.org/10.5194/tc-7-119-2013">https://doi.org/10.5194/tc-7-119-2013</a>, 2013. Paniconi, C. and Putti, M.: A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems, Water Resour. Res., 30, 3357–3374, 1994. Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson, G. H., Hindmarsh, R. C. A., 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 Cryosphere, 2, 95–108, <a href="http://dx.doi.org/10.5194/tc-2-95-2008">https://doi.org/10.5194/tc-2-95-2008</a>, 2008. 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, <a href="http://dx.doi.org/10.5194/tc-6-573-2012">https://doi.org/10.5194/tc-6-573-2012</a>, 2012. Pattyn, F., Perichon, L., Durand, G., Gagliardini, O., Hindmarsh, R. C. A., Zwinger, T., Albrecht, T., Cornford, S., Docquier, D., Fürst, J. J., Golberg, D., Gudmundsson, G. H., Humbert, A., Hütten, M. an Huybrechts, P., Jouvet, G., Kleiner, T., Laror, E., Martin, D., Morlighem, M., Payne, A. J., Pollard, D., Rückamp, M., Rybak, O., Seroussi, H., Thoma, M., and Wilkens, N.: Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison, J. Glaciol., 59, <a href="http://dx.doi.org/10.3189/2013JoG12J129">https://doi.org/10.3189/2013JoG12J129</a>, 2013. Payne, A. J., Vieli, A., Shepherd, A. P., Wingham, D. J., and Rignot, E.: Recent dramatic thinning of largest West Antarctic ice stream triggered by oceans, Geophys. Res. Lett., 31, L23401, <a href="http://dx.doi.org/10.1029/2004GL021284">https://doi.org/10.1029/2004GL021284</a>, 2004. Petra, N., Zhu, H., Stadler, G., Hughes, T., and Ghattas, O.: An inexact Gauss–Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model, J. Glaciol., 58, 889–903, 2012. Pettit, E. C., Thorsteinsson, T., Jacobson, P., and Waddington, E. D.: The role of crystal fabric in flow near an ice divide, J. Glaciol., 53, 277–288, 2007. Placidi, L., Greve, R., Seddik, H., and Faria, S.: Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic Flow Enhancement factor, Continuum Mech. Thermodynam., 22, 221–237, 2010. Pollard, D. and DeConto, R. M.: Modelling West Antarctic ice sheet growth and collapse through the past five million years, Nature, 458, 329–332, 2009. Pralong, A.: Dynamic damage model of crevasse opening and application to glacier calving, J. Geophys. Res., 110, B01309, <a href="http://dx.doi.org/10.1029/2004JB003104">https://doi.org/10.1029/2004JB003104</a>, 2005. Raymond Pralong, M. and Gudmundsson, G. H.: Bayesian estimation of basal conditions on Rutford Ice Stream, West Antarctica, from surface data, J. Glaciol., 57, 315–324, 2011. Reeh, N.: Parameterization of melt rate and surface temperature on the Greenland ice sheet, Polarforschung, 59, 113–128, 1991. Rignot, E., Koppes, M., and Velicogna, I.: Rapid submarine melting of the calving faces of West Greenland glaciers, Nat. Geosci., 3, 187–191, 2010. Rutt, I. C., Hagdorn, M., Hulton, N. R. J., and Payne, A. J.: The Glimmer community ice sheet model, J. Geophys. Res, 114, F02004, <a href="http://dx.doi.org/10.1029/2008JF001015">https://doi.org/10.1029/2008JF001015</a>, 2009. Sargent, A. and Fastook, J. L.: Manufactured analytical solutions for isothermal full-Stokes ice sheet models, The Cryosphere, 4, 285–311, <a href="http://dx.doi.org/10.5194/tc-4-285-2010">https://doi.org/10.5194/tc-4-285-2010</a>, 2010. Schäfer, M., Zwinger, T., Christoffersen, P., Gillet-Chaulet, F., Laakso, K., Pettersson, R., Pohjola, V. A., Strozzi, T., and Moore, J. C.: Sensitivity of basal conditions in an inverse model: Vestfonna ice cap, Nordaustlandet/Svalbard, The Cryosphere, 6, 771–783, <a href="http://dx.doi.org/10.5194/tc-6-771-2012">https://doi.org/10.5194/tc-6-771-2012</a>, 2012. Schoof, C.: The effect of cavitation on glacier sliding, Proc. R. Soc. A, 461, 609–627, 2005. Schoof, C.: Ice-sheet acceleration driven by melt supply variability, Nature, 468, 803–806, 2010. Seddik, H., Greve, R., Placidi, L., Hamann, I., and Gagliardini, O.: Application of a continuum-mechanical model for the flow of anisotropic polar ice to the EDML core, Antarctica, J. Glaciol., 54, 631–642, 2008. Seddik, H., Greve, R., Zwinger, T., and Placidi, L.: A full Stokes ice flow model for the vicinity of Dome Fuji, Antarctica, with induced anisotropy and fabric evolution, The Cryosphere, 5, 495–508, <a href="http://dx.doi.org/10.5194/tc-5-495-2011">https://doi.org/10.5194/tc-5-495-2011</a>, 2011. Seddik, H., Greve, R., Zwinger, T., Gillet-Chaulet, F., and Gagliardini, O.: Simulations of the Greenland ice sheet 100 years into the future with the full Stokes model Elmer/Ice, J. Glaciol., 58, 427–440, 2012. Shannon, S. R., Payne, A. J., Bartholomew, I. D., van den Broeke, M. R., Edwards, T. L., Fettweis, X., Gagliardini, O., Gillet-Chaulet, F., Goelzer, H., Hoffman, M., Huybrechts, P., Mair, D., Nienow, P., Perego, M., Price, S., Smeets, C. J. P. P., Solek, A., van de Wal, R. S. W., and Zwinger, T.: Enhanced basal lubrication and the contribution of the Greenland ice sheet to future sea level rise, Proc. Natl. Aca. Sci., <a href="http://dx.doi.org/10.1073/pnas.1212647110">https://doi.org/10.1073/pnas.1212647110</a>, 2013. Sole, A. J., Mair, D. W. F., Nienow, P. W., Bartholomew, I. D., King, M. A., Burke, M. J., and Joughin, I.: Seasonal speedup of a Greenland marine-terminating outlet glacier forced by surface melt–induced changes in subglacial hydrology, J. Geophys. Res., 116, F03014, <a href="http://dx.doi.org/10.1029/2010JF001948">https://doi.org/10.1029/2010JF001948</a>, 2011. Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K., Tignor, M., and Miller, H.: The physical science basis, New York and Cambridge: Cambridge University Press, 235–337, 2007. Staniforth, A. and C}ôté, J.: Semi-Lagrangian Integration Schemes for Atmospheric Models- A {Review., Mon. Weather Rev., 119, 2206–2223, 1991. ur Rehman, M., Geenen, T., Vuik, C., Segal, G., and MacLachlan, S.: On iterative methods for the incompressible Stokes problem, Int. J. Numer. Meth. Fluids, 65, 1180–1200, <a href="http://dx.doi.org/10.1002/fld.2235">https://doi.org/10.1002/fld.2235</a>, 2011. Vaughan, D. G. and Arthern, R.: Why Is It Hard to Predict the Future of Ice Sheets?, Science, 315, 1503–1504, <a href="http://dx.doi.org/10.1126/science.1141111">https://doi.org/10.1126/science.1141111</a>, 2007. Vieli, A. and Nick, F. M.: Understanding and Modelling Rapid Dynamic Changes of Tidewater Outlet Glaciers: Issues and Implications, Surv. Geophys., 32, 437–458, <a href="http://dx.doi.org/10.1007/s10712-011-9132-4">https://doi.org/10.1007/s10712-011-9132-4</a>, 2011. Walker, R., Dupont, T., Parizek, B., and Alley, R.: Effects of basal-melting distribution on the retreat of ice-shelf grounding lines, Geophys. Res. Lett., 35, <a href="http://dx.doi.org/10.1029/2008GL034947">https://doi.org/10.1029/2008GL034947</a>, 2008. Walkley, M. A., Gaskell, P. H., Jimack, P. K., and Kelmanson, M. A.: On the calculation of normals in free-surface flow problems, Comm. Num. Meth. Engrg, 20, 343–351, 2004. Winkelmann, R., Martin, M. A., Haseloff, M., Albrecht, T., Bueler, E., Khroulev, C., and Levermann, A.: The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 1: Model description, The Cryosphere, 5, 715–726, <a href="http://dx.doi.org/10.5194/tc-5-715-2011">https://doi.org/10.5194/tc-5-715-2011</a>, 2011. Zwinger, T. and Moore, J. C.: Diagnostic and prognostic simulations with a full Stokes model accounting for superimposed ice of Midtre Lovénbreen, Svalbard, The Cryosphere, 3, 217–229, <a href="http://dx.doi.org/10.5194/tc-3-217-2009">https://doi.org/10.5194/tc-3-217-2009</a>, 2009. 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. Zwinger, T., Schäfer, M., Mart\'in, C., and Moore, J. C.: Influence of anisotropy on velocity and age distribution at Scharffenbergbotnen blue ice area, The Cryosphere Discuss., 7, 3059–3093, <a href="http://dx.doi.org/10.5194/tcd-7-3059-2013">https://doi.org/10.5194/tcd-7-3059-2013</a>, 2013.