GMD Geoscientific Model Development GMD Geosci. Model Dev. 1991-9603 Copernicus Publications Göttingen, Germany 10.5194/gmd-5-1273-2012 Description of a hybrid ice sheet-shelf model, and application to Antarctica Pollard D. 1 DeConto R. M. 2 Earth and Environmental Systems Institute, Pennsylvania State University, University Park, PA, USA Department of Geosciences, University of Massachusetts, Amherst, MA, USA 17 10 2012 5 5 1273 1295 Copyright: © 2012 D. Pollard 2012 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/5/1273/2012/gmd-5-1273-2012.html The full text article is available as a PDF file from https://gmd.copernicus.org/articles/5/1273/2012/gmd-5-1273-2012.pdf

The formulation of a 3-D ice sheet-shelf model is described. The model is designed for long-term continental-scale applications, and has been used mostly in paleoclimatic studies. It uses a hybrid combination of the scaled shallow ice and shallow shelf approximations for ice flow. Floating ice shelves and grounding-line migration are included, with parameterized ice fluxes at grounding lines that allows relatively coarse resolutions to be used. All significant components and parameterizations of the model are described in some detail. Basic results for modern Antarctica are compared with observations, and simulations over the last 5 million years are compared with previously published results. The sensitivity of ice volumes during the last deglaciation to basal sliding coefficients is discussed.

 References Ackert, Jr. R. P., Mukhopadhyay, S., Pollard, D., DeConto, R. M., Putnam, A. E., and Borns, Jr. H. W.: West Antarctic Ice Sheet elevations in the Ohio Range: Geologic constraints and ice sheet modeling prior to the last highstand, Earth Plan. Sci. Lett., 307, 83–93, 2011. Albrecht, T. and Levermann, A.: Fracture field for large-scale ice dynamics, J. Glaciol., 58, 165–176, <a href="http://dx.doi.org/10.3189/2012JOG11J191">https://doi.org/10.3189/2012JOG11J191</a>, 2012. Albrecht, T., Martin, M., Haseloff, M., Winkelmann, R., and Levermann, A.: Parameterization for subgrid-scale motion of ice-shelf calving fronts, The Cryosphere, 5, 35–44, <a href="http://dx.doi.org/10.5194/tc-5-35-2011">https://doi.org/10.5194/tc-5-35-2011</a>, 2011. Alley, R. B. and Whillans, I. M.: Response of the East Antarctic Ice Sheet to sea-level rise, J. Geophys. Res., 89, 6487–6493, 1984. Alley, R. B., Anandakrishnan, S., Dupont, T. K., Parizek, B. R., and Pollard, D.: Effect of sedimentation on ice-sheet grounding-line stability, Science, 315, 1838–1841, 2007. Alley, R. B., Horgan, H. J., Joughin, I., Cuffey, K. M., Dupont, T. K., Parizek, B. R., Anandakrishnan, S., and Bassis, J.: A simple law for ice-shelf calving, Science, 322, 1344, 2008. Amundson, J. and Truffer, M.: A unifying framework for iceberg-calving models, J. Glaciol., 56, 822–830, 2010. Andrews, J. T. and Mahaffy M. A. W.: Growth rate of the Laurentide Ice Sheet and sea level lowering (with emphasis on the 115 000 BP sea level low), Quat. Res., 6, 167–183, 1976. Beckmann, A. and Goose, H.: A parameterization of ice shelf-ocean interaction for climate models, Ocean Modell., 5, 157–170, 2003. 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. Bindschadler, R. A., Nowicki, S., Abe-Ouchi, A., Aschwanden, A., Choi, H., Fastook, J., Granzow, G., Greve, R., Gutowski, G., Herzfeld, U., Jackson, C., Johnson, J., Khroulev, C., Levermann, A., Lipscomb, W. H., Martin, M. A., Morlighem, M., Parizek, B. R., Pollard, D., Price, S. F., Ren, D., Saito, F., Sato, T., Seddik, H., Seroussi, H., Takahashi, K., Walker, R., and Wang, W. L.: Ice-sheet model sensitivities to environmental forcing and their use in projecting future sea-level (the SeaRISE project), J. Glaciol., submitted, 2012. Briggs, R., Pollard, D., and Tarasov, L.: Past evolution of the Antarctic Ice Sheet: a Bayesian calibrated 3D glacial system modeling study. Abstract PS19.9, Programme and Abstracts, 11th International Symposium on Antarctic Earth Sciences, Edinburgh, Scotland, 246 pp., 10–16 July 2011. Brotchie, J. F. and Silvester, R.: On crustal flexure, J. Geophys. Res., 74, 22, 5240–5252, 1969. Budd, W. F. and Smith, I. N.: The growth and retreat of ice sheets in response to orbital radiation changes, in: Sea Level, Ice and Climatic Change, Int. Assoc. Hydrol. Sci. publ., 131, 369–409, 1979. Budd, W. F., Jenssen, D., Mavrakis, E., and Coutts, B.: Modelling the Antarctic ice-sheet changes through time, Ann. Glaciol., 20, 291–297, 1994. Bueler, E. and Brown, J.: Shallow shelf approximation as a "sliding law" in a thermomechanically coupled ice sheet model, J. Geophys. Res., 114, F03008, <a href="http://dx.doi.org/10.1029/2008JF001179">https://doi.org/10.1029/2008JF001179</a>, 2009. Calov, R., Greve, R., Abe-Ouchi, A., Bueler, E. L., Huybrechts, P., Johnson, J. V., Pattyn, F., Pollard, D., Ritz, C., Saito, F., and Tarasov, L.: Results from the Ice Sheet Model Intercomparison Project – Heinrich Event INtercOmparison (ISMIP HEINO), J. Glaciol., 56, 371–383, 2010. Comiso, J. C.: Variability and trends in Antarctic surface temperatures from in situ and satellite infrared measurements, J. Climate, 13, 1674–1696, 2000. Cuffey, K. M. and Paterson, W. S. B.: The Physics of Glaciers, Fourth Edition. Academic Press, Amsterdam, 704 pp., 2010. DeConto, R. M. and Pollard, D.: Rapid Cenozoic glaciation of Antarctica induced by declining atmospheric CO<sub>2</sub>, Nature, 421, 245–249, 2003a. DeConto, R. M. and Pollard, D.: A coupled climate-ice sheet modeling approach to the early Cenozoic history of the Antarctic ice sheet, Palaeogeogr. Palaeocl., 198, 39–52, 2003b. DeConto, R., Pollard, D., and Harwood, D.: Sea ice feedback and Cenozoic evolution of Antarctic climate and ice sheets, Paleoceanography, 22, PA3214, <a href="http://dx.doi.org/10.1029/2006PA001350">https://doi.org/10.1029/2006PA001350</a>, 2007. DeConto, R. M., Pollard, D., Wilson, P., Palike, H., Lear, C., and Pagani, M.: Thresholds for Cenozoic bipolar glaciation, Nature, 455, 653–656, 2008. DeConto, R. M., Pollard, D., and Kowalewski, D.: Past and future vulnerability of the West Antarctic Ice Sheet to surface ice-shelf melt. Abstract C42A-06, American Geophysical Union Fall Meeting, San Francisco, California, USA, December 4–9 2011. DeConto, R. M., Pollard, D., and Kowalewski, D.: Modeling Antarctic ice sheet and climate variations during Marine Isotope Stage 31, Glob. Plan. Change, 88–89, 45–52, 2012. Dinniman, M. S., Klinck, J. M., and Smith, Jr. W. O.: A model study of Circumpolar Deep Water on the Wext Antarctic Peninsula and Ross Sea continental shelves, Deep-Sea Res. Pt.&nbsp;II, 58, 1508–1523, 2011. Doake, C. S. M., Corr, H. F. J., Rott, H., Skvarca, P., and Young, N. W.: Breakup and conditions for stability of the northern Larsen Ice Shelf, Antarctica, Nature, 391, 778–780, 1998. Docquier, D., Perichon, L., and Pattyn, F.: Representing grounding line dynamics in numerical ice sheet models: Recent advances and outlook, Surveys Geophys., 32, 417–435, 2011. Drouet, A.-S., Durand, G., Favier, L., Peyaud, V., Gagliardini, O., Ritz, C., Zwinger, T., and Le Meur, E.: Testing the validity of the boundary layer flux-thickness relationship at the grounding line, Geophys. Res. Abstr., 13, EGU2011-3149-1, European Geosciences Union General Assembly, Vienna, Austria, 2011. Farrow, D. E. and Stevens, D. P.: A new tracer advection scheme for Bryan and Cox type ocean general circulation models, J. Phys. Oceanogr., 25, 1731–1741, 1995. 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, <a href="http://dx.doi.org/10.5194/tc-6-101-2012">https://doi.org/10.5194/tc-6-101-2012</a>, 2012. Fox Maule, C., Purucker, M. E., Olsen, N., and Mosegaard, K.: Heat flux anomalies in Antarctica revealed by satellite magnetic data, Science, 309, 464–467, 2005. Fricker, H. A., Coleman, R., Padman, L., Scambos, T. A., Bohlander, J., and Brunt, K. M.: Mapping the grounding zone of the Amery ice Shelf, East Antarctica, using InSAR, MODIS and ICESat, Antarc. Sci., 21, 515–532, 2009. Fyke, J. G., Weaver, A. J., Pollard, D., Eby, M., Carter, L., and Mackintosh, A.: A new coupled ice sheet/climate model: description and sensitivity to model physics under Eemian, Last Glacial Maximum, late Holocene and modern climate conditions, Geosci. Model Dev., 4, 117–136, <a href="http://dx.doi.org/10.5194/gmd-4-117-2011">https://doi.org/10.5194/gmd-4-117-2011</a>, 2011. Gagliardini, O., Durand, G., Zwinger, T., Hindmarsh, R. C. A., 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. Gladstone, R. M., Lee, V., Vieli, A., and Payne, A. J.: Grounding line migration in an adaptive mesh ice sheet model, J. Geophys. Res., 115, F04014, <a href="http://dx.doi.org/10.1029/2009JF001615">https://doi.org/10.1029/2009JF001615</a>, 2010a. Gladstone, R. M., Payne, A. J., and Cornford, S. L.: Parameterising the grounding line in flow-line ice sheet models, The Cryosphere, 4, 605–619, <a href="http://dx.doi.org/10.5194/tc-4-605-2010">https://doi.org/10.5194/tc-4-605-2010</a>, 2010b. Gladstone, R. M., Payne, A. J., and Cornford, S. L.: Resolution requirements for grounding-line modelling: sensitivity to basal drag and ice-shelf buttressing, Ann. Glaciol., 53, 97–105, 2012a. Gladstone, R. M., Lee, V., Rougier, J., Payne, A. J., Hellmer, H., Le Brocq, A., Shepherd, A., Edwards, T. L., Gregory, J., and Cornford, S. L.: Calibrated prediction of Pine Island Glacier retreat during the 21st and 22nd centuries with a coupled flowline model, Earth Plan. Sci. Lett., 333–334, 191–199, 2012b. Goldberg, D. N.: A variationally derived, depth-integrated approximation to a higher-order glaciological flow model, J. Glac, 57, 201, 157–170, 2011. Goldberg, D. N., Holland, D. M., and Schoof, C.: Grounding line movement and ice shelf buttressing in marine ice sheets, J. Geophys. Res., 114, F04026, <a href="http://dx.doi.org/10.1029/2008JF001227">https://doi.org/10.1029/2008JF001227</a>, 2009. Gomez, N., Pollard, D., Mitrovica, J. X., Huybers, P., and Clark, P. U.: Evolution of a coupled marine ice sheet-sea level model, J. Geophys. Res.-Earth Surf., 117, F01013, <a href="http://dx.doi.org/10.1029/2011JF002128">https://doi.org/10.1029/2011JF002128</a>, 2012. Gudmundsson, G. H., Krug, J., Durand, G., Favier, L., and Gagliardini, O.: The stability of grounding lines on retrograde slopes, The Cryosphere Discuss., 6, 2597–2619, <a href="http://dx.doi.org/10.5194/tcd-6-2597-2012">https://doi.org/10.5194/tcd-6-2597-2012</a>, 2012. Hellmer, H. H., Kauker, F., Timmermann, R., Determann, J., and Rae, J.: Twenty-first-century warming of a large Antarctic ice-shelf cavity by a redirected coastal current, Nature, 485, 225–228, 2012. Herrmann, A. D., Patzkowsky, M. E., and Pollard, D.: Obliquity forcing with 8-12x pre-industrial levels of atmospheric pCO<sub>2</sub> during the late Ordovician glaciation, Geology, 31, 6, 485–488, 2003. Herrmann, A. D., Patzkowsky, M. E., and Pollard, D.: The impact of paleogeography, pCO<sub>2</sub>, poleward ocean heat transport and sea level change on global cooling during the late Ordovician, Palaeogeogr. Palaeocl., 206, 59–74, 2004. Hindmarsh, R. C. A.: A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier flow, J. Geophys Res., 109, F01012, https://doi.org/19.1029/2003JF000065, 2004. Holland, P. R., Jenkins, A., and Holland, D. M.: The response of ice shelf basal melting to variations in ocean temperature, J. Climate, 21, 2558–2572, 2008. Horgan, H. J. and Anandakrishnan, S.: Static grounding lines and dynamic ice streams: Evidence from the Siple Coast, West Antarctica, Geophpys. Res. Lett., 33, L18502, <a href="http://dx.doi.org/10.1029/2006GL027091">https://doi.org/10.1029/2006GL027091</a>, 2006. Horton, D. E., Poulsen, C. J., and Pollard, D.: Orbital and CO<sub>2</sub> forcing of late Paleozoic continental ice sheets, Geophys. Res. Lett., 34, L19708, <a href="http://dx.doi.org/10.1029/2007GL031188">https://doi.org/10.1029/2007GL031188</a>, 2007. Horton, D. E., Poulsen, C. J., and Pollard, D.: Influence of high-latitude vegetation feedbacks on late Paleozoic glacial cycles, Nature Geosci., 3, 572–577, 2010. Hubbard, A.: High-resolution modeling of the advance of the Younger Dryas ice sheet and its climate in Scotland, Quatern. Res., 52, 27–43, 1999. Hubbard, A.: The validation and sensitivity of a model of the Icelandic ice sheet, Quatern. Sci. Rev., 25, 2297–2313, 2006. Hulbe, C. and MacAyeal, D. R.: A new numerical model of coupled inland ice sheet, ice stream, and ice shelf flow and its application to the West Antarctic Ice Sheet, J. Geophys. Res., 104, B11, 25349–25366, 1999. Hulbe, C. and Fahnestock, M.: Century-scale discharge stagnation and reactivation of the Ross ice streams, West Antarctica, J. Geophys. Res., 112, F03S27, <a href="http://dx.doi.org/10.1029/2006JF000603">https://doi.org/10.1029/2006JF000603</a>, 2007. Hulbe, C. L., LeDoux, C., and Cruikshank, K.: Propagation of long fractures in the Ronne Ice Shelf, Antarctica, investigated using a numerical model of fracture propagation, J. Glaciol., 56, 459–472, 2010. Huybrechts, P.: Report of the Third EISMINT Workshop on Model Intercomparison, European Science Foundation, Strasbourg, 140 pp., 1998. Huybrechts, P.: Sea-level changes at the LGM from ice-dynamic reconstructions of the Greenland and Antarctic ice sheets during the glacial cycles, Quat. Sci. Rev., 21, 203–231, 2002. Huybrechts, P. and de Wolde, J.: The dynamic response of the Greenland and Antarctic ice sheets to multiple-century climatic warming, J. Climate, 1, 2169–2188, 1999. Huybrechts, P. and Oerlemans, J.: Evolution of the East Antarctic Ice Sheet: a numerical study of thermomechanical response patterns with changing climate, Ann. Glaciol., 11, 52–59, 1988. Jacobs, S. S., Jenkins, A., Giulivi, C. F., and Dutrieux, P.: Stronger ocean circulation and increased melting under Pine Island Glacier ice shelf, Nat. Geosci., 4, 519–523, 2011. Jenkins, A. and Bombosch, A.: Modeling the effects of frazil ice crystals on the dynamics and thermodynamics of ice shelf water plumes, J. Geophys. Res., 100, C4, 6967–6981, 1995. Jenkins, A., Dutrieux, P., Jacobs, S. S., McPhail, S. D., Perrett, J. R., Webb, A. T., and White, D.: Observations beneath Pine Island Glacier in West Antarctica and implications for its retreat, Nature Geosci., 3, 468–472, 2010. Katz, R. F. and Worster, M. G.: Stability of ice-sheet grounding lines, Proc. Roy. Soc. A, 466, 1597–1620, <a href="http://dx.doi.org/10.1098/rspa.2009.0434">https://doi.org/10.1098/rspa.2009.0434</a>, 2010. Koenig, S. J., DeConto, R. M., and Pollard, D.: Late Pliocene to Pleistocene sensitivity of the Greenland Ice Sheet in response to external forcing and internal feedbacks, Clim. Dynam., 37, 1247–1268, 2011. Laskar, J., Robutel, P., Joutel, F., Gastineau, M., Correia, A. C. M., and Levrard, B.: A long-term numerical solution for the insolation quantities of the Earth, Astron. Astophys., 428, 261–285, 2004. Le Brocq, A. M., Payne, A. J., and Vieli, A.: An improved Antarctic dataset for high resolution numerical ice sheet models (ALBMAP v1), Earth Syst. Sci. Data, 2, 247–260, <a href="http://dx.doi.org/10.5194/essd-2-247-2010">https://doi.org/10.5194/essd-2-247-2010</a>, 2010. Le Brocq, A. M., Bentley, M. J., Hubbard, A., Fogwill, C. J., Sugden, D. E., and Whitehouse, P. L.: Reconstructing the Last Glacial Maximum ice sheet in the Weddell Sea embayment, Antarctica, using numerical modeling constrained by field evidence, Quat. Sci. Rev., 30, 2422–2432, 2011. Levermann, A., Albrecht, T., Winkelmann, R., Martin, M. A., Haseloff, M., and Joughin, I.: Kinematic first-order calving law implies potential for abrupt ice-shelf retreat, The Cryosphere, 6, 273–286, <a href="http://dx.doi.org/10.5194/tc-6-273-2012">https://doi.org/10.5194/tc-6-273-2012</a>, 2012. Lisiecki, L. E. and Raymo, M.: A Pliocene-Pleistocene stack of 57 globally distributed benthic δ<sup>18</sup>O records, Paleoceanogr., 20, 1–17, 2005. 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. Glaciool., 56, 805–812, 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, 4071–4087, 1989. MacAyeal, D. R.: EISMINT: Lessons in Ice-Sheet Modeling. Dept.of Geophysical Sciences, Univ. of Chicago, 428 pp., geosci.uchicago.edu/pdfs/macayeal/lessons.pdf, 1996. Mackintosh, A., Golledge, N., Domack, E., Dunbar, R., Leventer, A., White, D., Pollard, D., DeConto, R.M., Fink, D., Zwartz, D., Gore, D., and Lavoie, C.: Retreat of the East Antarctic ice sheet during the last glacial termination, Nat. Geosci., 4, 195–202, 2011. Mahaffy, M. W.: A Three-Dimensional Numerical Model of Ice Sheets: Tests on the Barnes Ice Cap, Northwest Territories. J. Geophys. Res., 81, 1059–1066, 1976. Marshall, S. J. and Clarke, G. K. C.: A continuum mixture model of ice stream thermodynamics in the Laurentide Ice Sheet, J. Geophys. Res., 1021, B9, 20599–20613, 1997. Marshall, S. J., Pollard, D., Hostetler, S., and Clark, P. U.: Coupling ice-sheet and climate models for simulation of former ice sheets, in: The Quaternary Period in the United States, edited by: Gillespie, A. R., Porter, S. C., and Atwater, B. F., Developments Quatern. Sci., 1, Elsevier, Amsterdam, 105–126, 2004. Marshall, S. J., Bjornsson, H., Flowers, G. E., and Clarke, G. K. C.: Simulation of Vatnajokull ice cap dynamics, J. Geophys. Res., 110, F03009, <a href="http://dx.doi.org/10.1029/2004JF000262">https://doi.org/10.1029/2004JF000262</a>, 2005. Martin, M. A., Winkelmann, R., Haseloff, M., Albrecht, T., Bueler, E., Khroulev, C., and Levermann, A.: The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet, The Cryosphere, 5, 727–740, <a href="http://dx.doi.org/10.5194/tc-5-727-2011">https://doi.org/10.5194/tc-5-727-2011</a>, 2011. Morland, L. W.: Unconfined ice-shelf flow, in: Dynamics of the West Antarctic Ice Sheet, edited by: van der Veen, C. J. and Oerlemans, J., Springer, New York, 99–116, 1987. Morlighem, M., Rignot, E., Seroussi, H., Larour, E., Ben 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. Motyka, R., Hunter, L., Echelmeyer, L., and Connor, C.: Submarine melting at the terminus of a temperate tidewater glacier, Leconte Glacier, Alaska, USA, Ann. Glaciol., 36, 57–65, 2003. Mukhopadhyay, S., Ackert, R. P. Jr., Pope, A. E., Pollard, D., and DeConto, R. M.: Miocene to recent ice elevation variations from the interior of the West Antarctic ice sheet: Constraints from geologic observations, cosmogenic nuclides and ice sheet modeling, Earth Plan. Sci. Lett., 337–338, 243–251, 2012. Nicholls, K. W., Osterhus, S., Makinson, K., Gammelsrod, T., and Fahrbach, E.: Ice-ocean processes over the continental shelf of the southern Weddell Sea, Antarctica: a review, Rev. Geophys. 47, 1–23, 2009. Nick, F. M., van der Veen, C. J., Vieli, A., and Benn, D. I.: A physically based calving model applied to marine outlet glaciers and implications for the glacier dynamics, J. Glaciol., 56, 199, 781–794, 2010. Olbers, D. and Hellmer, H.: A box model of circulation and melting in ice shelf caverns, Ocean Dynam., 60, 141–153, 2010. Pattyn, F.: Transient glacier response with a higher-order numerical ice-flow model, J. Glaciol., 48, 467–477, 2002. 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., Soucek, 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.: Antarctic subglacial conditions inferred from a hybrid ice sheet/stream model, Earth Plan. Sci. Lett., 295, 451–461, 2010. 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>, 2012a. Pattyn, F., Perichon, L., Durand, G., Favier, L., Gagliardini, O., Hindmarsh, R. C. A., Zwinger, T., Albrecht, T., Cornford, S., Docquier, D., Furst, J. J., Goldberg, D., Gudmundsson, G. H., Humbert, A., Hutten, M., Huybrechts, P., Jouvet, G., Kleiner, T., Larour, E., Martin, D., Morlighem, M., Payne, A. J., Pollard, D., Ruckamp, M., Rybak, O., Seroussi, H., Thoma, M., and Wilkens, N.: Grounding-line migration in plan-view marine ice-sheet models: results of the <i>ice2sea</i> MISMIP3d intercomparison, J. Glaciol., submitted, 2012b. Payne, A. J.: A thermomechanical model of ice flow in West Antarctica, Clim. Dynam., 15, 115–125, 1999. Payne, A. J., Holland, P. R., Shepherd, A. P., Rutt, I. C., Jenkins, A., and Joughin, I.: Numerical modeling of ocean-ice interactions under Pine Island Bay's ice shelf, J. Geophys. Res., 112, C10019, <a href="http://dx.doi.org/10.1029/2006JC003733">https://doi.org/10.1029/2006JC003733</a>, 2007. Pollard, D. and DeConto, R. M.: Antarctic ice and sediment flux in the Oligocene simulated by a climate-ice sheet-sediment model, Palaeogeogr. Palaeocl., 198, 53–67, 2003. Pollard, D. and DeConto, R. M.: Hysteresis in Cenozoic Antarctic ice sheet variations, Glob. Planet. Change, 45, 9–21, <a href="http://dx.doi.org/10.1016/j.gloplacha.2004.09.011">https://doi.org/10.1016/j.gloplacha.2004.09.011</a>, 2005. Pollard, D. and DeConto, R. M.: A coupled ice-sheet/ice-shelf/sediment model applied to a marine-margin flowline: forced and unforced variations, in: Glacial Sedimentary Processes and Products, edited by: Hambrey, M. J., Christoffersen, P., Glasser, N. F., and Hubbard, B., International Association of Sedimentologists Special Publication, 39, Blackwell Publ., Oxford, 37–52, 2007. 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. Pollard, D. and DeConto, R. M.: Antarctic Ice Sheet variations in response to changes in ice-shelf oceanic melting. Abstract, International Glaciological Society (IGS) Symposium on Interactions of Ice Sheets and Glaciers with the Ocean, 5–10 June 2011, Scripps Institution of Oceanography, California, USA, 2011. Pollard, D. and DeConto, R. M.: A simple inverse method for the distribution of basal sliding coefficients under ice sheets, applied to Antarctica, The Cryosphere, 6, 953–971, <a href="http://dx.doi.org/10.5194/tc-6-953-2012">https://doi.org/10.5194/tc-6-953-2012</a>, 2012. Pollard, D. and Kasting, J. F.: Climate-ice sheet simulations of Neoproterozoic glaciation before and after collapse to Snowball Earth, in: The Extreme Proterozoic: Geology, Geochemistry and Climate, edited by: Jenkins, G., McMenamin, M., McKay, C., and Sohl, L.: Geophysical Monograph 146, American Geophysical Union, Washington, D. C., 91–105, 2004. Pollard, D., DeConto, R. M., and Nyblade, A. A.: Sensitivity of Cenozoic Antarctic ice sheet variations to geothermal heat flux, Glob. Planet. Change, 49, 63–74, 2005. Pritchard, H. D., Ligtenberg, S. R. M., Fricker, H. A., Vaughan, D. G., van den Broeke, M. R., and Padman, L.: Antarctic ice-sheet loss driven by basal melting of shelves, Nature, 484, 502–505, 2012. Rignot, E., Koppes, M., and Velicogna, I.: Rapid submarine melting of the calving faces of West Greenland glaciers, Nature Geosci., 3, 187–191, 2010. Rignot, E., Mouginot, J., and Scheuchl, B.: Ice flow of the Antarctic Ice Sheet, Science, 333, 1428–1430, 2011. Ritz, C., Fabre, A., and Letreguilly, A.: Sensitivity of a Greenland ice sheet model to ice flow and ablation parameters: consequences for the evolution through the last climatic cycle, Clim. Dynam., 13, 11–24, 1997. Ritz, C., Rommelaere, V., and Dumas, C.: Modeling the evolution of Antarctic ice sheet over the last 420 000 years: Implications for altitude changes in the Vostok region, J. Geophys. Res., 106, D23, 31943–31964, 2001. Rogozhina, I., Hagedoorn, J. M., Martinec, Z., Fleming, K., Soucek, O., Greve, R., and Thomas, M.: Effects of uncertainties in the geothermal heat flux distribution on the Greenland Ice Sheet: An assessment of existing heat flow models, J. Geophys. Res., 117, F02025, <a href="http://dx.doi.org/10.1029/2011JF002098">https://doi.org/10.1029/2011JF002098</a>, 2012. Rommelaere, V. and Ritz, C.: A thermomechanical model of ice-shelf flow, Ann. Glaciol., 23, 13–20, 1996. Scambos, T. A., Bohlander, J. A., Shuman, C. A., and Skvarca, P.: Glacier acceleration and thinning after ice shelf collapse in the Larsen B embayment, Antarctica, Geophys. Res. Lett., 31, L18402, <a href="http://dx.doi.org/10.1029/2004GL020670">https://doi.org/10.1029/2004GL020670</a>, 2004. Schoof, C.: Ice sheet grounding line dynamics: Steady states, stability, and hysteresis, J. Geophys. Res., 112, F03S28, <a href="http://dx.doi.org/10.1029/2006JF000664">https://doi.org/10.1029/2006JF000664</a>, 2007. Schoof, C. and Hindmarsh, R. C. A.: Thin-film flows with wall slip: An asymptotic analysis of higher order glacier flow models, Q. J. Mech. Appl. Math., 63, 73–114, 2010. 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, 209, 427–440, 2012. Shapiro, N. M. and Ritzwoller, M. H.: Inferring surface heat flux distributions guided by a global seismic model: particular application to Antarctica. Earth Plan. Sci. Lett., 223, 213–224, 2004. Smith, N. R., Zhaoqian, D., Kerry, K. R., and Wright, S.: Water masses and circulation in the region of Prydz Bay, Antarctica, Deep-Sea Res., 31, 1121–1147, 1984. Stern, T. A. and ten Brink, U. S.: Flexural uplift of the Transantarctic Mountains, J. Geophys. Res., 94, B8, 10315–10330, 1989. Studinger, M., Bell, R. E., Blankenship, D. D., Finn, C. A., Arko, R. A., Morse, D. L., and Joughin, I.: Subglacial sediments: A regional geological template for ice flow in West Antarctica, Geophys. Res. Lett., 28, 18, 3493–3496, 2001. Timmermann, R., Le Brocq, A., Deen, T., Domack, E., Dutrieux, P., Galton-Fenzi, B., Hellmer, H., Humbert, A., Jansen, D., Jenkins, A., Lambrecht, A., Makinson, K., Niederjasper, F., Nitsche, F., Nost, O. A., Smedsrud, L. H., and Smith, W. H. F.: A consistent data set of Antarctic ice sheet topography, cavity geometry, and global bathymetry, Earth. Syst. Sci. Data, 2, 261–273, <a href="http://dx.doi.org/10.5194/essd-2-261-2010">https://doi.org/10.5194/essd-2-261-2010</a>, 2010. Tziperman, E., Abbot, D. S., Ashkenazy, Y., Gildor, H., Pollard, D., Schoof, C. G., and Schrag, D. P.: Continental constriction and sea ice thickness in a Snowball-Earth scenario, J. Geophys. Res.-Oceans, 117, C05016, 12 pp., <a href="http://dx.doi.org/10.1029/2011JC007730">https://doi.org/10.1029/2011JC007730</a>, 2012. van de Berg, W. J., van den Broeke M. R., and van Meijgaard, E.: Reassessment of the Antarctic surface mass balance using calibrated output of a regional atmospheric climate model, J. Geophys. Res., 111, D11104, <a href="http://dx.doi.org/10.1029/2005JD006495">https://doi.org/10.1029/2005JD006495</a>, 2006. van de Berg, W. J., van den Broeke, M., Ettema, J., van Meijgaard, E., and Kaspar, F.: Significant contribution of insolation to Eemian melting of the Greenland ice sheet, Nature Geosci., 4, 679–683, 2011. van den Berg, J., van de Wal, R. S. W., and Oerlemans, J.: Effects of spatial discretization in ice-sheet modelling using the shallow-ice approximation, J. Glaciol., 52, 176, 89–98, 2006. van der Veen, C. J.: Response of a marine ice sheet to changes at the grounding line, Quatern. Res., 24, 257–267, 1985. Vaughan, D. G., Barnes, D. K. A., Fretwell, P. T., and Bingham, R. G.: Potential seaways across West Antarctica, Geochem. Geophys. Geosyst., 12, Q10004, <a href="http://dx.doi.org/10.1029/2011GC003688">https://doi.org/10.1029/2011GC003688</a>, 2011. Walker, R. T., Dupont, T. K., Holland, D. M., Parizek, B. R., and Alley, R. B.: Initial effects of oceanic warming on a coupled ocean-ice shelf-ice stream system, Earth Plan. Sci. Lett., 287, 483–487, 2009. Whitehouse, P. L., Bentley, M. J., and Le Brocq, A. M.: A deglacial model for Antarctica: geological constraints and glaciological modeling as a basis for a new model of Antarctic glacial isostatic adjustment, Quat. Sci. Rev., 32, 1–24, 2012. 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. Winkelmann, R., Levermann, A., Frieler, K., and Martin, M. A.: Uncertainty in future solid ice discharge from Antarctica, The Cryosphere Discuss., 6, 673–714, <a href="http://dx.doi.org/10.5194/tcd-6-673-2012">https://doi.org/10.5194/tcd-6-673-2012</a>, 2012. Young, D. A., Wright, A. P., Roberts, J. L., Warner, R. C., Young, N. W., Greenbaum, J. S., Schroeder, D. M., Holt, J. W., Sugden, D. E., Blankenship, D. D., van Ommen, T. D., and Siegert, M. J.: A dynamic early East Antarctic Ice Sheet suggested by ice-covered fjord landscapes, Nature, 474, 72–75, 2011.