Description of a hybrid ice sheet-shelf model, and application to Antarctica

Abstract. 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.

[1]  Antony J. Payne,et al.  An improved Antarctic dataset for high resolution numerical ice sheet models (ALBMAP v1) , 2010 .

[2]  Frank Pattyn,et al.  Transient glacier response with a higher-order numerical ice-flow model , 2002 .

[3]  N. Smith,et al.  Water masses and circulation in the region of Prydz Bay, Antarctica , 1984 .

[4]  J. Oerlemans,et al.  EVOLUTION OF THE EAST ANTARCTIC ICE SHEET: A NUMERICAL STUDY OF THERMO- MECHANICAL RESPONSE PATTERNS WITH CHANGING CLIMATE , 1988 .

[5]  C. Ritz,et al.  Enhancement factors for grounded ice and ice shelves inferred from an anisotropic ice-flow model , 2010, Journal of Glaciology.

[6]  S. Cornford,et al.  Parameterising the grounding line in flow-line ice sheet models , 2010 .

[7]  David M. Holland,et al.  The Response of Ice Shelf Basal Melting to Variations in Ocean Temperature , 2008 .

[8]  H. Rott,et al.  Breakup and conditions for stability of the northern Larsen Ice Shelf, Antarctica , 1998, Nature.

[9]  Jonathan M. Gregory,et al.  Calibrated prediction of Pine Island Glacier retreat during the 21st and 22nd centuries with a coupled flowline model , 2012 .

[10]  R. DeConto,et al.  Sea ice feedback and Cenozoic evolution of Antarctic climate and ice sheets , 2007 .

[11]  T. Stern,et al.  Flexural uplift of the Transantarctic Mountains , 1989 .

[12]  D. Pollard,et al.  Evolution of a coupled marine ice sheet–sea level model , 2011 .

[13]  Jacques Laskar,et al.  A long-term numerical solution for the insolation quantities of the Earth , 2004 .

[14]  E. Bueler,et al.  The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 1: Model description , 2010 .

[15]  R. DeConto,et al.  A coupled ice-sheet/ice-shelf/sediment model applied to a marine-margin flowline: forced and unforced variations , 2009 .

[16]  M. Raymo,et al.  A Pliocene‐Pleistocene stack of 57 globally distributed benthic δ18O records , 2005 .

[17]  A. Jenkins,et al.  Modeling the effects of frazil ice crystals on the dynamics and thermodynamics of Ice Shelf Water plumes , 1995 .

[18]  A. Hubbard The validation and sensitivity of a model of the Icelandic ice sheet , 2006 .

[19]  Z. Martinec,et al.  Effects of uncertainties in the geothermal heat flux distribution on the Greenland Ice Sheet: An assessment of existing heat flow models , 2012 .

[20]  D. Goldberg,et al.  A variationally derived, depth-integrated approximation to a higher-order glaciological flow model , 2011, Journal of Glaciology.

[21]  I. Joughin,et al.  Kinematic first-order calving law implies potential for abrupt ice-shelf retreat , 2011 .

[22]  Gaël Durand,et al.  Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison , 2013, Journal of Glaciology.

[23]  E. van Meijgaard,et al.  Reassessment of the Antarctic surface mass balance using calibrated output of a regional atmospheric climate model , 2006 .

[24]  D. Vaughan,et al.  Potential seaways across West Antarctica , 2011 .

[25]  Martin Truffer,et al.  A unifying framework for iceberg-calving models , 2010, Journal of Glaciology.

[26]  Frank Pattyn,et al.  Antarctic subglacial conditions inferred from a hybrid ice sheet/ice stream model , 2010 .

[27]  R. DeConto,et al.  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 , 2012 .

[28]  D. Pollard,et al.  Climate‐Ice Sheet Simulations of Neoproterozoic Glaciation Before and After Collapse to Snowball Earth , 2013 .

[29]  D. Pollard,et al.  Influence of high-latitude vegetation feedbacks on late Palaeozoic glacial cycles , 2010 .

[30]  Philippe Huybrechts,et al.  Sea-level changes at the LGM from ice-dynamic reconstructions of the Greenland and Antarctic ice sheets during the glacial cycles , 2002 .

[31]  S. Marshall,et al.  Simulation of Vatnajökull ice cap dynamics , 2005 .

[32]  R. DeConto,et al.  Modeling Antarctic ice sheet and climate variations during Marine Isotope Stage 31 , 2012 .

[33]  Ian Joughin,et al.  Numerical modeling of ocean‐ice interactions under Pine Island Bay's ice shelf , 2007 .

[34]  E. Bueler,et al.  The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet , 2010 .

[35]  M. Dinniman,et al.  A model study of Circumpolar Deep Water on the West Antarctic Peninsula and Ross Sea continental shelves , 2011 .

[36]  D. Pollard,et al.  Obliquity forcing with 8–12 times preindustrial levels of atmospheric pCO2 during the Late Ordovician glaciation , 2003 .

[37]  R. Alley,et al.  Response of the East Antarctica ice sheet to sea-level rise , 1984 .

[38]  Cathy Connor,et al.  Submarine melting at the terminus of a temperate tidewater glacier, LeConte Glacier, Alaska, U.S.A. , 2003, Annals of Glaciology.

[39]  L. Morland Unconfined Ice-Shelf Flow , 1987 .

[40]  Rupert Gladstone,et al.  Grounding line migration in an adaptive mesh ice sheet model , 2010 .

[41]  D. Goldberg Numerical and theoretical treatment of grounding line movement and ice shelf buttressing in marine ice sheets , 2009 .

[42]  Douglas R. Macayeal,et al.  Large‐scale ice flow over a viscous basal sediment: Theory and application to ice stream B, Antarctica , 1989 .

[43]  A. Levermann,et al.  Fracture field for large-scale ice dynamics , 2012, Journal of Glaciology.

[44]  D. Pollard,et al.  Orbital and CO2 forcing of late Paleozoic continental ice sheets , 2007 .

[45]  R. Hindmarsh,et al.  Coupling of ice‐shelf melting and buttressing is a key process in ice‐sheets dynamics , 2010 .

[46]  Anne M. Le Brocq,et al.  A deglacial model for Antarctica: geological constraints and glaciological modelling as a basis for a new model of Antarctic glacial isostatic adjustment , 2012 .

[47]  D. Benn,et al.  Calving processes and the dynamics of calving glaciers , 2007 .

[48]  R. DeConto,et al.  A coupled climate–ice sheet modeling approach to the Early Cenozoic history of the Antarctic ice sheet , 2003 .

[49]  R. DeConto,et al.  Rapid Cenozoic glaciation of Antarctica induced by declining atmospheric CO2 , 2003, Nature.

[50]  S. Marshall,et al.  A continuum mixture model of ice stream thermomechanics in the Laurentide Ice Sheet 1. Theory , 1997 .

[51]  S. Jacobs,et al.  Stronger ocean circulation and increased melting under Pine Island Glacier ice shelf , 2011 .

[52]  J. Oerlemans,et al.  Effects of spatial discretization in ice-sheet modelling using the shallow-ice approximation , 2006, Journal of Glaciology.

[53]  Eric Rignot,et al.  Spatial patterns of basal drag inferred using control methods from a full‐Stokes and simpler models for Pine Island Glacier, West Antarctica , 2010 .

[54]  Nils Olsen,et al.  Heat Flux Anomalies in Antarctica Revealed by Satellite Magnetic Data , 2005, Science.

[55]  Josefino C. Comiso,et al.  Variability and Trends in Antarctic Surface Temperatures from In Situ and Satellite Infrared Measurements , 2000 .

[56]  William H. Lipscomb,et al.  Ice-sheet model sensitivities to environmental forcing and their use in projecting future sea level (the SeaRISE project) , 2012, Journal of Glaciology.

[57]  H. Hellmer,et al.  A box model of circulation and melting in ice shelf caverns , 2010 .

[58]  E. Fahrbach,et al.  Ice‐ocean processes over the continental shelf of the southern Weddell Sea, Antarctica: A review , 2009 .

[59]  Angelika Humbert,et al.  A consistent data set of Antarctic ice sheet topography, cavity geometry, and global bathymetry , 2010 .

[60]  D. Pollard,et al.  Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP , 2012 .

[61]  R. Hindmarsh,et al.  A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modeling , 2004 .

[62]  R. DeConto,et al.  Sensitivity of Cenozoic Antarctic ice sheet variations to geothermal heat flux , 2005 .

[63]  J. F. Brotchie,et al.  On crustal flexure , 1969 .

[64]  W. Paterson,et al.  The Physics of Glaciers Fourth Edition , 2010 .

[65]  A. Weaver,et al.  A new coupled ice sheet/climate model: description and sensitivity to model physics under Eemian, Last Glacial Maximum, late Holocene and modern climate conditions , 2010 .

[66]  C. Ritz,et al.  A thermomechanical model of ice-shelf flow , 1996 .

[67]  Antony J. Payne,et al.  A thermomechanical model of ice flow in West Antarctica , 1999 .

[68]  Ed Bueler,et al.  Shallow shelf approximation as a “sliding law” in a thermomechanically coupled ice sheet model , 2008, 0810.3449.

[69]  J. Andrews,et al.  Growth rate of the Laurentide Ice Sheet and sea Level Lowering (with Emphasis on the 115,000 BP Sea Level Low) , 1976, Quaternary Research.

[70]  D. Macayeal,et al.  A new numerical model of coupled inland ice sheet, ice stream, and ice shelf flow and its application to the West Antarctic Ice Sheet , 1999 .

[71]  David Pollard,et al.  A simple inverse method for the distribution of basal sliding coefficients under ice sheets, applied to Antarctica , 2012 .

[72]  Frank Kauker,et al.  Twenty-first-century warming of a large Antarctic ice-shelf cavity by a redirected coastal current , 2012, Nature.

[73]  David Pollard,et al.  Modelling West Antarctic ice sheet growth and collapse through the past five million years , 2009, Nature.

[74]  A. Vieli,et al.  A physically based calving model applied to marine outlet glaciers and implications for the glacier dynamics , 2010, Journal of Glaciology.

[75]  Kelly M. Brunt,et al.  Mapping the grounding zone of the Amery Ice Shelf, East Antarctica using InSAR, MODIS and ICESat , 2009, Antarctic Science.

[76]  S. Anandakrishnan,et al.  Static grounding lines and dynamic ice streams: Evidence from the Siple Coast, West Antarctica , 2006 .

[77]  F. Pattyn,et al.  Representing Grounding Line Dynamics in Numerical Ice Sheet Models: Recent Advances and Outlook , 2011 .

[78]  Stephen D. McPhail,et al.  Observations beneath Pine Island Glacier in West Antarctica and implications for its retreat , 2010 .

[79]  Richard F. Katz,et al.  Stability of ice-sheet grounding lines , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[80]  C. Veen Response of a marine ice sheet to changes at the grounding line , 1985 .

[81]  David Pollard,et al.  Rapid Cenozoic glaciation of Antarctica induced by declining atmospheric CO2 , 2003, Nature.

[82]  D. Vaughan,et al.  Antarctic ice-sheet loss driven by basal melting of ice shelves , 2012, Nature.

[83]  Michael H. Ritzwoller,et al.  Inferring surface heat flux distributions guided by a global seismic model: particular application to Antarctica , 2004 .

[84]  M. Fahnestock,et al.  Century-scale discharge stagnation and reactivation of the Ross ice streams, West Antarctica , 2007 .

[85]  Eric Rignot,et al.  Rapid submarine melting of the calving faces of West Greenland glaciers , 2010 .

[86]  D. Schrag,et al.  Continental constriction and oceanic ice‐cover thickness in a Snowball‐Earth scenario , 2012 .

[87]  R. Armstrong,et al.  The Physics of Glaciers , 1981 .

[88]  F. Pattyn,et al.  Report of the Third EISMINT Workshop on Model Intercomparison , 1998 .

[89]  R. Arko,et al.  Subglacial sediments: A regional geological template for ice flow in West Antarctica , 2001 .

[90]  Alun Hubbard,et al.  Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP-HOM) , 2008 .

[91]  Thomas Zwinger,et al.  A three-dimensional full Stokes model of the grounding line dynamics: effect of a pinning point beneath the ice shelf , 2011 .

[92]  B. Scheuchl,et al.  Ice Flow of the Antarctic Ice Sheet , 2011, Science.

[93]  Fabien Gillet-Chaulet,et al.  Simulations of the Greenland ice sheet 100 years into the future with the full Stokes model Elmer/Ice , 2011, Journal of Glaciology.

[94]  Alun Hubbard,et al.  High-Resolution Modeling of the Advance of the Younger Dryas Ice Sheet and Its Climate in Scotland , 1999, Quaternary Research.

[95]  Christian Schoof,et al.  Thin-Film Flows with Wall Slip: An Asymptotic Analysis of Higher Order Glacier Flow Models , 2010 .

[96]  Caroline H. Lear,et al.  Thresholds for Cenozoic bipolar glaciation , 2008, Nature.

[97]  P. Whitehouse,et al.  Reconstructing the Last Glacial Maximum ice sheet in the Weddell Sea embayment, Antarctica, using numerical modelling constrained by field evidence , 2011 .

[98]  D. Blankenship,et al.  A dynamic early East Antarctic Ice Sheet suggested by ice-covered fjord landscapes , 2011, Nature.

[99]  D. Pollard,et al.  The impact of paleogeography, pCO2, poleward ocean heat transport and sea level change on global cooling during the Late Ordovician , 2004 .

[100]  A. Payne,et al.  Resolution requirements for grounding-line modelling: sensitivity to basal drag and ice-shelf buttressing , 2012, Annals of Glaciology.

[101]  C. Schoof Ice sheet grounding line dynamics: Steady states, stability, and hysteresis , 2007 .

[102]  C. Ritz,et al.  Sensitivity of a Greenland ice sheet model to ice flow and ablation parameters: consequences for the evolution through the last climatic cycle , 1996 .

[103]  D. Pollard,et al.  Results from the Ice-Sheet Model Intercomparison Project–Heinrich Event Intercomparison (ISMIP HEINO) , 2010, Journal of Glaciology.

[104]  Sridhar Anandakrishnan,et al.  Effect of Sedimentation on Ice-Sheet Grounding-Line Stability , 2007, Science.

[105]  Catherine Ritz,et al.  Modeling the evolution of Antarctic ice sheet over the last 420,000 years: Implications for altitude changes in the Vostok region , 2001 .

[106]  J. Ettema,et al.  Significant contribution of insolation to Eemian melting of the Greenland ice sheet , 2011 .

[107]  Philippe Huybrechts,et al.  The Dynamic Response of the Greenland and Antarctic Ice Sheets to Multiple-Century Climatic Warming , 1999 .

[108]  R. DeConto,et al.  Retreat of the East Antarctic ice sheet during the last glacial termination , 2011 .

[109]  K. Frieler,et al.  Uncertainty in future solid ice discharge from Antarctica , 2012 .

[110]  S. Marshall,et al.  Coupling ice-sheet and climate models for simulation of former ice sheets , 2003 .

[111]  R. DeConto,et al.  West Antarctic Ice Sheet elevations in the Ohio Range: Geologic constraints and ice sheet modeling prior to the last highstand , 2011 .

[112]  Sridhar Anandakrishnan,et al.  A Simple Law for Ice-Shelf Calving , 2008, Science.

[113]  R. DeConto,et al.  Late Pliocene to Pleistocene sensitivity of the Greenland Ice Sheet in response to external forcing and internal feedbacks , 2011 .

[114]  Richard B. Alley,et al.  Initial effects of oceanic warming on a coupled ocean–ice shelf–ice stream system , 2009 .

[115]  O. Gagliardini,et al.  The stability of grounding lines on retrograde slopes , 2012 .

[116]  M. Mahaffy A three‐dimensional numerical model of ice sheets: Tests on the Barnes Ice Cap, Northwest Territories , 1976 .

[117]  R. DeConto,et al.  Hysteresis in Cenozoic Antarctic ice-sheet variations , 2005 .

[118]  T. Scambos,et al.  Glacier acceleration and thinning after ice shelf collapse in the Larsen B embayment, Antarctica , 2004 .

[119]  C. Hulbe,et al.  Propagation of long fractures in the Ronne Ice Shelf, Antarctica, investigated using a numerical model of fracture propagation , 2010, Journal of Glaciology.

[120]  David Pollard,et al.  Antarctic ice and sediment flux in the Oligocene simulated by a climate–ice sheet–sediment model , 2003 .

[121]  David P. Stevens,et al.  A New Tracer Advection Scheme for Bryan and Cox Type Ocean General Circulation Models , 1995 .

[122]  H. Goosse,et al.  A parameterization of ice shelf-ocean interaction for climate models , 2003 .