Skip to main content Accessibility help
×
Home

Marine ice-sheet profiles and stability under Coulomb basal conditions

  • Victor C. Tsai (a1), Andrew L. Stewart (a2) and Andrew F. Thompson (a3)

Abstract

The behavior of marine-terminating ice sheets, such as the West Antarctic ice sheet, is of interest due to the possibility of rapid grounding-line retreat and consequent catastrophic loss of ice. Critical to modeling this behavior is a choice of basal rheology, where the most popular approach is to relate the ice-sheet velocity to a power-law function of basal stress. Recent experiments, however, suggest that near-grounding line tills exhibit Coulomb friction behavior. Here we address how Coulomb conditions modify ice-sheet profiles and stability criteria. The basal rheology necessarily transitions to Coulomb friction near the grounding line, due to low effective stresses, leading to changes in ice-sheet properties within a narrow boundary layer. Ice-sheet profiles ‘taper off’ towards a flatter upper surface, compared with the power-law case, and basal stresses vanish at the grounding line, consistent with observations. In the Coulomb case, the grounding-line ice flux also depends more strongly on flotation ice thickness, which implies that ice sheets are more sensitive to climate perturbations. Furthermore, with Coulomb friction, the ice sheet grounds stably in shallower water than with a power-law rheology. This implies that smaller perturbations are required to push the grounding line into regions of negative bed slope, where it would become unstable. These results have important implications for ice-sheet stability in a warming climate.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Marine ice-sheet profiles and stability under Coulomb basal conditions
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Marine ice-sheet profiles and stability under Coulomb basal conditions
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Marine ice-sheet profiles and stability under Coulomb basal conditions
      Available formats
      ×

Copyright

Corresponding author

Correspondence: Victor C. Tsai <tsai@caltech.edu>

References

Hide All
Alley, RB, Clark, PU, Huybrechts, P and Joughin, I (2005) Ice-sheet and sea-level changes. Science, 310(5747), 456460 (doi: 10.1126/science.1114613 )
Bamber, JL, Riva, REM, Vermeersen, BLA and LeBrocq, AM (2009) Reassessment of the potential sea-level rise from a collapse of the West Antarctic Ice Sheet. Science, 324(5929), 901903 (doi: 10.1126/science.1169335)
Boulton, GS and Hindmarsh, RCA (1987) Sediment deformation beneath glaciers: rheology and geological consequences. J. Geophys. Res., 92(B9), 90599082 (doi: 10.1029/JB092iB09p09059)
Brace, WF and Kohlstedt, DL (1980) Limits on lithospheric stress imposed by laboratory experiments. J. Geophys. Res., 85(B11), 62486252 (doi: 10.1029/JB085iB11p06248)
Bueler, E and Brown, J (2009) Shallow shelf approximation as a ‘sliding law’ in a thermomechanically coupled ice sheet model. J. Geophys. Res., 114(F3), F03008 (doi: 10.1029/2008JF001179)
Dupont, TK and Alley, RB (2005) Assessment of the importance of ice-shelf buttressing to ice-sheet flow. Geophys. Res. Lett., 32(4), L04503 (doi: 10.1029/2004GL022024)
Durand, G, Gagliardini, O, De Fleurian, B, Zwinger, T and Le Meur, E (2009) Marine ice-sheet dynamics: hysteresis and neutral equilibrium. J. Geophys. Res., 114(F3), F03009 (doi: 10.1029/2008JF001170)
Favier, L and 8 others (2014) Retreat of Pine Island Glacier controlled by marine ice-sheet instability. Nature Clim. Change, 4(2), 117121 (doi: 10.1038/nclimate2094)
Fretwell, P and 59 others (2013) Bedmap2: improved ice bed, surface and thickness datasets for Antarctica. Cryosphere, 7(1), 375393 (doi: 10.5194/tc-7-375-2013)
Glen, JW (1952) Experiments on the deformation of ice. J. Glaciol., 2(12), 111114
Gudmundsson, GH, Krug, J, Durand, G, Favier, L and Gagliardini, O (2012) The stability of grounding lines on retrograde slopes. Cryosphere, 6(6), 14971505 (doi: 10.5194/tc-6-1497-2012)
Hindmarsh, RCA and Le Meur, E (2001) Dynamical processes involved in the retreat of marine ice sheets. J. Glaciol., 47(157), 271282 (doi: 10.3189/172756501781832269)
Hughes, T (1973) Is the West Antarctic ice sheet disintegrating? J. Geophys. Res., 78(33), 78847910 (doi: 10.1029/JC078i033p07884)
Iverson, NR, Hooyer, TS and Baker, RW (1998) Ring-shear studies of till deformation: Coulomb-plastic behavior and distributed strain in glacier beds. J. Glaciol., 44(148), 634642
Joughin, I, Smith, BE and Medley, B (2014) Marine ice sheet collapse potentially under way for the Thwaites Glacier Basin, West Antarctica. Science, 344(6185), 735738 (doi: 10.1126/science.1249055)
MacAyeal, DR (1989) Large-scale ice flow over a viscous basal sediment: theory and application to Ice Stream B, Antarctica. J. Geophys. Res., 94(B4), 40714087 (doi: 10.1029/JB094iB04p04071)
Mengel, M and Levermann, A (2014) Ice plug prevents irreversible discharge from East Antarctica. Nature Climate Change, 4(6), 451455 (doi: 10.1038/nclimate2226)
Mercer, JH (1978) West Antarctic ice sheet and CO2 greenhouse effect: a threat of disaster. Nature, 271(5643), 321325 (doi: 10.1038/271321a0)
Mitrovica, JX, Tamisiea, ME, Davis, JL and Milne, GA (2001) Recent mass balance of polar ice sheets inferred from patterns of global sea-level change. Nature, 409(6823), 10261029 (doi: 10.1038/35059054)
Mitrovica, JX, Gomez, N and Clark, PU (2009) The sea-level fingerprint of West Antarctic collapse. Science, 323(5915), 753 (doi: 10.1126/science.1166510)
Moré, JJ (1978) The Levenberg–Marquardt algorithm: implementation and theory. In Watson, GA ed. Numerical Analysis. Proceedings of the Biennial Conference 28 June–1 July 1977, Dundee, Scotland. Springer, Dordrecht, 105116
Nowicki, SMJ and Wingham, DJ (2008) Conditions for a steady ice sheet–ice shelf junction. Earth Planet. Sci. Lett., 265(1–2), 246255 (doi: 10.1016/j.epsl.2007.10.018)
Nye, JF (1951) The flow of glaciers and ice-sheets as a problem in plasticity. Proc. R. Soc. London, Ser. A, 207(1091), 554572 (doi: 10.1098/rspa.1951.0140)
Paterson, WSB (1994) The physics of glaciers, 3rd edn. Elsevier, Oxford
Pattyn, F and 27 others (2013) Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison. J. Glaciol., 59(215), 410422 (doi: 10.3189/2013JoG12J129)
Rignot, E, Mouginot, J, Morlighem, M, Seroussi, H and Scheuchl, B (2014) Widespread, rapid grounding line retreat of Pine Island, Thwaites, Smith, and Kohler glaciers, West Antarctica, from 1992 to 2011. Geophys. Res. Lett., 41(10), 35023509 (doi: 10.1002/2014GL060140)
Schoof, C (2006) Variational methods for glacier flow over plastic till. J. Fluid Mech., 555, 299320 (doi: 10.1017/S0022112006009104)
Schoof, C (2007a) Marine ice-sheet dynamics. Part 1. The case of rapid sliding. J. Fluid Mech., 573, 2755 (doi: 10.1017/S0022112006003570)
Schoof, C (2007b) Ice sheet grounding line dynamics: steady states, stability, and hysteresis. J. Geophys. Res., 112(F3), F03S28 (doi: 10.1029/2006JF000664)
Schoof, C (2012) Marine ice sheet stability. J. Fluid Mech., 698, 6272 (doi: 10.1017/jfm.2012.43)
Truffer, M, Harrison, WD and Echelmeyer, KA (2000) Glacier motion dominated by processes deep in underlying till. J. Glaciol., 46(153), 213221 (doi: 10.3189/172756500781832909)
Truffer, M, Echelmeyer, KA and Harrison, WD (2001) Implications of till deformation on glacier dynamics. J. Glaciol., 47(156), 123134 (doi: 10.3189/172756501781832449)
Tulaczyk, SM, Kamb, B and Engelhardt, HF (2000a) Basal mechanics of Ice Stream B, West Antarctica. I. Till mechanics. J. Geophys. Res., 105(B1), 463481 (doi: 10.1029/1999JB900329)
Tulaczyk, SM, Kamb, B and Engelhardt, HF (2000b) Basal mechanics of Ice Stream B, West Antarctica. II. Undrained-plastic-bed model. J. Geophys. Res., 105(B1), 483494 (doi: 10.1029/1999JB900328)
Weertman, J (1957) On the sliding of glaciers. J. Glaciol., 3(21), 3338
Weertman, J (1974) Stability of the junction of an ice sheet and an ice shelf. J. Glaciol., 13(67), 311
Wilchinsky, AV (2001) Studying ice sheet stability using the method of separation of variables. Geophys. Astrophys. Fluid Dyn., 94(1–2), 1545 (doi: 10.1080/03091920108204130)
Wilchinsky, AV (2007) The effect of bottom boundary conditions in the ice-sheet to ice-shelf transition zone problem. J. Glaciol., 53(182), 363367 (doi: 10.3189/002214307783258477)

Keywords

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed