Skip to main content Accessibility help

An improved model for tidally modulated grounding-line migration

  • Victor C. Tsai (a1) and G. Hilmar Gudmundsson (a2)


Understanding grounding-line dynamics is necessary for predictions of long-term ice-sheet stability. However, despite growing observations of the tidal influence on grounding-line migration, this short-timescale migration is poorly understood, with most modeling attempts assuming beam theory to calculate displacements. Here we present an improved model of tidal grounding-line migration that treats migration as an elastic fracture problem, forced by the additional ocean water pressure from the tide. This new model predicts that the grounding line cannot be assumed to be in hydrostatic equilibrium and, furthermore, that migration is inherently asymmetric and nonlinear, with migration distances that are not proportional to the tidal load. Specifically, for constant surface slope, the grounding line migrates upstream approximately ten times further as the tide rises from mean sea level to high tide than it migrates downstream as the tide falls from mean sea level to low tide, and migration distances are substantially larger than simple flotation arguments suggest. Numerical tests also show that the dependence of migration distance on elastic moduli and ice-sheet thickness are inconsistent with predictions of beam theory for a range of realistic values. Finally, applying the new model to observations in Antarctica results in new estimates of bed slopes, though these estimates remain uncertain due to imperfect knowledge of the relevant rheological parameters.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure 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 or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ 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.

      An improved model for tidally modulated grounding-line migration
      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.

      An improved model for tidally modulated grounding-line migration
      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.

      An improved model for tidally modulated grounding-line migration
      Available formats


Corresponding author

Correspondence: Victor C. Tsai <>


Hide All
Anandakrishnan, S and Alley, RB (1997) Tidal forcing of basal seismicity of Ice Stream C, West Antarctica, observed far inland. J. Geophys. Res., 102(B7), 1518315196 (doi: 10.1029/97JB01073)
Bindschadler, RA, King, MA, Alley, RB, Anandakrishnan, S and Padman, L (2003) Tidally controlled stick–slip discharge of a West Antarctic ice stream. Science, 301(5636), 10871089 (doi: 10.1 126/science.1087231)
Brunt, KM, Fricker, HA and Padman, L (2011) Analysis of ice plains of the Filchner–Ronne Ice Shelf, Antarctica, using ICESat laser altimetry. J. Glaciol., 57(205), 965975 (doi: 10.3189/002214311798043753)
Budd, WF and Jacka, TH (1989) A review of ice rheology for ice sheet modelling. Cold Reg. Sci. Technol., 16(2), 107144 (doi: 10.1016/0165-232X(89)90014-1)
Erdogan, F, Gupta, GD and Cook, TS (1973) Numerical solution of angular integral equations. In Sih, GC ed. Methods of analysis and solution of crack problems: recent developments in fracture mechanics. Noordhoff International Publishing, San Diego, CA, and Leyden, 368425
Favier, L and 8 others (2014) Retreat of Pine Island Glacier controlled by marine ice-sheet instability. Nature Climate 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)
Goldberg, N, Schoof, C and Sergienko, OV (2014) Stick–slip motion of an Antarctic ice stream: the effects of viscoelasticity. J. Geophys. Res. Earth Surf., 119(7), 15641580 (doi: 10.1002/2014JF003132)
Gudmundsson, GH (2006) Fortnightly variations in the flow velocity of Rutford Ice Stream, West Antarctica. Nature, 444(7122), 10631064 (doi: 10.1038/nature05430)
Gudmundsson, GH (2007) Tides and the flow of Rutford Ice Stream, West Antarctica. J. Geophys. Res., 112(F4), F04007 (doi: 10.1029/2006JF000731)
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)
Holdsworth, G (1969) Flexure of a floating ice tongue. J. Glaciol., 8(54), 385397
Holdsworth, G (1977) Tidal interaction with ice shelves. Ann. Géophys., 33(1/2), 133146
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)
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)
Reeh, N (1978) On the application of beam theory to glacier mechanics. (PhD Thesis, Technical University of Denmark)
Reeh, N, Lintz Christensen, E, Mayer, C and Olesen, OB (2003) Tidal bending of glaciers: a linear viscoelastic approach. Ann. Glaciol., 37, 8389 (doi: 10.3189/172756403781815663)
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)
Rist, MA and 6 others (1999) Experimental and theoretical fracture mechanics applied to Antarctic ice fracture and surface crevassing. J. Geophys. Res., 104(B2), 29732987 (doi: 10.1029/1998JB900026)
Rosier, SHR, Gudmundsson, GH and Green, JAM (2014) Insights into ice stream dynamics through modelling their response to tidal forcing. Cryosphere, 8(5), 17631775 (doi: 10.5194/tc-8-1763-2014)
Sayag, R and Worster, MG (2011) Elastic response of a grounded ice sheet coupled to a floating ice shelf. Phys. Rev. E, 84(3), 036111 (doi: 10.1103/PhysRevE.84.036111)
Sayag, R and Worster, MG (2013) Elastic dynamics and tidal migration of grounding lines modify subglacial lubrication and melting. Geophys. Res. Lett., 40(22), 58775881 (doi: 10.1002/2013GL057942)
Schoof, C (2007) Marine ice-sheet dynamics. Part 1. The case of rapid sliding. J. Fluid Mech., 573, 2755 (doi: 10.1017/S0022112006003570)
Shepherd, A and 46 others (2012) A reconciled estimate of ice-sheet mass balance. Science, 338(6111), 11831189 (doi: 10.1126/science.1228102)
Thompson, J, Simons, M and Tsai, VC (2014) Modeling the elastic transmission of tidal stresses to great distances inland in channelized ice streams. Cryosphere, 8(6), 20072029 (doi: 10.5194/tc-8-2007-2014)
Tsai, VC and Rice, JR (2010) A model for turbulent hydraulic fracture and application to crack propagation at glacier beds. J. Geophys. Res., 115(F3), F03007 (doi: 10.1029/2009JF001474)
Tsai, VC and Rice, JR (2012) Modeling turbulent hydraulic fracture near a free surface. J. Appl. Mech., 79(3), 031003 (doi: 10.1115/1.4005879)
Vaughan, DG (1995) Tidal flexure at ice shelf margins. J. Geophys. Res., 100(B4), 62136224 (doi: 10.1029/94JB02467)
Walker, RT, Parizek, BR, Alley, RB, Anandakrishnan, S, Riverman, KL and Christianson, K (2013) Ice-shelf tidal flexure and subglacial pressure variations. Earth Planet. Sci. Lett., 361, 422428 (doi: 10.1016/j.epsl.2012.11.008)



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