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Melt-under-cutting and buoyancy-driven calving from tidewater glaciers: new insights from discrete element and continuum model simulations


The simple calving laws currently used in ice-sheet models do not adequately reflect the complexity and diversity of calving processes. To be effective, calving laws must be grounded in a sound understanding of how calving actually works. Here, we develop a new strategy for formulating calving laws, using (a) the Helsinki Discrete Element Model (HiDEM) to explicitly model fracture and calving processes, and (b) the continuum model Elmer/Ice to identify critical stress states associated with HiDEM calving events. A range of observed calving processes emerges spontaneously from HiDEM in response to variations in ice-front buoyancy and the size of subaqueous undercuts. Calving driven by buoyancy and melt under-cutting is under-predicted by existing calving laws, but we show that the location and magnitude of HiDEM calving events can be predicted in Elmer/Ice from characteristic stress patterns. Our results open the way to developing calving laws that properly reflect the diversity of calving processes, and provide a framework for a unified theory of the calving process continuum.

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      Melt-under-cutting and buoyancy-driven calving from tidewater glaciers: new insights from discrete element and continuum model simulations
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      Melt-under-cutting and buoyancy-driven calving from tidewater glaciers: new insights from discrete element and continuum model simulations
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Correspondence: Douglas I. Benn <>
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Åström JA and 6 others (2013) A particle based simulation model for glacier dynamics. Cryosphere, 7(2), 15911602
Åström JA and 10 others (2014) Termini of calving glaciers as self-organized critical systems. Nat. Geosci., 7, 874878
Bartholomaus TC, Larsen CF, O'Neel S and West ME (2012) Calving seismicity from iceberg–sea surface interactions. J. Geophys. Res.: Earth Surf., 117(F4)
Bassis J and Jacobs S (2013) Diverse calving patterns linked to glacier geometry. Nat. Geosci., 6, 833836
Bassis JN and Walker CC (2012) Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice. Proc. R. Soc. A, Math. Phys. Eng. Sci., 468, 913931
Benn DI, Warren CR and Mottram RH (2007a) Calving processes and the dynamics of calving glaciers. Earth Sci. Rev., 82, 143179
Benn DI, Hulton NRJ and Mottram RH (2007b) ‘Calving laws’, ‘sliding laws’ and the stability of tidewater glaciers. Ann. Glaciol., 46, 123130
Boyce E, Motyka R and Truffer M (2007) Flotation and retreat of a lake-calving terminus, Mendenhall Glacier, Southeast Alaska, USA. J. Glaciol., 53(181), 211224
Church JA and 13 others (2013) Sea level change. In Stocker TF 9 others eds. Climate change 2013: the physical science basis. contribution of working group I to the fifth assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge, UK and New York, NY, USA
Cook S, Zwinger T, Rutt IC, O'Neel S and Murray T (2012) Testing the effect of water in crevasses on a physically based calving model. Ann. Glaciol., 53(60), 9096
Cook S and 7 others (2014) Modelling environmental influences on calving at Helheim Glacier in eastern Greenland. Cryosphere, 8, 827841
Cowton T, Slater D, Sole A, Goldberg D and Nienow P (2015) Modeling the impact of glacial runoff on fjord circulation and submarine melt rate using a new parameterization for glacial plumes. J. Geophys. Res. Oceans, 120, 796812
Enderlin EM, Howat IM and Vieli A (2013) High sensitivity of outlet glacier dynamics to shape. Cryosphere, 7, 10071015
Enderlin EM and 5 others (2014) An improved mass budget for the Greenland ice sheet. Geophys. Res. Lett., 41(3), 866872
Faillettaz J, Sornette D and Funk M (2011) Numerical modeling of a gravity-driven instability of a cold hanging glacier: reanalysis of the 1895 break-off of Altelsgletscher, Switzerland. J. Glaciol., 57(205), 817831
Faillettaz J, Funk M and Vincent C (2015) Avalanching glacier instabilities: review of processes and early warning perspectives. Rev. Geophys., 53(2), 203224
Gagliardini O and 10 others (2013) Capabilities and performance of Elmer/Ice, a new-generation ice sheet model. Geosci. Model Dev., 6(4), 12991318
Gardner AS and 10 others (2013) A reconciled estimate of glacier contributions to sea level rise: 2003 to 2009. Science, 340(6134), 852857
Hanson B and Hooke R Le B (2003) Buckling rate and overhang development at a calving face. J. Glaciol., 49(167), 577586
Hooke R LeB (2005) Principles of glacier mechanics, 2nd edn. Cambridge University Press, Cambridge, 429 pp
Howarth PJ and Price RJ (1969) The proglacial lakes of Breiðamerkurjökull and Fláarjokull, Iceland. Geograph. J., 135, 573581
James TD, Murray T, Selmes N, Scharrer K and O'Leary M (2014) Buoyant flexure and basal crevassing in dynamic mass loss at Helheim Glacier. Nat. Geosci., 7(8), 593596
Jenkins A (2011) Convection-driven melting near the grounding lines of ice shelves and tidewater glaciers. J. Phys. Oceanogr., 41(12), 22792294
Joughin I and 8 others (2008) Ice-front variation and tidewater behavior on Helheim and Kangerdlugssuaq Glaciers, Greenland. J. Geophys. Res., 113, F01004 (doi: 10.1029/2007JF000837)
Krug J, Weiss J, Gagliardini O and Durand G (2014) Combining damage and fracture mechanics to model calving. Cryosphere, 8, 21012117
Lea JM and 8 others (2014) Terminus-driven retreat of a major southwest Greenland tidewater glacier during the early 19th century: insights from glacier reconstructions and numerical modelling. J. Glaciol., 60(220), 333344
Levermann A and 5 others (2012) Kinematic first-order calving law implies potential for abrupt ice-shelf retreat. Cryosphere, 6(2), 273
Luckman A and 5 others (2015) Calving rates at tidewater glaciers vary strongly with ocean temperature. Nat. Commun. 6 (doi: 10.1038/ncomms9566)
Medrzycka D, Benn DI, Box JE, Copland L and Balog J (2016) Calving behaviour at Rink Isbrae, west Greenland, from time-lapse photos. Arct. Antarct. Alpine Res., 48(2), 263277
Morlighem M and 6 others (2016) Modeling of Store Gletscher's calving dynamics, West Greenland, in response to ocean thermal forcing. Geophys. Res. Lett. 43, 26592666 (doi: 10.1002/2016GL067695)
Motyka RJ, Dryer WP, Amundson J, Truffer M and Fahnestock M (2013) Rapid submarine melting driven by subglacial discharge, Le Conte Glacier, Alaska. Geophys. Res. Lett. 40, 51535158 (doi: 10.1002/GRL51011)
Murray T and 9 others (2015) Dynamics of glacier calving at the ungrounded margin of Helheim Glacier, southeast Greenland. J. Geophys. Res. Earth Surf., 120, 964982
Nick FM, van der Veen CJ, Vieli A and Benn DI (2010) A physically based calving model applied to marine outlet glaciers and implications for the glacier dynamics. J. Glaciol., 56(199), 781794
Nick FM and 7 others (2013) Future sea-level rise from Greenland's main outlet glaciers in a warming climate. Nature, 497 (doi: 10.1038/nature12068)
Nye JF (1957) The distribution of stress and velocity in glaciers and ice-sheets. Proc. R. Soc. Lon. A: Math. Phys. Eng. Sci., 239, 113133
O'Leary M and Christoffersen P (2013) Calving on tidewater glaciers amplified by submarine frontal melting. Cryosphere, 7(1), 119128
Otero J, Navarro FJ, Martin C, Cuadrado ML and Corcuera MI (2010) A three-dimensional calving model: numerical experiments on Johnsons Glacier, Livingston Island, Antarctica. J. Glaciol., 56(196), 200214
Pollard D, DeConto RM and Alley RB (2015) Potential Antarctic Ice Sheet retreat driven by hydrofracturing and ice cliff failure. Earth Planet. Sci. Lett., 412, 112121
Rignot E, Fenty I, Xu Y, Cai C and Kemp C (2015) Undercutting of marine-terminating glaciers in West Greenland. Geophys. Res. Lett., 42, 59095917
Riikilä TI, Tallinen T, Åström J and Timonen J (2015) A discrete-element model for viscoelastic deformation and fracture of glacial ice. Comput. Phys. Commun., 195, 1422
Schulson EM (1999) The structure and mechanical behavior of ice. JOM: J. Miner. Metals Mater. Soc., 51(2), 2127
Slater DA, Nienow PW, Cowton TR, Goldberg DN and Sole AJ (2015) Effect of near-terminus subglacial hydrology on tidewater glacier submarine melt rates. Geophys. Res. Lett., 42(8), 28612868
Todd J (2016) A 3D full stokes calving model for Store Glacier, West Greenland. (Unpublished PhD thesis, University of Cambridge, Cambridge, UK)
Todd J and Christoffersen P (2014) Are seasonal calving dynamics forced by buttressing from ice mélange or undercutting by melting? Outcomes from full-Stokes simulations of Store Glacier, West Greenland. Cryosphere, 8, 23532365
Truffer M and Motyka RJ (2016) Where glaciers meet water: subaqueous melt and its relevance to glaciers in various settings. Rev. Geophys., 54 (doi: 10.1002/2015RG000494)
Wagner TJW, James TD, Murray T and Vella D (2016) On the role of buoyant flexure in glacier calving. Geophys. Res. Lett. 43, 232240 (doi: 10.1002/2015GL067247)
Walter F and 5 others (2010) Iceberg calving during transition from grounded to floating ice: Columbia Glacier, Alaska. Geophys. Res. Lett., 37, L15501 (doi: 10.1029/2010GL043201)
Warren CR, Benn DI, Winchester V and Harrison S (2001) Buoyancy-driven lacustrine calving, Glaciar Nef, Chilean Patagonia. J. Glaciol., 47, 135146
Xie S and 5 others (2016) Precursor motion to iceberg calving at Jakobshavn Isbræ, Greenland, observed with terrestrial radar interferometry. J. Glaciol., 62(236), 11341142
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