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A three-dimensional calving model: numerical experiments on Johnsons Glacier, Livingston Island, Antarctica

  • Jaime Otero (a1), Francisco J. Navarro (a1), Carlos Martin (a2), Maria L. Cuadrado (a1) and Maria I. Corcuera (a1)...

Abstract

Calving from tidewater glaciers and ice shelves accounts for around half the mass loss from both polar ice sheets, yet the process is not well represented in prognostic models of ice dynamics. Benn and others proposed a calving criterion appropriate for both grounded and floating glacier tongues or ice shelves, based on the penetration depth of transverse crevasses near the calving front, computed using Nye’s formula. The criterion is readily incorporated into glacier and ice-sheet models, but has not been fully validated with observations. We apply a three-dimensional extension of Benn and others’ criterion, incorporated into a full-Stokes model of glacier dynamics, to estimate the current position of the calving front of Johnsons Glacier, Antarctica. We find that two improvements to the original model are necessary to accurately reproduce the observed calving front: (1) computation of the tensile deviatoric stress opening the crevasse using the full-stress solution and (2) consideration of such a tensile stress as a function of depth. Our modelling results also suggest that Johnsons Glacier has a polythermal structure, rather than the temperate structure suggested by earlier studies.

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References

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Alley, R.B. and 7 others. 2008. A simple law for ice-shelf calving. Science, 322(5906), 1344.
Benjumea, B., Macheret, Yu.Ya., Navarro, F.J. and Teixidó, T.. 2003. Estimation of water content in a temperate glacier from radar and seismic sounding data. Ann. Glaciol., 37, 317324.
Benn, D.I. and Evans, D.J.A.. 2010. Glaciers and glaciation. Second edition. London, Hodder Arnold.
Benn, D.I., Hulton, N.R.J. and Mottram, R.H.. 2007a. ‘Calving laws’, ‘sliding laws’ and the stability of tidewater glaciers. Ann. Glaciol., 46, 123130.
Benn, D.I., Warren, C.W. and Mottram, R.H.. 2007b. Calving processes and the dynamics of calving glaciers. Earth-Sci. Rev., 82(3–4), 143179.
Bentley, C.R. 2004. Mass balance of the Antarctic ice sheet: observational aspects. In Bamber, J.L. and Payne, A.J., eds. Mass balance of the cryosphere: observations and modelling of contemporary and future changes. Cambridge, Cambridge University Press, 459489.
Blatter, H. and Hutter, K.. 1991. Polythermal conditions in Arctic glaciers. J. Glaciol., 37(126), 261269.
Brown, C.S., Meier, M.F. and Post, A.. 1982. Calving speed of Alaska tidewater glaciers, with application to Columbia Glacier. USGS Prof. Pap. 1258-C, C1–C13.
Carey, G.F. and Oden, J.T.. 1986. Finite elements: fluid mechanics. Englewood Cliffs, NJ, Prentice-Hall.
Corcuera, M.I., Navarro, F.J., Martín, C., Calvet, J. and Ximenis, L.. 2001. Finite element modelling of the steady-state dynamics of Johnsons Glacier. Mater. Glyatsiol. Issled. 90, 156168.
Dowdeswell, J.A., Benham, T.J., Strozzi, T. and Hagen, J.O.. 2008. Iceberg calving flux and mass balance of the Austfonna ice cap on Nordaustlandet, Svalbard. J. Geophys. Res., 113(F3), F03022. (10.1029/2007JF000905.)
Fowler, A.C. 1981. A theoretical treatment of the sliding of glaciers in the absence of cavitation. Philos. Trans. R. Soc. London, Ser. A, 298(1445), 637681.
Fowler, A.C. 1986. A sliding law for glaciers of constant viscosity in the presence of subglacial cavitation. Proc. R. Soc. London, Ser. A, 407(1832), 147170.
Funk, M. and Röthlisberger, H.. 1989. Forecasting the effects of a planned reservoir which will partially flood the tongue of Unteraargletscher in Switzerland. Ann. Glaciol., 13, 7681.
Furdada, G., Pourchet, M. and Vilaplana, J.M.. 1999. Study of Johnsons Glacier (Livingston Island, Antarctica) by means of shallow ice cores and their tephra and by analysis of 137Cs content. Acta Geol. Hispán., 34(4), 391401.
Gagliardini, O., Cohen, D., Råback, P. and Zwinger, T.. 2007. Finite-element modeling of subglacial cavities and related friction law. J. Geophys. Res., 112(F2), F02027. (10.1029/2006JF000576.)
Glenn, J.W. 1955. The creep of polycrystalline ice. Proc. R. Soc. London, Ser.A., 228(1175), 519538.
Hanson, B. 1995. A fully three-dimensional finite-element model applied to velocities on Storglaciären, Sweden. J. Glaciol., 41(137), 91102.
Haresign, E.C. 2004. Glacio-limnological interactions at lake-calving glaciers. (PhD thesis, University of St Andrews.)
Hindmarsh, R.C.A. 2006. The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic Ice Sheets: back pressure and grounding line motion. Philos. Trans. R. Soc. London, Ser. A, 364(1844), 17331767.
Holdsworth, G. 1969. Primary transverse crevasses. J. Glaciol., 8(52), 107129.
Holland, D.M., Thomas, R.H., de Young, B., Ribergaard, M.H. and Lyberth, B.. 2008. Acceleration of Jakobshavn Isbræ triggered by warm subsurface ocean waters. Nature Geosci., 1(10), 659664.
Howat, I.M., Joughin, I.R. and Scambos, T.A.. 2007. Rapid changes in ice discharge from Greenland outlet glaciers. Science, 315(5818), 15591561.
Howat, I.M., Joughin, I., Fahnestock, M., Smith, B.E. and Scambos, T.. 2008. Synchronous retreat and acceleration of southeast Greenland outlet glaciers 2000–2006: ice dynamics and coupling to climate. J. Glaciol., 54(187), 646660.
Joughin, I. and 7 others. 2008. Continued evolution of Jakobshavn Isbræ following its rapid speedup. J. Geophys. Res., 113(F4), F04006. (10.1029/2008JF001023.)
MacAyeal, D.R., Scambos, T.A., Hulbe, C.L. and Fahnestock, M.A.. 2003. Catastrophic ice-shelf break-up by an ice-shelf-fragmentcapsize mechanism. J. Glaciol., 49(164), 2236.
Martín, C., Navarro, F.J., Otero, J., Cuadrado, M.L. and Corcuera, M.I.. 2004. Three-dimensional modelling of the dynamics of Johnsons Glacier, Livingston Island, Antarctica. Ann. Glaciol., 39, 18.
Meier, M.F. and Post, A.. 1987. Fast tidewater glaciers. J. Geophys. Res., 92(B9), 90519058.
Molina, C., Navarro, F.J., Calver, J., García-Sellés, D. and Lapazaran, J.J.. 2007. Hurd Peninsula glaciers, Livingston Island, Antarctica, as indicators of regional warming: ice-volume changes during the period 1956–2000. Ann. Glaciol., 46, 4349.
Mottram, R.H. 2007. Processes of crevasse formation and the dynamics of calving glaciers: a study at Breiðamerkurjökull, Iceland. (PhD thesis, University of St Andrews.)
Mottram, R.H. and Benn, D.I.. 2009. Testing crevasse-depth models: a field study at Breiðamerkurjökull, Iceland. J. Glaciol., 55(192), 746752.
Navarro, F.J., Macheret, Yu.Ya. and Benjumea, B.. 2005. Application of radar and seismic methods for the investigation of temperate glaciers. J. Appl. Geophys., 57(3), 193211.
Navarro, F.J. and 6 others. 2009. Radioglaciological studies on Hurd Peninsula glaciers, Livingston Island, Antarctica. Ann. Glaciol., 50(51), 1724.
Nick, F.M., Vieli, A., Howat, I.M. and Joughin, I.. 2009. Large-scale changes in Greenland outlet glacier dynamics triggered at the terminus. Nature Geosci., 2(2), 110114.
Nye, J.F. 1955. Correspondence. Comments on Dr. Loewe’s letter and notes on crevasses. J. Glaciol., 2(17), 512514.
Nye, J.F. 1957. The distribution of stress and velocity in glaciers and ice-sheets. Proc. R. Soc. London, Ser. A, 239(1216), 113133.
O’Neel, S., Marshall, H.P., McNamara, D.E. and Pfeffer, W.T.. 2007. Seismic detection and analysis of icequakes at Columbia Glacier, Alaska. J. Geophys. Res., 112(F3), F03S23. (10.1029/2006JF000595.)
Otero, J. 2008. Generación automática de malla de elementos finitos en modelos evolutivos de dinámica de glaciares. (PhD thesis, Universidad Politécnica de Madrid.)
Parizek, B.R. and Alley, R.B.. 2004. Implications of increased Greenland surface melt under global-warming scenarios: ice-sheet simulations. Quat. Sci. Rev., 23(9–10), 10131027.
Paterson, W.S.B. 1994. The physics of glaciers. Third edition. Oxford, etc., Elsevier.
Pelto, M.S. and Warren, C.R.. 1991. Relationship between tidewater glacier calving velocity and water depth at the calving front. Ann. Glaciol., 15, 115118.
Qin, D., Zielinski, G.A., Germani, M.S., Ren, J., Wang, X.X. and Wang, W.T.. 1994. Use of tephrochronology in the evaluation of accumulation rates on Nelson Ice Cap, South Shetland Islands, Antarctica. Sci. China B, 37(10), 12721278.
Quarteroni, A. and Valli, A.. 1994. Numerical approximation of partial differential equations. Berlin, etc., Springer-Verlag.
Rignot, E., Casassa, G., Gogineni, P., Krabill, W., Rivera, A. and Thomas, R.. 2004. Accelerated ice discharge from the Antarctic Peninsula following the collapse of Larsen B ice shelf. Geophys. Res. Lett., 31(18), L18401. (10.1029/2004GL020697.)
Rist, M.A. and 6 others. 1999. Experimental and theoretical fracture mechanics applied to Antarctic ice fracture and surface crevassing. J. Geophys. Res., 104(B2), 29732987.
Rott, H., Skvarca, P. and Nagler, T.. 1996. Rapid collapse of northern Larsen Ice Shelf, Antarctica. Science, 271(5250), 788792.
Scambos, T.A., Bohlander, J.A., Shuman, C.A. and Skvarca, P.. 2004. Glacier acceleration and thinning after ice shelf collapse in the Larsen B embayment, Antarctica. Geophys. Res. Lett., 31(18), L18402. (10.1029/2004GL020670.)
Schiavi, E. 1997. Sobre algunas ecuaciones en derivadas parciales cuasilineales que aparecen en glaciología. (PhD thesis, Universidad Complutense de Madrid.)
Schoof, C. 2005. The effect of cavitation on glacier sliding. Proc. R. Soc. London, Ser. A, 461(2055), 609627.
Schoof, C. 2007a. Ice sheet grounding line dynamics: steady states, stability, and hysteresis. J. Geophys. Res., 112(F3), F03S28. (10.1029/2006JF000664.)
Schoof, C. 2007b. Marine ice-sheet dynamics. Part 1. The case of rapid sliding. J. Fluid Mech., 573, 2755.
Schoof, C. In press. Coulomb friction and other sliding laws in a higher order glacier flow model. Math. Models Meth. Appl. Sci. (10.1142/S0218202510004180.)
Shepherd, A., Wingham, D., Payne, T. and Skvarca, P.. 2003. Larsen ice shelf has progressively thinned. Science, 302(5646), 856859.
Shreve, R.L. 1972. Movement of water in glaciers. J. Glaciol., 11(62), 205214.
Siegert, M.J. and Dowdeswell, J.A.. 2004. Numerical reconstructions of the Eurasian Ice Sheet and climate during the Late Weichselian. Quat. Sci. Rev., 23(11–13), 12731283.
Sikonia, W.G. 1982. Finite-element glacier dynamics model applied to Columbia Glacier, Alaska. USGS Prof. Pap. 1258-B.
Smith, R.A. 1976. The application of fracture mechanics to the problem of crevasse penetration. J. Glaciol., 17(76), 223228.
Thomas, R.H. 2004. Greenland: recent mass balance observations. In Bamber, J.L. and Payne, A.J., eds. Mass balance of the cryosphere: observations and modelling of contemporary and future changes. Cambridge, Cambridge University Press.
Van der Veen, C.J. 1996. Tidewater calving. J. Glaciol., 42(141), 375385.
Van der Veen, C.J. 1998. Fracture mechanics approach to penetration of surface crevasses on glaciers. Cold Reg. Sci. Technol., 27(1), 3147.
Van der Veen, C.J. 1999. Crevasses on glaciers. Polar Geogr., 23(3), 213245.
Van der Veen, C.J. 2002. Calving glaciers. Progr. Phys. Geogr., 26(1), 96122.
Vaughan, D.G. 1993. Relating the occurrence of crevasses to surface strain rates. J. Glaciol., 39(132), 255266.
Venteris, E.R. 1999. Rapid tidewater glacier retreat: a comparison between Columbia Glacier, Alaska and Patagonian calving glaciers. Global Planet. Change, 22(1–4), 131138.
Vieli, A., Funk, M. and Blatter, H.. 2000. Tidewater glaciers: frontal flow acceleration and basal sliding. Ann. Glaciol., 31, 217221.
Vieli, A., Funk, M. and Blatter, H.. 2001. Flow dynamics of tidewater glaciers: a numerical modelling approach. J. Glaciol., 47(159), 595606.
Vieli, A., Jania, J. and Kolondra, L.. 2002. The retreat of a tidewater glacier: observations and model calculations on Hansbreen, Spitsbergen. J. Glaciol., 48(163), 592600.
Weertman, J. 1973. Can a water-filled crevasse reach the bottom surface of a glacier? IASH Publ. 95 (Symposium at Cambridge 1969 – Hydrology of Glaciers), 139145.
Ximenis, L. 2001. Dinàmica de la glacera Johnsons (Livingston, Shetland del Sud, Antàrtida). (PhD thesis, Universitat de Barcelona.)
Ximenis, L., Calvet, J., Garcia, D., Casas, J.M. and Sàbat, F.. 2000. Folding in the Johnsons Glacier, Livingston Island, Antarctica. In Maltman, A.J., Hubbard, B. and Hambrey, M.J., eds. Deformation of glacial materials. London, Geological Society, 147157. (Special Publication 176.)
Zwally, H.J., Abdalati, W., Herring, T., Larson, K., Saba, J. and Steffen, K.. 2002. Surface melt-induced acceleration of Greenland ice-sheet flow. Science, 297(5579), 218222.
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