Creep deformation and buttressing capacity of damaged ice shelves: Theory and application to Larsen C ice shelf

Cryosphere

Volumn 7, Issue 6, 2013, Pages 1931-1947

  Borstad, C P ^a   Rignot, E ^a,b   Mouginot, J ^b   Schodlok, M P ^a,c  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Los Angeles   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; DEFORMATION MECHANISM; ICE SHEET; ICE SHELF; MASS BALANCE; MONITORING; NUMERICAL MODEL; SEA LEVEL; STABILIZATION;

ANTARCTICA;

EID: 84890948398     PISSN: 19940416     EISSN: 19940424     Source Type: Journal    
DOI: 10.5194/tc-7-1931-2013     Document Type: Article

References (82)

1. Albrecht, T. and Levermann, A.: Fracture field for large-scale ice dynamics, J. Glaciol., 58, 165-176, doi:10.3189/2012JoG11J191, 2012.
2. Barkov, N. I.: Ice Shelves of Antarctica, Amerind Pub. Co., New Delhi, NY, 1985.
3. Bassis, J. N., Fricker, H. A., Coleman, R., Bock, Y., Behrens, J., Darnell, D., Okal, M., and Minster, J.-B.: Seismicity and deformation associated with ice-shelf rift propagation, J. Glaciol., 53, 523-536, 2007.
4. Bažant, Z. P.: Scaling of Structural Strength, Butterworth- Heinemann, 2nd Edn., 2005.
5. Bažant, Z. P. and Jirásek, M.: Nonlocal integral formulations of plasticity and damage: Survey of progress, J. Eng. Mech.-ASCE, 128, 1119-1149, doi:10.1061/(ASCE)0733- 9399(2002)128:11(1119), 2002. (Pubitemid 35289099)
6. Borstad, C. P. and McClung, D. M.: Numerical modeling of tensile fracture initiation and propagation in snow slabs using nonlocal damage mechanics, Cold Reg. Sci. Technol., 69, 145-155, doi:10.1016/j.coldregions.2011.09.010, 2011.
7. Borstad, C. P. and McClung, D. M.: A higher-order method for determining quasi-brittle tensile fracture parameters governing the release of slab avalanches and a new tool for in situ indexing, J. Geophys. Res.-Earth, 118, 900-912, doi:10.1002/jgrf.20065, 2013.
8. Borstad, C. P., Khazendar, A., Larour, E., Morlighem, M., Rignot, E., Schodlok, M. P., and Seroussi, H.: A damage mechanics assessment of the Larsen B ice shelf prior to collapse: Toward a physically-based calving law, Geophys. Res. Lett., 39, L18502, doi:10.1029/2012GL053317, 2012.
9. Cochran, J. R. and Bell, R. E.: Inversion of IceBridge gravity data for continental shelf bathymetry beneath the Larsen Ice Shelf, Antarctica, J. Glaciol., 58, 540-552, doi:10.3189/2012JoG11J033, 2012.
10. Cuffey, K. and Paterson,W. S. B.: The Physics of Glaciers, 4th Edn., Elsevier, Oxford, 2010.
11. Doake, C. S. M. and Vaughan, D. G.: Rapid disintegration of the Wordie Ice Shelf in response to atmospheric warming, Nature, 350, 328-330, 1991. (Pubitemid 21912220)
12. Duddu, R. and Waisman, H.: A temperature dependent creep damage model for polycrystalline ice, Mech. Mater., 46, 23-41, doi:10.1016/j.mechmat.2011.11. 007, 2012.
13. Dupont, T. and Alley, R.: Assessment of the importance of ice-shelf buttressing to ice-sheet flow, Geophys. Res. Lett., 32, L04503, doi:10.1029/2004GL022024, 2005. (Pubitemid 40746859)
14. Favier, L., Gagliardini, O., Durand, G., and Zwinger, T.: A threedimensional full Stokes model of the grounding line dynamics: effect of a pinning point beneath the ice shelf, The Cryosphere, 6, 101-112, doi:10.5194/tc-6-101-2012, 2012.
15. Fretwell, P., Pritchard, H. D., Vaughan, D. G., Bamber, J. L., Barrand, N. E., Bell, R., Bianchi, C., Bingham, R. G., Blankenship, D. D., Casassa, G., Catania, G., Callens, D., Conway, H., Cook, A. J., Corr, H. F. J., Damaske, D., Damm, V., Ferraccioli, F., Forsberg, R., Fujita, S., Gim, Y., Gogineni, P., Griggs, J. A., Hindmarsh, R. C. A., Holmlund, P., Holt, J. W., Jacobel, R. W., Jenkins, A., Jokat, W., Jordan, T., King, E. C., Kohler, J., Krabill, W., Riger-Kusk, M., Langley, K. A., Leitchenkov, G., Leuschen, C., Luyendyk, B. P., Matsuoka, K., Mouginot, J., Nitsche, F. O., Nogi, Y., Nost, O. A., Popov, S. V., Rignot, E., Rippin, D. M., Rivera, A., Roberts, J., Ross, N., Siegert, M. J., Smith, A. M., Steinhage, D., Studinger, M., Sun, B., Tinto, B. K., Welch, B. C., Wilson, D., Young, D. A., Xiangbin, C., and Zirizzotti, A.: Bedmap2: improved ice bed, surface and thickness datasets for Antarctica, The Cryosphere, 7, 375-393, doi:10.5194/tc-7-375- 2013, 2013.
16. Fricker, H. A. and Padman, L.: Thirty years of elevation change on Antarctic Peninsula ice shelves from multimission satellite radar altimetry, J. Geophys. Res., 117, C02026, doi:10.1029/2011JC007126, 2012.
17. Gagliardini, O., Durand, G., Zwinger, T., Hindmarsh, R. C. A., and Le Meur, E.: Coupling of ice-shelf melting and buttressing is a key process in ice-sheets dynamics, Geophys. Res. Lett., 37, L14501, doi:10.1029/2010GL043334, 2010.
18. Glasser, N. F., Kulessa, B., Luckman, A., Jansen, D., King, E. C., Sammonds, P. R., Scambos, T. A., and Jezek, K. C.: Surface structure and stability of the Larsen C ice shelf, Antarctic Peninsula, J. Glaciol., 55, 400-410, 2009.
19. Goldberg, D., Holland, D. M., and Schoof, C.: Grounding line movement and ice shelf buttressing in marine ice sheets, J. Geophys. Res., 114, F04026, doi:10.1029/2008JF001227, 2009.
20. Griggs, J. A. and Bamber, J. L.: Antarctic ice-shelf thickness from satellite radar altimetry, J. Glaciol., 57, 485-498, 2011.
21. Gudmundsson, G. H.: Ice-shelf buttressing and the stability of marine ice sheets, The Cryosphere, 7, 647-655, doi:10.5194/tc-7- 647-2013, 2013.
22. Holland, D. and Jenkins, A.: Modeling thermodynamic ice-ocean interactions at the base of an ice shelf, J. Phys. Oceanogr., 29, 1787-1800, 1999. (Pubitemid 30061299)
23. Holland, P. R., Corr, H. F. J., Vaughan, D. G., Jenkins, A., and Skvarca, P.: Marine ice in Larsen Ice Shelf, Geophys. Res. Lett., 36, L11604, doi:10.1029/2009GL038162, 2009.
24. Jansen, D., Kulessa, B., Sammonds, P., Luckman, A., King, E., and Glasser, N.: Present stability of the Larsen C ice shelf, Antarctic Peninsula, J. Glaciol., 56, 593-600, 2010.
25. Jezek, K.: A modified theory of bottom crevasses used as a means for measuring the buttressing effect of ice shelves on inland ice sheets, J. Geophys. Res., 89, 1925-1931, 1984. (Pubitemid 14546983)
26. Jezek, K. C., Alley, R. B., and Thomas, R. H.: Rheology of glacier ice, Science, 227, 1335-1337, 1985.
27. Kenneally, J. P. and Hughes, T. J.: Fracture and back stress along the Byrd Glacier flowband on the Ross Ice Shelf, Antarct. Sci., 16, 345-354, doi:10.1017/S0954102004002056, 2004. (Pubitemid 39320634)
28. Khazendar, A. and Jenkins, A.: A model of marine ice formation within Antarctic ice shelf rifts, J. Geophys. Res., 108, 3235, doi:10.1029/ 2002JC001673, 2003.
29. Khazendar, A., Rignot, E., and Larour, E.: Larsen B Ice Shelf rheology preceding its disintegration inferred by a control method, Geophys. Res. Lett., 34, L19503, doi:10.1029/2007GL030980, 2007. (Pubitemid 350263018)
30. Khazendar, A., Rignot, E., and Larour, E.: Roles of marine ice, rheology, and fracture in the flow and stability of the Brunt/Stancomb-Wills Ice Shelf, J. Geophys. Res., 114, F04007, doi:10.1029/2008JF001124, 2009.
31. Khazendar, A., Rignot, E., and Larour, E.: Acceleration and spatial rheology of Larsen C Ice Shelf, Antarctic Peninsula, Geophys. Res. Lett., 38, L09502, doi:10.1029/2011GL046775, 2011.
32. Larour, E., Rignot, E., and Aubry, D.: Processes involved in the propagation of rifts near Hemmen Ice Rise, Ronne Ice Shelf, Antarctica, J. Glaciol., 50, 329-341, 2004a.
33. Larour, E., Rignot, E., and Aubry, D.: Modelling of rift propagation on Ronne Ice Shelf, Antarctica, and sensitivity to climate change, Geophys. Res. Lett., 31, L16404, doi:10.1029/2004GL020077, 2004b. (Pubitemid 39428493)
34. Larour, E., Rignot, E., Joughin, I., and Aubry, D.: Rheology of the Ronne Ice Shelf, Antarctica, inferred from satellite radar interferometry data using an inverse control method, Geophys. Res. Lett., 32, L05503, doi:10.1029/ 2004GL021693, 2005. (Pubitemid 40815094)
35. Larour, E., Seroussi, H., Morlighem, M., and Rignot, E.: Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM), J. Geophys. Res., 117, F01022, doi:10.1029/ 2011JF002140, 2012.
36. Lemaitre, J.: A course on damage mechanics, Springer, New York, 1996.
37. Luckman, A., Jansen, D., Kulessa, B., King, E. C., Sammonds, P., and Benn, D. I.: Basal crevasses in Larsen C Ice Shelf and implications for their global abundance, The Cryosphere, 6, 113-123, doi:10.5194/tc-6-113-2012, 2012.
38. MacAyeal, D.: Large-scale ice flow over a viscous basal sediment: Theory and application to Ice Stream B, Antarctica, J. Geophys. Res., 94, 4071-4087, 1989.
39. MacAyeal, D.: A tutorial on the use of control methods in ice-sheet modeling, J. Glaciol., 39, 91-98, 1993. (Pubitemid 23383661)
40. MacAyeal, D. R. and Holdsworth, G.: An investigation of low-stress ice rheology on the Ward-Hunt Ice Shelf, J. Geophys. Res., 91, 6347-6358, 1986.
41. MacAyeal, D. R. and Sergienko, O. V.: The flexural dynamics of melting ice shelves, Ann. Glaciol., 54, 1-10, doi:10.3189/2013AoG63A256, 2013.
42. McGrath, D., Steffen, K., Scambos, T., Rajaram, H., Casassa, G., and Lagos, J.: Basal crevasses and associated surface crevassing on the Larsen C ice shelf, Antarctica, and their role in ice-shelf instability, Ann. Glaciol., 58, 10-18, doi:10.3189/2012AoG60A005, 2012.
43. Menemenlis, D., Campin, C., Heimbach, P., Hill, C., Lee, T., Nguyen, M., Schodlok, M., and Zhang, M.: ECCO 2: High resolution global ocean and sea ice data synthesis, Mercator Ocean Quart. Newsl., 31, 13-21, 2008.
44. Morlighem, M., Rignot, E., Seroussi, H., Larour, E., Ben Dhia, H., and Aubry, D.: Spatial patterns of basal drag inferred using control methods from a full-Stokes and simpler models for Pine Island Glacier, West Antarctica, Geophys. Res. Lett., 37, L14502, doi:10.1029/2010GL043853, 2010.
45. Mouginot, J., Scheuchl, B., and Rignot, E.: Mapping of Ice Motion in Antarctica Using Synthetic-Aperture Radar Data, Remote Sens., 4, 2753-2767, doi:10.3390/rs4092753, 2012.
46. Murakami, S. and Ohno, N.: A continuum theory of creep and creep damage, in: Creep in Structures, 422-444, Springer-Verlag, Berlin, Leicester, UK, 1981.
47. Pralong, A. and Funk, M.: Dynamic damage model of crevasse opening and application to glacier calving, J. Geophys. Res., 110, B01309, doi:10.1029/2004JB003104, 2005.
48. Pralong, A., Hutter, K., and Funk, M.: Anisotropic damage mechanics for viscoelastic ice, Continuum Mech. Therm., 17, 387-408, doi:10.1007/s00161-005- 0002-5, 2006. (Pubitemid 43254062)
49. Pritchard, H., Arthern, R., Vaughan, D., and Edwards, L.: Extensive dynamic thinning on the margins of the Greenland and Antarctic ice sheets, Nature, 461, 971-975, doi:10.1038/nature08471, 2009.
50. Pritchard, H. D., Ligtenberg, S. R. M., Fricker, H. A., Vaughan, D. G., van den Broeke, M. R., and Padman, L.: Antarctic icesheet loss driven by basal melting of ice shelves, Nature, 484, 502-505, doi:10.1038/nature10968, 2012.
51. Rack, W., Doake, C. S. M., Rott, H., Siegel, A., and Skvarca, P.: Interferometric analysis of the deformation pattern of the northern Larsen Ice Shelf, Antarctic Peninsula, compared to field measurements and numerical modeling, Ann. Glaciol., 31, 205-210, 2000.
52. Rignot, E. and Jacobs, S.: Rapid bottom melting widespread near Antarctic ice sheet grounding lines, Science, 296, 2020-2023, doi:10.1126/science. 1070942, 2002. (Pubitemid 34627523)
53. Rignot, E., Casassa, G., Gogineni, P., Krabill, W., Rivera, A., and Thomas, R.: Accelerated ice discharge from the Antarctic Peninsula following the collapse of Larsen B ice shelf, Geophys. Res. Lett., 31, L18401, doi:10.1029/2004GL020697, 2004. (Pubitemid 39660802)
54. Rignot, E., Bamber, J., van den Broeke, M., Davis, C., Li, Y., van de Berg, W., and van Meijgaard, E.: Recent Antarctic ice mass loss from radar interferometry and regional climate modelling, Nature Geosci., 1, 106-110, doi:10.1038/ngeo102, 2008.
55. Rignot, E., Mouginot, J., and Scheuchl, B.: Antarctic grounding line mapping from differential satellite radar interferometry, Geophys. Res. Lett., 38, L10504, doi:10.1029/2011GL047109, 2011a.
56. Rignot, E., Mouginot, J., and Scheuchl, B.: Ice Flow of the Antarctic Ice Sheet, Science, 333, 1427-1430, doi:10.1126/science.1208336, 2011b.
57. Rignot, E., Jacobs, S., Mouginot, J., and Scheuchl, B.: Ice shelf melting around Antarctica, Science, 341, 266-270, doi:10.1126/science.1235798, 2013.
58. Rist, M., Sammonds, P., Oerter, H., and Doake, C.: Fracture of Antarctic shelf ice, J. Geophys. Res., 107, ECV 2-1-ECV 2-13, doi:10.1029/2000JB000058, 2002.
59. Rommelaere, V. and MacAyeal, D.: Large-scale rheology of the Ross Ice Shelf, Antarctica, computed by a control method, Ann. Glaciol., 24, 43-48, 1997.
60. Rott, H., Müller, F., Nagler, T., and Floricioiu, D.: The imbalance of glaciers after disintegration of Larsen-B ice shelf, Antarctic Peninsula, The Cryosphere, 5, 125-134, doi:10.5194/tc-5-125- 2011, 2011.
61. Sandhäger, H., Rack, W., and Jansen, D.: Model investigations of Larsen B Ice Shelf dynamics prior to the breakup, FRISP Report, 16, 5-12, 2005.
62. Scambos, T., Hulbe, C., Fahnestock, M., and Bohlander, J.: The link between climate warming and break-up of ice shelves in the Antarctic Peninsula, J. Glaciol., 46, 516-530, 2000. (Pubitemid 32065360)
63. Scambos, T., Bohlander, J., Shuman, C., and Skvarca, P.: Glacier acceleration and thinning after ice shelf collapse in the Larsen B embayment, Antarctica, Geophys. Res. Lett., 31, L18402, doi:10.1029/2004GL020670, 2004. (Pubitemid 39660803)
64. Scambos, T. A., Haran, T. M., Fahnestock, M. A., Painter, T. H., and Bohlander, J.: MODIS-based Mosaic of Antarctica (MOA) data sets: Continent-wide surface morphology and snow grain size, Remote Sens. Environ., 111, 242-257, doi:10.1016/j.rse.2006.12.020, 2007. (Pubitemid 350001197)
65. Schodlok, M., Menemenlis, D., Rignot, E., and Studinger, M.: Sensitivity of the ice-shelf/ocean system to the sub-ice-shelf cavity shape measured by NASA IceBridge in Pine Island Glacier, West Antarctica, Ann. Glaciol., 53, 156-162, doi:10.3189/2012AoG60A073, 2012.
66. Schoof, C.: Ice sheet grounding line dynamics: Steady states, stability, and hysteresis, J. Geophys. Res., 112, F03S28, doi:10.1029/2006JF000664, 2007. (Pubitemid 350120788)
67. Sergienko, O. V., Goldberg, D. N., and Little, C. M.: Alternative ice shelf equilibria determined by ocean environment, J. Geophys. Res., 118, 970-981, doi:10.1002/jgrf.20054, 2013.
68. Shepherd, A., Wingham, D., Payne, T., and Skvarca, P.: Larsen ice shelf has progressively thinned, Science, 302, 856-859, 2003. (Pubitemid 37339623)
69. Thomas, R.: Force-perturbation analysis of recent thinning and acceleration of Jakobshavn Isbrae, Greenland, J. Glaciol., 50, 57- 66, doi:10.3189/172756504781830321, 2004. (Pubitemid 40067989)
70. Thomas, R. and MacAyeal, D.: Derived characteristics of the Ross Ice Shelf, Antarctica, J. Glaciol., 28, 397-412, 1982.
71. Thomas, R., Rignot, E., Kanagaratnam, P., Krabill,W., and Casassa, G.: Force-perturbation analysis of Pine Island Glacier, Antarctica, suggests cause for recent acceleration, Ann. Glaciol., 39, 133-138, 2004. (Pubitemid 41167013)
72. Thomas, R. H.: The creep of ice shelves: Theory, J. Glaciol., 12, 45-53, 1973a.
73. Thomas, R. H.: The creep of ice shelves: Interpretation of observed behaviour, J. Glaciol., 12, 55-70, 1973b.
74. Thomas, R. H.: Ice shelves: A review, J. Glaciol., 24, 273-286, 1979.
75. van den Broeke, M. R. and van Lipzig, N. P.: Changes in Antarctic temperature, wind and precipitation in response to the Antarctic Oscillation, Ann. Glaciol., 39, 119-126, 2004.
76. van Der Veen, C.: Fracture mechanics approach to penetration of bottom crevasses on glaciers, Cold Reg. Sci. Technol., 27, 213- 223, 1998a. (Pubitemid 28508024)
77. van der Veen, C.: Fracture mechanics approach to penetration of surface crevasses on glaciers, Cold Reg. Sci. Technol., 27, 31- 47, 1998b. (Pubitemid 28393356)
78. van Meijgaard, E., van Ulft, L. H., Van de Berg,W. J., Bosvelt, F. C., Van den Hurk, B. J. J. M., Lenderink, G., and Siebesma, A. P.: The KNMI regional atmospheric model RACMO version 2.1, Technical Report 302, Tech. rep., KNMI, De Bilt, the Netherlands, 2008.
79. Vaughan, D.: Relating the occurence of crevasses to surface strain rates, J. Glaciol., 39, 255-266, 1993. (Pubitemid 24398271)
80. Vieli, A., Payne, A. J., Shepherd, A., and Du, Z.: Causes of precollapse changes of the Larsen B ice shelf: Numerical modelling and assimilation of satellite observations, Earth Planet. Sc. Lett., 259, 297-306, doi:10.1016/j.epsl.2007.04.050, 2007. (Pubitemid 46971664)
81. Weertman, J.: Deformation of floating ice shelves, J. Glaciol., 3, 38-42, 1957.
82. Wu, Z. and Mahrenholtz, O.: Creep and creep damage of polycrystalline ice under multi-axial variable loading, in: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, Vol. 4, 1-10, ASME, Glasgow, Scotland, 1993. (Pubitemid 23715633)