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Modelled stress distributions at the Dome Summit South borehole, Law Dome, East Antarctica: a comparison of anisotropic ice flow relations

  • Adam Treverrow (a1), Roland C. Warner (a1), William F. Budd (a1), T.H. Jacka (a1) and Jason L. Roberts (a1) (a2)...

Abstract

In this study we compare the anisotropic flow relations for polycrystalline ice of Azuma and Goto-Azuma (1996), Thorsteinsson (2002), Placidi and others (2010) and Budd and others (2013). Observations from the Dome Summit South (DSS) ice-coring site at Law Dome, East Antarctica, are used to model the vertical distribution of deviatoric stress components at the borehole site. The flow relations in which the anisotropic rheology is parameterized by a scalar function, so that the strain-rate and deviatoric stress tensor components are collinear, provide simple shear and vertical compression deviatoric stress profiles that are most consistent with laboratory observations of tertiary creep in combined stress configurations. Those flow relations where (1) the anisotropy is derived from the magnitude of applied stresses resolved onto the basal planes of individual grains and (2) the macroscopic deformation is obtained via homogenization of individual grain responses provide stress estimates less consistent with laboratory observations. This is most evident in combined simple shear and vertical compression flow regimes where shear is dominant. Our results highlight the difficulties associated with developing flow relations which incorporate a physically based description of microdeformation processes. In particular, this requires that all relevant microdeformation, recrystallization and recovery processes are adequately parameterized.

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      Modelled stress distributions at the Dome Summit South borehole, Law Dome, East Antarctica: a comparison of anisotropic ice flow relations
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Corresponding author

Correspondence: Adam Treverrow <adam.treverrow@utas.edu.au>

References

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Alley, R and Joughin, I (2012) Modeling ice-sheet flow. Science, 336, 551552 (doi: 10.1126/science.1220530)
Azuma, N (1995) A flow law for anisotropic polycrystalline ice under uniaxial compressive deformation. Cold Reg. Sci. Technol., 23, 137147 (doi: 10.1016/0165-232X(94)00011-L)
Azuma, N and Goto-Azuma, K (1996) An anisotropic flow law for ice sheet ice and its implications. Ann. Glaciol., 23, 202208
Azuma, N and Higashi, A (1984) Mechanical properties of Dye 3 Greenland deep ice cores. Ann. Glaciol., 5, 18
Bamber, J, Gomez-Dans, J and Griggs, JA (2009) A new 1 km digital elevation model of the Antarctic derived from combined satellite radar and laser data – Part 1: Data and methods. Cryosphere, 3(1), 101111 (doi: 10.5194/tc-3-101-2009)
Bindschadler, R and 8 others (2008) The Landsat Image Mosaic of Antarctica. Remote Sens. Environ., 112(12), 42144226 (doi: 10.1016/j.rse.2008.07.006)
Budd, W and Jacka, T (1989) A review of ice rheology for ice sheet modelling. Cold Reg. Sci. Technol., 16, 107144 (doi: 10.1016/0165-232X(89)90014-1)
Budd, W, Warner, R, Jacka, T, Li, J and Treverrow, A (2013) Ice flow relations for stress and strain-rate components from combined shear and compression laboratory experiments. J. Glaciol., 59(214), 374392 (doi: 10.3189/2013JoG12J106)
Calov, R and 10 others (2010) Results from the Ice-Sheet Model Intercomparison Project–Heinrich Event INtercOmparison (ISMIP HEINO). J. Glaciol., 56(197), 371383 (doi: 10.3189/002214310792447789)
Carson, CJ, McLaren, S, Roberts, JL, Boger, SD and Blankenship, DD (2014) Hot rocks in a cold place: high sub-glacial heat flow in East Antarctica. J. Geol. Soc., 171(1), 912 (doi: 10.1144/jgs2013-030)
Cuffey, K and Paterson, W (2010) The physics of glaciers, 4th edn. Academic Press, Amsterdam
Dahl-Jensen, D and Gundestrup, N (1987) Constitutive properties of ice at Dye 3, Greenland. IAHS Publ. 170 (Symposium at Vancouver 1987 – The Physical Basis of Ice Sheet Modelling), 3143
Durand, G, Gagliardini, O, Thorsteinsson, T, Svensson, A, Kipfstuhl, S and Dahl-Jensen, D (2006) Ice microstructure and fabric: an up-to-date approach for measuring textures. J. Glaciol., 52(179), 619630 (doi: 10.3189/172756506781828377)
Durand, G and 8 others (2007) Change in ice rheology during climate variations – implications for ice flow modelling and dating of the EPICA Dome C core. Climate Past, 3, 155167 (doi: 10.5194/cp-3-155-2007)
Duval, P (1981) Creep and fabrics of polycrystalline ice under shear and compression. J. Glaciol., 27(95), 129140
Duval, P, Ashby, M and Anderman, I (1983) Rate-controlling processes in the creep of polycrystalline ice. J. Phys. Chem., 87(21), 40664074
Etheridge, D (1989) Dynamics of the Law Dome ice cap, Antarctica, as found from bore-hole measurements. Ann. Glaciol., 12, 4650
Faria, S (2006) Creep and recrystallization of large polycrystalline masses. III. Continuum theory of ice sheets. Proc. R. Soc. London, Ser. A, 462(2073), 27972816 (doi: 10.1098/rspa.2006.1698)
Faria, S (2008) The symmetry group of the CAFFE model. J. Glaciol., 54(187), 643645 (doi: 10.3189/002214308786570935)
Faria, SH, Weikusat, I and Azuma, N (2014) The microstructure of polar ice. Part II: State of the art. J. Struct. Geol., 61, 2149 (doi: 10.1016/j.jsg.2013.11.003)
Gagliardini, O and Meyssonnier, J (2000) Simulation of anisotropic ice flow and fabric evolution along the GRIP-GISP2 flowline, central Greenland. Ann. Glaciol., 30, 217223 (doi: 10.3189/172756400781820697)
Gagliardini, O, Gillet-Chaulet, F and Montagnat, M (2009) A review of anisotropic polar ice models: from crystal to ice-sheet flow models. In Hondoh, T ed. Physics of Ice Core Records II, 149166. Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan
Gagliardini, O and 14 others (2013) Capabilities and performance of Elmer/Ice, a new-generation ice sheet model. Geosci. Model Dev., 6(4), 12991318 (doi: 10.5194/gmd-6-1299-2013)
Gao, X and Jacka, T (1987) The approach to similar tertiary creep rates for Antarctic core ice and laboratory prepared ice. J. Phys. [Paris], 48, Colloq. C1 (Supplement au 3), 289296
Gillet-Chaulet, F, Gagliardini, O, Meyssonnier, J, Montagnat, M and Castelnau, O (2005) A user-friendly anisotropic flow law for ice-sheet modelling. J. Glaciol., 51(172), 314 (doi: 10.3189/172756505781829584)
Gillet-Chaulet, F and 8 others (2012) Greenland ice sheet contribution to sea-level rise from a new-generation ice-sheet model. Cryosphere, 6(6), 15611576 (doi: 10.5194/tc-6-1561-2012)
Glen, J (1955) The creep of polycrystalline ice. Proc. R. Soc. London, Ser. A, 1175(228), 519538 (doi: 10.1098/rspa.1955.0066)
Glen, J (1958) The flow law of ice. IAHS Publ. 47 (Symposium at Chamonix 1958 – Physics of the Movement of the Ice), 171183
Gödert, G (2003) A mesoscopic approach for modelling texture evolution of polar ice including recrystallisation phenomena. Ann. Glaciol., 37, 2328 (doi: 10.3189/172756403781815375)
Golledge, NR, Fogwill, CJ, Mackintosh, AN and Buckley, KM (2012) Dynamics of the Last Glacial Maximum Antarctic ice-sheet and its response to ocean forcing. Proc. Natl Acad. Sci. (PNAS), 109(40), 16 05216 056 (doi: 10.1073/pnas.1205385109)
Gow, A and Meese, D (2007) Physical properties, crystalline textures and c-axis fabrics of the Siple Dome (Antarctica) ice core. J. Glaciol., 183(53), 573584 (doi: 10.3189/002214307784409252)
Gow, A and Williamson, T (1976) Rheological implications of the internal structure and crystal fabrics of the West Antarctic ice sheet as revealed by deep ice core drilling at Byrd Station. Geol. Soc. Am. Bull., 87, 16651677
Gregory, J and 17 others (2013) Twentieth-century global-mean sea-level rise: is the whole greater than the sum of the parts? J. Climate, 26(13), 44764499 (doi: 10.1175/JCLI-D-12-00319.1)
Jones, S and Glen, J (1969) The effect of dissolved impurities on the mechanical properties of ice crystals. Philos. Mag., 19(157), 1324 (doi: 10.1080/14786436908217758)
Kamb, W (1961) The glide direction in ice. J. Glaciol., 3(30), 10971106
Li, J (1995) Interrelation between the flow properties and crystal structure of snow and ice. (PhD thesis, School of Earth Sciences, University of Melbourne)
Li, J, Jacka, T and Budd, W (1996) Deformation rates in combined compression and shear for ice which is initially isotropic and after the development of strong anisotropy. Ann. Glaciol., 23, 247252
Li, J, Jacka, T and Morgan, V (1998) Crystal-size and microparticle record in the ice core from Dome Summit South, Law Dome, East Antarctica. Ann. Glaciol., 27, 343348
Lile, R (1978) The effect of anisotropy on the creep of polycrystalline ice. J. Glaciol., 21(85), 475483
Lile, R (1984) The flow law for isotropic and anisotropic ice at low strain rates. ANARE Rep. 132
Llorens, MG and 6 others (2014) FFT simulation of dynamic recrystallization in polar ice. Geophys. Res. Abstr., 16, EGU2014-12880
Marshall, S (2005) Recent advances in understanding ice sheet dynamics. Earth Planet. Sci. Lett., 240, 191204 (doi: 10.1016/j.epsl.2005.08.016)
Martín, C, Gudmundsson, GH and King, EC (2014) Modelling of Kealey Ice Rise, Antarctica, reveals stable ice-flow conditions in East Ellsworth Land over millennia. J. Glaciol., 60, 139146 (doi: 10.3189/2014JoG13J089)
Montagnat, M and 9 others (2014a) Fabric along the NEEM ice core, Greenland, and its comparison with GRIP and NGRIP ice cores. Cryosphere, 8(4), 11291138 (doi: 10.5194/tc-8-1129-2014)
Montagnat, M and 11 others (2014b) Multiscale modeling of ice deformation behavior. J. Structural Geology, 61, 78108 (doi: 10.1016/j.jsg.2013.05.002)
Morgan, V, Wookey, C, Li, J, Van Ommen, T, Skinner, W and Fitzpatrick, M (1997) Site information and initial results from deep ice drilling on Law Dome, Antarctica. J. Glaciol., 43(143), 310
Morgan, V, Van Ommen, T, Elcheikh, A and Li, J (1998) Variations in shear deformation rate with depth at Dome Summit South, Law Dome, East Antarctica. Ann. Glaciol., 27, 135139
Morland, L and Staroszczyk, R (2003) Strain-rate formulation of ice fabric evolution. Ann. Glaciol., 37, 3539 (doi: 10.3189/172756403781815942)
Morlighem, M, Rignot, E, Seroussi, H, Larour, E, Ben Dhia, H and Aubry, D (2010) 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)
Nye, J (1957) The distribution of stress and velocity in glaciers and ice sheets. Proc. R. Soc. London, Ser. A, 239, 113133 (doi: 10.1098/rspa.1957.0026)
Pattyn, F and 20 others (2008) Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIS-HOM). Cryosphere, 2, 95108 (doi: 10.5194/tc-2-95-2008)
Pettit, E and Waddington, E (2003) Ice flow at low deviatoric stresses. J. Glaciol., 49(166), 359369 (doi: 10.3189/172756503781830584)
Pettit, E, Thorsteinsson, T, Jacobson, H and Waddington, E (2007) The role of crystal fabric in flow near an ice divide. J. Glaciol., 53(181), 277288 (doi: 10.3189/172756507782202766)
Pettit, E and 6 others (2011) The crossover stress, anisotropy and the ice flow law at Siple Dome, West Antarctica. J. Glaciol., 57(201), 3952 (doi: 10.3189/002214311795306619)
Piazolo, S, Wilson, CJ, Luzin, V, Brouzet, C and Peternell, M (2013) Dynamics of ice mass deformation: linking processes to rheology, texture and microstructure. Geochem. Geophys. Geosyst., 14 (doi: 10.1002/ggge.20246)
Pimienta, P, Duval, P and Lipenkov, VY (1987) Mechanical behaviour of anisotropic polar ice. IAHS Publ. 170 (Symposium at Vancouver 1987 – The Physical Basis of Ice Sheet Modelling), 5765
Placidi, L, Hutter, K and Faria, S (2006) A critical review of the mechanics of polycrystalline polar ice. GAMM-Mitt., 29(1), 77114 (doi: 10.1002/gamm.201490025)
Placidi, L, Greve, R, Seddik, H and Faria, S (2010) Continuum-mechanical, Anisotropic Flow model, for polar ice masses, based on an anisotropic Flow Enhancement factor. Cont. Mech. Thermodyn., 22, 221237 (doi: 10.1007/s00161-009-0126-0)
Reeh, N (1988) A flow-line model for calculating the surface profile and the velocity, strain-rate and stress fields in an ice sheet. J. Glaciol., 34(116), 4654
Roberts, J and 8 others (2015) A 2000-year annual record of snow accumulation rates for Law Dome, East Antarctica. Climate Past, 11(5), 697707 (doi: 10.5194/cp-11-697-2015)
Russell-Head, D and Budd, W (1979) Ice-sheet flow properties derived from bore-hole shear measurements combined with ice-core studies. J. Glaciol., 24(90), 117130
Seddik, H, Greve, R, Placidi, L, Hamann, I and Gagliardini, O (2008) Application of a continuum-mechanical model for the flow of anisotropic polar ice to the EDML core, Antarctica. J. Glaciol., 54(187), 631642 (doi: 10.3189/002214308786570755)
Seddik, H, Greve, R, Zwinger, T and Placidi, L (2011) A full Stokes ice flow model for the vicinity of Dome Fuji, Antarctica, with induced anisotropy and fabric evolution. Cryosphere, 5, 495508 (doi: 10.5194/tc-5-495-2011)
Seddik, H, Greve, R, Zwinger, T, Gillet-Chaulet, F and Gagliardini, O (2012) Simulations of the Greenland ice sheet 100 years into the future with the full Stokes model Elmer/Ice. J. Glaciol., 58(209), 427440 (doi: 10.3189/2012JoG11J177)
Staroszczyk, R (2003) Plane ice-sheet flow with evolving and recrystallizing fabric. Ann. Glaciol., 37, 247251 (doi: 10.3189/172756403781815834)
Svendsen, B and Hutter, K (1996) A continuum approach for modelling induced anisotropy in glaciers and ice sheets. Ann. Glaciol., 23, 262269
Thorsteinsson, T (2001) An analytical approach to deformation of anisotropic ice-crystal aggregates. J. Glaciol., 47(158), 507516 (doi: 10.3189/172756501781832124)
Thorsteinsson, T (2002) Fabric development with nearest-neighbour interaction and dynamic recrystallization. J. Geophys. Res. Solid Earth, 107(B1)
Thorsteinsson, T, Waddington, E, Taylor, K, Alley, R and Blankenship, D (1999) Strain-rate enhancement at Dye 3, Greenland. J. Glaciol., 45(150), 338345 (doi: 10.3189/002214399793377185)
Tison, JL, Thorsteinsson, T, Lorrain, R and Kipfstuhl, J (1994) Origin and development of textures and fabrics in basal ice as Summit, Central Greenland. Earth Planet. Sci. Lett., 125, 421437 (doi: 10.1016/0012-821X(94)90230-5)
Treverrow, A (2009) The flow of polycrystalline anisotropic ice: laboratory and model studies. (PhD thesis, Institute of Antarctic and Southern Ocean Studies, University of Tasmania)
Treverrow, A, Budd, W, Jacka, T and Warner, R (2012) The tertiary creep of polycrystalline ice: experimental evidence for stress-dependent levels of strain-rate enhancement. J. Glaciol., 58(208), 301314 (doi: 10.3189/2012JoG11J149)
Trickett, Y, Baker, I and Pradhan, P (2000a) The orientation dependence of the strength of ice single crystals. J. Glaciol., 46(152), 4144 (doi: 10.3189/172756500781833296)
Trickett, Y, Baker, I and Pradhan, P (2000b) The effects of sulfuric acid on the mechanical properties of ice single crystals. J. Glaciol., 46(153), 239243 (doi: 10.3189/172756500781832819)
Van der Veen, C and Whillans, I (1994) Development of fabric in ice. Cold Reg. Sci. Technol., 22, 171195 (doi: 10.1016/0165-232X(94)90027-2)
Van Ommen, T, Morgan, V, Jacka, T, Woon, S and Elcheikh, A (1999) Near surface temperatures in the Dome Summit South (Law Dome, East Antarctica) borehole. Ann. Glaciol., 29, 141144 (doi: 10.3189/172756499781821382)
Van Ommen, TD, Morgan, V and Curran, MAJ (2004) Deglacial and Holocene changes in accumulation at Law Dome, East Antarctica. Ann. Glaciol., 39, 359365 (doi: 10.3189/172756404781814221)
Vaughan, D and 13 others (2013) Observations: cryosphere. In Stocker, TF and 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 and New York
Wang, W and Warner, R (1999) Modelling of anisotropic ice flow in Law Dome, East Antarctica. Ann. Glaciol., 29, 184190 (doi: 10.3189/172756499781820932)
Wang, W, Warner, R and Budd, W (2002) Ice flow properties at Dome Summit South, Law Dome, East Antarctica. Ann. Glaciol., 35, 567573 (doi: 10.3189/172756402781816924)
Warner, R, Jacka, T, Li, J and Budd, W (1999) Tertiary flow relations for compression and shear components in combined stress tests on ice. In Hutter, K, Wang, Y and Beer, H eds Advances in cold region thermal engineering and sciences. Springer-Verlag, Berlin, 259270
Weertman, J (1983) Creep deformation of ice. Ann. Rev. Earth Planet. Sci., 11, 215240 (doi: 10.1146/annurev.ea.11.050183.001243)
Willis, J and Church, J (2012) Regional sea-level projection. Science, 336, 550551 (doi: 10.1126/science.1220366)
Wilson, CJ, Peternell, M, Piazolo, S and Luzin, V (2014) Microstructure and fabric development in ice: lessons learned from in situ experiments and implications for understanding rock evolution. J. Struct. Geol., 61, 5077 (doi: 10.1016/j.jsg.2013.05.006)
Woodcock, N (1977) Specification of fabric shapes using an eigenvalue method. Geol. Soc. Am. Bull., 88(9), 12311236 (doi: 10.1130/0016-7606(1977)88<1231:SOFSUA>2.0.CO;2)

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