Surveys in Geophysics

, Volume 35, Issue 6, pp 1441–1458 | Cite as

The Deformational Response of a Viscoelastic Solid Earth Model Coupled to a Thermomechanical Ice Sheet Model

  • Hannes KonradEmail author
  • Malte Thoma
  • Ingo Sasgen
  • Volker Klemann
  • Klaus Grosfeld
  • Dirk Barbi
  • Zdeněk Martinec


We apply a coupled thermomechanical ice sheet—self-gravitating viscoelastic solid Earth model (SGVEM), allowing for the dynamic exchange of ice thickness and bedrock deformation, in order to investigate the effect of viscoelastic deformation on ice dynamics and vice versa. In a synthetic glaciation scenario, we investigate the interaction between the ice sheet and the solid Earth deformation, the glacial-isostatic adjustment (GIA), accounting for an atmospheric forcing depending on the ice sheet surface altitude. We compare the results from the coupled model to runs with the common elastic lithosphere/relaxing asthenosphere (ELRA) model, where the lithosphere is represented by a thin plate and the mantle relaxes with one characteristic relaxation time, as well as to a rigid Earth without any deformation. We find that the deformational behaviour of the SGVEM on ice dynamics (i.e. stored ice volume, ice thickness and velocity field) is comparable to the ELRA for an optimal choice of the parameters in steady state, but exhibits differences in the transient behaviour. Beyond the ice sheet, in the region of peripheral forebulge, the differences in the transient surface deformation between ELRA and SGVEM are substantial, demonstrating the inadequacy of the ELRA model for interpreting constraints on GIA in the periphery of the ice sheet, such as sea-level indicators and GPS uplift rates.


Viscoelastic deformation Glacial-isostatic adjustment Thermomechanical ice sheet model Peripheral forebulge 



We thank two anonymous referees for their attentive work and Jürgen Kusche for editing the manuscript. HK and IS are funded by the Deutsche Forschungsgemeinschaft (DFG) through Grant SA 1734/2-2, VK through Grant KL 2284/1-3, both within the framework of the DFG priority program SPP1257 ‘Mass transport and mass distribution in the Earth system’. This work is a contribution to the Helmholtz Climate Initiative REKLIM, a joint research project of the Helmholtz Association of German Research Centres (HGF).


  1. Bassett SE, Milne GA, Mitrovica JX, Clark PU (2005) Ice sheet and solid earth influences on far-field sea-level histories. Science 309(5736):925–928. doi: 10.1126/science.1111575 CrossRefGoogle Scholar
  2. Brotchie JF, Silvester R (1969) On crustal flexure. J Geophys Res 74(22):5240–5252. doi: 10.1029/JB074i022p05240 CrossRefGoogle Scholar
  3. Cuffey K, Paterson WSB (2010) The physics of glaciers. Elsevier, Butterworth-HeinemannGoogle Scholar
  4. Dziewonski AM, Anderson DL (1981) Preliminary reference Earth model. Phys Earth Planet Interiors 25(4):297–356. doi: 10.1016/0031-9201(81)90046-7 CrossRefGoogle Scholar
  5. Farrell W, Clark J (1976) On postglacial sea level. Geophys J Astr Soc 46:647–667. doi: 10.1111/j.1365-246X.1976.tb01252.x CrossRefGoogle Scholar
  6. Gomez N, Pollard D, Mitrovica JX, Huybers P, Clark PU (2012) Evolution of a coupled marine ice sheet–sea level model. J Geophys Res 117:F01,013. doi: 10.1029/2011JF002128 Google Scholar
  7. Greve R, Blatter H (2009) Dynamics of ice sheets and glaciers. Adv Geophys Environ Mech Math. Springer, Berlin. doi: 10.1007/978-3-642-03415-2_5
  8. Hagedoorn JM, Wolf D, Martinec Z (2007) An estimate of global mean sea-level rise inferred from tide-gauge measurements using glacial-isostatic models consistent with the relative sea-level record. Pure Appl Geophys 164(4):791–818. doi: 10.1007/s00024-007-0186-7 CrossRefGoogle Scholar
  9. Hooke RL (1981) Flow law for polycrystalline ice in glaciers: comparison of theoretical predictions, laboratory data, and field measurements. Rev Geophys 19(4):664–672 doi: 10.1029/RG019i004p00664 CrossRefGoogle Scholar
  10. Huybrechts P (1993) Glaciological Modelling of the Late Cenozoic East Antarctic Ice Sheet: Stability or Dynamism? Geografiska Ann Ser A Phys Geogr 75(4):221–238Google Scholar
  11. Huybrechts P, Goelzer H, Janssens I, Driesschaert E, Fichefet T, Goosse H, Loutre MF (2011) Response of the Greenland and Antarctic Ice Sheets to multi-millennial greenhouse warming in the Earth system model of intermediate complexity LOVECLIM. Surv Geophys 32(4–5):397–416. doi: 10.1007/s10712-011-9131-5 CrossRefGoogle Scholar
  12. Ivins E, James T (2005) Antarctic glacial isostatic adjustment: a new assessment. Antarct Sci 17(4):541–553. doi: 10.1017/S0954102005002968 CrossRefGoogle Scholar
  13. Lambeck K, Nakiboglu SM (1980) Seamount loading and stress in the ocean lithosphere. J Geophys Res 85(B11):6403–6418. doi: 10.1029/0JGREA000085000B11006403000001 CrossRefGoogle Scholar
  14. Le Meur E, Huybrechts P (1996) A comparison of different ways of dealing with isostasy: examples from modeling the Antarctic ice sheet during the last glacial cycle. Ann Glaciol 23:309–317Google Scholar
  15. Martinec Z (1989) Program to calculate the spectral harmonic expansion coefficients of the two scalar fields product. Comput Phys Commun 54(1):177–182. doi: 10.1016/0010-4655(89)90043-X CrossRefGoogle Scholar
  16. Martinec Z (2000) Spectral-finite element approach to three-dimensional viscoelastic relaxation in a spherical earth. Geophys J Int 142(1):117–141. doi: 10.1046/j.1365-246x.2000.00138.x Google Scholar
  17. Olaizola M, van de Wal RSW, Helsen MM, de Boer B (2012) An ice flow modeling perspective on bedrock adjustment patterns of the Greenland ice sheet. The Cryosphere 6(6):1263–1274. doi: 10.5194/tc-6-1263-2012 CrossRefGoogle Scholar
  18. Pattyn F (2003) A new three-dimensional higher-order thermomechanical ice sheet model: basic sensitivity, ice stream development, and ice flow across subglacial lakes. J Geophys Res Solid Earth 108(B8). doi: 10.1029/2002JB002329
  19. Payne AJ, Huybrechts P, Abe-Ouchi A, Calov R, Fastook JL, Greve R, Marshall SJ, Marsiat I, Ritz C, Tarasov L, Thomassen MPA (2000) Results from the EISMINT model intercomparison: the effects of thermomechanical coupling. J Glaciol 46(153):227–238. doi: 10.3189/172756400781820534 CrossRefGoogle Scholar
  20. Peltier WR (2004) Global glacial isostasy and the surface of the ice-age earth: the ICE5G (VM2) model and GRACE. Annu Rev Earth Planet Sci 32:111–149. doi: 10.1146/ CrossRefGoogle Scholar
  21. Petit JR, Jouzel J, Raynaud D, Barkov NI, Barnola JM, Basile I, Bender M, Chappellaz J, Davis M, Delaygue G, Delmotte M, Kotlyakov VM, Legrand M, Lipenkov VY, Lorius C, Pépin L, Ritz C, Saltzman E, Stievenard M (1999) Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature 399(6735):429–436. doi: 10.1038/20859 CrossRefGoogle Scholar
  22. Sabadini R, Vermeersen B (2004) Global dynamics of the earth: applications of normal mode relaxation theory to solid-earth geophysics. Modern approaches in geophysics. Springer, New YorkCrossRefGoogle Scholar
  23. Sasgen I, Klemann V, Martinec Z (2012) Toward the inversion of GRACE gravity fields for present-day ice-mass changes and glacial-isostatic adjustment in North America and Greenland. J Geodyn 59–60:49–63. doi: 10.1016/j.jog.2012.03.004 CrossRefGoogle Scholar
  24. Sneeuw N (1994) Global spherical harmonic analysis by least-squares and numerical quadrature methods in historical perspective. Geophys J Int 118(3):707–716. doi: 10.1111/j.1365-246X.1994.tb03995.x CrossRefGoogle Scholar
  25. Spada G, Barletta VR, Klemann V, Riva REM, Martinec Z, Gasperini P, Lund B, Wolf D, Vermeersen LLA, King MA (2011) A benchmark study for glacial isostatic adjustment codes. Geophys J Int 185(1):106–132. doi: 10.1111/j.1365-246X.2011.04952.x CrossRefGoogle Scholar
  26. Thoma M, Grosfeld K, Mayer C, Pattyn F (2010) Interaction between ice sheet dynamics and subglacial lake circulation: a coupled modelling approach. The Cryosphere 4(1):1–12. doi: 10.5194/tc-4-1-2010 CrossRefGoogle Scholar
  27. Thoma M, Grosfeld K, Mayer C, Pattyn F (2012) Ice flow sensitivity to boundary processes: a coupled model study in the Vostok Subglacial Lake area. Ann Glaciol 53(60):173–180. doi: 10.3189/2012AoG60A009 CrossRefGoogle Scholar
  28. Thoma M, Grosfeld K, Barbi D, Determann J, Göller S, Mayer C, Pattyn F (2013) RIMBAY—a multi-physics 3-D ice-dynamics model for comprehensive applications: model-description and examples. Geosci Model Dev Discuss 6(2):3289–3347. doi: 10.5194/gmdd-6-3289-2013 CrossRefGoogle Scholar
  29. van den Berg J, van de Wal RSW, Milne GA, Oerlemans J (2008) Effect of isostasy on dynamical ice sheet modeling: a case study for Eurasia. J Geophys Res 113:B05,412 doi: 10.1029/2007JB004994 Google Scholar
  30. Watts AB (2001) Isostasy and flexure of the lithosphere. Cambridge University Press, CambridgeGoogle Scholar
  31. Wessel P, Smith WHF (1991) Free software helps map and display data. Eos Trans AGU 72(41):441. doi: 10.1029/90EO00319 CrossRefGoogle Scholar
  32. Whitehouse PL, Bentley MJ, Brocq AML (2012a) A deglacial model for Antarctica: geological constraints and glaciological modelling as a basis for a new model of Antarctic glacial isostatic adjustment. Quat Sci Rev 32(0):1–24. doi: 10.1016/j.quascirev.2011.11.016 CrossRefGoogle Scholar
  33. Whitehouse PL, Bentley MJ, Milne GA, King MA, Thomas ID (2012b) A new glacial isostatic adjustment model for Antarctica: calibrated and tested using observations of relative sea-level change and present-day uplift rates. Geophys J Int 190(3):1464–1482. doi: 10.1111/j.1365-246X.2012.05557.x CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Hannes Konrad
    • 1
    Email author
  • Malte Thoma
    • 2
  • Ingo Sasgen
    • 1
  • Volker Klemann
    • 1
  • Klaus Grosfeld
    • 2
  • Dirk Barbi
    • 2
  • Zdeněk Martinec
    • 3
  1. 1.Department for Geodesy and Remote SensingGFZ German Research Centre for GeosciencesPotsdamGermany
  2. 2.Alfred Wegener Institute Helmholtz Centre for Polar and Marine ResearchBremerhavenGermany
  3. 3.Dublin Institute for Advanced StudiesDublinIreland

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