Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T19:51:38.376Z Has data issue: false hasContentIssue false
  • English
  • Français

A Parallel Computational Model for Three-Dimensional, Thermo-Mechanical Stokes Flow Simulations of Glaciers and Ice Sheets

Published online by Cambridge University Press:  03 June 2015

Wei Leng ,
Lili Ju ,
Max Gunzburger  and
Stephen Price
Wei Leng*
Affiliation:
State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing 100190, China
Lili Ju*
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
Max Gunzburger*
Affiliation:
Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA
Stephen Price*
Affiliation:
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
*
Email:[email protected]
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Get access

Abstract

This paper focuses on the development of an efficient, three-dimensional, thermo-mechanical, nonlinear-Stokes flow computational model for ice sheet simulation. The model is based on the parallel finite element model developed in [14] which features high-order accurate finite element discretizations on variable resolution grids. Here, we add an improved iterative solution method for treating the nonlinearity of the Stokes problem, a new high-order accurate finite element solver for the temperature equation, and a new conservative finite volume solver for handling mass conservation. The result is an accurate and efficient numerical model for thermo-mechanical glacier and ice-sheet simulations. We demonstrate the improved efficiency of the Stokes solver using the ISMIP-HOM Benchmark experiments and a realistic test case for the Greenland ice-sheet. We also apply our model to the EISMINT-II benchmark experiments and demonstrate stable thermo-mechanical ice sheet evolution on both structured and unstructured meshes. Notably, we find no evidence for the “cold spoke” instabilities observed for these same experiments when using finite difference, shallow-ice approximation models on structured grids.

Keywords

86A4065N3065M08Stokes-flow modelingice-sheet modelingfinite element approximationfinite volume approximationparallel implementation
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 4 , October 2014 , pp. 1056 - 1080
Copyright
Copyright © Global Science Press Limited 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Alley, R.B. and Joughin, I., Modeling Ice-Sheet Flow, Science, 336 (2012), 551–552.Google Scholar
[2]Alley, R.B., Clark, P.U., Huybrechts, P., P.,, and Joughin, I., Ice sheet and sea-level changes, Science, 310 (2005), 456–460.Google Scholar
[3]Bamber, J.L., Alley, R.B., and Joughin, I., Rapid response of modern day ice sheets to external forcing, Earth Planet Sci. Lett., 257 (2007), 1–13.Google Scholar
[4]Bahr, D.B., Analytical modeling of glacier dynamics, Math. Geology, 28 (1996), 229–251.Google Scholar
[5]Brinkerhoff, D.J. and Johnson, J.V., Data assimilation and prognostic whole ice-sheet modelling with the variationally derived, higher-order, open source, and fully parallel ice sheet model VarGlaS, The Cryosphere, 7 (2013), 1161–1184.Google Scholar
[6]Brooks, A.N. and Hughes, T., Streamline upwind/Petrov-Galerkin formulations for advection dominated flows, Proc Inter. Conf. on Finite Element Methods in Fluid Flow, Banff, Canada, 1980.Google Scholar
[7]Bueler, E., Brown, J., and Lingle, C.S., Exact solutions to the thermomechanically coupled shallow-ice approximation: effective tools for verification, J. Glaciol., 53 (2007), 499–516.Google Scholar
[8]Burstedde, C., Ghattas, O., Stadler, G., Tu, T., and Wilcox, L.C., Parallel scalable adjoint-based adaptive solution of variable-viscosity Stokes flow problems, Comput. Methods Appl. Mech. Engrg., 198 (2009), 1691–1700.Google Scholar
[9]Carlos, M., Gudmundsson, G. H., Pritchard, H. D., and Gagliardini, O., On the effects of anisotropic rheology on ice flow, internal structure, and the age-depth relationship at ice divides, J. Geophys. Res., 114 (2009), F04001.Google Scholar
[10]Dahl-Jensen, D., Steady thermomechanical flow along two-dimensional flow lines in large grounded ice sheets, J. Geophys. Res., 94 (1989), B8,10355–10362.Google Scholar
[11]Dukowicz, J.K., Price, S., and Lipscomb, W., Consistent approximations and boundary conditions for ice-sheet dynamics from a principle of least action, J. Glaciol., 56 (2010), 480–496.Google Scholar
[12]Ju, L., Conforming centroidal Voronoi Delaunay triangulation for quality mesh generation, Inter. J. Numer. Anal. Model., 4 (2007), pp. 531–547.Google Scholar
[13]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 (2012), F01022, doi:10.1029/2011JF002140.Google Scholar
[14]Leng, W., Ju, L., Gunzburger, M., Price, S., and Ringler, T., A parallel high-order accurate finite element Stokes ice sheet model. J. Geophys. Res., 117 (2012), F01001, doi:10.1029/2011JF001962.Google Scholar
[15]Leng, W., Ju, L., Gunzburger, M., and Price, S., Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models, The Cryosphere, 7 (2013), pp. 19–29.Google Scholar
[16]Meur, E. Le, Gagliardini, O., Zwinger, T., and Ruokolainen, J., Glacier flow modelling: A com-parison of the shallow ice approximation and the full-Stokes solution, Comptes Rendus Physique, 5(7) (2004), 709–722.CrossRefGoogle Scholar
[17]Morlighem, M., Rignot, E., Seroussi, H., Larour, E., Dhia, H.B., and Aubry, D., Spatial patterns of basal drag inferred using control methods for a full-Stokes and simpler models for Pine Island Glacier, West Antarctica, J. Geophys. Res., 37 (2010), L14502, doi:10.1029/2010GL043853.Google Scholar
[18]Nereson, N.A., Raymond, C. F., Waddington, E. D., and Jacobel, R. W., Migration of the Siple Dome ice divide, West Antarctica, J. Glaciol., 44 (1998), 643–652.Google Scholar
[19]Nye, J., The distribution of stress and velocity in glaciers and ice-sheets, Proc. R. Soc. London, Ser.A, 239 (1957), 113–133.Google Scholar
[20]Paterson, W.S.B. and Budd, W.F., Flow parameters for ice sheet modelling, Cold Reg. Sci. Technol., 6 (1982), 175–177.Google Scholar
[21]Paterson, W.S.B, The Physics of Glaciers, Elsevier Science, Oxford, U. K, 1994.Google Scholar
[22]Pattyn, F., A new 3D higher-order thermomechanical ice-sheet model: Basic sensitivity, ice-stream development and ice flow across subglacial lakes, J. Geophys. Res., 108(B8) (2003), 2382, doi:10.1029/2002JB002329.Google Scholar
[23]Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., Smedt, D.B., Gagliardini, O., Gud-mundsson, G.H., Hindmarsh, R.C.A., Hubbard, A., Johnson, J.V., Kleiner, T., Konovalov, Y., Martin, C., Payne, A.J., Pollard, D., Price, S., Ruckamp, M., Saito, F., Sugiyama, S., S., , and Zwinger, T., Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP-HOM), The Cryosphere, 2 (2008), 95–108.Google Scholar
[24]Payne, A.J. and Baldwin, D.J., Analysis of ice-flow instabilities identified in the EISMINT intercomparison exercise, Annals of Glaciology, 30 (2000), 204–210.Google Scholar
[25]Payne, A.J., Huybrechts, P., Abe-Ouchi, A., Calov, R., Fastook, J.L., Greve, R., Marshall, S.J., Marsiat, I., Ritz, C., Tarasov, L., and Thomassen, M.P.A., Results from the EISMINT model intercomparison: the effects of thermomechanical coupling, J. Glaciol., 46 (2000), 227–238.Google Scholar
[26]Price, S., Conway, H., and Waddington, E.D., A full-stress, thermomechanical flow band model using the finite volume method, J. Geophys. Res., 112 (2007), F03021, doi:10.1029/2006JF000725.Google Scholar
[27]Rutt, I.C., Hagdorn, M., Hulton, N.R.J., and Payne, A.J., The Glimmer community ice sheet model, J. Geophys. Res., 114 (2009), F02004.Google Scholar
[28]Shannon, S.R., Payne, A.J., Bartholomew, I.D., van den Broeke, M.R., Edwards, T.L., Fettweis, X., Gagliardini, O., Gillet-Chaulet, F., Goelzer, H., Hoffman, M.J., Huybrechts, P., Mair, D., Nienow, P., Perego, M., Price, S.F., Smeets, C.J.P., Sole, A.J., van de Wal, R.S.W., and Zwinger, T., Enhanced basal lubrication and contribution of the Greenland ice sheet to future sea-level rise, PNAS, in press (2013), doi: 10.1073/pnas.1212647110.CrossRefGoogle ScholarPubMed
[29]Raymond, C.F., Deformation in the vicinity of ice divides, J. Glaciol., 29 (1983), 357–373.CrossRefGoogle Scholar
[30]Saito, F., Abe-Ouchi, A., and Blatter, H., European Ice Sheet Modelling Initiative (EISMINT) model intercomparison experiments with first-order mechanics. J. Geophys. Res., 111(F2) (2006), F02012.Google Scholar
[31]Schoof, C. and Hindmarsh, R.C.A., Thin-Film Flows with Wall Slip: An Asymptotic Analysis of Higher Order Glacier Flow Models, Quarterly J. Mech. & App. Math., 63(1) (2010), 73–114.Google Scholar
[32]Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M., and Miller, H.L. (eds.), Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2007.Google Scholar
[33]Stocker, T.F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P.M. (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, United Kingdom and New York, NY, USA, 2013.Google Scholar
[34]Vaughan, D.G., Corr, H.F.J., Doake, C.S.M., and Waddington, E. D., Distortion of isochronous layers in ice revealed by ground-penetrating radar, Nature, 398 (1999), 323–326.Google Scholar
[35]Zhang, H., Ju, L., Gunzburger, M., Ringler, T., and Price, S., Coupled models and parallel simulations for three dimensional full-Stokes ice sheet modeling, Numer. Math. Theo. Meth. Appl.,4 (2011), 359–381.Google Scholar
[36]Zwinger, T., Greve, R., Gagliardini, O., Shiraiwa, T., and Lyly, M., A full Stokes-flow thermo-mechanical model for firn and ice applied to the Gorshkov crater glacier, Kamchatka, Ann. Glaciol., 45 (2007), 29–37.CrossRefGoogle Scholar