Abstract
The application of two different methods for the computation of the age of ice is discussed within the frame of numerical ice sheet modelling. The first method solves the purely advective equation for the age field in the Eulerian frame, which requires the addition of a numerical diffusion term to stabilize the solution and therefore produces arbitrary results in a near-basal boundary layer. The second method makes more efficient use of the simplicity of the equation in the Lagrangian frame by tracing particle paths in the flowing ice body, and it does without artificial diffusion.
We compute the age field for the Antarctic ice sheet with both methods for a time-dependent simulation driven by a 242200 year surface temperature history derived from stable isotope data of the Vostok deep ice core, and discuss the differences of the age computation schemes. Emphasis is put on two regions: (i) western Dronning Maud Land (DML), where reconnaissance for a deep ice core within the European Project for Ice Coring in Antarctica (EPICA) is currently carried out, and (ii) the eastern part of central East Antarctica with the deep-ice-core locations Vostok and Dome C (the former completed, the latter currently drilled within EPICA). The Eulerian scheme provides good results except for the lower parts of the ice sheet where the numerical diffusion falsifies the computed ages. The particletracing scheme does not show this shortcoming; however, it yields ages generally somewhat too small because it does not yet account for the time-dependence of the ice flow.
Preview
Unable to display preview. Download preview PDF.
References
Calov, R. and K. Hutter (1997) Large scale motion and temperature distributions in land based ice shields — the Greenland Ice Sheet in response to various climatic scenarios. Arch. Mech., 49 (5), 919–962.
Calov, R., A. Savvin, R. Greve, I. Hansen and K. Hutter (1998) Simulation of the Antarctic ice sheet with a three-dimensional polythermal ice sheet model, in support of the EPICA project. Ann. Glaciol., 27, 201–206.
Dansgaard, W. and S. J. Johnsen (1969) A flow model and a time scale for the ice core from Camp Century, Greenland. J. Glaciol., 8 (53), 215–223.
Drewry, D. J. (1983) Antarctica: Glaciological and geophysical folio. Scott Polar Research Institute, University of Cambridge.
Greve, R. (1997a) A continuum-mechanical formulation for shallow polythermal ice sheets. Phil. Trans. R. Soc. Lond., A 355, 921–974.
Greve, R. (1997b) Application of a polythermal three-dimensional ice sheet model to the Greenland Ice Sheet: Response to steady-state and transient climate scenarios. J. Climate, 10 (5), 901–918.
Greve, R., M. Weis and K. Hutter (1998) Palaeoclimatic evolution and present conditions of the Greenland ice sheet in the vicinity of Summit: An approach by large-scale modelling. Paleoclimates, 2 (2–3), 133–161.
Hutter, K. (1982) A mathematical model of polythermal glaciers and ice sheets. J. Geophys. Astrophys. Fluid Dyn. 21, 201–224.
Hutter, K. (1993) Thermo-mechanically coupled ice sheet response. Cold, polythermal, temperate. J. Glaciol., 39 (131), 65–86.
Huybrechts, P. (1993) Glaciological modelling of the Late Cenozoic East Antarctic ice sheet: stability or dynamism? Geografiska Annaler, 75 A (4), 221–238.
Huybrechts, P. (1994) The present evolution of the Greenland ice sheet: an assessment by modelling. Global Planet. Change, 9, 39–51.
Imbrie, J., J. D. Hays, D. G. Martinson, A. McIntyre, A. C. Mix, J. J. Morley, N. G. Pisias, W. L. Prell and N. J. Shackleton (1984) The orbital theory of Pleistocene climate: Support from a revised chronology of the marine δ 18O record. In: A. Berger et. al. (eds.), Milankovitch and climate, part I, D. Reidel Publishing Company, Dordrecht, Holland, 269–305 (NATO ASI Series C: Mathematical and Physical Sciences 126).
Jouzel, J. and 16 others (1993) Extending the Vostok ice-core record of paleoclimate to the penultimate glacial period. Nature, 364, 407–412.
Jouzel, J., K. Hammer, H. Miller, G. Orombelli, D. Peel and B. Stauffer (1994) European project for ice coring in Antarctica. Science Plan. [Available from Laboratoire de Modélisation du Climat et de l’Environnement, CEA/DSM SE Saclay, F-91191 Gif sur Yvette Cedex, France.]
Jouzel, J. and 14 others (1996) Climatic interpretation of the recently extended Vostok ice records. Climate Dynamics, 12, 513–521.
Mügge, B. (1998) Eisalterberechnung im antarktischen Eisschild mit einem Algorithmus zur Teilchenverfolgung. Diploma thesis, Institut für Mechanik, Technische Universität Darmstadt, Germany.
Reeh, N. (1991) Parameterization of melt rate and surface temperature on the Greenland Ice Sheet. Polarforschung, 59 (3), 113–128.
Salamatin, A. N., V. Y. Lipenkov, N. I. Barkov, J. Jouzel, J. R. Petit and D. Raynaud (1998) Ice core age dating and paleothermometer calibrations based on isotope and temperature profiles from deep boreholes at Vostok Station (East Antarctica). J. Geophys. Res., 103 (D8), 8963–8977.
Savvin, A. (1999) Grenzschichttheorie nichtlinearer Kriechströmungen und ihre Anwendung auf das EPICA-Vorhaben. Ph.D. thesis, Institut für Mechanik, Technische Universität Darmstadt, Germany (received 14 April 1999, accepted 28 April 1999).
Savvin, A., R. Greve, R. Calov, B. Mügge and K. Hutter (1999) Simulation of the Antarctic ice sheet with a 3-d polythermal ice-sheet model, in support of the EPICA project. Part II: Nested high-resolution treatment of Dronning Maud Land. Ann. Glaciol., 30 (submitted).
Steinhage, D. (1999) Ph.D. thesis in preparation, Alfred-Wegener-Institut für Polar-und Meeresforschung, Bremerhaven, Germany.
Törnig, W. and P. Spellucci (1990) Numerische Mathematik für Ingenieure und Physiker. Band 2: Numerische Methoden der Analysis. Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag
About this paper
Cite this paper
Mügge, B., Savvin, A., Calov, R., Greve, R. (1999). Numerical age computation of the antarctic ice sheet for dating deep ice cores. In: Hutter, K., Wang, Y., Beer, H. (eds) Advances in Cold-Region Thermal Engineering and Sciences. Lecture Notes in Physics, vol 533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104191
Download citation
DOI: https://doi.org/10.1007/BFb0104191
Received:
Accepted:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66333-1
Online ISBN: 978-3-540-48410-3
eBook Packages: Springer Book Archive