Skip to main content

Numerical simulations of cyclic behaviour in the Parallel Ice Sheet Model (PISM)

  • Ward J.J. Van Pelt (a1) and Johannes Oerlemans (a1)

Numerical experiments are conducted on a synthetic topography with a three-dimensional thermomechanically coupled ice-sheet model, the Parallel Ice Sheet Model (PISM). Within the model, combined stress balances are connected to evolving thermodynamics and hydrology. The sensitivity of cyclic behaviour to changes in sliding-law parameters and the climate input is studied. Multiple types of oscillations were found, with strong variations in both amplitude and frequency. A physical description is given, in which these variations and transitions from one oscillation type to another are linked to the interplay of stresses, heat transport and hydrological processes. High-frequency oscillations (period 114-169 years), which are shown to have a major impact on ice velocities and a small effect on the ice volume, are related to variations in the water distribution at the base. Low-frequency cycles (period 1000+ years), which have a major impact on both velocities and ice volume, are linked to changes in the thermal regime. Oscillation characteristics are shown to be strongly sensitive to changes in sliding-law parameters and the prescribed surface temperature and mass balance. Incorporating a surface-height dependence of the mass balance is shown to provide an additional feedback, which may induce long- period oscillations.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Numerical simulations of cyclic behaviour in the Parallel Ice Sheet Model (PISM)
      Available formats
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Numerical simulations of cyclic behaviour in the Parallel Ice Sheet Model (PISM)
      Available formats
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Numerical simulations of cyclic behaviour in the Parallel Ice Sheet Model (PISM)
      Available formats
Hide All
Alley, RB, Anandakrishnan, S, Bentley, CR and Lord, N (1994) A water- piracy hypothesis for the stagnation of Ice Stream C, Antarctica. Ann. Glaciol., 20, 187-194
Anandakrishnan, S and Alley, RB (1997) Stagnation of Ice Stream C, West Antarctica by water piracy. Geophys. Res. Lett., 24(3), 265-268
Anandakrishnan, S, Alley, RB, Jacobel, RW and Conway, H (2001) The flow regime of Ice Stream C and hypotheses concerning its recent stagnation. In Alley, RB and Bindschadler, RA eds. The West Antarctic ice sheet: behavior and environment. American Geophysical Union, Washington, DC, 283-296
Aschwanden, A and Blatter, H (2009) Mathematical modeling and numerical simulation of polythermal glaciers. J. Geophys. Res., 114(F1), F01027 (doi: 10.1029/2008JF001028)
Bindschadler, R and Vornberger, P (1998) Changes in the West Antarctic ice sheet since 1963 from declassified satellite photography. Science, 279(5351), 689-692
Bond, G and 13 others (1992) Evidence for massive discharges of icebergs into the North Atlantic Ocean during the last glacial period. Nature, 360(6401), 245-249
Bougamont, M, Tulaczyk, S and Joughin, I (2003) Response of subglacial sediments to basal freeze-on: 2. Application in numerical modeling of the recent stoppage of Ice Stream C, West Antarctica. J. Geophys. Res., 108(B4), 2223 (doi: 10.1019/2002JB001936)
Budd, WF (1975) A first simple model for periodically self-surging glaciers. J. Glaciol., 14(70), 3-21
Bueler, E and Brown, J (2009) Shallow shelf approximation as a ‘sliding law’ in a thermomechanically coupled ice sheet model. J. Geophys. Res., 114(F3), F03008 (doi: 10.1029/2008JF001179)
Bueler, E, Brown, J and Lingle, C (2007) Exact solutions to the thermomechanically coupled shallow-ice approximation: effective tools for verification. J. Glaciol., 53(182), 499-516 (doi: 10.3189/002214307783258396)
Calov, R, Ganopolski, A, Petoukhov, V, Claussen, M and Greve, R (2002) Large-scale instabilities of the Laurentide ice sheet simulated in a fully coupled climate-system model. Geophys. Res. Lett., 29(24), 2216 (doi: 10.1029/2002GL016078)
Calov, R and 9 others (2010) Results from the Ice-Sheet Model Intercomparison Project-Heinrich Event INtercOmparison (ISMIP HEINO). J. Glaciol., 56(197), 371-383
Clarke, GKC (1976) Thermal regulation of glacier surging. J. Glaciol., 16(74), 231-250
Clarke, GKC (1987) Fast glacier flow: ice streams, surging and tidewater glaciers. J. Geophys. Res., 92(B9), 8835-8841
Clarke, GKC (2005) Subglacial processes. Annu. Rev. Earth Planet. Sci., 33, 247-276 (doi: 10.1146/ 092203.122621)
Clarke, GKC, Nitsan, U and Paterson, WSB (1977) Strain heating and creep instability in glaciers and ice sheets. Rev. Geophys. Space Phys., 15(2), 235-247
Clarke, GKC, Collins, SG and Thompson, DE (1984) Flow, thermal structure, and subglacial conditions of a surge-type glacier. Can. J. Earth Sci., 21(2), 232-240
Clarke, GKC, Marshall, SJ, Hillaire-Marcel, C, Bilodeau, G and Veiga- Pires, C (1999) A glaciological perspective on Heinrich events. In Clark, PU, Webb, RS and Keigwin, LD eds. Mechanisms of global climate change at millennial time scales. American Geophysical Union, Washington, DC, 243-262
Dowdeswell, JA, Hamilton, GS and Hagen, JO (1991) The duration of the active phase on surge-type glaciers: contrasts between Svalbard and other regions. J. Glaciol., 37(127), 388-400
Dowdeswell, JA, Hodgkins, R, Nuttall, A-M, Hagen, JO and Hamilton, GS (1995) Mass balance change as a control on the frequency and occurrence of glacier surges in Svalbard, Norwegian High Arctic. Geophys. Res. Lett., 22(21), 2909-2912
Dunse, T, Greve, R, Schuler, TV and Hagen, JO (2011) Permanent fast flow versus cyclic surge behaviour: numerical simulations of the Austfonna ice cap, Svalbard. J. Glaciol., 57(202), 247-259 (doi: 10.3189/002214311796405979)
Eisen, O, Harrison, WD and Raymond, CF (2001) The surges of Variegated Glacier, Alaska, USA, and their connection to climate and mass balance. J. Glaciol., 47(158), 351-358 (doi: 10.3189/172756501781832179)
Eisen, O, Harrison, WD, Raymond, CF, Echelmeyer, KA, Bender, GA and Gorda, LD (2005) Variegated Glacier, Alaska, USA: a century of surges. J. Glaciol., 51(174), 399-406 (doi: 10.3189/172756505781829250)
Fahnestock, MA, Scambos, TA, Bindschadler, RA and Kvaran, G (2000) A millennium of variable ice flow recorded by the Ross Ice Shelf, Antarctica. J. Glaciol., 46(155), 652-664 (doi: 10.3189/172756500781832693)
Flowers, GE and Clarke, GKC (2002) A multicomponent coupled model of glacier hydrology: 1. Theory and synthetic examples. J. Geophys. Res., 107(B11), 2287 (doi: 10.1029/2001JB001122)
Fowler, AC (1997) Mathematical models in the applied sciences. Cambridge University Press, Cambridge
Fowler, AC (2001) Modelling the flow of glaciers and ice sheets. In Straughan, B, Greve, R, Ehrentraut, H and Wang, Y eds. Continuum mechanics and applications in geophysics and the environment. Springer-Verlag, Berlin, 276-304
Fowler, AC, Murray, T and Ng, FSL (2001) Thermally controlled glacier surging. J. Glaciol., 47(159), 527-538 (doi: 10.3189/172756501781831792)
Goldberg, DN (2011) A variationally derived, depth-integrated approximation to a higher-order glaciological flow model. J. Glaciol., 57(201), 157-170 (doi: 10.3189/002214311795306763)
Greve, R, Takahama, R and Calov, R (2006) Simulation of large-scale ice-sheet surges: the ISMIP Heino experiments. Polar Meteorol. Glaciol., 20, 1-15
Harrison, WD and Post, AS (2003) How much do we really know about glacier surging? Ann. Glaciol., 36, 1-6 (doi: 10.3189/172756403781816185)
Heinrich, H (1988) Origin and consequences of cyclic ice rafting in the northeast Atlantic Ocean during the past 130 000 years. Quat. Res, 29(2), 142-152
Hutter, K (1983) Theoretical glaciology; material science of ice and the mechanics of glaciers and ice sheets. D Reidel, Dordrecht/Terra Scientific, Tokyo
Jacobel, RW, Scambos, TA, Nereson, NA and Raymond, CF (2000) Changes in the margin of Ice Stream C, Antarctica. J. Glaciol., 46(152), 102-110 (doi: 10.3189/172756500781833485)
Jiskoot, H, Murray, T and Boyle, P (2000) Controls on the distribution of surge-type glaciers in Svalbard. J. Glaciol., 46(154), 412-422 (doi: 10.3189/172756500781833115)
Jóhannesson, T, Raymond, CF and Waddington, ED (1989) A simple method for determining the response time of glaciers. In Oerlemans, J ed. Glacier fluctuations and climatic change. Kluwer Academic, Dordrecht, 343-352
Kamb, B (1987) Glacier surge mechanism based on linked cavity configuration of the basal water conduit system. J. Geophys. Res., 92(B9), 9083-9100
Kamb, B and 7 others (1985) Glacier surge mechanism: 19821983 surge of Variegated Glacier, Alaska. Science, 227(4686), 469-479
Lingle, CS and Fatland, DR (2003) Does englacial water storage drive temperate glacier surges? Ann. Glaciol., 36, 14-20 (doi: 10.3189/172756403781816464)
Lüthi, M, Funk, M, Iken, A, Gogineni, S and Truffer, M (2002) Mechanisms of fast flow in Jakobshavn Isbr?, West Greenland. Part III. Measurements of ice deformation, temperature and crossborehole conductivity in boreholes to the bedrock. J. Glaciol., 48(162), 369-385 (doi: 10.3189/172756502781831322)
MacAyeal, DR (1989) Large-scale ice flow over a viscous basal sediment: theory and application to Ice Stream B, Antarctica. J. Geophys. Res., 94(B4), 4071-4087 (doi: 10.1029/88JB03848)
MacAyeal, DR (1993) Binge/purge oscillations of the Laurentide ice sheet as a cause of the North Atlantic’s Heinrich events. Paleoceanography, 8(6), 775-784
Marshall, SJ and Clarke, GKC (1997) A continuum mixture model of ice stream thermomechanics in the Laurentide ice sheet.1. Theory. J. Geophys. Res., 102(B9), 20 599-20 614
Morland, LW and Johnson, IR (1980) Steady motion of ice sheets. J.Glaciol., 25(92), 229-246
Murray, T and 6 others (2000) Glacier surge propagation by thermal evolution at the bed. J. Geophys. Res., 105(B6), 13 491-13 507
Murray, T, Strozzi, T, Luckman, A, Jiskoot, H and Christakos, P (2003) Is there a single surge mechanism? Contrasts in dynamics between glacier surges in Svalbard and other regions. J. Geophys. Res., 108(B5), 2237 (doi: 10.1029/2002JB001906)
Oerlemans, J (1983) A numerical study on cyclic behaviour of polar ice sheets. Tellus, 35A(2), 81-87
Oerlemans, J and Van der Veen, CJ (1984) Ice sheets and climate. D Reidel, Dordrecht
Papa, BD, Mysak, LA and Wang, Z (2006) Intermittent ice sheet discharge events in northeastern North America during the last glacial period. Climate Dyn., 26(2-3), 201-216 (doi: 10.1007/s00382-005-0078-4)
Payne, AJ (1995) Limit cycles in the basal thermal regime of ice sheets. J. Geophys. Res., 100(B3), 4249-4263
Payne, AJ (1999) A thermomechanical model of ice flow in West Antarctica. Climate Dyn., 15(2), 115-125
Payne, AJ and Dongelmans, PW (1997) Self-organization in the thermomechanical flow of ice sheets. J. Geophys. Res., 102(B6), 12 219-12 233 (doi: 10.1029/97JB00513)
Pham, QT (1995) Comparison of general-purpose finite-element methods for the Stefan problem. Num. Heat Trans. B, 27(4), 417-435 (doi: 10.1080/10407799508914965)
Retzlaff, R and Bentley, CR (1993) Timing of stagnation of Ice Stream C, West Antarctica, from short-pulse radar studies of buried surface crevasses. J. Glaciol., 39(133), 553-561
Robin, GdeQ (1955) Ice movement and temperature distribution in glaciers and ice sheets. J. Glaciol., 2(18), 523-532
Rose, KE (1979) Characteristics of ice flow in Marie Byrd Land, Antarctica. J. Glaciol., 24(90), 63-75
Schoof, C (2006) A variational approach to ice stream flow. J. Fluid Mech., 556, 227-251 (doi: 10.1017/S0022112006009591)
Tulaczyk, SM, Kamb, B and Engelhardt, HF (2000a) Basal mechanics of Ice Stream B, West Antarctica. I. Till mechanics. J. Geophys. Res., 105(B1), 463-481
Tulaczyk, SM, Kamb, B and Engelhardt, HF (2000b) Basal mechanics of Ice Stream B, West Antarctica. II. Undrained-plastic-bed model. J. Geophys. Res., 105(B1), 483-494
Weis, M, Greve, R and Hutter, K (1999) Theory of shallow ice shelves. Contin. Mech. Thermodyn., 11(1), 15-50 (doi: 10.1007/s001610050102)
Winkelmann, R and 6 others (2011) The Potsdam Parallel Ice Sheet Model (PISM-PIK) - Part 1: Model description. Cryosphere, 5(3), 715-726
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Glaciology
  • ISSN: 0022-1430
  • EISSN: 1727-5652
  • URL: /core/journals/journal-of-glaciology
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed