A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers

Bassis, J. N.; Ultee, L.

doi:10.1029/2019JF005160

A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers

Journal Article · Fri Aug 02 00:00:00 EDT 2019 · Journal of Geophysical Research. Earth Surface

DOI:https://doi.org/10.1029/2019JF005160· OSTI ID:1561406

^[1]; ^[1]

Department of Climate and Space Science and Engineering University of Michigan Ann Arbor MI USA

Projections of the growth and demise of ice sheets and glaciers require physical models of the processes governing flow and fracture of ice. The flow of glacier ice has been treated using increasingly sophisticated models. By contrast, fracture, the process ultimately responsible for half of the mass lost from ice sheets through iceberg calving, is often included using ad hoc parameterizations. In this study we seek to bridge this gap by introducing a model where ice obeys a power law rheology appropriate for intact ice below a yield strength. Above the yield strength, we introduce a separate rheology appropriate for the flow of heavily fractured ice, where ice deformation occurs more readily along faults and fractures. We show that, provided the motion of fractured ice is sufficiently rapid compared to that of intact ice, the behavior of glaciers depends solely on the rheology of intact ice and the yield strength of ice and is insensitive to the precise rheology of fractured ice. Moreover, assuming that glacier ice is unyielded allows us to bound the long‐term average rate of terminus advance, providing a first principles estimate of rates of retreat associated with the marine ice cliff instability. We illustrate model behavior using idealized geometries and climate forcing and show that the model not only exhibits realistic patterns of advance and retreat but also has the potential to exhibit hysteresis. This hysteresis could provide an explanation for the sudden onset of rapid retreat observed in marine‐terminating glaciers.

View Journal Article

Sponsoring Organization:: USDOE

OSTI ID:: 1561406

Alternate ID(s):: OSTI ID: 1561407

Journal Information:: Journal of Geophysical Research. Earth Surface, Journal Name: Journal of Geophysical Research. Earth Surface Journal Issue: 8 Vol. 124; ISSN 2169-9003

Publisher:: American Geophysical Union (AGU)Copyright Statement

Country of Publication:: United States

Language:: English

References (43)

A constitutive framework for predicting weakening and reduced buttressing of ice shelves based on observations of the progressive deterioration of the remnant Larsen B Ice Shelf: CONSTITUTIVE FRAMEWORK FOR ICE WEAKENING Borstad, Chris; Khazendar, Ala; Scheuchl, Bernd Geophysical Research Letters, Vol. 43, Issue 5 https://doi.org/10.1002/2015GL067365	journal	March 2016
Dynamics of glacier calving at the ungrounded margin of Helheim Glacier, southeast Greenland: DYNAMICS OF GLACIER CALVING Murray, Tavi; Selmes, Nick; James, Timothy D. Journal of Geophysical Research: Earth Surface, Vol. 120, Issue 6 https://doi.org/10.1002/2015JF003531	journal	June 2015
A numerical investigation of surface crevasse propagation in glaciers using nonlocal continuum damage mechanics: AN INVESTIGATION OF CREVASSE PROPAGATION Duddu, R.; Bassis, J. N.; Waisman, H. Geophysical Research Letters, Vol. 40, Issue 12 https://doi.org/10.1002/grl.50602	journal	June 2013
Dynamics of Ice Sheets and Glaciers Greve, Ralf; Blatter, Heinz Advances in Geophysical and Environmental Mechanics and Mathematics https://doi.org/10.1007/978-3-642-03415-2	book	December 2008
Brittle failure of ice Schulson, Erland M. Engineering Fracture Mechanics, Vol. 68, Issue 17-18 https://doi.org/10.1016/S0013-7944(01)00037-6	journal	December 2001
A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials Moresi, L.; Dufour, F.; Mühlhaus, H. -B. Journal of Computational Physics, Vol. 184, Issue 2 https://doi.org/10.1016/S0021-9991(02)00031-1	journal	January 2003
A consistent thin-layer theory for Bingham plastics Balmforth, N. J.; Craster, R. V. Journal of Non-Newtonian Fluid Mechanics, Vol. 84, Issue 1 https://doi.org/10.1016/S0377-0257(98)00133-5	journal	July 1999
Ellipsis 3D: A particle-in-cell finite-element hybrid code for modelling mantle convection and lithospheric deformation O’Neill, Craig; Moresi, Louis; Müller, Dietmar Computers & Geosciences, Vol. 32, Issue 10 https://doi.org/10.1016/j.cageo.2006.04.006	journal	December 2006
Calving processes and the dynamics of calving glaciers Benn, Douglas I.; Warren, Charles R.; Mottram, Ruth H. Earth-Science Reviews, Vol. 82, Issue 3-4 https://doi.org/10.1016/j.earscirev.2007.02.002	journal	June 2007
Evolution of basal crevasses links ice shelf stability to ocean forcing Bassis, J. N.; Ma, Y. Earth and Planetary Science Letters, Vol. 409 https://doi.org/10.1016/j.epsl.2014.11.003	journal	January 2015
Marine ice-sheet dynamics. Part 1. The case of rapid sliding Schoof, Christian Journal of Fluid Mechanics, Vol. 573 https://doi.org/10.1017/S0022112006003570	journal	February 2007
Tidewater calving Van Der Veen, С. J. Journal of Glaciology, Vol. 42, Issue 141 https://doi.org/10.1017/S0022143000004226	journal	January 1996
Bottom Crevasses Weertman, J. Journal of Glaciology, Vol. 25, Issue 91 https://doi.org/10.1017/S0022143000010418	journal	January 1980
Relating the occurrence of crevasses to surface strain rates Vaughan, David G. Journal of Glaciology, Vol. 39, Issue 132 https://doi.org/10.1017/S0022143000015926	journal	January 1993
Stability of the Junction of an Ice Sheet and an Ice Shelf Weertman, J. Journal of Glaciology, Vol. 13, Issue 67 https://doi.org/10.1017/S0022143000023327	journal	January 1974
The future is Nye: an extension of the perfect plastic approximation to tidewater glaciers Ultee, Lizz; Bassis, Jeremy Journal of Glaciology, Vol. 62, Issue 236 https://doi.org/10.1017/jog.2016.108	journal	September 2016
Fracture of Antarctic shelf ice: FRACTURE OF ANTARCTIC SHELF ICE Rist, M. A.; Sammonds, P. R.; Oerter, H. Journal of Geophysical Research: Solid Earth, Vol. 107, Issue B1 https://doi.org/10.1029/2000JB000058	journal	January 2002
Dynamic damage model of crevasse opening and application to glacier calving Pralong, A. Journal of Geophysical Research, Vol. 110, Issue B1 https://doi.org/10.1029/2004JB003104	journal	January 2005
Rapid retreat and acceleration of Helheim Glacier, east Greenland: ACCELERATION AND RETREAT OF HELHEIM GLACIER Howat, I. M.; Joughin, I.; Tulaczyk, S. Geophysical Research Letters, Vol. 32, Issue 22 https://doi.org/10.1029/2005GL024737	journal	November 2005
Evolving force balance at Columbia Glacier, Alaska, during its rapid retreat O'Neel, Shad Journal of Geophysical Research, Vol. 110, Issue F3 https://doi.org/10.1029/2005JF000292	journal	January 2005
Ice-front variation and tidewater behavior on Helheim and Kangerdlugssuaq Glaciers, Greenland Joughin, Ian; Howat, Ian; Alley, Richard B. Journal of Geophysical Research, Vol. 113, Issue F1 https://doi.org/10.1029/2007JF000837	journal	January 2008
Changes in the dynamics of marine terminating outlet glaciers in west Greenland (2000-2009): WEST GREENLAND OUTLET GLACIERS McFadden, Ellyn M.; Howat, Ian M.; Joughin, Ian Journal of Geophysical Research: Earth Surface, Vol. 116, Issue F2 https://doi.org/10.1029/2010JF001757	journal	June 2011
Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise: ACCELERATION OF ICE SHEET LOSS Rignot, E.; Velicogna, I.; van den Broeke, M. R. Geophysical Research Letters, Vol. 38, Issue 5 https://doi.org/10.1029/2011GL046583	journal	March 2011
A damage mechanics assessment of the Larsen B ice shelf prior to collapse: Toward a physically-based calving law: A CALVING LAW BASED ON DAMAGE MECHANICS Borstad, C. P.; Khazendar, A.; Larour, E. Geophysical Research Letters, Vol. 39, Issue 18 https://doi.org/10.1029/2012GL053317	journal	September 2012
Geometric Controls on Tidewater Glacier Retreat in Central Western Greenland Catania, G. A.; Stearns, L. A.; Sutherland, D. A. Journal of Geophysical Research: Earth Surface, Vol. 123, Issue 8 https://doi.org/10.1029/2017JF004499	journal	August 2018
Evolving Environmental and Geometric Controls on Columbia Glacier's Continued Retreat Enderlin, Ellyn M.; O'Neel, Shad; Bartholomaus, Timothy C. Journal of Geophysical Research: Earth Surface, Vol. 123, Issue 7 https://doi.org/10.1029/2017JF004541	journal	July 2018
Fast tidewater glaciers Meier, M. F.; Post, Austin Journal of Geophysical Research, Vol. 92, Issue B9 https://doi.org/10.1029/JB092iB09p09051	journal	January 1987
Tidewater glaciers move at their own pace Pfeffer, W. T. Nature, Vol. 426, Issue 6967 https://doi.org/10.1038/426602b	journal	December 2003
Contribution of Antarctica to past and future sea-level rise DeConto, Robert M.; Pollard, David Nature, Vol. 531, Issue 7596 https://doi.org/10.1038/nature17145	journal	March 2016
Heinrich events triggered by ocean forcing and modulated by isostatic adjustment Bassis, Jeremy N.; Petersen, Sierra V.; Mac Cathles, L. Nature, Vol. 542, Issue 7641 https://doi.org/10.1038/nature21069	journal	February 2017
Diverse calving patterns linked to glacier geometry Bassis, J. N.; Jacobs, S. Nature Geoscience, Vol. 6, Issue 10 https://doi.org/10.1038/ngeo1887	journal	July 2013
Termini of calving glaciers as self-organized critical systems Åström, J. A.; Vallot, D.; Schäfer, M. Nature Geoscience, Vol. 7, Issue 12 https://doi.org/10.1038/ngeo2290	journal	November 2014
The distribution of stress and velocity in glaciers and ice-sheets Nye, John Frederick Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 239, Issue 1216, p. 113-133 https://doi.org/10.1098/rspa.1957.0026	journal	February 1957
Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice Bassis, J. N.; Walker, C. C. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue 2140 https://doi.org/10.1098/rspa.2011.0422	journal	November 2011
Rapid Changes in Ice Discharge from Greenland Outlet Glaciers Howat, I. M.; Joughin, I.; Scambos, T. A. Science, Vol. 315, Issue 5818 https://doi.org/10.1126/science.1138478	journal	March 2007
Critical Taper Model of Fold-And-Thrust Belts and Accretionary Wedges Dahlen, F. A. Annual Review of Earth and Planetary Sciences, Vol. 18, Issue 1 https://doi.org/10.1146/annurev.ea.18.050190.000415	journal	May 1990
Challenges to Understanding the Dynamic Response of Greenland's Marine Terminating Glaciers to Oceanic and Atmospheric Forcing Straneo, Fiammetta; Heimbach, Patrick; Sergienko, Olga Bulletin of the American Meteorological Society, Vol. 94, Issue 8 https://doi.org/10.1175/BAMS-D-12-00100.1	journal	August 2013
A physically based calving model applied to marine outlet glaciers and implications for the glacier dynamics Nick, F. M.; Van Der Veen, C. J.; Vieli, A. Journal of Glaciology, Vol. 56, Issue 199 https://doi.org/10.3189/002214310794457344	journal	January 2010
The statistical physics of iceberg calving and the emergence of universal calving laws Bassis, J. N. Journal of Glaciology, Vol. 57, Issue 201 https://doi.org/10.3189/002214311795306745	journal	January 2011
The link between climate warming and break-up of ice shelves in the Antarctic Peninsula Scambos, Ted A.; Hulbe, Christina; Fahnestock, Mark Journal of Glaciology, Vol. 46, Issue 154 https://doi.org/10.3189/172756500781833043	journal	January 2000
Fracture field for large-scale ice dynamics Albrecht, Torsten; Levermann, Anders Journal of Glaciology, Vol. 58, Issue 207 https://doi.org/10.3189/2012JoG11J191	journal	January 2012
Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA Mcnabb, R. W.; Hock, R.; O’Neel, S. Journal of Glaciology, Vol. 58, Issue 212 https://doi.org/10.3189/2012JoG11J249	journal	January 2012
Calving Bay dynamics and ice sheet retreat up the St. Lawrence Valley system Thomas, R. H. Géographie physique et Quaternaire, Vol. 31, Issue 3-4 https://doi.org/10.7202/1000282ar	journal	January 1977

Similar Records

Glacier calving, dynamics, and sea-level rise. Final report

Technical Report · Sat Aug 01 00:00:00 EDT 1998 · OSTI ID:638181

A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers

Citation Formats

References (43)

Similar Records

Related Subjects