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

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

Abstract

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 behaviormore »« less

Authors:

^[1];

^[1]

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

Publication Date:: 2019-08-02

Sponsoring Org.:: USDOE

OSTI Identifier:: 1561406

Alternate Identifier(s):: OSTI ID: 1561407

Resource Type:: Published Article

Journal Name:: Journal of Geophysical Research. Earth Surface

Additional Journal Information:: Journal Name: Journal of Geophysical Research. Earth Surface Journal Volume: 124 Journal Issue: 8; Journal ID: ISSN 2169-9003

Publisher:: American Geophysical Union (AGU)

Country of Publication:: United States

Language:: English

Citation Formats


                    Bassis, J. N., and Ultee, L. A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers.  United States: N. p., 2019. 
Web.  doi:10.1029/2019JF005160.

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                    Bassis, J. N., & Ultee, L. A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers.  United States.  https://doi.org/10.1029/2019JF005160

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                    Bassis, J. N., and Ultee, L. Fri .  
"A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers".  United States.  https://doi.org/10.1029/2019JF005160.

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@article{osti_1561406,

  title        = {A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers},

  author       = {Bassis, J. N. and Ultee, L.},

  abstractNote = {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.},

  doi          = {10.1029/2019JF005160},

  journal      = {Journal of Geophysical Research. Earth Surface},

  number       = 8,

  volume       = 124,

  place        = {United States},

  year         = {2019},

  month        = {8}

}

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

Abstract

Citation Formats

A physically based calving model applied to marine outlet glaciers and implications for the glacier dynamics journal, January 2010

Rapid Changes in Ice Discharge from Greenland Outlet Glaciers journal, March 2007

Challenges to Understanding the Dynamic Response of Greenland's Marine Terminating Glaciers to Oceanic and Atmospheric Forcing journal, August 2013

Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice journal, November 2011

Evolving Environmental and Geometric Controls on Columbia Glacier's Continued Retreat journal, July 2018

A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials journal, January 2003

Brittle failure of ice journal, December 2001

Relating the occurrence of crevasses to surface strain rates journal, January 1993

Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA journal, January 2012

A consistent thin-layer theory for Bingham plastics journal, July 1999

Fracture of Antarctic shelf ice: FRACTURE OF ANTARCTIC SHELF ICE journal, January 2002

Stability of the Junction of an Ice Sheet and an Ice Shelf journal, January 1974

Critical Taper Model of Fold-And-Thrust Belts and Accretionary Wedges journal, May 1990

Dynamics of glacier calving at the ungrounded margin of Helheim Glacier, southeast Greenland: DYNAMICS OF GLACIER CALVING journal, June 2015

Fracture field for large-scale ice dynamics journal, January 2012

A numerical investigation of surface crevasse propagation in glaciers using nonlocal continuum damage mechanics: AN INVESTIGATION OF CREVASSE PROPAGATION journal, June 2013

Dynamic damage model of crevasse opening and application to glacier calving journal, January 2005

Ellipsis 3D: A particle-in-cell finite-element hybrid code for modelling mantle convection and lithospheric deformation journal, December 2006

Bottom Crevasses journal, January 1980

The future is Nye: an extension of the perfect plastic approximation to tidewater glaciers journal, September 2016

Ice-front variation and tidewater behavior on Helheim and Kangerdlugssuaq Glaciers, Greenland journal, January 2008

Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise: ACCELERATION OF ICE SHEET LOSS journal, March 2011

Heinrich events triggered by ocean forcing and modulated by isostatic adjustment journal, February 2017

Tidewater glaciers move at their own pace journal, December 2003

The link between climate warming and break-up of ice shelves in the Antarctic Peninsula journal, January 2000

Changes in the dynamics of marine terminating outlet glaciers in west Greenland (2000-2009): WEST GREENLAND OUTLET GLACIERS journal, June 2011

Termini of calving glaciers as self-organized critical systems journal, November 2014

Geometric Controls on Tidewater Glacier Retreat in Central Western Greenland journal, August 2018

Rapid retreat and acceleration of Helheim Glacier, east Greenland: ACCELERATION AND RETREAT OF HELHEIM GLACIER journal, November 2005

Marine ice-sheet dynamics. Part 1. The case of rapid sliding journal, February 2007

Contribution of Antarctica to past and future sea-level rise journal, March 2016

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 journal, March 2016

Fast tidewater glaciers journal, January 1987

Tidewater calving journal, January 1996

Diverse calving patterns linked to glacier geometry journal, July 2013

Calving processes and the dynamics of calving glaciers journal, June 2007

Calving Bay dynamics and ice sheet retreat up the St. Lawrence Valley system journal, January 1977

Evolution of basal crevasses links ice shelf stability to ocean forcing journal, January 2015

Evolving force balance at Columbia Glacier, Alaska, during its rapid retreat journal, January 2005

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 journal, September 2012

The statistical physics of iceberg calving and the emergence of universal calving laws journal, January 2011

A physically based calving model applied to marine outlet glaciers and implications for the glacier dynamics
journal, January 2010

Rapid Changes in Ice Discharge from Greenland Outlet Glaciers
journal, March 2007

Challenges to Understanding the Dynamic Response of Greenland's Marine Terminating Glaciers to Oceanic and Atmospheric Forcing
journal, August 2013

Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice
journal, November 2011

Evolving Environmental and Geometric Controls on Columbia Glacier's Continued Retreat
journal, July 2018

A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials
journal, January 2003

Brittle failure of ice
journal, December 2001

Relating the occurrence of crevasses to surface strain rates
journal, January 1993

Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA
journal, January 2012

A consistent thin-layer theory for Bingham plastics
journal, July 1999

Fracture of Antarctic shelf ice: FRACTURE OF ANTARCTIC SHELF ICE
journal, January 2002

Stability of the Junction of an Ice Sheet and an Ice Shelf
journal, January 1974

Critical Taper Model of Fold-And-Thrust Belts and Accretionary Wedges
journal, May 1990

Dynamics of glacier calving at the ungrounded margin of Helheim Glacier, southeast Greenland: DYNAMICS OF GLACIER CALVING
journal, June 2015

Fracture field for large-scale ice dynamics
journal, January 2012

A numerical investigation of surface crevasse propagation in glaciers using nonlocal continuum damage mechanics: AN INVESTIGATION OF CREVASSE PROPAGATION
journal, June 2013

Dynamic damage model of crevasse opening and application to glacier calving
journal, January 2005

Ellipsis 3D: A particle-in-cell finite-element hybrid code for modelling mantle convection and lithospheric deformation
journal, December 2006

Bottom Crevasses
journal, January 1980

The future is Nye: an extension of the perfect plastic approximation to tidewater glaciers
journal, September 2016

Ice-front variation and tidewater behavior on Helheim and Kangerdlugssuaq Glaciers, Greenland
journal, January 2008

Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise: ACCELERATION OF ICE SHEET LOSS
journal, March 2011

Heinrich events triggered by ocean forcing and modulated by isostatic adjustment
journal, February 2017

Tidewater glaciers move at their own pace
journal, December 2003

The link between climate warming and break-up of ice shelves in the Antarctic Peninsula
journal, January 2000

Changes in the dynamics of marine terminating outlet glaciers in west Greenland (2000-2009): WEST GREENLAND OUTLET GLACIERS
journal, June 2011

Termini of calving glaciers as self-organized critical systems
journal, November 2014

Geometric Controls on Tidewater Glacier Retreat in Central Western Greenland
journal, August 2018

Rapid retreat and acceleration of Helheim Glacier, east Greenland: ACCELERATION AND RETREAT OF HELHEIM GLACIER
journal, November 2005

Marine ice-sheet dynamics. Part 1. The case of rapid sliding
journal, February 2007

Contribution of Antarctica to past and future sea-level rise
journal, March 2016

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
journal, March 2016

Fast tidewater glaciers
journal, January 1987

Tidewater calving
journal, January 1996

Diverse calving patterns linked to glacier geometry
journal, July 2013

Calving processes and the dynamics of calving glaciers
journal, June 2007

Calving Bay dynamics and ice sheet retreat up the St. Lawrence Valley system
journal, January 1977

Evolution of basal crevasses links ice shelf stability to ocean forcing
journal, January 2015

Evolving force balance at Columbia Glacier, Alaska, during its rapid retreat
journal, January 2005

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
journal, September 2012

The statistical physics of iceberg calving and the emergence of universal calving laws
journal, January 2011