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Ice Volume and Subglacial Topography for Western Canadian Glaciers from Mass Balance Fields, Thinning Rates, and a Bed Stress Model

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  • 1 * Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, British Columbia, Canada
  • | 2 Pacific Climate Impacts Consortium, University of Victoria, Victoria, British Columbia, Canada
  • | 3 Centre for Climate and Cryosphere, University of Innsbruck, Innsbruck, Austria
  • | 4 Natural Resources and Environmental Studies Institute, University of Northern British Columbia, Prince George, British Columbia, Canada
  • | 5 Department of Geography, University of Zurich, Zurich, Switzerland, and Institut für Kartographie, Technische Universität Dresden, Dresden, Germany
  • | 6 ** Université de Toulouse–OMP/LEGOS, and Centre National de la Recherche Scientifique–LEGOS, Toulouse, France
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Abstract

A method is described to estimate the thickness of glacier ice using information derived from the measured ice extent, surface topography, surface mass balance, and rate of thinning or thickening of the ice column. Shear stress beneath an ice column is assumed to be simply related to ice thickness and surface slope, as for an inclined slab, but this calculation is cast as a linear optimization problem so that a smoothness regularization can be applied. Assignment of bed stress is based on the flow law for ice and a mass balance calculation but must be preceded by delineation of the ice flow drainage basin. Validation of the method is accomplished by comparing thickness estimates to the known thickness generated by a numerical ice dynamics model. Once validated, the method is used to estimate the subglacial topography for all glaciers in western Canada that lie south of 60°N. Adding the present ice volume of each glacier gives the estimated total volume as 2320 km3, equivalent to 5.8 mm of sea level rise. Taking the glaciated area as 26 590 km2 gives the average glacier thickness as 87.2 m. A detailed error analysis indicates that systematic errors are likely to increase the estimated sea level rise and when random errors are included the combined result is 6.3 ± 0.6 mm or, expressed as ice volume, 2530 ± 220 km3.

Corresponding author address: Garry K. C. Clarke, Earth, Ocean and Atmospheric Sciences, University of British Columbia, 6339 Stores Road, Vancouver BC V6T 1Z4, Canada. E-mail: clarke@eos.ubc.ca

Abstract

A method is described to estimate the thickness of glacier ice using information derived from the measured ice extent, surface topography, surface mass balance, and rate of thinning or thickening of the ice column. Shear stress beneath an ice column is assumed to be simply related to ice thickness and surface slope, as for an inclined slab, but this calculation is cast as a linear optimization problem so that a smoothness regularization can be applied. Assignment of bed stress is based on the flow law for ice and a mass balance calculation but must be preceded by delineation of the ice flow drainage basin. Validation of the method is accomplished by comparing thickness estimates to the known thickness generated by a numerical ice dynamics model. Once validated, the method is used to estimate the subglacial topography for all glaciers in western Canada that lie south of 60°N. Adding the present ice volume of each glacier gives the estimated total volume as 2320 km3, equivalent to 5.8 mm of sea level rise. Taking the glaciated area as 26 590 km2 gives the average glacier thickness as 87.2 m. A detailed error analysis indicates that systematic errors are likely to increase the estimated sea level rise and when random errors are included the combined result is 6.3 ± 0.6 mm or, expressed as ice volume, 2530 ± 220 km3.

Corresponding author address: Garry K. C. Clarke, Earth, Ocean and Atmospheric Sciences, University of British Columbia, 6339 Stores Road, Vancouver BC V6T 1Z4, Canada. E-mail: clarke@eos.ubc.ca
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