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

• Published in: Journal of climate Vol. 26; no. 12; pp. 4282 - 4303
• Main Authors: Clarke, Garry K. C., Anslow, Faron S., Jarosch, Alexander H., Radić, Valentina, Menounos, Brian, Bolch, Tobias, Berthier, Etienne
• Format: Journal Article
• Language: English
• Published: Boston, MA American Meteorological Society 01-06-2013
• Subjects: Atmospheric sciences; Digital elevation models; Drainage basins; Earth Sciences; Earth, ocean, space; Error analysis; Errors; Estimates; Estimation methods; Exact sciences and technology; External geophysics; Freshwater; Geophysics. Techniques, methods, instrumentation and models; Glacial landforms; Glacier ice; Glacier thickness; Glaciers; Glaciohydrology; Ice; Ice cover; Ice sheets; Ice thickness; Ice volume; Marine; Mass; Mass balance; Mass balance of glaciers; Mathematical models; Methods; Mountain glaciers; Neural networks; Oceanography; Optimization; Physics; Problems; Random errors; Regularization; Remote sensing; Sciences of the Universe; Sea level; Sea level changes; Sea level rise; Shear stress; Smoothness; Snow. Ice. Glaciers; Stresses; Subglacial topography; Systematic errors; Thickness; Thinning; Topographical elevation; Topography; Water surface slope; Watersheds; Yield stress; Canada; Europe; Alps; North America; Greenland; ANW, Canada; Thinning; mass balance; thickness; topography; Glacier variation; Glacier balance; Glacier bed; Subpolar zone; North America; Computing method
• ISSN: 0894-8755; 1520-0442
• DOI: 10.1175/JCLI-D-12-00513.1

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 mmor, expressed as ice volume, 2530 ± 220 km³.