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A FORCE BALANCE ANALYSIS OVER THE LOWER REACHES OF COLUMBIA GLACIER, ALASKA DURING ITS RAPID RETREAT

O'NEEL, SHAD  INSTAAR.
Pfeffer, Tad  INSTAAR.
Krimmel, Robert  USGS.
Meier, Mark  INSTAAR.

Tidewater glaciers are known to undergo cycles of slow advance and rapid retreat (Post, 1975). A mass balance deficit may initiate the retreat, but observational and modeling evidence suggests that retreats are largely controlled by factors other than climate forcing (e.g. Vieli and others, 2001). This is nicely illustrated by the state of Alaskan tidewater glaciers today: many tidewater glaciers (i.e. Glacier Bay; Hunter, 1997) initiated rapid retreat phases around the turn of the 20th century, Columbia and LeConte Glaciers (Krimmel, 2001; O’Neel and others, 2001) are in the midst of rapid retreat today, while Taku and Hubbard Glaciers continue to undergo slow advance (Motyka and others, 2003). All these glaciers are located in south-central or southeast Alaska, thus experience roughly similar mass balance trends.

During retreat phase, a tidewater glacier may retreat on the order of 1-2 km yr-1, concurrent with dramatic increases in ice velocity (Krimmel, 2001). Mass loss is dominantly through calving, rather than ablation. Catastrophic retreats of this style are thought to be irreversible (e.g. Post, 1975; Meier and Post, 1987) until the terminus retreats to a position above local sea level. Understanding the dynamics of such systems is crucial to our comprehension of rapid retreats, applicable to modern tidewater glacier retreats as well as historical ice sheet collapse (e.g. van der Veen, 1997). Analysis of forces that both propel and restrain tidewater glaciers and the evolution of forces through a retreat provide insight into the processes governing retreats.

We present a top down force balance analysis is performed over the lower reaches of Columbia Glacier following van der Veen and Whillans (1989) and making the assumption of depth-independent strain. The assumption is validated because the deformation component of flow at Columbia Glacier is known to be small (e.g. Meier and Post, 1987, Meier and others, 1994 [direct borehole observation]). In this analysis, total stress is partitioned into lithostatic and resistive components in the following way:

where basal drag ( ) balances the sum of the driving stress ( ), along flow stress gradients ( ), and lateral drag ( ). Stresses are related to surface strain rates via the constitutive law, and strain rates are calculated from surface velocities. Surface velocities are derived from aerial photogrammetry over a time interval spanning 1957 to 2000 (Krimmel, 2001); our analysis covers only the latter part of this record.

Also necessary is ice thickness at each measurement point. The intensely fracture glacier and temperate ice have prevented reliable ice thickness measurements using radar or seismic techniques. We present a new bed geometry estimation using a flux divergence analysis of surface velocity (Rassmussen, 1989) over the time interval 1988 to 2000. Forebay bathymetry performed in 1995, 1997 (Krimmel, 2001) and 2003 (D. Trabant, unpublished data) are used to constrain the bed estimate. The calculation suggests the glacier has eroded a large over deepening behind a constriction near the present location of the terminus. This constriction and overdeepened area create both large driving and resistive stresses as ice is squeezed through it.



Preliminary analysis suggests that longitudinal stress gradients are important to the dynamics of Columbia Glacier during this phase of the retreat. While important to the shape of the transverse velocity profile, lateral drag only accounts for ~ 25% of resistance to driving stress in the terminus region. The large surface area of the bed provides much greater resistance to ice flow. When performed over the entire interval, the analysis shows the time dependence of all stress components in the study area.

REFERENCES
Hunter, L. E. (1997) Tidewater terminus dynamics in Glacier Bay, Alaska. In van der Veen, C.J. (ed.). Calving Glaciers: report of a workshop, February 28-March 2, 1997. BPRC Report No. 15, Byrd Polar Research Center, The Ohio State University, Columbus, Ohio, 85-94.



Krimmel, R. (2001). Photogrammetric data set, 1957-2000, and bathymetric measurements for Columbia Glacier, Alaska. USGS Water-Resources Investigations Report 01-4089, 40 pp.



Meier, M F. and A. Post. 1987. Fast tidewater glaciers. J. Geophys. Res., 92(B9), 9051-9058.



Motyka, R.J. and Echelemeyer, K.E. (2003) Taku Glacier (Alaska, U.S.A.) on the move again: active deformation of proglacial sediments. J. Glaciol. 49(164), p. 50-58.



O’Neel, S., Echelmeyer, K.A., and Motyka, R.J. 2001. Short-term flow dynamics of a retreating tidewater glacier, LeConte Glacier, Alaska, U.S.A. J. Glaciol., 47(159), 567-578.



Post, A. 1975. Preliminary hydrography and historic terminal changes of Columbia Glacier, Alaska. U.S. Geol. Sur. Hydrol. Invest. Atlas HA-559. (3 maps, scale 1:10,000).



Rasmussen, A.L. (1989). Surface velocity variations of the lower part of Columbia Glacier, Alaska, 1977-1981. U.S.G.S. Prof. Paper. 1258-H. 52 pp.



Van der Veen, C.J., and Whillans, I.M. (1989). Force budget: I. Theory and numerical methods. J. Glac.35(119). P. 53-60.



Van der Veen, C.J. 1997. Calving Glaciers Report of a workshop, February 28-March 2, 1997. BPRC Report No. 15, Byrd Polar Research Center, The Ohio State University, Columbus, Ohio, 194 p.



Vieli, A., Funk, M., and Blatter, H. (2001). Tidewater glaciers: frontal flow acceleration and basal sliding. J. Glaciol. 47(159), p. 595-606.



Figure 1. equation to be inserted into abstract


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