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AMUNDSON, JASON M  University of Alaska Fairbanks.
Iverson, Neal R  Iowa State University.

Glacial erosion plays an important role in landscape evolution, geochemical cycling, and uplift of mountain belts. Models of these processes are hindered by limited knowledge of the factors affecting glacial erosion rates. Glaciers erode bedrock primarily through abrasion and quarrying. Mechanical models demonstrate that abrasion rates depend on sliding velocity. There is little consensus, however, regarding the factors that control rates of quarrying, arguably the most important mechanism of erosion. Studies of quarrying mechanics suggest that quarrying rates should depend on water-pressure fluctuations at glacier beds. For convenience, however, most modelers neglect the role of water-pressure fluctuations and assume that erosion rates are a simple function of basal sliding velocity. Thus, there is strong motivation to test, over the large time and length scales of erosion models, if erosion rates can be adequately characterized with a simple rule based on sliding velocity.

Our hypothesis is that the difference in elevation between the floors of hanging valleys and their trunk valleys, herein called the step height, can be used to determine whether long-term erosion rates are proportional to sliding velocity. Hanging valleys form because tributary glaciers erode bedrock more slowly than trunk glaciers. Step height, which is easily measurable, is therefore an indicator of relative erosion rate. Thus, if the sliding velocities of former tributary and trunk glaciers can be estimated, step heights can be used to determine if and how sliding velocity and erosion rate are related.

We use a well-accepted approximation for basal shear stress, a widely applied empirical rule that relates basal shear stress to sliding speed, and mass continuity to express the sliding velocity of a valley glacier in terms of its area, width, and slope. This expression, when substituted into a power-law erosion rule (de/dt = C1Usn, where de/dt is erosion rate, Us is sliding speed, and C1 and n are constants), yields the step height as the product of a constant C2 and a variable Y that depends on drainage areas, widths, and slopes of tributary and trunk glaciers. Embedded in C2 are factors such as accumulation rate, the fraction of glacier speed due to sliding, effective normal stress on the bed and C1, which are assumed to be uniform and the same for tributary and trunk glaciers.

We studied 46 hanging valleys and their three trunk valleys in southern Jasper National Park, Alberta, Canada. The drainage areas, widths, and slopes of the glaciers that occupied these valleys were estimated from topographic maps and used to calculate Y. Step heights for each hanging valley were measured and then linearly correlated with Y to test the erosion rule. The correlation was weak for the hanging valleys considered as a single group for all values of n, but was quite strong for hanging valleys of a particular trunk valley. For two of the three sets of hanging valleys, the correlation was optimized when n=1, yielding coefficients of determination of 0.52 and 0.65. For the other set, a coefficient of determination of 0.79 was achieved when n=2. The correlation between step heights and values of Y was surprisingly strong, given the likely spatial variability of the many parameters lumped in the constant C2. This spatial variability was probably responsible for the weak correlation when hanging valleys were considered as a single group.

Our results indicate that erosion rate is indeed proportional to sliding velocity and that a linear or mildly nonlinear erosion rule accounts best for the step heights of hanging valleys. Sliding velocity, therefore, apparently controls or limits quarrying rates. This result is consistent with the likely effect of water-pressure fluctuations on subglacial rock fracture if quarrying rates are limited, not by crack-growth rates, but by the removal rate of detached rock fragments from the bed.

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