[1] Changes in driving and resistive stresses play an essential role in governing the buoyancy forces that are important controls on the speed and irreversibility of tidewater glacier retreats. We describe changes in geometry, velocity, and strain rate and present a top-down force balance analysis performed over the lower reach of Columbia Glacier. Our analysis uses new measurements and estimates of basal topography and photogrammetric surface velocity measurements made between 1977 and 2001, while assuming depth-independent strain. Sensitivity tests show that the method is robust and insensitive to small changes in the calculation parameters. Spatial distributions of ice speed show little correspondence with driving stress. Instead, spatial patterns of ice speed exhibit a nonlinear correspondence with basal drag. Primary resistance to flow comes from basal drag, but lateral drag becomes increasingly more important throughout the retreat, which may account for observed increases in speed. Maximum basal drag is always located in a prominent constriction located $12 km upstream from the preretreat terminus. Once the terminus retreated into deep water off the terminal moraine marking the modern maximum extent, the upstream location of this maximum basal drag helped to promote thinning and decrease effective pressure in the lower region by limiting replenishing ice flow from upstream. An increase in both ice velocity and calving resulted, initiating what appears to be an irreversible retreat.

When a mass balance is computed using an outdated map, that computation does not reveal the actual mass change. But older maps often must be used for practical reasons. We present a method by which, with a few additional measurements each year, a mass balance computed with an outdated map can be transformed into an actual mass change. This is done by taking into account the influence of changes in areal extent and changes in the surface elevation of the glacier since the map was made. This method is applied to South Cascade Glacier, Washington, U.S.A., as an example. The computed cumulative mass balance from 1970 to 1997 would have been 16% too negative if the 1970 map had not been updated.While the actual volume change of a glacier is relevant to hydrological studies, the change that would have occurred on a constant (or static) surface is more relevant to certain glacier dynamics problems and most climate problems. We term this the reference-surface balance and propose that such a balance, which deliberately omits the influence of changes in area and surface elevation, is better correlated to climatic variations than the conventional one, which incorporates those influences.

ABSTRACT. Glacier response to climate can be characterized by a single time-scale when the glacier changes sufficiently slowly. Then the derivative of volume with respect to area defines a thickness scale similar to that of Jo¨hannesson and others, and the time-scale follows from it. Our version of the time-scale is different from theirs because it explicitly includes the effect of surface elevation on mass-balance rate, which can cause a major increase in the time-scale or even lead to unstable response. The time constant has a dual role, controlling both the rate and magnitude of response to a given climate change. Data from South Cascade Glacier, Washington, U.S.A., illustrate the ideas, some of the difficulty in obtaining accurate values for the thickness and time-scales, and the susceptibility of all response models to potentially large errors.

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