HIGH-RESOLUTION TEMPERATE GLACIER DEFORMATION -- IMPLICATIONS ABOUT THE FORM OF THE FLOW LAW OF ICE
MARSHALL, HANS-PETER . INSTAAR and Dept of Civil, Environmental, and Architectural Eng; Univ of Colorado at Boulder.
Pfeffer, Tad . INSTAAR and Dept of Civil, Environmental, and Architectural Eng; Univ of Colorado at Boulder.
Harper, Joel . Dept of Geology and Geophysics; Univ of Wyoming.
Humphrey, Neil . Dept of Geology and Geophysics; Univ of Wyoming.
The rheological behavior of ice plays a pivotal role in predicting the response of glaciers and ice sheets to climate change, understanding the evolution of glacial landscapes, and assigning time-depth scales to ice cores for measurement of long-term climate history. While interest in glacier and ice sheet mechanics has grown substantially during the last 50 years, the material properties of glacial ice are still not well established. Ice appears to deform solely in response to deviatoric stress with a stress dependent viscosity. The commonly applied flow law for glacial ice gives the strain rate as a function of the deviatoric stress raised to a power “n”.
The value of this parameter “n” has been a long debated and unresolved issue; 3 is commonly used, but values from 1 to more than 4 have been reported. Because natural glacier ice deforms in secondary (or steady-state) creep, very long test durations are required to accurately represent this behavior in the laboratory. To prevent errors in measurements arising from year-long laboratory tests, most experiments have been performed at stresses much higher than those found in glaciers and ice sheets. These high-stress experiments have yielded values of “n” of 3-4, which agree reasonably well with results from in-situ measurements on the large ice sheets and have become the values most often used by modelers. Deviations from this flow law are usually attributed to fabric and other heterogeneous ice properties, or inaccurate assumptions about the applied stress (at low stresses).
Using the highest-resolution data set to-date of deformation in temperate glacier ice (1), we examined the three-dimensional strain-rate tensor and its relationship to the inferred stress acting on this 198m X 165m X 240m block of natural glacial ice on Worthington Glacier, AK. Deformation of the block was evaluated by more than 21,000 measurements of the tilting of 31 boreholes extending to near the glacier’s bed, located at a depth of 180-200 m. The borehole tilt observations yielded the two horizontal components of the velocity vector. These velocity data were then interpolated to a three-dimensional grid (24 X 11 X 99 nodes) with vertical coordinates referenced to the irregular surface of the glacier (Fig. 1).
Our results show that below a depth of 115 m, the ice follows a non-linear flow law with a power exponent of approximately 3, as expected from past work. Above 115m, however, our analysis indicates linear viscous flow (Fig. 2). A sharp transition between the two flow regimes is likely caused by a change in the dominant mechanism from grain boundary sliding (diffusional flow) near the surface to dislocation and intra-granular deformation at depth. This type of behavior at low stress has very recently been reported from laboratory experiments using new methods (2), and has long been observed in high-temperature metals (which deform in a manner similar to ice) (3).
The deformation observed in the upper half of this 200 m thick glacier implies that much of the ice in the world’s small mountain glaciers may best be defined by a linear viscous flow law. This finding bears on forecasts of short-term global response to climate change, for the world’s small glaciers are the fastest-acting component of global glacier mass balance; on century time-scales they area dominant contribution to sea level change (4).
1. J.T. Harper et. al.,. Journal of Geophysical Research 106, 8547 (2001).
2. D.L. Goldsby, D. L. Kohlstedt, Journal of Geophysical Research 106, 11017 (2001).
3. I. Servi, N. Grant, Journal of Metals 3, 909 (1951).
4. M. F. Meier, Science 226, 1418 (1984).
Figure 1. 3-D grid of velocity / strain-rate data on
Worthington Glacier, Alaska.
Figure 2. Log-log plot of effective strain rate and
effective deviatoric stress. The slope of a linear fit to this data defines the flow law exponent "n".
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