Role of permafrost in ice sheet dynamics and landform evolution

For decades, glacial geologists have speculated on the effects that bed conditions have on ice sheet profiles and dynamics (see, for example, Matthews, 1974; Fisher et al., 1985) and on the relation between basal

Figure 11.6. Contours of

(a) horizontal velocity and

(b) a'xx in a glacier 200 m thick at the calving face, calculated with the use of a finite-element model. (Reproduced from Hanson and Hooke, 2000. Used with permission of the authors and the International Glaciological Society.)

Water level 140 m

500 400 300 200 100 Distance from calving face, m

thermal conditions and glacial landforms (see, for example, Moran etal., 1980; Mooers, 1990b; Attig etal., 1989). Models of increasing sophistication have been used to study these effects. Here we discuss a recent time-dependent modeling effort by Cutler et al.(2000), using a flow-band finite-element model.

The modeled domain was a ~1700 km flow band extending from James Bay in Canada across the eastern end of Lake Superior and down the axis of the Green Bay lobe in Wisconsin to a Late Glacial Maximum terminal moraine and beyond. This flow band was chosen because ice-wedge casts and similar features demonstrate that permafrost was present along the margin in Wisconsin, and the modeling team wanted to estimate the thickness and horizontal extent, measured along a flowline extending upglacier from the margin, of the submarginal permafrost zone. Their ultimate goal was to investigate the role that permafrost may have played in the development of certain landforms.

The model domain was broken into ~100 columns with 50 nodes in the ice and 75 nodes in the substrate - a total of nearly 9000 nodes when the ice sheet extended to the terminal moraine. The particular model

Longitudinal stress deviator, kPa

1 1

* A

-

/ / •TA

du/dz /

A /

/

- / i/ ■ i i

1 i 1 i

Figure 11.7. Variation of the rate of overhang development and of a'xx at bed with water depth. Subaerial part of calving face was 60 m high in all simulations. (Reproduced from Hanson and Hooke, 2000. Used with permission of the authors and the International Glaciological Society.)

0.04 0.08 0.12 0.16 0.2 Rate of overhang development, a-1

run discussed here began at 55 ka, with ice already covering the first 275 km of the flowline, and ran to 21 ka, the Late Glacial Maximum. Time steps were 25 years. The model was forced with a mass balance pattern that depended on mean annual temperature and precipitation, and on the daily temperature range. The latter was essential to ensure melting when the mean daily temperature was still a few degrees below 0 ° C. Temperature and precipitation were specified at the margin and were assumed to decrease in specified ways with increasing elevation and latitude along the ice sheet surface. The variation in margin temperature with time was based on well-dated paleoclimate studies (Figure 11.8a). Included in the model is a routine for keeping track of the amount of meltwater produced by subglacial melt and lost by flow through subglacial aquifers. The viscous energy dissipated by this groundwater flow was added to the geothermal flux. Divergence of the ice flow was not included.

Results of the model run are shown in Figure 11.8b-e. Figure 11.8b shows profiles of the ice sheet at eight times between 48 and 21 ka, and Figure 11.8c shows the ice extent as a function of time. The abrupt decrease in thickness of the ice sheet at distances greater than about 900 km from the divide (Figure 11.8b) is a consequence of the transition in the bed from crystalline rocks to a deformable substrate at ~30 ka as E

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