Box 33 Estimates Of Basal Shear Stress And The Accuracy Of Glacial Reconstructions

During the last glacial period the Yellowstone National Park in North America was covered by a number of small mountain icefields, one of which is referred to as the Pinedale ice mass. From a careful field study of the landforms and sediments within this area Pierce (1979) was able to reconstruct the morphology of this ice mass. Any reconstruction of a former icefield, on the basis of geomorphological evidence, is likely to be speculative in some respect. Pierce (1979) argued that glaciology offers a method of independently evaluating glacier reconstructions: former glaciers should obey the same physical laws as modern glaciers. In particular the calculation of basal shear stress provides a powerful tool. The two parameters that together specify the shape of a reconstructed glacier - ice thickness and surface slope - are also the primary variables that determine basal shear stress. Empirical observations suggest that the vast majority of modern glaciers, flowing over rigid substrata, have basal shear stresses between 50 and 150 kPa. Pierce (1979) used this to test the validity of his reconstruction of the former Pinedale icefield: if the reconstruction is valid it should give basal shear stress values of this order.

Pierce (1979) calculated the basal shear stress of 50 reaches, each 5-15 km in length, along flow lines within his reconstructed icefield. The results are displayed below on a graph with the ice thickness on one axis and the angle of the former glacier slope on the other. All the values of basal stress fall between 60 and 150 kPa, which is fairly consistent with modern glaciers. The high values of basal shear stress tend to occur in areas likely to have experienced extending flow, whereas the lower values are typical of areas of compressive or decelerating flow. Pierce (1979) concluded that his glacier reconstruction had values of basal shear stress that are both internally consistent and consistent with the values of basal shear stress obtained for modern glaciers. This strongly supports the validity of his reconstruction and illustrates how basic glaciological principles can be used to test the accuracy of glacier reconstructions based on geomorphological evidence.

Surface slope (degrees)

Surface slope (degrees)

Source: Pierce, K.L. (1979) History and dynamics of glaciation in the Northern Yellowstone National Park area. US Geological Survey Professional Paper, 729-F. [Modified from: Pierce (1979) US Geological Survey Professional Paper, 729-F, figure 48, p. 71].

Ice can flow in response to the shear stress applied to it through three different mechanisms: (i) by internal deformation; (ii) by basal sliding; and (iii) by subglacial bed deformation.

3.3.1 Internal Deformation

The internal deformation of ice is achieved in two ways: (i) by the process of creep; and (ii) by large-scale folding and faulting.

Creep involves both the deformation of ice crystals and at higher temperatures the mutual displacement of ice crystals relative to one another in response to the shear stress placed upon the ice. The rate of ice creep is a function of the shear stress applied: the greater the shear stress, the greater the rate of ice creep. This relationship is known as Glen's flow law. It emphasises the sensitivity of ice creep to shear stress: simply doubling the shear stress will increase the rate of creep by a factor of eight. This explains why most creep takes place in the basal layers of a glacier where shear stress is greatest, because of the greater ice thickness. The rate of deformation is also controlled by temperature, because ice is more plastic at higher temperatures.

The rate of glacier creep may vary down-glacier depending upon whether the glacier is experiencing accelerating (extensional) or decelerating (compressional) flow. The distribution of zones of extending or compressional flow varies with scale. Compressive flow tends to occur on a glacier where the ice thickness decreases down-glacier (in the ablation zone) and extending flow occurs where ice thickness tends to increase down-glacier (in the accumulation zone). At a small scale, extending flow tends to occur on slopes beneath the ice that steepen down-glacier, whereas compressive flow tends to occur where basal slopes shallow down-glacier. The pattern of surface fractures, crevasses (Figure 3.7), on the glacier reflects the type of flow, extending or compressional, that takes place (Figure 3.8). The rate of ice creep is also proportional to temperature. The closer the temperature comes to the melting point the greater the creep rate. For example, in experiments at a fixed stress it was found that the creep rate at -1°C is 1000 times greater than at -20 °C.

Under certain conditions creep cannot adjust sufficiently fast to the stresses set up within the ice. As a result, faults and folds may develop. The type of faults that form depend upon whether the ice is experiencing a zone of longitudinal extension or one of compression (Figure 3.8). Areas of compressive flow are also controlled by the temperature of the basal ice as discussed in Section 7.5.

3.3.2 Basal Sliding

There are two main processes by which ice sheets can slide over their beds: (i) enhanced basal creep; and (ii) regelation slip.

Enhanced basal creep is an extension of the normal ice-creep process. It explains how basal ice deforms around irregularities on the ice-bed interface. A glacier bed is not smooth but will contain irregularities, such as bedrock bumps or lodged

Erosion Accumulation Obstacles
Figure 3.7 Crevasses in the accumulation area of the Tasman Glacier, New Zealand. Ice flow is from bottom right to top left. [Photograph: N.F. Glasser]

boulders, which protrude into the bottom of the moving glacier. Basal ice pressure within the ice increases on the upstream side of such obstacles (see Figure 4.6), and this increases the rate of ice deformation at this point, allowing the ice to flow more efficiently around the obstacle. The larger the obstacle the higher the increase in basal pressure and the greater the rate of deformation. Consequently the process is most efficient for larger obstacles.

Regelation slip occurs when ice at its pressure melting point moves across a series of irregularities or bumps. On the upstream side of each obstacle the basal ice pressure is higher as the ice moves against the obstacle. The melting point of ice falls as pressure rises and as a consequence basal ice melts on the upstream side of obstacles. The meltwater produced will flow around the bump to the downstream side where the pressure is lower and consequently it will refreeze to form regelation ice. This process is most effective for small obstacles because the higher temperature gradients across them can drive the heat flux generated by the freezing of the meltwater (release of latent heat) from the downstream side of the obstacle through the rock bump to assist ice melting on the upstream side.

There are, therefore, two processes of basal sliding. One of these, regelation slip, operates best in passing small obstacles, whereas enhanced basal creep works best for larger obstacles. In between the two there is a critical obstacle size range where

Transverse crevasses: extending flow

Transverse crevasses: extending flow

Radial crevasses: compressive flow

Radial crevasses: compressive flow

Compressive Extending flow flow

Compressive Extending flow flow

Figure 3.8 Compressive and extending flow in glaciers. Compressive flow is associated with a decrease in subglacial slope angle or a warm-based to cold-based thermal boundary, while extending flow is encountered where the glacier bed steepens or with a cold-based to warm-based thermal boundary. Note that the pattern of surface crevasses differs between the two flow types.

neither process is particularly effective. A bed with obstacles in this size range will, therefore, pose the greatest resistance to basal sliding.

The efficiency of basal sliding depends not only upon the size of obstacles, but also more generally upon the overall level of bed friction. Bed friction is a function of the number of points of contact between the ice and the bed: if these are few then the friction resisting basal sliding will be low. The number of points of contact depends primarily on the amount of water present at the ice-bed interface and its pressure (see Section 4.6). A film of water only a few millimetres thick will reduce friction sufficiently to increase the rate of basal sliding. The presence of water-filled basal cavities between the ice-bed interface can also dramatically increase the rate of basal sliding (see Section 4.6). The rate of basal sliding is also affected by the amount of debris within the basal ice; if the debris content is very large the rate of basal sliding may be reduced (see Section 5.1.3).

3.3.3 Subglacial Bed Deformation

When an ice sheet flows over unfrozen sediment it may cause this sediment to deform beneath the weight of the ice. This deformation occurs when the water pressure in the pores or spaces between the sediment grains increases sufficiently to reduce the resistance between individual grains. This allows them to move or flow relative to one another as a slurry-like mass. In response to the shearing force imposed by the overriding glacier this slurry forms a continuously deforming layer on which the glacier moves (Box 3.4). This process can be dramatic. For example, 90% of the forward motion of the Brei9amerkurjokull in southeast Iceland may be due to subglacial bed or subsole deformation.

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