## Tests of sliding theories

The only sliding theory that can be reasonably tested with field data is Kamb's approximate nonlinear one. The sliding speed and other data used for the test were collected on Blue and Athabasca Glaciers, using boreholes to the bed and tunnels along the bed. In neither of these techniques was a large enough area of the bed exposed to permit direct measurement of the roughness. Thus, instead, Kamb calculated g and kc from the measured sliding speeds and known glacier geometry (Table 7.1).

When Kamb used a full white roughness spectrum in his calculations, the values of g were about one-third those in the table. Thus, in accord with his observations, he assumed that obstacles with short wavelengths had been abraded away, and instead of the full white roughness spectrum he used a truncated spectrum that did not have obstacles with those wavelengths. This yielded values of g (Table 7.1) that are consistent with observations on exposed bedrock outcrops, thus providing support for the theory. (It is noteworthy that in the absence of these shorter wavelengths, S a t3 (our Equation (7.5); Kamb's Equation (90)).)

Another test of the theory comes from observations of the thickness of the regelation layer at the base of a glacier. Regelation ice can be

 Measured Calculated Calculated Location S, m a-1 ? Xc, m Blue Glacier Borehole K 22 0.05 0.32-0.45 Borehole V 4 0.09 0.47-0.67 Western ice fall 6 0.02-0.04 0.62-1.12 Central ice fall On ridge 128 0.03 0.15-0.28 In trough 4 0.13 0.37-0.53 Athabasca Glacier Hole 1B 41 0.02 0.50-0.70 Hole 1A 42 0.02 0.33-0.47 Hole 209 3 0.06 0.59-0.84 Means 0.054 Figure 7.5. In the lee of a bump of the controlling size, regelation ice should fill the lower half of the space between bumps. Regelation ice distinguished from more highly deformed ice by grain size and crystal orientation. Thin sections of the ice viewed through crossed polarizers are used for this purpose. Kamb and LaChapelle (1964) measured thicknesses of the regelation layer in ice tunnels beneath Blue Glacier. They judged the average thickness to be about 5 mm while the maximum was 29 mm. These values can be compared with those calculated from Kamb's theory. The calculation is based on the fact that the thickness of the regelation layer in a depression in the lee of a bump is proportional to the degree to which the bump was accommodated by regelation. For example, for obstacles of the controlling size, accommodated half by regelation and half by plastic flow, regelation ice should half fill the depression between bumps (Figure 7.5). The predicted thicknesses were 1-10 mm. The fact that these thicknesses were less than those observed suggests that regelation may be more important than predicted by the theory.
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