## Box 32 The Prediction Of Ice Sheet Profiles

It is a reasonable approximation to regard ice as perfectly plastic with a yield stress of 100 kPa: that is, ice will deform plastically if a stress of 100 kPa is applied. Nye (1952) used this assumption to derive a simple equation with which to calculate ice-surface profiles. On a horizontal bed the altitude of the ice surface at any point inland from a known margin can be found from the formula:

Pg where h is ice altitude (m), t is basal shear stress, s is the horizontal distance from the margin (m), P is the density of ice and g is acceleration due to gravity.

From comparison with real profiles, it seems that Nye's profile slightly overestimates the slope near the centre of an ice sheet, as shown below.

Despite this, Nye's simple equation has been used widely in reconstructing former ice sheets.

Source: Nye, J.F. (1952) A method of calculating the thickness of ice sheets. Nature, 169, 529-30. [Modified from: Sugden and John (1976) Glaciers and Landscapes, Arnold, figure 4.4, p. 60].

critically testing glacier reconstruction based on geomorphological evidence. Former glaciers should obey the same physical laws as glaciers today and should therefore have reconstructed basal shear stress values of between about 50 and 100 kPa over hard substrates (Box 3.3).

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