The boundary condition at the surface

As noted, the boundary condition at the surface, z = H, is the ice temperature, 0 s, and this must be known in order to calculate a temperature profile from Equations (6.24) or (6.25). Below, we will show that the temperature at a depth of about 10 m in a glacier is very close to the mean annual atmospheric temperature, 0a, so it is normally assumed that 0 s = 0 a. However, it may be well to note some situations in which this approximation is not very good.

Temperatures in the ablation zones of some glaciers may be somewhat warmer than the mean annual temperature. This is because snow insulates the ice during the winter, preventing cooling. In addition, percolating meltwater reaches the snow/ice interface soon after melting starts in the spring, thus warming the ice faster than would be the case with conduction alone. On Barnes Ice Cap, these two effects result in near-surface ice temperatures that are about 2 °C above the mean annual temperature (Hooke etal., 1983).

Somewhat higher on a glacier, near and above the equilibrium line, percolating meltwater can penetrate into the firn of prior years. When this water refreezes the heat of fusion is released at a significant depth in the glacier, not just at the snow/ice interface. The warming effect is thus much enhanced, and ice temperatures in this zone may be several degrees warmer than the mean annual temperature.

At high latitudes and altitudes on polar ice sheets, the ice temperature may be slightly below the mean annual temperature because radiative cooling during the clear winter night is more effective than heating during the summer day.

Further discussion of these effects and additional references may be found in Hooke et al. (1983).

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