Temperature profiles in the ablation zone

In the ablation area, except very near the equilibrium line, w is positive, or upward. In this case, the solution for the temperature gradient becomes:

Again, this equation cannot be integrated in closed form, and the integral has not been tabulated. Examples of profiles obtained by a numerical integration are shown in Figure 6.6b. Of particular interest is the exponential increase in gradient near the surface, a result that is apparent from Equation (6.29). A consequence of this behavior is that basal temperatures must commonly reach the melting point in the ablation zone, even with modest ice thicknesses and vertical velocities. Furthermore, when basal temperatures do reach the melting point, Ao becomes small, so most of the geothermal heat is trapped at the bed resulting in high basal melt rates.

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