If the seasonal variation can be represented by a sinusoidal function, this depth is given by: 2 The atmospheric temperature at a glacier surface changes seasonally thus measurements of the “surface” temperature for use with Equation (1) are generally made at some depth, z 0, in the glacier below which the effect of these seasonal variations is negligible. In this paper I examine the reasons for the break down of this assumption, and attempt to indicate the magnitude of the error introduced. This assumption is incorrect in the ablation area and in the percolation and saturation zones of the accumulation area. The boundary condition at the surface is the ice temperature, which is usually assumed to be equal to the mean annual atmospheric temperature. The boundary condition at the bed is generally taken to be the temperature gradient in the ice required to conduct the geothermal heat upward into the glacier, with certain modifications where the pressure melting temperature is reached. To obtain a solution to this equation, boundary conditions at the surface and bed must be known. Where K is the thermal diffusivity of ice, Q is the internal heat generation, p is the ice density, and C is the heat capacity.
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