Near-Surface Temperatures in the Superimposed Ice Zone and Lower Part of the Soaked Zone of Polar Ice Sheets

• Published in: Journal of Glaciology
• Main Author: Hooke, Roger LeB.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 1976
• Subjects: Earth-Surface Processes; Journal of Glaciology
• Online Access: http://dx.doi.org/10.1017/s0022143000031695; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000031695

Abstract The temperature distribution in a polar glacier is described by the equation of heat conduction, 1 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. To obtain a solution to this equation, boundary conditions at the surface and bed must be known. 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. The boundary condition at the surface is the ice temperature, which is usually assumed to be equal to the mean annual atmospheric temperature. This assumption is incorrect in the ablation area and in the percolation and saturation zones of the accumulation area. In this paper I examine the reasons for the break down of this assumption, and attempt to indicate the magnitude of the error introduced. 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. If the seasonal variation can be represented by a sinusoidal function, this depth is given by: 2 (Carslaw and Jaeger, 1959, p. 65) where w is the period of the fluctuations (in this case 2π/year), θ r is the temperature range from winter minimum to summer maximum, and A is the maximum acceptable change in temperature at depth z 0 . For example, in the dry zone of the accumulation area if we take K = 16 m 2 /year, a value appropriate for unpacked snow, θ r = 30 deg, and Δ = 0.4 deg, we obtain z 0 = 10 m. This is the basis for the common assumption that the 10 m temperature is approximately equal to the mean annual temperature. In the superimposed ice zone superimposed ice occurs immediately beneath the winter snow cover, and K for ice at — 10°C is about 38 m 2 /year. Furthermore, the temperature ...