Summary

We began this chapter by deriving the energy balance equation. Given boundary conditions appropriate for a polar ice sheet, solutions to this equation yield the temperature distribution in the ice sheet. The boundary conditions most commonly used are: (1) the temperature at the surface, which is approximated by the mean annual temperature, perhaps with a correction for heating by percolating melt water; and (2) the temperature gradient at the bed. The latter is based on estimates of the geothermal

Figure 6.18. Formation of ribbed moraine. (a) Map of ribbed moraine ridges near Lake Rogen in west-central Sweden. The line pattern on the ridges shows the direction of faint fluting. (b) Inferred original relative positions of ridges. Areas of overlap are attributed to streamlining after the ridges were pulled apart. (c) Schematic cross section through a series of ridges showing thickness of material above decollement. (d) Schematic diagram showing how a layer of frozen soil overlying thawed material could be pulled apart by extensional flow in the ice. ((a) and (b) from Hattestrand and Kleman, 1999. Reproduced with permission of the authors and Elsevier Science.)

Figure 6.18. Formation of ribbed moraine. (a) Map of ribbed moraine ridges near Lake Rogen in west-central Sweden. The line pattern on the ridges shows the direction of faint fluting. (b) Inferred original relative positions of ridges. Areas of overlap are attributed to streamlining after the ridges were pulled apart. (c) Schematic cross section through a series of ridges showing thickness of material above decollement. (d) Schematic diagram showing how a layer of frozen soil overlying thawed material could be pulled apart by extensional flow in the ice. ((a) and (b) from Hattestrand and Kleman, 1999. Reproduced with permission of the authors and Elsevier Science.)

flux. If calculations suggest that the bed is at the pressure melting point, the temperature gradient is adjusted to ensure that calculated basal temperatures do not exceed the melting point.

By using appropriate simplifications, we studied solutions to the energy balance equation for the situation at an ice divide, for the situation near the glacier surface but some distance from the divide, and for a column of ice extending through an ice sheet some distance from the divide. Two key assumptions in the latter, the so-called Column model, are that w decreases linearly with depth and that longitudinal advection can be approximated by assuming a warming rate at depth that equals that at the surface. Both of these lead to basal temperatures that are too cold, and the second may result in physically impossible temperature distributions in areas where surface temperatures are changing rapidly in the longitudinal direction. With suitable caution, however, we found that the

Column model was useful for illustrating how various physical processes that affect the temperature distribution were reflected in calculated temperatures along a flowline of the Laurentide Ice Sheet. Comparison of basal temperatures beneath the Antarctic ice sheet calculated by using the Column model and with a state-of-the-art numerical model served to emphasize both the value and the limitations of the former.

Finally, we discussed some geomorphic features formed at boundaries between zones of thawed and frozen bed, and noted that these could be used to constrain numerical models of ice sheets.

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