Book contents
- Frontmatter
- Contents
- Preface to the first edition
- Preface to the second edition
- Physical constants relevant to ice
- Derived SI units and conversion factors
- 1 Why study glaciers?
- 2 Some basic concepts
- 3 Mass balance
- 4 Flow and fracture of a crystalline material
- 5 The velocity field in a glacier
- 6 Temperature distribution in polar ice sheets
- 7 The coupling between a glacier and its bed
- 8 Water flow in and under glaciers: geomorphic implications
- 9 Stress and deformation
- 10 Stress and velocity distribution in an idealized glacier
- 11 Numerical modeling
- 12 Applications of stress and deformation principles to classical problems
- 13 Finite strain and the origin of foliation
- 14 Response of glaciers to changes in mass balance
- Appendix: Problems
- References
- Index
6 - Temperature distribution in polar ice sheets
Published online by Cambridge University Press: 24 November 2009
- Frontmatter
- Contents
- Preface to the first edition
- Preface to the second edition
- Physical constants relevant to ice
- Derived SI units and conversion factors
- 1 Why study glaciers?
- 2 Some basic concepts
- 3 Mass balance
- 4 Flow and fracture of a crystalline material
- 5 The velocity field in a glacier
- 6 Temperature distribution in polar ice sheets
- 7 The coupling between a glacier and its bed
- 8 Water flow in and under glaciers: geomorphic implications
- 9 Stress and deformation
- 10 Stress and velocity distribution in an idealized glacier
- 11 Numerical modeling
- 12 Applications of stress and deformation principles to classical problems
- 13 Finite strain and the origin of foliation
- 14 Response of glaciers to changes in mass balance
- Appendix: Problems
- References
- Index
Summary
In this chapter, we will derive the energy balance equation for a polar ice sheet. Solutions to this equation yield the temperature distribution in an ice sheet and the rate of melting or refreezing at its base. We will study some analytical solutions of the equation for certain relatively simple situations. A solution of the full equation is possible, however, only with numerical models. This is because: (1) ice sheets have irregular top and bottom surfaces; (2) the boundary conditions – that is, the temperature or temperature gradient at every place along the boundaries – vary in space and time; (3) longitudinal transport (or advection) of heat by ice flow cannot be handled well with the analytical solutions; and (4) there may be extension or compression transverse to the flowline, which makes the problem three dimensional. Furthermore, because the temperature distribution is governed, in part, by ice flow, and conversely, because the flow rate is strongly temperature dependent, a full solution requires coupling of the energy and flow (momentum) equations.
The thermal conditions in and at the base of an ice sheet are of interest not only to the glacier modeler, concerned with flow rates and the possibility of sliding, but also to the glacial geologist with interest in the erosive potential of the ice and processes of subglacial deposition.
Energy balance in an ice sheet
Advection
Consider a control volume of length dx, width dy, and height dz, as shown in Figure 6.1.
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- Principles of Glacier Mechanics , pp. 112 - 146Publisher: Cambridge University PressPrint publication year: 2005
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