Hostname: page-component-5d59c44645-lfgmx Total loading time: 0 Render date: 2024-02-24T04:07:04.568Z Has data issue: false hasContentIssue false

Flotation and free surface flow in a model for subglacial drainage. Part 2. Channel flow

Published online by Cambridge University Press:  23 May 2012

I. J. Hewitt*
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2
C. Schoof
Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BC, Canada V6T 1Z4
M. A. Werder
Department of Earth Sciences, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada V5A 1S6
Email address for correspondence:


We present a new model of subglacial drainage incorporating flow in a network of channels and a porous sheet, with water exchange between the two determined by pressure gradients. The sheet represents the average effect of many linked cavities, whilst the channels emerge from individual cavities that enlarge due to dissipation-induced melting. The model distinguishes cases when the water pressure drops to zero, in which case it allows for the drainage space to be only partially filled with water (free surface flow), and when the pressure reaches the ice overburden pressure, in which case it allows for uplift of the ice to whatever extent is needed to accommodate the water (flotation). Numerical solutions are found for a one-dimensional flow-line version of the model. The results capture typically observed or inferred features of subglacial drainage systems, including open channel flow at the ice margin, seasonal channel evolution, and high water pressures and uplift of the ice surface driven by rapid changes in water supply.

Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


1. Bartholomew, I., Nienow, P., Mair, D., Hubbard, A., King, M. A. & Sole, A. 2010 Seasonal evolution of subglacial drainage and acceleration in a Greenland outlet glacier. Nat. Geosci. 3, 408411.Google Scholar
2. Bindschadler, R. 1983 The importance of pressurized subglacial water in separation and sliding at the glacier bed. J. Glaciol. 28, 239265.Google Scholar
3. Budd, W. F., Keage, P. L. & Blundy, N. A. 1979 Empirical studies of ice sliding. J. Glaciol. 23, 157170.Google Scholar
4. Copland, L., Sharp, M. J. & Nienow, P. W. 2003 Links between short-term velocity variations and the subglacial hydrology of a predominantly cold polythermal glacier. J. Glaciol. 49, 337348.Google Scholar
5. Creyts, T. T. & Schoof, C. 2009 Drainage through subglacial water sheets. J. Geophys. Res. 114, F04008.Google Scholar
6. Ekeland, I. & Temam, R. 1976 Convex Analysis and Variational Problems. North-Holland.Google Scholar
7. Evatt, G. W., Fowler, A. C., Clark, C. D. & Hulton, N. R. J. 2006 Subglacial floods beneath ice sheets. Phil. Trans. R. Soc. A 364, 17691794.Google Scholar
8. Flowers, G., Clarke, G. K. C., Björnsson, H. & Pálsson, F. 2004 A coupled sheet-conduit mechanism for Jökulhlaup propagation. Geophy. Res. Lett. 31.Google Scholar
9. Flowers, G. E. & Clarke, G. K. C. 2002 A multicomponent coupled model of glacier hydrology 1. Theory and synthetic examples. J. Geophys. Res. 107.Google Scholar
10. Fountain, A. G. & Walder, J. S. 1998 Water flow through temperate glaciers. Rev. Geophys. 36, 299328.Google Scholar
11. Fowler, A. C. 1986 A sliding law for glaciers of constant viscosity in the presence of subglacial cavitation. Proc. R. Soc. Lond. A 407, 147170.Google Scholar
12. Fowler, A. C. 1987 A theory of glacier surges. J. Geophys. Res. 92, 91119120.Google Scholar
13. Glowinski, R. 1984 Numerical Methods for Nonlinear Variational Problems. Springer.Google Scholar
14. Gordon, S., Sharp, M., Hubbard, B., Smart, C., Ketterling, B. & Willis, I. 1998 Seasonal reorganization of subglacial drainage inferred from measurements in boreholes. Hydrol. Process. 12, 105133.Google Scholar
15. Hewitt, I. J. 2011 Modelling distributed and channelized subglacial drainage: the spacing of channels. J. Glaciol. 57, 302314.Google Scholar
16. Hewitt, I. J. & Fowler, A. C. 2008 Seasonal waves on glaciers. Hydrol. Process. 22, 39193930.Google Scholar
17. Hock, R. & Hooke, R. LeB 1993 Evolution of the internal drainage system in the lower part of the ablation area of Storglaciären, Sweden. Geol. Soc. Am. Bull. 105, 537546.Google Scholar
18. Hooke, R. LeB., Brzozowski, J. & Bronge, C. 1983 Seasonal variations in surface velocity, Storglaciären, Sweden. Geografis. Annal. 65, 263277.Google Scholar
19. Iken, A. & Bindschadler, R. A. 1986 Combined measurements of subglacial water pressure and surface velocity of Findelengletscher, Switzerland: conclusions about drainage system and sliding mechanism. J. Glaciol. 32, 101119.Google Scholar
20. Jansson, P. 1996 Dynamics and hydrology of a small polythermal valley glacier. Geografis. Annal. 78, 171180.Google Scholar
21. Joughin, I., Das, S. B., King, M. A., Smith, B. E., Howat, I. M. & Moon, T. 2008 Seasonal speedup along the Western flank of the Greenland ice sheet. Science 320, 781783.Google Scholar
22. Kamb, B. 1987 Glacier surge mechanism based on linked cavity configuration of the basal water system. J. Geophys. Res. 92, 90839100.Google Scholar
23. Kamb, B., Raymond, W. D., Harrison, W. D., Engelhardt, H., Echelmeyer, K. A., Humphrey, N., Brugman, M. M. & Pfeffer, T. 1985 Glacier surge mechanism: 1982–1983 surge of Variegated Glacier, Alaska. Science 227, 469479.Google Scholar
24. LeVeque, R. 2002 Finite Volume Methods for Hyperbolic Equaions. Cambridge University Press.Google Scholar
25. Lliboutry, L. 1969 Contribution à la théorie des ondes glaciaires. Can. J. Earth Sci. 6, 943953.Google Scholar
26. Nienow, P., Sharp, M. & Willis, I. 1998 Seasonal changes in the morphology of the subglacial drainage system, Haut Glacier d’Arolla, Switzerland. Earth Surf. Process. Landforms 23, 825843.Google Scholar
27. Nye, J. F. 1976 Water flow in glaciers: Jökulhlaups, tunnels and veins. J. Glaciol. 17, 181207.Google Scholar
28. Paterson, W. S. B. 1994 The Physics of Glaciers. Butterworth-Heinemann.Google Scholar
29. Pimentel, S. & Flowers, G. E. 2010 A numerical study of hydrologically driven glacier dynamics and subglacial flooding. Proc. R. Soc. A 467, 537558.Google Scholar
30. Raymond, C. F., Benedict, R. J., Harrison, W. D., Echelmeyer, K. A. & Sturm, M. 1995 Hydrological discharges and motion of Fels and Black Rapids Glaciers, Alaska, USA: implications for the structure of their drainage systems. J. Glaciol. 41, 290304.Google Scholar
31. Röthlisberger, H. 1972 Water pressure in intra- and subglacial channels. J. Glaciol. 11, 177203.Google Scholar
32. Schoof, C. 2005 The effect of cavitation on glacier sliding. Proc. R. Soc. Lond. A 461, 609627.Google Scholar
33. Schoof, C. 2010 Ice-sheet acceleration driven by melt supply variability. Nature 468, 803806.Google Scholar
34. Schoof, C., Hewitt, I. J. & Werder, M. A. 2012 Flotation and open water flow in a model for subglacial drainage. Part 1. Distributed drainage. J. Fluid Mech. 702, 126156.Google Scholar
35. Schuler, T. V. & Fischer, U. H. 2009 Modelling the diurnal variation of tracer transit velocity through a subglacial channel. J. Geophys. Res. 114.Google Scholar
36. Shepherd, A., Hubbard, A., Nienow, P., King, M., McMillan, M. & Joughin, I. 2009 Greenland ice sheet motion coupled with daily melting in late summer. Geophys. Res. Lett. 36.Google Scholar
37. Shreve, R. L. 1972 Movement of water in glaciers. J. Glaciol. 11, 205214.Google Scholar
38. Spring, U. & Hutter, K. 1982 Conduit flow of a fluid through its solid phase and its application to intraglacial channel flow. Intl J. Engng Sci. 20, 327363.Google Scholar
39. Tsai, V. C. & Rice, J. R. 2010 A model for turbulent hydraulic fracture and application to crack propagation at glacier beds. J. Geophys. Res. 115.Google Scholar
40. Van de Wal, R. S. W., Boot, W., van den Broeke, M. R., Smeets, C. J. P. P, Reijmer, C. H., Donker, J. J. A. & Oerlemans, J. 2008 Large and rapid melt-induced velocity changes in the ablation zone of the Greenland ice sheet. Science 321, 111113.Google Scholar
41. Walder, J. S. 1986 Hydraulics of subglacial cavities. J. Glaciol. 32, 439445.Google Scholar
42. Walder, J. S. & Fowler, A. C. 1994 Channelized subglacial drainage over a deformable bed. J. Glaciol. 40, 315.Google Scholar
43. Willis, I. C. 1995 Interannual variations in glacier motion - a review. Prog. Phys. Geog. 19, 61106.Google Scholar
44. Zwally, H. J., Abdalati, W., Herring, T., Larson, K, Saba, J. & Steffen, K. 2002 Surface melt-induced acceleration of Greenland ice-sheet flow. Science 297, 218222.Google Scholar