References

The Cryosphere

1994-0424

Copernicus Publications

Göttingen, Germany

10.5194/tc-7-1557-2013

A note on the water budget of temperate glaciers

Oerlemans

https://orcid.org/0000-0001-5701-4161

Institute for Marine and Atmospheric Research Utrecht, Utrecht University, P.O. Box 80005, 3508 TA Utrecht, the Netherlands

27 09 2013

7 5 1557 1564

2013

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In this note, the total dissipative melting in temperate glaciers is studied. The analysis is based on the notion that the dissipation is determined by the loss of potential energy due to the downward motion of mass (ice, snow, meltwater and rain). A mathematical formulation of the dissipation is developed and applied to a simple glacier geometry. In the next step, meltwater production resulting from enhanced ice motion during a glacier surge is calculated. The amount of melt energy available follows directly from the lowering of the centre of gravity of the glacier. To illustrate the concept, schematic calculations are presented for a number of glaciers with different geometric characteristics. Typical dissipative melt rates, expressed as water-layer depth averaged over the glacier, range from a few centimetres per year for smaller glaciers to half a metre per year for Franz Josef Glacier, one of the most active glaciers in the world (in terms of mass turnover). The total generation of meltwater during a surge is typically half a metre. For Variegated Glacier a value of 70 cm is found, for Kongsvegen 20 cm. These values refer to water layer depth averaged over the entire glacier. The melt \textit{rate} depends on the duration of the surge. It is generally an order of magnitude greater than water production by `normal' dissipation. On the other hand, the additional basal melt rate during a surge is comparable in magnitude with the water input from meltwater and precipitation. This suggests that enhanced melting during a surge does not grossly change the total water budget of a glacier. Basal water generated by enhanced sliding is an important ingredient in many theories of glacier surges. It provides a positive feedback mechanism that actually makes the surge happen. The results found here suggest that this can only work if water generated by enhanced sliding accumulates in a part of the glacier base where surface meltwater and rain have no or very limited access. This finding seems compatible with the fact that, on many glaciers, surges are initiated in the lower accumulation zone.

References 1

Anderson, B., Lawson, W., Owens, I., and Goodsell, B.: Past and future mass balance of Ka Roimata o Hine Hukatere (Franz Josef Glacier), J. Glaciol., 52, 597–607, 2006.

Anderson, R. S., Anderson, S. P., MacGregor, K. R., Waddington, E. D., O'Neel, S., Riihimaki, C. A., and Loso, M. G. : Strong feedbacks between hydrology and sliding of a small alpine glacier, J. Geophys. Res., 109, F03005, <a href="http://dx.doi.org/10.1029/2004JF000120">https://doi.org/10.1029/2004JF000120</a>, 2004.

Andreassen, L. M. and Winsvold, S. H.: Inventory of Norwegian Glaciers, NVE, Oslo, 236 pp., 2012.

Björnsson H., Pálsson, F., Sigurdsson, O., and Flowers, G. E.: Surges of glaciers in Iceland, Ann. Glaciol., 36, 82–90, 2003.

Budd, W. F.: A first simple model of periodically self-surging glaciers, J. Glaciol., 14, 3–21, 1975.

Dunse, T., Schuler, T. V., Hagen, J. O., and Reijmer, C. H.: Seasonal speed-up of two outlet glaciers of Austfonna, Svalbard, inferred from continuous GPS measurements, The Cryosphere, 6, 453–466, <a href="http://dx.doi.org/10.5194/tc-6-453-2012">https://doi.org/10.5194/tc-6-453-2012</a>, 2012.

Flowers, G. E., Roux, N., Pimentel, S., and Schoof, C. G.: Present dynamics and future prognosis of a slowly surging glacier, The Cryosphere, 5, 299–313, <a href="http://dx.doi.org/10.5194/tc-5-299-2011">https://doi.org/10.5194/tc-5-299-2011</a>, 2011.

Fountain, A. G. and Walder, J. S.: Water flow through temperate glaciers, Rev. Geophys., 36, 299–328, 1998.

Fowler, A. C., Murray, T., and Ng, F. S. L.: Thermally controlled glacier surging, J. Glaciol., 42, 527–538, 2001.

Iken, A. and Bindschadler, R. A.: Combined measurements of subglacial water pressures and surface velocity of the Findelengletscher, Switzerland, Conclusions about drainage systems and sliding mechanism, J. Glaciol., 32, 101–119, 1986.

Jansson, A., Tveito, O. E., Pirinen, P., and Scharling, M.: NORDGRID: a preliminary investigation on the potential for creation of a joint Nordic gridded climate dataset. Norwegian Meteorological Institute, Oslo (DNMI Rapp. 03-2007), 2007.

Jansson, P., Hock, R., and Schneider, T.: The concept of glacier storage: a review, J. Hydrol., 282, 116–129, 2003.

Kamb B., Raymond, C. F., Harrison, W. D., Engelhardt, H. F., Echelmeyer, K. A., Humphrey, N. F., Brugmann, M. M., and Pfeffer, T.: Glacier surge mechanism, 1982-1983 surge of Variegated Glacier, Alaska, Science, 227, 469–479, 1985.

Mayer, C., Fowler, A. C., Lambrecht, A., and Scharrer, K.: A surge of North Gasherbrum Glacier, Karakorum, China, J. Glaciol., 57, 904–916, 2011.

Melvold, K. and Hagen, J. O.: Evolution of a surge-type glacier in its quiescent phase: Kongsvegen, Spitsbergen, 1964–95, J. Glaciol., 44, 394–404, 1998.

Oerlemans J.: The Microclimate of Valley Glaciers. Igitur, Utrecht University, 138 pp., ISBN 987-90-393-5303-5, 2010.

Oerlemans J.: Minimal Glacier Models, 2nd Edn., Igitur, Utrecht University, 103 pp., ISBN 978-90-6701-022-1, 2011.

Oerlemans, J. and Jonker, P. J.: The heat budget of the Antarctic Ice Sheet, Z. Gletscherk. Glazialgeol., 21, 291–299, 1985.

Osipova, G. B. and Tsvetkov, D. G.: Kinematics of the surface of a surging glacier (comparison of the Medvezhiy and Variagated Glacier, IAHS Publ. no.208 (Glaciers-Ocean-Atmosphere Interactions), 345–357, 1991

Østrem, G., Selvig, K. D., and Tandberg, K.: Atlas over breer i Ser-Norge, Norges "Vassdrags- og Energiverk, Hydrologisk" Avdeling, Meddelelse, 61, 1988

Raymond, C. F.: How do glaciers surge? A review, J. Geophys. Res., 92, 9121–9134, 1987.

Sevruk, B.: Regional dependency of precipitation-altitude relationship in the Swiss Alps, Climate Change, 36, 355–369, 1997.

Sharp, M.: Surging glaciers: behaviour and mechanisms, Prog. Phys. Geog., 12, 349–370, 1988.

Sund, M., Eiken, T., Hagen, J. O., and Kääb, A.: Svalbard surge dynamics derived from geometric changes, Ann. Glaciol., 50, 50–60, 2009.

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., and Oerlemans, J.: Large and rapid velocity changes in the ablation zone of the Greenland ice sheet, Science, 321, 111–113, 2008.

Van Pelt, W. J. J. and Oerlemans, J.: Numerical simulations of cyclic behaviour in the Parallel Ice Sheet Model (PISM), J. Glaciol., 58, 347–360, <a href="http://dx.doi.org/10.3189/2012JoG11J217">https://doi.org/10.3189/2012JoG11J217</a>, 2012.

Van Pelt, W. J. J., Oerlemans, J., Reijmer, C. H., Pohjola, V. A., Pettersson, R., and van Angelen, J. H.: Simulating melt, runoff and refreezing on Nordenskiöldbreen, Svalbard, using a coupled snow and energy balance model, The Cryosphere, 6, 641–659, <a href="http://dx.doi.org/10.5194/tc-6-641-2012">https://doi.org/10.5194/tc-6-641-2012</a>, 2012.