Abstract
To evaluate the water storage and project the future evolution of glaciers, the ice-thickness of glaciers is an essential input. However, direct measurements of ice thickness are laborious, not feasible everywhere, and necessarily restricted to a small number of glaciers. In this article, we develop a simple method to estimate the ice-thickness along flow-line of mountain glaciers. Different from the traditional method based on shallow ice approximation (SIA), which gives a relationship between ice thickness, surface slope, and yield stress of glaciers, the improved method considers and presents a simple way to calibrate the influence of valley wall on ice discharge. The required inputs are the glacier surface topography and outlines. This shows the potential of the method for estimating the ice-thickness distribution and volume of glaciers without using of direct thickness measurements.
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Aðalgeirsdóttir, G., Jóhannesson, T., Björnsson, H., et al., 2006. Response of Hofsjökull and Southern Vatnajökull, Iceland, to Climate Change. Journal of Geophysical Research, 111(F3): F03001
Aniya, M., Welch, R., 1981. Morphological Analyses of Glacial Valleys and Estimates of Sediment Thickness on the Valley Floor: Victoria Valley System, Antarctica. Antarctic Record, 71: 76–95
Arendt, A., Echelmeyer, K., Harrison, W., et al., 2006. Updated Estimates of Glacier Volume Changes in the Western Chugach Mountains, Alaska, and a Comparison of Regional Extrapolation Methods. Journal of Geophysical Research, 111(F3): F03019
Bahr, D. B., Meier, M. F., Peckham, S. D., 1997. The Physical Basis of Glacier Volume-Area Scaling. Journal of Geophysical Research, 102(B9): 20355–20362
Beget, J., 1987. Low Profile of the Northwest Laurentide Ice Sheet. Arctic and Alpine Research, 19(1): 81–88
Björnsson, H., Aðalgeirsdóttir, G., Guðmundsson, S., et al., 2006. Climate Change Response of Vatnajökull, Hofsjökull and Langjökull Ice Caps, Iceland. In: European Conference on Impacts of Climate Change on Renewable Energy Sources. Reykjavik June 5–9, Iceland
Budd, W. F., 1969. The Dynamics of Ice Masses. Australian National Antarctic Research Expeditions, ANARE Scientific Reports, Series A, 108: 216
Chen, J. Y., Ohmura, A., 1990. Estimation of Alpine Glacier Water Resources and Their Change since the 1870s. Hydrology in Mountainous Regions, 193: 127–135
Doornkamp, J. C., King, C. A. M., 1971. Numerical Analysis in Geomorphology: An Introduction. Edward Arnold, London
Driedger, C. L., Kennard, P. M., 1986. Glacier Volume Estimation on Cascade Volcanoes: An Analysis and Comparison with Other Methods. Annals of Glaciology, 8: 59–64
Gerrard, J. A. F., Perutz, M. F., Roch, A., 1952. Measurement of the Velocity Distribution along a Vertical Line through a Glacier. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 213(1115): 546–558
Graf, W. L., 1970. The Geomorphology of the Glacial Valley Cross Section. Arctic and Alpine Research, 2(4): 303–312
Haeberli, W., Hoelzle, M., 1995. Application of Inventory Data for Estimating Characteristics of and Regional Climate-Change Effects on Mountain Glaciers: A Pilot Study with the European Alps. Annals of Glaciology, 21: 206–212
Harbor, J. M., 1990. A Discussion of Hirano and Aniya’s (1988, 1989) Explanation of Glacial-Valley Cross Profile Development. Earth Surface Processes and Landforms, 15(4): 369–377
Harbor, J. M., Wheeler, D. A., 1992. On the Mathematical Description of Glaciated Valley Cross Sections. Earth Surface Processes and Landforms, 17(5): 477–485
Hirano, M., Aniya, M., 1988. A Rational Explanation of Cross-Profile Morphology for Glacial Valleys and of Glacial Valley Development. Earth Surface Processes and Landforms, 13(8): 707–716
Hubbard, A., Blatter, H., Nienow, P., et al., 1998. Comparison of a Three-Dimensional Model for Glacier Flow with Field Data from Haut Glacier d’Arolla, Switzerland. Journal of Glaciology, 44(147): 368–378
Huss, M., Farinotti, D., Bauder, A., et al., 2008. Modelling Runoff from Highly Glacierized Alpine Drainage Basins in a Changing Climate. Hydrological Processes, 22(19): 3888–3902
Huybrechts, P., De Wolde, J., 1999. The Dynamic Response of the Greenland and Antarctic Ice Sheets to Multiple-Century Climatic Warming. Journal of Climate, 12(8): 2169–2188
Huybrechts, P., Nooze, P. D., Decleir, H., 1989. Numerical Modeling of Glacier d’Argentiere and Its Historic Front Variations. In: Oerlemans, J., ed., Glacier Fluctuations and Climate Change. Kluwer Academic Publishers, Dordrecht. 373–389
Li, Y. K., Liu, G. N., Cui, Z. J., 2001a. Glacial Valley Cross-Profile Morphology, Tian Shan Mountains, China. Geomorphology, 38(1–2): 153–166
Li, Y. K., Liu, G. N., Cui, Z. J., 2001b. Longitudinal Variations in Cross-Section Morphology along a Glacial Valley: A Case-Study from the Tienshan, China. Journal of Glaciology, 47(157): 243–250
Li, Z. Q., Li, K. M., Wang, L., 2010. Study on Recent Glacier Changes and Their Impact on Water Resources in Xinjiang, North Western China. Quaternary Sciences, 30(1): 96–106 (in Chinese with English Abstract)
Mayer, C., Siegert, M. J., 2000. Numerical Modelling of Ice-Sheet Dynamics across the Vostok Subglacial Lake, Central East Antarctica. Journal of Glaciology, 46(153): 197–205
Nye, J. F., 1952. The Mechanics of Glacier Flow. Journal of Glaciology, 2(12): 82–93
Nye, J. F., 1964. The Flow of a Glacier in a Channel of Rectangular, Elliptic or Parabolic Cross-Section. Journal of Glaciology, 5(41): 661–690
Oerlemans, J., 1997. Climate Sensitivity of Franz Josef Glacier, New Zealand: As Revealed by Numerical Modeling. Arctic and Alpine Research, 29(2): 233–239
Oerlemans, J., 2008. Minimal Glacier Models. Utrecht Publishing & Archiving Services, Utrecht
Oerlemans, J., Anderson, B., Hubbard, A., et al., 1998. Modelling the Response of Glaciers to Climate Warming. Climate Dynamics, 14(4): 267–274
Paterson, W. S. B., 1970a. The Application of Ice Physics to Glacier Studies. In: Glaciers. Secr. Can. Natl. Comm. Int. Hydrol. Decade, Ottawa. 43–46
Paterson, W. S. B., 1970b. The Sliding Velocity of Athabasca Glacier, Canada. Journal of Glaciology, 9(55): 55–63
Paterson, W. S. B., 1994. The Physics of Glaciers. 3rd ed.. Pergamon Press, Oxford
Paul, F., Svoboda, F., 2009. A New Glacier Inventory on Southern Baffin Island, Canada, from ASTER Data, II. Data Analysis, Glacier Change and Applications. Annals of Glaciology, 50(53): 22–31
Radic, V., Hock, R., 2010. Regional and Global Volumes of Glaciers Derived from Statistical Upscaling of Glacier Inventory Data. Journal of Geophysical Research, 115: F01010
Raymond, M. J., Gudmundsson, G. H., 2009. Estimating Basal Properties of Ice Streams from Surface Measurements: A Non-Linear Bayesian Inverse Approach Applied to Synthetic Data. Cryosphere, 3(2): 265–278
Reeh, N., 1982. A Plasticity Theory Approach to the Steady-State Shape of a Three-Dimensional Ice Sheet. Journal of Glaciology, 28(100): 431–455
Shi, Y. F., Huang, M. H., Yao, T. D., et al., 2008. Glaciers and Related Environments in China. Science Press, Beijing. 1–539
Shi, Y. F., Liu, C. H., Kang, E. S., 2009. The Glacier Inventory of China. Annals of Glaciology, 50(53): 1–4
Svensson, H., 1959. Is the Cross-Section of a Glacial Valley a Parabola? Journal of Glaciology, 3(25): 362–363
Thorsteinsson, T., Raymond, C. F., Gudmundsson, G. H., et al., 2003. Bed Topography and Lubrication Inferred from Surface Measurements on Fast-Flowing Ice Streams. Journal of Glaciology, 49(167): 481–490
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This study was supported by the National Basic Research Program of China (No. 2007CB411501), the Knowledge Innovation Project of the Chinese Academy of Sciences (No. KZCX2-EW-311), the National Natural Science Foundation of China (Nos. 91025012, J0930003/J0109) and the Project for Outstanding Young Scientists of the National Natural Science Foundation of China (No. 40121101).
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Li, H., Li, Z., Zhang, M. et al. An improved method based on shallow ice approximation to calculate ice thickness along flow-line and volume of mountain glaciers. J. Earth Sci. 22, 441–448 (2011). https://doi.org/10.1007/s12583-011-0198-1
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DOI: https://doi.org/10.1007/s12583-011-0198-1