Skip to main content
Log in

An improved method based on shallow ice approximation to calculate ice thickness along flow-line and volume of mountain glaciers

  • Published:
Journal of Earth Science Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References Cited

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Beget, J., 1987. Low Profile of the Northwest Laurentide Ice Sheet. Arctic and Alpine Research, 19(1): 81–88

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Doornkamp, J. C., King, C. A. M., 1971. Numerical Analysis in Geomorphology: An Introduction. Edward Arnold, London

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Graf, W. L., 1970. The Geomorphology of the Glacial Valley Cross Section. Arctic and Alpine Research, 2(4): 303–312

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Nye, J. F., 1952. The Mechanics of Glacier Flow. Journal of Glaciology, 2(12): 82–93

    Google Scholar 

  • 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

    Google Scholar 

  • Oerlemans, J., 1997. Climate Sensitivity of Franz Josef Glacier, New Zealand: As Revealed by Numerical Modeling. Arctic and Alpine Research, 29(2): 233–239

    Article  Google Scholar 

  • Oerlemans, J., 2008. Minimal Glacier Models. Utrecht Publishing & Archiving Services, Utrecht

    Google Scholar 

  • Oerlemans, J., Anderson, B., Hubbard, A., et al., 1998. Modelling the Response of Glaciers to Climate Warming. Climate Dynamics, 14(4): 267–274

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Paterson, W. S. B., 1970b. The Sliding Velocity of Athabasca Glacier, Canada. Journal of Glaciology, 9(55): 55–63

    Google Scholar 

  • Paterson, W. S. B., 1994. The Physics of Glaciers. 3rd ed.. Pergamon Press, Oxford

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Shi, Y. F., Huang, M. H., Yao, T. D., et al., 2008. Glaciers and Related Environments in China. Science Press, Beijing. 1–539

    Google Scholar 

  • Shi, Y. F., Liu, C. H., Kang, E. S., 2009. The Glacier Inventory of China. Annals of Glaciology, 50(53): 1–4

    Google Scholar 

  • Svensson, H., 1959. Is the Cross-Section of a Glacial Valley a Parabola? Journal of Glaciology, 3(25): 362–363

    Google Scholar 

  • 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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Huilin Li  (李慧林).

Additional information

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).

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12583-011-0198-1

Key words

Navigation