Skip to main content Accessibility help

Self-similarity in glacier surface characteristics

  • Neil S. Arnold (a1) and W. Gareth Rees (a1)


Catchment-wide information on glacier snow-cover depth, surface albedo and surface roughness is important input data for distributed models of glacier energy balance. In this study, we investigate the small-scale (mm to 100 m) spatial variability in these properties, with a view to better simulating this variability in such models. Data were collected on midre Lovénbreen, a 6 km2 valley glacier in northwest Svalbard. The spatial variability of all three properties was found to be self-similar over the range of scales under investigation. Snow depth and albedo exhibit a correlation length within which measurements were spatially autocorrelated. Late-winter and summer properties of snow depth differed, with smaller depths in summer due to melt, and shorter correlation lengths. Similar correlation lengths for snow depth and surface albedo may suggest that snow-depth variation is an important control on the small-scale spatial variability of glacier surface albedo. For surface roughness, the data highlight a possible problem in energy-balance studies which use microtopographic surveys to calculate aerodynamic roughness, in that the scale of the measurements made affects the calculated roughness value. This suggests that further investigations of the relationships between surface form and aerodynamic roughness of glacier surfaces are needed.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Self-similarity in glacier surface characteristics
      Available formats

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Self-similarity in glacier surface characteristics
      Available formats

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Self-similarity in glacier surface characteristics
      Available formats



Hide All
Arnold, N. S., Willis, I. C., Sharp, M. J., Richards, K. S. and Lawson, W. J.. 1996. A distributed surface energy-balance model for a small valley glacier. I. Development and testing for Haut Glacier d’Arolla,Valais, Switzerland. J. Glaciol., 42(140), 7789.
Arnold, N., Richards, K., Willis, I. and Sharp, M.. 1998. Initial results from a distributed, physically based model of glacier hydrology. Hydrol. Processes, 12, 191219.
Braithwaite, R. J. and Olesen, O. B.. 1990. A simple energy-balance model to calculate ice ablation at the margin of the Greenland ice sheet. J. Glaciol., 36(123), 222228.
Braithwaite, R. J. and Zhang, Y.. 2000. Sensitivity of mass balance of five Swiss glaciers to temperature changes assessed by tuning a degree-day model. J. Glaciol., 46(152), 714.
Brock, B.W., Willis, I. C. and Sharp, M. J.. 2000a. Measurement and parameterization of albedo variations at Haut Glacier d’Arolla, Switzerland. J. Glaciol., 46(155), 675688.
Brock, B.W., Willis, I. C., Sharp, M. J. and Arnold, N. S.. 2000b. Modelling seasonal and spatial variations in the surface energy balance of Haut Glacier d’Arolla, Switzerland. Ann. Glaciol., 31, 5362.
Burrough, P. A. 1986. Principles of geographical information systems for land resources assessment. Oxford, Clarendon Press. (Monographs on Soils and Resources Survey 12.)
Denby, B. and Greuell, W.. 2000. The use of bulk and profile methods for determining surface heat fluxes in the presence of glacier winds. J. Glaciol., 46(154), 445452.
Escher-Vetter, H. 1985. Energy balance calculations for the ablation period 1982 at Vernagtferner, Oetztal Alps. Ann. Glaciol., 6, 158160.
Hay, J. E. and Fitzharris, B. B.. 1988. A comparison of the energy-balance and bulk-aerodynamic approaches for estimating glacier melt. J. Glaciol., 34(117), 145153.
Hock, R. and Holmgren, B.. 1996. Some aspects of energy balance and ablation of Storglaci ren, northern Sweden. Geogr. Ann., 78A(2–3), 121131.
Hock, R. and Noetzli, C.. 1997. Areal melt and discharge modelling of Storglaciären, Sweden. Ann. Glaciol., 24, 211216.
King, J. C. and Anderson, P. S.. 1994. Heat and water vapour fluxes and scalar roughness lengths over an Antarctic ice shelf. Boundary-Layer Meteorol., 69(1–2), 101121.
Kitanidis, P. K. 1997. Introduction to geostatistics. Cambridge, Cambridge University Press.
Knap, W. H., Brock, B.W., Oerlemans, J. and Willis, I. C.. 1999. Comparison of Landsat TM-derived and ground-based albedos of Haut Glacier d’Arolla, Switzerland. Int. J. Remote Sensing, 20(17), 32933310.
Laumann, T. and Reeh, N.. 1993. Sensitivity to climate change of the mass balance of glaciers in southern Norway. J. Glaciol., 39(133), 656665.
Lefebre, F., Gallée, H., vanYpersele, J. P. and Greuell, W.. 2003. Modeling of snow and ice melt at ETH camp (West Greenland): a study of surface albedo. J. Geophys. Res, 108(D8), Art. No. 4231.
Lettau, H. 1969. Note on aerodynamic roughness-parameter estimation on the basis of roughness element description. J. Appl. Meteorol, 8(5), 828832.
Lovejoy, S. and Mandelbrot, B. B.. 1985. Fractal properties of rain, and a fractal model. Tellus, 37(3), 209232.
Mannstein, H. 1985. The interpretation of albedo measurements on a snow covered slope. Arch. Meteorol. Geophys. Bioklimatol., Ser. B, 36(1), 7381.
Munro, D.S. 1990. Comparison of melt energy computations and ablatometer measurements on melting ice and snow. Arct. Alp. Res, 22(2), 153162.
Munro, D. S. and Young, G. J.. 1982. An operational net shortwave radiation model for glacier basins. Water Resour. Res, 18(2), 220230.
Oerlemans, J. 1993. A model for the surface balance of ice masses: Part 1. Alpine glaciers. Z. Gletscherkd. Glazialgeol, 27–28, [1991–1992], 6383.
Rees, W. G. 1992. Measurement of the fractal dimension of ice-sheet surfaces using Landsat data. Int. J. Remote Sensing, 13(4), 663671.
Rees, W. G. 1998. Correspondence. A rapid method for measuring snow surface profiles. J. Glaciol., 44(148), 674675.
Schwerdtfeger, P. 1976. Physical principles of micrometeorological measurements. Amsterdam, Elsevier. (Developments in Atmospheric Science 6.)
Shook, K. and Gray, D. M.. 1996. Small-scale spatial structure of shallow snowcovers. Hydrol. Processes, 10, 12831292.
Shook, K. and Gray, D. M.. 1997. Synthesizing shallow seasonal snowcovers. Water Resour. Res, 33(3), 419424.
Van de Wal, R. S.W., Oerlemans, J. and van der Hage, J. C.. 1992. A study of ablation variations on the tongue of Hintereisferner, Austrian Alps. J. Glaciol., 38(130), 319324.
Willis, I. C., Sharp, M. J. and Richards, K. S.. 1993. Studies of the water balance of Midtdalsbreen, Hardangerjökulen, Norway: 1. The calculation of surface water inputs from basic meteorological data. Z. Gletscherkd. Glazialgeol, 27–28, [1991–1992], 97115.
Willis, I., Arnold, N. and Brock, B.. 2002. Effect of snowpack removal on energy balance, melt and runoff in a small supraglacial catchment. Hydrol. Processes, 16, 27212749.
Wiscombe, W. J. and Warren, S. G.. 1980. A model for the spectral albedo of snow. I. Pure snow. J. Atmos. Sci, 37(12), 27122733.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed