Skip to main content Accessibility help
×
Home

Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA

  • R.W. Mcnabb (a1), R. Hock (a1) (a2), S. O’Neel (a3), L.A. Rasmussen (a4), Y. Ahn (a5), M. Braun (a6), H. Conway (a4), S. Herreid (a1), I. Joughin (a7), W.T. Pfeffer (a8), B.E. Smith (a8) and M. Truffer (a1)...

Abstract

Information about glacier volume and ice thickness distribution is essential for many glaciological applications, but direct measurements of ice thickness can be difficult and costly. We present a new method that calculates ice thickness via an estimate of ice flux. We solve the familiar continuity equation between adjacent flowlines, which decreases the computational time required compared to a solution on the whole grid. We test the method on Columbia Glacier, a large tidewater glacier in Alaska, USA, and compare calculated and measured ice thicknesses, with favorable results. This shows the potential of this method for estimating ice thickness distribution of glaciers for which only surface data are available. We find that both the mean thickness and volume of Columbia Glacier were approximately halved over the period 1957–2007, from 281 m to 143 m, and from 294 km3 to 134 km3, respectively. Using bedrock slope and considering how waves of thickness change propagate through the glacier, we conduct a brief analysis of the instability of Columbia Glacier, which leads us to conclude that the rapid portion of the retreat may be nearing an end.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org 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 @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ 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.

      Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA
      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.

      Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA
      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.

      Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA
      Available formats
      ×

Copyright

References

Hide All
Ahn, Y and Howat, IM (2011) Efficient automated glacier surface velocity measurement from repeat images using multiimage/multichip and null exclusion feature tracking. IEEE Trans. Geosci. Remote Sens., 49(8), 28382846 (doi: 10.1109/TGRS. 2011.2114891)
Arendt, AA, Echelmeyer, KA, Harrison, WD, Lingle, CS and Valentine, VB (2002) Rapid wastage of Alaska glaciers and their contribution to rising sea level. Science, 297(5580), 382386 (doi: 10.1126/science.1072497)
Arendt, A and 7 others (2006) Updated estimates of glacier volume changes in the western Chugach Mountains, Alaska, and a comparison of regional extrapolation methods. J. Geophys. Res., 111(F3), F03019 (doi: 10.1029/2005JF000436)
Bahr, DB, Meier, MF and Peckham, SD (1997) The physical basis of glacier volume-area scaling. J. Geophys. Res., 102(B9), 20 355-20 362 (doi: 10.1029/97JB01696)
Bamber, JL, Layberry, RL and Gogineni, SP (2001) A new ice thickness and bed data set for the Greenland ice sheet. 1. Measurement, data reduction, and errors. J. Geophys. Res., 106(D24), 33 773-33 780 (doi: 10.1029/2001JD900054)
Barclay, DJ, Barclay, JL, Calkin, PE and Wiles, GC (2006) A revised and extended Holocene glacial history of Icy Bay, southern Alaska, U.S.A.Arct. Antarct. Alp. Res., 38(2), 153162
Barclay, DJ, Wiles, GC and Calkin, PE (2009) Holocene glacier fluctuations in Alaska. Quat. Sci. Rev., 28(21–22), 20342048 (doi: 10.1016/j.quascirev.2009.01.016)
Berthier, E, Schiefer, E, Clarke, GKC, Menounos, B and Rémy, F (2010) Contribution of Alaskan glaciers to sea-level rise derived from satellite imagery. Nature Geosci., 3(2), 9295 (doi: 10.1038/ngeo737)
Bevington, PR (1969) Data reduction and error analysis for the physical sciences. McGraw-Hill, New York
Calkin, PE, Wiles, GC and Barclay, DJ (2001) Holocene coastal glaciation of Alaska. Quat. Sci. Rev., 20(1–3), 449461 (doi: 10.1016/S0277–3791(00)00105–0)
Clarke, GKC, Berthier, E, Schoof, CG and Jarosch, AH (2009) Neural networks applied to estimating subglacial topography and glacier volume. J. Climate, 22(8), 21462160 (doi: 10.1175/2008JCLI2572.1)
Cogley, JG and 10 others (2011) Glossary of glacier mass balance and related terms. UNESCO-International Hydrological Programme, Paris. IHP-VII Technical Documents in Hydrology 86
Conway, H, Smith, B, Vaswani, P, Matsuoka, K, Rignot, E and Claus, P (2009) A low-frequency ice-penetrating radar system adapted for use from an airplane: test results from Bering and Malaspina Glaciers, Alaska, USA. Ann. Glaciol., 50(51), 9397 (doi: 10.3189/172756409789097487)
Cuffey, KM and Paterson, WSB (2010) The physics of glaciers, 4th edn. Butterworth-Heinemann, Oxford
Engel, CS (2008) Defining basal geometry and force balance at Columbia Glacier, Alaska. (MS thesis, University of Colorado, Boulder)
Farinotti, D, Huss, M, Bauder, A, Funk, M and Truffer, M (2009a) A method to estimate ice volume and ice-thickness distribution of alpine glaciers. J. Glaciol., 55(191), 422430 (doi: 10.3189/002214309788816759)
Farinotti, D, Huss, M, Bauder, A and Funk, M (2009b) An estimate of the glacier ice volume in the Swiss Alps. Global Planet. Change, 68(3), 225231 (doi: 10.1016/j.gloplacha.2009.05.004)
Fastook, JL, Brecher, HH and Hughes, TJ (1995) Derived bedrock elevations, strain rates and stresses from measured surface elevations and velocities: Jakobshavns Isbræ, Greenland. J. Glaciol., 41(137), 161173
Hock, R, De Woul, M and Radić, V (2009) Mountain glaciers and ice caps around Antarctica make a large sea-level rise contribution. Geophys. Res. Lett., 36(7), L07501 (doi: 10.1029/2008GL037020)
Howat, IM,Joughin, I, Tulaczyk, S and Gogineni, S (2005) Rapid retreat and acceleration of Helheim Glacier, east Greenland. Geophys. Res. Lett., 32(22), L22502 (doi: 10.1029/2005GL024737)
Huss, M, Usselmann, S, Farinotti, D and Bauder, A (2010) Glacier mass balance in the south-eastern Swiss Alps since 1900 and perspectives for the future. Erdkunde, 64(2), 119140 (doi: 10.3112/erdkunde.2010.02.02)
Joughin, I (2002) Ice-sheet velocity mapping: a combined interferometric and speckle-tracking approach. Ann. Glaciol., 34, 195201 (doi: 10.3189/172756402781817978)
Joughin, I, Kwok, R and Fahnestock, M (1996) Estimation of ice- sheet motion using satellite radar interferometry: method and error analysis with application to Humboldt Glacier, Greenland. J. Glaciol., 42(142), 564575
Kienholz, C (2010) Shrinkage of selected south-central Alaskan glaciers AD 1900–2010: a spatio-temporal analysis applying photogrammetric, GIS-based and historical methods. (Master’s thesis, University of Bern)
Korona, J, Berthier, E, Bernard, M, Rmy, F and Thouvenot, E (2009) SPIRIT. SPOT 5 stereoscopic survey of polar ice: reference images and topographies during the fourth International Polar Year (2007–2009). ISPRS J. Photogramm. Remote Sens., 64(2), 204212 (doi: 10.1016/j.isprsjprs.2008.10.005)
Krimmel, RM (2001) Photogrammetric data set, 1957–2000, and bathymetric measurements for Columbia Glacier, Alaska. USGS Water-Resour. Invest. Rep. 014089
Larsen, CF, Motyka, RJ, Freymueller, JT, Echelmeyer, KA and Ivins, ER (2005) Rapid viscoelastic uplift in southeast Alaska caused by post-Little Ice Age glacial retreats. Earth Planet. Sci. Lett., 237(3–4), 548560
Larsen, CF, Motyka, RJ, Arendt, AA, Echelmeyer, KA and Geissler, PE (2007) Glacier changes in southeast Alaska and northwest British Columbia and contribution to sea level rise. J. Geophys. Res., 112(F1), F01007 (doi: 10.1029/2006JF000586)
Li, H, Li, Z, Zhang, M and Li, W (2011) An improved method based on shallow ice approximation to calculate ice thickness along flow-line and volume of mountain glaciers. J. Earth Sci., 22(4), 441–338 (doi: 10.1007/s12583–011–0198–1)
Mayo, LR, Trabant, DC, March, R and Haeberli, W (1979) Columbia Glacier stake location, mass balance, glacier surface altitude, and ice radar data: 1978 measurement year. USGS Open File Rep. 791168
Meier, MF and Post, A (1987) Fast tidewater glaciers. J. Geophys. Res., 92(B9), 90519058 (doi: 10.1029/JB092iB09p09051)
Meier, MF, Rasmussen, LA, Krimmel, RM, Olsen, RW and Frank, D (1985) Photogrammetric determination of surface altitude, terminus position, and ice velocity of Columbia Glacier, Alaska. USGS Prof. Pap. 1258-F
Meier, MF and 7 others (2007) Glaciers dominate eustatic sea-level rise in the 21st century. Science, 317(5841), 10641067 (doi: 10.1126/science.1143906)
Molnia, BF (2008) Glaciers of North America: glaciers of Alaska. In Williams, RS Jr and Ferrigno, JG eds. Satellite image atlas of glaciers of the world. United States Geological Survey, Denver, CO (USGS Professional Paper 1386-K)
Moon, T and Joughin, I (2008) Changes in ice front position on Greenland’s outlet glaciers from 1992 to 2007. J. Geophys. Res., 113(F2), F02022 (doi: 10.1029/2007JF000927)
Morlighem, M, Rignot, E, Seroussi, H, Larour, E, Ben Dhia, H and Aubry, D (2011) A mass conservation approach for mapping glacier ice thickness. Geophys. Res. Lett., 38(19), L19503 (doi: 10.1029/2011GL048659)
Noll, GT (2005) Report of equipment and methods to accompany data from Project OPR-P132-RA-05, Eastern Prince William Sound, AK. National Oceanographic and Atmospheric Administration. National Geophysical Data Center, National Ocean Service, Boulder, CO. Columbia Bay Hydrographic Survey RAP Sheets H11493/H11494
O’Neel, S (2012) Surface mass balance of the Columbia Glacier, Alaska, 1978 and 2010 balance years. US Geological Survey, Reston, VA. USGS Data Series 676
O’Neel, S, Pfeffer, WT, Krimmel, R and Meier, M (2005) Evolving force balance at Columbia Glacier, Alaska, during its rapid retreat. J. Geophys. Res., 110(F3), F03012 (doi: 10.1029/2005JF000292)
Paden, J, Akins, T, Dunson, D, Allen, C and Gogineni, S (2010) Ice-sheet bed 3-D tomography. J. Glaciol., 56(195), 311 (doi: 10.3189/002214310791190811)
Pfeffer, WT (2007) A simple mechanism for irreversible tidewater glacier retreat. J. Geophys. Res., 112(F3), F03S25 (doi: 10.1029/2006JF000590)
Pfeffer, WT, Harper, JT and O’Neel, S (2008) Kinematic constraints on glacier contributions to 21st-century sea-level rise. Science, 321(5894), 13401343 (doi: 10.1126/science.1159099)
Porter, SC (1989) Late Holocene fluctuations of the fiord glacier system in Icy Bay, Alaska, USA. Arct. Alp. Res., 21(4), 364379
Radić, V and Hock, R (2010) Regional and global volumes of glaciers derived from statistical upscaling of glacier inventory data. J. Geophys. Res., 115(F1), F01010 (doi: 10.1029/2009JF001373)
Radić, V, Hock Rand Oerlemans, J (2008) Analysis of scaling methods in deriving future volume evolutions of valley glaciers. J. Glaciol., 54(187), 601612 (doi: 10.3189/002214308786570809)
Rasmussen, LA (1988) Bed topography and mass-balance distribution of Columbia Glacier, Alaska, U.S.A., determined from sequential aerial photography. J. Glaciol., 34(117), 208216
Rasmussen, LA, Conway, HB, Krimmel, RM and Hock, R (2011) Surface mass balance, thinning, and iceberg production, Columbia Glacier, Alaska, 1948–2007. J. Glaciol., 57(203), 431440 (doi: 10.3189/002214311796905532)
Rignot, E and Kanagaratnam, P (2006) Changes in the velocity structure of the Greenland Ice Sheet. Science, 311(5673), 986990 (doi: 10.1126/science.1121381)
Seroussi, H and 6 others (2011) Ice flux divergence anomalies on 79north Glacier, Greenland. Geophys. Res. Lett., 38(9), L09501 (doi: 10.1029/2011GL047338)
Strozzi, T, Luckman, A, Murray, T, Wegmuller, U and Werner, CL (2002) Glacier motion estimation using satellite-radar offsettracking procedures. IEEE Trans. Geosci. Remote Sens., 40(11), 2834–2391 (doi: 10.1109/TGRS.2002.805079)
Vieli, A, Funk, M and Blatter, H (2001) Flow dynamics of tidewater glaciers: a numerical modelling approach. J. Glaciol., 47(159), 595606 (doi: 10.3189/172756501781831747)
Walter, F, O’Neel, S, McNamara, DE, Pfeffer, T, Bassis, J and Fricker, HA (2010) Iceberg calving during transition from grounded to floating ice: Columbia Glacier, Alaska. Geophys. Res. Lett., 37(15), L15501 (doi: 10.1029/2010GL043201)
Warner, RC and Budd, WF (2000) Derivation of ice thickness and bedrock topography in data-gap regions over Antarctica. Ann. Glaciol., 31, 191197 (doi: 10.3189/172756400781820011)
Weertman, J (1974) Stability of the junction of an ice sheet and an ice shelf. J. Glaciol., 13(67), 311
Wilson, FH, Dover, JH, Bradley, DC, Weber, FR, Bundtzen, TK and Haeussler, PJ (1998) Geologic map of central (interior) Alaska. USGS Open File Rep. 98133-A, version 1.2

Metrics

Altmetric attention score

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