Skip to main content Accessibility help

Roughness of a subglacial conduit under Hansbreen, Svalbard



Hydraulic roughness exerts an important but poorly understood control on water pressure in subglacial conduits. Where relative roughness values are <5%, hydraulic roughness can be related to relative roughness using empirically-derived equations such as the Colebrook–White equation. General relationships between hydraulic roughness and relative roughness do not exist for relative roughness >5%. Here we report the first quantitative assessment of roughness heights and hydraulic diameters in a subglacial conduit. We measured roughness heights in a 125 m long section of a subglacial conduit using structure-from-motion to produce a digital surface model, and hand-measurements of the b-axis of rocks. We found roughness heights from 0.07 to 0.22 m and cross-sectional areas of 1–2 m2, resulting in relative roughness of 3–12% and >5% for most locations. A simple geometric model of varying conduit diameter shows that when the conduit is small relative roughness is >30% and has large variability. Our results suggest that parameterizations of conduit hydraulic roughness in subglacial hydrological models will remain challenging until hydraulic diameters exceed roughness heights by a factor of 20, or the conduit radius is >1 m for the roughness elements observed here.

  • 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.

      Roughness of a subglacial conduit under Hansbreen, Svalbard
      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.

      Roughness of a subglacial conduit under Hansbreen, Svalbard
      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.

      Roughness of a subglacial conduit under Hansbreen, Svalbard
      Available formats


This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Correspondence: Ken Mankoff <>


Hide All
Aberle, J and Nikora, V (2006) Statistical properties of armored gravel bed surfaces. Water Resour. Res., 42(11) (doi: 10.1029/2005WR004674)
Banwell, AF, MacAyeal, DR and Sergienko, OV (2013) Break-up of the Larsen B ice shelf triggered by chain-reaction drainage of Supraglacial Lakes. Geophys. Res. Lett., 40(22), 58725876 (doi: 10.1002/2013GL057694)
Bertin, S and Freidrich, H (2014) Measurement of gravel-bed topography: evaluation study applying statistical roughness analysis. J. Hydraulic Eng., 140(3), 269279 (doi: 10.1061/(ASCE)HY.1943-7900.0000823)
Bindschadler, RA (1983) The importance of pressurized subglacial water in separation and sliding at the glacier bed. J. Glaciol., 29(101), 319
Chikita, KA, Kaminaga, R, Kudo, I, Wada, T and Kim, Y (2010) Parameters determining water temperature of a proglacial stream: the Phelan Creek and the Gulkana Glacier, Alaska. River Res. Appl., 26, 9951004
Covington, MD, Luhmann, AJ, Gabrovšek, F, Saar, MO and Wicks, CM (2011) Mechanisms of heat exchange between water and rock in karst conduits. Water Resour. Res., 47(W10514) (doi: 10.1029/2011WR010683)
Crosby, C and 6 others (2011) Points2Grid: A Local Gridding Method for DEM Generation from Lidar Point Cloud Data. [Software]
Cuffey, KM and Paterson, WSB (2010) The physics of glaciers, 4th edn. Academic Press
Curl, RL (1974) Deducing flow velocity in cave conduits from scallops. Natl. Speleol. Soc. Bull., 36(2), 15, (Errata: ibid. Vol. 36, No. 3, p. 22)
Fonstad, MA, Dietrich, JT, Courville, BC, Jensen, JL and Carbonneau, PE (2013) Topographic structure from motion: a new development in photogrammetric measurement. Earth Surf. Process. Landforms, 38, 421430 (doi: 10.1002/esp.3366)
Gulley, JD (2009) Structural control of englacial conduits in the temperate Matanuska Glacier, Alaska, USA. J. Glaciol., 55(192), 681690
Gulley, JD and 5 others (2012) The effect of discrete recharge by moulins and heterogeneity in flow-path efficiency at glacier beds on subglacial hydrology. J. Glaciol., 58(211), 926940 (doi: 10.3189/2012JoG11J189)
Gulley, JD and 5 others (2014) Large values of hydraulic roughness in subglacial conduits during conduit enlargement: implications for modeling conduit evolution. Earth Surf. Process. Landforms, 39(3), 296310 (doi: 10.1002/esp.3447)
Hewitt, IJ (2011) Modelling distributed and channelized subglacial drainage: the spacing of channels. J. Glaciol., 57(202)
Hodge, RA, Brasington, J and Richards, K (2009) Analysing laser-scanned digital terrain models of gravel bed surfaces: linking morphology to sediment transport processes and hydraulics. Sedimentology, 56(7), 20242043 (doi: 10.1111/j.1365-3091.2009.01068.x)
Isenko, E, Naruse, R and Mavlyudov, B (2005) Water temperature in englacial and supraglacial channels: change along the flow and contribution to ice melting on the channel wall. Cold Reg. Sci. Technol., 42, 5362 (doi: 10.1016/j.coldregions.2004.12.003)
James, MR and Robson, S (2012) Straightforward reconstruction of 3D surfaces and topography with a camera: accuracy and geoscience applications. J. Geophys. Res., 117(F03017) (doi: 10.1029/2011JF002289)
Jarrett, RD (1984) Hydraulics of high-gradient streams. J. Hydraulic Eng., 110(11), 15191539 (doi: 10.1061/(ASCE)0733-9429(1984)110:11(1519))
Jezek, KC, Wu, X, Paden, J and Leuschen, C (2013) Radar mapping of Isunguata Sermia, Greenland. J. Glaciol., 59(218), 1135 (doi: 10.3189/2013JoG12J248)
Kolmogorov, AN (1991) The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Proc. Math. Phys. Sci., 434(1890), 913.
Liestøl, O (1956) Glacier Dammed Lakes in Norway, vol. 81. Fabritius & Sønners Forlag, Oslo
Limerinos, J (1970) Determination of the manning coefficient from measured bed roughness in natural channels. United States Government Printing Office, geological survey water-supply paper 1898-b edition, Washington, DC
Mankoff, KD and Russo, TA (2013) The Kinect: a low-cost, high-resolution, short-range, 3D camera. Earth Surf. Process. Landforms, 38(9), 926936 (doi: 10.1002/esp.3332)
Mankoff, KD and 5 others (2016) Structure and dynamics of a subglacial discharge plume in a Greenlandic fjord. J. Geophys. Res.: Oceans, 121 (doi: 10.1002/2016JC011764)
Moody, LF (1944) Friction factors for pipe flow. Trans. A.S.M.E., 66(8), 671684
Munson, BR, Young, DF, Okiishi, TH and Heubsch, WW (2009) Fundamentals of fluid mechanics, 6th edn. John Wiley & Sons, Inc.
Nienow, PW, Sharp, M and Willis, IC (1998) Seasonal changes in the morphology of the subglacial drainage system, Haut Glacier d'Arolla, Switzerland. Earth Surf. Process. Landforms, 23(9), 825843 (doi: 10.1002/(SICI)1096-9837(199809)23:9<825::AID-ESP893>3.0.CO;2-2)
Nikora, VI and Walsh, J (2004) Water-worked gravel surfaces: high-order structure functions at the particle scale. Water Resour. Res., 40(12) (doi: 10.1029/2004WR003346)
Nikora, VI, Goring, DG and Biggs, BJF (1998) On gravel-bed roughness characterization. Water Resour. Res., 34(3), 517527 (doi: 10.1029/97WR02886)
Nikuradse, J (1950) Laws of flow in rough pipes. Technical Memorandum 1292, National Advisory Committee for Aeronautics (NACA), translation of ‘Strömungsgesetze in rauhen Rohren.’ 1933
Nye, JF (1976) Water flow in glaciers: jökulhlaups, tunnels and veins. J. Glaciol., 17(76), 181207
Perol, T, Rice, JR, Platt, JD and Suckale, J (2015) Subglacial hydrology and ice stream margin locations. J. Geophys. Res.: Earth Surf., 120(7), 13521368 (doi: 10.1002/2015JF003542)
Powell, M (2014) Flow resistance in gravel-bed rivers: progress in research. Earth-Sci. Rev., 136, 301338 (doi: 10.1016/j.earscirev.2014.06.001)
Röthlisberger, H (1972) Water pressure in intra- and subglacial channels. J. Glaciol., 11(62), 177203
Rusu, RB and Cousins, S (2011) 3D is here: Point Cloud Library (PCL). In IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China
Schoof, CG (2010) Ice-sheet acceleration driven by melt supply variability. Nature, 468(7325), 803806 (doi: 10.1038/nature09618)
Shreve, RL (1972) Movement of water in glaciers. J. Glaciol., 11(62), 205214
Smart, G, Aberle, J, Duncan, M and Walsh, J (2004) Measurement and analysis of alluvial bed roughness/mesure et analyse de la rugosité de lit d'alluvion. J. Hydraulic Res., 42(3), 227237 (doi: 10.1080/00221686.2004.9641191)
Smart, GM, Duncan, MJ and Walsh, JM (2002) Relatively rough flow resistance equations. J. Hydraulic Eng., 128, 568578 (doi: 10.1061/(ASCE)0733-9429(2002)128:6(568))
Smith, MW (2014) Roughness in the earth sciences. Earth-Sci. Rev., 136, 202225 (doi: 10.1016/j.earscirev.2014.05.016)
Westoby, MJ, Brasington, J, Glasser, NF, Hambrey, MJ and Reynolds, JM (2012) ‘Structure-from-Motion’ photogrammetry: a low-cost, effective tool for geoscience applications. Geomorphology, 179, 300314 (doi: 10.1016/j.geomorph.2012.08.021)
Whelan, T and 5 others (2012) Kintinuous: spatially extended KinectFusion. In RSS Workshop on RGB-D: Advanced Reasoning with Depth Cameras, Sydney, Australia
Wolman, MG (1954) A method of sampling coarse river-bed material. Trans. Am. Geophys. Union, 35(6), 951956



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