Skip to main content Accessibility help

Inversion of a glacier hydrology model

  • Douglas J. Brinkerhoff (a1), Colin R. Meyer (a2), Ed Bueler (a1), Martin Truffer (a1) and Timothy C. Bartholomaus (a3)...


The subglacial hydrologic system exerts strong controls on the dynamics of the overlying ice, yet the parameters that govern the evolution of this system are not widely known or observable. To gain a better understanding of these parameters, we invert a spatially averaged model of subglacial hydrology from observations of ice surface velocity and outlet stream discharge at Kennicott Glacier, Wrangell Mountains, AK, USA. To identify independent parameters, we formally non-dimensionalize the forward model. After specifying suitable prior distributions, we use a Markov-chain Monte Carlo algorithm to sample from the distribution of parameter values conditioned on the available data. This procedure gives us not only the most probable parameter values, but also a rigorous estimate of their covariance structure. We find that the opening of cavities due to sliding over basal topography and turbulent melting are of a similar magnitude during periods of large input flux, though turbulent melting also exhibits the greatest uncertainty. We also find that both the storage of water in the englacial system and the exchange of water between englacial and subglacial systems are necessary in order to explain both surface velocity observations and the relative attenuation in the amplitude of diurnal signals between input and output flux observations.

  • 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.

      Inversion of a glacier hydrology model
      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.

      Inversion of a glacier hydrology model
      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.

      Inversion of a glacier hydrology model
      Available formats


This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use.


Hide All
Amundson, JM, Truffer, M and Lüthi, MP (2006) Time-dependent basal stress conditions beneath Black Rapids Glacier, Alaska, USA, inferred from measurements of ice deformation and surface motion. J. Glaciol., 52(178), 347357 (doi: 10.3189/172756506781828593)
Arnold, N, Richards, K, Willis, I and Sharp, M (1998) Initial results from a distributed, physically based model of glacier hydrology. Hydrol. Process., 12(2), 191219 (doi: 10.1002/(SICI)1099-1085(199802)12:2<191::AID-HYP571>3.0.CO;2-C)
Bartholomaus, TC, Anderson, R and Anderson, S (2008) Response of glacier basal motion to transient water storage. Nat. Geosci., 1, 3337 (doi: 10.1038/ngeo.2007.52)
Bartholomaus, TC, Anderson, RS and Anderson, SP (2011) Growth and collapse of the distributed subglacial hydrologic system of Kennicott Glacier, Alaska, USA, and its effects on basal motion. J. Glaciol., 57(206), 9851002 (doi: 10.3189/002214311798843269)
Bindschadler, R (1983) The importance of pressurized subglacial water in separation and sliding at the glacier bed. J. Glaciol., 29(101), 319
Bueler, E (2014) Extending the lumped subglacial–englacial hydrology model of Bartholomaus and others (2011). J. Glaciol., 60(222), 808810 (doi: 10.3189/2014JoG14J075)
Bueler, E and Van Pelt, W (2015) Mass-conserving subglacial hydrology in the Parallel Ice Sheet Model version 0.6. Geosci. Model Dev., 8(6), 16131635 (doi: 10.5194/gmd-8-1613-2015)
Clarke, GKC (2003) Hydraulics of subglacial outburst floods: new insights from the Spring–Hutter formulation. J. Glaciol., 49(165), 299313 (doi: 10.3189/172756503781830728)
Engelhardt, H and Kamb, B (1998) Basal sliding of Ice Stream B, West Antarctica. J. Glaciol., 44(147), 223230
Fischer, UH and Clarke, GKC (1997) Stick–slip sliding behaviour at the base of a glacier. Ann. Glaciol., 24, 390396
Flowers, GE and Clarke, GKC (2002a) A multicomponent coupled model of glacier hydrology 1. Theory and synthetic examples. J. Geophys. Res., 107(B11), ECV-9 (doi: 10.1029/2001JB001122)
Flowers, GE and Clarke, GKC (2002b) A multicomponent coupled model of glacier hydrology 2. Application to Trapridge Glacier, Yukon, Canada. J. Geophys. Res.: Solid Earth, 107(B11), ECV-10 (doi: 10.1029/2001JB001124)
Flowers, GE, Björnsson, H and Pálsson, F (2002) New insights into the subglacial and periglacial hydrology of Vatnajökull, Iceland, from a distributed physical model. J. Glaciol., 49(165), 257270 (doi: 10.3189/172756503781830827)
Fountain, AG, Jacobel, RW, Schlichting, R and Jansson, P (2005) Fractures as the main pathways of water flow in temperate glaciers. Nature, 433, 618621 (doi: 10.1038/nature03296)
Fowler, AC (1986) A sliding law for glaciers of constant viscosity in the presence of subglacial cavitation. Proc. R. Soc. London, Ser. A, 407, 147170 (doi: 10.1098/rspa.1986.0090)
Gagliardini, O, Cohen, D, Råback, P and Zwinger, T (2007) Finite-element modeling of subglacial cavities and related friction law. J. Geophys. Res.: Earth Surf., 112(F2) (doi: 10.1029/2006JF000576)
Gelman, A and Rubin, DR (1992) A single series from the Gibbs sampler provides a false sense of security. In Bernardo, JM, Berger, JO, Dawid, AP and Smith, AFM eds. Bayesian statistics 4. Oxford University Press, Oxford, 625631
Haario, H, Saksman, E and Tamminen, J (2001) An adaptive Metropolis algorithm. Bernoulli, 7(2), 223242
Harper, JT, Humphrey, NF, Pfeffer, WT and Lazar, B (2007) Two modes of accelerated glacier sliding related to water. Geophys. Res. Lett., 34(12), L12503 (doi: 10.1029/2007GL030233)
Harper, JT, Bradford, JH, Humphrey, NF and Meierbachtol, TW (2010) Vertical extension of the subglacial drainage system into basal crevasses. Nature, 467, 579582 (doi: 10.1038/nature09398)
Hastings, WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97109
Hewitt, IJ (2011) Modelling distributed and channelized subglacial drainage: the spacing of channels. J. Glaciol., 57(202), 302314 (doi: 10.3189/002214311796405951)
Hock, R (2005) Glacier melt: a review of processes and their modelling. Progr. Phys. Geogr., 29(3), 362391 (doi: 10.1191/0309133305pp453ra)
Hubbard, B and Sharp, M (1995) Basal ice facies and their formation in the western Alps. Arct. Alp. Res., 27(4), 301310
Iken, A (1981) The effect of the subglacial water pressure on the sliding velocity of a glacier in an idealized numerical model. J. Glaciol., 27(97), 407421
Iken, A and Bindschadler, RA (1986) Combined measurements of subglacial water pressure and surface velocity of Findelengletscher, Switzerland: conclusions about drainage system and sliding mechanism. J. Glaciol., 32(110), 101119
Iken, A and Truffer, M (1997) The relationship between subglacial water pressure and velocity of Findelengletscher, Switzerland, during its advance and retreat. J. Glaciol., 43(144), 328338
Iken, A, Röthlisberger, H, Flotron, A and Haeberli, W (1983) The uplift of Unteraargletscher at the beginning of the melt season: a consequence of water storage at the bed? J. Glaciol., 29(101), 2847
Jansson, P (1995) Water pressure and basal sliding on Storglaciären, northern Sweden. J. Glaciol., 41(138), 232240
Kamb, B (1987) Glacier surge mechanism based on linked cavity configuration of the basal water conduit system. J. Geophys. Res., 92(B9), 90839100
Lliboutry, L (1968) General theory of subglacial cavitation and sliding of temperate glaciers. J. Glaciol., 7(49), 2158
Nienow, P, Sharp, M and Willis, I (1998) Seasonal changes in the morphology of the subglacial drainage system, Haut Glacier d'Arolla, Switzerland. Earth Surf. Process. Landf., 23(9), 825843
Nye, JF (1976) Water flow in glaciers: jökulhlaups, tunnels and veins. J. Glaciol., 17, 181207
Patil, A, Huard, D and Fonnesbeck, CJ (2010) PyMC: Bayesian stochastic modelling in Python. J. Stat. Softw, 35(4), 181
Röthlisberger, H (1972) Water pressure in intra- and subglacial channels. J. Glaciol., 11, 177203
Schoof, C (2005) The effect of cavitation on glacier sliding. Proc. R. Soc. London, Ser. A: Math., Phys., Eng. Sci., 461(2055), 609627 (doi: 10.1098/rspa.2004.1350)
Schoof, C (2010) Ice-sheet acceleration driven by melt supply variability. Nature, 468(7325), 803806 (doi: 10.1038/nature09618)
Schoof, C, Hewitt, IJ and Werder, MA (2012) Flotation and free surface flow in a model for subglacial drainage. Part 1. Distributed drainage. J. Fluid Mech., 702, 126156 (doi: 10.1017/jfm.2012.165)
Sugiyama, S and Gudmundsson, GH (2004) Short-term variations in glacier flow controlled by subglacial water pressure at Lauteraargletscher, Bernese Alps, Switzerland. J. Glaciol., 50(170), 353362 (doi: 10.3189/172756504781829846)
Tarantola, A (2005) Inverse problem theory and methods for model parameter estimation. Society for Industrial and Applied Mathematics, Philadelphia, PA
Truffer, M and Harrison, WD (2006) In situ measurements of till deformation and water pressure. J. Glaciol., 52(177), 175182 (doi: 10.3189/172756506781828700)
Tsai, VC and Rice, JR (2010) A model for turbulent hydraulic fracture and application to crack propagation at glacier beds. J. Geophys. Res.: Earth Surf., 115(F3) (doi: 10.1029/2009JF001474)
Walder, JS (1986) Hydraulics of subglacial cavities. J. Glaciol., 32(112), 439445
Werder, MA, Hewitt, IJ, Schoof, CG and Flowers, GE (2013) Modeling channelized and distributed subglacial drainage in two dimensions. J. Geophys. Res.: Earth Surf., 118(4), 21402158 (doi: 10.1002/jgrf.20146)
Willis, I and 11 others (1995) Water storage, drainage evolution and water quality in alpine glacial environments – final report on NERC grant GR3/8114. Technical Report. Natural Environment Research Council, Cambridge
Zwally, HJ and 5 others (2002) Surface melt-induced acceleration of Greenland ice-sheet flow. Science, 297, 218222 (doi: 10.1126/science.1072708)


Related content

Powered by UNSILO

Inversion of a glacier hydrology model

  • Douglas J. Brinkerhoff (a1), Colin R. Meyer (a2), Ed Bueler (a1), Martin Truffer (a1) and Timothy C. Bartholomaus (a3)...


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.