How accurate are estimates of glacier ice thickness? Results from ITMIX, the Ice Thickness Models Intercomparison eXperiment

Abstract. Knowledge of the ice thickness distribution of glaciers and ice caps is an important prerequisite for many glaciological and hydrological investigations. A wealth of approaches has recently been presented for inferring ice thickness from characteristics of the surface. With the Ice Thickness Models Intercomparison eXperiment (ITMIX) we performed the first coordinated assessment quantifying individual model performance. A set of 17 different models showed that individual ice thickness estimates can differ considerably – locally by a spread comparable to the observed thickness. Averaging the results of multiple models, however, significantly improved the results: on average over the 21 considered test cases, comparison against direct ice thickness measurements revealed deviations on the order of 10 ± 24 % of the mean ice thickness (1σ estimate). Models relying on multiple data sets – such as surface ice velocity fields, surface mass balance, or rates of ice thickness change – showed high sensitivity to input data quality. Together with the requirement of being able to handle large regions in an automated fashion, the capacity of better accounting for uncertainties in the input data will be a key for an improved next generation of ice thickness estimation approaches.

Ankur Pandit | Fabien Gillet-Chaulet | Thomas J. Reerink | Raaj Ramsankaran | Mathieu Morlighem | Antoine Rabatel | Andreas Linsbauer | Huilin Li | Liss M. Andreassen | Andrea Fischer | Garry K. C. Clarke | Matthias Huss | Julian A. Dowdeswell | Daniel Farinotti | Holger Frey | Prateek Gantayat | Horst Machguth | Ward J. J. van Pelt | Douglas J. Brinkerhoff | Daniel Binder | H. Frey | Huilin Li | G. Clarke | M. Morlighem | J. Dowdeswell | M. Huss | D. Farinotti | L. Andreassen | P. A. Stentoft | K. Helfricht | F. Maussion | G. Gudmundsson | W. V. Pelt | R. Ramsankaran | I. Lavrentiev | F. Gillet-Chaulet | J. Fürst | T. Reerink | B. Anderson | P. Gantayat | A. Fischer | S. Kutuzov | R. McNabb | A. Rabatel | Olivier Sanchez | C. Mosbeux | Carlos Martín | H. Machguth | A. Linsbauer | D. Brinkerhoff | Johannes J. Fürst | G. Hilmar Gudmundsson | Fabien Maussion | Stanislav Kutuzov | Toby J. Benham | P. Leclercq | Brian Anderson | A. Pandit | Carlos Martin | T. Benham | Cyrille Mosbeux | Robert McNabb | P. W. Leclercq | Olivier Sanchez | Claire Girard | Andrea Portmann | S. Kumari | D. Binder | Kay Helfricht | Claire Girard | Andrea Portmann | Peter Alexander Stentoft | Sangita Singh Kumari | Ivan Lavrentiev | C. Martín | G. H. Gudmundsson | Holger Frey | Garry K. C. Clarke | Claire Girard | P. W. Leclercq | Carlos Martin | Andrea Portmann | Thomas | J. Reerink | Sangita Singh Kumari | Brian Anderson | Daniel Binder | Andrea Fischer | Huilin Li | F. Gillet‐Chaulet | Mathieu Morlighem | P. Leclercq

[1]  P. Whitfield,et al.  Effects of Temperature Forcing Provenance and Extrapolation on the Performance of an Empirical Glacier-Melt Model , 2014 .

[2]  Aslak Grinsted,et al.  An estimate of global glacier volume , 2012 .

[3]  T. Reerink,et al.  Mapping technique of climate fields between GCM's and ice models , 2009 .

[4]  A. Bauder,et al.  An estimate of the glacier ice volume in the Swiss Alps , 2008 .

[5]  T. Bolch,et al.  Ice Volume and Subglacial Topography for Western Canadian Glaciers from Mass Balance Fields, Thinning Rates, and a Bed Stress Model , 2013 .

[6]  S. Peckham,et al.  The physical basis of glacier volume-area scaling , 1997 .

[7]  E. Isaksson,et al.  An iterative inverse method to estimate basal topography and initialize ice flow models , 2013 .

[8]  Frank Paul,et al.  Modeling of glacier bed topography from glacier outlines, central branch lines, and a DEM , 2012, Int. J. Geogr. Inf. Sci..

[9]  M. Hutchinson.  A new procedure for gridding elevation and stream line data with automatic removal of spurious pits , 1989 .

[10]  M. Lüthi.  Transient response of idealized glaciers to climate variations , 2009, Journal of Glaciology.

[11]  Laurent D. Michel,et al.  Estimating the ice thickness of shallow glaciers from surface topography and mass-balance data with a shape optimization algorithm , 2014, Comput. Geosci..

[12]  I. Willis,et al.  Subglacial drainage system structure and morphology of Brewster Glacier, New Zealand , 2009 .

[13]  Huilin Li,et al.  Analyses of recent observations of Urumqi Glacier No. 1, Chinese Tianshan Mountains , 2016, Environmental Earth Sciences.

[14]  Mika Malinen,et al.  Capabilities and performance of Elmer/Ice, a new-generation ice sheet model , 2013 .

[15]  G. Flowers,et al.  Comparison of thermal structure and evolution between neighboring subarctic glaciers , 2013 .

[16]  Douglas J. Brinkerhoff,et al.  Data assimilation and prognostic whole ice sheet modelling with the variationally derived, higher order, open source, and fully parallel ice sheet model VarGlaS , 2013 .

[17]  Konrad Schindler,et al.  OPTICAL FLOW FOR GLACIER MOTION ESTIMATION , 2012 .

[18]  S. Shyam Sunder,et al.  Creep of Polycrystalline Ice , 1990 .

[19]  Julian A. Dowdeswell,et al.  Form and flow of the Devon Island Ice Cap, Canadian Arctic , 2004 .

[20]  F. Paul,et al.  Modeling glacier thickness distribution and bed topography over entire mountain ranges with GlabTop: Application of a fast and robust approach , 2012 .

[21]  C. Kelley,et al.  Convergence Analysis of Pseudo-Transient Continuation , 1998 .

[22]  K. Hutter.  Theoretical Glaciology: Material Science of Ice and the Mechanics of Glaciers and Ice Sheets , 1983 .

[23]  A. Ohmura,et al.  Estimation of Alpine glacier water resources and their change since the 1870s , 1990 .

[24]  L. A. Rasmussen.  Bed Topography and Mass-Balance Distribution of Columbia Glacier, Alaska, U.S.A., Determined from Sequential Aerial Photography , 1988, Journal of Glaciology.

[25]  Matthias Huss,et al.  Distributed ice thickness and volume of all glaciers around the globe , 2012 .

[26]  Ed Bueler,et al.  Shallow shelf approximation as a “sliding law” in a thermomechanically coupled ice sheet model , 2008, 0810.3449.

[27]  Barclay Kamb,et al.  Stress-Gradient Coupling in Glacier Flow: I. Longitudinal Averaging of the Influence of Ice Thickness and Surface Slope , 1986, Journal of Glaciology.

[28]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[29]  D. Brinkerhoff,et al.  Dynamics of thermally induced ice streams simulated with a higher‐order flow model , 2015 .

[30]  Georg Kaser,et al.  A review of volume‐area scaling of glaciers , 2015, Reviews of geophysics.

[31]  F. Pattyn.  A new three-dimensional higher-order thermomechanical ice sheet model: Basic sensitivity, ice stream development, and ice flow across subglacial lakes , 2003 .

[32]  M. Hoelzle,et al.  The Swiss Alps without glaciers – a GIS-based modelling approach for reconstruction of glacier beds , 2009 .

[33]  Andreas Bauder,et al.  Ice volume distribution and implications on runoff projections in a glacierized catchment , 2012 .

[34]  Edward C. King,et al.  The bedrock topography of Starbuck Glacier, Antarctic Peninsula, as determined by radio-echo soundings and flow modeling , 2014, Annals of Glaciology.

[35]  Mélanie Raymond Pralong,et al.  Bayesian estimation of basal conditions on Rutford Ice Stream, West Antarctica, from surface data , 2011, Journal of Glaciology.

[36]  Maohuan Huang,et al.  SOME DYNAMICS STUDIES ON URUMQI GLACIER No. 1, TIANSHAN GLACIOlOGICAl STATION, CHINA , 1989 .

[37]  J. F. Nye,et al.  The Mechanics of Glacier Flow , 1952, Journal of Glaciology.

[38]  Matthias Huss,et al.  A high-resolution bedrock map for the Antarctic Peninsula , 2014 .

[39]  Andreas Kääb,et al.  Landsat-derived glacier inventory for Jotunheimen, Norway, and deduced glacier changes since the 1930s , 2008 .

[40]  Tavi Murray,et al.  A new 100-m Digital Elevation Model of the Antarctic Peninsula derived from ASTER Global DEM: methods and accuracy assessment , 2012 .

[41]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[42]  Eric Rignot,et al.  Deeply incised submarine glacial valleys beneath the Greenland ice sheet , 2014 .

[43]  Alexander H. Jarosch,et al.  Past and future sea-level change from the surface mass balance of glaciers , 2012 .

[44]  R. Bindschadler,et al.  Bed topography and lubrication inferred from surface measurements on fast-flowing ice streams , 2003, Journal of Glaciology.

[45]  J. Oerlemans,et al.  Modelling and climatic interpretation of the length fluctuations of Glaciar Frías (north Patagonian Andes, Argentina) 1639–2009 AD , 2012 .

[46]  Anthony A. Arendt,et al.  A new method for deriving glacier centerlines applied to glaciers in Alaska and northwest Canada , 2013 .

[47]  M. Truffer,et al.  Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA , 2012, Journal of Glaciology.

[48]  D. A. Larson,et al.  On the flow of polythermal glaciers - I. Model and preliminary analysis , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[49]  M. Kuhn,et al.  Glacier mass balances and elevation zones of Kesselwandferner, Ötztal Alps, Austria, 1952/1953 to 2012/2013 , 2014 .

[50]  Anil V. Kulkarni,et al.  Estimating the volume of glaciers in the Himalayan–Karakoram region using different methods , 2014 .

[51]  R. Hock,et al.  Regionally differentiated contribution of mountain glaciers and ice caps to future sea-level rise , 2011 .

[52]  Xavier Fettweis,et al.  Application of a two-step approach for mapping ice thickness to various glacier types on Svalbard , 2017 .

[53]  J. Dowdeswell,et al.  Digital Mapping of the Nordaustlandet Ice Caps from Airborne Geophysical Investigations , 1986, Annals of Glaciology.

[54]  Andreas Kääb,et al.  A new DEM of the Austfonna ice cap by combining differential SAR interferometry with ICESat laser altimetry , 2012 .

[55]  D. Qin,et al.  An extended “perfect‐plasticity” method for estimating ice thickness along the flow line of mountain glaciers , 2012 .

[56]  K. Jain,et al.  Modelling of Gangotri glacier thickness and volume using an artificial neural network , 2014 .

[57]  C. Mitterer,et al.  Tracing glacier changes in Austria from the Little Ice Age to the present using a lidar-based high-resolution glacier inventory in Austria , 2015 .

[58]  A. Shepherd,et al.  Form and flow of the Academy of Sciences Ice Cap, Severnaya Zemlya, Russian High Arctic , 2002 .

[59]  M. Zemp,et al.  A database of worldwide glacier thickness observations , 2014 .

[60]  A. Raftery,et al.  Using Bayesian Model Averaging to Calibrate Forecast Ensembles , 2005 .

[61]  M. Hoelzle,et al.  Application of inventory data for estimating characteristics of and regional climate-change effects on mountain glaciers: a pilot study with the European Alps , 1995, Annals of Glaciology.

[62]  L. Michel,et al.  Estimating the ice thickness of mountain glaciers with an inverse approach using surface topography and mass-balance , 2013 .

[63]  Solveig H. Winsvold,et al.  Ice thickness measurements and volume estimates for glaciers in Norway , 2014 .

[64]  R. Hock,et al.  Regional and global volumes of glaciers derived from statistical upscaling of glacier inventory data , 2010 .

[65]  A. Kulkarni,et al.  Estimation of ice thickness using surface velocities and slope: case study at Gangotri Glacier, India , 2014, Journal of Glaciology.

[66]  Bryn Hubbard,et al.  A review of the use of radio-echo sounding in glaciology , 2001 .

[67]  D. A. Larson,et al.  On the flow of polythermal glaciers. II. Surface wave analysis , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[68]  J. Hagen,et al.  Iceberg calving flux and mass balance of the Austfonna ice cap on Nordaustlandet, Svalbard , 2008 .

[69]  M. Kuhn,et al.  Ground-penetrating radar measurements of 64 Austrian glaciers between 1995 and 2010 , 2013, Annals of Glaciology.

[70]  Rune Engeset,et al.  Reanalysis of long-term series of glaciological and geodetic mass balance for 10 Norwegian glaciers , 2016 .

[71]  Gaël Durand,et al.  Greenland ice sheet contribution to sea-level rise from a new-generation ice-sheet model , 2012 .

[72]  D. Farinotti,et al.  The ice thickness distribution of Flask Glacier, Antarctic Peninsula, determined by combining radio-echo soundings, surface velocity data and flow modelling , 2013, Annals of Glaciology.

[73]  P. A. Stentoft,et al.  Three Decades of Volume Change of a Small Greenlandic Glacier Using Ground Penetrating Radar, Structure from Motion, and Aerial Photogrammetry , 2017, Arctic, Antarctic, and Alpine Research.

[74]  E. Berthier,et al.  Neural Networks Applied to Estimating Subglacial Topography and Glacier Volume , 2009 .

[75]  G. Flowers,et al.  Present dynamics and future prognosis of a slowly surging glacier , 2010 .

[76]  A. Bauder,et al.  A method to estimate the ice volume and ice-thickness distribution of alpine glaciers , 2009 .

[77]  J. F. Nye.  The flow of a glacier in a channel of rectangular, elliptic or parabolic cross-section , 1965 .

[78]  L. George,et al.  Climate sensitivity of a high-precipitation glacier in New Zealand , 2010, Journal of Glaciology.

[79]  M. Truffer,et al.  Bayesian Inference of Subglacial Topography Using Mass Conservation , 2016, Front. Earth Sci..

[80]  R. Taylor.  The Finite Element Method, the Basis , 2000 .

[81]  Fabien Gillet-Chaulet,et al.  Comparison of adjoint and nudging methods to initialise ice sheet model basal conditions , 2016 .

[82]  Douglas R. Macayeal,et al.  A tutorial on the use of control methods in ice-sheet modeling , 1993, Journal of Glaciology.

[83]  Claude Lemaréchal,et al.  Some numerical experiments with variable-storage quasi-Newton algorithms , 1989, Math. Program..

[84]  A. Bauder,et al.  The ice-thickness distribution of Unteraargletscher, Switzerland , 2003, Annals of Glaciology.

[85]  P. Jones,et al.  Updated high‐resolution grids of monthly climatic observations – the CRU TS3.10 Dataset , 2014 .

[86]  K. Cuffey,et al.  Dynamics of an alpine cirque glacier , 2010, American Journal of Science.

[87]  M. Morlighem,et al.  A mass conservation approach for mapping glacier ice thickness , 2011, Geophysical Research Letters.