Articles | Volume 8, issue 6
https://doi.org/10.5194/tc-8-2101-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/tc-8-2101-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Combining damage and fracture mechanics to model calving
J. Krug
CORRESPONDING AUTHOR
CNRS, LGGE, 38041 Grenoble, France
Univ. Grenoble Alpes, LGGE, 38041 Grenoble, France
J. Weiss
CNRS, LGGE, 38041 Grenoble, France
Univ. Grenoble Alpes, LGGE, 38041 Grenoble, France
O. Gagliardini
CNRS, LGGE, 38041 Grenoble, France
Univ. Grenoble Alpes, LGGE, 38041 Grenoble, France
Institut Universitaire de France, Paris, France
G. Durand
CNRS, LGGE, 38041 Grenoble, France
Univ. Grenoble Alpes, LGGE, 38041 Grenoble, France
Related authors
J. Krug, J. Weiss, O. Gagliardini, and G. Durand
The Cryosphere Discuss., https://doi.org/10.5194/tcd-8-1111-2014, https://doi.org/10.5194/tcd-8-1111-2014, 2014
Preprint withdrawn
Juan-Pedro Roldán-Blasco, Adrien Gilbert, Luc Piard, Florent Gimbert, Christian Vincent, Olivier Gagliardini, Anuar Togaibekov, Andrea Walpersdorf, and Nathan Maier
EGUsphere, https://doi.org/10.5194/egusphere-2024-1600, https://doi.org/10.5194/egusphere-2024-1600, 2024
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The flow of glaciers and ice sheets is due to ice deformation and basal sliding driven by gravitational forces. Quantifying the rate at which ice deforms under its own weight is critical to assessing glacier evolution. This study uses borehole instrumentation in an Alpine glacier to quantify ice deformation and constrain its viscosity in a natural setting. Our results show that the viscosity of ice at 0° C is largely influenced by interstitial liquid water which enhances ice deformation.
Nicolas C. Jourdain, Charles Amory, Christoph Kittel, and Gaël Durand
EGUsphere, https://doi.org/10.5194/egusphere-2024-58, https://doi.org/10.5194/egusphere-2024-58, 2024
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A mixed statistical-physical approach is used to reproduce the behaviour of a regional climate model. From that, we estimate the contribution of snowfall and melting at the surface of the Antarctic Ice Sheet to changes in global mean sea level. We also investigate the impact of surface melting in a warmer climate on the stability of the Antarctic ice shelves that provide a back stress on the ice flow to the ocean.
Emily A. Hill, Benoît Urruty, Ronja Reese, Julius Garbe, Olivier Gagliardini, Gaël Durand, Fabien Gillet-Chaulet, G. Hilmar Gudmundsson, Ricarda Winkelmann, Mondher Chekki, David Chandler, and Petra M. Langebroek
The Cryosphere, 17, 3739–3759, https://doi.org/10.5194/tc-17-3739-2023, https://doi.org/10.5194/tc-17-3739-2023, 2023
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The grounding lines of the Antarctic Ice Sheet could enter phases of irreversible retreat or advance. We use three ice sheet models to show that the present-day locations of Antarctic grounding lines are reversible with respect to a small perturbation away from their current position. This indicates that present-day retreat of the grounding lines is not yet irreversible or self-enhancing.
Ronja Reese, Julius Garbe, Emily A. Hill, Benoît Urruty, Kaitlin A. Naughten, Olivier Gagliardini, Gaël Durand, Fabien Gillet-Chaulet, G. Hilmar Gudmundsson, David Chandler, Petra M. Langebroek, and Ricarda Winkelmann
The Cryosphere, 17, 3761–3783, https://doi.org/10.5194/tc-17-3761-2023, https://doi.org/10.5194/tc-17-3761-2023, 2023
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We use an ice sheet model to test where current climate conditions in Antarctica might lead. We find that present-day ocean and atmosphere conditions might commit an irreversible collapse of parts of West Antarctica which evolves over centuries to millennia. Importantly, this collapse is not irreversible yet.
Jeremy Rohmer, Remi Thieblemont, Goneri Le Cozannet, Heiko Goelzer, and Gael Durand
The Cryosphere, 16, 4637–4657, https://doi.org/10.5194/tc-16-4637-2022, https://doi.org/10.5194/tc-16-4637-2022, 2022
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To improve the interpretability of process-based projections of the sea-level contribution from land ice components, we apply the machine-learning-based
SHapley Additive exPlanationsapproach to a subset of a multi-model ensemble study for the Greenland ice sheet. This allows us to quantify the influence of particular modelling decisions (related to numerical implementation, initial conditions, or parametrisation of ice-sheet processes) directly in terms of sea-level change contribution.
Christian Vincent, Diego Cusicanqui, Bruno Jourdain, Olivier Laarman, Delphine Six, Adrien Gilbert, Andrea Walpersdorf, Antoine Rabatel, Luc Piard, Florent Gimbert, Olivier Gagliardini, Vincent Peyaud, Laurent Arnaud, Emmanuel Thibert, Fanny Brun, and Ugo Nanni
The Cryosphere, 15, 1259–1276, https://doi.org/10.5194/tc-15-1259-2021, https://doi.org/10.5194/tc-15-1259-2021, 2021
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In situ glacier point mass balance data are crucial to assess climate change in different regions of the world. Unfortunately, these data are rare because huge efforts are required to conduct in situ measurements on glaciers. Here, we propose a new approach from remote sensing observations. The method has been tested on the Argentière and Mer de Glace glaciers (France). It should be possible to apply this method to high-spatial-resolution satellite images and on numerous glaciers in the world.
Vincent Peyaud, Coline Bouchayer, Olivier Gagliardini, Christian Vincent, Fabien Gillet-Chaulet, Delphine Six, and Olivier Laarman
The Cryosphere, 14, 3979–3994, https://doi.org/10.5194/tc-14-3979-2020, https://doi.org/10.5194/tc-14-3979-2020, 2020
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Alpine glaciers are retreating at an accelerating rate in a warming climate. Numerical models allow us to study and anticipate these changes, but the performance of a model is difficult to evaluate. So we compared an ice flow model with the long dataset of observations obtained between 1979 and 2015 on Mer de Glace (Mont Blanc area). The model accurately reconstructs the past evolution of the glacier. We simulate the future evolution of Mer de Glace; it could retreat by 2 to 6 km by 2050.
Stephen L. Cornford, Helene Seroussi, Xylar S. Asay-Davis, G. Hilmar Gudmundsson, Rob Arthern, Chris Borstad, Julia Christmann, Thiago Dias dos Santos, Johannes Feldmann, Daniel Goldberg, Matthew J. Hoffman, Angelika Humbert, Thomas Kleiner, Gunter Leguy, William H. Lipscomb, Nacho Merino, Gaël Durand, Mathieu Morlighem, David Pollard, Martin Rückamp, C. Rosie Williams, and Hongju Yu
The Cryosphere, 14, 2283–2301, https://doi.org/10.5194/tc-14-2283-2020, https://doi.org/10.5194/tc-14-2283-2020, 2020
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We present the results of the third Marine Ice Sheet Intercomparison Project (MISMIP+). MISMIP+ is one in a series of exercises that test numerical models of ice sheet flow in simple situations. This particular exercise concentrates on the response of ice sheet models to the thinning of their floating ice shelves, which is of interest because numerical models are currently used to model the response to contemporary and near-future thinning in Antarctic ice shelves.
Lionel Favier, Nicolas C. Jourdain, Adrian Jenkins, Nacho Merino, Gaël Durand, Olivier Gagliardini, Fabien Gillet-Chaulet, and Pierre Mathiot
Geosci. Model Dev., 12, 2255–2283, https://doi.org/10.5194/gmd-12-2255-2019, https://doi.org/10.5194/gmd-12-2255-2019, 2019
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The melting at the base of floating ice shelves is the main driver of the Antarctic ice sheet current retreat. Here, we use an ideal set-up to assess a wide range of melting parameterisations depending on oceanic properties with regard to a new ocean–ice-sheet coupled model, published here for the first time. A parameterisation that depends quadratically on thermal forcing in both a local and a non-local way yields the best results and needs to be further assessed with more realistic set-ups.
Julien Brondex, Fabien Gillet-Chaulet, and Olivier Gagliardini
The Cryosphere, 13, 177–195, https://doi.org/10.5194/tc-13-177-2019, https://doi.org/10.5194/tc-13-177-2019, 2019
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Here, we apply a synthetic perturbation to the most active drainage basin of Antarctica and show that centennial mass loss projections obtained through ice flow models depend strongly on the implemented friction law, i.e. the mathematical relationship between basal drag and sliding velocities. In particular, the commonly used Weertman law considerably underestimates the sea-level contribution of this basin in comparison to two water pressure-dependent laws which rely on stronger physical bases.
Marianne Haseloff, Christian Schoof, and Olivier Gagliardini
The Cryosphere, 12, 2545–2568, https://doi.org/10.5194/tc-12-2545-2018, https://doi.org/10.5194/tc-12-2545-2018, 2018
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The widths of the Siple Coast ice streams evolve on decadal to centennial timescales. We investigate how the rate of thermally driven ice stream widening depends on heat dissipation in the ice stream margin and at the bed, and on the inflow of cold ice from the ice ridge. As determining the migration rate requires resolving heat transfer processes on very small scales, we derive a parametrization of the migration rate in terms of parameters that are available from large-scale model outputs.
Olivier Passalacqua, Marie Cavitte, Olivier Gagliardini, Fabien Gillet-Chaulet, Frédéric Parrenin, Catherine Ritz, and Duncan Young
The Cryosphere, 12, 2167–2174, https://doi.org/10.5194/tc-12-2167-2018, https://doi.org/10.5194/tc-12-2167-2018, 2018
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Locating a suitable drill site is a key step in the Antarctic oldest-ice challenge. Here we have conducted a 3-D ice flow simulation in the region of Dome C using a refined bedrock description. Five selection criteria are computed that together provide an objective overview on the local ice flow conditions. We delineate kilometer-scale favorable areas that overlap with the ones recently proposed by another group. We propose a few drill sites that should be surveyed during the next field seasons.
Heiko Goelzer, Sophie Nowicki, Tamsin Edwards, Matthew Beckley, Ayako Abe-Ouchi, Andy Aschwanden, Reinhard Calov, Olivier Gagliardini, Fabien Gillet-Chaulet, Nicholas R. Golledge, Jonathan Gregory, Ralf Greve, Angelika Humbert, Philippe Huybrechts, Joseph H. Kennedy, Eric Larour, William H. Lipscomb, Sébastien Le clec'h, Victoria Lee, Mathieu Morlighem, Frank Pattyn, Antony J. Payne, Christian Rodehacke, Martin Rückamp, Fuyuki Saito, Nicole Schlegel, Helene Seroussi, Andrew Shepherd, Sainan Sun, Roderik van de Wal, and Florian A. Ziemen
The Cryosphere, 12, 1433–1460, https://doi.org/10.5194/tc-12-1433-2018, https://doi.org/10.5194/tc-12-1433-2018, 2018
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We have compared a wide spectrum of different initialisation techniques used in the ice sheet modelling community to define the modelled present-day Greenland ice sheet state as a starting point for physically based future-sea-level-change projections. Compared to earlier community-wide comparisons, we find better agreement across different models, which implies overall improvement of our understanding of what is needed to produce such initial states.
Frédéric Parrenin, Marie G. P. Cavitte, Donald D. Blankenship, Jérôme Chappellaz, Hubertus Fischer, Olivier Gagliardini, Valérie Masson-Delmotte, Olivier Passalacqua, Catherine Ritz, Jason Roberts, Martin J. Siegert, and Duncan A. Young
The Cryosphere, 11, 2427–2437, https://doi.org/10.5194/tc-11-2427-2017, https://doi.org/10.5194/tc-11-2427-2017, 2017
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The oldest dated deep ice core drilled in Antarctica has been retrieved at EPICA Dome C (EDC), reaching ~ 800 000 years. Obtaining an older palaeoclimatic record from Antarctica is one of the greatest challenges of the ice core community. Here, we estimate the age of basal ice in the Dome C area. We find that old ice (> 1.5 Myr) likely exists in two regions a few tens of kilometres away from EDC:
Little Dome C Patchand
North Patch.
Rupert Michael Gladstone, Roland Charles Warner, Benjamin Keith Galton-Fenzi, Olivier Gagliardini, Thomas Zwinger, and Ralf Greve
The Cryosphere, 11, 319–329, https://doi.org/10.5194/tc-11-319-2017, https://doi.org/10.5194/tc-11-319-2017, 2017
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Computer models are used to simulate the behaviour of glaciers and ice sheets. It has been found that such models are required to be run at very high resolution (which means high computational expense) in order to accurately represent the evolution of marine ice sheets (ice sheets resting on bedrock below sea level), in certain situations which depend on sub-glacial physical processes.
Tong Zhang, Stephen Price, Lili Ju, Wei Leng, Julien Brondex, Gaël Durand, and Olivier Gagliardini
The Cryosphere, 11, 179–190, https://doi.org/10.5194/tc-11-179-2017, https://doi.org/10.5194/tc-11-179-2017, 2017
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Stokes-flow models are the highest-fidelity representation of the equations governing ice sheet flow and they are often treated as the standard against which other models are compared in model benchmark activities. We compare two different Stokes models applied to a canonical set of idealized marine ice sheet experiments and demonstrate that the solutions converge with increasing grid resolution. This provides confidence in the use of Stokes models for generating test case solution metrics.
Olivier Passalacqua, Olivier Gagliardini, Frédéric Parrenin, Joe Todd, Fabien Gillet-Chaulet, and Catherine Ritz
Geosci. Model Dev., 9, 2301–2313, https://doi.org/10.5194/gmd-9-2301-2016, https://doi.org/10.5194/gmd-9-2301-2016, 2016
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In ice-flow modelling, computing in 3-D requires a lot of resources, but 2-D models lack physical likelihood when the flow is diverging. That is why 2-D models accounting for the divergence, so-called 2.5-D models, are an interesting trade-off. However, the applicability of these 2.5-D models has never been systematically examined. We show that these models are ineffective in the case of highly diverging flows, but also for varying temperature, which was not suspected.
O. Gagliardini, J. Brondex, F. Gillet-Chaulet, L. Tavard, V. Peyaud, and G. Durand
The Cryosphere, 10, 307–312, https://doi.org/10.5194/tc-10-307-2016, https://doi.org/10.5194/tc-10-307-2016, 2016
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In this paper it is shown that the sensitivity to the mesh resolution is not
improved for a vanishing friction at the grounding line (GL). For a discontinuous friction at the GL, we further show that the results are moreover very sensitive to the way the friction is interpolated in the close vicinity of the GL. In the light of these new insights, new results for the MISMIP3d experiments obtained for higher resolutions than previously published are made available for future comparisons.
G. Durand and F. Pattyn
The Cryosphere, 9, 2043–2055, https://doi.org/10.5194/tc-9-2043-2015, https://doi.org/10.5194/tc-9-2043-2015, 2015
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Projections of Antarctic dynamics and contribution to sea-level rise are evaluated in the light of intercomparison exercises dedicated to evaluate models' ability of representing coastal changes. Uncertainties in projections can be substantially decreased if a selection of models is made and models that are unqualified for the representation of coastal dynamics are excluded.
J.-L. Tison, M. de Angelis, G. Littot, E. Wolff, H. Fischer, M. Hansson, M. Bigler, R. Udisti, A. Wegner, J. Jouzel, B. Stenni, S. Johnsen, V. Masson-Delmotte, A. Landais, V. Lipenkov, L. Loulergue, J.-M. Barnola, J.-R. Petit, B. Delmonte, G. Dreyfus, D. Dahl-Jensen, G. Durand, B. Bereiter, A. Schilt, R. Spahni, K. Pol, R. Lorrain, R. Souchez, and D. Samyn
The Cryosphere, 9, 1633–1648, https://doi.org/10.5194/tc-9-1633-2015, https://doi.org/10.5194/tc-9-1633-2015, 2015
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The oldest paleoclimatic information is buried within the lowermost layers of deep ice cores. It is therefore essential to judge how deep these records remain unaltered. We study the bottom 60 meters of the EPICA Dome C ice core from central Antarctica to show that the paleoclimatic signal is only affected at the small scale (decimeters) in terms of some of the global ice properties. However our data suggest that the time scale has been considerably distorted by mechanical stretching.
J. J. Fürst, G. Durand, F. Gillet-Chaulet, N. Merino, L. Tavard, J. Mouginot, N. Gourmelen, and O. Gagliardini
The Cryosphere, 9, 1427–1443, https://doi.org/10.5194/tc-9-1427-2015, https://doi.org/10.5194/tc-9-1427-2015, 2015
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We present a comprehensive high-resolution assimilation of Antarctic surface velocities with a flow model. The inferred velocities are in very good agreement with observations, even when compared to recent studies on individual shelves. This quality allows to identify a pattern in the velocity mismatch that points at pinning points not present in the input geometry. We identify seven potential pinning points around Antarctica, for now uncharted, providing prominent resistance to the ice flow.
J. Krug, G. Durand, O. Gagliardini, and J. Weiss
The Cryosphere, 9, 989–1003, https://doi.org/10.5194/tc-9-989-2015, https://doi.org/10.5194/tc-9-989-2015, 2015
E. Le Meur, M. Sacchettini, S. Garambois, E. Berthier, A. S. Drouet, G. Durand, D. Young, J. S. Greenbaum, J. W. Holt, D. D. Blankenship, E. Rignot, J. Mouginot, Y. Gim, D. Kirchner, B. de Fleurian, O. Gagliardini, and F. Gillet-Chaulet
The Cryosphere, 8, 1331–1346, https://doi.org/10.5194/tc-8-1331-2014, https://doi.org/10.5194/tc-8-1331-2014, 2014
J. Krug, J. Weiss, O. Gagliardini, and G. Durand
The Cryosphere Discuss., https://doi.org/10.5194/tcd-8-1111-2014, https://doi.org/10.5194/tcd-8-1111-2014, 2014
Preprint withdrawn
T. L. Edwards, X. Fettweis, O. Gagliardini, F. Gillet-Chaulet, H. Goelzer, J. M. Gregory, M. Hoffman, P. Huybrechts, A. J. Payne, M. Perego, S. Price, A. Quiquet, and C. Ritz
The Cryosphere, 8, 181–194, https://doi.org/10.5194/tc-8-181-2014, https://doi.org/10.5194/tc-8-181-2014, 2014
T. L. Edwards, X. Fettweis, O. Gagliardini, F. Gillet-Chaulet, H. Goelzer, J. M. Gregory, M. Hoffman, P. Huybrechts, A. J. Payne, M. Perego, S. Price, A. Quiquet, and C. Ritz
The Cryosphere, 8, 195–208, https://doi.org/10.5194/tc-8-195-2014, https://doi.org/10.5194/tc-8-195-2014, 2014
A. Legchenko, C. Vincent, J. M. Baltassat, J. F. Girard, E. Thibert, O. Gagliardini, M. Descloitres, A. Gilbert, S. Garambois, A. Chevalier, and H. Guyard
The Cryosphere, 8, 155–166, https://doi.org/10.5194/tc-8-155-2014, https://doi.org/10.5194/tc-8-155-2014, 2014
B. de Fleurian, O. Gagliardini, T. Zwinger, G. Durand, E. Le Meur, D. Mair, and P. Råback
The Cryosphere, 8, 137–153, https://doi.org/10.5194/tc-8-137-2014, https://doi.org/10.5194/tc-8-137-2014, 2014
O. Gagliardini, T. Zwinger, F. Gillet-Chaulet, G. Durand, L. Favier, B. de Fleurian, R. Greve, M. Malinen, C. Martín, P. Råback, J. Ruokolainen, M. Sacchettini, M. Schäfer, H. Seddik, and J. Thies
Geosci. Model Dev., 6, 1299–1318, https://doi.org/10.5194/gmd-6-1299-2013, https://doi.org/10.5194/gmd-6-1299-2013, 2013
V. Favier, C. Agosta, S. Parouty, G. Durand, G. Delaygue, H. Gallée, A.-S. Drouet, A. Trouvilliez, and G. Krinner
The Cryosphere, 7, 583–597, https://doi.org/10.5194/tc-7-583-2013, https://doi.org/10.5194/tc-7-583-2013, 2013
A. S. Drouet, D. Docquier, G. Durand, R. Hindmarsh, F. Pattyn, O. Gagliardini, and T. Zwinger
The Cryosphere, 7, 395–406, https://doi.org/10.5194/tc-7-395-2013, https://doi.org/10.5194/tc-7-395-2013, 2013
F. Gillet-Chaulet, O. Gagliardini, H. Seddik, M. Nodet, G. Durand, C. Ritz, T. Zwinger, R. Greve, and D. G. Vaughan
The Cryosphere, 6, 1561–1576, https://doi.org/10.5194/tc-6-1561-2012, https://doi.org/10.5194/tc-6-1561-2012, 2012
G. H. Gudmundsson, J. Krug, G. Durand, L. Favier, and O. Gagliardini
The Cryosphere, 6, 1497–1505, https://doi.org/10.5194/tc-6-1497-2012, https://doi.org/10.5194/tc-6-1497-2012, 2012
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A quasi-one-dimensional ice mélange flow model based on continuum descriptions of granular materials
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Modelling the historical and future evolution of six ice masses in the Tien Shan, Central Asia, using a 3D ice-flow model
Thinning and surface mass balance patterns of two neighbouring debris-covered glaciers in the southeastern Tibetan Plateau
Everest South Col Glacier did not thin during the period 1984–2017
Meltwater runoff and glacier mass balance in the high Arctic: 1991–2022 simulations for Svalbard
Impact of tides on calving patterns at Kronebreen, Svalbard – insights from three-dimensional ice dynamical modelling
Brief communication: Glacier mapping and change estimation using very high-resolution declassified Hexagon KH-9 panoramic stereo imagery (1971–1984)
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Glacier geometry and flow speed determine how Arctic marine-terminating glaciers respond to lubricated beds
A regionally resolved inventory of High Mountain Asia surge-type glaciers, derived from a multi-factor remote sensing approach
Geometric controls of tidewater glacier dynamics
Towards ice-thickness inversion: an evaluation of global digital elevation models (DEMs) in the glacierized Tibetan Plateau
Record summer rains in 2019 led to massive loss of surface and cave ice in SE Europe
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A simple parametrization of mélange buttressing for calving glaciers
Full crystallographic orientation (c and a axes) of warm, coarse-grained ice in a shear-dominated setting: a case study, Storglaciären, Sweden
A decade of variability on Jakobshavn Isbræ: ocean temperatures pace speed through influence on mélange rigidity
Contribution of calving to frontal ablation quantified from seismic and hydroacoustic observations calibrated with lidar volume measurements
Brief communication: Updated GAMDAM glacier inventory over high-mountain Asia
Ice cliff contribution to the tongue-wide ablation of Changri Nup Glacier, Nepal, central Himalaya
Effects of undercutting and sliding on calving: a global approach applied to Kronebreen, Svalbard
Surface lowering of the debris-covered area of Kanchenjunga Glacier in the eastern Nepal Himalaya since 1975, as revealed by Hexagon KH-9 and ALOS satellite observations
Initiation of a major calving event on the Bowdoin Glacier captured by UAV photogrammetry
Calving localization at Helheim Glacier using multiple local seismic stations
Frontal destabilization of Stonebreen, Edgeøya, Svalbard
Spatial variability in mass loss of glaciers in the Everest region, central Himalayas, between 2000 and 2015
Diagnosing the decline in climatic mass balance of glaciers in Svalbard over 1957–2014
Recent changes in area and thickness of Torngat Mountain glaciers (northern Labrador, Canada)
Brief communication: Thinning of debris-covered and debris-free glaciers in a warming climate
Concentration, sources and light absorption characteristics of dissolved organic carbon on a medium-sized valley glacier, northern Tibetan Plateau
3-D surface properties of glacier penitentes over an ablation season, measured using a Microsoft Xbox Kinect
Rapid glacial retreat on the Kamchatka Peninsula during the early 21st century
Reduced melt on debris-covered glaciers: investigations from Changri Nup Glacier, Nepal
Basal buoyancy and fast-moving glaciers: in defense of analytic force balance
The climatic mass balance of Svalbard glaciers: a 10-year simulation with a coupled atmosphere–glacier mass balance model
Correction of broadband snow albedo measurements affected by unknown slope and sensor tilts
Ablation from calving and surface melt at lake-terminating Bridge Glacier, British Columbia, 1984–2013
Brief Communication: Global reconstructions of glacier mass change during the 20th century are consistent
Surface speed and frontal ablation of Kronebreen and Kongsbreen, NW Svalbard, from SAR offset tracking
Improving semi-automated glacier mapping with a multi-method approach: applications in central Asia
Area, elevation and mass changes of the two southernmost ice caps of the Canadian Arctic Archipelago between 1952 and 2014
Modelling annual mass balances of eight Scandinavian glaciers using statistical models
Winter speed-up of quiescent surge-type glaciers in Yukon, Canada
Modelling glacier change in the Everest region, Nepal Himalaya
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Harry Zekollari, Matthias Huss, Lilian Schuster, Fabien Maussion, David R. Rounce, Rodrigo Aguayo, Nicolas Champollion, Loris Compagno, Romain Hugonnet, Ben Marzeion, Seyedhamidreza Mojtabavi, and Daniel Farinotti
The Cryosphere, 18, 5045–5066, https://doi.org/10.5194/tc-18-5045-2024, https://doi.org/10.5194/tc-18-5045-2024, 2024
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Glaciers are major contributors to sea-level rise and act as key water resources. Here, we model the global evolution of glaciers under the latest generation of climate scenarios. We show that the type of observations used for model calibration can strongly affect the projections at the local scale. Our newly projected 21st century global mass loss is higher than the current community estimate as reported in the latest Intergovernmental Panel on Climate Change (IPCC) report.
Fumeng Zhao, Wenping Gong, Silvia Bianchini, and Zhongkang Yang
EGUsphere, https://doi.org/10.5194/egusphere-2024-1083, https://doi.org/10.5194/egusphere-2024-1083, 2024
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Glacier retreat patterns and climatic drivers on the Tibetan Plateau are uncertain at finer resolutions. This study introduces a new glacier mapping method covering 1988 to 2022, with downscaled air temperature and precipitation data. It quantifies the impacts of annual and seasonal temperature and precipitation on retreat. Results show rapid and varied retreat, with annual temperature influencing retreat in the west and spring precipitation in the northwest.
Jason M. Amundson, Alexander A. Robel, Justin C. Burton, and Kavinda Nissanka
EGUsphere, https://doi.org/10.5194/egusphere-2024-297, https://doi.org/10.5194/egusphere-2024-297, 2024
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Some fjords contain dense packs of icebergs referred to as ice mélange. Ice mélange can affect the stability of marine-terminating glaciers by resisting the calving of new icebergs and by modifying fjord currents and water properties. We have developed the first numerical model of ice mélange that captures its granular nature and that is suitable for long time-scale simulations. The model is capable of explaining why some glaciers are more strongly influenced by ice mélange than others.
Oliver J. Marsh, Adrian J. Luckman, and Dominic A. Hodgson
The Cryosphere, 18, 705–710, https://doi.org/10.5194/tc-18-705-2024, https://doi.org/10.5194/tc-18-705-2024, 2024
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The Brunt Ice Shelf has accelerated rapidly after calving an iceberg in January 2023. A decade of GPS data show that the rate of acceleration in August 2023 was 30 times higher than before calving, and velocity has doubled in 6 months. Satellite velocity maps show the extent of the change. The acceleration is due to loss of contact between the ice shelf and a pinning point known as the McDonald Ice Rumples. The observations highlight how iceberg calving can directly impact ice shelves.
Lander Van Tricht and Philippe Huybrechts
The Cryosphere, 17, 4463–4485, https://doi.org/10.5194/tc-17-4463-2023, https://doi.org/10.5194/tc-17-4463-2023, 2023
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We modelled the historical and future evolution of six ice masses in the Tien Shan, Central Asia, with a 3D ice-flow model under the newest climate scenarios. We show that in all scenarios the ice masses retreat significantly but with large differences. It is highlighted that, because the main precipitation occurs in spring and summer, the ice masses respond to climate change with an accelerating retreat. In all scenarios, the total runoff peaks before 2050, with a (drastic) decrease afterwards.
Chuanxi Zhao, Wei Yang, Evan Miles, Matthew Westoby, Marin Kneib, Yongjie Wang, Zhen He, and Francesca Pellicciotti
The Cryosphere, 17, 3895–3913, https://doi.org/10.5194/tc-17-3895-2023, https://doi.org/10.5194/tc-17-3895-2023, 2023
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This paper quantifies the thinning and surface mass balance of two neighbouring debris-covered glaciers in the southeastern Tibetan Plateau during different seasons, based on high spatio-temporal resolution UAV-derived (unpiloted aerial
vehicle) data and in situ observations. Through a comparison approach and high-precision results, we identify that the glacier dynamic and debris thickness are strongly related to the future fate of the debris-covered glaciers in this region.
Fanny Brun, Owen King, Marion Réveillet, Charles Amory, Anton Planchot, Etienne Berthier, Amaury Dehecq, Tobias Bolch, Kévin Fourteau, Julien Brondex, Marie Dumont, Christoph Mayer, Silvan Leinss, Romain Hugonnet, and Patrick Wagnon
The Cryosphere, 17, 3251–3268, https://doi.org/10.5194/tc-17-3251-2023, https://doi.org/10.5194/tc-17-3251-2023, 2023
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The South Col Glacier is a small body of ice and snow located on the southern ridge of Mt. Everest. A recent study proposed that South Col Glacier is rapidly losing mass. In this study, we examined the glacier thickness change for the period 1984–2017 and found no thickness change. To reconcile these results, we investigate wind erosion and surface energy and mass balance and find that melt is unlikely a dominant process, contrary to previous findings.
Louise Steffensen Schmidt, Thomas Vikhamar Schuler, Erin Emily Thomas, and Sebastian Westermann
The Cryosphere, 17, 2941–2963, https://doi.org/10.5194/tc-17-2941-2023, https://doi.org/10.5194/tc-17-2941-2023, 2023
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Here, we present high-resolution simulations of glacier mass balance (the gain and loss of ice over a year) and runoff on Svalbard from 1991–2022, one of the fastest warming regions in the Arctic. The simulations are created using the CryoGrid community model. We find a small overall loss of mass over the simulation period of −0.08 m yr−1 but with no statistically significant trend. The average runoff was found to be 41 Gt yr−1, with a significant increasing trend of 6.3 Gt per decade.
Felicity A. Holmes, Eef van Dongen, Riko Noormets, Michał Pętlicki, and Nina Kirchner
The Cryosphere, 17, 1853–1872, https://doi.org/10.5194/tc-17-1853-2023, https://doi.org/10.5194/tc-17-1853-2023, 2023
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Glaciers which end in bodies of water can lose mass through melting below the waterline, as well as by the breaking off of icebergs. We use a numerical model to simulate the breaking off of icebergs at Kronebreen, a glacier in Svalbard, and find that both melting below the waterline and tides are important for iceberg production. In addition, we compare the modelled glacier front to observations and show that melting below the waterline can lead to undercuts of up to around 25 m.
Sajid Ghuffar, Owen King, Grégoire Guillet, Ewelina Rupnik, and Tobias Bolch
The Cryosphere, 17, 1299–1306, https://doi.org/10.5194/tc-17-1299-2023, https://doi.org/10.5194/tc-17-1299-2023, 2023
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The panoramic cameras (PCs) on board Hexagon KH-9 satellite missions from 1971–1984 captured very high-resolution stereo imagery with up to 60 cm spatial resolution. This study explores the potential of this imagery for glacier mapping and change estimation. The high resolution of KH-9PC leads to higher-quality DEMs which better resolve the accumulation region of glaciers in comparison to the KH-9 mapping camera, and KH-9PC imagery can be useful in several Earth observation applications.
Ann-Sofie Priergaard Zinck and Aslak Grinsted
The Cryosphere, 16, 1399–1407, https://doi.org/10.5194/tc-16-1399-2022, https://doi.org/10.5194/tc-16-1399-2022, 2022
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The Müller Ice Cap will soon set the scene for a new drilling project. To obtain an ice core with stratified layers and a good time resolution, thickness estimates are necessary for the planning. Here we present a new and fast method of estimating ice thicknesses from sparse data and compare it to an existing ice flow model. We find that the new semi-empirical method is insensitive to mass balance, is computationally fast, and provides good fits when compared to radar measurements.
Whyjay Zheng
The Cryosphere, 16, 1431–1445, https://doi.org/10.5194/tc-16-1431-2022, https://doi.org/10.5194/tc-16-1431-2022, 2022
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A glacier can speed up when surface water reaches the glacier's bottom via crevasses and reduces sliding friction. This paper builds up a physical model and finds that thick and fast-flowing glaciers are sensitive to this friction disruption. The data from Greenland and Austfonna (Svalbard) glaciers over 20 years support the model prediction. To estimate the projected sea-level rise better, these sensitive glaciers should be frequently monitored for potential future instabilities.
Gregoire Guillet, Owen King, Mingyang Lv, Sajid Ghuffar, Douglas Benn, Duncan Quincey, and Tobias Bolch
The Cryosphere, 16, 603–623, https://doi.org/10.5194/tc-16-603-2022, https://doi.org/10.5194/tc-16-603-2022, 2022
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Surging glaciers show cyclical changes in flow behavior – between slow and fast flow – and can have drastic impacts on settlements in their vicinity.
One of the clusters of surging glaciers worldwide is High Mountain Asia (HMA).
We present an inventory of surging glaciers in HMA, identified from satellite imagery. We show that the number of surging glaciers was underestimated and that they represent 20 % of the area covered by glaciers in HMA, before discussing new physics for glacier surges.
Thomas Frank, Henning Åkesson, Basile de Fleurian, Mathieu Morlighem, and Kerim H. Nisancioglu
The Cryosphere, 16, 581–601, https://doi.org/10.5194/tc-16-581-2022, https://doi.org/10.5194/tc-16-581-2022, 2022
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The shape of a fjord can promote or inhibit glacier retreat in response to climate change. We conduct experiments with a synthetic setup under idealized conditions in a numerical model to study and quantify the processes involved. We find that friction between ice and fjord is the most important factor and that it is possible to directly link ice discharge and grounding line retreat to fjord topography in a quantitative way.
Wenfeng Chen, Tandong Yao, Guoqing Zhang, Fei Li, Guoxiong Zheng, Yushan Zhou, and Fenglin Xu
The Cryosphere, 16, 197–218, https://doi.org/10.5194/tc-16-197-2022, https://doi.org/10.5194/tc-16-197-2022, 2022
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A digital elevation model (DEM) is a prerequisite for estimating regional glacier thickness. Our study first compared six widely used global DEMs over the glacierized Tibetan Plateau by using ICESat-2 (Ice, Cloud and land Elevation Satellite) laser altimetry data. Our results show that NASADEM had the best accuracy. We conclude that NASADEM would be the best choice for ice-thickness estimation over the Tibetan Plateau through an intercomparison of four ice-thickness inversion models.
Aurel Perşoiu, Nenad Buzjak, Alexandru Onaca, Christos Pennos, Yorgos Sotiriadis, Monica Ionita, Stavros Zachariadis, Michael Styllas, Jure Kosutnik, Alexandru Hegyi, and Valerija Butorac
The Cryosphere, 15, 2383–2399, https://doi.org/10.5194/tc-15-2383-2021, https://doi.org/10.5194/tc-15-2383-2021, 2021
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Extreme precipitation events in summer 2019 led to catastrophic loss of cave and surface ice in SE Europe at levels unprecedented during the last century. The projected continuous warming and increase in precipitation extremes could pose an additional threat to glaciers in southern Europe, resulting in a potentially ice-free SE Europe by the middle of the next decade (2035 CE).
Naomi E. Ochwat, Shawn J. Marshall, Brian J. Moorman, Alison S. Criscitiello, and Luke Copland
The Cryosphere, 15, 2021–2040, https://doi.org/10.5194/tc-15-2021-2021, https://doi.org/10.5194/tc-15-2021-2021, 2021
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In May 2018 we drilled into Kaskawulsh Glacier to study how it is being affected by climate warming and used models to investigate the evolution of the firn since the 1960s. We found that the accumulation zone has experienced increased melting that has refrozen as ice layers and has formed a perennial firn aquifer. These results better inform climate-induced changes on northern glaciers and variables to take into account when estimating glacier mass change using remote-sensing methods.
Tanja Schlemm and Anders Levermann
The Cryosphere, 15, 531–545, https://doi.org/10.5194/tc-15-531-2021, https://doi.org/10.5194/tc-15-531-2021, 2021
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Ice loss from Greenland and Antarctica is often cloaked by a mélange of icebergs and sea ice. Here we provide a simple method to parametrize the resulting back stress on the ice flow for large-scale projection models.
Morgan E. Monz, Peter J. Hudleston, David J. Prior, Zachary Michels, Sheng Fan, Marianne Negrini, Pat J. Langhorne, and Chao Qi
The Cryosphere, 15, 303–324, https://doi.org/10.5194/tc-15-303-2021, https://doi.org/10.5194/tc-15-303-2021, 2021
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We present full crystallographic orientations of warm, coarse-grained ice deformed in a shear setting, enabling better characterization of how crystals in glacial ice preferentially align as ice flows. A commonly noted c-axis pattern, with several favored orientations, may result from bias due to overcounting large crystals with complex 3D shapes. A new sample preparation method effectively increases the sample size and reduces bias, resulting in a simpler pattern consistent with the ice flow.
Ian Joughin, David E. Shean, Benjamin E. Smith, and Dana Floricioiu
The Cryosphere, 14, 211–227, https://doi.org/10.5194/tc-14-211-2020, https://doi.org/10.5194/tc-14-211-2020, 2020
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Jakobshavn Isbræ, considered to be Greenland's fastest glacier, has varied its speed and thinned dramatically since the 1990s. Here we examine the glacier's behaviour over the last decade to better understand this behaviour. We find that when the floating ice (mélange) in front of the glacier freezes in place during the winter, it can control the glacier's speed and thinning rate. A recently colder ocean has strengthened this mélange, allowing the glacier to recoup some of its previous losses.
Andreas Köhler, Michał Pętlicki, Pierre-Marie Lefeuvre, Giuseppa Buscaino, Christopher Nuth, and Christian Weidle
The Cryosphere, 13, 3117–3137, https://doi.org/10.5194/tc-13-3117-2019, https://doi.org/10.5194/tc-13-3117-2019, 2019
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Ice loss at the front of glaciers can be observed with high temporal resolution using seismometers. We combine seismic and underwater sound measurements of iceberg calving at Kronebreen, a glacier in Svalbard, with laser scanning of the glacier front. We develop a method to determine calving ice loss directly from seismic and underwater calving signals. This allowed us to quantify the contribution of calving to the total ice loss at the glacier front, which also includes underwater melting.
Akiko Sakai
The Cryosphere, 13, 2043–2049, https://doi.org/10.5194/tc-13-2043-2019, https://doi.org/10.5194/tc-13-2043-2019, 2019
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The Glacier Area Mapping for Discharge from the Asian Mountains (GAMDAM) glacier inventory was updated to revise the underestimated glacier area in the first version. The total number and area of glaciers are 134 770 and 100 693 ± 11 790 km2 from 453 Landsat images, which were carefully selected for the period from 1990 to 2010, to avoid mountain shadow, cloud cover, and seasonal snow cover.
Fanny Brun, Patrick Wagnon, Etienne Berthier, Joseph M. Shea, Walter W. Immerzeel, Philip D. A. Kraaijenbrink, Christian Vincent, Camille Reverchon, Dibas Shrestha, and Yves Arnaud
The Cryosphere, 12, 3439–3457, https://doi.org/10.5194/tc-12-3439-2018, https://doi.org/10.5194/tc-12-3439-2018, 2018
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On debris-covered glaciers, steep ice cliffs experience dramatically enhanced melt compared with the surrounding debris-covered ice. Using field measurements, UAV data and submetre satellite imagery, we estimate the cliff contribution to 2 years of ablation on a debris-covered tongue in Nepal, carefully taking into account ice dynamics. While they occupy only 7 to 8 % of the tongue surface, ice cliffs contributed to 23 to 24 % of the total tongue ablation.
Dorothée Vallot, Jan Åström, Thomas Zwinger, Rickard Pettersson, Alistair Everett, Douglas I. Benn, Adrian Luckman, Ward J. J. van Pelt, Faezeh Nick, and Jack Kohler
The Cryosphere, 12, 609–625, https://doi.org/10.5194/tc-12-609-2018, https://doi.org/10.5194/tc-12-609-2018, 2018
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This paper presents a new perspective on the role of ice dynamics and ocean interaction in glacier calving processes applied to Kronebreen, a tidewater glacier in Svalbard. A global modelling approach includes ice flow modelling, undercutting estimation by a combination of glacier energy balance and plume modelling as well as calving by a discrete particle model. We show that modelling undercutting is necessary and calving is influenced by basal friction velocity and geometry.
Damodar Lamsal, Koji Fujita, and Akiko Sakai
The Cryosphere, 11, 2815–2827, https://doi.org/10.5194/tc-11-2815-2017, https://doi.org/10.5194/tc-11-2815-2017, 2017
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This study presents the geodetic mass balance of Kanchenjunga Glacier, a heavily debris-covered glacier in the easternmost Nepal Himalaya, between 1975 and 2010 using high-resolution DEMs. The rate of elevation change positively correlates with elevation and glacier velocity, and significant surface lowering is observed at supraglacial ponds. A difference in pond density would strongly affect the different geodetic mass balances of the Kanchenjunga and Khumbu glaciers.
Guillaume Jouvet, Yvo Weidmann, Julien Seguinot, Martin Funk, Takahiro Abe, Daiki Sakakibara, Hakime Seddik, and Shin Sugiyama
The Cryosphere, 11, 911–921, https://doi.org/10.5194/tc-11-911-2017, https://doi.org/10.5194/tc-11-911-2017, 2017
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In this study, we combine UAV (unmanned aerial vehicles) images taken over the Bowdoin Glacier, north-western Greenland, and a model describing the viscous motion of ice to track the propagation of crevasses responsible for the collapse of large icebergs at the glacier-ocean front (calving). This new technique allows us to explain the systematic calving pattern observed in spring and summer of 2015 and anticipate a possible rapid retreat in the future.
M. Jeffrey Mei, David M. Holland, Sridhar Anandakrishnan, and Tiantian Zheng
The Cryosphere, 11, 609–618, https://doi.org/10.5194/tc-11-609-2017, https://doi.org/10.5194/tc-11-609-2017, 2017
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We determine a method to locate calving at Helheim Glacier. By using local seismometers, we are able to find the calving location at a much higher precision than previous studies. The signal–onset time differences at four local seismic stations are used to determine possible seismic-wave origins. We present a catalogue of 12 calving events from 2014 to 2015, which shows that calving preferentially happens at the northern end of Helheim Glacier, which will help to constrain models of calving.
Tazio Strozzi, Andreas Kääb, and Thomas Schellenberger
The Cryosphere, 11, 553–566, https://doi.org/10.5194/tc-11-553-2017, https://doi.org/10.5194/tc-11-553-2017, 2017
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The strong atmospheric warming observed since the 1990s in polar regions requires quantifying the contribution to sea level rise of glaciers and ice caps, but for large areas we do not have much information on ice dynamic fluctuations. The recent increase in satellite data opens up new possibilities to monitor ice flow. We observed over Stonebreen on Edgeøya (Svalbard) a strong increase since 2012 in ice surface velocity along with a decrease in volume and an advance in frontal extension.
Owen King, Duncan J. Quincey, Jonathan L. Carrivick, and Ann V. Rowan
The Cryosphere, 11, 407–426, https://doi.org/10.5194/tc-11-407-2017, https://doi.org/10.5194/tc-11-407-2017, 2017
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We used multiple digital elevation models to quantify melt on 32 glaciers in the Everest region of the Himalayas. We examined whether patterns of melt differed depending on whether the glacier terminated on land or in water. We found that glaciers terminating in large lakes had the highest melt rates, but that those terminating in small lakes had comparable melt rates to those terminating on land. We carried out this research because Himalayan people are highly dependent on glacier meltwater.
Torbjørn Ims Østby, Thomas Vikhamar Schuler, Jon Ove Hagen, Regine Hock, Jack Kohler, and Carleen H. Reijmer
The Cryosphere, 11, 191–215, https://doi.org/10.5194/tc-11-191-2017, https://doi.org/10.5194/tc-11-191-2017, 2017
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We present modelled climatic mass balance for all glaciers in Svalbard for the period 1957–2014 at 1 km resolution using a coupled surface energy balance and snowpack model, thereby closing temporal and spatial gaps in direct and geodetic mass balance estimates.
Supporting previous studies, our results indicate increased mass loss over the period.
A detailed analysis of the involved energy fluxes reveals that increased mass loss is caused by atmospheric warming further amplified by feedbacks.
Nicholas E. Barrand, Robert G. Way, Trevor Bell, and Martin J. Sharp
The Cryosphere, 11, 157–168, https://doi.org/10.5194/tc-11-157-2017, https://doi.org/10.5194/tc-11-157-2017, 2017
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This paper provides a comprehensive assessment of the state of small glaciers in the Canadian province of Labrador. These glaciers, the last in continental northeast North America, exist in heavily shaded locations within the remote Torngat Mountains National Park. Fieldwork, and airborne and spaceborne remote-sensing analyses were used to measure regional glacier area changes and individual glacier thinning rates. These results were then linked to trends in prevailing climatic conditions.
Argha Banerjee
The Cryosphere, 11, 133–138, https://doi.org/10.5194/tc-11-133-2017, https://doi.org/10.5194/tc-11-133-2017, 2017
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Measurements of debris-covered and debris-free glaciers in the Himalaya-Karakoram show similar decadal scale thinning, despite a suppression of melt under the debris. Using physical arguments, supported by simulations of 1-D idealised glaciers, we analyse the evolution of thinning rates on both glacier types under a warming climate. The dynamics of the emergence velocity profile control the thinning rate evolution in general and lead to the observed trends in the thinning rate data.
Fangping Yan, Shichang Kang, Chaoliu Li, Yulan Zhang, Xiang Qin, Yang Li, Xiaopeng Zhang, Zhaofu Hu, Pengfei Chen, Xiaofei Li, Bin Qu, and Mika Sillanpää
The Cryosphere, 10, 2611–2621, https://doi.org/10.5194/tc-10-2611-2016, https://doi.org/10.5194/tc-10-2611-2016, 2016
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DOC release of Laohugou Glacier No. 12 was 192 kg km−2 yr−1, of which 43.2 % could be decomposed and return to atmosphere as CO2 within 28 days, producing positive feedback in the warming process and influencing downstream ecosystems. Radiative forcing of snow pit DOC was calculated to be 0.43 W m−2, accounting for about 10 % of the radiative forcing caused by BC. Therefore, DOC is also a light-absorbing agent in glacierized regions, influencing the albedo of glacier surface and glacier melting.
Lindsey I. Nicholson, Michał Pętlicki, Ben Partan, and Shelley MacDonell
The Cryosphere, 10, 1897–1913, https://doi.org/10.5194/tc-10-1897-2016, https://doi.org/10.5194/tc-10-1897-2016, 2016
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An Xbox Kinect sensor was used as a close-range surface scanner to produce the first accurate 3D surface models of spikes of snow and ice (known as penitentes) that develop in cold, dry, sunny conditions. The data collected show how penitentes develop over time and how they affect the surface roughness of a glacier. These surface models are useful inputs to modelling studies of how penitentes alter energy exchanges between the atmosphere and the surface and how this affects meltwater production.
Colleen M. Lynch, Iestyn D. Barr, Donal Mullan, and Alastair Ruffell
The Cryosphere, 10, 1809–1821, https://doi.org/10.5194/tc-10-1809-2016, https://doi.org/10.5194/tc-10-1809-2016, 2016
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Early 21st century changes in the extent of glaciers on Kamchatka were manually mapped from satellite imagery. This revealed 673 glaciers, with a total surface area of 775.7 ± 27.9 km2 in 2000, and 738 glaciers, with a total area of 592.9 ± 20.4 km2 in 2014. This ~24 % decline in glacier surface area is considered to reflect variations in climate (particularly rising summer temperatures), though the response of individual glaciers was likely modulated by other (non-climatic) factors.
Christian Vincent, Patrick Wagnon, Joseph M. Shea, Walter W. Immerzeel, Philip Kraaijenbrink, Dibas Shrestha, Alvaro Soruco, Yves Arnaud, Fanny Brun, Etienne Berthier, and Sonam Futi Sherpa
The Cryosphere, 10, 1845–1858, https://doi.org/10.5194/tc-10-1845-2016, https://doi.org/10.5194/tc-10-1845-2016, 2016
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Approximately 25 % of the glacierized area in the Everest region is covered by debris, yet the surface mass balance of these glaciers has not been measured directly. From terrestrial photogrammetry and unmanned aerial vehicle (UAV) methods, this study shows that the ablation is strongly reduced by the debris cover. The insulating effect of the debris cover has a larger effect on total mass loss than the enhanced ice ablation due to supraglacial ponds and exposed ice cliffs.
C. J. van der Veen
The Cryosphere, 10, 1331–1337, https://doi.org/10.5194/tc-10-1331-2016, https://doi.org/10.5194/tc-10-1331-2016, 2016
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This paper evaluates the geometric force balance, with application to Byrd Glacier, Antarctica. It is concluded that this approach does not yield physically reasonable results.
Kjetil S. Aas, Thorben Dunse, Emily Collier, Thomas V. Schuler, Terje K. Berntsen, Jack Kohler, and Bartłomiej Luks
The Cryosphere, 10, 1089–1104, https://doi.org/10.5194/tc-10-1089-2016, https://doi.org/10.5194/tc-10-1089-2016, 2016
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A high-resolution, coupled atmosphere--climatic mass balance (CMB) model is applied to Svalbard for the period 2003 to 2013. The mean CMB during this period is negative but displays large spatial and temporal variations. Comparison with observations on different scales shows a good overall model performance except for one particular glacier, where wind strongly affects the spatial patterns of CMB. The model also shows considerable sensitivity to model resolution, especially on local scales.
Ursula Weiser, Marc Olefs, Wolfgang Schöner, Gernot Weyss, and Bernhard Hynek
The Cryosphere, 10, 775–790, https://doi.org/10.5194/tc-10-775-2016, https://doi.org/10.5194/tc-10-775-2016, 2016
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Geometric effects induced by tilt errors lead to erroneous measurement of snow albedo. These errors are corrected where tilts of sensors and slopes are unknown. Atmospheric parameters are taken from a nearby reference measurement or a radiation model. The developed model is fitted to the measured data to determine tilts and directions which vary daily due to changing atmospheric conditions and snow cover. The results show an obvious under- or overestimation of albedo depending on the slope direction.
M. Chernos, M. Koppes, and R. D. Moore
The Cryosphere, 10, 87–102, https://doi.org/10.5194/tc-10-87-2016, https://doi.org/10.5194/tc-10-87-2016, 2016
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Ice loss from calving and surface melt is estimated at lake-terminating Bridge Glacier, British Columbia, Canada, from 1984 to 2013. Since the glacier's terminus began to float in 1991, calving has accounted for 10-25% of the glacier's total ice loss below the ELA. Overall, calving is a relatively small component of ice loss and is expected to decrease in importance in the future as the glacier retreats onto dry land. Hence, projections of future retreat remain dependent on climatic conditions.
B. Marzeion, P. W. Leclercq, J. G. Cogley, and A. H. Jarosch
The Cryosphere, 9, 2399–2404, https://doi.org/10.5194/tc-9-2399-2015, https://doi.org/10.5194/tc-9-2399-2015, 2015
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We show that estimates of global glacier mass change during the 20th century, obtained from glacier-length-based reconstructions and from a glacier model driven by gridded climate observations are now consistent with each other and also with an estimate for the years 2003-2009 that is mostly based on remotely sensed data. This consistency is found throughout the entire common periods of the respective data sets. Inconsistencies of reconstructions and observations persist on regional scales.
T. Schellenberger, T. Dunse, A. Kääb, J. Kohler, and C. H. Reijmer
The Cryosphere, 9, 2339–2355, https://doi.org/10.5194/tc-9-2339-2015, https://doi.org/10.5194/tc-9-2339-2015, 2015
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Kronebreen and Kongsbreen are among the fastest flowing glaciers on Svalbard, and surface speeds reached up to 3.2m d-1 at Kronebreen in summer 2013 and 2.7m d-1 at Kongsbreen in late autumn 2012 as retrieved from SAR satellite data. Both glaciers retreated significantly during the observation period, Kongsbreen up to 1800m or 2.5km2 and Kronebreen up to 850m or 2.8km2. Both glaciers are important contributors to the total dynamic mass loss from the Svalbard archipelago.
T. Smith, B. Bookhagen, and F. Cannon
The Cryosphere, 9, 1747–1759, https://doi.org/10.5194/tc-9-1747-2015, https://doi.org/10.5194/tc-9-1747-2015, 2015
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We describe and apply a newly developed glacial mapping algorithm which uses spectral, topographic, velocity, and spatial data to quickly and accurately map glacial extents over a wide area. This method maps both clean glacier ice and debris-covered glacier tongues across diverse topographic, land cover, and spectral settings using primarily open-source tools.
C. Papasodoro, E. Berthier, A. Royer, C. Zdanowicz, and A. Langlois
The Cryosphere, 9, 1535–1550, https://doi.org/10.5194/tc-9-1535-2015, https://doi.org/10.5194/tc-9-1535-2015, 2015
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Located at the far south (~62.5° N) of the Canadian Arctic, Grinnell and Terra Nivea Ice Caps are good climate proxies in this scarce data region. Multiple data sets (in situ, airborne and spaceborne) reveal changes in area, elevation and mass over the past 62 years. Ice wastage sharply accelerated during the last decade for both ice caps, as illustrated by the strongly negative mass balance of Terra Nivea over 2007-2014 (-1.77 ± 0.36 m a-1 w.e.). Possible climatic drivers are also discussed.
M. Trachsel and A. Nesje
The Cryosphere, 9, 1401–1414, https://doi.org/10.5194/tc-9-1401-2015, https://doi.org/10.5194/tc-9-1401-2015, 2015
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We employ statistical models to model annual glacier mass balances of eight Scandinavian glaciers as function of summer temperature and winter precipitation.
Relative importances of winter precipitation and summer temperature vary in time.
Relative importances are influenced by AMO and NAO.
T. Abe and M. Furuya
The Cryosphere, 9, 1183–1190, https://doi.org/10.5194/tc-9-1183-2015, https://doi.org/10.5194/tc-9-1183-2015, 2015
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Whereas glacier surge is known to often initiate in winter, we show significant winter speed-up signals in the upstream region even at quiescent surge-type glaciers in Yukon, Canada. Moreover, the winter speed-up region expanded from upstream to downstream. Given the absence of surface meltwater input in winter, we speculate the presence of englacial water storage that does not directly connect to the surface, yet can promote basal sliding through increased water pressure.
J. M. Shea, W. W. Immerzeel, P. Wagnon, C. Vincent, and S. Bajracharya
The Cryosphere, 9, 1105–1128, https://doi.org/10.5194/tc-9-1105-2015, https://doi.org/10.5194/tc-9-1105-2015, 2015
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A glacier mass balance and redistribution model that integrates field observations and downscaled climate fields is developed to examine glacier sensitivity to future climate in the Everest region of Nepal. The modelled sensitivity of glaciers to future climate change is high, and glacier mass loss is sustained through the 21st century for both middle- and high-emission scenarios. Projected temperature increases will expose large glacier areas to melt and reduce snow accumulations.
T. Nuimura, A. Sakai, K. Taniguchi, H. Nagai, D. Lamsal, S. Tsutaki, A. Kozawa, Y. Hoshina, S. Takenaka, S. Omiya, K. Tsunematsu, P. Tshering, and K. Fujita
The Cryosphere, 9, 849–864, https://doi.org/10.5194/tc-9-849-2015, https://doi.org/10.5194/tc-9-849-2015, 2015
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We present a new glacier inventory for high-mountain Asia named “Glacier Area Mapping for Discharge from the Asian Mountains” (GAMDAM). Glacier outlines were delineated manually using 356 Landsat ETM+ scenes in 226 path-row sets from the period 1999–2003, in conjunction with a digital elevation model and high-resolution Google EarthTM imagery. Our GAMDAM Glacier Inventory includes 87,084 glaciers covering a total area of 91,263 ± 13,689 km2 throughout high-mountain Asia.
A. Sakai, T. Nuimura, K. Fujita, S. Takenaka, H. Nagai, and D. Lamsal
The Cryosphere, 9, 865–880, https://doi.org/10.5194/tc-9-865-2015, https://doi.org/10.5194/tc-9-865-2015, 2015
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Among meteorological elements, precipitation has a large spatial variability and less observation, particularly in high-mountain Asia, although precipitation in mountains is an important parameter for hydrological circulation. Based on the GAMDAM glacier inventory, we estimated precipitation contributing to glacier mass at the median elevation of glaciers, which is presumed to be at equilibrium-line altitude, by tuning adjustment parameters of precipitation.
J. Oerlemans and W. J. J. van Pelt
The Cryosphere, 9, 767–779, https://doi.org/10.5194/tc-9-767-2015, https://doi.org/10.5194/tc-9-767-2015, 2015
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Many glaciers on Svalbard are surging glaciers. A surge is a rapid advance of the glacier snout during a few years, followed by a long period of quiescence. During the surge ice flows to lower terrain and experiences higher melt rates in summer. Here we investigate the impact of surging on the long-term effects of climate warming. We have modelled Abrahamsenbreen in northern Spitsbergen as a typical case. We show that surges tend to accelerate glacier retreat when temperature increases.
Cited articles
Albrecht, T. and Levermann, A.: Fracture field for large-scale ice dynamics, J. Glaciol., 58, 165–-177, 2012.
Albrecht, T. and Levermann, A.: Fracture-induced softening for large-scale ice dynamics, The Cryosphere, 8, 587–605, https://doi.org/10.5194/tc-8-587-2014, 2014.
Andresen, C. S., Straneo, F., Ribergaard, M. H., Bjørk, A. A., Andersen, T. J., Kuijpers, A., Nørgaard-Pedersen, N., Kjær, K. H., Schjøth, F., Weckström, K., and Ahlstrøm, A. P.: Rapid response of Helheim Glacier in Greenland to climate variability over the past century, Nat. Geosci., 5, 37–41, 2011.
Åström, J. A., Riikilä, T. I., Tallinen, T., Zwinger, T., Benn, D., Moore, J. C., and Timonen, J.: A particle based simulation model for glacier dynamics, The Cryosphere, 7, 1591–1602, https://doi.org/10.5194/tc-7-1591-2013, 2013.
Bassis, J. and Jacobs, S.: Diverse calving patterns linked to glacier geometry, Nat. Geosci., 6, 833–836, 2013.
Benn, D. I., Hulton, N. R., and Mottram, R. H.: 'Calving laws', 'sliding laws' and the stability of tidewater glaciers, Ann. Glaciol., 46, 123–130, 2007a.
Benn, D. I., Warren, C. R., and Mottram, R. H.: Calving processes and the dynamics of calving glaciers, Earth-Sci. Rev., 82, 143–179, 2007b.
Bevan, S. L., Luckman, A. J., and Murray, T.: Glacier dynamics over the last quarter of a century at Helheim, Kangerdlugssuaq and 14 other major Greenland outlet glaciers, The Cryosphere, 6, 923–937, https://doi.org/10.5194/tc-6-923-2012, 2012.
Borstad, C. P.: Tensile strength and fracture mechanics of cohesive dry snow related to slab avalanches, Ph.D. thesis, The University of British Columbia, British Columbia, 2011.
Borstad, C. P., Khazendar, A., Larour, E., Morlighem, M., Rignot, E., Schodlok, M. P., and Seroussi, H.: A damage mechanics assessment of the Larsen B ice shelf prior to collapse: Toward a physically-based calving law, Geophys. Res. Lett., 39, L18502, https://doi.org/10.1029/2012GL053317, 2012.
Cook, S., Rutt, I. C., Murray, T., Luckman, A., Zwinger, T., Selmes, N., Goldsack, A., and James, T. D.: Modelling environmental influences on calving at Helheim Glacier in eastern Greenland, The Cryosphere, 8, 827–841, https://doi.org/10.5194/tc-8-827-2014, 2014.
Cook, S. J.: Environmental Controls on Calving in Grounded Tidewater Glaciers, Ph.D. thesis, Swansea University, Swansea, UK, 2012.
Depoorter, M., Bamber, J., Griggs, J., Lenaerts, J., Ligtenberg, S., van den Broeke, M., and Moholdt, G.: Calving fluxes and basal melt rates of Antarctic ice shelves, Nature, 502, 82–92, 2013.
Duddu, R. and Waisman, H.: A temperature dependent creep damage model for polycrystalline ice, Mech. Mater., 46, 23–41, 2012.
Duddu, R. and Waisman, H.: A nonlocal continuum damage mechanics approach to simulation of creep fracture in ice sheets, Comput. Mech., 51, 1–14, 2013.
Durand, G., Gagliardini, O., De Fleurian, B., Zwinger, T., and Le Meur, E.: Marine ice sheet dynamics: Hysteresis and neutral equilibrium, J. Geophys. Res.-Earth, 114, F03009, https://doi.org/10.1029/2008JF001170, 2009.
Favier, L., Gagliardini, O., Durand, G., and Zwinger, T.: A three-dimensional full Stokes model of the grounding line dynamics: effect of a pinning point beneath the ice shelf, The Cryosphere, 6, 101–112, https://doi.org/10.5194/tc-6-101-2012, 2012.
Fischer, M., Alley, R., and Engelder, T.: Fracture toughness of ice and firn determined from the modified ring test, J. Glaciol., 41, 383–394, 1995.
Gagliardini, O., Durand, G., Zwinger, T., Hindmarsh, R., and Le Meur, E.: Coupling of ice-shelf melting and buttressing is a key process in ice-sheets dynamics, Geophys. Res. Lett., 37, L14501, https://doi.org/10.1029/2010GL043334, 2010.
Gagliardini, O., Weiss, J., Duval, P., and Montagnat, M.: On Duddu and Waisman (2012a,b) concerning continuum damage mechanics applied to crevassing and icebergs calving, J. Glaciol., 59, 797–798, 2013a.
Gagliardini, O., Zwinger, T., Gillet-Chaulet, F., Durand, G., Favier, L., de Fleurian, B., Greve, R., Malinen, M., Martín, C., Råback, P., Ruokolainen, J., Sacchettini, M., Schäfer, M., Seddik, H., and Thies, J.: Capabilities and performance of Elmer/Ice, a new-generation ice sheet model, Geosci. Model Dev., 6, 1299–1318, https://doi.org/10.5194/gmd-6-1299-2013, 2013b.
Gillet-Chaulet, F., Gagliardini, O., Seddik, H., Nodet, M., Durand, G., Ritz, C., Zwinger, T., Greve, R., and Vaughan, D. G.: Greenland ice sheet contribution to sea-level rise from a new-generation ice-sheet model, The Cryosphere, 6, 1561–1576, https://doi.org/10.5194/tc-6-1561-2012, 2012.
Glinka, G.: Development of weight functions and computer integration procedures for calculating stress intensity factors around cracks subjected to complex stress fields, Progress Report 1, Stress and Fatigue-Fracture Design, Petersburg, Ontario, Canada, 1996.
Hayhurst, D.: Creep rupture under multi-axial states of stress, J. Mech. Phys. Solids, 20, 381–382, 1972.
Howat, I. M., Joughin, I., and Scambos, T. A.: Rapid changes in ice discharge from Greenland outlet glaciers, Science, 315, 1559–1561, 2007.
Jay-Allemand, M., Gillet-Chaulet, F., Gagliardini, O., and Nodet, M.: Investigating changes in basal conditions of Variegated Glacier prior to and during its 1982–1983 surge, The Cryosphere, 5, 659–672, https://doi.org/10.5194/tc-5-659-2011, 2011.
Joughin, I., Das, S. B., King, M. A., Smith, B. E., Howat, I. M., and Moon, T.: Seasonal speedup along the western flank of the Greenland Ice Sheet, Science, 320, 781–783, 2008a.
Joughin, I., Howat, I., Alley, R. B., Ekstrom, G., Fahnestock, M., Moon, T., Nettles, M., Truffer, M., and Tsai, V. C.: Ice-front variation and tidewater behavior on Helheim and Kangerdlugssuaq Glaciers, Greenland, J. Geophys. Res.-Earth, 113, F01004, https://doi.org/10.1029/2007JF000837, 2008b.
Jouvet, G., Picasso, M., Rappaz, J., Huss, M., and Funk, M.: Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects, Math. Model. Nat. Phenom., 6, 263–280, 2011.
Kachanov, L.: Time of the rupture process under creep conditions, Isv. Akad. Nauk. SSR. Otd Tekh. Nauk, 8, 26–31, 1958.
Labbens, R., Pellissier-Tanon, A., and Heliot, J.: Application de la théorie linéaire de la mécanique de la rupture aux structures métalliques épaisses-Méthodes pratiques de calcul des facteurs d'intensité de contrainte, Revue de Physique Appliquée, 9, 587–598, 1974.
Lemaitre, J., Chaboche, J., and Germain, P.: Mécanique des matériaux solides, vol. 7, Dunod, Paris, 1988.
Luckman, A., Murray, T., De Lange, R., and Hanna, E.: Rapid and synchronous ice-dynamic changes in East Greenland, Geophys. Res. Lett., 33, L03503, https://doi.org/10.1029/2005GL025428, 2006.
Ma, Y., Gagliardini, O., Ritz, C., Gillet-Chaulet, F., Durand, G., and Montagnat, M.: Enhancement factors for grounded ice and ice shelves inferred from an anisotropic ice-flow model, J. Glaciol., 56, 805–812, 2010.
Mottram, R. H. and Benn, D. I.: Testing crevasse-depth models: a field study at Breioamerkurjokull, Iceland, J. Glaciol., 55, 746–752, 2009.
Motyka, R.: Deep-water calving at Le Conte Glacier, southeast Alaska, Byrd Polar Res. Cent. Rep, 15, 115–118, 1997.
Murakami, S. and Ohno, N.: A continuum theory of creep and creep damage, in: Creep in structures, pp. 422–444, Springer, Tempaku-cho, Toyohashi, 440, Japan, 1981.
Nath, P. and Vaughan, D.: Subsurface crevasse formation in glaciers and ice sheets, J. Geophys. Res.-Solid, 108, ECV 7-1–ECV 7–12, https://doi.org/10.1029/2001JB000453, 2003.
Nick, F. M., Vieli, A., Howat, I. M., and Joughin, I.: Large-scale changes in Greenland outlet glacier dynamics triggered at the terminus, Nat. Geosci., 2, 110–114, 2009.
Nick, F. M., van der Veen, C. J., Vieli, A., and Benn, D. I.: A physically based calving model applied to marine outlet glaciers and implications for the glacier dynamics, J. Glaciol., 56, 781–794, 2010.
Nick, F. M., Vieli, A., Andersen, M. L., Joughin, I., Payne, A., Edwards, T. L., Pattyn, F., and van de Wal, R. S.: Future sea-level rise from Greenland/'s main outlet glaciers in a warming climate, Nature, 497, 235–238, 2013.
Nye, J.: The distribution of stress and velocity in glaciers and ice-sheets, P. Roy. Soc. Lond. A, 239, 113–133, 1957.
Otero, J., Navarro, F. J., Martin, C., Cuadrado, M. L., and Corcuera, M. I.: A three-dimensional calving model: numerical experiments on Johnsons Glacier, Livingston Island, Antarctica, J. Glaciol., 56, 200–214, 2010.
Pralong, A. and Funk, M.: Dynamic damage model of crevasse opening and application to glacier calving, J. Geophys. Res., 110, B01309, https://doi.org/10.1029/2004JB003104, 2005.
Pralong, A., Funk, M., and Lüthi, M. P.: A description of crevasse formation using continuum damage mechanics, Ann. Glaciol., 37, 77–82, 2003.
Ravi-Chandar, K. and Knauss, W.: An experimental investigation into dynamic fracture: I. Crack initiation and arrest, Int. J. Fract., 25, 247–262, 1984.
Rignot, E. and Kanagaratnam, P.: Changes in the velocity structure of the Greenland Ice Sheet, Science, 311, 986–990, 2006.
Rignot, E., Koppes, M., and Velicogna, I.: Rapid submarine melting of the calving faces of West Greenland glaciers, Nat. Geosci., 3, 187–191, 2010.
Rist, M. A., Sammonds, P. R., Murrell, S. A. F., Meredith, P. G., Oerter, H., and Doake, C. S. M.: Experimental fracture and mechanical properties of Antarctic ice preliminary results, Ann. Glaciol., 23, 284–292, 1996.
Rist, M. A., Sammonds, P. R., Murrell, S. A. F., Meredith, P. G., Doake, C. S. M., Oerter, H., and Matsuki, K.: Experimental and theoretical fracture mechanics applied to Antarctic ice fracture and surface crevassing, J. Geophys. Res., 104, 2973–2987, 1999.
Scambos, T. A., Bohlander, J., Shuman, C., and Skvarca, P.: Glacier acceleration and thinning after ice shelf collapse in the Larsen B embayment, Antarctica, Geophys. Res. Lett., 31, L18402, https://doi.org/10.1029/2004GL020670, 2004.
Schulson, E. M. and Duval, P.: Creep and fracture of ice, Cambridge University Press, Cambridge, 2009.
Shepherd, A., Ivins, E. R., Geruo, A., Barletta, V. R., Bentley, M. J., Bettadpur, S., Briggs, K. H., Bromwich, D. H., Forsberg, R., Galin, N., Horwath, M., Jacobs, S., Joughin, I., King, M. A., Lenaerts, J. T. M., Li, J., Ligtenberg, S. R. M., Luckman, A., Luthcke, S. B., McMillan, M., Meister, R., Milne, G., Mouginot, J., Muir, A., Nicolas, J. P., Paden, J., Payne, A. J., Pritchard, H., Rignot, E., Rott, H., Sandberg Sørensen, L., Scambos, T. A., Scheuchl, B., Schrama, E. J. O., Smith, B., Sundal, A. V., van Angelen, J. H., van de Berg, W. J., van den Broeke, M. R., Vaughan, D. G., Velicogna, I., Wahr, J., Whitehouse, P. L., Wingham, D. J., Yi, D., Young, D., and Zwally, H. J.: A reconciled estimate of ice-sheet mass balance, Science, 338, 1183–1189, 2012.
Smith, R. A.: The application of fracture mechanics to the problem of crevasse penetration, J. Glaciol., 17, 223–228, 1976.
Todd, J. and Christoffersen, P.: Are seasonal calving dynamics forced by buttressing from ice mélange or undercutting by melting? Outcomes from full-Stokes simulations of Store Gletscher, West Greenland, The Cryosphere Discuss., 8, 3525–3561, https://doi.org/10.5194/tcd-8-3525-2014, 2014.
van der Veen, C.: Fracture mechanics approach to penetration of bottom crevasses on glaciers, Cold Reg. Sci. Technol., 27, 213–223, 1998a.
van der Veen, C.: Fracture mechanics approach to penetration of surface crevasses on glaciers, Cold Reg. Sci. Technol, 27, 31–47, 1998b.
Vaughan, D. G.: Relating the occurrence of crevasses to surface strain rates, J. Glaciol., 39, 255–266, 1993.
Weiss, J.: Subcritical crack propagation as a mechanism of crevasse formation and iceberg calving, J. Glaciol., 50, 109–115, 2004.
Weiss, J. and Schulson, E. M.: Coulombic faulting from the grain scale to the geophysical scale: lessons from ice, J. Phys. D, 42, 214017, https://doi.org/10.1088/0022-3727/42/21/214017, 2009.
Xiao, J. and Jordaan, I.: Application of damage mechanics to ice failure in compression, Cold Reg. Sci. Technol., 24, 305–322, 1996.