Articles | Volume 10, issue 3
https://doi.org/10.5194/tc-10-1339-2016
© Author(s) 2016. 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-10-1339-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
01 Jul 2016
Research article |
| 01 Jul 2016
A Maxwell elasto-brittle rheology for sea ice modelling
Véronique Dansereau
CORRESPONDING AUTHOR
Laboratoire de Glaciologie et Géophysique de l'Environnement, CNRS UMR 5183, Université de Grenoble, Grenoble, France
Jérôme Weiss
Institut des Sciences de la Terre, CNRS UMR 5275, Université de Grenoble, Grenoble, France
Pierre Saramito
Laboratoire Jean Kuntzmann, CNRS UMR 5224, Université de Grenoble, Grenoble, France
Philippe Lattes
TOTAL S.A. – DGEP/DEV/TEC/GEO, Paris, France
Related authors
Laurent Brodeau, Pierre Rampal, Einar Òlason, and Véronique Dansereau
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2023-231, https://doi.org/10.5194/gmd-2023-231, 2024
Preprint under review for GMD
Short summary
Short summary
A new sea-ice rheology, known as BBM, has been implemented into the sea-ice component of NEMO. We describe how a new spatial discretization framework was introduced in order to achieve this. A set of realistic ocean/sea-ice simulations of the Arctic have been performed, using BBM and the standard rheology of NEMO. When compared to satellite data, our simulations show that our implementation of BBM leads to a better representation of sea-ice deformations than the standard rheology of NEMO.
Yumeng Chen, Polly Smith, Alberto Carrassi, Ivo Pasmans, Laurent Bertino, Marc Bocquet, Tobias Sebastian Finn, Pierre Rampal, and Véronique Dansereau
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Short summary
Short summary
We explore the multivariate state and parameter estimation using data assimilation approach through idealised simulations in a dynamics-only sea ice model based on novel rheology. We identify various potential issues that can arise in complex operational sea ice model when model parameters are estimated. Even though further investigation will be needed for such complex sea ice models, we show possibilities to improve both the observed and unobserved model state forecast and parameters accuracy.
Tobias Sebastian Finn, Charlotte Durand, Alban Farchi, Marc Bocquet, Yumeng Chen, Alberto Carrassi, and Véronique Dansereau
The Cryosphere, 17, 2965–2991, https://doi.org/10.5194/tc-17-2965-2023, https://doi.org/10.5194/tc-17-2965-2023, 2023
Short summary
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We combine deep learning with a regional sea-ice model to correct model errors in the sea-ice dynamics of low-resolution forecasts towards high-resolution simulations. The combined model improves the forecast by up to 75 % and thereby surpasses the performance of persistence. As the error connection can additionally be used to analyse the shortcomings of the forecasts, this study highlights the potential of combined modelling for short-term sea-ice forecasting.
Thomas Richter, Véronique Dansereau, Christian Lessig, and Piotr Minakowski
Geosci. Model Dev., 16, 3907–3926, https://doi.org/10.5194/gmd-16-3907-2023, https://doi.org/10.5194/gmd-16-3907-2023, 2023
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Sea ice covers not only the pole regions but affects the weather and climate globally. For example, its white surface reflects more sunlight than land. The oceans around the poles are therefore kept cool, which affects the circulation in the oceans worldwide. Simulating the behavior and changes in sea ice on a computer is, however, very difficult. We propose a new computer simulation that better models how cracks in the ice change over time and show this by comparing to other simulations.
Einar Ólason, Pierre Rampal, and Véronique Dansereau
The Cryosphere, 15, 1053–1064, https://doi.org/10.5194/tc-15-1053-2021, https://doi.org/10.5194/tc-15-1053-2021, 2021
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We analyse the fractal properties observed in the pattern of the long, narrow openings that form in Arctic sea ice known as leads. We use statistical tools to explore the fractal properties of the lead fraction observed in satellite data and show that our sea-ice model neXtSIM displays the same behaviour. Building on this result we then show that the pattern of heat loss from ocean to atmosphere in the model displays similar fractal properties, stemming from the fractal properties of the leads.
Pierre Rampal, Véronique Dansereau, Einar Olason, Sylvain Bouillon, Timothy Williams, Anton Korosov, and Abdoulaye Samaké
The Cryosphere, 13, 2457–2474, https://doi.org/10.5194/tc-13-2457-2019, https://doi.org/10.5194/tc-13-2457-2019, 2019
Short summary
Short summary
In this article, we look at how the Arctic sea ice cover, as a solid body, behaves on different temporal and spatial scales. We show that the numerical model neXtSIM uses a new approach to simulate the mechanics of sea ice and reproduce the characteristics of how sea ice deforms, as observed by satellite. We discuss the importance of this model performance in the context of simulating climate processes taking place in polar regions, like the exchange of energy between the ocean and atmosphere.
Véronique Dansereau, Jérôme Weiss, Pierre Saramito, Philippe Lattes, and Edmond Coche
The Cryosphere, 11, 2033–2058, https://doi.org/10.5194/tc-11-2033-2017, https://doi.org/10.5194/tc-11-2033-2017, 2017
Short summary
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A new mechanical framework is used to model the drift of sea ice in a narrow channel between Greenland and Ellesmere Island. It is able to reproduce its main features : curved cracks, ice “bridges” that stop the flow of ice for several months of the year and some thick, strongly localized ridged ice. The simulations suggest that a mechanical weakening of the sea ice cover can shorten the lifespan of ice bridges and result in an increased export of ice through the narrow channels of the Arctic.
Laurent Brodeau, Pierre Rampal, Einar Òlason, and Véronique Dansereau
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2023-231, https://doi.org/10.5194/gmd-2023-231, 2024
Preprint under review for GMD
Short summary
Short summary
A new sea-ice rheology, known as BBM, has been implemented into the sea-ice component of NEMO. We describe how a new spatial discretization framework was introduced in order to achieve this. A set of realistic ocean/sea-ice simulations of the Arctic have been performed, using BBM and the standard rheology of NEMO. When compared to satellite data, our simulations show that our implementation of BBM leads to a better representation of sea-ice deformations than the standard rheology of NEMO.
Yumeng Chen, Polly Smith, Alberto Carrassi, Ivo Pasmans, Laurent Bertino, Marc Bocquet, Tobias Sebastian Finn, Pierre Rampal, and Véronique Dansereau
EGUsphere, https://doi.org/10.5194/egusphere-2023-1809, https://doi.org/10.5194/egusphere-2023-1809, 2023
Short summary
Short summary
We explore the multivariate state and parameter estimation using data assimilation approach through idealised simulations in a dynamics-only sea ice model based on novel rheology. We identify various potential issues that can arise in complex operational sea ice model when model parameters are estimated. Even though further investigation will be needed for such complex sea ice models, we show possibilities to improve both the observed and unobserved model state forecast and parameters accuracy.
Tobias Sebastian Finn, Charlotte Durand, Alban Farchi, Marc Bocquet, Yumeng Chen, Alberto Carrassi, and Véronique Dansereau
The Cryosphere, 17, 2965–2991, https://doi.org/10.5194/tc-17-2965-2023, https://doi.org/10.5194/tc-17-2965-2023, 2023
Short summary
Short summary
We combine deep learning with a regional sea-ice model to correct model errors in the sea-ice dynamics of low-resolution forecasts towards high-resolution simulations. The combined model improves the forecast by up to 75 % and thereby surpasses the performance of persistence. As the error connection can additionally be used to analyse the shortcomings of the forecasts, this study highlights the potential of combined modelling for short-term sea-ice forecasting.
Thomas Richter, Véronique Dansereau, Christian Lessig, and Piotr Minakowski
Geosci. Model Dev., 16, 3907–3926, https://doi.org/10.5194/gmd-16-3907-2023, https://doi.org/10.5194/gmd-16-3907-2023, 2023
Short summary
Short summary
Sea ice covers not only the pole regions but affects the weather and climate globally. For example, its white surface reflects more sunlight than land. The oceans around the poles are therefore kept cool, which affects the circulation in the oceans worldwide. Simulating the behavior and changes in sea ice on a computer is, however, very difficult. We propose a new computer simulation that better models how cracks in the ice change over time and show this by comparing to other simulations.
Einar Ólason, Pierre Rampal, and Véronique Dansereau
The Cryosphere, 15, 1053–1064, https://doi.org/10.5194/tc-15-1053-2021, https://doi.org/10.5194/tc-15-1053-2021, 2021
Short summary
Short summary
We analyse the fractal properties observed in the pattern of the long, narrow openings that form in Arctic sea ice known as leads. We use statistical tools to explore the fractal properties of the lead fraction observed in satellite data and show that our sea-ice model neXtSIM displays the same behaviour. Building on this result we then show that the pattern of heat loss from ocean to atmosphere in the model displays similar fractal properties, stemming from the fractal properties of the leads.
Pierre Rampal, Véronique Dansereau, Einar Olason, Sylvain Bouillon, Timothy Williams, Anton Korosov, and Abdoulaye Samaké
The Cryosphere, 13, 2457–2474, https://doi.org/10.5194/tc-13-2457-2019, https://doi.org/10.5194/tc-13-2457-2019, 2019
Short summary
Short summary
In this article, we look at how the Arctic sea ice cover, as a solid body, behaves on different temporal and spatial scales. We show that the numerical model neXtSIM uses a new approach to simulate the mechanics of sea ice and reproduce the characteristics of how sea ice deforms, as observed by satellite. We discuss the importance of this model performance in the context of simulating climate processes taking place in polar regions, like the exchange of energy between the ocean and atmosphere.
Véronique Dansereau, Jérôme Weiss, Pierre Saramito, Philippe Lattes, and Edmond Coche
The Cryosphere, 11, 2033–2058, https://doi.org/10.5194/tc-11-2033-2017, https://doi.org/10.5194/tc-11-2033-2017, 2017
Short summary
Short summary
A new mechanical framework is used to model the drift of sea ice in a narrow channel between Greenland and Ellesmere Island. It is able to reproduce its main features : curved cracks, ice “bridges” that stop the flow of ice for several months of the year and some thick, strongly localized ridged ice. The simulations suggest that a mechanical weakening of the sea ice cover can shorten the lifespan of ice bridges and result in an increased export of ice through the narrow channels of the Arctic.
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
T. Vihma, R. Pirazzini, I. Fer, I. A. Renfrew, J. Sedlar, M. Tjernström, C. Lüpkes, T. Nygård, D. Notz, J. Weiss, D. Marsan, B. Cheng, G. Birnbaum, S. Gerland, D. Chechin, and J. C. Gascard
Atmos. Chem. Phys., 14, 9403–9450, https://doi.org/10.5194/acp-14-9403-2014, https://doi.org/10.5194/acp-14-9403-2014, 2014
Related subject area
Rheology
Grain growth of ice doped with soluble impurities
Multivariate state and parameter estimation with data assimilation on sea-ice models using a Maxwell-Elasto-Brittle rheology
Damaging viscous-plastic sea ice
The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law
Non-normal flow rules affect fracture angles in sea ice viscous–plastic rheologies
Behavior of saline ice under cyclic flexural loading
The temperature change shortcut: effects of mid-experiment temperature changes on the deformation of polycrystalline ice
Parameter optimization in sea ice models with elastic–viscoplastic rheology
Temperature and strain controls on ice deformation mechanisms: insights from the microstructures of samples deformed to progressively higher strains at −10, −20 and −30 °C
Landfast sea ice material properties derived from ice bridge simulations using the Maxwell elasto-brittle rheology
Recrystallization processes, microstructure and crystallographic preferred orientation evolution in polycrystalline ice during high-temperature simple shear
Melting and fragmentation laws from the evolution of two large Southern Ocean icebergs estimated from satellite data
Implementing an empirical scalar constitutive relation for ice with flow-induced polycrystalline anisotropy in large-scale ice sheet models
Healing of snow surface-to-surface contacts by isothermal sintering
Qinyu Wang, Sheng Fan, and Chao Qi
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Short summary
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We explored how the grain size of polycrystalline ice is affected by soluble impurities by conducting experiments on ice-containing salts. Results showed that above/below the eutectic point, impurities enhance/hinder grain growth, due to production of melts/precipitation of salt hydrates. Our findings offer insights into the dynamics of natural ice masses.
Yumeng Chen, Polly Smith, Alberto Carrassi, Ivo Pasmans, Laurent Bertino, Marc Bocquet, Tobias Sebastian Finn, Pierre Rampal, and Véronique Dansereau
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Short summary
Short summary
We explore the multivariate state and parameter estimation using data assimilation approach through idealised simulations in a dynamics-only sea ice model based on novel rheology. We identify various potential issues that can arise in complex operational sea ice model when model parameters are estimated. Even though further investigation will be needed for such complex sea ice models, we show possibilities to improve both the observed and unobserved model state forecast and parameters accuracy.
Antoine Savard and Bruno Tremblay
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We include a suitable damage parametrization in the standard viscous-plastic (VP) sea ice model to disentangle its effect from model physics (visco-elastic or elasto-brittle vs. visco-plastic) on its ability to reproduce observed scaling laws of deformation. This study shows that including a damage parametrization in the VP model improves its performance in simulating the statistical behavior of fracture patterns. Therefore, a damage parametrization is a powerful tuning knob.
Mark D. Behn, David L. Goldsby, and Greg Hirth
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Grain size is a key microphysical property of ice, controlling the rheological behavior of ice sheets and glaciers. In this study, we develop a new model for grain size evolution in ice and show that it accurately predicts grain size in laboratory experiments and in natural ice core data. The model provides a physical explanation for the power-law relationship between stress and strain rate known as the Glen law and can be used as a predictive tool for modeling ice flow in natural systems.
Damien Ringeisen, L. Bruno Tremblay, and Martin Losch
The Cryosphere, 15, 2873–2888, https://doi.org/10.5194/tc-15-2873-2021, https://doi.org/10.5194/tc-15-2873-2021, 2021
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Deformations in the Arctic sea ice cover take the shape of narrow lines. High-resolution sea ice models recreate these deformation lines. Recent studies have shown that the most widely used sea ice model creates fracture lines with intersection angles larger than those observed and cannot create smaller angles. In our work, we change the way sea ice deforms post-fracture. This change allows us to understand the link between the sea ice model and intersection angles and create more acute angles.
Andrii Murdza, Erland M. Schulson, and Carl E. Renshaw
The Cryosphere, 15, 2415–2428, https://doi.org/10.5194/tc-15-2415-2021, https://doi.org/10.5194/tc-15-2415-2021, 2021
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It has been suggested that the observed sudden breakup of Arctic and Antarctic floating ice covers may be due to fatigue failure associated with cyclic loading from ocean swells that can penetrate deeply into an ice pack. To investigate this possibility, we measured the flexural strength of saline ice after cyclic loading. Contrary to expectations, we find that the flexural strength of saline ice increases upon cycling, similar to the behavior of laboratory-grown ice and natural lake ice.
Lisa Craw, Adam Treverrow, Sheng Fan, Mark Peternell, Sue Cook, Felicity McCormack, and Jason Roberts
The Cryosphere, 15, 2235–2250, https://doi.org/10.5194/tc-15-2235-2021, https://doi.org/10.5194/tc-15-2235-2021, 2021
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Ice sheet and ice shelf models rely on data from experiments to accurately represent the way ice moves. Performing experiments at the temperatures and stresses that are generally present in nature takes a long time, and so there are few of these datasets. Here, we test the method of speeding up an experiment by running it initially at a higher temperature, before dropping to a lower target temperature to generate the relevant data. We show that this method can reduce experiment time by 55 %.
Gleb Panteleev, Max Yaremchuk, Jacob N. Stroh, Oceana P. Francis, and Richard Allard
The Cryosphere, 14, 4427–4451, https://doi.org/10.5194/tc-14-4427-2020, https://doi.org/10.5194/tc-14-4427-2020, 2020
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In the CICE6 community model, rheology and landfast grounding/arching effects are simulated by functions of sea ice thickness and concentration with a set of fixed parameters empirically adjusted to optimize model performance. In this study we consider a spatially variable extension for representing these parameters in the two-dimensional elastic–viscoplastic (EVP) sea ice model and analyze the feasibility of the optimization of these parameters through the 4D-Var data assimilation approach.
Sheng Fan, Travis F. Hager, David J. Prior, Andrew J. Cross, David L. Goldsby, Chao Qi, Marianne Negrini, and John Wheeler
The Cryosphere, 14, 3875–3905, https://doi.org/10.5194/tc-14-3875-2020, https://doi.org/10.5194/tc-14-3875-2020, 2020
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We performed uniaxial compression experiments on synthetic ice samples. We report ice microstructural evolution at –20 and –30 °C that has never been reported before. Microstructural data show the opening angle of c-axis cones decreases with increasing strain or with decreasing temperature, suggesting a more active grain rotation. CPO intensity weakens with temperature because CPO of small grains is weaker, and it can be explained by grain boundary sliding or nucleation with random orientations.
Mathieu Plante, Bruno Tremblay, Martin Losch, and Jean-François Lemieux
The Cryosphere, 14, 2137–2157, https://doi.org/10.5194/tc-14-2137-2020, https://doi.org/10.5194/tc-14-2137-2020, 2020
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We study the formation of ice arches between two islands using a model that resolves crack initiation and propagation. This model uses a damage parameter to parameterize the presence or absence of cracks in the ice. We find that the damage parameter allows for cracks to propagate in the ice but in a different orientation than predicted by theory. The results call for improvement in how stress relaxation associated with this damage is parameterized.
Baptiste Journaux, Thomas Chauve, Maurine Montagnat, Andrea Tommasi, Fabrice Barou, David Mainprice, and Léa Gest
The Cryosphere, 13, 1495–1511, https://doi.org/10.5194/tc-13-1495-2019, https://doi.org/10.5194/tc-13-1495-2019, 2019
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Ice mechanics is an important tool to better predict the response of glaciers or polar ice sheets to climate variations.
Nevertheless our current predictive abilities are limited as the microscale mechanisms responsible for ice creep are poorly identified.
We show in this study, using state-of-the-art experimental techniques, which recrystallization processes control ice deformation. This will allow realistic simulations, necessary to predict the long-term effects on ice landmasses.
Nicolas Bouhier, Jean Tournadre, Frédérique Rémy, and Rozenn Gourves-Cousin
The Cryosphere, 12, 2267–2285, https://doi.org/10.5194/tc-12-2267-2018, https://doi.org/10.5194/tc-12-2267-2018, 2018
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The evolution of two large Southern Ocean icebergs, in terms of area and thickness, are used to study the melting and fragmentation laws of icebergs. The area and thickness are estimated by the mean of satellite images and radar altimeter data. Two classical formulations of melting are tested and a fragmentation law depending on the sea temperature and iceberg velocity is proposed and tested. The size distribution of the pieces generated by fragmentation is also estimated.
Felicity S. Graham, Mathieu Morlighem, Roland C. Warner, and Adam Treverrow
The Cryosphere, 12, 1047–1067, https://doi.org/10.5194/tc-12-1047-2018, https://doi.org/10.5194/tc-12-1047-2018, 2018
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Ice sheet flow is anisotropic, depending on the nature of the stress applied. However, most large-scale ice sheet models rely on the Glen flow relation, which ignores anisotropic effects. We implement a flow relation (ESTAR) for anisotropic ice in a large-scale ice sheet model. In ice shelf simulations, the Glen flow relation overestimates velocities by up to 17 % compared with ESTAR. Our results have implications for ice sheet model simulations of paleo-ice extent and sea level rise prediction.
E. A. Podolskiy, M. Barbero, F. Barpi, G. Chambon, M. Borri-Brunetto, O. Pallara, B. Frigo, B. Chiaia, and M. Naaim
The Cryosphere, 8, 1651–1659, https://doi.org/10.5194/tc-8-1651-2014, https://doi.org/10.5194/tc-8-1651-2014, 2014
Cited articles
Agnon, A. and Lyakhovsky, V.: Damage distribution and localization during dyke intrusion, 65–78, edited by: Balkema, A. A., Brookfield, Vt, 1995.
Amitrano, D., Grasso, J.-R., and Hantz, D.: From diffuse to localised damage through elastic interaction, Geophys. Res. Lett., 26, 2109–2112, 1999.
Aranson, I. S. and Tsimring, L. S.: Patterns and collective behavior in granular media: Theoretical concepts, Rev. Mod. Phys., 78, 641–692, https://doi.org/10.1103/RevModPhys.78.641, 2006.
Bažant, Z. P.: Instability ductility and size effect in strain-softening concrete, Journal of Engineering Mechanics Division, 102, 331–344, 1976.
Bažant, Z. P. and Jirásek, M.: Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress, J. Eng. Mech.-ASCE, 128, 1119–1149, https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119), 2002.
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, https://doi.org/10.1029/2012GL053317, l18502, 2012.
Bouillon, S. and Rampal, P.: Presentation of the dynamical core of neXtSIM a new sea ice model, Ocean Model., 91, 23–37, https://doi.org/10.1016/j.ocemod.2015.04.005, 2015.
Byerlee, J.: Friction of rocks, Pure Appl. Geophys., 116, 615–626, https://doi.org/10.1007/BF00876528, 1978.
Cakir, Z., Ergintav, S., Ozener, H., Dogan, U., Akoglu, A. M., Meghraoui, M., and Reilinger, R.: Onset of aseismic creep on major strike-slip faults, Geology, 40, 1115–1118, https://doi.org/10.1130/G33522.1, 2012.
Cetin, E., Cakir, Z., Meghraoui, M., Ergintav, S., and Akoglu, A. M.: Extent and distribution of aseismic slip on the Ismetpaşa segment of the North Anatolian Fault (Turkey) from Persistent Scatterer InSAR, Geochem. Geophy. Geosy., 15, 2883–2894, https://doi.org/10.1002/2014GC005307, 2014.
Coon, M., Kwok, R., Levy, G., Puis, M., Schreyer, H., and Sulsky, D.: Arctic Ice Dynamics Joint Experiment (AIDJEX) assumptions revisited and found inadequate, J. Geophys. Res., 112, C11S90, https://doi.org/10.1029/2005JC003393, 2007.
Cowie, P. A., Vanneste, C., and Sornette, D.: Statistical Physics Model for the Spatiotemporal evolution of faults, J. Geophys. Res., 98, 21809–21821, 1993.
Cowie, P. A., Sornette, D., and Vanneste, C.: Multifractal scaling properties of a growing fault population, Geophys. J. Int., 122, 457–469, 1995.
Duval, P., Ashby, M. F., and Anderman, I.: Rate-controlling processes in the creep of polycrystalline ice, J. Phys. Chem., 87, 4066–4074, https://doi.org/10.1021/j100244a014, 1983.
Eshelby, J. D.: The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems, P. Roy. Soc. Lond. A-Mat., 241, 376–396, https://doi.org/10.1098/rspa.1957.0133, 1957.
Fattal, R. and Kupferman, R.: Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newton. Fluid, 123, 281–285, 2004.
Fattal, R. and Kupferman, R.: Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation, J. Non-Newton. Fluid, 126, 23–37, 2005.
Flato, G., Marotzke, J., Abiodun, B., Braconnot, P., Chou, S. C., Collins, W., Cox, P., Driouech, F., Emori, S., Eyring, V., Forest, C., Gleckler, P., Guilyardi, E., Jakob, C., Kattsov, V. C. R., and Rummukainen, M.: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, chap. Evaluation of Climate Models, 126 pp., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2013.
Fortt, A. L. and Schulson, E. M.: The resistance to sliding along Coulombic shear faaults in ice, Acta Mater., 55, 2253–2264, 2007.
Frederiksen, S. and Braun, J.: Numerical modelling of strain localisation during extension of the continental lithosphere, Earth Planet. Sc. Lett., 188, 241–251, 2001.
Girard, L., Weiss, J., Molines, J. M., Barnier, B., and Bouillon, S.: Evaluation of high-resolution sea ice models on the basis of statistical and scaling properties of Arctic sea ice drift and deformation, J. Geophys. Res., 114, C08015, https://doi.org/10.1029/2008JC005182, 2009.
Girard, L., Amitrano, D., and Weiss, J.: Failure as a critical phenomenon in a progressive damage model, J. Stat. Mech.-Theory E, 2010, P01013, https://doi.org/10.1088/1742-5468/2010/01/P01013, 2010.
Girard, L., Bouillon, S., Weiss, J., Amitrano, D., Fichefet, T., and Legat, V.: A new modeling framework for sea ice models based on elasto-brittle rheology, Ann. Glaciol., 52, 123–132, https://doi.org/10.3189/172756411795931499, 2011.
Gratier, J. P., Renard, F., and Vial, B.: Postseismic pressure solution creep: Evidence and time-dependent change from dynamic indenting experiments, J. Geophys. Res.-Sol. Ea., 119, 2764–2779, https://doi.org/10.1002/2013JB010768, 2014.
Hamiel, Y., Liu, Y., Lyakhovsky, V., Ben-Zion, Y., and Lockner, D.: A viscoelastic damage model with applications to stable and unstable fracturing, Geophys. J. Int., 159, 1155–1165, https://doi.org/10.1111/j.1365-246X.2004.02452.x, 2004.
Herrmann, H. J. and Roux, S. (Eds.): Statistical Models for the Fracture of Disordered Media, North-Holland, Elsevier Science Publishers B.V., Amsterdam, 1990.
Hibler, W. D. I.: A viscous sea ice law as a stochastic average of plasticity, J. Geophys. Res., 82, 3932–3938, 1977.
Hibler, W. D. I.: A dynamic thermodynamic sea ice model, J. Phys. Oceanogr., 9, 815–846, 1979.
Hibler, W. I.: Sea ice fracturing on the large scale, Eng. Fract. Mech., 68, 2013–2043, https://doi.org/10.1016/S0013-7944(01)00035-2, 2001.
Hutchings, J. K., Roberts, A., Geiger, C. A., and Richter-Menge, J.: Spatial and temporal characterization of sea-ice deformation, Ann. Glaciol., 52, 360–368, 2011.
Jaeger, J. C. and Cook, N. G. W.: Fundamentals of Rock Mechanics, Chapman and Hall, Cambridge UK, ISBN 0470150637, 1979.
Jop, P., Forterre, Y., and Pouliquen, O.: A constitutive law for dense granular flows, Nature, 441, 727–230, https://doi.org/10.1038/nature04801, 2006.
Kagan, Y.: Fractal dimension of brittle fracture, J. Nonlinear Sci., 1, 1–16, https://doi.org/10.1007/BF01209146, 1991.
Kagan, Y. Y. and Jackson, D. D.: Long-Term Earthquake Clustering, Geophys. J. Int., 104, 117–134, https://doi.org/10.1111/j.1365-246X.1991.tb02498.x, 1991.
Kagan, Y. Y. and Knopoff, L.: Spatial distribution of earthquakes: the two-point correlation function, Geophys. J. Int., 62, 303–320, https://doi.org/10.1111/j.1365-246X.1980.tb04857.x, 1980.
Keller, A. and Hutter, K.: A viscoelastic damage model for polycrystalline ice, inspired by Weibull-distributed fiber bundle models. Part I: Constitutive models, Continuum Mech. Therm., 26, 879–894, https://doi.org/10.1007/s00161-014-0348-7, 2014.
Keunings, R.: On the high Weissenberg number problem, J. Non-Newton. Fluid, 20, 209–226, 1986.
King, G. C. P., Stein, R. S., and Lin, J.: Static stress change and the triggering of earthquakes, B. Seismol. Soc. Am., 84, 935–953, 1994.
Krug, J., Weiss, J., Gagliardini, O., and Durand, G.: Combining damage and fracture mechanics to model calving, The Cryosphere, 8, 2101–2117, https://doi.org/10.5194/tc-8-2101-2014, 2014.
Kwok, R.: Deformation of the Arctic Ocean sea ice cover: November 1996 through April 1997, in: IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics, edited by: Dempsey, J. and Shen, H. H., Solid Mechanics and Its Applications, 315–323, Springer Netherlands, https://doi.org/10.1007/978-94-015-9735-7, 2001.
Kwok, R., Hunke, E. C., Maslowski, W., Menemenlis, D., and Zhang, J.: Variability of sea ice simulations assessed with RGPS kinematics, J. Geophys. Res.-Oceans, 113, c11012, https://doi.org/10.1029/2008JC004783, 2008.
Lindsay, R. W., Zhang, J., and Rothrock, D. A.: Sea-ice deformation rates from satellite measurements and in a model, Atmos.-Ocean, 41, 35–47, https://doi.org/10.3137/ao.410103, 2003.
Lyakhovsky, V., Ben-Zion, Y., and Agnon, A.: Distributed damage, faulting and friction, J. Geophys. Res., 102, 27635–27649, 1997.
Marsan, D. and Weiss, J.: Space/time coupling in brittle deformation at geophysical scales, Earth Planet. Sc. Lett., 296, 353–359, 2010.
Marsan, D., Stern, H., Lindsay, R., and Weiss, J.: Scale dependance and localization of the deformation of Arctic sea ice, Phys. Rev. Lett., 93, 178501, https://doi.org/10.1103/PhysRevLett.93.178501, 2004.
Marsan, D., Weiss, J., Metaxian, J.-P., Grangeon, J., Roux, P.-F., and Haapala, J.: Low frequency bursts of horizontally-polarized waves in the Arctic sea-ice cover, J. Glaciol., 57, 231–237, 2011.
Maxwell, J. C.: On the dynamical theory of gases, Philos. T. R. Soc. Lond., 157, 49–88, 1867.
Maykut, G. A.: The surface heat and mass balance, 395–463, NATO ASI series, Series B: Physics, Springer US, https://doi.org/10.1007/978-1-4899-5352-0_6, 1986.
Nye, J. F.: Is there any physical basis for assuming linear viscous behavior for sea ice?, Aidjex Bulletin, 6, 18–19, 1973.
Paul, B.: A modification of the Coulomb-Mohr theory of fracture, J. Appl. Mech., 28, 259–268, 1961.
Petrich, C., Langhorne, P., and Haskell, T.: Formation and structure of refrozen cracks in land-fast first-year sea ice, J. Geophys. Res., 112, C04006, https://doi.org/10.1029/2006JC003466, 2007.
Pijaudier-Cabot, G. and Bažant, Z. P.: Nonlocal damage theory, J. Eng. Mech., 113, 1512–1533, 1987.
Pralong, A. and Funk, M.: Dynamic damage model of crevasse opening and application to glacier calving, J. Geophys. Res.-Sol. Ea., 110, https://doi.org/10.1029/2004JB003104, b01309, 2005.
Rampal, P., Weiss, J., Marsan, D., Lindsay, R., and Stern, H.: Scaling properties of sea ice deformation from buoy dispersion analysis, J. Geophys. Res.-Oceans, 113, c03002, https://doi.org/10.1029/2007JC004143, 2008.
Rampal, P., Weiss, J., Marsan, D., and Bourgoin, M.: Arctic sea ice velocity field: General circulation and turbulent-like fluctuations, J. Geophys. Res.-Oceans, 114, c10014, https://doi.org/10.1029/2008JC005227, 2009.
Rothrock, D. A.: The energetics of the plastic deformation of pack ice by ridging, J. Geophys. Res., 80, 4514–4519, 1975.
Sakov, P., Counillon, F., Bertino, L., Lisæter, K. A., Oke, P. R., and Korablev, A.: TOPAZ4: an ocean-sea ice data assimilation system for the North Atlantic and Arctic, Ocean Sci., 8, 633–656, https://doi.org/10.5194/os-8-633-2012, 2012.
Saramito, P.: On a modified non-singular log-conformation formulation for Johnson-Segalman viscoelastic fluids, J. Non-Newton. Fluid, 211, 16–30, 2014.
Saramito, P.: Complex fluids, Modelling and algorithms, Springer, 2016.
Schapery, R. A.: Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage, Int. J. Fracture, 97, 33–66, 1999.
Scholz, C. H.: The Mechanics of Earthquakes and Faulting, Cambridge University Press, New York, 2 Edn., ISBN 9780521655408, 2002.
Schreyer, H. L., Sulsky, D. L., Munday, L. B., Coon, M. D., and Kwok, R.: Elastic-decohesive constitutive model for sea ice, J. Geophys. Res., 111, C11S26, https://doi.org/10.1029/2005JC003334, 2006.
Schulson, E. M.: Compressive shear faults within arctic sea ice: Fractures on scales large and small, J. Geophys. Res., 109, C07016, https://doi.org/10.1029/2003JC002108, 2004.
Schulson, E. M.: Failure envelope of first-year Arctic sea ice: The role of friction in compressive fracture, J. Geophys. Res., 111, C11S25, https://doi.org/10.1029/2005JC003235, 2006.
Schulson, E. M. and Duval, P.: Creep and Fracture of Ice, Cambridge University Press, Cambridge, UK, 416 pp., 2009.
Schulson, E. M., Fortt, A. L., Iliescu, D., and Renshaw, C. E.: On the role of frictional sliding in the compressive fracture of ice and granite: Terminal vs. post-terminal failure, Acta Mater., 54, 3923–3932, https://doi.org/10.1016/j.actamat.2006.04.024, 2006.
Smith, G. C., Roy, F., Rezka, M., Surcel, M., Colan, D., Deacu, Z. He, D., Bélanger, J.-M., Skachko, S., Liu, Y., Dupont, F., Lemieux, J.-F., Beaudoin, C., Tranchant, B., Drévillon, M., Garric, G., Testut, C.-E., Lellouche, J.-M., Pellerin, P., Ritchie, H., Lu, Y., Davidson, F., Buehner, M., Caya, A., and Lajoie, M.: Sea ice forecast verification in the Canadian Global Ice Ocean Prediction System, Q. J. Roy. Meteor. Soc., 142, 659–671, https://doi.org/10.1002/qj.2555, 2016.
Stein, R. S.: The role of stress transfer in earthquake occurrence, Nature, 402, 605–609, https://doi.org/10.1038/45144, 1999.
Stern, H. L. and Lindsay, R. W.: Spatial scaling of Arctic sea ice deformation, J. Geophys. Res., 114, C10017, https://doi.org/10.1029/2009JC005380, 2009.
Stern, H. L., Rothrock, D. A., and Kwok, R.: Open water production in arctic sea ice: Satellite measurements and model parameterizations, J. Geophys. Res., 100, 20601–20612, 1995.
Tang, C.: Numerical Simulation of Progressive Rock Failure and Associated Seismicity, Int. J. Rock Mech. Min., 34, 249–261, 1997.
Timco, G. and Weeks, W.: A review of the engineering properties of sea ice, Cold Reg. Sci. Technol., 60, 107–129, https://doi.org/10.1016/j.coldregions.2009.10.003, 2010.
Tsamados, M., Feltham, D. L., and Wilchinsky, A. V.: Impact of a new anisotropic rheology on simulations of Arctic sea ice, J. Geophys. Res.-Oceans, 118, 91–107, https://doi.org/10.1029/2012JC007990, 2013.
Turcotte, D. L.: Fractals and Chaos in geology and geophysics, Cambridge University Press, New York, 398 pp., 1992.
Weiss, J.: Scaling of Fracture and Faulting of Ice on Earth, Surv. Geophys., 24, 185–227, https://doi.org/10.1023/A:1023293117309, 2003.
Weiss, J. and Schulson, E. M.: Coulombic faulting from the grain scale to the geophysical scale: lessons from ice, J. Phys. D-Appl. Phys., 42, 214017, https://doi.org/10.1088/0022-3727/42/21/214017, 2009.
Weiss, J., Schulson, E. M., and Stern, H. L.: Sea ice rheology from in-situ, satellite and laboratory observations: Fracture and friction, Earth Planet. Sc. Lett., 255, 1–8, 2007.
Wilchinsky, A. V. and Feltham, D. L.: Modelling the rheology of sea ice as a collection of diamond-shaped floes, J. Non-Newton. Fluid, 138, 22–32, 2006.
Short summary
In this paper we present a new mechanical modelling framework for the deformation of sea ice on regional and larger scales named Maxwell elasto-brittle. The model successfully reproduces the formation of narrow, oriented leads which concentrate the deformation within the damaged, i.e., fractured, ice as well as the intermittency of the damaging process, and hence represents a relevant contribution to the ongoing development of operational modelling platforms, regional and global climate models.
In this paper we present a new mechanical modelling framework for the deformation of sea ice on...
