Articles | Volume 11, issue 4
https://doi.org/10.5194/tc-11-1913-2017
© Author(s) 2017. 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-11-1913-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
From cyclic ice streaming to Heinrich-like events: the grow-and-surge instability in the Parallel Ice Sheet Model
Johannes Feldmann
CORRESPONDING AUTHOR
Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany
Anders Levermann
Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany
Institute of Physics, University of Potsdam, Potsdam, Germany
LDEO, Columbia University, New York, USA
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Johannes Feldmann, Anders Levermann, and Ricarda Winkelmann
The Cryosphere, 18, 4011–4028, https://doi.org/10.5194/tc-18-4011-2024, https://doi.org/10.5194/tc-18-4011-2024, 2024
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Here we show in simplified simulations that the (ir)reversibility of the retreat of instability-prone, Antarctica-type glaciers can strongly depend on the depth of the bed depression they rest on. If it is sufficiently deep, then the destabilized glacier does not recover from its collapsed state. Our results suggest that glaciers resting on a wide and deep bed depression, such as Antarctica's Thwaites Glacier, are particularly susceptible to irreversible retreat.
Johannes Feldmann and Anders Levermann
The Cryosphere, 17, 327–348, https://doi.org/10.5194/tc-17-327-2023, https://doi.org/10.5194/tc-17-327-2023, 2023
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Here we present a scaling relation that allows the comparison of the timescales of glaciers with geometric similarity. According to the relation, thicker and wider glaciers on a steeper bed slope have a much faster timescale than shallower, narrower glaciers on a flatter bed slope. The relation is supported by observations and simplified numerical simulations. We combine the scaling relation with a statistical analysis of the topography of 13 instability-prone Antarctic outlet glaciers.
Tanja Schlemm, Johannes Feldmann, Ricarda Winkelmann, and Anders Levermann
The Cryosphere, 16, 1979–1996, https://doi.org/10.5194/tc-16-1979-2022, https://doi.org/10.5194/tc-16-1979-2022, 2022
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Marine cliff instability, if it exists, could dominate Antarctica's contribution to future sea-level rise. It is likely to speed up with ice thickness and thus would accelerate in most parts of Antarctica. Here, we investigate a possible mechanism that might stop cliff instability through cloaking by ice mélange. It is only a first step, but it shows that embayment geometry is, in principle, able to stop marine cliff instability in most parts of West Antarctica.
Johannes Feldmann, Ronja Reese, Ricarda Winkelmann, and Anders Levermann
The Cryosphere, 16, 1927–1940, https://doi.org/10.5194/tc-16-1927-2022, https://doi.org/10.5194/tc-16-1927-2022, 2022
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We use a numerical model to simulate the flow of a simplified, buttressed Antarctic-type outlet glacier with an attached ice shelf. We find that after a few years of perturbation such a glacier responds much stronger to melting under the ice-shelf shear margins than to melting in the central fast streaming part of the ice shelf. This study explains the underlying physical mechanism which might gain importance in the future if melt rates under the Antarctic ice shelves continue to increase.
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.
Anders Levermann and Johannes Feldmann
The Cryosphere, 13, 1621–1633, https://doi.org/10.5194/tc-13-1621-2019, https://doi.org/10.5194/tc-13-1621-2019, 2019
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Using scaling analysis we propose that the currently observed marine ice-sheet instability in the Amundsen Sea sector might be faster than all other potential instabilities in Antarctica.
Johannes Feldmann, Ronja Reese, Ricarda Winkelmann, and Anders Levermann
The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-109, https://doi.org/10.5194/tc-2018-109, 2018
Revised manuscript not accepted
Johannes Feldmann and Anders Levermann
The Cryosphere, 10, 1753–1769, https://doi.org/10.5194/tc-10-1753-2016, https://doi.org/10.5194/tc-10-1753-2016, 2016
J. Feldmann and A. Levermann
The Cryosphere, 9, 631–645, https://doi.org/10.5194/tc-9-631-2015, https://doi.org/10.5194/tc-9-631-2015, 2015
Johannes Feldmann, Anders Levermann, and Ricarda Winkelmann
The Cryosphere, 18, 4011–4028, https://doi.org/10.5194/tc-18-4011-2024, https://doi.org/10.5194/tc-18-4011-2024, 2024
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Here we show in simplified simulations that the (ir)reversibility of the retreat of instability-prone, Antarctica-type glaciers can strongly depend on the depth of the bed depression they rest on. If it is sufficiently deep, then the destabilized glacier does not recover from its collapsed state. Our results suggest that glaciers resting on a wide and deep bed depression, such as Antarctica's Thwaites Glacier, are particularly susceptible to irreversible retreat.
Anja Katzenberger and Anders Levermann
Earth Syst. Dynam., 15, 1137–1151, https://doi.org/10.5194/esd-15-1137-2024, https://doi.org/10.5194/esd-15-1137-2024, 2024
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A fifth of the world's population lives in eastern China, whose climate is dominated by the East Asian Summer Monsoon (EASM). Therefore, it is important to know how the EASM will change under global warming. Here, we use the data of 34 climate models of the latest generation to understand how the EASM will change throughout the 21st century. The models project that the EASM will intensify and that variability between years will increase associated with an increase in extremely wet seasons.
Robert E. Kopp, Gregory G. Garner, Tim H. J. Hermans, Shantenu Jha, Praveen Kumar, Alexander Reedy, Aimée B. A. Slangen, Matteo Turilli, Tamsin L. Edwards, Jonathan M. Gregory, George Koubbe, Anders Levermann, Andre Merzky, Sophie Nowicki, Matthew D. Palmer, and Chris Smith
Geosci. Model Dev., 16, 7461–7489, https://doi.org/10.5194/gmd-16-7461-2023, https://doi.org/10.5194/gmd-16-7461-2023, 2023
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Future sea-level rise projections exhibit multiple forms of uncertainty, all of which must be considered by scientific assessments intended to inform decision-making. The Framework for Assessing Changes To Sea-level (FACTS) is a new software package intended to support assessments of global mean, regional, and extreme sea-level rise. An early version of FACTS supported the development of the IPCC Sixth Assessment Report sea-level projections.
Johannes Feldmann and Anders Levermann
The Cryosphere, 17, 327–348, https://doi.org/10.5194/tc-17-327-2023, https://doi.org/10.5194/tc-17-327-2023, 2023
Short summary
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Here we present a scaling relation that allows the comparison of the timescales of glaciers with geometric similarity. According to the relation, thicker and wider glaciers on a steeper bed slope have a much faster timescale than shallower, narrower glaciers on a flatter bed slope. The relation is supported by observations and simplified numerical simulations. We combine the scaling relation with a statistical analysis of the topography of 13 instability-prone Antarctic outlet glaciers.
Tanja Schlemm, Johannes Feldmann, Ricarda Winkelmann, and Anders Levermann
The Cryosphere, 16, 1979–1996, https://doi.org/10.5194/tc-16-1979-2022, https://doi.org/10.5194/tc-16-1979-2022, 2022
Short summary
Short summary
Marine cliff instability, if it exists, could dominate Antarctica's contribution to future sea-level rise. It is likely to speed up with ice thickness and thus would accelerate in most parts of Antarctica. Here, we investigate a possible mechanism that might stop cliff instability through cloaking by ice mélange. It is only a first step, but it shows that embayment geometry is, in principle, able to stop marine cliff instability in most parts of West Antarctica.
Johannes Feldmann, Ronja Reese, Ricarda Winkelmann, and Anders Levermann
The Cryosphere, 16, 1927–1940, https://doi.org/10.5194/tc-16-1927-2022, https://doi.org/10.5194/tc-16-1927-2022, 2022
Short summary
Short summary
We use a numerical model to simulate the flow of a simplified, buttressed Antarctic-type outlet glacier with an attached ice shelf. We find that after a few years of perturbation such a glacier responds much stronger to melting under the ice-shelf shear margins than to melting in the central fast streaming part of the ice shelf. This study explains the underlying physical mechanism which might gain importance in the future if melt rates under the Antarctic ice shelves continue to increase.
Anja Katzenberger, Jacob Schewe, Julia Pongratz, and Anders Levermann
Earth Syst. Dynam., 12, 367–386, https://doi.org/10.5194/esd-12-367-2021, https://doi.org/10.5194/esd-12-367-2021, 2021
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All state-of-the-art global climate models that contributed to the latest Coupled Model Intercomparison Project (CMIP6) show a robust increase in Indian summer monsoon rainfall that is even stronger than in the previous intercomparison (CMIP5). Furthermore, they show an increase in the year-to-year variability of this seasonal rainfall that crucially influences the livelihood of more than 1 billion people in India.
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.
Maria Zeitz, Anders Levermann, and Ricarda Winkelmann
The Cryosphere, 14, 3537–3550, https://doi.org/10.5194/tc-14-3537-2020, https://doi.org/10.5194/tc-14-3537-2020, 2020
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The flow of ice drives mass losses in the large ice sheets. Sea-level rise projections rely on ice-sheet models, solving the physics of ice flow and melt. Unfortunately the parameters in the physics of flow are uncertain. Here we show, in an idealized setup, that these uncertainties can double flow-driven mass losses within the possible range of parameters. It is possible that this uncertainty carries over to realistic sea-level rise projections.
Ronja Reese, Anders Levermann, Torsten Albrecht, Hélène Seroussi, and Ricarda Winkelmann
The Cryosphere, 14, 3097–3110, https://doi.org/10.5194/tc-14-3097-2020, https://doi.org/10.5194/tc-14-3097-2020, 2020
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We compare 21st century projections of Antarctica's future sea-level contribution simulated with the Parallel Ice Sheet Model submitted to ISMIP6 with projections following the LARMIP-2 protocol based on the same model configuration. We find that (1) a preceding historic simulation increases mass loss by 5–50 % and that (2) the order of magnitude difference in the ice loss in our experiments following the two protocols can be explained by the translation of ocean forcing to sub-shelf melting.
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.
Torsten Albrecht, Ricarda Winkelmann, and Anders Levermann
The Cryosphere, 14, 633–656, https://doi.org/10.5194/tc-14-633-2020, https://doi.org/10.5194/tc-14-633-2020, 2020
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A large ensemble of glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM) was analyzed in which four relevant model parameters were systematically varied. These parameters were selected in a companion study and are associated with uncertainties in ice dynamics, climatic forcing, basal sliding and solid Earth deformation. For each ensemble member a statistical score is computed, which enables calibrating the model against both modern and geologic data.
Torsten Albrecht, Ricarda Winkelmann, and Anders Levermann
The Cryosphere, 14, 599–632, https://doi.org/10.5194/tc-14-599-2020, https://doi.org/10.5194/tc-14-599-2020, 2020
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During the last glacial cycles the Antarctic Ice Sheet experienced alternating climatic conditions and varying sea-level history. In response, changes in ice sheet volume and ice-covered area occurred, implying feedbacks on the global sea level. We ran model simulations of the ice sheet with the Parallel Ice Sheet Model (PISM) over the last two glacial cycles to evaluate the model's sensitivity to different choices of boundary conditions and parameters to gain confidence for future projections.
Anders Levermann, Ricarda Winkelmann, Torsten Albrecht, Heiko Goelzer, Nicholas R. Golledge, Ralf Greve, Philippe Huybrechts, Jim Jordan, Gunter Leguy, Daniel Martin, Mathieu Morlighem, Frank Pattyn, David Pollard, Aurelien Quiquet, Christian Rodehacke, Helene Seroussi, Johannes Sutter, Tong Zhang, Jonas Van Breedam, Reinhard Calov, Robert DeConto, Christophe Dumas, Julius Garbe, G. Hilmar Gudmundsson, Matthew J. Hoffman, Angelika Humbert, Thomas Kleiner, William H. Lipscomb, Malte Meinshausen, Esmond Ng, Sophie M. J. Nowicki, Mauro Perego, Stephen F. Price, Fuyuki Saito, Nicole-Jeanne Schlegel, Sainan Sun, and Roderik S. W. van de Wal
Earth Syst. Dynam., 11, 35–76, https://doi.org/10.5194/esd-11-35-2020, https://doi.org/10.5194/esd-11-35-2020, 2020
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We provide an estimate of the future sea level contribution of Antarctica from basal ice shelf melting up to the year 2100. The full uncertainty range in the warming-related forcing of basal melt is estimated and applied to 16 state-of-the-art ice sheet models using a linear response theory approach. The sea level contribution we obtain is very likely below 61 cm under unmitigated climate change until 2100 (RCP8.5) and very likely below 40 cm if the Paris Climate Agreement is kept.
Falko Ueckerdt, Katja Frieler, Stefan Lange, Leonie Wenz, Gunnar Luderer, and Anders Levermann
Earth Syst. Dynam., 10, 741–763, https://doi.org/10.5194/esd-10-741-2019, https://doi.org/10.5194/esd-10-741-2019, 2019
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We compute the global mean temperature increase at which the costs from climate-change damages and climate-change mitigation are minimal. This temperature is computed robustly around 2 degrees of global warming across a wide range of normative assumptions on the valuation of future welfare and inequality aversion.
Tanja Schlemm and Anders Levermann
The Cryosphere, 13, 2475–2488, https://doi.org/10.5194/tc-13-2475-2019, https://doi.org/10.5194/tc-13-2475-2019, 2019
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We provide a simple stress-based parameterization for cliff calving of ice sheets. According to the resulting increasing dependence of the calving rate on ice thickness, the parameterization might lead to a runaway ice loss in large parts of Greenland and Antarctica.
Anders Levermann and Johannes Feldmann
The Cryosphere, 13, 1621–1633, https://doi.org/10.5194/tc-13-1621-2019, https://doi.org/10.5194/tc-13-1621-2019, 2019
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Using scaling analysis we propose that the currently observed marine ice-sheet instability in the Amundsen Sea sector might be faster than all other potential instabilities in Antarctica.
Johannes Feldmann, Ronja Reese, Ricarda Winkelmann, and Anders Levermann
The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-109, https://doi.org/10.5194/tc-2018-109, 2018
Revised manuscript not accepted
Jacob Schewe and Anders Levermann
Earth Syst. Dynam., 8, 495–505, https://doi.org/10.5194/esd-8-495-2017, https://doi.org/10.5194/esd-8-495-2017, 2017
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Monsoon systems have undergone abrupt changes in past climates, and theoretical considerations show that threshold behavior can follow from the internal dynamics of monsoons. So far, however, the possibility of abrupt changes has not been explored for modern monsoon systems. We analyze state-of-the-art climate model simulations and show that some models project abrupt changes in Sahel rainfall in response to a dynamic shift in the West African monsoon under 21st century climate change.
Jan Wohland, Torsten Albrecht, and Anders Levermann
The Cryosphere Discuss., https://doi.org/10.5194/tc-2016-191, https://doi.org/10.5194/tc-2016-191, 2016
Preprint withdrawn
Anders Levermann and Ricarda Winkelmann
The Cryosphere, 10, 1799–1807, https://doi.org/10.5194/tc-10-1799-2016, https://doi.org/10.5194/tc-10-1799-2016, 2016
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In recent decades, the Greenland Ice Sheet has been losing mass and has thereby contributed to global sea-level rise. Here we derive the basic equations for the melt elevation feedback that can lead to self-amplifying melt of the Greenland Ice Sheet and ice sheets in general. The theory unifies the results of complex models when the feedback dominates the dynamics and it allows us to estimate the melt time of ice sheets from data in cases where ice dynamic loss can be neglected.
Johannes Feldmann and Anders Levermann
The Cryosphere, 10, 1753–1769, https://doi.org/10.5194/tc-10-1753-2016, https://doi.org/10.5194/tc-10-1753-2016, 2016
K. Frieler, M. Mengel, and A. Levermann
Earth Syst. Dynam., 7, 203–210, https://doi.org/10.5194/esd-7-203-2016, https://doi.org/10.5194/esd-7-203-2016, 2016
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Sea level will continue to rise for centuries. We investigate the option of delaying sea-level rise by pumping ocean water onto Antarctica. Due to wave propagation ice is discharged much faster back into the ocean than expected from pure advection. A millennium-scale storage of > 80 % of the additional ice requires a distance of > 700 km from the coastline. The pumping energy required to elevate ocean water to mitigate a sea-level rise of 3 mm yr−1 exceeds 7 % of current global primary energy supply.
K. Frieler, A. Levermann, J. Elliott, J. Heinke, A. Arneth, M. F. P. Bierkens, P. Ciais, D. B. Clark, D. Deryng, P. Döll, P. Falloon, B. Fekete, C. Folberth, A. D. Friend, C. Gellhorn, S. N. Gosling, I. Haddeland, N. Khabarov, M. Lomas, Y. Masaki, K. Nishina, K. Neumann, T. Oki, R. Pavlick, A. C. Ruane, E. Schmid, C. Schmitz, T. Stacke, E. Stehfest, Q. Tang, D. Wisser, V. Huber, F. Piontek, L. Warszawski, J. Schewe, H. Lotze-Campen, and H. J. Schellnhuber
Earth Syst. Dynam., 6, 447–460, https://doi.org/10.5194/esd-6-447-2015, https://doi.org/10.5194/esd-6-447-2015, 2015
J. Feldmann and A. Levermann
The Cryosphere, 9, 631–645, https://doi.org/10.5194/tc-9-631-2015, https://doi.org/10.5194/tc-9-631-2015, 2015
M. A. Martin, A. Levermann, and R. Winkelmann
The Cryosphere Discuss., https://doi.org/10.5194/tcd-9-1705-2015, https://doi.org/10.5194/tcd-9-1705-2015, 2015
Preprint withdrawn
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Numerical ice sheet modelling shows that idealized, step-function type ocean warming in the Weddell Sea, where the ice sheet is close to floatation, leads to more immediate ice discharge with a higher sensitivity to small warming levels than the same warming in the Amundsen Sea. While the cumulative ice loss in the Amundsen Sea Sector is of similar magnitude after five centuries of continued warming, ice loss increases at a slower pace and only for significantly higher warming levels.
D. Ehlert and A. Levermann
Earth Syst. Dynam., 5, 383–397, https://doi.org/10.5194/esd-5-383-2014, https://doi.org/10.5194/esd-5-383-2014, 2014
A. Levermann, R. Winkelmann, S. Nowicki, J. L. Fastook, K. Frieler, R. Greve, H. H. Hellmer, M. A. Martin, M. Meinshausen, M. Mengel, A. J. Payne, D. Pollard, T. Sato, R. Timmermann, W. L. Wang, and R. A. Bindschadler
Earth Syst. Dynam., 5, 271–293, https://doi.org/10.5194/esd-5-271-2014, https://doi.org/10.5194/esd-5-271-2014, 2014
T. Albrecht and A. Levermann
The Cryosphere, 8, 587–605, https://doi.org/10.5194/tc-8-587-2014, https://doi.org/10.5194/tc-8-587-2014, 2014
C. F. Schleussner, J. Runge, J. Lehmann, and A. Levermann
Earth Syst. Dynam., 5, 103–115, https://doi.org/10.5194/esd-5-103-2014, https://doi.org/10.5194/esd-5-103-2014, 2014
A. Menon, A. Levermann, J. Schewe, J. Lehmann, and K. Frieler
Earth Syst. Dynam., 4, 287–300, https://doi.org/10.5194/esd-4-287-2013, https://doi.org/10.5194/esd-4-287-2013, 2013
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Marek Muchow and Arttu Polojärvi
The Cryosphere, 18, 4765–4774, https://doi.org/10.5194/tc-18-4765-2024, https://doi.org/10.5194/tc-18-4765-2024, 2024
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We present the first explicit three-dimensional simulations of sea-ice ridge formation, which enables us to observe failure in several locations simultaneously. Sea-ice ridges are formed when ice converges and fails due to wind and ocean currents, so broken ice accumulates in a ridge. Previous two-dimensional models could not capture this behavior. We conclude that non-simultaneous failure is necessary to simulate ridging forces to assess how ridging forces relate to other ice properties.
Aslak Grinsted, Nicholas Mossor Rathmann, Ruth Mottram, Anne Munck Solgaard, Joachim Mathiesen, and Christine Schøtt Hvidberg
The Cryosphere, 18, 1947–1957, https://doi.org/10.5194/tc-18-1947-2024, https://doi.org/10.5194/tc-18-1947-2024, 2024
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Ice fracture can cause glacier crevassing and calving. These natural hazards can also modulate the flow and evolution of ice sheets. In a new study, we use a new high-resolution dataset to determine a new failure criterion for glacier ice. Surprisingly, the strength of ice depends on the mode of deformation, and this has potential implications for the currently used flow law of ice.
Rasha Abbasi, Markus Ackermann, Jenni Adams, Nakul Aggarwal, Juanan Aguilar, Markus Ahlers, Maryon Ahrens, Jean-Marco Alameddine, Antonio Augusto Alves Junior, Najia Moureen Binte Amin, Karen Andeen, Tyler Anderson, Gisela Anton, Carlos Argüelles, Yosuke Ashida, Sofia Athanasiadou, Spencer Axani, Xinhua Bai, Aswathi Balagopal V, Moreno Baricevic, Steve Barwick, Vedant Basu, Ryan Bay, James Beatty, Karl Heinz Becker, Julia Becker Tjus, Jakob Beise, Chiara Bellenghi, Samuel Benda, Segev BenZvi, David Berley, Elisa Bernardini, Dave Besson, Gary Binder, Daniel Bindig, Erik Blaufuss, Summer Blot, Federico Bontempo, Julia Book, Jürgen Borowka, Caterina Boscolo Meneguolo, Sebastian Böser, Olga Botner, Jakob Böttcher, Etienne Bourbeau, Jim Braun, Bennett Brinson, Jannes Brostean-Kaiser, Ryan Burley, Raffaela Busse, Michael Campana, Erin Carnie-Bronca, Chujie Chen, Zheyang Chen, Dmitry Chirkin, Koun Choi, Brian Clark, Lew Classen, Alan Coleman, Gabriel Collin, Amy Connolly, Janet Conrad, Paul Coppin, Pablo Correa, Stefan Countryman, Doug Cowen, Robert Cross, Christian Dappen, Pranav Dave, Catherine De Clercq, James DeLaunay, Diyaselis Delgado López, Hans Dembinski, Kunal Deoskar, Abhishek Desai, Paolo Desiati, Krijn de Vries, Gwenhael de Wasseige, Tyce DeYoung, Alejandro Diaz, Juan Carlos Díaz-Vélez, Markus Dittmer, Hrvoje Dujmovic, Michael DuVernois, Thomas Ehrhardt, Philipp Eller, Ralph Engel, Hannah Erpenbeck, John Evans, Paul Evenson, Kwok Lung Fan, Ali Fazely, Anatoli Fedynitch, Nora Feigl, Sebastian Fiedlschuster, Aaron Fienberg, Chad Finley, Leander Fischer, Derek Fox, Anna Franckowiak, Elizabeth Friedman, Alexander Fritz, Philipp Fürst, Tom Gaisser, Jay Gallagher, Erik Ganster, Alfonso Garcia, Simone Garrappa, Lisa Gerhardt, Ava Ghadimi, Christian Glaser, Thorsten Glüsenkamp, Theo Glauch, Noah Goehlke, Javier Gonzalez, Sreetama Goswami, Darren Grant, Shannon Gray, Timothée Grégoire, Spencer Griswold, Christoph Günther, Pascal Gutjahr, Christian Haack, Allan Hallgren, Robert Halliday, Lasse Halve, Francis Halzen, Hassane Hamdaoui, Martin Ha Minh, Kael Hanson, John Hardin, Alexander Harnisch, Patrick Hatch, Andreas Haungs, Klaus Helbing, Jonas Hellrung, Felix Henningsen, Lars Heuermann, Stephanie Hickford, Colton Hill, Gary Hill, Kara Hoffman, Kotoyo Hoshina, Wenjie Hou, Thomas Huber, Klas Hultqvist, Mirco Hünnefeld, Raamis Hussain, Karolin Hymon, Seongjin In, Nadege Iovine, Aya Ishihara, Matti Jansson, George Japaridze, Minjin Jeong, Miaochen Jin, Ben Jones, Donghwa Kang, Woosik Kang, Xinyue Kang, Alexander Kappes, David Kappesser, Leonora Kardum, Timo Karg, Martina Karl, Albrecht Karle, Uli Katz, Matt Kauer, John Kelley, Ali Kheirandish, Ken'ichi Kin, Joanna Kiryluk, Spencer Klein, Alina Kochocki, Ramesh Koirala, Hermann Kolanoski, Tomas Kontrimas, Lutz Köpke, Claudio Kopper, Jason Koskinen, Paras Koundal, Michael Kovacevich, Marek Kowalski, Tetiana Kozynets, Emmett Krupczak, Emma Kun, Naoko Kurahashi, Neha Lad, Cristina Lagunas Gualda, Michael Larson, Frederik Lauber, Jeffrey Lazar, Jiwoong Lee, Kayla Leonard, Agnieszka Leszczyńska, Massimiliano Lincetto, Qinrui Liu, Maria Liubarska, Elisa Lohfink, Christina Love, Cristian Jesus Lozano Mariscal, Lu Lu, Francesco Lucarelli, Andrew Ludwig, William Luszczak, Yang Lyu, Wing Yan Ma, Jim Madsen, Kendall Mahn, Yuya Makino, Sarah Mancina, Wenceslas Marie Sainte, Ioana Mariş, Szabolcs Marka, Zsuzsa Marka, Matthew Marsee, Ivan Martinez-Soler, Reina Maruyama, Thomas McElroy, Frank McNally, James Vincent Mead, Kevin Meagher, Sarah Mechbal, Andres Medina, Maximilian Meier, Stephan Meighen-Berger, Yarno Merckx, Jessie Micallef, Daniela Mockler, Teresa Montaruli, Roger Moore, Bob Morse, Marjon Moulai, Tista Mukherjee, Richard Naab, Ryo Nagai, Uwe Naumann, Amid Nayerhoda, Jannis Necker, Miriam Neumann, Hans Niederhausen, Mehr Nisa, Sarah Nowicki, Anna Obertacke Pollmann, Marie Oehler, Bob Oeyen, Alex Olivas, Rasmus Orsoe, Jesse Osborn, Erin O'Sullivan, Hershal Pandya, Daria Pankova, Nahee Park, Grant Parker, Ek Narayan Paudel, Larissa Paul, Carlos Pérez de los Heros, Lilly Peters, Josh Peterson, Saskia Philippen, Sarah Pieper, Alex Pizzuto, Matthias Plum, Yuiry Popovych, Alessio Porcelli, Maria Prado Rodriguez, Brandon Pries, Rachel Procter-Murphy, Gerald Przybylski, Christoph Raab, John Rack-Helleis, Mohamed Rameez, Katherine Rawlins, Zoe Rechav, Abdul Rehman, Patrick Reichherzer, Giovanni Renzi, Elisa Resconi, Simeon Reusch, Wolfgang Rhode, Mike Richman, Benedikt Riedel, Ella Roberts, Sally Robertson, Steven Rodan, Gerrit Roellinghoff, Martin Rongen, Carsten Rott, Tim Ruhe, Li Ruohan, Dirk Ryckbosch, Devyn Rysewyk Cantu, Ibrahim Safa, Julian Saffer, Daniel Salazar-Gallegos, Pranav Sampathkumar, Sebastian Sanchez Herrera, Alexander Sandrock, Marcos Santander, Sourav Sarkar, Subir Sarkar, Merlin Schaufel, Harald Schieler, Sebastian Schindler, Berit Schlüter, Torsten Schmidt, Judith Schneider, Frank Schröder, Lisa Schumacher, Georg Schwefer, Steve Sclafani, Dave Seckel, Surujhdeo Seunarine, Ankur Sharma, Shefali Shefali, Nobuhiro Shimizu, Manuel Silva, Barbara Skrzypek, Ben Smithers, Robert Snihur, Jan Soedingrekso, Andreas Søgaard, Dennis Soldin, Christian Spannfellner, Glenn Spiczak, Christian Spiering, Michael Stamatikos, Todor Stanev, Robert Stein, Thorsten Stezelberger, Timo Stürwald, Thomas Stuttard, Greg Sullivan, Ignacio Taboada, Samvel Ter-Antonyan, Will Thompson, Jessie Thwaites, Serap Tilav, Kirsten Tollefson, Christoph Tönnis, Simona Toscano, Delia Tosi, Alexander Trettin, Chun Fai Tung, Roxanne Turcotte, Jean Pierre Twagirayezu, Bunheng Ty, Martin Unland Elorrieta, Karriem Upshaw, Nora Valtonen-Mattila, Justin Vandenbroucke, Nick van Eijndhoven, David Vannerom, Jakob van Santen, Javi Vara, Joshua Veitch-Michaelis, Stef Verpoest, Doga Veske, Christian Walck, Winnie Wang, Timothy Blake Watson, Chris Weaver, Philip Weigel, Andreas Weindl, Jan Weldert, Chris Wendt, Johannes Werthebach, Mark Weyrauch, Nathan Whitehorn, Christopher Wiebusch, Nathan Willey, Dawn Williams, Martin Wolf, Gerrit Wrede, Johan Wulff, Xianwu Xu, Juan Pablo Yanez, Emre Yildizci, Shigeru Yoshida, Shiqi Yu, Tianlu Yuan, Zelong Zhang, and Pavel Zhelnin
The Cryosphere, 18, 75–102, https://doi.org/10.5194/tc-18-75-2024, https://doi.org/10.5194/tc-18-75-2024, 2024
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The IceCube Neutrino Observatory instruments 1 km3 of deep, glacial ice using 5160 sensors to detect light emitted by elementary particles. An unexpected effect observed is anisotropic light attenuation, aligned with the flow direction of the ice. Curved light trajectories resulting from asymmetric diffusion in the birefringent polycrystalline microstructure of the ice have been identified as the primary cause of this effect. This allows us to deduce ice crystal properties.
Damien Ringeisen, Nils Hutter, and Luisa von Albedyll
The Cryosphere, 17, 4047–4061, https://doi.org/10.5194/tc-17-4047-2023, https://doi.org/10.5194/tc-17-4047-2023, 2023
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When sea ice is put into motion by wind and ocean currents, it deforms following narrow lines. Our two datasets at different locations and resolutions show that the intersection angle between these lines is often acute and rarely obtuse. We use the orientation of narrow lines to gain indications about the mechanical properties of sea ice and to constrain how to design sea-ice mechanical models for high-resolution simulation of the Arctic and improve regional predictions of sea-ice motion.
Sheng Fan, David J. Prior, Brent Pooley, Hamish Bowman, Lucy Davidson, David Wallis, Sandra Piazolo, Chao Qi, David L. Goldsby, and Travis F. Hager
The Cryosphere, 17, 3443–3459, https://doi.org/10.5194/tc-17-3443-2023, https://doi.org/10.5194/tc-17-3443-2023, 2023
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The microstructure of ice controls the behaviour of polar ice flow. Grain growth can modify the microstructure of ice; however, its processes and kinetics are poorly understood. We conduct grain-growth experiments on synthetic and natural ice samples at 0 °C. Microstructural data show synthetic ice grows continuously with time. In contrast, natural ice does not grow within a month. The inhibition of grain growth in natural ice is largely contributed by bubble pinning at ice grain boundaries.
Jan Mudler, Andreas Hördt, Dennis Kreith, Madhuri Sugand, Kirill Bazhin, Lyudmila Lebedeva, and Tino Radić
The Cryosphere, 16, 4727–4744, https://doi.org/10.5194/tc-16-4727-2022, https://doi.org/10.5194/tc-16-4727-2022, 2022
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The spectral electrical signal of ice exhibits a strong characteristic behaviour in the frequency range from 100 Hz to 100 kHz, due to polarization effects. With our geophysical method, we can analyse this characteristic to detect subsurface ice. Moreover, we use a model to quantify 2-D ground ice content based on our data. The potential of our new measurement device is showed up. Data were taken on a permafrost site in Yakutia, and the results are in agreement with other existing field data.
Daniel H. Richards, Samuel S. Pegler, and Sandra Piazolo
The Cryosphere, 16, 4571–4592, https://doi.org/10.5194/tc-16-4571-2022, https://doi.org/10.5194/tc-16-4571-2022, 2022
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Understanding the orientation of ice grains is key for predicting ice flow. We explore the evolution of these orientations using a new efficient model. We present an exploration of the patterns produced under a range of temperatures and 2D deformations, including for the first time a universal regime diagram. We do this for deformations relevant to ice sheets but not studied in experiments. These results can be used to understand drilled ice cores and improve future modelling of ice sheets.
Franz Lutz, David J. Prior, Holly Still, M. Hamish Bowman, Bia Boucinhas, Lisa Craw, Sheng Fan, Daeyeong Kim, Robert Mulvaney, Rilee E. Thomas, and Christina L. Hulbe
The Cryosphere, 16, 3313–3329, https://doi.org/10.5194/tc-16-3313-2022, https://doi.org/10.5194/tc-16-3313-2022, 2022
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Ice crystal alignment in the sheared margins of fast-flowing polar ice is important as it may control the ice sheet flow rate, from land to the ocean. Sampling shear margins is difficult because of logistical and safety considerations. We show that crystal alignments in a glacier shear margin in Antarctica can be measured using sound waves. Results from a seismic experiment on the 50 m scale and from ultrasonic experiments on the decimetre scale match ice crystal measurements from an ice core.
Falk M. Oraschewski and Aslak Grinsted
The Cryosphere, 16, 2683–2700, https://doi.org/10.5194/tc-16-2683-2022, https://doi.org/10.5194/tc-16-2683-2022, 2022
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Old snow (denoted as firn) accumulates in the interior of ice sheets and gets densified into glacial ice. Typically, this densification is assumed to only depend on temperature and accumulation rate. However, it has been observed that stretching of the firn by horizontal flow also enhances this process. Here, we show how to include this effect in classical firn models. With the model we confirm that softening of the firn controls firn densification in areas with strong horizontal stretching.
M. Reza Ershadi, Reinhard Drews, Carlos Martín, Olaf Eisen, Catherine Ritz, Hugh Corr, Julia Christmann, Ole Zeising, Angelika Humbert, and Robert Mulvaney
The Cryosphere, 16, 1719–1739, https://doi.org/10.5194/tc-16-1719-2022, https://doi.org/10.5194/tc-16-1719-2022, 2022
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Radio waves transmitted through ice split up and inform us about the ice sheet interior and orientation of single ice crystals. This can be used to infer how ice flows and improve projections on how it will evolve in the future. Here we used an inverse approach and developed a new algorithm to infer ice properties from observed radar data. We applied this technique to the radar data obtained at two EPICA drilling sites, where ice cores were used to validate our results.
Yu Wang, Chen Zhao, Rupert Gladstone, Ben Galton-Fenzi, and Roland Warner
The Cryosphere, 16, 1221–1245, https://doi.org/10.5194/tc-16-1221-2022, https://doi.org/10.5194/tc-16-1221-2022, 2022
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The thermal structure of the Amery Ice Shelf and its spatial pattern are evaluated and analysed through temperature observations from six boreholes and numerical simulations. The simulations demonstrate significant ice warming downstream along the ice flow and a great variation of the thermal structure across the ice flow. We suggest that the thermal structure of the Amery Ice Shelf is unlikely to be affected by current climate changes on decadal timescales.
Reza Zeinali-Torbati, Ian D. Turnbull, Rocky S. Taylor, and Derek Mueller
The Cryosphere, 15, 5601–5621, https://doi.org/10.5194/tc-15-5601-2021, https://doi.org/10.5194/tc-15-5601-2021, 2021
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Using the reanalysis datasets and the Canadian Ice Island Drift, Deterioration and Detection database, a probabilistic model was developed to quantify ice island fracture probability under various atmospheric and oceanic conditions. The model identified water temperature as the most dominant variable behind ice island fracture events, while ocean currents played a minor role. The developed model offers a predictive capability and could be of particular interest to offshore and marine activities.
Rowan Romeyn, Alfred Hanssen, Bent Ole Ruud, and Tor Arne Johansen
The Cryosphere, 15, 2939–2955, https://doi.org/10.5194/tc-15-2939-2021, https://doi.org/10.5194/tc-15-2939-2021, 2021
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Air-coupled flexural waves are produced by the interaction between pressure waves in air and bending waves in a floating ice sheet. The frequency of these waves is related to the physical properties of the ice sheet, specifically its thickness and rigidity. We demonstrate the usefulness of air-coupled flexural waves for estimating ice thickness and give a theoretical description of the governing physics that highlights their similarity to related phenomena in other fields.
Pavel Talalay, Yazhou Li, Laurent Augustin, Gary D. Clow, Jialin Hong, Eric Lefebvre, Alexey Markov, Hideaki Motoyama, and Catherine Ritz
The Cryosphere, 14, 4021–4037, https://doi.org/10.5194/tc-14-4021-2020, https://doi.org/10.5194/tc-14-4021-2020, 2020
Maria Zeitz, Anders Levermann, and Ricarda Winkelmann
The Cryosphere, 14, 3537–3550, https://doi.org/10.5194/tc-14-3537-2020, https://doi.org/10.5194/tc-14-3537-2020, 2020
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The flow of ice drives mass losses in the large ice sheets. Sea-level rise projections rely on ice-sheet models, solving the physics of ice flow and melt. Unfortunately the parameters in the physics of flow are uncertain. Here we show, in an idealized setup, that these uncertainties can double flow-driven mass losses within the possible range of parameters. It is possible that this uncertainty carries over to realistic sea-level rise projections.
Mingdong Wei, Arttu Polojärvi, David M. Cole, and Malith Prasanna
The Cryosphere, 14, 2849–2867, https://doi.org/10.5194/tc-14-2849-2020, https://doi.org/10.5194/tc-14-2849-2020, 2020
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Laboratory-scale work on saline ice is usually limited to the use of dry isothermal specimens. Here we developed techniques for conducting floating-ice experiments. The mechanical behavior of floating-ice specimens under cyclic compression was compared with that of dry specimens. Moreover, both of them were successfully analyzed using a theoretical model. Results demonstrate the importance of the work on warm and floating ice, increasingly existing in the polar regions due to climate change.
Martin Rongen, Ryan Carlton Bay, and Summer Blot
The Cryosphere, 14, 2537–2543, https://doi.org/10.5194/tc-14-2537-2020, https://doi.org/10.5194/tc-14-2537-2020, 2020
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We report on the observation of a directional anisotropy in the intensity of backscattered light. The measurement was performed using a laser dust logger in the SPC14 drill hole at the geographic South Pole. We find the anisotropy axis to be compatible with the ice flow direction. It is discussed in comparison to a similar anisotropy observed by the IceCube Neutrino Observatory. In future, the measurement principle may provide a continuous record of crystal properties along entire drill holes.
Ernst-Jan N. Kuiper, Ilka Weikusat, Johannes H. P. de Bresser, Daniela Jansen, Gill M. Pennock, and Martyn R. Drury
The Cryosphere, 14, 2429–2448, https://doi.org/10.5194/tc-14-2429-2020, https://doi.org/10.5194/tc-14-2429-2020, 2020
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A composite flow law model applied to crystal size distributions from the NEEM deep ice core predicts that fine-grained layers in ice from the last Glacial period localize deformation as internal shear zones in the Greenland ice sheet deforming by grain-size-sensitive creep. This prediction is consistent with microstructures in Glacial age ice.
Ernst-Jan N. Kuiper, Johannes H. P. de Bresser, Martyn R. Drury, Jan Eichler, Gill M. Pennock, and Ilka Weikusat
The Cryosphere, 14, 2449–2467, https://doi.org/10.5194/tc-14-2449-2020, https://doi.org/10.5194/tc-14-2449-2020, 2020
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Fast ice flow occurs in deeper parts of polar ice sheets, driven by high stress and high temperatures. Above 262 K ice flow is further enhanced, probably by the formation of thin melt layers between ice crystals. A model applying an experimentally derived composite flow law, using temperature and grain size values from the deepest 540 m of the NEEM ice core, predicts that flow in fine-grained layers is enhanced by a factor of 10 compared to coarse-grained layers in the Greenland ice sheet.
Christopher C. Schneck, Tadros R. Ghobrial, and Mark R. Loewen
The Cryosphere, 13, 2751–2769, https://doi.org/10.5194/tc-13-2751-2019, https://doi.org/10.5194/tc-13-2751-2019, 2019
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Properties of suspended frazil ice and flocs in water of different salinities were measured in the lab using high-resolution images. It was found that freshwater frazil particles and flocs were larger than in saline water by ~13 % and 75 %, respectively. Both the growth rate of particles and the porosity of flocs decreased with salinity and ranged between 0.174 and 0.024 mm min−1 and 86 % and 75 % for freshwater and 35 ‰ saline water, respectively.
Ľubica Vetráková, Vilém Neděla, Jiří Runštuk, and Dominik Heger
The Cryosphere, 13, 2385–2405, https://doi.org/10.5194/tc-13-2385-2019, https://doi.org/10.5194/tc-13-2385-2019, 2019
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We froze salty solutions to examine where and how the brine is distributed within the ice by using an environmental scanning electron microscope. The structures are highly heterogeneous, consisting of almost pure ice intertwined with brine, which can form lamellae, veins, or pools on the surface. Considering various concentrations and methods for laboratory ice preparation, we determined how the freezing technique influences the microstructure of the brine on and in the ice.
Alexander Meyer, Dmitry Eliseev, Dirk Heinen, Peter Linder, Franziska Scholz, Lars Steffen Weinstock, Christopher Wiebusch, and Simon Zierke
The Cryosphere, 13, 1381–1394, https://doi.org/10.5194/tc-13-1381-2019, https://doi.org/10.5194/tc-13-1381-2019, 2019
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The acoustic damping in natural glaciers is a largely unexplored physical property that has relevance for various applications particularly for the exploration of glaciers with probes. We present measurements of the attenuation of sound in situ on the Italian glacier Langenferner. The tested frequency ranges from 2 to 35 kHz. The attenuation length ranges between 13 m for low frequencies and 5 m for high frequencies.
Carie M. Frantz, Bonnie Light, Samuel M. Farley, Shelly Carpenter, Ross Lieblappen, Zoe Courville, Mónica V. Orellana, and Karen Junge
The Cryosphere, 13, 775–793, https://doi.org/10.5194/tc-13-775-2019, https://doi.org/10.5194/tc-13-775-2019, 2019
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This paper provides a characterization of the physical and optical properties of "rotten" Arctic sea ice collected in two field seasons from off the coast of Utqiaġvik (formerly Barrow), Alaska. Rotten ice is physically and optically distinct when compared to ice from earlier in the melt season. It is marked by large connected pores, has lost most of its brine content, and scatters more light. This fragile, permeable ice type may become increasingly important in a warming Arctic.
Chao Qi, David J. Prior, Lisa Craw, Sheng Fan, Maria-Gema Llorens, Albert Griera, Marianne Negrini, Paul D. Bons, and David L. Goldsby
The Cryosphere, 13, 351–371, https://doi.org/10.5194/tc-13-351-2019, https://doi.org/10.5194/tc-13-351-2019, 2019
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Ice deformed in nature develops crystallographic preferred orientations, CPOs, which induce an anisotropy in ice viscosity. Shear experiments of ice revealed a transition in CPO with changing temperature/strain, which is due to the change of dominant CPO-formation mechanism: strain-induced grain boundary migration dominates at higher temperatures and lower strains, while lattice rotation dominates at other conditions. Understanding these mechanisms aids the interpretation of CPOs in natural ice.
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.
Johanna Kerch, Anja Diez, Ilka Weikusat, and Olaf Eisen
The Cryosphere, 12, 1715–1734, https://doi.org/10.5194/tc-12-1715-2018, https://doi.org/10.5194/tc-12-1715-2018, 2018
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We investigate the effect of crystal anisotropy on seismic velocities in glacier ice by calculating seismic phase velocities using the exact c axis angles to describe the crystal orientations in ice-core samples for an alpine and a polar ice core. Our results provide uncertainty estimates for earlier established approximative calculations. Additionally, our findings highlight the variation in seismic velocity at non-vertical incidence as a function of the horizontal azimuth of the seismic plane.
Adam J. Campbell, Betzalel Massarano, Edwin D. Waddington, and Stephen G. Warren
The Cryosphere, 11, 1141–1148, https://doi.org/10.5194/tc-11-1141-2017, https://doi.org/10.5194/tc-11-1141-2017, 2017
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How could plant life, that needs light to survive, live on a planet covered with ice? Such a situation is thought to have existed during what are called the Snowball Earth events over 600 million years ago. Here we find that
ice shadows, regions where ice has difficulty flowing into, may have a played a role in that survival of early plant life.
Ian J. Hewitt and Christian Schoof
The Cryosphere, 11, 541–551, https://doi.org/10.5194/tc-11-541-2017, https://doi.org/10.5194/tc-11-541-2017, 2017
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Many glaciers contain ice both below and at the melting temperature. Predicting the evolution of temperature and water content in such ice masses is important because they exert a strong control on the flow of the ice. We present two new models to calculate these quantities, demonstrate a number of example numerical calculations, and compare the results with existing methods. The novelty of the new methods is the inclusion of gravity-driven water transport within the ice.
Matthew J. Vaughan, Kasper van Wijk, David J. Prior, and M. Hamish Bowman
The Cryosphere, 10, 2821–2829, https://doi.org/10.5194/tc-10-2821-2016, https://doi.org/10.5194/tc-10-2821-2016, 2016
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The physical properties of ice are of interest in the study of the dynamics of sea ice, glaciers, and ice sheets. We used resonant ultrasound spectroscopy to estimate the effects of temperature on the elastic and anelastic characteristics of polycrystalline ice, which control the propagation of sound waves. This information helps calibrate seismic data, in order to determine regional-scale ice properties, improving our ability to predict ice sheet behaviour in response to climate change.
J. Feldmann and A. Levermann
The Cryosphere, 9, 631–645, https://doi.org/10.5194/tc-9-631-2015, https://doi.org/10.5194/tc-9-631-2015, 2015
D. Besson and I. Kravchenko
The Cryosphere, 7, 855–866, https://doi.org/10.5194/tc-7-855-2013, https://doi.org/10.5194/tc-7-855-2013, 2013
D. N. Goldberg and O. V. Sergienko
The Cryosphere, 5, 315–327, https://doi.org/10.5194/tc-5-315-2011, https://doi.org/10.5194/tc-5-315-2011, 2011
H. Hausmann and M. Behm
The Cryosphere, 5, 329–340, https://doi.org/10.5194/tc-5-329-2011, https://doi.org/10.5194/tc-5-329-2011, 2011
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