Articles | Volume 12, issue 1
https://doi.org/10.5194/tc-12-301-2018
© Author(s) 2018. 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-12-301-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
26 Jan 2018
Research article |
| 26 Jan 2018
Simple models for the simulation of submarine melt for a Greenland glacial system model
Earth System Analysis – Research Domain 1, Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany
Mahé Perrette
Earth System Analysis – Research Domain 1, Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany
Andrey Ganopolski
Earth System Analysis – Research Domain 1, Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany
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EGUsphere, https://doi.org/10.5194/egusphere-2025-709, https://doi.org/10.5194/egusphere-2025-709, 2025
This preprint is open for discussion and under review for The Cryosphere (TC).
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This study explores how the Greenland Ice Sheet (GrIS) responds to different levels of stabilized global warming, and if the climate cools back. Our findings show that global temperature increases beyond +2.3 °C mark a critical threshold. We also highlight the importance of limiting warming to avoid irreversible ice loss, as well as the potential for recovery after temporarily exceeding warming thresholds if action is taken quickly to lower global temperatures.
Lawrence A. Bird, Felicity S. McCormack, Johanna Beckmann, Richard S. Jones, and Andrew N. Mackintosh
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Vanderford Glacier is the fastest-retreating glacier in East Antarctica and may have important implications for future ice loss from the Aurora Subglacial Basin. Our ice sheet model simulations suggest that grounding line retreat is driven by sub-ice-shelf basal melting, in which warm ocean waters melt ice close to the grounding line. We show that current estimates of basal melt are likely too low, highlighting the need for improved estimates and direct measurements of basal melt in the region.
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Greenland blocking, which enhances ice sheet melting, has increased, but climate models fail to capture this trend. Analysis using ERA5 data and SEAS5.1 forecasts shows model improvements help but miss the role of early North American snowmelt in blocking patterns. This gap may explain the discrepancy and suggests future projections could underestimate Greenland blocking and its impact on melting. Better representation of snow cover processes is essential for improving climate model accuracy.
Alison Delhasse, Johanna Beckmann, Christoph Kittel, and Xavier Fettweis
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Aiming to study the long-term influence of an extremely warm climate in the Greenland Ice Sheet contribution to sea level rise, a new regional atmosphere–ice sheet model setup was established. The coupling, explicitly considering the melt–elevation feedback, is compared to an offline method to consider this feedback. We highlight mitigation of the feedback due to local changes in atmospheric circulation with changes in surface topography, making the offline correction invalid on the margins.
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Over the past decade, Greenland has experienced several extreme melt events.
With progressing climate change, such extreme melt events can be expected to occur more frequently and potentially become more severe and persistent.
Strong melt events may considerably contribute to Greenland's mass loss, which in turn strongly determines future sea level rise. How important these extreme melt events could be in the future is assessed in this study for the first time.
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With the increasing melt of the Greenland Ice Sheet, which contributes to sea level rise, the surface of the ice darkens. The dark surfaces absorb more radiation and thus experience increased melt, resulting in the melt–albedo feedback. Using a simple surface melt model, we estimate that this positive feedback contributes to an additional 60 % ice loss in a high-warming scenario and additional 90 % ice loss for moderate warming. Albedo changes are important for Greenland’s future ice loss.
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The Cryosphere, 13, 2281–2301, https://doi.org/10.5194/tc-13-2281-2019, https://doi.org/10.5194/tc-13-2281-2019, 2019
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Submarine melting (SM) has been discussed as potentially triggering the recently observed retreat at outlet glaciers in Greenland. How much it may contribute in terms of future sea level rise (SLR) has not been quantified yet. When accounting for SM in our experiments, SLR contribution of 12 outlet glaciers increases by over 3-fold until the year 2100 under RCP8.5. Scaling up from 12 to all of Greenland's outlet glaciers increases future SLR contribution of Greenland by 50 %.
Alison Delhasse, Christoph Kittel, and Johanna Beckmann
EGUsphere, https://doi.org/10.5194/egusphere-2025-709, https://doi.org/10.5194/egusphere-2025-709, 2025
This preprint is open for discussion and under review for The Cryosphere (TC).
Short summary
Short summary
This study explores how the Greenland Ice Sheet (GrIS) responds to different levels of stabilized global warming, and if the climate cools back. Our findings show that global temperature increases beyond +2.3 °C mark a critical threshold. We also highlight the importance of limiting warming to avoid irreversible ice loss, as well as the potential for recovery after temporarily exceeding warming thresholds if action is taken quickly to lower global temperatures.
Lawrence A. Bird, Felicity S. McCormack, Johanna Beckmann, Richard S. Jones, and Andrew N. Mackintosh
The Cryosphere, 19, 955–973, https://doi.org/10.5194/tc-19-955-2025, https://doi.org/10.5194/tc-19-955-2025, 2025
Short summary
Short summary
Vanderford Glacier is the fastest-retreating glacier in East Antarctica and may have important implications for future ice loss from the Aurora Subglacial Basin. Our ice sheet model simulations suggest that grounding line retreat is driven by sub-ice-shelf basal melting, in which warm ocean waters melt ice close to the grounding line. We show that current estimates of basal melt are likely too low, highlighting the need for improved estimates and direct measurements of basal melt in the region.
Johanna Beckmann, Giorgia Di Capua, and Paolo Davini
EGUsphere, https://doi.org/10.5194/egusphere-2024-3998, https://doi.org/10.5194/egusphere-2024-3998, 2025
Short summary
Short summary
Greenland blocking, which enhances ice sheet melting, has increased, but climate models fail to capture this trend. Analysis using ERA5 data and SEAS5.1 forecasts shows model improvements help but miss the role of early North American snowmelt in blocking patterns. This gap may explain the discrepancy and suggests future projections could underestimate Greenland blocking and its impact on melting. Better representation of snow cover processes is essential for improving climate model accuracy.
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Despite significant progress in modelling Quaternary climate dynamics, a comprehensive theory of glacial cycles is still lacking. Here, using the results of model simulations and data analysis, I present a framework of the generalized Milankovitch theory (GMT), which further advances the concept proposed by Milutin Milankovitch over a century ago. The theory explains a number of facts which were not known during Milankovitch time's, such as the 100 kyr periodicity of the late Quaternary.
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The Cryosphere, 17, 3083–3099, https://doi.org/10.5194/tc-17-3083-2023, https://doi.org/10.5194/tc-17-3083-2023, 2023
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Over the past decade, Greenland has experienced several extreme melt events.
With progressing climate change, such extreme melt events can be expected to occur more frequently and potentially become more severe and persistent.
Strong melt events may considerably contribute to Greenland's mass loss, which in turn strongly determines future sea level rise. How important these extreme melt events could be in the future is assessed in this study for the first time.
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In this paper we present the climate component of the newly developed fast Earth system model CLIMBER-X. It has a horizontal resolution of 5°x5° and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to >100 000 years. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.
Maria Zeitz, Ronja Reese, Johanna Beckmann, Uta Krebs-Kanzow, and Ricarda Winkelmann
The Cryosphere, 15, 5739–5764, https://doi.org/10.5194/tc-15-5739-2021, https://doi.org/10.5194/tc-15-5739-2021, 2021
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With the increasing melt of the Greenland Ice Sheet, which contributes to sea level rise, the surface of the ice darkens. The dark surfaces absorb more radiation and thus experience increased melt, resulting in the melt–albedo feedback. Using a simple surface melt model, we estimate that this positive feedback contributes to an additional 60 % ice loss in a high-warming scenario and additional 90 % ice loss for moderate warming. Albedo changes are important for Greenland’s future ice loss.
Stefanie Talento and Andrey Ganopolski
Earth Syst. Dynam., 12, 1275–1293, https://doi.org/10.5194/esd-12-1275-2021, https://doi.org/10.5194/esd-12-1275-2021, 2021
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We propose a model for glacial cycles and produce an assessment of possible trajectories for the next 1 million years. Under natural conditions, the next glacial inception would most likely occur ∼50 kyr after present. We show that fossil-fuel CO2 releases can have an extremely long-term effect. Potentially achievable CO2 anthropogenic emissions during the next centuries will most likely provoke ice-free conditions in the Northern Hemisphere landmasses throughout the next half a million years.
Johanna Beckmann, Mahé Perrette, Sebastian Beyer, Reinhard Calov, Matteo Willeit, and Andrey Ganopolski
The Cryosphere, 13, 2281–2301, https://doi.org/10.5194/tc-13-2281-2019, https://doi.org/10.5194/tc-13-2281-2019, 2019
Short summary
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Submarine melting (SM) has been discussed as potentially triggering the recently observed retreat at outlet glaciers in Greenland. How much it may contribute in terms of future sea level rise (SLR) has not been quantified yet. When accounting for SM in our experiments, SLR contribution of 12 outlet glaciers increases by over 3-fold until the year 2100 under RCP8.5. Scaling up from 12 to all of Greenland's outlet glaciers increases future SLR contribution of Greenland by 50 %.
Reinhard Calov, Sebastian Beyer, Ralf Greve, Johanna Beckmann, Matteo Willeit, Thomas Kleiner, Martin Rückamp, Angelika Humbert, and Andrey Ganopolski
The Cryosphere, 12, 3097–3121, https://doi.org/10.5194/tc-12-3097-2018, https://doi.org/10.5194/tc-12-3097-2018, 2018
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We present RCP 4.5 and 8.5 projections for the Greenland glacial system with the new glacial system model IGLOO 1.0, which incorporates the ice sheet model SICOPOLIS 3.3, a model of basal hydrology and a parameterization of submarine melt of outlet glaciers. Surface temperature and mass balance anomalies from the MAR climate model serve as forcing delivering projections for the contribution of the Greenland ice sheet to sea level rise and submarine melt of Helheim and Store outlet glaciers.
Matteo Willeit and Andrey Ganopolski
Clim. Past, 14, 697–707, https://doi.org/10.5194/cp-14-697-2018, https://doi.org/10.5194/cp-14-697-2018, 2018
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The surface energy and mass balance of ice sheets strongly depends on surface albedo. Here, using an Earth system model of intermediate complexity, we explore the role played by surface albedo for the simulation of glacial cycles. We show that the evolution of the Northern Hemisphere ice sheets over the last glacial cycle is very sensitive to the parameterization of snow grain size and the effect of dust deposition on snow albedo.
Andrey Ganopolski and Victor Brovkin
Clim. Past, 13, 1695–1716, https://doi.org/10.5194/cp-13-1695-2017, https://doi.org/10.5194/cp-13-1695-2017, 2017
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Ice cores reveal that atmospheric CO2 concentration varied synchronously with the global ice volume. Explaining the mechanism of glacial–interglacial variations of atmospheric CO2 concentrations and the link between CO2 and ice sheets evolution still remains a challenge. Here using the Earth system model of intermediate complexity we performed for the first time simulations of co-evolution of climate, ice sheets and carbon cycle using the astronomical forcing as the only external forcing.
Eva Bauer and Andrey Ganopolski
Clim. Past, 13, 819–832, https://doi.org/10.5194/cp-13-819-2017, https://doi.org/10.5194/cp-13-819-2017, 2017
Short summary
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Transient glacial cycle simulations with an EMIC and the PDD method require smaller melt factors for inception than for termination and larger factors for American than European ice sheets. The PDD online method with standard values simulates a sea level drop of 250 m at the LGM. The PDD online run reproducing the LGM ice volume has deficient ablation for reversing from glacial to interglacial climate, so termination is delayed. The SEB method with dust impact on snow albedo is seen as superior.
Mario Krapp, Alexander Robinson, and Andrey Ganopolski
The Cryosphere, 11, 1519–1535, https://doi.org/10.5194/tc-11-1519-2017, https://doi.org/10.5194/tc-11-1519-2017, 2017
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We present the snowpack model SEMIC. It calculates snow height, surface temperature, surface albedo, and the surface mass balance of snow- and ice-covered surfaces while using meteorological data as input. In this paper we describe how SEMIC works and how well it compares with snowpack data of a more sophisticated regional climate model applied to the Greenland ice sheet. Because of its simplicity and efficiency, SEMIC can be used as a coupling interface between atmospheric and ice sheet models.
Matteo Willeit and Andrey Ganopolski
Geosci. Model Dev., 9, 3817–3857, https://doi.org/10.5194/gmd-9-3817-2016, https://doi.org/10.5194/gmd-9-3817-2016, 2016
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PALADYN is presented; it is a new comprehensive and computationally efficient land surface–vegetation–carbon cycle model designed to be used in Earth system models of intermediate complexity for long-term simulations and paleoclimate studies.
M. Willeit and A. Ganopolski
Clim. Past, 11, 1165–1180, https://doi.org/10.5194/cp-11-1165-2015, https://doi.org/10.5194/cp-11-1165-2015, 2015
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In this paper we explore the permafrost–ice-sheet interaction using the fully coupled climate–ice-sheet model CLIMBER-2 with the addition of a newly developed permafrost module. We find that permafrost has a moderate but significant effect on ice sheet dynamics during the last glacial cycle. In particular at the Last Glacial Maximum the inclusion of permafrost leads to a 15m sea level equivalent increase in Northern Hemisphere ice volume when permafrost is included.
A. Robinson and M. Perrette
Geosci. Model Dev., 8, 1877–1883, https://doi.org/10.5194/gmd-8-1877-2015, https://doi.org/10.5194/gmd-8-1877-2015, 2015
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Here we present a concise interface to the NetCDF library designed to simplify reading and writing tasks of up to 6-D arrays in Fortran programs.
R. Calov, A. Robinson, M. Perrette, and A. Ganopolski
The Cryosphere, 9, 179–196, https://doi.org/10.5194/tc-9-179-2015, https://doi.org/10.5194/tc-9-179-2015, 2015
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Ice discharge into the ocean from outlet glaciers is an important
component of mass loss of the Greenland ice sheet. Here, we present a
simple parameterization of ice discharge for coarse resolution ice
sheet models, suitable for large ensembles or long-term palaeo
simulations. This parameterization reproduces in a good approximation
the present-day ice discharge compared with estimates, and the
simulation of the present-day ice sheet elevation is considerably
improved.
E. Bauer and A. Ganopolski
Clim. Past, 10, 1333–1348, https://doi.org/10.5194/cp-10-1333-2014, https://doi.org/10.5194/cp-10-1333-2014, 2014
M. Willeit, A. Ganopolski, and G. Feulner
Biogeosciences, 11, 17–32, https://doi.org/10.5194/bg-11-17-2014, https://doi.org/10.5194/bg-11-17-2014, 2014
M. Willeit, A. Ganopolski, and G. Feulner
Clim. Past, 9, 1749–1759, https://doi.org/10.5194/cp-9-1749-2013, https://doi.org/10.5194/cp-9-1749-2013, 2013
M. Eby, A. J. Weaver, K. Alexander, K. Zickfeld, A. Abe-Ouchi, A. A. Cimatoribus, E. Crespin, S. S. Drijfhout, N. R. Edwards, A. V. Eliseev, G. Feulner, T. Fichefet, C. E. Forest, H. Goosse, P. B. Holden, F. Joos, M. Kawamiya, D. Kicklighter, H. Kienert, K. Matsumoto, I. I. Mokhov, E. Monier, S. M. Olsen, J. O. P. Pedersen, M. Perrette, G. Philippon-Berthier, A. Ridgwell, A. Schlosser, T. Schneider von Deimling, G. Shaffer, R. S. Smith, R. Spahni, A. P. Sokolov, M. Steinacher, K. Tachiiri, K. Tokos, M. Yoshimori, N. Zeng, and F. Zhao
Clim. Past, 9, 1111–1140, https://doi.org/10.5194/cp-9-1111-2013, https://doi.org/10.5194/cp-9-1111-2013, 2013
M. Perrette, F. Landerer, R. Riva, K. Frieler, and M. Meinshausen
Earth Syst. Dynam., 4, 11–29, https://doi.org/10.5194/esd-4-11-2013, https://doi.org/10.5194/esd-4-11-2013, 2013
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Antarctic sub-shelf melt rates via PICO
Grounding line migration through the calving season at Jakobshavn Isbræ, Greenland, observed with terrestrial radar interferometry
William H. Lipscomb, David Behar, and Monica Ainhorn Morrison
The Cryosphere, 19, 793–803, https://doi.org/10.5194/tc-19-793-2025, https://doi.org/10.5194/tc-19-793-2025, 2025
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As communities try to adapt to climate change, they look for "actionable science" that can inform decision-making. There are risks in relying on novel results that are not yet accepted by the science community. We propose a practical criterion for determining which scientific claims are actionable. We show how premature acceptance of sea-level-rise predictions can lead to confusion and backtracking, and we suggest best practices for communication between scientists and adaptation planners.
Irena Vaňková, Xylar Asay-Davis, Carolyn Branecky Begeman, Darin Comeau, Alexander Hager, Matthew Hoffman, Stephen F. Price, and Jonathan Wolfe
The Cryosphere, 19, 507–523, https://doi.org/10.5194/tc-19-507-2025, https://doi.org/10.5194/tc-19-507-2025, 2025
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We study the effect of subglacial discharge on basal melting for Antarctic ice shelves. We find that the results from previous studies of vertical ice fronts and two-dimensional ice tongues do not translate to the rotating ice-shelf framework. The melt rate dependence on discharge is stronger in the rotating framework. Further, there is a substantial melt-rate sensitivity to the location of the discharge along the grounding line relative to the directionality of the Coriolis force.
Jana Krause, Dustin Carroll, Juan Höfer, Jeremy Donaire, Eric P. Achterberg, Emilio Alarcón, Te Liu, Lorenz Meire, Kechen Zhu, and Mark J. Hopwood
The Cryosphere, 18, 5735–5752, https://doi.org/10.5194/tc-18-5735-2024, https://doi.org/10.5194/tc-18-5735-2024, 2024
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Here we analysed calved ice samples from both the Arctic and Antarctic to assess the variability in the composition of iceberg meltwater. Our results suggest that low concentrations of nitrate and phosphate in ice are primarily from the ice matrix, whereas sediment-rich layers impart a low concentration of silica and modest concentrations of iron and manganese. At a global scale, there are very limited differences in the nutrient composition of ice.
Nicole Abib, David A. Sutherland, Rachel Peterson, Ginny Catania, Jonathan D. Nash, Emily L. Shroyer, Leigh A. Stearns, and Timothy C. Bartholomaus
The Cryosphere, 18, 4817–4829, https://doi.org/10.5194/tc-18-4817-2024, https://doi.org/10.5194/tc-18-4817-2024, 2024
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The melting of ice mélange, or dense packs of icebergs and sea ice in glacial fjords, can influence the water column by releasing cold fresh water deep under the ocean surface. However, direct observations of this process have remained elusive. We use measurements of ocean temperature, salinity, and velocity bookending an episodic ice mélange event to show that this meltwater input changes the density profile of a glacial fjord and has implications for understanding tidewater glacier change.
Sam De Abreu, Rosalie M. Cormier, Mikhail G. Schee, Varvara E. Zemskova, Erica Rosenblum, and Nicolas Grisouard
The Cryosphere, 18, 3159–3176, https://doi.org/10.5194/tc-18-3159-2024, https://doi.org/10.5194/tc-18-3159-2024, 2024
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Arctic sea ice is becoming more mobile and thinner, which will affect the upper Arctic Ocean in unforeseen ways. Using numerical simulations, we find that mixing by ice keels (ridges underlying sea ice) depends significantly on their speeds and depths and the density structure of the upper ocean. Large uncertainties in our results highlight the need for more realistic numerical simulations and better measurements of ice keel characteristics.
Gemma M. Brett, Greg H. Leonard, Wolfgang Rack, Christian Haas, Patricia J. Langhorne, Natalie J. Robinson, and Anne Irvin
The Cryosphere, 18, 3049–3066, https://doi.org/10.5194/tc-18-3049-2024, https://doi.org/10.5194/tc-18-3049-2024, 2024
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Glacial meltwater with ice crystals flows from beneath ice shelves, causing thicker sea ice with sub-ice platelet layers (SIPLs) beneath. Thicker sea ice and SIPL reveal where and how much meltwater is outflowing. We collected continuous measurements of sea ice and SIPL. In winter, we observed rapid SIPL growth with strong winds. In spring, SIPLs grew when tides caused offshore circulation. Wind-driven and tidal circulation influence glacial meltwater outflow from ice shelf cavities.
Matthew J. Hoffman, Carolyn Branecky Begeman, Xylar S. Asay-Davis, Darin Comeau, Alice Barthel, Stephen F. Price, and Jonathan D. Wolfe
The Cryosphere, 18, 2917–2937, https://doi.org/10.5194/tc-18-2917-2024, https://doi.org/10.5194/tc-18-2917-2024, 2024
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The Filchner–Ronne Ice Shelf in Antarctica is susceptible to the intrusion of deep, warm ocean water that could increase the melting at the ice-shelf base by a factor of 10. We show that representing this potential melt regime switch in a low-resolution climate model requires careful treatment of iceberg melting and ocean mixing. We also demonstrate a possible ice-shelf melt domino effect where increased melting of nearby ice shelves can lead to the melt regime switch at Filchner–Ronne.
Elena Bianco, Doroteaciro Iovino, Simona Masina, Stefano Materia, and Paolo Ruggieri
The Cryosphere, 18, 2357–2379, https://doi.org/10.5194/tc-18-2357-2024, https://doi.org/10.5194/tc-18-2357-2024, 2024
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Changes in ocean heat transport and surface heat fluxes in recent decades have altered the Arctic Ocean heat budget and caused warming of the upper ocean. Using two eddy-permitting ocean reanalyses, we show that this has important implications for sea ice variability. In the Arctic regional seas, upper-ocean heat content acts as an important precursor for sea ice anomalies on sub-seasonal timescales, and this link has strengthened since the 2000s.
Kenneth G. Hughes
The Cryosphere, 18, 1315–1332, https://doi.org/10.5194/tc-18-1315-2024, https://doi.org/10.5194/tc-18-1315-2024, 2024
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A mathematical and conceptual model of how the melting of hundreds of icebergs generates currents within a fjord.
Alexander O. Hager, David A. Sutherland, and Donald A. Slater
The Cryosphere, 18, 911–932, https://doi.org/10.5194/tc-18-911-2024, https://doi.org/10.5194/tc-18-911-2024, 2024
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Warming ocean temperatures cause considerable ice loss from the Greenland Ice Sheet; however climate models are unable to resolve the complex ocean processes within fjords that influence near-glacier ocean temperatures. Here, we use a computer model to test the accuracy of assumptions that allow climate and ice sheet models to project near-glacier ocean temperatures, and thus glacier melt, into the future. We then develop new methods that improve accuracy by accounting for local ocean processes.
Momme C. Hell and Christopher Horvat
The Cryosphere, 18, 341–361, https://doi.org/10.5194/tc-18-341-2024, https://doi.org/10.5194/tc-18-341-2024, 2024
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Sea ice is heavily impacted by waves on its margins, and we currently do not have routine observations of waves in sea ice. Here we propose two methods to separate the surface waves from the sea-ice height observations along each ICESat-2 track using machine learning. Both methods together allow us to follow changes in the wave height through the sea ice.
Kazuya Kusahara, Daisuke Hirano, Masakazu Fujii, Alexander D. Fraser, Takeshi Tamura, Kohei Mizobata, Guy D. Williams, and Shigeru Aoki
The Cryosphere, 18, 43–73, https://doi.org/10.5194/tc-18-43-2024, https://doi.org/10.5194/tc-18-43-2024, 2024
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This study focuses on the Totten and Moscow University ice shelves, East Antarctica. We used an ocean–sea ice–ice shelf model to better understand regional interactions between ocean, sea ice, and ice shelf. We found that a combination of warm ocean water and local sea ice production influences the regional ice shelf basal melting. Furthermore, the model reproduced the summertime undercurrent on the upper continental slope, regulating ocean heat transport onto the continental shelf.
Alberto Alvarez
The Cryosphere, 17, 3343–3361, https://doi.org/10.5194/tc-17-3343-2023, https://doi.org/10.5194/tc-17-3343-2023, 2023
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A near-surface temperature maximum (NSTM) layer is typically observed under different Arctic basins. Although its development seems to be related to solar heating in leads, its formation mechanism is under debate. This study uses numerical modeling in an idealized framework to demonstrate that the NSTM layer forms under a summer lead exposed to a combination of calm and moderate wind periods. Future warming of this layer could modify acoustic propagation with implications for marine mammals.
Erwin Lambert, André Jüling, Roderik S. W. van de Wal, and Paul R. Holland
The Cryosphere, 17, 3203–3228, https://doi.org/10.5194/tc-17-3203-2023, https://doi.org/10.5194/tc-17-3203-2023, 2023
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A major uncertainty in the study of sea level rise is the melting of the Antarctic ice sheet by the ocean. Here, we have developed a new model, named LADDIE, that simulates this ocean-driven melting of the floating parts of the Antarctic ice sheet. This model simulates fine-scale patterns of melting and freezing and requires significantly fewer computational resources than state-of-the-art ocean models. LADDIE can be used as a new tool to force high-resolution ice sheet models.
Jonathan Wiskandt, Inga Monika Koszalka, and Johan Nilsson
The Cryosphere, 17, 2755–2777, https://doi.org/10.5194/tc-17-2755-2023, https://doi.org/10.5194/tc-17-2755-2023, 2023
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Understanding ice–ocean interactions under floating ice tongues in Greenland and Antarctica is a major challenge in climate modelling and a source of uncertainty in future sea level projections. We use a high-resolution ocean model to investigate basal melting and melt-driven circulation under the floating tongue of Ryder Glacier, northwestern Greenland. We study the response to oceanic and atmospheric warming. Our results are universal and relevant for the development of climate models.
Benjamin Richaud, Katja Fennel, Eric C. J. Oliver, Michael D. DeGrandpre, Timothée Bourgeois, Xianmin Hu, and Youyu Lu
The Cryosphere, 17, 2665–2680, https://doi.org/10.5194/tc-17-2665-2023, https://doi.org/10.5194/tc-17-2665-2023, 2023
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Sea ice is a dynamic carbon reservoir. Its seasonal growth and melt modify the carbonate chemistry in the upper ocean, with consequences for the Arctic Ocean carbon sink. Yet, the importance of this process is poorly quantified. Using two independent approaches, this study provides new methods to evaluate the error in air–sea carbon flux estimates due to the lack of biogeochemistry in ice in earth system models. Those errors range from 5 % to 30 %, depending on the model and climate projection.
Mattia Poinelli, Michael Schodlok, Eric Larour, Miren Vizcaino, and Riccardo Riva
The Cryosphere, 17, 2261–2283, https://doi.org/10.5194/tc-17-2261-2023, https://doi.org/10.5194/tc-17-2261-2023, 2023
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Rifts are fractures on ice shelves that connect the ice on top to the ocean below. The impact of rifts on ocean circulation below Antarctic ice shelves has been largely unexplored as ocean models are commonly run at resolutions that are too coarse to resolve the presence of rifts. Our model simulations show that a kilometer-wide rift near the ice-shelf front modulates heat intrusion beneath the ice and inhibits basal melt. These processes are therefore worthy of further investigation.
Fabien Souillé, Cédric Goeury, and Rem-Sophia Mouradi
The Cryosphere, 17, 1645–1674, https://doi.org/10.5194/tc-17-1645-2023, https://doi.org/10.5194/tc-17-1645-2023, 2023
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Models that can predict temperature and ice crystal formation (frazil) in water are important for river and coastal engineering. Indeed, frazil has direct impact on submerged structures and often precedes the formation of ice cover. In this paper, an uncertainty analysis of two mathematical models that simulate supercooling and frazil is carried out within a probabilistic framework. The presented methodology offers new insight into the models and their parameterization.
Karita Kajanto, Fiammetta Straneo, and Kerim Nisancioglu
The Cryosphere, 17, 371–390, https://doi.org/10.5194/tc-17-371-2023, https://doi.org/10.5194/tc-17-371-2023, 2023
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Many outlet glaciers in Greenland are connected to the ocean by narrow glacial fjords, where warm water melts the glacier from underneath. Ocean water is modified in these fjords through processes that are poorly understood, particularly iceberg melt. We use a model to show how iceberg melt cools down Ilulissat Icefjord and causes circulation to take place deeper in the fjord than if there were no icebergs. This causes the glacier to melt less and from a smaller area than without icebergs.
Ji Sung Na, Taekyun Kim, Emilia Kyung Jin, Seung-Tae Yoon, Won Sang Lee, Sukyoung Yun, and Jiyeon Lee
The Cryosphere, 16, 3451–3468, https://doi.org/10.5194/tc-16-3451-2022, https://doi.org/10.5194/tc-16-3451-2022, 2022
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Beneath the Antarctic ice shelf, sub-ice-shelf plume flow that can cause turbulent mixing exists. In this study, we investigate how this flow affects ocean dynamics and ice melting near the ice front. Our results obtained by validated simulation show that higher turbulence intensity results in vigorous ice melting due to the high heat entrainment. Moreover, this flow with meltwater created by this flow highly affects the ocean overturning circulations near the ice front.
Yixi Zheng, David P. Stevens, Karen J. Heywood, Benjamin G. M. Webber, and Bastien Y. Queste
The Cryosphere, 16, 3005–3019, https://doi.org/10.5194/tc-16-3005-2022, https://doi.org/10.5194/tc-16-3005-2022, 2022
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New observations reveal the Thwaites gyre in a habitually ice-covered region in the Amundsen Sea for the first time. This gyre rotates anticlockwise, despite the wind here favouring clockwise gyres like the Pine Island Bay gyre – the only other ocean gyre reported in the Amundsen Sea. We use an ocean model to suggest that sea ice alters the wind stress felt by the ocean and hence determines the gyre direction and strength. These processes may also be applied to other gyres in polar oceans.
Mimmi Oksman, Anna Bang Kvorning, Signe Hillerup Larsen, Kristian Kjellerup Kjeldsen, Kenneth David Mankoff, William Colgan, Thorbjørn Joest Andersen, Niels Nørgaard-Pedersen, Marit-Solveig Seidenkrantz, Naja Mikkelsen, and Sofia Ribeiro
The Cryosphere, 16, 2471–2491, https://doi.org/10.5194/tc-16-2471-2022, https://doi.org/10.5194/tc-16-2471-2022, 2022
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One of the questions facing the cryosphere community today is how increasing runoff from the Greenland Ice Sheet impacts marine ecosystems. To address this, long-term data are essential. Here, we present multi-site records of fjord productivity for SW Greenland back to the 19th century. We show a link between historical freshwater runoff and productivity, which is strongest in the inner fjord – influenced by marine-terminating glaciers – where productivity has increased since the late 1990s.
Ole Richter, David E. Gwyther, Matt A. King, and Benjamin K. Galton-Fenzi
The Cryosphere, 16, 1409–1429, https://doi.org/10.5194/tc-16-1409-2022, https://doi.org/10.5194/tc-16-1409-2022, 2022
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Tidal currents may play an important role in Antarctic ice sheet retreat by changing the rate at which the ocean melts glaciers. Here, using a computational ocean model, we derive the first estimate of present-day tidal melting that covers all of Antarctica. Our results suggest that large-scale ocean models aiming to accurately predict ice melt rates will need to account for the effects of tides. The inclusion of tide-induced friction at the ice–ocean interface should be prioritized.
Alexander A. Robel, Earle Wilson, and Helene Seroussi
The Cryosphere, 16, 451–469, https://doi.org/10.5194/tc-16-451-2022, https://doi.org/10.5194/tc-16-451-2022, 2022
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Warm seawater may intrude as a thin layer below glaciers in contact with the ocean. Mathematical theory predicts that this intrusion may extend over distances of kilometers under realistic conditions. Computer models demonstrate that if this warm seawater causes melting of a glacier bottom, it can cause rates of glacier ice loss and sea level rise to be up to 2 times faster in response to potential future ocean warming.
Ryan Schubert, Andrew F. Thompson, Kevin Speer, Lena Schulze Chretien, and Yana Bebieva
The Cryosphere, 15, 4179–4199, https://doi.org/10.5194/tc-15-4179-2021, https://doi.org/10.5194/tc-15-4179-2021, 2021
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The Antarctic Coastal Current (AACC) is an ocean current found along the coast of Antarctica. Using measurements of temperature and salinity collected by instrumented seals, the AACC is shown to be a continuous circulation feature throughout West Antarctica. Due to its proximity to the coast, the AACC's structure influences oceanic melting of West Antarctic ice shelves. These melt rates impact the stability of the West Antarctic Ice Sheet with global implications for future sea level change.
Kazuya Kusahara, Daisuke Hirano, Masakazu Fujii, Alexander D. Fraser, and Takeshi Tamura
The Cryosphere, 15, 1697–1717, https://doi.org/10.5194/tc-15-1697-2021, https://doi.org/10.5194/tc-15-1697-2021, 2021
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We used an ocean–sea ice–ice shelf model with a 2–3 km horizontal resolution to investigate ocean–ice shelf/glacier interactions in Lützow-Holm Bay, East Antarctica. The numerical model reproduced the observed warm water intrusion along the deep trough in the bay. We examined in detail (1) water mass changes between the upper continental slope and shelf regions and (2) the fast-ice role in the ocean conditions and basal melting at the Shirase Glacier tongue.
Guillaume Boutin, Timothy Williams, Pierre Rampal, Einar Olason, and Camille Lique
The Cryosphere, 15, 431–457, https://doi.org/10.5194/tc-15-431-2021, https://doi.org/10.5194/tc-15-431-2021, 2021
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In this study, we investigate the interactions of surface ocean waves with sea ice. We focus on the evolution of sea ice after it has been fragmented by the waves. Fragmented sea ice is expected to experience less resistance to deformation. We reproduce this evolution using a new coupling framework between a wave model and the recently developed sea ice model neXtSIM. We find that waves can significantly increase the mobility of compact sea ice over wide areas in the wake of storm events.
Joey J. Voermans, Jean Rabault, Kirill Filchuk, Ivan Ryzhov, Petra Heil, Aleksey Marchenko, Clarence O. Collins III, Mohammed Dabboor, Graig Sutherland, and Alexander V. Babanin
The Cryosphere, 14, 4265–4278, https://doi.org/10.5194/tc-14-4265-2020, https://doi.org/10.5194/tc-14-4265-2020, 2020
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In this work we demonstrate the existence of an observational threshold which identifies when waves are most likely to break sea ice. This threshold is based on information from two recent field campaigns, supplemented with existing observations of sea ice break-up. We show that both field and laboratory observations tend to converge to a single quantitative threshold at which the wave-induced sea ice break-up takes place, which opens a promising avenue for operational forecasting models.
Agnieszka Herman, Maciej Dojczman, and Kamila Świszcz
The Cryosphere, 14, 3707–3729, https://doi.org/10.5194/tc-14-3707-2020, https://doi.org/10.5194/tc-14-3707-2020, 2020
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Under typical conditions favorable for sea ice formation in many regions (strong wind and waves, low air temperature), ice forms not at the sea surface but within the upper, turbulent layer of the ocean. Although interactions between ice and ocean dynamics are very important for the evolution of sea ice cover, many aspects of them are poorly understood. We use a numerical model to analyze three-dimensional water circulation and ice transport and show that ice strongly modifies that circulation.
Lisa Thompson, Madison Smith, Jim Thomson, Sharon Stammerjohn, Steve Ackley, and Brice Loose
The Cryosphere, 14, 3329–3347, https://doi.org/10.5194/tc-14-3329-2020, https://doi.org/10.5194/tc-14-3329-2020, 2020
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The offshore winds around Antarctica can reach hurricane strength and produce intense cooling, causing the surface ocean to form a slurry of seawater and ice crystals. For the first time, we observed a buildup of heat and salt in the surface ocean, caused by loose ice crystal formation. We conclude that up to 1 m of ice was formed per day by the intense cooling, suggesting that unconsolidated crystals may be an important part of the total freezing that happens around Antarctica.
Laura C. Gillard, Xianmin Hu, Paul G. Myers, Mads Hvid Ribergaard, and Craig M. Lee
The Cryosphere, 14, 2729–2753, https://doi.org/10.5194/tc-14-2729-2020, https://doi.org/10.5194/tc-14-2729-2020, 2020
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Greenland's glaciers in contact with the ocean drain the majority of the ice sheet (GrIS). Deep troughs along the shelf branch into fjords, connecting glaciers with ocean waters. The heat from the ocean entering deep troughs may then accelerate the mass loss. Onshore heat transport through troughs was investigated with an ocean model. Processes that drive the delivery of ocean heat respond differently by region to increasing GrIS meltwater, mean circulation, and filtering out of storms.
Yoshihiro Nakayama, Ralph Timmermann, and Hartmut H. Hellmer
The Cryosphere, 14, 2205–2216, https://doi.org/10.5194/tc-14-2205-2020, https://doi.org/10.5194/tc-14-2205-2020, 2020
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Previous studies have shown accelerations of West Antarctic glaciers, implying that basal melt rates of these glaciers were small and increased in the middle of the 20th century. We conduct coupled sea ice–ice shelf–ocean simulations with different levels of ice shelf melting from West Antarctic glaciers. This study reveals how far and how quickly glacial meltwater from ice shelves in the Amundsen and Bellingshausen seas propagates downstream into the Ross Sea and along the East Antarctic coast.
Eva De Andrés, Donald A. Slater, Fiamma Straneo, Jaime Otero, Sarah Das, and Francisco Navarro
The Cryosphere, 14, 1951–1969, https://doi.org/10.5194/tc-14-1951-2020, https://doi.org/10.5194/tc-14-1951-2020, 2020
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Buoyant plumes at tidewater glaciers result from localized subglacial discharges of surface melt. They promote glacier submarine melting and influence the delivery of nutrients to the fjord's surface waters. Combining plume theory with observations, we have found that increased fjord stratification, which is due to larger meltwater content, prevents the vertical growth of the plume and buffers submarine melting. We discuss the implications for nutrient fluxes, CO2 trapping and water export.
Mark J. Hopwood, Dustin Carroll, Thorben Dunse, Andy Hodson, Johnna M. Holding, José L. Iriarte, Sofia Ribeiro, Eric P. Achterberg, Carolina Cantoni, Daniel F. Carlson, Melissa Chierici, Jennifer S. Clarke, Stefano Cozzi, Agneta Fransson, Thomas Juul-Pedersen, Mie H. S. Winding, and Lorenz Meire
The Cryosphere, 14, 1347–1383, https://doi.org/10.5194/tc-14-1347-2020, https://doi.org/10.5194/tc-14-1347-2020, 2020
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Here we compare and contrast results from five well-studied Arctic field sites in order to understand how glaciers affect marine biogeochemistry and marine primary production. The key questions are listed as follows. Where and when does glacial freshwater discharge promote or reduce marine primary production? How does spatio-temporal variability in glacial discharge affect marine primary production? And how far-reaching are the effects of glacial discharge on marine biogeochemistry?
Anna J. Crawford, Derek Mueller, Gregory Crocker, Laurent Mingo, Luc Desjardins, Dany Dumont, and Marcel Babin
The Cryosphere, 14, 1067–1081, https://doi.org/10.5194/tc-14-1067-2020, https://doi.org/10.5194/tc-14-1067-2020, 2020
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Large tabular icebergs (
ice islands) are symbols of climate change as well as marine hazards. We measured thickness along radar transects over two visits to a 14 km2 Arctic ice island and left automated equipment to monitor surface ablation and thickness over 1 year. We assess variation in thinning rates and calibrate an ice–ocean melt model with field data. Our work contributes to understanding ice island deterioration via logistically complex fieldwork in a remote environment.
Oskar Glowacki and Grant B. Deane
The Cryosphere, 14, 1025–1042, https://doi.org/10.5194/tc-14-1025-2020, https://doi.org/10.5194/tc-14-1025-2020, 2020
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Marine-terminating glaciers are shrinking rapidly in response to the warming climate and thus provide large quantities of fresh water to the ocean system. However, accurate estimates of ice loss at the ice–ocean boundary are difficult to obtain. Here we demonstrate that ice mass loss from iceberg break-off (calving) can be measured by analyzing the underwater noise generated as icebergs impact the sea surface.
Donald A. Slater, Denis Felikson, Fiamma Straneo, Heiko Goelzer, Christopher M. Little, Mathieu Morlighem, Xavier Fettweis, and Sophie Nowicki
The Cryosphere, 14, 985–1008, https://doi.org/10.5194/tc-14-985-2020, https://doi.org/10.5194/tc-14-985-2020, 2020
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Changes in the ocean around Greenland play an important role in determining how much the ice sheet will contribute to global sea level over the coming century. However, capturing these links in models is very challenging. This paper presents a strategy enabling an ensemble of ice sheet models to feel the effect of the ocean for the first time and should therefore result in a significant improvement in projections of the Greenland ice sheet's contribution to future sea level change.
Guillaume Boutin, Camille Lique, Fabrice Ardhuin, Clément Rousset, Claude Talandier, Mickael Accensi, and Fanny Girard-Ardhuin
The Cryosphere, 14, 709–735, https://doi.org/10.5194/tc-14-709-2020, https://doi.org/10.5194/tc-14-709-2020, 2020
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We investigate the interactions of surface ocean waves with sea ice taking place at the interface between the compact sea ice cover and the open ocean. We use a newly developed coupling framework between a wave and an ocean–sea ice numerical model. Our results show how the push on sea ice exerted by waves changes the amount and the location of sea ice melting, with a strong impact on the ocean surface properties close to the ice edge.
Sebastian H. R. Rosier and G. Hilmar Gudmundsson
The Cryosphere, 14, 17–37, https://doi.org/10.5194/tc-14-17-2020, https://doi.org/10.5194/tc-14-17-2020, 2020
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The flow of ice shelves is now known to be strongly affected by ocean tides, but the mechanism by which this happens is unclear. We use a viscoelastic model to try to reproduce observations of this behaviour on the Filchner–Ronne Ice Shelf in Antarctica. We find that tilting of the ice shelf explains the short-period behaviour, while tidally induced movement of the grounding line (the boundary between grounded and floating ice) explains the more complex long-period response.
Agnieszka Herman, Sukun Cheng, and Hayley H. Shen
The Cryosphere, 13, 2901–2914, https://doi.org/10.5194/tc-13-2901-2019, https://doi.org/10.5194/tc-13-2901-2019, 2019
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Sea ice interactions with waves are extensively studied in recent years, but mechanisms leading to wave energy attenuation in sea ice remain poorly understood. One of the reasons limiting progress in modelling is a lack of observational data for model validation. The paper presents an analysis of laboratory observations of waves propagating in colliding ice floes. We show that wave attenuation is sensitive to floe size and wave period. A numerical model is calibrated to reproduce this behaviour.
David A. Lilien, Ian Joughin, Benjamin Smith, and Noel Gourmelen
The Cryosphere, 13, 2817–2834, https://doi.org/10.5194/tc-13-2817-2019, https://doi.org/10.5194/tc-13-2817-2019, 2019
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We used a number of computer simulations to understand the recent retreat of a rapidly changing group of glaciers in West Antarctica. We found that significant melt underneath the floating extensions of the glaciers, driven by relatively warm ocean water at depth, was likely needed to cause the large retreat that has been observed. If melt continues around current rates, retreat is likely to continue through the coming century and extend beyond the present-day drainage area of these glaciers.
Sarah U. Neuhaus, Slawek M. Tulaczyk, and Carolyn Branecky Begeman
The Cryosphere, 13, 1785–1799, https://doi.org/10.5194/tc-13-1785-2019, https://doi.org/10.5194/tc-13-1785-2019, 2019
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Relatively few studies have been carried out on icebergs inside fjords, despite the fact that the majority of recent sea level rise has resulted from glaciers terminating in fjords. We examine the size and spatial distribution of icebergs in Columbia Fjord, Alaska, over a period of 8 months to determine their influence on fjord dynamics.
Joe Todd, Poul Christoffersen, Thomas Zwinger, Peter Råback, and Douglas I. Benn
The Cryosphere, 13, 1681–1694, https://doi.org/10.5194/tc-13-1681-2019, https://doi.org/10.5194/tc-13-1681-2019, 2019
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The Greenland Ice Sheet loses 30 %–60 % of its ice due to iceberg calving. Calving processes and their links to climate are not well understood or incorporated into numerical models of glaciers. Here we use a new 3-D calving model to investigate calving at Store Glacier, West Greenland, and test its sensitivity to increased submarine melting and reduced support from ice mélange (sea ice and icebergs). We find Store remains fairly stable despite these changes, but less so in the southern side.
Tyler Pelle, Mathieu Morlighem, and Johannes H. Bondzio
The Cryosphere, 13, 1043–1049, https://doi.org/10.5194/tc-13-1043-2019, https://doi.org/10.5194/tc-13-1043-2019, 2019
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How ocean-induced melt under floating ice shelves will change as ocean currents evolve remains a big uncertainty in projections of sea level rise. In this study, we combine two of the most recently developed melt models to form PICOP, which overcomes the limitations of past models and produces accurate ice shelf melt rates. We find that our model is easy to set up and computationally efficient, providing researchers an important tool to improve the accuracy of their future glacial projections.
Till J. W. Wagner, Fiamma Straneo, Clark G. Richards, Donald A. Slater, Laura A. Stevens, Sarah B. Das, and Hanumant Singh
The Cryosphere, 13, 911–925, https://doi.org/10.5194/tc-13-911-2019, https://doi.org/10.5194/tc-13-911-2019, 2019
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This study shows how complex and varied the processes are that determine the frontal position of tidewater glaciers. Rather than uniform melt or calving rates, a single (medium-sized) glacier can feature regions that retreat almost exclusively due to melting and other regions that retreat only due to calving. This has far-reaching consequences for our understanding of how glaciers retreat or advance.
Chen Cheng, Adrian Jenkins, Paul R. Holland, Zhaomin Wang, Chengyan Liu, and Ruibin Xia
The Cryosphere, 13, 265–280, https://doi.org/10.5194/tc-13-265-2019, https://doi.org/10.5194/tc-13-265-2019, 2019
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The sub-ice platelet layer (SIPL) under fast ice is most prevalent in McMurdo Sound, Antarctica. Using a modified plume model, we investigated the responses of SIPL thickening rate and frazil concentration to variations in ice shelf water supercooling in McMurdo Sound. It would be key to parameterizing the relevant process in more complex three-dimensional, primitive equation ocean models, which relies on the knowledge of the suspended frazil size spectrum within the ice–ocean boundary layer.
Xiying Liu
The Cryosphere, 12, 3033–3044, https://doi.org/10.5194/tc-12-3033-2018, https://doi.org/10.5194/tc-12-3033-2018, 2018
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Numerical experiments have been performed to study the effect of basal melting of the Ross Ice Shelf on the ocean southward of 35° S. It is shown that the melt rate averaged over the entire Ross Ice Shelf is 0.253 m year-1, which is associated with a freshwater flux of 3150 m3 s-1. The extra freshwater flux decreases the salinity in the Southern Ocean substantially, leading to anomalies in circulation, sea ice, and heat transport in certain parts of the ocean.
Chad A. Greene, Duncan A. Young, David E. Gwyther, Benjamin K. Galton-Fenzi, and Donald D. Blankenship
The Cryosphere, 12, 2869–2882, https://doi.org/10.5194/tc-12-2869-2018, https://doi.org/10.5194/tc-12-2869-2018, 2018
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We show that Totten Ice Shelf accelerates each spring in response to the breakup of seasonal landfast sea ice at the ice shelf calving front. The previously unreported seasonal flow variability may have aliased measurements in at least one previous study of Totten's response to ocean forcing on interannual timescales. The role of sea ice in buttressing the flow of the ice shelf implies that long-term changes in sea ice cover could have impacts on the mass balance of the East Antarctic Ice Sheet.
Ronja Reese, Torsten Albrecht, Matthias Mengel, Xylar Asay-Davis, and Ricarda Winkelmann
The Cryosphere, 12, 1969–1985, https://doi.org/10.5194/tc-12-1969-2018, https://doi.org/10.5194/tc-12-1969-2018, 2018
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Floating ice shelves surround most of Antarctica and ocean-driven melting at their bases is a major reason for its current sea-level contribution. We developed a simple model based on a box model approach that captures the vertical ocean circulation generally present in ice-shelf cavities and allows simulating melt rates in accordance with physical processes beneath the ice. We test the model for all Antarctic ice shelves and find that melt rates and melt patterns agree well with observations.
Surui Xie, Timothy H. Dixon, Denis Voytenko, Fanghui Deng, and David M. Holland
The Cryosphere, 12, 1387–1400, https://doi.org/10.5194/tc-12-1387-2018, https://doi.org/10.5194/tc-12-1387-2018, 2018
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Time-varying velocity and topography of the terminus of Jakobshavn Isbræ were observed with a terrestrial radar interferometer in three summer campaigns (2012, 2015, 2016). Surface elevation and tidal responses of ice speed suggest a narrow floating zone in early summer, while in late summer the entire glacier is likely grounded. We hypothesize that Jakobshavn Isbræ advances a few km in winter to form a floating zone but loses this floating portion in the subsequent summer through calving.
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Short summary
Greenland's glaciers that are in contact with the ocean undergo a special ice–ocean melting. To project numerically Greenland's centennial contribution to sea level rise, it is crucial to incorporate this special melting. We demonstrate that a numerically cheap model shows the qualitative same behavior as numerical expensive 2–3-dimensional models and calculates the same melting as empirical data show. Our analytical solution gives some insight in the yet poorly understood melting behavior.
Greenland's glaciers that are in contact with the ocean undergo a special ice–ocean melting. To...
