Articles | Volume 6, issue 6
The Cryosphere, 6, 1497–1505, 2012
https://doi.org/10.5194/tc-6-1497-2012
© Author(s) 2012. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
The Cryosphere, 6, 1497–1505, 2012
https://doi.org/10.5194/tc-6-1497-2012
© Author(s) 2012. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| Highlight paper
12 Dec 2012
Research article
| Highlight paper
| 12 Dec 2012
The stability of grounding lines on retrograde slopes
G. H. Gudmundsson et al.
Related authors
Bertie W. J. Miles, Chris R. Stokes, Adrian Jenkins, Jim R. Jordan, Stewart S. R. Jamieson, and G. Hilmar Gudmundsson
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-126, https://doi.org/10.5194/tc-2022-126, 2022
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Satellite observations have shown that the Shirase Glacier catchment in East Antarctica has been gaining mass over the past two decades, a trend largely attributed to increased snowfall. Our multi-decadal observations of Shirase Glacier show that ocean forcing has also contributed to some of this recent mass gain. This has been caused by strengthening alongshore winds reducing the inflow of warm water underneath the Shirase ice tongue.
Benoît Urruty, Emily A. Hill, Ronja Reese, Julius Garbe, Olivier Gagliardini, Gael Durand, Fabien Gillet-Chaulet, G. Hilmar Gudmundsson, Ricarda Winkelmann, Mondher Chekki, David Chandler, and Petra M. Langebroek
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-104, https://doi.org/10.5194/tc-2022-104, 2022
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Retreat of the Antarctic grounding lines could destabilise large parts of the ice sheet. We use three ice sheet models to show that the present-day locations of Antarctic grounding lines are stable with respect to a small perturbation away from their current position. This suggests that self-sustained retreat of grounding lines, due to an internal instability, has not begun. Instead, the currently observed retreat is likely due to external forcing alone.
Jowan Menhinick Barnes and G. Hilmar Gudmundsson
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-109, https://doi.org/10.5194/tc-2022-109, 2022
Preprint under review for TC
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Models must represent how glaciers slide along the bed, but there are many ways to do so. In this paper, several sliding laws are tested, and found to affect different regions of the Antarctic ice sheet in different ways, and at different speeds. However, the variability in ice volume loss due to sliding law choices is low compared to other factors, so limited empirical knowledge of sliding does not prevent us from making predictions of how an ice sheet will evolve.
Tom Mitcham, G. Hilmar Gudmundsson, and Jonathan L. Bamber
The Cryosphere, 16, 883–901, https://doi.org/10.5194/tc-16-883-2022, https://doi.org/10.5194/tc-16-883-2022, 2022
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We modelled the response of the Larsen C Ice Shelf (LCIS) and its tributary glaciers to the calving of the A68 iceberg and validated our results with observations. We found that the impact was limited, confirming that mostly passive ice was calved. Through further calving experiments we quantified the total buttressing provided by the LCIS and found that over 80 % of the buttressing capacity is generated in the first 5 km of the ice shelf downstream of the grounding line.
Sebastian Harry Reid Rosier, Christopher Y. S. Bull, and G. Hilmar Gudmundsson
The Cryosphere Discuss., https://doi.org/10.5194/tc-2021-396, https://doi.org/10.5194/tc-2021-396, 2022
Preprint under review for TC
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Future ice loss from Antarctica could raise sea levels by several metres, and key to this is the rate at which the ocean melts the ice sheet from below. Existing methods for modelling this process are either too time-consuming or very simplified. We present a new approach, using machine learning to mimic the melt rates calculated by a full ocean model but in a fraction of the time. This could replace to existing methods, providing accurate and efficient melt rate for use in an ice sheet model.
Emily A. Hill, Sebastian H. R. Rosier, G. Hilmar Gudmundsson, and Matthew Collins
The Cryosphere, 15, 4675–4702, https://doi.org/10.5194/tc-15-4675-2021, https://doi.org/10.5194/tc-15-4675-2021, 2021
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Using an ice flow model and uncertainty quantification methods, we provide probabilistic projections of future sea level rise from the Filchner–Ronne region of Antarctica. We find that it is most likely that this region will contribute negatively to sea level rise over the next 300 years, largely as a result of increased surface mass balance. We identify parameters controlling ice shelf melt and snowfall contribute most to uncertainties in projections.
Jowan M. Barnes, Thiago Dias dos Santos, Daniel Goldberg, G. Hilmar Gudmundsson, Mathieu Morlighem, and Jan De Rydt
The Cryosphere, 15, 1975–2000, https://doi.org/10.5194/tc-15-1975-2021, https://doi.org/10.5194/tc-15-1975-2021, 2021
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Some properties of ice flow models must be initialised using observed data before they can be used to produce reliable predictions of the future. Different models have different ways of doing this, and the process is generally seen as being specific to an individual model. We compare the methods used by three different models and show that they produce similar outputs. We also demonstrate that the outputs from one model can be used in other models without introducing large uncertainties.
Sebastian H. R. Rosier, Ronja Reese, Jonathan F. Donges, Jan De Rydt, G. Hilmar Gudmundsson, and Ricarda Winkelmann
The Cryosphere, 15, 1501–1516, https://doi.org/10.5194/tc-15-1501-2021, https://doi.org/10.5194/tc-15-1501-2021, 2021
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Pine Island Glacier has contributed more to sea-level rise over the past decades than any other glacier in Antarctica. Ice-flow modelling studies have shown that it can undergo periods of rapid mass loss, but no study has shown that these future changes could cross a tipping point and therefore be effectively irreversible. Here, we assess the stability of Pine Island Glacier, quantifying the changes in ocean temperatures required to cross future tipping points using statistical methods.
Bertie W. J. Miles, Jim R. Jordan, Chris R. Stokes, Stewart S. R. Jamieson, G. Hilmar Gudmundsson, and Adrian Jenkins
The Cryosphere, 15, 663–676, https://doi.org/10.5194/tc-15-663-2021, https://doi.org/10.5194/tc-15-663-2021, 2021
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We provide a historical overview of changes in Denman Glacier's flow speed, structure and calving events since the 1960s. Based on these observations, we perform a series of numerical modelling experiments to determine the likely cause of Denman's acceleration since the 1970s. We show that grounding line retreat, ice shelf thinning and the detachment of Denman's ice tongue from a pinning point are the most likely causes of the observed acceleration.
Jan De Rydt, Ronja Reese, Fernando S. Paolo, and G. Hilmar Gudmundsson
The Cryosphere, 15, 113–132, https://doi.org/10.5194/tc-15-113-2021, https://doi.org/10.5194/tc-15-113-2021, 2021
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We used satellite observations and numerical simulations of Pine Island Glacier, West Antarctica, between 1996 and 2016 to show that the recent increase in its flow speed can only be reproduced by computer models if stringent assumptions are made about the material properties of the ice and its underlying bed. These assumptions are not commonly adopted in ice flow modelling, and our results therefore have implications for future simulations of Antarctic ice flow and sea level projections.
Kate Winter, Emily A. Hill, G. Hilmar Gudmundsson, and John Woodward
Earth Syst. Sci. Data, 12, 3453–3467, https://doi.org/10.5194/essd-12-3453-2020, https://doi.org/10.5194/essd-12-3453-2020, 2020
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Satellite measurements of the English Coast in the Antarctic Peninsula reveal that glaciers are thinning and losing mass, but ice thickness data are required to assess these changes, in terms of ice flux and sea level contribution. Our ice-penetrating radar measurements reveal that low-elevation subglacial channels control fast-flowing ice streams, which release over 39 Gt of ice per year to floating ice shelves. This topography could make ice flows susceptible to future instability.
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, 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.
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.
Jan De Rydt, Gudmundur Hilmar Gudmundsson, Thomas Nagler, and Jan Wuite
The Cryosphere, 13, 2771–2787, https://doi.org/10.5194/tc-13-2771-2019, https://doi.org/10.5194/tc-13-2771-2019, 2019
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Two large icebergs are about to break off from the Brunt Ice Shelf in Antarctica. Rifting started several years ago and is now approaching its final phase. Satellite data and computer simulations show that over the past 2 decades, growth of the ice shelf has caused a build-up of forces within the ice, which culminated in its fracture. These natural changes in geometry coincided with large variations in flow speed, a process that is thought to be relevant for all Antarctic ice shelf margins.
Emily A. Hill, G. Hilmar Gudmundsson, J. Rachel Carr, and Chris R. Stokes
The Cryosphere, 12, 3907–3921, https://doi.org/10.5194/tc-12-3907-2018, https://doi.org/10.5194/tc-12-3907-2018, 2018
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Floating ice tongues in Greenland buttress inland ice, and their removal could accelerate ice flow. Petermann Glacier recently lost large sections of its ice tongue, but there was little glacier acceleration. Here, we assess the impact of future calving events on ice speeds. We find that removing the lower portions of the ice tongue does not accelerate flow. However, future iceberg calving closer to the grounding line could accelerate ice flow and increase ice discharge and sea level rise.
Edward C. King, Jan De Rydt, and G. Hilmar Gudmundsson
The Cryosphere, 12, 3361–3372, https://doi.org/10.5194/tc-12-3361-2018, https://doi.org/10.5194/tc-12-3361-2018, 2018
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Ice shelves are thick sheets of ice floating on the ocean off the coasts of Antarctica and Greenland. They help regulate the flow of ice off the continent. Ice shelves undergo a natural cycle of seaward flow, fracture, iceberg production and regrowth. The Brunt Ice Shelf recently developed two large cracks. We used ground-penetrating radar to find out how the internal structure of the ice might influence the present crack development and the future stability of the ice shelf.
Ronja Reese, Ricarda Winkelmann, and G. Hilmar Gudmundsson
The Cryosphere, 12, 3229–3242, https://doi.org/10.5194/tc-12-3229-2018, https://doi.org/10.5194/tc-12-3229-2018, 2018
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Accurately representing grounding-line flux is essential for modelling the evolution of the Antarctic Ice Sheet. Currently, in some large-scale ice-flow modelling studies a condition on ice flux across grounding lines is imposed using an analytically motivated parameterisation. Here we test this expression for Antarctic grounding lines and find that it provides inaccurate and partly unphysical estimates of ice flux for the highly buttressed ice streams.
Emily A. Hill, J. Rachel Carr, Chris R. Stokes, and G. Hilmar Gudmundsson
The Cryosphere, 12, 3243–3263, https://doi.org/10.5194/tc-12-3243-2018, https://doi.org/10.5194/tc-12-3243-2018, 2018
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The dynamic behaviour (i.e. acceleration and retreat) of outlet glaciers in northern Greenland remains understudied. Here, we provide a new long-term (68-year) record of terminus change. Overall, recent retreat rates (1995–2015) are higher than the last 47 years. Despite region-wide retreat, we found disparities in dynamic behaviour depending on terminus type; grounded glaciers accelerated and thinned following retreat, while glaciers with floating ice tongues were insensitive to recent retreat.
Sebastian H. R. Rosier and G. Hilmar Gudmundsson
The Cryosphere, 12, 1699–1713, https://doi.org/10.5194/tc-12-1699-2018, https://doi.org/10.5194/tc-12-1699-2018, 2018
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Ocean tides cause strong modulation of horizontal ice shelf flow, most notably at a fortnightly frequency that is absent in the vertical tidal forcing. We propose that tidal bending in the margins of the ice shelf produces sufficiently large stresses that the effective viscosity of ice in these regions is reduced during high and low tide. This effect can explain many features of the observed behaviour and implies that ice shelves in areas with strong tides move faster than they otherwise would.
Jan De Rydt, G. Hilmar Gudmundsson, Thomas Nagler, Jan Wuite, and Edward C. King
The Cryosphere, 12, 505–520, https://doi.org/10.5194/tc-12-505-2018, https://doi.org/10.5194/tc-12-505-2018, 2018
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We provide an unprecedented view into the dynamics of two active rifts in the Brunt Ice Shelf through a unique set of field observations, novel satellite data products, and a state-of-the-art ice flow model. We describe the evolution of fracture width and length in great detail, pushing the boundaries of both spatial and temporal coverage, and provide a deeper insight into the process of iceberg formation, which exerts an important control over the mass balance of the Antarctic Ice Sheet.
Werner M. J. Lazeroms, Adrian Jenkins, G. Hilmar Gudmundsson, and Roderik S. W. van de Wal
The Cryosphere, 12, 49–70, https://doi.org/10.5194/tc-12-49-2018, https://doi.org/10.5194/tc-12-49-2018, 2018
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Basal melting of ice shelves is a major factor in the decline of the Antarctic Ice Sheet, which can contribute significantly to sea-level rise. Here, we investigate a new basal melt model based on the dynamics of meltwater plumes. For the first time, this model is applied to all Antarctic ice shelves. The model results in a realistic melt-rate pattern given suitable data for the topography and ocean temperature, making it a promising tool for future simulations of the Antarctic Ice Sheet.
Sebastian H. R. Rosier, G. Hilmar Gudmundsson, Matt A. King, Keith W. Nicholls, Keith Makinson, and Hugh F. J. Corr
Earth Syst. Sci. Data, 9, 849–860, https://doi.org/10.5194/essd-9-849-2017, https://doi.org/10.5194/essd-9-849-2017, 2017
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Tides can affect the flow of ice at hourly to yearly timescales. In some cases the ice responds at a different frequency than is found in the tidal forcing; for example, on Rutford Ice Stream the strongest response is at a fortnightly period. A new compilation of GPS data across the Ronne Ice Shelf and adjoining ice streams shows that this fortnightly modulation in ice flow is found across the entire region. Measurements of this kind can provide insights into ice rheology and basal processes.
Daniel Farinotti, Douglas J. Brinkerhoff, Garry K. C. Clarke, Johannes J. Fürst, Holger Frey, Prateek Gantayat, Fabien Gillet-Chaulet, Claire Girard, Matthias Huss, Paul W. Leclercq, Andreas Linsbauer, Horst Machguth, Carlos Martin, Fabien Maussion, Mathieu Morlighem, Cyrille Mosbeux, Ankur Pandit, Andrea Portmann, Antoine Rabatel, RAAJ Ramsankaran, Thomas J. Reerink, Olivier Sanchez, Peter A. Stentoft, Sangita Singh Kumari, Ward J. J. van Pelt, Brian Anderson, Toby Benham, Daniel Binder, Julian A. Dowdeswell, Andrea Fischer, Kay Helfricht, Stanislav Kutuzov, Ivan Lavrentiev, Robert McNabb, G. Hilmar Gudmundsson, Huilin Li, and Liss M. Andreassen
The Cryosphere, 11, 949–970, https://doi.org/10.5194/tc-11-949-2017, https://doi.org/10.5194/tc-11-949-2017, 2017
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ITMIX – the Ice Thickness Models Intercomparison eXperiment – was the first coordinated performance assessment for models inferring glacier ice thickness from surface characteristics. Considering 17 different models and 21 different test cases, we show that although solutions of individual models can differ considerably, an ensemble average can yield uncertainties in the order of 10 ± 24 % the mean ice thickness. Ways forward for improving such estimates are sketched.
Xylar S. Asay-Davis, Stephen L. Cornford, Gaël Durand, Benjamin K. Galton-Fenzi, Rupert M. Gladstone, G. Hilmar Gudmundsson, Tore Hattermann, David M. Holland, Denise Holland, Paul R. Holland, Daniel F. Martin, Pierre Mathiot, Frank Pattyn, and Hélène Seroussi
Geosci. Model Dev., 9, 2471–2497, https://doi.org/10.5194/gmd-9-2471-2016, https://doi.org/10.5194/gmd-9-2471-2016, 2016
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Coupled ice sheet–ocean models capable of simulating moving grounding lines are just becoming available. Such models have a broad range of potential applications in studying the dynamics of ice sheets and glaciers, including assessing their contributions to sea level change. Here we describe the idealized experiments that make up three interrelated Model Intercomparison Projects (MIPs) for marine ice sheet models and regional ocean circulation models incorporating ice shelf cavities.
David H. Jones, Carl Robinson, and G. Hilmar Gudmundsson
Geosci. Instrum. Method. Data Syst., 5, 65–73, https://doi.org/10.5194/gi-5-65-2016, https://doi.org/10.5194/gi-5-65-2016, 2016
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Long-term records from high-precision GPS receivers are essential for studying geophysical movement. Existing, commercially available, precision GPS receivers are not intended for long-term, autonomous deployment. We have designed a GPS receiver that is better suited for this application. In this paper, we discuss the receiver design and compare its performance with that of some of the commercially available receivers.
S. H. R. Rosier, G. H. Gudmundsson, and J. A. M. Green
The Cryosphere, 9, 1649–1661, https://doi.org/10.5194/tc-9-1649-2015, https://doi.org/10.5194/tc-9-1649-2015, 2015
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We use a full-Stokes model to investigate the long period modulation of Rutford Ice Stream flow by the ocean tide. We find that using a nonlinear sliding law cannot fully explain the measurements and an additional mechanism, whereby tidally induced subglacial pressure variations are transmitted upstream from the grounding line, is also required to match the large amplitude and decay length scale of the observations.
D. H. Jones and G. H. Gudmundsson
Nat. Hazards Earth Syst. Sci., 15, 1243–1250, https://doi.org/10.5194/nhess-15-1243-2015, https://doi.org/10.5194/nhess-15-1243-2015, 2015
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Icebergs are a natural hazard to maritime operations in polar regions. Iceberg populations are increasing, as is the demand for access to both Arctic and Antarctic seas. Soon the ability to reliably track icebergs may become a necessity for continued operational safety. In this paper we describe the design of a tracking sensor that can be deployed from an aircraft during surveys of Antarctic icebergs, and detail the results of its first deployment operation on iceberg B-31.
J. Wuite, H. Rott, M. Hetzenecker, D. Floricioiu, J. De Rydt, G. H. Gudmundsson, T. Nagler, and M. Kern
The Cryosphere, 9, 957–969, https://doi.org/10.5194/tc-9-957-2015, https://doi.org/10.5194/tc-9-957-2015, 2015
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We present new analysis of satellite data showing the variability of glacier velocities in the Larsen B area, Antarctic Peninsula, back to 1995. Velocity data and estimates of ice thickness are used to derive ice discharge at different epochs. Velocities of the glaciers remain to date well above the velocities of the pre-collapse period. The response of individual glaciers differs, and velocities show significant temporal fluctuations, implying major variations in ice discharge and mass balance.
C. Martín, R. Mulvaney, G. H. Gudmundsson, and H. Corr
Clim. Past, 11, 547–557, https://doi.org/10.5194/cp-11-547-2015, https://doi.org/10.5194/cp-11-547-2015, 2015
S. H. R. Rosier, G. H. Gudmundsson, and J. A. M. Green
The Cryosphere, 8, 1763–1775, https://doi.org/10.5194/tc-8-1763-2014, https://doi.org/10.5194/tc-8-1763-2014, 2014
R. Anderson, D. H. Jones, and G. H. Gudmundsson
Nat. Hazards Earth Syst. Sci., 14, 917–927, https://doi.org/10.5194/nhess-14-917-2014, https://doi.org/10.5194/nhess-14-917-2014, 2014
G. H. Gudmundsson
The Cryosphere, 7, 647–655, https://doi.org/10.5194/tc-7-647-2013, https://doi.org/10.5194/tc-7-647-2013, 2013
J. De Rydt, G. H. Gudmundsson, H. F. J. Corr, and P. Christoffersen
The Cryosphere, 7, 407–417, https://doi.org/10.5194/tc-7-407-2013, https://doi.org/10.5194/tc-7-407-2013, 2013
Bertie W. J. Miles, Chris R. Stokes, Adrian Jenkins, Jim R. Jordan, Stewart S. R. Jamieson, and G. Hilmar Gudmundsson
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-126, https://doi.org/10.5194/tc-2022-126, 2022
Preprint under review for TC
Short summary
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Satellite observations have shown that the Shirase Glacier catchment in East Antarctica has been gaining mass over the past two decades, a trend largely attributed to increased snowfall. Our multi-decadal observations of Shirase Glacier show that ocean forcing has also contributed to some of this recent mass gain. This has been caused by strengthening alongshore winds reducing the inflow of warm water underneath the Shirase ice tongue.
Benoît Urruty, Emily A. Hill, Ronja Reese, Julius Garbe, Olivier Gagliardini, Gael Durand, Fabien Gillet-Chaulet, G. Hilmar Gudmundsson, Ricarda Winkelmann, Mondher Chekki, David Chandler, and Petra M. Langebroek
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-104, https://doi.org/10.5194/tc-2022-104, 2022
Preprint under review for TC
Short summary
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Retreat of the Antarctic grounding lines could destabilise large parts of the ice sheet. We use three ice sheet models to show that the present-day locations of Antarctic grounding lines are stable with respect to a small perturbation away from their current position. This suggests that self-sustained retreat of grounding lines, due to an internal instability, has not begun. Instead, the currently observed retreat is likely due to external forcing alone.
Jeremy Rohmer, Remi Thieblemont, Goneri Le Cozannet, Heiko Goelzer, and Gael Durand
EGUsphere, https://doi.org/10.5194/egusphere-2022-435, https://doi.org/10.5194/egusphere-2022-435, 2022
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To improve the interpretability of process-based projections of the sea-level contribution from land ice components, we apply the machine-learning-based ‘SHapley Additive exPlanation’ approach to a subset of the multi-model ensemble study for Greenland ice sheet. This allows us to quantify the influence of particular modelling decisions (either related to numerical implementation, initial conditions, or parametrisation of ice-sheet processes) directly in terms of sea level change contribution.
Jowan Menhinick Barnes and G. Hilmar Gudmundsson
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-109, https://doi.org/10.5194/tc-2022-109, 2022
Preprint under review for TC
Short summary
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Models must represent how glaciers slide along the bed, but there are many ways to do so. In this paper, several sliding laws are tested, and found to affect different regions of the Antarctic ice sheet in different ways, and at different speeds. However, the variability in ice volume loss due to sliding law choices is low compared to other factors, so limited empirical knowledge of sliding does not prevent us from making predictions of how an ice sheet will evolve.
Ronja Reese, Julius Garbe, Emily A. Hill, Benoît Urruty, Kaitlin A. Naughten, Olivier Gagliardini, Gael Durand, Fabien Gillet-Chaulet, David Chandler, Petra M. Langebroek, and Ricarda Winkelmann
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-105, https://doi.org/10.5194/tc-2022-105, 2022
Preprint under review for TC
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We use an ice sheet model to test where current climate conditions in Antarctica might lead. We find that, depending on model parameters, present-day ocean and atmosphere conditions might commit a collapse of parts of West Antarctica which evolves over centuries to millennia. Importantly, this collapse is not yet irreversible as shown in our accompanying study.
Tom Mitcham, G. Hilmar Gudmundsson, and Jonathan L. Bamber
The Cryosphere, 16, 883–901, https://doi.org/10.5194/tc-16-883-2022, https://doi.org/10.5194/tc-16-883-2022, 2022
Short summary
Short summary
We modelled the response of the Larsen C Ice Shelf (LCIS) and its tributary glaciers to the calving of the A68 iceberg and validated our results with observations. We found that the impact was limited, confirming that mostly passive ice was calved. Through further calving experiments we quantified the total buttressing provided by the LCIS and found that over 80 % of the buttressing capacity is generated in the first 5 km of the ice shelf downstream of the grounding line.
Sebastian Harry Reid Rosier, Christopher Y. S. Bull, and G. Hilmar Gudmundsson
The Cryosphere Discuss., https://doi.org/10.5194/tc-2021-396, https://doi.org/10.5194/tc-2021-396, 2022
Preprint under review for TC
Short summary
Short summary
Future ice loss from Antarctica could raise sea levels by several metres, and key to this is the rate at which the ocean melts the ice sheet from below. Existing methods for modelling this process are either too time-consuming or very simplified. We present a new approach, using machine learning to mimic the melt rates calculated by a full ocean model but in a fraction of the time. This could replace to existing methods, providing accurate and efficient melt rate for use in an ice sheet model.
Emily A. Hill, Sebastian H. R. Rosier, G. Hilmar Gudmundsson, and Matthew Collins
The Cryosphere, 15, 4675–4702, https://doi.org/10.5194/tc-15-4675-2021, https://doi.org/10.5194/tc-15-4675-2021, 2021
Short summary
Short summary
Using an ice flow model and uncertainty quantification methods, we provide probabilistic projections of future sea level rise from the Filchner–Ronne region of Antarctica. We find that it is most likely that this region will contribute negatively to sea level rise over the next 300 years, largely as a result of increased surface mass balance. We identify parameters controlling ice shelf melt and snowfall contribute most to uncertainties in projections.
Jowan M. Barnes, Thiago Dias dos Santos, Daniel Goldberg, G. Hilmar Gudmundsson, Mathieu Morlighem, and Jan De Rydt
The Cryosphere, 15, 1975–2000, https://doi.org/10.5194/tc-15-1975-2021, https://doi.org/10.5194/tc-15-1975-2021, 2021
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Some properties of ice flow models must be initialised using observed data before they can be used to produce reliable predictions of the future. Different models have different ways of doing this, and the process is generally seen as being specific to an individual model. We compare the methods used by three different models and show that they produce similar outputs. We also demonstrate that the outputs from one model can be used in other models without introducing large uncertainties.
Sebastian H. R. Rosier, Ronja Reese, Jonathan F. Donges, Jan De Rydt, G. Hilmar Gudmundsson, and Ricarda Winkelmann
The Cryosphere, 15, 1501–1516, https://doi.org/10.5194/tc-15-1501-2021, https://doi.org/10.5194/tc-15-1501-2021, 2021
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Pine Island Glacier has contributed more to sea-level rise over the past decades than any other glacier in Antarctica. Ice-flow modelling studies have shown that it can undergo periods of rapid mass loss, but no study has shown that these future changes could cross a tipping point and therefore be effectively irreversible. Here, we assess the stability of Pine Island Glacier, quantifying the changes in ocean temperatures required to cross future tipping points using statistical methods.
Christian Vincent, Diego Cusicanqui, Bruno Jourdain, Olivier Laarman, Delphine Six, Adrien Gilbert, Andrea Walpersdorf, Antoine Rabatel, Luc Piard, Florent Gimbert, Olivier Gagliardini, Vincent Peyaud, Laurent Arnaud, Emmanuel Thibert, Fanny Brun, and Ugo Nanni
The Cryosphere, 15, 1259–1276, https://doi.org/10.5194/tc-15-1259-2021, https://doi.org/10.5194/tc-15-1259-2021, 2021
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In situ glacier point mass balance data are crucial to assess climate change in different regions of the world. Unfortunately, these data are rare because huge efforts are required to conduct in situ measurements on glaciers. Here, we propose a new approach from remote sensing observations. The method has been tested on the Argentière and Mer de Glace glaciers (France). It should be possible to apply this method to high-spatial-resolution satellite images and on numerous glaciers in the world.
Bertie W. J. Miles, Jim R. Jordan, Chris R. Stokes, Stewart S. R. Jamieson, G. Hilmar Gudmundsson, and Adrian Jenkins
The Cryosphere, 15, 663–676, https://doi.org/10.5194/tc-15-663-2021, https://doi.org/10.5194/tc-15-663-2021, 2021
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We provide a historical overview of changes in Denman Glacier's flow speed, structure and calving events since the 1960s. Based on these observations, we perform a series of numerical modelling experiments to determine the likely cause of Denman's acceleration since the 1970s. We show that grounding line retreat, ice shelf thinning and the detachment of Denman's ice tongue from a pinning point are the most likely causes of the observed acceleration.
Jan De Rydt, Ronja Reese, Fernando S. Paolo, and G. Hilmar Gudmundsson
The Cryosphere, 15, 113–132, https://doi.org/10.5194/tc-15-113-2021, https://doi.org/10.5194/tc-15-113-2021, 2021
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We used satellite observations and numerical simulations of Pine Island Glacier, West Antarctica, between 1996 and 2016 to show that the recent increase in its flow speed can only be reproduced by computer models if stringent assumptions are made about the material properties of the ice and its underlying bed. These assumptions are not commonly adopted in ice flow modelling, and our results therefore have implications for future simulations of Antarctic ice flow and sea level projections.
Kate Winter, Emily A. Hill, G. Hilmar Gudmundsson, and John Woodward
Earth Syst. Sci. Data, 12, 3453–3467, https://doi.org/10.5194/essd-12-3453-2020, https://doi.org/10.5194/essd-12-3453-2020, 2020
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Satellite measurements of the English Coast in the Antarctic Peninsula reveal that glaciers are thinning and losing mass, but ice thickness data are required to assess these changes, in terms of ice flux and sea level contribution. Our ice-penetrating radar measurements reveal that low-elevation subglacial channels control fast-flowing ice streams, which release over 39 Gt of ice per year to floating ice shelves. This topography could make ice flows susceptible to future instability.
Vincent Peyaud, Coline Bouchayer, Olivier Gagliardini, Christian Vincent, Fabien Gillet-Chaulet, Delphine Six, and Olivier Laarman
The Cryosphere, 14, 3979–3994, https://doi.org/10.5194/tc-14-3979-2020, https://doi.org/10.5194/tc-14-3979-2020, 2020
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Alpine glaciers are retreating at an accelerating rate in a warming climate. Numerical models allow us to study and anticipate these changes, but the performance of a model is difficult to evaluate. So we compared an ice flow model with the long dataset of observations obtained between 1979 and 2015 on Mer de Glace (Mont Blanc area). The model accurately reconstructs the past evolution of the glacier. We simulate the future evolution of Mer de Glace; it could retreat by 2 to 6 km by 2050.
Stephen L. Cornford, Helene Seroussi, Xylar S. Asay-Davis, G. Hilmar Gudmundsson, Rob Arthern, Chris Borstad, Julia Christmann, Thiago Dias dos Santos, Johannes Feldmann, Daniel Goldberg, Matthew J. Hoffman, Angelika Humbert, Thomas Kleiner, Gunter Leguy, William H. Lipscomb, Nacho Merino, Gaël Durand, Mathieu Morlighem, David Pollard, Martin Rückamp, C. Rosie Williams, and Hongju Yu
The Cryosphere, 14, 2283–2301, https://doi.org/10.5194/tc-14-2283-2020, https://doi.org/10.5194/tc-14-2283-2020, 2020
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We present the results of the third Marine Ice Sheet Intercomparison Project (MISMIP+). MISMIP+ is one in a series of exercises that test numerical models of ice sheet flow in simple situations. This particular exercise concentrates on the response of ice sheet models to the thinning of their floating ice shelves, which is of interest because numerical models are currently used to model the response to contemporary and near-future thinning in Antarctic ice shelves.
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.
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.
Jan De Rydt, Gudmundur Hilmar Gudmundsson, Thomas Nagler, and Jan Wuite
The Cryosphere, 13, 2771–2787, https://doi.org/10.5194/tc-13-2771-2019, https://doi.org/10.5194/tc-13-2771-2019, 2019
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Two large icebergs are about to break off from the Brunt Ice Shelf in Antarctica. Rifting started several years ago and is now approaching its final phase. Satellite data and computer simulations show that over the past 2 decades, growth of the ice shelf has caused a build-up of forces within the ice, which culminated in its fracture. These natural changes in geometry coincided with large variations in flow speed, a process that is thought to be relevant for all Antarctic ice shelf margins.
Lionel Favier, Nicolas C. Jourdain, Adrian Jenkins, Nacho Merino, Gaël Durand, Olivier Gagliardini, Fabien Gillet-Chaulet, and Pierre Mathiot
Geosci. Model Dev., 12, 2255–2283, https://doi.org/10.5194/gmd-12-2255-2019, https://doi.org/10.5194/gmd-12-2255-2019, 2019
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The melting at the base of floating ice shelves is the main driver of the Antarctic ice sheet current retreat. Here, we use an ideal set-up to assess a wide range of melting parameterisations depending on oceanic properties with regard to a new ocean–ice-sheet coupled model, published here for the first time. A parameterisation that depends quadratically on thermal forcing in both a local and a non-local way yields the best results and needs to be further assessed with more realistic set-ups.
Julien Brondex, Fabien Gillet-Chaulet, and Olivier Gagliardini
The Cryosphere, 13, 177–195, https://doi.org/10.5194/tc-13-177-2019, https://doi.org/10.5194/tc-13-177-2019, 2019
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Here, we apply a synthetic perturbation to the most active drainage basin of Antarctica and show that centennial mass loss projections obtained through ice flow models depend strongly on the implemented friction law, i.e. the mathematical relationship between basal drag and sliding velocities. In particular, the commonly used Weertman law considerably underestimates the sea-level contribution of this basin in comparison to two water pressure-dependent laws which rely on stronger physical bases.
Emily A. Hill, G. Hilmar Gudmundsson, J. Rachel Carr, and Chris R. Stokes
The Cryosphere, 12, 3907–3921, https://doi.org/10.5194/tc-12-3907-2018, https://doi.org/10.5194/tc-12-3907-2018, 2018
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Floating ice tongues in Greenland buttress inland ice, and their removal could accelerate ice flow. Petermann Glacier recently lost large sections of its ice tongue, but there was little glacier acceleration. Here, we assess the impact of future calving events on ice speeds. We find that removing the lower portions of the ice tongue does not accelerate flow. However, future iceberg calving closer to the grounding line could accelerate ice flow and increase ice discharge and sea level rise.
Edward C. King, Jan De Rydt, and G. Hilmar Gudmundsson
The Cryosphere, 12, 3361–3372, https://doi.org/10.5194/tc-12-3361-2018, https://doi.org/10.5194/tc-12-3361-2018, 2018
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Ice shelves are thick sheets of ice floating on the ocean off the coasts of Antarctica and Greenland. They help regulate the flow of ice off the continent. Ice shelves undergo a natural cycle of seaward flow, fracture, iceberg production and regrowth. The Brunt Ice Shelf recently developed two large cracks. We used ground-penetrating radar to find out how the internal structure of the ice might influence the present crack development and the future stability of the ice shelf.
Ronja Reese, Ricarda Winkelmann, and G. Hilmar Gudmundsson
The Cryosphere, 12, 3229–3242, https://doi.org/10.5194/tc-12-3229-2018, https://doi.org/10.5194/tc-12-3229-2018, 2018
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Accurately representing grounding-line flux is essential for modelling the evolution of the Antarctic Ice Sheet. Currently, in some large-scale ice-flow modelling studies a condition on ice flux across grounding lines is imposed using an analytically motivated parameterisation. Here we test this expression for Antarctic grounding lines and find that it provides inaccurate and partly unphysical estimates of ice flux for the highly buttressed ice streams.
Emily A. Hill, J. Rachel Carr, Chris R. Stokes, and G. Hilmar Gudmundsson
The Cryosphere, 12, 3243–3263, https://doi.org/10.5194/tc-12-3243-2018, https://doi.org/10.5194/tc-12-3243-2018, 2018
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The dynamic behaviour (i.e. acceleration and retreat) of outlet glaciers in northern Greenland remains understudied. Here, we provide a new long-term (68-year) record of terminus change. Overall, recent retreat rates (1995–2015) are higher than the last 47 years. Despite region-wide retreat, we found disparities in dynamic behaviour depending on terminus type; grounded glaciers accelerated and thinned following retreat, while glaciers with floating ice tongues were insensitive to recent retreat.
Marianne Haseloff, Christian Schoof, and Olivier Gagliardini
The Cryosphere, 12, 2545–2568, https://doi.org/10.5194/tc-12-2545-2018, https://doi.org/10.5194/tc-12-2545-2018, 2018
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The widths of the Siple Coast ice streams evolve on decadal to centennial timescales. We investigate how the rate of thermally driven ice stream widening depends on heat dissipation in the ice stream margin and at the bed, and on the inflow of cold ice from the ice ridge. As determining the migration rate requires resolving heat transfer processes on very small scales, we derive a parametrization of the migration rate in terms of parameters that are available from large-scale model outputs.
Olivier Passalacqua, Marie Cavitte, Olivier Gagliardini, Fabien Gillet-Chaulet, Frédéric Parrenin, Catherine Ritz, and Duncan Young
The Cryosphere, 12, 2167–2174, https://doi.org/10.5194/tc-12-2167-2018, https://doi.org/10.5194/tc-12-2167-2018, 2018
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Locating a suitable drill site is a key step in the Antarctic oldest-ice challenge. Here we have conducted a 3-D ice flow simulation in the region of Dome C using a refined bedrock description. Five selection criteria are computed that together provide an objective overview on the local ice flow conditions. We delineate kilometer-scale favorable areas that overlap with the ones recently proposed by another group. We propose a few drill sites that should be surveyed during the next field seasons.
Sebastian H. R. Rosier and G. Hilmar Gudmundsson
The Cryosphere, 12, 1699–1713, https://doi.org/10.5194/tc-12-1699-2018, https://doi.org/10.5194/tc-12-1699-2018, 2018
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Ocean tides cause strong modulation of horizontal ice shelf flow, most notably at a fortnightly frequency that is absent in the vertical tidal forcing. We propose that tidal bending in the margins of the ice shelf produces sufficiently large stresses that the effective viscosity of ice in these regions is reduced during high and low tide. This effect can explain many features of the observed behaviour and implies that ice shelves in areas with strong tides move faster than they otherwise would.
Heiko Goelzer, Sophie Nowicki, Tamsin Edwards, Matthew Beckley, Ayako Abe-Ouchi, Andy Aschwanden, Reinhard Calov, Olivier Gagliardini, Fabien Gillet-Chaulet, Nicholas R. Golledge, Jonathan Gregory, Ralf Greve, Angelika Humbert, Philippe Huybrechts, Joseph H. Kennedy, Eric Larour, William H. Lipscomb, Sébastien Le clec'h, Victoria Lee, Mathieu Morlighem, Frank Pattyn, Antony J. Payne, Christian Rodehacke, Martin Rückamp, Fuyuki Saito, Nicole Schlegel, Helene Seroussi, Andrew Shepherd, Sainan Sun, Roderik van de Wal, and Florian A. Ziemen
The Cryosphere, 12, 1433–1460, https://doi.org/10.5194/tc-12-1433-2018, https://doi.org/10.5194/tc-12-1433-2018, 2018
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We have compared a wide spectrum of different initialisation techniques used in the ice sheet modelling community to define the modelled present-day Greenland ice sheet state as a starting point for physically based future-sea-level-change projections. Compared to earlier community-wide comparisons, we find better agreement across different models, which implies overall improvement of our understanding of what is needed to produce such initial states.
Jan De Rydt, G. Hilmar Gudmundsson, Thomas Nagler, Jan Wuite, and Edward C. King
The Cryosphere, 12, 505–520, https://doi.org/10.5194/tc-12-505-2018, https://doi.org/10.5194/tc-12-505-2018, 2018
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We provide an unprecedented view into the dynamics of two active rifts in the Brunt Ice Shelf through a unique set of field observations, novel satellite data products, and a state-of-the-art ice flow model. We describe the evolution of fracture width and length in great detail, pushing the boundaries of both spatial and temporal coverage, and provide a deeper insight into the process of iceberg formation, which exerts an important control over the mass balance of the Antarctic Ice Sheet.
Werner M. J. Lazeroms, Adrian Jenkins, G. Hilmar Gudmundsson, and Roderik S. W. van de Wal
The Cryosphere, 12, 49–70, https://doi.org/10.5194/tc-12-49-2018, https://doi.org/10.5194/tc-12-49-2018, 2018
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Basal melting of ice shelves is a major factor in the decline of the Antarctic Ice Sheet, which can contribute significantly to sea-level rise. Here, we investigate a new basal melt model based on the dynamics of meltwater plumes. For the first time, this model is applied to all Antarctic ice shelves. The model results in a realistic melt-rate pattern given suitable data for the topography and ocean temperature, making it a promising tool for future simulations of the Antarctic Ice Sheet.
Sebastian H. R. Rosier, G. Hilmar Gudmundsson, Matt A. King, Keith W. Nicholls, Keith Makinson, and Hugh F. J. Corr
Earth Syst. Sci. Data, 9, 849–860, https://doi.org/10.5194/essd-9-849-2017, https://doi.org/10.5194/essd-9-849-2017, 2017
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Tides can affect the flow of ice at hourly to yearly timescales. In some cases the ice responds at a different frequency than is found in the tidal forcing; for example, on Rutford Ice Stream the strongest response is at a fortnightly period. A new compilation of GPS data across the Ronne Ice Shelf and adjoining ice streams shows that this fortnightly modulation in ice flow is found across the entire region. Measurements of this kind can provide insights into ice rheology and basal processes.
Frédéric Parrenin, Marie G. P. Cavitte, Donald D. Blankenship, Jérôme Chappellaz, Hubertus Fischer, Olivier Gagliardini, Valérie Masson-Delmotte, Olivier Passalacqua, Catherine Ritz, Jason Roberts, Martin J. Siegert, and Duncan A. Young
The Cryosphere, 11, 2427–2437, https://doi.org/10.5194/tc-11-2427-2017, https://doi.org/10.5194/tc-11-2427-2017, 2017
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The oldest dated deep ice core drilled in Antarctica has been retrieved at EPICA Dome C (EDC), reaching ~ 800 000 years. Obtaining an older palaeoclimatic record from Antarctica is one of the greatest challenges of the ice core community. Here, we estimate the age of basal ice in the Dome C area. We find that old ice (> 1.5 Myr) likely exists in two regions a few tens of kilometres away from EDC:
Little Dome C Patchand
North Patch.
Daniel Farinotti, Douglas J. Brinkerhoff, Garry K. C. Clarke, Johannes J. Fürst, Holger Frey, Prateek Gantayat, Fabien Gillet-Chaulet, Claire Girard, Matthias Huss, Paul W. Leclercq, Andreas Linsbauer, Horst Machguth, Carlos Martin, Fabien Maussion, Mathieu Morlighem, Cyrille Mosbeux, Ankur Pandit, Andrea Portmann, Antoine Rabatel, RAAJ Ramsankaran, Thomas J. Reerink, Olivier Sanchez, Peter A. Stentoft, Sangita Singh Kumari, Ward J. J. van Pelt, Brian Anderson, Toby Benham, Daniel Binder, Julian A. Dowdeswell, Andrea Fischer, Kay Helfricht, Stanislav Kutuzov, Ivan Lavrentiev, Robert McNabb, G. Hilmar Gudmundsson, Huilin Li, and Liss M. Andreassen
The Cryosphere, 11, 949–970, https://doi.org/10.5194/tc-11-949-2017, https://doi.org/10.5194/tc-11-949-2017, 2017
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ITMIX – the Ice Thickness Models Intercomparison eXperiment – was the first coordinated performance assessment for models inferring glacier ice thickness from surface characteristics. Considering 17 different models and 21 different test cases, we show that although solutions of individual models can differ considerably, an ensemble average can yield uncertainties in the order of 10 ± 24 % the mean ice thickness. Ways forward for improving such estimates are sketched.
Rupert Michael Gladstone, Roland Charles Warner, Benjamin Keith Galton-Fenzi, Olivier Gagliardini, Thomas Zwinger, and Ralf Greve
The Cryosphere, 11, 319–329, https://doi.org/10.5194/tc-11-319-2017, https://doi.org/10.5194/tc-11-319-2017, 2017
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Computer models are used to simulate the behaviour of glaciers and ice sheets. It has been found that such models are required to be run at very high resolution (which means high computational expense) in order to accurately represent the evolution of marine ice sheets (ice sheets resting on bedrock below sea level), in certain situations which depend on sub-glacial physical processes.
Tong Zhang, Stephen Price, Lili Ju, Wei Leng, Julien Brondex, Gaël Durand, and Olivier Gagliardini
The Cryosphere, 11, 179–190, https://doi.org/10.5194/tc-11-179-2017, https://doi.org/10.5194/tc-11-179-2017, 2017
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Stokes-flow models are the highest-fidelity representation of the equations governing ice sheet flow and they are often treated as the standard against which other models are compared in model benchmark activities. We compare two different Stokes models applied to a canonical set of idealized marine ice sheet experiments and demonstrate that the solutions converge with increasing grid resolution. This provides confidence in the use of Stokes models for generating test case solution metrics.
Xylar S. Asay-Davis, Stephen L. Cornford, Gaël Durand, Benjamin K. Galton-Fenzi, Rupert M. Gladstone, G. Hilmar Gudmundsson, Tore Hattermann, David M. Holland, Denise Holland, Paul R. Holland, Daniel F. Martin, Pierre Mathiot, Frank Pattyn, and Hélène Seroussi
Geosci. Model Dev., 9, 2471–2497, https://doi.org/10.5194/gmd-9-2471-2016, https://doi.org/10.5194/gmd-9-2471-2016, 2016
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Coupled ice sheet–ocean models capable of simulating moving grounding lines are just becoming available. Such models have a broad range of potential applications in studying the dynamics of ice sheets and glaciers, including assessing their contributions to sea level change. Here we describe the idealized experiments that make up three interrelated Model Intercomparison Projects (MIPs) for marine ice sheet models and regional ocean circulation models incorporating ice shelf cavities.
Olivier Passalacqua, Olivier Gagliardini, Frédéric Parrenin, Joe Todd, Fabien Gillet-Chaulet, and Catherine Ritz
Geosci. Model Dev., 9, 2301–2313, https://doi.org/10.5194/gmd-9-2301-2016, https://doi.org/10.5194/gmd-9-2301-2016, 2016
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In ice-flow modelling, computing in 3-D requires a lot of resources, but 2-D models lack physical likelihood when the flow is diverging. That is why 2-D models accounting for the divergence, so-called 2.5-D models, are an interesting trade-off. However, the applicability of these 2.5-D models has never been systematically examined. We show that these models are ineffective in the case of highly diverging flows, but also for varying temperature, which was not suspected.
David H. Jones, Carl Robinson, and G. Hilmar Gudmundsson
Geosci. Instrum. Method. Data Syst., 5, 65–73, https://doi.org/10.5194/gi-5-65-2016, https://doi.org/10.5194/gi-5-65-2016, 2016
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Long-term records from high-precision GPS receivers are essential for studying geophysical movement. Existing, commercially available, precision GPS receivers are not intended for long-term, autonomous deployment. We have designed a GPS receiver that is better suited for this application. In this paper, we discuss the receiver design and compare its performance with that of some of the commercially available receivers.
O. Gagliardini, J. Brondex, F. Gillet-Chaulet, L. Tavard, V. Peyaud, and G. Durand
The Cryosphere, 10, 307–312, https://doi.org/10.5194/tc-10-307-2016, https://doi.org/10.5194/tc-10-307-2016, 2016
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In this paper it is shown that the sensitivity to the mesh resolution is not
improved for a vanishing friction at the grounding line (GL). For a discontinuous friction at the GL, we further show that the results are moreover very sensitive to the way the friction is interpolated in the close vicinity of the GL. In the light of these new insights, new results for the MISMIP3d experiments obtained for higher resolutions than previously published are made available for future comparisons.
G. Durand and F. Pattyn
The Cryosphere, 9, 2043–2055, https://doi.org/10.5194/tc-9-2043-2015, https://doi.org/10.5194/tc-9-2043-2015, 2015
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Projections of Antarctic dynamics and contribution to sea-level rise are evaluated in the light of intercomparison exercises dedicated to evaluate models' ability of representing coastal changes. Uncertainties in projections can be substantially decreased if a selection of models is made and models that are unqualified for the representation of coastal dynamics are excluded.
S. H. R. Rosier, G. H. Gudmundsson, and J. A. M. Green
The Cryosphere, 9, 1649–1661, https://doi.org/10.5194/tc-9-1649-2015, https://doi.org/10.5194/tc-9-1649-2015, 2015
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We use a full-Stokes model to investigate the long period modulation of Rutford Ice Stream flow by the ocean tide. We find that using a nonlinear sliding law cannot fully explain the measurements and an additional mechanism, whereby tidally induced subglacial pressure variations are transmitted upstream from the grounding line, is also required to match the large amplitude and decay length scale of the observations.
J.-L. Tison, M. de Angelis, G. Littot, E. Wolff, H. Fischer, M. Hansson, M. Bigler, R. Udisti, A. Wegner, J. Jouzel, B. Stenni, S. Johnsen, V. Masson-Delmotte, A. Landais, V. Lipenkov, L. Loulergue, J.-M. Barnola, J.-R. Petit, B. Delmonte, G. Dreyfus, D. Dahl-Jensen, G. Durand, B. Bereiter, A. Schilt, R. Spahni, K. Pol, R. Lorrain, R. Souchez, and D. Samyn
The Cryosphere, 9, 1633–1648, https://doi.org/10.5194/tc-9-1633-2015, https://doi.org/10.5194/tc-9-1633-2015, 2015
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The oldest paleoclimatic information is buried within the lowermost layers of deep ice cores. It is therefore essential to judge how deep these records remain unaltered. We study the bottom 60 meters of the EPICA Dome C ice core from central Antarctica to show that the paleoclimatic signal is only affected at the small scale (decimeters) in terms of some of the global ice properties. However our data suggest that the time scale has been considerably distorted by mechanical stretching.
J. J. Fürst, G. Durand, F. Gillet-Chaulet, N. Merino, L. Tavard, J. Mouginot, N. Gourmelen, and O. Gagliardini
The Cryosphere, 9, 1427–1443, https://doi.org/10.5194/tc-9-1427-2015, https://doi.org/10.5194/tc-9-1427-2015, 2015
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We present a comprehensive high-resolution assimilation of Antarctic surface velocities with a flow model. The inferred velocities are in very good agreement with observations, even when compared to recent studies on individual shelves. This quality allows to identify a pattern in the velocity mismatch that points at pinning points not present in the input geometry. We identify seven potential pinning points around Antarctica, for now uncharted, providing prominent resistance to the ice flow.
D. H. Jones and G. H. Gudmundsson
Nat. Hazards Earth Syst. Sci., 15, 1243–1250, https://doi.org/10.5194/nhess-15-1243-2015, https://doi.org/10.5194/nhess-15-1243-2015, 2015
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Icebergs are a natural hazard to maritime operations in polar regions. Iceberg populations are increasing, as is the demand for access to both Arctic and Antarctic seas. Soon the ability to reliably track icebergs may become a necessity for continued operational safety. In this paper we describe the design of a tracking sensor that can be deployed from an aircraft during surveys of Antarctic icebergs, and detail the results of its first deployment operation on iceberg B-31.
J. Krug, G. Durand, O. Gagliardini, and J. Weiss
The Cryosphere, 9, 989–1003, https://doi.org/10.5194/tc-9-989-2015, https://doi.org/10.5194/tc-9-989-2015, 2015
J. Wuite, H. Rott, M. Hetzenecker, D. Floricioiu, J. De Rydt, G. H. Gudmundsson, T. Nagler, and M. Kern
The Cryosphere, 9, 957–969, https://doi.org/10.5194/tc-9-957-2015, https://doi.org/10.5194/tc-9-957-2015, 2015
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We present new analysis of satellite data showing the variability of glacier velocities in the Larsen B area, Antarctic Peninsula, back to 1995. Velocity data and estimates of ice thickness are used to derive ice discharge at different epochs. Velocities of the glaciers remain to date well above the velocities of the pre-collapse period. The response of individual glaciers differs, and velocities show significant temporal fluctuations, implying major variations in ice discharge and mass balance.
C. Martín, R. Mulvaney, G. H. Gudmundsson, and H. Corr
Clim. Past, 11, 547–557, https://doi.org/10.5194/cp-11-547-2015, https://doi.org/10.5194/cp-11-547-2015, 2015
J. Krug, J. Weiss, O. Gagliardini, and G. Durand
The Cryosphere, 8, 2101–2117, https://doi.org/10.5194/tc-8-2101-2014, https://doi.org/10.5194/tc-8-2101-2014, 2014
S. H. R. Rosier, G. H. Gudmundsson, and J. A. M. Green
The Cryosphere, 8, 1763–1775, https://doi.org/10.5194/tc-8-1763-2014, https://doi.org/10.5194/tc-8-1763-2014, 2014
E. Le Meur, M. Sacchettini, S. Garambois, E. Berthier, A. S. Drouet, G. Durand, D. Young, J. S. Greenbaum, J. W. Holt, D. D. Blankenship, E. Rignot, J. Mouginot, Y. Gim, D. Kirchner, B. de Fleurian, O. Gagliardini, and F. Gillet-Chaulet
The Cryosphere, 8, 1331–1346, https://doi.org/10.5194/tc-8-1331-2014, https://doi.org/10.5194/tc-8-1331-2014, 2014
R. Anderson, D. H. Jones, and G. H. Gudmundsson
Nat. Hazards Earth Syst. Sci., 14, 917–927, https://doi.org/10.5194/nhess-14-917-2014, https://doi.org/10.5194/nhess-14-917-2014, 2014
J. Krug, J. Weiss, O. Gagliardini, and G. Durand
The Cryosphere Discuss., https://doi.org/10.5194/tcd-8-1111-2014, https://doi.org/10.5194/tcd-8-1111-2014, 2014
Preprint withdrawn
T. L. Edwards, X. Fettweis, O. Gagliardini, F. Gillet-Chaulet, H. Goelzer, J. M. Gregory, M. Hoffman, P. Huybrechts, A. J. Payne, M. Perego, S. Price, A. Quiquet, and C. Ritz
The Cryosphere, 8, 181–194, https://doi.org/10.5194/tc-8-181-2014, https://doi.org/10.5194/tc-8-181-2014, 2014
T. L. Edwards, X. Fettweis, O. Gagliardini, F. Gillet-Chaulet, H. Goelzer, J. M. Gregory, M. Hoffman, P. Huybrechts, A. J. Payne, M. Perego, S. Price, A. Quiquet, and C. Ritz
The Cryosphere, 8, 195–208, https://doi.org/10.5194/tc-8-195-2014, https://doi.org/10.5194/tc-8-195-2014, 2014
A. Legchenko, C. Vincent, J. M. Baltassat, J. F. Girard, E. Thibert, O. Gagliardini, M. Descloitres, A. Gilbert, S. Garambois, A. Chevalier, and H. Guyard
The Cryosphere, 8, 155–166, https://doi.org/10.5194/tc-8-155-2014, https://doi.org/10.5194/tc-8-155-2014, 2014
B. de Fleurian, O. Gagliardini, T. Zwinger, G. Durand, E. Le Meur, D. Mair, and P. Råback
The Cryosphere, 8, 137–153, https://doi.org/10.5194/tc-8-137-2014, https://doi.org/10.5194/tc-8-137-2014, 2014
O. Gagliardini, T. Zwinger, F. Gillet-Chaulet, G. Durand, L. Favier, B. de Fleurian, R. Greve, M. Malinen, C. Martín, P. Råback, J. Ruokolainen, M. Sacchettini, M. Schäfer, H. Seddik, and J. Thies
Geosci. Model Dev., 6, 1299–1318, https://doi.org/10.5194/gmd-6-1299-2013, https://doi.org/10.5194/gmd-6-1299-2013, 2013
G. H. Gudmundsson
The Cryosphere, 7, 647–655, https://doi.org/10.5194/tc-7-647-2013, https://doi.org/10.5194/tc-7-647-2013, 2013
V. Favier, C. Agosta, S. Parouty, G. Durand, G. Delaygue, H. Gallée, A.-S. Drouet, A. Trouvilliez, and G. Krinner
The Cryosphere, 7, 583–597, https://doi.org/10.5194/tc-7-583-2013, https://doi.org/10.5194/tc-7-583-2013, 2013
A. S. Drouet, D. Docquier, G. Durand, R. Hindmarsh, F. Pattyn, O. Gagliardini, and T. Zwinger
The Cryosphere, 7, 395–406, https://doi.org/10.5194/tc-7-395-2013, https://doi.org/10.5194/tc-7-395-2013, 2013
J. De Rydt, G. H. Gudmundsson, H. F. J. Corr, and P. Christoffersen
The Cryosphere, 7, 407–417, https://doi.org/10.5194/tc-7-407-2013, https://doi.org/10.5194/tc-7-407-2013, 2013
F. Gillet-Chaulet, O. Gagliardini, H. Seddik, M. Nodet, G. Durand, C. Ritz, T. Zwinger, R. Greve, and D. G. Vaughan
The Cryosphere, 6, 1561–1576, https://doi.org/10.5194/tc-6-1561-2012, https://doi.org/10.5194/tc-6-1561-2012, 2012
Related subject area
Numerical Modelling
A data exploration tool for averaging and accessing large data sets of snow stratigraphy profiles useful for avalanche forecasting
Sea ice floe size: its impact on pan-Arctic and local ice mass and required model complexity
Land–atmosphere interactions in sub-polar and alpine climates in the CORDEX flagship pilot study Land Use and Climate Across Scales (LUCAS) models – Part 1: Evaluation of the snow-albedo effect
Impact of runoff temporal distribution on ice dynamics
Can changes in deformation regimes be inferred from crystallographic preferred orientations in polar ice?
Stabilizing effect of mélange buttressing on the marine ice-cliff instability of the West Antarctic Ice Sheet
A probabilistic seabed–ice keel interaction model
Modelling supraglacial debris-cover evolution from the single-glacier to the regional scale: an application to High Mountain Asia
The effect of changing sea ice on wave climate trends along Alaska's central Beaufort Sea coast
Strong increase in thawing of subsea permafrost in the 22nd century caused by anthropogenic climate change
Arctic sea ice anomalies during the MOSAiC winter 2019/20
Effective coefficient of diffusion and permeability of firn at Dome C and Lock In, Antarctica, and of various snow types – estimates over the 100–850 kg m−3 density range
Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes
The instantaneous impact of calving and thinning on the Larsen C Ice Shelf
Derivation of bedrock topography measurement requirements for the reduction of uncertainty in ice-sheet model projections of Thwaites Glacier
A comparison of the stability and performance of depth-integrated ice-dynamics solvers
A new vertically integrated MOno-Layer Higher-Order (MOLHO) ice flow model
On the contribution of grain boundary sliding type creep to firn densification – an assessment using an optimization approach
Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes
Evaluation of six geothermal heat flux maps for the Antarctic Lambert-Amery glacial system
Assessment of neutrons from secondary cosmic rays at mountain altitudes – Geant4 simulations of environmental parameters including soil moisture and snow cover
A seasonal algorithm of the snow-covered area fraction for mountainous terrain
Edge displacement scores
The 21st-century fate of the Mocho-Choshuenco ice cap in southern Chile
Lateral thermokarst patterns in permafrost peat plateaus in northern Norway
Modelling steady states and the transient response of debris-covered glaciers
Marine ice sheet experiments with the Community Ice Sheet Model
Twentieth century global glacier mass change: an ensemble-based model reconstruction
A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation
The transferability of adjoint inversion products between different ice flow models
Inferring the basal sliding coefficient field for the Stokes ice sheet model under rheological uncertainty
The tipping points and early warning indicators for Pine Island Glacier, West Antarctica
Effects of multi-scale heterogeneity on the simulated evolution of ice-rich permafrost lowlands under a warming climate
Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations
Snow cover duration trends observed at sites and predicted by multiple models
Mapping the age of ice of Gauligletscher combining surface radionuclide contamination and ice flow modeling
Modelling the evolution of Djankuat Glacier, North Caucasus, from 1752 until 2100 CE
Quantifying the effect of ocean bed properties on ice sheet geometry over 40 000 years with a full-Stokes model
Toward a method for downscaling sea ice pressure for navigation purposes
Deep ice layer formation in an alpine snowpack: monitoring and modeling
Forty-year Simulations of Firn Processes over the Greenland and Antarctic Ice Sheets
Brief communication: Time step dependence (and fixes) in Stokes simulations of calving ice shelves
Modelling regional glacier length changes over the last millennium using the Open Global Glacier Model
Evaluating permafrost physics in the Coupled Model Intercomparison Project 6 (CMIP6) models and their sensitivity to climate change
Bayesian calibration of firn densification models
A kinematic formalism for tracking ice–ocean mass exchange on the Earth's surface and estimating sea-level change
The contrasting response of outlet glaciers to interior and ocean forcing
The Arctic Ocean Observation Operator for 6.9 GHz (ARC3O) – Part 1: How to obtain sea ice brightness temperatures at 6.9 GHz from climate model output
The Arctic Ocean Observation Operator for 6.9 GHz (ARC3O) – Part 2: Development and evaluation
Results of the third Marine Ice Sheet Model Intercomparison Project (MISMIP+)
Florian Herla, Pascal Haegeli, and Patrick Mair
The Cryosphere, 16, 3149–3162, https://doi.org/10.5194/tc-16-3149-2022, https://doi.org/10.5194/tc-16-3149-2022, 2022
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We present an averaging algorithm for multidimensional snow stratigraphy profiles that elicits the predominant snow layering among large numbers of profiles and allows for compiling of informative summary statistics and distributions of snowpack layer properties. This creates new opportunities for presenting and analyzing operational snowpack simulations in support of avalanche forecasting and may inspire new ways of processing profiles and time series in other geophysical contexts.
Adam William Bateson, Daniel L. Feltham, David Schröder, Yanan Wang, Byongjun Hwang, Jeff K. Ridley, and Yevgeny Aksenov
The Cryosphere, 16, 2565–2593, https://doi.org/10.5194/tc-16-2565-2022, https://doi.org/10.5194/tc-16-2565-2022, 2022
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Numerical models are used to understand the mechanisms that drive the evolution of the Arctic sea ice cover. The sea ice cover is formed of pieces of ice called floes. Several recent studies have proposed variable floe size models to replace the standard model assumption of a fixed floe size. In this study we show the need to include floe fragmentation processes in these variable floe size models and demonstrate that model design can determine the impact of floe size on size ice evolution.
Anne Sophie Daloz, Clemens Schwingshackl, Priscilla Mooney, Susanna Strada, Diana Rechid, Edouard L. Davin, Eleni Katragkou, Nathalie de Noblet-Ducoudré, Michal Belda, Tomas Halenka, Marcus Breil, Rita M. Cardoso, Peter Hoffmann, Daniela C. A. Lima, Ronny Meier, Pedro M. M. Soares, Giannis Sofiadis, Gustav Strandberg, Merja H. Toelle, and Marianne T. Lund
The Cryosphere, 16, 2403–2419, https://doi.org/10.5194/tc-16-2403-2022, https://doi.org/10.5194/tc-16-2403-2022, 2022
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Snow plays a major role in the regulation of the Earth's surface temperature. Together with climate change, rising temperatures are already altering snow in many ways. In this context, it is crucial to better understand the ability of climate models to represent snow and snow processes. This work focuses on Europe and shows that the melting season in spring still represents a challenge for climate models and that more work is needed to accurately simulate snow–atmosphere interactions.
Basile de Fleurian, Richard Davy, and Petra M. Langebroek
The Cryosphere, 16, 2265–2283, https://doi.org/10.5194/tc-16-2265-2022, https://doi.org/10.5194/tc-16-2265-2022, 2022
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As temperature increases, more snow and ice melt at the surface of ice sheets. Here we use an ice dynamics and subglacial hydrology model with simplified geometry and climate forcing to study the impact of variations in meltwater on ice dynamics. We focus on the variations in length and intensity of the melt season. Our results show that a longer melt season leads to faster glaciers, but a more intense melt season reduces glaciers' seasonal velocities, albeit leading to higher peak velocities.
Maria-Gema Llorens, Albert Griera, Paul D. Bons, Ilka Weikusat, David J. Prior, Enrique Gomez-Rivas, Tamara de Riese, Ivone Jimenez-Munt, Daniel García-Castellanos, and Ricardo A. Lebensohn
The Cryosphere, 16, 2009–2024, https://doi.org/10.5194/tc-16-2009-2022, https://doi.org/10.5194/tc-16-2009-2022, 2022
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Polar ice is formed by ice crystals, which form fabrics that are utilised to interpret how ice sheets flow. It is unclear whether fabrics result from the current flow regime or if they are inherited. To understand the extent to which ice crystals can be reoriented when ice flow conditions change, we simulate and evaluate multi-stage ice flow scenarios according to natural cases. We find that second deformation regimes normally overprint inherited fabrics, with a range of transitional fabrics.
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.
Frédéric Dupont, Dany Dumont, Jean-François Lemieux, Elie Dumas-Lefebvre, and Alain Caya
The Cryosphere, 16, 1963–1977, https://doi.org/10.5194/tc-16-1963-2022, https://doi.org/10.5194/tc-16-1963-2022, 2022
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In some shallow seas, grounded ice ridges contribute to stabilizing and maintaining a landfast ice cover. A scheme has already proposed where the keel thickness varies linearly with the mean thickness. Here, we extend the approach by taking into account the ice thickness and bathymetry distributions. The probabilistic approach shows a reasonably good agreement with observations and previous grounding scheme while potentially offering more physical insights into the formation of landfast ice.
Loris Compagno, Matthias Huss, Evan Stewart Miles, Michael James McCarthy, Harry Zekollari, Amaury Dehecq, Francesca Pellicciotti, and Daniel Farinotti
The Cryosphere, 16, 1697–1718, https://doi.org/10.5194/tc-16-1697-2022, https://doi.org/10.5194/tc-16-1697-2022, 2022
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We present a new approach for modelling debris area and thickness evolution. We implement the module into a combined mass-balance ice-flow model, and we apply it using different climate scenarios to project the future evolution of all glaciers in High Mountain Asia. We show that glacier geometry, volume, and flow velocity evolve differently when modelling explicitly debris cover compared to glacier evolution without the debris-cover module, demonstrating the importance of accounting for debris.
Kees Nederhoff, Li Erikson, Anita Engelstad, Peter Bieniek, and Jeremy Kasper
The Cryosphere, 16, 1609–1629, https://doi.org/10.5194/tc-16-1609-2022, https://doi.org/10.5194/tc-16-1609-2022, 2022
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Diminishing sea ice is impacting waves across the Arctic region. Recent work shows the effect of the sea ice on offshore waves; however, effects within the nearshore are less known. This study characterizes the wave climate in the central Beaufort Sea coast of Alaska. We show that the reduction of sea ice correlates strongly with increases in the average and extreme waves. However, found trends deviate from offshore, since part of the increase in energy is dissipated before reaching the shore.
Stiig Wilkenskjeld, Frederieke Miesner, Paul P. Overduin, Matteo Puglini, and Victor Brovkin
The Cryosphere, 16, 1057–1069, https://doi.org/10.5194/tc-16-1057-2022, https://doi.org/10.5194/tc-16-1057-2022, 2022
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Thawing permafrost releases carbon to the atmosphere, enhancing global warming. Part of the permafrost soils have been flooded by rising sea levels since the last ice age, becoming subsea permafrost (SSPF). The SSPF is less studied than the part on land. In this study we use a global model to obtain rates of thawing of SSPF under different future climate scenarios until the year 3000. After the year 2100 the scenarios strongly diverge, closely connected to the eventual disappearance of sea ice.
Klaus Dethloff, Wieslaw Maslowski, Stefan Hendricks, Younjoo J. Lee, Helge F. Goessling, Thomas Krumpen, Christian Haas, Dörthe Handorf, Robert Ricker, Vladimir Bessonov, John J. Cassano, Jaclyn Clement Kinney, Robert Osinski, Markus Rex, Annette Rinke, Julia Sokolova, and Anja Sommerfeld
The Cryosphere, 16, 981–1005, https://doi.org/10.5194/tc-16-981-2022, https://doi.org/10.5194/tc-16-981-2022, 2022
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Sea ice thickness anomalies during the MOSAiC (Multidisciplinary drifting Observatory for the Study of Arctic Climate) winter in January, February and March 2020 were simulated with the coupled Regional Arctic climate System Model (RASM) and compared with CryoSat-2/SMOS satellite data. Hindcast and ensemble simulations indicate that the sea ice anomalies are driven by nonlinear interactions between ice growth processes and wind-driven sea-ice transports, with dynamics playing a dominant role.
Neige Calonne, Alexis Burr, Armelle Philip, Frédéric Flin, and Christian Geindreau
The Cryosphere, 16, 967–980, https://doi.org/10.5194/tc-16-967-2022, https://doi.org/10.5194/tc-16-967-2022, 2022
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Modeling gas transport in ice sheets from surface to close-off is key to interpreting climate archives. Estimates of the diffusion coefficient and permeability of snow and firn are required but remain a large source of uncertainty. We present a new dataset of diffusion coefficients and permeability from 20 to 120 m depth at two Antarctic sites. We suggest predictive formulas to estimate both properties over the entire 100–850 kg m3 density range, i.e., anywhere within the ice sheet column.
Konstantin Schürholt, Julia Kowalski, and Henning Löwe
The Cryosphere, 16, 903–923, https://doi.org/10.5194/tc-16-903-2022, https://doi.org/10.5194/tc-16-903-2022, 2022
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This companion paper deals with numerical particularities of partial differential equations underlying 1D snow models. In this first part we neglect mechanical settling and demonstrate that the nonlinear coupling between diffusive transport (heat and vapor), phase changes and ice mass conservation contains a wave instability that may be relevant for weak layer formation. Numerical requirements are discussed in view of the underlying homogenization scheme.
Tom Mitcham, G. Hilmar Gudmundsson, and Jonathan L. Bamber
The Cryosphere, 16, 883–901, https://doi.org/10.5194/tc-16-883-2022, https://doi.org/10.5194/tc-16-883-2022, 2022
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We modelled the response of the Larsen C Ice Shelf (LCIS) and its tributary glaciers to the calving of the A68 iceberg and validated our results with observations. We found that the impact was limited, confirming that mostly passive ice was calved. Through further calving experiments we quantified the total buttressing provided by the LCIS and found that over 80 % of the buttressing capacity is generated in the first 5 km of the ice shelf downstream of the grounding line.
Blake A. Castleman, Nicole-Jeanne Schlegel, Lambert Caron, Eric Larour, and Ala Khazendar
The Cryosphere, 16, 761–778, https://doi.org/10.5194/tc-16-761-2022, https://doi.org/10.5194/tc-16-761-2022, 2022
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In the described study, we derive an uncertainty range for global mean sea level rise (SLR) contribution from Thwaites Glacier in a 200-year period under an extreme ocean warming scenario. We derive the spatial and vertical resolutions needed for bedrock data acquisition missions in order to limit global mean SLR contribution from Thwaites Glacier to ±2 cm in a 200-year period. We conduct sensitivity experiments in order to present the locations of critical regions in need of accurate mapping.
Alexander Robinson, Daniel Goldberg, and William H. Lipscomb
The Cryosphere, 16, 689–709, https://doi.org/10.5194/tc-16-689-2022, https://doi.org/10.5194/tc-16-689-2022, 2022
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Here we investigate the numerical stability of several commonly used methods in order to determine which of them are capable of resolving the complex physics of the ice flow and are also computationally efficient. We find that the so-called DIVA solver outperforms the others. Its representation of the physics is consistent with more complex methods, while it remains computationally efficient at high resolution.
Thiago Dias dos Santos, Mathieu Morlighem, and Douglas Brinkerhoff
The Cryosphere, 16, 179–195, https://doi.org/10.5194/tc-16-179-2022, https://doi.org/10.5194/tc-16-179-2022, 2022
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Projecting the future evolution of Greenland and Antarctica and their potential contribution to sea level rise often relies on computer simulations carried out by numerical ice sheet models. Here we present a new vertically integrated ice sheet model and assess its performance using different benchmarks. The new model shows results comparable to a three-dimensional model at relatively lower computational cost, suggesting that it is an excellent alternative for long-term simulations.
Timm Schultz, Ralf Müller, Dietmar Gross, and Angelika Humbert
The Cryosphere, 16, 143–158, https://doi.org/10.5194/tc-16-143-2022, https://doi.org/10.5194/tc-16-143-2022, 2022
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Firn is the interstage product between snow and ice. Simulations describing the process of firn densification are used in the context of estimating mass changes of the ice sheets and past climate reconstructions. The first stage of firn densification takes place in the upper few meters of the firn column. We investigate how well a material law describing the process of grain boundary sliding works for the numerical simulation of firn densification in this stage.
Anna Simson, Henning Löwe, and Julia Kowalski
The Cryosphere, 15, 5423–5445, https://doi.org/10.5194/tc-15-5423-2021, https://doi.org/10.5194/tc-15-5423-2021, 2021
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This companion paper deals with numerical particularities of partial differential equations underlying one-dimensional snow models. In this second part we include mechanical settling and develop a new hybrid (Eulerian–Lagrangian) method for solving the advection-dominated ice mass conservation on a moving mesh alongside Eulerian diffusion (heat and vapor) and phase changes. The scheme facilitates a modular and extendable solver strategy while retaining controls on numerical accuracy.
Haoran Kang, Liyun Zhao, Michael Wolovick, and John C. Moore
The Cryosphere Discuss., https://doi.org/10.5194/tc-2021-357, https://doi.org/10.5194/tc-2021-357, 2021
Revised manuscript accepted for TC
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Basal thermal conditions are important to ice dynamics, and sensitive to geothermal heat flux (GHF). We estimate basal thermal conditions of the Lambert-Amery glacier system with six GHFs. The two most-recent GHFs inverted from aerial geomagnetic observations produce a larger warm-based area, and match the observed subglacial lakes better than the other GHFs. The modelled basal melt rate is ten to hundreds of mm per year in fast flowing glaciers feeding Amery ice shelf, and smaller inland.
Thomas Brall, Vladimir Mares, Rolf Bütikofer, and Werner Rühm
The Cryosphere, 15, 4769–4780, https://doi.org/10.5194/tc-15-4769-2021, https://doi.org/10.5194/tc-15-4769-2021, 2021
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Neutrons from secondary cosmic rays, measured at 2660 m a.s.l. at Zugspitze, Germany, are highly affected by the environment, in particular by snow, soil moisture, and mountain shielding. To quantify these effects, computer simulations were carried out, including a sensitivity analysis on snow depth and soil moisture. This provides a possibility for snow depth estimation based on the measured number of secondary neutrons. This method was applied at Zugspitze in 2018.
Nora Helbig, Michael Schirmer, Jan Magnusson, Flavia Mäder, Alec van Herwijnen, Louis Quéno, Yves Bühler, Jeff S. Deems, and Simon Gascoin
The Cryosphere, 15, 4607–4624, https://doi.org/10.5194/tc-15-4607-2021, https://doi.org/10.5194/tc-15-4607-2021, 2021
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The snow cover spatial variability in mountains changes considerably over the course of a snow season. In applications such as weather, climate and hydrological predictions the fractional snow-covered area is therefore an essential parameter characterizing how much of the ground surface in a grid cell is currently covered by snow. We present a seasonal algorithm and a spatiotemporal evaluation suggesting that the algorithm can be applied in other geographic regions by any snow model application.
Arne Melsom
The Cryosphere, 15, 3785–3796, https://doi.org/10.5194/tc-15-3785-2021, https://doi.org/10.5194/tc-15-3785-2021, 2021
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This study presents new methods to assess how well observations of sea ice expansion are reproduced by results from models. The aim is to provide information about the quality of forecasts for changes in the sea ice extent to operators in or near ice-infested waters. A test using 2 years of model results demonstrates the practical applicability and usefulness of the methods that are presented.
Matthias Scheiter, Marius Schaefer, Eduardo Flández, Deniz Bozkurt, and Ralf Greve
The Cryosphere, 15, 3637–3654, https://doi.org/10.5194/tc-15-3637-2021, https://doi.org/10.5194/tc-15-3637-2021, 2021
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We simulate the current state and future evolution of the Mocho-Choshuenco ice cap in southern Chile (40°S, 72°W) with the ice-sheet model SICOPOLIS. Under different global warming scenarios, we project ice mass losses between 56 % and 97 % by the end of the 21st century. We quantify the uncertainties based on an ensemble of climate models and on the temperature dependence of the equilibrium line altitude. Our results suggest a considerable deglaciation in southern Chile in the next 80 years.
Léo C. P. Martin, Jan Nitzbon, Johanna Scheer, Kjetil S. Aas, Trond Eiken, Moritz Langer, Simon Filhol, Bernd Etzelmüller, and Sebastian Westermann
The Cryosphere, 15, 3423–3442, https://doi.org/10.5194/tc-15-3423-2021, https://doi.org/10.5194/tc-15-3423-2021, 2021
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It is important to understand how permafrost landscapes respond to climate changes because their thaw can contribute to global warming. We investigate how a common permafrost morphology degrades using both field observations of the surface elevation and numerical modeling. We show that numerical models accounting for topographic changes related to permafrost degradation can reproduce the observed changes in nature and help us understand how parameters such as snow influence this phenomenon.
James C. Ferguson and Andreas Vieli
The Cryosphere, 15, 3377–3399, https://doi.org/10.5194/tc-15-3377-2021, https://doi.org/10.5194/tc-15-3377-2021, 2021
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Debris-covered glaciers have a greater extent than their debris-free counterparts due to insulation from the debris cover. However, the transient response to climate change remains poorly understood. We use a numerical model that couples ice dynamics and debris transport and varies the climate signal. We find that debris cover delays the transient response, especially for the extent. However, adding cryokarst features near the terminus greatly enhances the response.
Gunter R. Leguy, William H. Lipscomb, and Xylar S. Asay-Davis
The Cryosphere, 15, 3229–3253, https://doi.org/10.5194/tc-15-3229-2021, https://doi.org/10.5194/tc-15-3229-2021, 2021
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We present numerical features of the Community Ice Sheet Model in representing ocean termini glaciers. Using idealized test cases, we show that applying melt in a partly grounded cell is beneficial, in contrast to recent studies. We confirm that parameterizing partly grounded cells yields accurate ice sheet representation at a grid resolution of ~2 km (arguably 4 km), allowing ice sheet simulations at a continental scale. The choice of basal friction law also influences the ice flow.
Jan-Hendrik Malles and Ben Marzeion
The Cryosphere, 15, 3135–3157, https://doi.org/10.5194/tc-15-3135-2021, https://doi.org/10.5194/tc-15-3135-2021, 2021
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To better estimate the uncertainty in glacier mass change modeling during the 20th century we ran an established model with an ensemble of meteorological data sets. We find that the total ensemble uncertainty, especially in the early 20th century, when glaciological and meteorological observations at glacier locations were sparse, increases considerably compared to individual ensemble runs. This stems from regions with a lot of ice mass but few observations (e.g., Greenland periphery).
Niccolò Tubini, Stephan Gruber, and Riccardo Rigon
The Cryosphere, 15, 2541–2568, https://doi.org/10.5194/tc-15-2541-2021, https://doi.org/10.5194/tc-15-2541-2021, 2021
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We present a new method to compute temperature changes with melting and freezing – a fundamental challenge in cryosphere research – extremely efficiently and with guaranteed correctness of the energy balance for any time step size. This is a key feature since the integration time step can then be chosen according to the timescale of the processes to be studied, from seconds to days.
Jowan M. Barnes, Thiago Dias dos Santos, Daniel Goldberg, G. Hilmar Gudmundsson, Mathieu Morlighem, and Jan De Rydt
The Cryosphere, 15, 1975–2000, https://doi.org/10.5194/tc-15-1975-2021, https://doi.org/10.5194/tc-15-1975-2021, 2021
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Some properties of ice flow models must be initialised using observed data before they can be used to produce reliable predictions of the future. Different models have different ways of doing this, and the process is generally seen as being specific to an individual model. We compare the methods used by three different models and show that they produce similar outputs. We also demonstrate that the outputs from one model can be used in other models without introducing large uncertainties.
Olalekan Babaniyi, Ruanui Nicholson, Umberto Villa, and Noémi Petra
The Cryosphere, 15, 1731–1750, https://doi.org/10.5194/tc-15-1731-2021, https://doi.org/10.5194/tc-15-1731-2021, 2021
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We consider the problem of inferring unknown parameter fields under additional uncertainty for an ice sheet model from synthetic surface ice flow velocity measurements. Our results indicate that accounting for model uncertainty stemming from the presence of nuisance parameters is crucial. Namely our findings suggest that using nominal values for these parameters, as is often done in practice, without taking into account the resulting modeling error can lead to overconfident and biased results.
Sebastian H. R. Rosier, Ronja Reese, Jonathan F. Donges, Jan De Rydt, G. Hilmar Gudmundsson, and Ricarda Winkelmann
The Cryosphere, 15, 1501–1516, https://doi.org/10.5194/tc-15-1501-2021, https://doi.org/10.5194/tc-15-1501-2021, 2021
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Pine Island Glacier has contributed more to sea-level rise over the past decades than any other glacier in Antarctica. Ice-flow modelling studies have shown that it can undergo periods of rapid mass loss, but no study has shown that these future changes could cross a tipping point and therefore be effectively irreversible. Here, we assess the stability of Pine Island Glacier, quantifying the changes in ocean temperatures required to cross future tipping points using statistical methods.
Jan Nitzbon, Moritz Langer, Léo C. P. Martin, Sebastian Westermann, Thomas Schneider von Deimling, and Julia Boike
The Cryosphere, 15, 1399–1422, https://doi.org/10.5194/tc-15-1399-2021, https://doi.org/10.5194/tc-15-1399-2021, 2021
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We used a numerical model to investigate how small-scale landscape heterogeneities affect permafrost thaw under climate-warming scenarios. Our results show that representing small-scale heterogeneities in the model can decide whether a landscape is water-logged or well-drained in the future. This in turn affects how fast permafrost thaws under warming. Our research emphasizes the importance of considering small-scale processes in model assessments of permafrost thaw under climate change.
Gong Cheng, Nina Kirchner, and Per Lötstedt
The Cryosphere, 15, 715–742, https://doi.org/10.5194/tc-15-715-2021, https://doi.org/10.5194/tc-15-715-2021, 2021
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We present an inverse modeling approach to improve the understanding of spatiotemporally variable processes at the inaccessible base of an ice sheet by determining the sensitivity of direct surface observations to perturbations of basal conditions. Time dependency is proved to be important in these types of problems. The effect of perturbations is analyzed based on analytical and numerical solutions.
Richard Essery, Hyungjun Kim, Libo Wang, Paul Bartlett, Aaron Boone, Claire Brutel-Vuilmet, Eleanor Burke, Matthias Cuntz, Bertrand Decharme, Emanuel Dutra, Xing Fang, Yeugeniy Gusev, Stefan Hagemann, Vanessa Haverd, Anna Kontu, Gerhard Krinner, Matthieu Lafaysse, Yves Lejeune, Thomas Marke, Danny Marks, Christoph Marty, Cecile B. Menard, Olga Nasonova, Tomoko Nitta, John Pomeroy, Gerd Schädler, Vladimir Semenov, Tatiana Smirnova, Sean Swenson, Dmitry Turkov, Nander Wever, and Hua Yuan
The Cryosphere, 14, 4687–4698, https://doi.org/10.5194/tc-14-4687-2020, https://doi.org/10.5194/tc-14-4687-2020, 2020
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Climate models are uncertain in predicting how warming changes snow cover. This paper compares 22 snow models with the same meteorological inputs. Predicted trends agree with observations at four snow research sites: winter snow cover does not start later, but snow now melts earlier in spring than in the 1980s at two of the sites. Cold regions where snow can last until late summer are predicted to be particularly sensitive to warming because the snow then melts faster at warmer times of year.
Guillaume Jouvet, Stefan Röllin, Hans Sahli, José Corcho, Lars Gnägi, Loris Compagno, Dominik Sidler, Margit Schwikowski, Andreas Bauder, and Martin Funk
The Cryosphere, 14, 4233–4251, https://doi.org/10.5194/tc-14-4233-2020, https://doi.org/10.5194/tc-14-4233-2020, 2020
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We show that plutonium is an effective tracer to identify ice originating from the early 1960s at the surface of a mountain glacier after a long time within the ice flow, giving unique information on the long-term former ice motion. Combined with ice flow modelling, the dating can be extended to the entire glacier, and we show that an airplane which crash-landed on the Gauligletscher in 1946 will likely soon be released from the ice close to the place where pieces have emerged in recent years.
Yoni Verhaegen, Philippe Huybrechts, Oleg Rybak, and Victor V. Popovnin
The Cryosphere, 14, 4039–4061, https://doi.org/10.5194/tc-14-4039-2020, https://doi.org/10.5194/tc-14-4039-2020, 2020
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We use a numerical flow model to simulate the behaviour of the Djankuat Glacier, a WGMS reference glacier situated in the North Caucasus (Republic of Kabardino-Balkaria, Russian Federation), in response to past, present and future climate conditions (1752–2100 CE). In particular, we adapt a more sophisticated and physically based debris model, which has not been previously applied in time-dependent numerical flow line models, to look at the impact of a debris cover on the glacier’s evolution.
Clemens Schannwell, Reinhard Drews, Todd A. Ehlers, Olaf Eisen, Christoph Mayer, Mika Malinen, Emma C. Smith, and Hannes Eisermann
The Cryosphere, 14, 3917–3934, https://doi.org/10.5194/tc-14-3917-2020, https://doi.org/10.5194/tc-14-3917-2020, 2020
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To reduce uncertainties associated with sea level rise projections, an accurate representation of ice flow is paramount. Most ice sheet models rely on simplified versions of the underlying ice flow equations. Due to the high computational costs, ice sheet models based on the complete ice flow equations have been restricted to < 1000 years. Here, we present a new model setup that extends the applicability of such models by an order of magnitude, permitting simulations of 40 000 years.
Jean-François Lemieux, L. Bruno Tremblay, and Mathieu Plante
The Cryosphere, 14, 3465–3478, https://doi.org/10.5194/tc-14-3465-2020, https://doi.org/10.5194/tc-14-3465-2020, 2020
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Sea ice pressure poses great risk for navigation; it can lead to ship besetting and damages. Sea ice forecasting systems can predict the evolution of pressure. However, these systems have low spatial resolution (a few km) compared to the dimensions of ships. We study the downscaling of pressure from the km-scale to scales relevant for navigation. We find that the pressure applied on a ship beset in heavy ice conditions can be markedly larger than the pressure predicted by the forecasting system.
Louis Quéno, Charles Fierz, Alec van Herwijnen, Dylan Longridge, and Nander Wever
The Cryosphere, 14, 3449–3464, https://doi.org/10.5194/tc-14-3449-2020, https://doi.org/10.5194/tc-14-3449-2020, 2020
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Deep ice layers may form in the snowpack due to preferential water flow with impacts on the snowpack mechanical, hydrological and thermodynamical properties. We studied their formation and evolution at a high-altitude alpine site, combining a comprehensive observation dataset at a daily frequency (with traditional snowpack observations, penetration resistance and radar measurements) and detailed snowpack modeling, including a new parameterization of ice formation in the 1-D SNOWPACK model.
Brooke Medley, Thomas A. Neumann, H. Jay Zwally, and Benjamin E. Smith
The Cryosphere Discuss., https://doi.org/10.5194/tc-2020-266, https://doi.org/10.5194/tc-2020-266, 2020
Revised manuscript accepted for TC
Brandon Berg and Jeremy Bassis
The Cryosphere, 14, 3209–3213, https://doi.org/10.5194/tc-14-3209-2020, https://doi.org/10.5194/tc-14-3209-2020, 2020
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Computer models of ice sheets and glaciers are an important component of projecting sea level rise due to climate change. For models that seek to simulate the full balance of forces within the ice, if portions of the glacier are allowed to quickly break off in a process called iceberg calving, a numerical issue arises that can cause inaccurate results. We examine the issue and propose a solution so that future models can more accurately predict the future behavior of ice sheets and glaciers.
David Parkes and Hugues Goosse
The Cryosphere, 14, 3135–3153, https://doi.org/10.5194/tc-14-3135-2020, https://doi.org/10.5194/tc-14-3135-2020, 2020
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Direct records of glacier changes rarely go back more than the last 100 years and are few and far between. We used a sophisticated glacier model to simulate glacier length changes over the last 1000 years for those glaciers that we do have long-term records of, to determine whether the model can run in a stable, realistic way over a long timescale, reproducing recent observed trends. We find that post-industrial changes are larger than other changes in this time period driven by recent warming.
Eleanor J. Burke, Yu Zhang, and Gerhard Krinner
The Cryosphere, 14, 3155–3174, https://doi.org/10.5194/tc-14-3155-2020, https://doi.org/10.5194/tc-14-3155-2020, 2020
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Permafrost will degrade under future climate change. This will have implications locally for the northern high-latitude regions and may well also amplify global climate change. There have been some recent improvements in the ability of earth system models to simulate the permafrost physical state, but further model developments are required. Models project the thawed volume of soil in the top 2 m of permafrost will increase by 10 %–40 % °C−1 of global mean surface air temperature increase.
Vincent Verjans, Amber A. Leeson, Christopher Nemeth, C. Max Stevens, Peter Kuipers Munneke, Brice Noël, and Jan Melchior van Wessem
The Cryosphere, 14, 3017–3032, https://doi.org/10.5194/tc-14-3017-2020, https://doi.org/10.5194/tc-14-3017-2020, 2020
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Ice sheets are covered by a firn layer, which is the transition stage between fresh snow and ice. Accurate modelling of firn density properties is important in many glaciological aspects. Current models show disagreements, are mostly calibrated to match specific observations of firn density and lack thorough uncertainty analysis. We use a novel calibration method for firn models based on a Bayesian statistical framework, which results in improved model accuracy and in uncertainty evaluation.
Surendra Adhikari, Erik R. Ivins, Eric Larour, Lambert Caron, and Helene Seroussi
The Cryosphere, 14, 2819–2833, https://doi.org/10.5194/tc-14-2819-2020, https://doi.org/10.5194/tc-14-2819-2020, 2020
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The mathematical formalism presented in this paper aims at simplifying computational strategies for tracking ice–ocean mass exchange in the Earth system. To this end, we define a set of generic, and quite simple, descriptions of evolving land, ocean and ice interfaces and present a unified method to compute the sea-level contribution of evolving ice sheets. The formalism can be applied to arbitrary geometries and at all timescales.
John Erich Christian, Alexander A. Robel, Cristian Proistosescu, Gerard Roe, Michelle Koutnik, and Knut Christianson
The Cryosphere, 14, 2515–2535, https://doi.org/10.5194/tc-14-2515-2020, https://doi.org/10.5194/tc-14-2515-2020, 2020
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We use simple, physics-based models to compare how marine-terminating glaciers respond to changes at their marine margin vs. inland surface melt. Initial glacier retreat is more rapid for ocean changes than for inland changes, but in both cases, glaciers will continue responding for millennia. We analyze several implications of these differing pathways of change. In particular, natural ocean variability must be better understood to correctly identify the anthropogenic role in glacier retreat.
Clara Burgard, Dirk Notz, Leif T. Pedersen, and Rasmus T. Tonboe
The Cryosphere, 14, 2369–2386, https://doi.org/10.5194/tc-14-2369-2020, https://doi.org/10.5194/tc-14-2369-2020, 2020
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The high disagreement between observations of Arctic sea ice makes it difficult to evaluate climate models with observations. We investigate the possibility of translating the model state into what a satellite could observe. We find that we do not need complex information about the vertical distribution of temperature and salinity inside the ice but instead are able to assume simplified distributions to reasonably translate the simulated sea ice into satellite
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Clara Burgard, Dirk Notz, Leif T. Pedersen, and Rasmus T. Tonboe
The Cryosphere, 14, 2387–2407, https://doi.org/10.5194/tc-14-2387-2020, https://doi.org/10.5194/tc-14-2387-2020, 2020
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The high disagreement between observations of Arctic sea ice inhibits the evaluation of climate models with observations. We develop a tool that translates the simulated Arctic Ocean state into what a satellite could observe from space in the form of brightness temperatures, a measure for the radiation emitted by the surface. We find that the simulated brightness temperatures compare well with the observed brightness temperatures. This tool brings a new perspective for climate model evaluation.
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.
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