Articles | Volume 7, issue 4
https://doi.org/10.5194/tc-7-1161-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/tc-7-1161-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
25 Jul 2013
Research article |
| 25 Jul 2013
Data assimilation and prognostic whole ice sheet modelling with the variationally derived, higher order, open source, and fully parallel ice sheet model VarGlaS
D. J. Brinkerhoff
University of Montana, Missoula, MT, USA
J. V. Johnson
University of Montana, Missoula, MT, USA
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Douglas J. Brinkerhoff, Brandon S. Tober, Michael Daniel, Victor Devaux-Chupin, Michael S. Christoffersen, John W. Holt, Christopher F. Larsen, Mark Fahnestock, Michael G. Loso, Kristin M. F. Timm, Russell C. Mitchell, and Martin Truffer
The Cryosphere, 19, 2321–2353, https://doi.org/10.5194/tc-19-2321-2025, https://doi.org/10.5194/tc-19-2321-2025, 2025
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Sít' Tlein is one of the largest glaciers in the world outside of the polar regions, and we know that it has been rapidly thinning. To forecast how this glacier will change in the future, we combine a computer model of ice flow with measurements from many different sources. Our model tells us that with high probability, Sít' Tlein's lower reaches are going to disappear in the next century and a half, creating a new bay or lake along Alaska's coastline.
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.
Andy Aschwanden, Timothy C. Bartholomaus, Douglas J. Brinkerhoff, and Martin Truffer
The Cryosphere, 15, 5705–5715, https://doi.org/10.5194/tc-15-5705-2021, https://doi.org/10.5194/tc-15-5705-2021, 2021
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Estimating how much ice loss from Greenland and Antarctica will contribute to sea level rise is of critical societal importance. However, our analysis shows that recent efforts are not trustworthy because the models fail at reproducing contemporary ice melt. Here we present a roadmap towards making more credible estimates of ice sheet melt.
D. Brinkerhoff and J. Johnson
Geosci. Model Dev., 8, 1275–1283, https://doi.org/10.5194/gmd-8-1275-2015, https://doi.org/10.5194/gmd-8-1275-2015, 2015
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We present a novel numerical method for computing velocity fields in ice sheets using the principle of mass conservation, and show that, for suitable smoothing of flow directions, the velocity converges to a unique solution under grid refinement. We use this method as the forward model in a constrained optimization problem, and use these so-called balance velocities to seamlessly fill in gaps between satellite-based velocity observations.
Douglas J. Brinkerhoff, Brandon S. Tober, Michael Daniel, Victor Devaux-Chupin, Michael S. Christoffersen, John W. Holt, Christopher F. Larsen, Mark Fahnestock, Michael G. Loso, Kristin M. F. Timm, Russell C. Mitchell, and Martin Truffer
The Cryosphere, 19, 2321–2353, https://doi.org/10.5194/tc-19-2321-2025, https://doi.org/10.5194/tc-19-2321-2025, 2025
Short summary
Short summary
Sít' Tlein is one of the largest glaciers in the world outside of the polar regions, and we know that it has been rapidly thinning. To forecast how this glacier will change in the future, we combine a computer model of ice flow with measurements from many different sources. Our model tells us that with high probability, Sít' Tlein's lower reaches are going to disappear in the next century and a half, creating a new bay or lake along Alaska's coastline.
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
Short summary
Short summary
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.
Andy Aschwanden, Timothy C. Bartholomaus, Douglas J. Brinkerhoff, and Martin Truffer
The Cryosphere, 15, 5705–5715, https://doi.org/10.5194/tc-15-5705-2021, https://doi.org/10.5194/tc-15-5705-2021, 2021
Short summary
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Estimating how much ice loss from Greenland and Antarctica will contribute to sea level rise is of critical societal importance. However, our analysis shows that recent efforts are not trustworthy because the models fail at reproducing contemporary ice melt. Here we present a roadmap towards making more credible estimates of ice sheet melt.
Jacob Downs, Jesse Johnson, Jason Briner, Nicolás Young, Alia Lesnek, and Josh Cuzzone
The Cryosphere, 14, 1121–1137, https://doi.org/10.5194/tc-14-1121-2020, https://doi.org/10.5194/tc-14-1121-2020, 2020
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We use an inverse modeling approach based on the unscented transform (UT) and a new reconstruction of Holocene ice sheet retreat in western central Greenland to infer precipitation changes throughout the Holocene. Our results indicate that warming during the Holocene Thermal Maximum (HTM) was linked to elevated snowfall that slowed retreat despite high temperatures. We also find that the UT provides a computationally inexpensive approach to Bayesian inversion and uncertainty quantification.
D. Brinkerhoff and J. Johnson
Geosci. Model Dev., 8, 1275–1283, https://doi.org/10.5194/gmd-8-1275-2015, https://doi.org/10.5194/gmd-8-1275-2015, 2015
Short summary
Short summary
We present a novel numerical method for computing velocity fields in ice sheets using the principle of mass conservation, and show that, for suitable smoothing of flow directions, the velocity converges to a unique solution under grid refinement. We use this method as the forward model in a constrained optimization problem, and use these so-called balance velocities to seamlessly fill in gaps between satellite-based velocity observations.
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Sít' Tlein is one of the largest glaciers in the world outside of the polar regions, and we know that it has been rapidly thinning. To forecast how this glacier will change in the future, we combine a computer model of ice flow with measurements from many different sources. Our model tells us that with high probability, Sít' Tlein's lower reaches are going to disappear in the next century and a half, creating a new bay or lake along Alaska's coastline.
Lea-Sophie Höyns, Thomas Kleiner, Andreas Rademacher, Martin Rückamp, Michael Wolovick, and Angelika Humbert
The Cryosphere, 19, 2133–2158, https://doi.org/10.5194/tc-19-2133-2025, https://doi.org/10.5194/tc-19-2133-2025, 2025
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The sliding of glaciers over bedrock is influenced by water pressure in the underlying hydrological system and the roughness of the land underneath the glacier. We estimate this roughness through a modeling approach that optimizes this unknown parameter. Additionally, we simulate water pressure, enhancing the reliability of the computed drag at the ice sheet base. The resulting data are provided to other modelers and scientists conducting geophysical field observations.
Ziad Rashed, Alexander A. Robel, and Hélène Seroussi
The Cryosphere, 19, 1775–1788, https://doi.org/10.5194/tc-19-1775-2025, https://doi.org/10.5194/tc-19-1775-2025, 2025
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Sermeq Kujalleq, Greenland's largest glacier, has significantly retreated since the late 1990s in response to warming ocean temperatures. Using a large-ensemble approach, our simulations show that the retreat is mainly initiated by the arrival of warm water but sustained and accelerated by the glacier's position over deeper bed troughs and vigorous calving. We highlight the need for models of ice mélange to project glacier behavior under rapid calving regimes.
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Glacier models have historically been used to understand glacier melt’s contribution to sea level rise. The capacity to project seasonal glacier runoff is a relatively recent development for these models. In this study we provide the first model intercomparison of runoff projections for the glacier evolution models capable of simulating future runoff globally. We compare model projections from 2000 to 2100 for all major river basins larger than 3000 km2 with over 30 km2 of initial glacier cover.
Enrico Zorzetto, Paul Ginoux, Sergey Malyshev, and Elena Shevliakova
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Light-absorbing particle (LAP) deposition on snow leads to a darkening of the snow surface and can thus accelerate snow melt. Understanding the extent to which different types of LAPs contribute to snow melt is important to both predict changes in water availability and improve global climate model predictions. Here, we extend a recently developed snow model to account for the deposition of LAPs in the snowpack and evaluate the effect of snow darkening on accelerating snow melt.
Marijn van der Meer, Harry Zekollari, Matthias Huss, Jordi Bolibar, Kamilla Hauknes Sjursen, and Daniel Farinotti
The Cryosphere, 19, 805–826, https://doi.org/10.5194/tc-19-805-2025, https://doi.org/10.5194/tc-19-805-2025, 2025
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Glacier retreat poses big challenges, making understanding how climate affects glaciers vital. But glacier measurements worldwide are limited. We created a simple machine-learning model called miniML-MB, which estimates annual changes in glacier mass in the Swiss Alps. As input, miniML-MB uses two climate variables: average temperature (May–Aug) and total precipitation (Oct–Feb). Our model can accurately predict glacier mass from 1961 to 2021 but struggles for extreme years (2022 and 2023).
Manon Gaillard, Vincent Vionnet, Matthieu Lafaysse, Marie Dumont, and Paul Ginoux
The Cryosphere, 19, 769–792, https://doi.org/10.5194/tc-19-769-2025, https://doi.org/10.5194/tc-19-769-2025, 2025
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This study presents an efficient method to improve large-scale snow albedo simulations by considering the spatial variability in light-absorbing particles (LAPs) like black carbon and dust. A global climatology of LAP deposition was created and used to optimize a parameter in the Crocus snow model. Testing at 10 global sites improved albedo predictions by 10 % on average and over 25 % in the Arctic. This method can enhance other snow models' predictions without complex simulations.
Jonathan D. Mackay, Nicholas E. Barrand, David M. Hannah, Emily Potter, Nilton Montoya, and Wouter Buytaert
The Cryosphere, 19, 685–712, https://doi.org/10.5194/tc-19-685-2025, https://doi.org/10.5194/tc-19-685-2025, 2025
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We combine two globally capable glacier evolution models to include processes that are typically neglected but thought to control tropical glacier retreat (e.g. sublimation). We apply the model to Peru's Vilcanota-Urubamba Basin. The model captures observed glacier mass changes,but struggles with surface albedo dynamics. Projections show glacier mass shrinking to 17 % or 6 % of 2000 levels by 2100 under moderate- and high-emission scenarios, respectively.
Tim van den Akker, William H. Lipscomb, Gunter R. Leguy, Jorjo Bernales, Constantijn J. Berends, Willem Jan van de Berg, and Roderik S. W. van de Wal
The Cryosphere, 19, 283–301, https://doi.org/10.5194/tc-19-283-2025, https://doi.org/10.5194/tc-19-283-2025, 2025
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In this study, we present an improved way of representing ice thickness change rates in an ice sheet model. We apply this method using two ice sheet models of the Antarctic Ice Sheet. We found that the two largest outlet glaciers on the Antarctic Ice Sheet, Thwaites Glacier and Pine Island Glacier, will collapse without further warming on a timescale of centuries. This would cause a sea level rise of about 1.2 m globally.
Saskia Kahl, Carolin Mehlmann, and Dirk Notz
The Cryosphere, 19, 129–141, https://doi.org/10.5194/tc-19-129-2025, https://doi.org/10.5194/tc-19-129-2025, 2025
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Ice mélange, a mixture of sea ice and icebergs, can impact sea-ice–ocean interactions. But climate models do not yet represent it due to computational limits. To address this shortcoming and include ice mélange into climate models, we suggest representing icebergs as particles. We integrate their feedback into mathematical equations used to model the sea-ice motion in climate models. The setup is computationally efficient due to the iceberg particle usage and enables a realistic representation.
Ward van Pelt and Thomas Frank
The Cryosphere, 19, 1–17, https://doi.org/10.5194/tc-19-1-2025, https://doi.org/10.5194/tc-19-1-2025, 2025
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Accurate information on the ice thickness of Svalbard's glaciers is important for assessing the contribution to sea level rise in a present and a future climate. However, direct observations of the glacier bed are scarce. Here, we use an inverse approach and high-resolution surface observations to infer basal conditions. We present and analyse the new bed and thickness maps, quantify the ice volume (6800 km3), and compare these against radar data and previous studies.
Felicity Alice Holmes, Jamie Barnett, Henning Åkesson, Mathieu Morlighem, Johan Nilsson, Nina Kirchner, and Martin Jakobsson
EGUsphere, https://doi.org/10.5194/egusphere-2024-3839, https://doi.org/10.5194/egusphere-2024-3839, 2024
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Northern Greenland contains some of the ice sheet's last remaining glaciers with floating ice tongues. One of these is Ryder Glacier, which has been relatively stable in recent decades in contrast to nearby glaciers. Here, we use a computer model to simulate Ryder Glacier until 2300 under both a low and high emissions scenario. Very high levels of surface melt under a high emissions future leads to a sea-level rise contribution an order of magnitude higher than under a low emissions future.
Richard Parsons, Sainan Sun, G. Hilmar Gudmundsson, Jan Wuite, and Thomas Nagler
The Cryosphere, 18, 5789–5801, https://doi.org/10.5194/tc-18-5789-2024, https://doi.org/10.5194/tc-18-5789-2024, 2024
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In 2022, multi-year landfast sea ice in Antarctica's Larsen B embayment disintegrated, after which time an increase in the rate at which Crane Glacier discharged ice into the ocean was observed. As the fast ice was joined to the glacier terminus, it could provide resistance against the glacier's flow, slowing down the rate of ice discharge. We used numerical modelling to quantify this resistive stress and found that the fast ice provided significant support to Crane prior to its disintegration.
Georgina J. Woolley, Nick Rutter, Leanne Wake, Vincent Vionnet, Chris Derksen, Richard Essery, Philip Marsh, Rosamond Tutton, Branden Walker, Matthieu Lafaysse, and David Pritchard
The Cryosphere, 18, 5685–5711, https://doi.org/10.5194/tc-18-5685-2024, https://doi.org/10.5194/tc-18-5685-2024, 2024
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Parameterisations of Arctic snow processes were implemented into the multi-physics ensemble version of the snow model Crocus (embedded within the Soil, Vegetation, and Snow version 2 land surface model) and evaluated at an Arctic tundra site. Optimal combinations of parameterisations that improved the simulation of density and specific surface area featured modifications that raise wind speeds to increase compaction in surface layers, prevent snowdrift, and increase viscosity in basal layers.
George Lu and Jonathan Kingslake
The Cryosphere, 18, 5301–5321, https://doi.org/10.5194/tc-18-5301-2024, https://doi.org/10.5194/tc-18-5301-2024, 2024
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Water below ice sheets affects ice-sheet motion, while the evolution of ice sheets likewise affects the water below. We create a model that allows for water and ice to affect each other and use it to see how this coupling or lack thereof may impact ice-sheet retreat. We find that coupling an evolving water system with the ice sheet results in more retreat than if we assume unchanging conditions under the ice, which indicates a need to better represent the effects of water in ice-sheet models.
Yu Wang, Chen Zhao, Rupert Gladstone, Thomas Zwinger, Benjamin K. Galton-Fenzi, and Poul Christoffersen
The Cryosphere, 18, 5117–5137, https://doi.org/10.5194/tc-18-5117-2024, https://doi.org/10.5194/tc-18-5117-2024, 2024
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Our research delves into the future evolution of Antarctica's Wilkes Subglacial Basin (WSB) and its potential contribution to sea level rise, focusing on how basal melt is implemented at the grounding line in ice flow models. Our findings suggest that these implementation methods can significantly impact the magnitude of future ice loss projections. Under a high-emission scenario, the WSB ice sheet could undergo massive and rapid retreat between 2200 and 2300.
Sylvie Charbit, Christophe Dumas, Fabienne Maignan, Catherine Ottlé, Nina Raoult, Xavier Fettweis, and Philippe Conesa
The Cryosphere, 18, 5067–5099, https://doi.org/10.5194/tc-18-5067-2024, https://doi.org/10.5194/tc-18-5067-2024, 2024
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The evolution of the Greenland ice sheet is highly dependent on surface melting and therefore on the processes operating at the snow–atmosphere interface and within the snow cover. Here we present new developments to apply a snow model to the Greenland ice sheet. The performance of this model is analysed in terms of its ability to simulate ablation processes. Our analysis shows that the model performs well when compared with the MAR regional polar atmospheric model.
Matt Trevers, Antony J. Payne, and Stephen L. Cornford
The Cryosphere, 18, 5101–5115, https://doi.org/10.5194/tc-18-5101-2024, https://doi.org/10.5194/tc-18-5101-2024, 2024
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The form of the friction law which determines the speed of ice sliding over the bedrock remains a major source of uncertainty in ice sheet model projections of future sea level rise. Jakobshavn Isbræ, the fastest-flowing glacier in Greenland, which has undergone significant changes in the last few decades, is an ideal case for testing sliding laws. We find that a regularised Coulomb friction law reproduces the large seasonal and inter-annual flow speed variations most accurately.
Alexander H. Jarosch, Paul Hofer, and Christoph Spötl
The Cryosphere, 18, 4811–4816, https://doi.org/10.5194/tc-18-4811-2024, https://doi.org/10.5194/tc-18-4811-2024, 2024
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Mechanical damage to stalagmites is commonly observed in mid-latitude caves. In this study we investigate ice flow along the cave bed as a possible mechanism for stalagmite damage. Utilizing models which simulate forces created by ice flow, we study the structural integrity of different stalagmite geometries. Our results suggest that structural failure of stalagmites caused by ice flow is possible, albeit unlikely.
Donald A. Slater and Till J. W. Wagner
EGUsphere, https://doi.org/10.5194/egusphere-2024-2927, https://doi.org/10.5194/egusphere-2024-2927, 2024
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Calving is when icebergs break off glaciers and fall into the ocean. It is an important process determining how ice sheets will respond to change in climate, but it is currently poorly understood and hard to include in numerical models that are used for sea level projections. We revised an existing theory for how this process works, overcoming shortcomings of the existing theory and explaining observations showing that calving style depends on how thick the ice is.
Cecile B. Menard, Sirpa Rasmus, Ioanna Merkouriadi, Gianpaolo Balsamo, Annett Bartsch, Chris Derksen, Florent Domine, Marie Dumont, Dorothee Ehrich, Richard Essery, Bruce C. Forbes, Gerhard Krinner, David Lawrence, Glen Liston, Heidrun Matthes, Nick Rutter, Melody Sandells, Martin Schneebeli, and Sari Stark
The Cryosphere, 18, 4671–4686, https://doi.org/10.5194/tc-18-4671-2024, https://doi.org/10.5194/tc-18-4671-2024, 2024
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Computer models, like those used in climate change studies, are written by modellers who have to decide how best to construct the models in order to satisfy the purpose they serve. Using snow modelling as an example, we examine the process behind the decisions to understand what motivates or limits modellers in their decision-making. We find that the context in which research is undertaken is often more crucial than scientific limitations. We argue for more transparency in our research practice.
Giulia Mazzotti, Jari-Pekka Nousu, Vincent Vionnet, Tobias Jonas, Rafife Nheili, and Matthieu Lafaysse
The Cryosphere, 18, 4607–4632, https://doi.org/10.5194/tc-18-4607-2024, https://doi.org/10.5194/tc-18-4607-2024, 2024
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As many boreal and alpine forests have seasonal snow, models are needed to predict forest snow under future environmental conditions. We have created a new forest snow model by combining existing, very detailed model components for the canopy and the snowpack. We applied it to forests in Switzerland and Finland and showed how complex forest cover leads to a snowpack layering that is very variable in space and time because different processes prevail at different locations in the forest.
Xu Zhou, Binbin Wang, Xiaogang Ma, Zhu La, and Kun Yang
The Cryosphere, 18, 4589–4605, https://doi.org/10.5194/tc-18-4589-2024, https://doi.org/10.5194/tc-18-4589-2024, 2024
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The simulation of the ice phenology of Nam Co by WRF is investigated. Compared with the default model, improving the key lake schemes, such as water surface roughness length for heat fluxes and the shortwave radiation transfer for lake ice, can better simulate the lake ice phenology. The still existing errors in the spatial patterns of lake ice phenology imply that challenges still exist in modelling key lake and non-lake physics such as grid-scale water circulation and snow-related processes.
Amir Sedaghatkish, Frédéric Doumenc, Pierre-Yves Jeannin, and Marc Luetscher
The Cryosphere, 18, 4531–4546, https://doi.org/10.5194/tc-18-4531-2024, https://doi.org/10.5194/tc-18-4531-2024, 2024
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We developed a model to simulate the natural convection of water within frozen rock crevices subject to daily warming in mountain permafrost regions. Traditional models relying on conduction and latent heat flux typically overlook free convection. The results reveal that free convection can significantly accelerate the melting rate by an order of magnitude compared to conduction-based models. Our results are important for assessing the impact of climate change on mountain infrastructure.
Joseph Fogarty, Elie Bou-Zeid, Mitchell Bushuk, and Linette Boisvert
The Cryosphere, 18, 4335–4354, https://doi.org/10.5194/tc-18-4335-2024, https://doi.org/10.5194/tc-18-4335-2024, 2024
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We hypothesize that using a broad set of surface characterization metrics for polar sea ice surfaces will lead to more accurate representations in general circulation models. However, the first step is to identify the minimum set of metrics required. We show via numerical simulations that sea ice surface patterns can play a crucial role in determining boundary layer structures. We then statistically analyze a set of high-resolution sea ice surface images to obtain this minimal set of parameters.
Antonio Juarez-Martinez, Javier Blasco, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
The Cryosphere, 18, 4257–4283, https://doi.org/10.5194/tc-18-4257-2024, https://doi.org/10.5194/tc-18-4257-2024, 2024
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We present sea level projections for Antarctica in the context of ISMIP6-2300 with several forcings but extend the simulations to 2500, showing that more than 3 m of sea level contribution could be reached. We also test the sensitivity on a basal melting parameter and determine the timing of the loss of ice in the west region. All the simulations were carried out with the ice sheet model Yelmo.
Daniel Moreno-Parada, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
The Cryosphere, 18, 4215–4232, https://doi.org/10.5194/tc-18-4215-2024, https://doi.org/10.5194/tc-18-4215-2024, 2024
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Our study tries to understand how the ice temperature evolves in a large mass as in the case of Antarctica. We found a relation that tells us the ice temperature at any point. These results are important because they also determine how the ice moves. In general, ice moves due to slow deformation (as if pouring honey from a jar). Nevertheless, in some regions the ice base warms enough and melts. The liquid water then serves as lubricant and the ice slides and its velocity increases rapidly.
Tim Hageman, Jessica Mejía, Ravindra Duddu, and Emilio Martínez-Pañeda
The Cryosphere, 18, 3991–4009, https://doi.org/10.5194/tc-18-3991-2024, https://doi.org/10.5194/tc-18-3991-2024, 2024
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Due to surface melting, meltwater lakes seasonally form on the surface of glaciers. These lakes drive hydrofractures that rapidly transfer water to the base of ice sheets. This paper presents a computational method to capture the complicated hydrofracturing process. Our work reveals that viscous ice rheology has a great influence on the short-term propagation of fractures, enabling fast lake drainage, whereas thermal effects (frictional heating, conduction, and freezing) have little influence.
Alex Cabaj, Paul J. Kushner, and Alek A. Petty
EGUsphere, https://doi.org/10.5194/egusphere-2024-2562, https://doi.org/10.5194/egusphere-2024-2562, 2024
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The output of snow-on-sea-ice models is influenced by the choice of snowfall input used. We ran such a model with different snowfall inputs and calibrated it to observations, produced a new calibrated snow product, and regionally compared the model outputs to another snow-on-sea-ice model. The two models agree best on the seasonal cycle of snow in the central Arctic Ocean. However, estimated snow trends in some regions can depend more on the snowfall input than on the choice of model.
Clémence Herny, Pascal Hagenmuller, Guillaume Chambon, Isabel Peinke, and Jacques Roulle
The Cryosphere, 18, 3787–3805, https://doi.org/10.5194/tc-18-3787-2024, https://doi.org/10.5194/tc-18-3787-2024, 2024
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This paper presents the evaluation of a numerical discrete element method (DEM) by simulating cone penetration tests in different snow samples. The DEM model demonstrated a good ability to reproduce the measured mechanical behaviour of the snow, namely the force evolution on the cone and the grain displacement field. Systematic sensitivity tests showed that the mechanical response depends not only on the microstructure of the sample but also on the mechanical parameters of grain contacts.
Louis Quéno, Rebecca Mott, Paul Morin, Bertrand Cluzet, Giulia Mazzotti, and Tobias Jonas
The Cryosphere, 18, 3533–3557, https://doi.org/10.5194/tc-18-3533-2024, https://doi.org/10.5194/tc-18-3533-2024, 2024
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Snow redistribution by wind and avalanches strongly influences snow hydrology in mountains. This study presents a novel modelling approach to best represent these processes in an operational context. The evaluation of the simulations against airborne snow depth measurements showed remarkable improvement in the snow distribution in mountains of the eastern Swiss Alps, with a representation of snow accumulation and erosion areas, suggesting promising benefits for operational snow melt forecasts.
André Löfgren, Thomas Zwinger, Peter Råback, Christian Helanow, and Josefin Ahlkrona
The Cryosphere, 18, 3453–3470, https://doi.org/10.5194/tc-18-3453-2024, https://doi.org/10.5194/tc-18-3453-2024, 2024
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This paper investigates a stabilization method for free-surface flows in the context of glacier simulations. Previous applications of the stabilization on ice flows have only considered simple ice-sheet benchmark problems; in particular the method had not been tested on real-world glacier domains. This work addresses this shortcoming by demonstrating that the stabilization works well also in this case and increases stability and robustness without negatively impacting computation times.
Ange Haddjeri, Matthieu Baron, Matthieu Lafaysse, Louis Le Toumelin, César Deschamps-Berger, Vincent Vionnet, Simon Gascoin, Matthieu Vernay, and Marie Dumont
The Cryosphere, 18, 3081–3116, https://doi.org/10.5194/tc-18-3081-2024, https://doi.org/10.5194/tc-18-3081-2024, 2024
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Our study addresses the complex challenge of evaluating distributed alpine snow simulations with snow transport against snow depths from Pléiades stereo imagery and snow melt-out dates from Sentinel-2 and Landsat-8 satellites. Additionally, we disentangle error contributions between blowing snow, precipitation heterogeneity, and unresolved subgrid variability. Snow transport enhances the snow simulations at high elevations, while precipitation biases are the main error source in other areas.
Sebastian H. R. Rosier, G. Hilmar Gudmundsson, Adrian Jenkins, and Kaitlin A. Naughten
EGUsphere, https://doi.org/10.5194/egusphere-2024-1838, https://doi.org/10.5194/egusphere-2024-1838, 2024
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Glaciers in the Amundsen Sea region of Antarctica have been retreating and losing mass, but their future contribution to global sea level rise remains highly uncertain. We use an ice sheet model and uncertainty quantification methods to evaluate the probable range of mass loss from this region for two future climate scenarios and find that the rate of ice loss until 2100 will likely remain similar to present-day observations, with little sensitivity to climate scenario over this short timeframe.
Christopher Riedel and Jeffrey Anderson
The Cryosphere, 18, 2875–2896, https://doi.org/10.5194/tc-18-2875-2024, https://doi.org/10.5194/tc-18-2875-2024, 2024
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Accurate sea ice conditions are crucial for quality sea ice projections, which have been connected to rapid warming over the Arctic. Knowing which observations to assimilate into models will help produce more accurate sea ice conditions. We found that not assimilating sea ice concentration led to more accurate sea ice states. The methods typically used to assimilate observations in our models apply assumptions to variables that are not well suited for sea ice because they are bounded variables.
Julia Selivanova, Doroteaciro Iovino, and Francesco Cocetta
The Cryosphere, 18, 2739–2763, https://doi.org/10.5194/tc-18-2739-2024, https://doi.org/10.5194/tc-18-2739-2024, 2024
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Climate models show differences in sea ice representation in comparison to observations. Increasing the model resolution is a recognized way to improve model realism and obtain more reliable future projections. We find no strong impact of resolution on sea ice representation; it rather depends on the analysed variable and the model used. By 2050, the marginal ice zone (MIZ) becomes a dominant feature of the Arctic ice cover, suggesting a shift to a new regime similar to that in Antarctica.
Ailsa Chung, Frédéric Parrenin, Robert Mulvaney, Luca Vittuari, Massimo Frezzotti, Antonio Zanutta, David A. Lilien, Marie G. P. Cavitte, and Olaf Eisen
EGUsphere, https://doi.org/10.5194/egusphere-2024-1650, https://doi.org/10.5194/egusphere-2024-1650, 2024
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We applied an ice flow model to a flow line from the summit of Dome C to the Beyond EPICA ice core drill site on Little Dome C in Antarctica. Results show that the oldest ice at the drill site may be 1.12 Ma (at age density of 20 kyr/m) and originate from around 15 km upstream. We also discuss the nature of the 200–250 m thick basal layer which could be composed of accreted ice, stagnant ice, or even disturbed ice containing debris.
Alexander A. Robel, Vincent Verjans, and Aminat A. Ambelorun
The Cryosphere, 18, 2613–2623, https://doi.org/10.5194/tc-18-2613-2024, https://doi.org/10.5194/tc-18-2613-2024, 2024
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The average size of many glaciers and ice sheets changes when noise is added to the system. The reasons for this drift in glacier state is intrinsic to the dynamics of how ice flows and the bumpiness of the Earth's surface. We argue that not including noise in projections of ice sheet evolution over coming decades and centuries is a pervasive source of bias in these computer models, and so realistic variability in glacier and climate processes must be included in models.
John K. Dukowicz
EGUsphere, https://doi.org/10.5194/egusphere-2024-1052, https://doi.org/10.5194/egusphere-2024-1052, 2024
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A novel transformation of the Stokes ice sheet equations is presented that expands the scope of traditional methods. The new formulation is closely related to a widely used Stokes approximation, the Blatter-Pattyn model, such that an ice sheet model may be easily switched between the two formulations, allowing for adaptive applications. The new formulation also facilitates new approximations that improve on the Blatter-Pattyn model, heretofore the best approximate ice sheet model.
José M. Muñoz-Hermosilla, Jaime Otero, Eva De Andrés, Kaian Shahateet, Francisco Navarro, and Iván Pérez-Doña
The Cryosphere, 18, 1911–1924, https://doi.org/10.5194/tc-18-1911-2024, https://doi.org/10.5194/tc-18-1911-2024, 2024
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A large fraction of the mass loss from marine-terminating glaciers is attributed to frontal ablation. In this study, we used a 3D ice flow model of a real glacier that includes the effects of calving and submarine melting. Over a 30-month simulation, we found that the model reproduced the seasonal cycle for this glacier. Besides, the front positions were in good agreement with observations in the central part of the front, with longitudinal differences, on average, below 15 m.
Charlotte Durand, Tobias Sebastian Finn, Alban Farchi, Marc Bocquet, Guillaume Boutin, and Einar Ólason
The Cryosphere, 18, 1791–1815, https://doi.org/10.5194/tc-18-1791-2024, https://doi.org/10.5194/tc-18-1791-2024, 2024
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This paper focuses on predicting Arctic-wide sea-ice thickness using surrogate modeling with deep learning. The model has a predictive power of 12 h up to 6 months. For this forecast horizon, persistence and daily climatology are systematically outperformed, a result of learned thermodynamics and advection. Consequently, surrogate modeling with deep learning proves to be effective at capturing the complex behavior of sea ice.
Mathieu Plante, Jean-François Lemieux, L. Bruno Tremblay, Adrienne Tivy, Joey Angnatok, François Roy, Gregory Smith, Frédéric Dupont, and Adrian K. Turner
The Cryosphere, 18, 1685–1708, https://doi.org/10.5194/tc-18-1685-2024, https://doi.org/10.5194/tc-18-1685-2024, 2024
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We use a sea ice model to reproduce ice growth observations from two buoys deployed on coastal sea ice and analyze the improvements brought by new physics that represent the presence of saline liquid water in the ice interior. We find that the new physics with default parameters degrade the model performance, with overly rapid ice growth and overly early snow flooding on top of the ice. The performance is largely improved by simple modifications to the ice growth and snow-flooding algorithms.
Joshua Cuzzone, Matias Romero, and Shaun A. Marcott
The Cryosphere, 18, 1381–1398, https://doi.org/10.5194/tc-18-1381-2024, https://doi.org/10.5194/tc-18-1381-2024, 2024
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We simulate the retreat history of the Patagonian Ice Sheet (PIS) across the Chilean Lake District from 22–10 ka. These results improve our understanding of the response of the PIS to deglacial warming and the patterns of deglacial ice margin retreat where gaps in the geologic record still exist, and they indicate that changes in large-scale precipitation during the last deglaciation played an important role in modulating the response of ice margin change across the PIS to deglacial warming.
Larissa van der Laan, Anouk Vlug, Adam A. Scaife, Fabien Maussion, and Kristian Förster
EGUsphere, https://doi.org/10.5194/egusphere-2024-387, https://doi.org/10.5194/egusphere-2024-387, 2024
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Usually, glacier models are supplied with climate information from long (e.g. 100 year) simulations by global climate models. In this paper, we test the feasibility of supplying glacier models with shorter simulations, to get more accurate information on 5–10 year time scales. Reliable information on these time scales is very important, especially for water management experts to know how much meltwater to expect, for rivers, agriculture and drinking water.
Chao-Yuan Yang, Jiping Liu, and Dake Chen
The Cryosphere, 18, 1215–1239, https://doi.org/10.5194/tc-18-1215-2024, https://doi.org/10.5194/tc-18-1215-2024, 2024
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We present a new atmosphere–ocean–wave–sea ice coupled model to study the influences of ocean waves on Arctic sea ice simulation. Our results show (1) smaller ice-floe size with wave breaking increases ice melt, (2) the responses in the atmosphere and ocean to smaller floe size partially reduce the effect of the enhanced ice melt, (3) the limited oceanic energy is a strong constraint for ice melt enhancement, and (4) ocean waves can indirectly affect sea ice through the atmosphere and the ocean.
Yurii Batrak, Bin Cheng, and Viivi Kallio-Myers
The Cryosphere, 18, 1157–1183, https://doi.org/10.5194/tc-18-1157-2024, https://doi.org/10.5194/tc-18-1157-2024, 2024
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Atmospheric reanalyses provide consistent series of atmospheric and surface parameters in a convenient gridded form. In this paper, we study the quality of sea ice in a recently released regional reanalysis and assess its added value compared to a global reanalysis. We show that the regional reanalysis, having a more complex sea ice model, gives an improved representation of sea ice, although there are limitations indicating potential benefits in using more advanced approaches in the future.
Michael A. Rawlins and Ambarish V. Karmalkar
The Cryosphere, 18, 1033–1052, https://doi.org/10.5194/tc-18-1033-2024, https://doi.org/10.5194/tc-18-1033-2024, 2024
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Flows of water, carbon, and materials by Arctic rivers are being altered by climate warming. We used simulations from a permafrost hydrology model to investigate future changes in quantities influencing river exports. By 2100 Arctic rivers will receive more runoff from the far north where abundant soil carbon can leach in. More water will enter them via subsurface pathways particularly in summer and autumn. An enhanced water cycle and permafrost thaw are changing river flows to coastal areas.
Oreste Marquis, Bruno Tremblay, Jean-François Lemieux, and Mohammed Islam
The Cryosphere, 18, 1013–1032, https://doi.org/10.5194/tc-18-1013-2024, https://doi.org/10.5194/tc-18-1013-2024, 2024
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We developed a standard viscous–plastic sea-ice model based on the numerical framework called smoothed particle hydrodynamics. The model conforms to the theory within an error of 1 % in an idealized ridging experiment, and it is able to simulate stable ice arches. However, the method creates a dispersive plastic wave speed. The framework is efficient to simulate fractures and can take full advantage of parallelization, making it a good candidate to investigate sea-ice material properties.
Soňa Tomaškovičová and Thomas Ingeman-Nielsen
The Cryosphere, 18, 321–340, https://doi.org/10.5194/tc-18-321-2024, https://doi.org/10.5194/tc-18-321-2024, 2024
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We present the results of a fully coupled modeling framework for simulating the ground thermal regime using only surface measurements to calibrate the thermal model. The heat conduction model is forced by surface ground temperature measurements and calibrated using the field measurements of time lapse apparent electrical resistivity. The resistivity-calibrated thermal model achieves a performance comparable to the traditional calibration of borehole temperature measurements.
Cited articles
Aschwanden, A., Bueler, E., Khroulev, C., and Blatter, H.: An enthalpy formulation for glaciers and ice sheets, J. Glaciol., 58, 441–457, https://doi.org/10.3189/2012JoG11J088, 2012.
Baiocchi, C., Brezzi, F., and Franca, L. P.: Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.), Comput. Method. Appl. M., 105, 125–141, https://doi.org/10.1016/0045-7825(93)90119-I, 1993.
Balay, S., Brown, J., Buschelman, K., Gropp, W. D., Kaushik, D., Knepley, M. G., McInnes, L. C., Smith, B. F., and Zhang, H.: PETSc Web page, http://www.mcs.anl.gov/petsc, 2012.
Balise, M. J. and Raymond, C. F.: Transfer of basal sliding variations to the surface of a linearly viscous glacier, J. Glaciol., 31, 308–318, 1985.
Bamber, J. L., Layberry, R. L., and Gogineni, S. P.: A new ice thickness and bed data set for the Greenland ice sheet 1. Measurement, data reduction, and errors, J. Geophys. Res., 106, 33773–33780, 2001.
Bassis, J. N.: Hamilton's Principle Applied to Ice Sheet Dynamics: New approximations for the large-scale flow of ice sheets, J. Glaciol., 56, 497–513, 2010.
Baur, O., Kuhn, M., and Featherstone, W. E.: GRACE-derived ice-mass variations over Greenland by accounting for leakage effects, J. Geophys. Res.-Sol. Ea., 114, B06407, https://doi.org/10.1029/2008JB006239, 2009.
Bird, R. B.: New Variational Principle for Incompressible Non-Newtonian Flow, Phys. Fluids, 3, 539–541, https://doi.org/10.1063/1.1706087, 1960.
Blatter, H.: Velocity and stress fields in grounded glaciers: A simple algorithm for including deviatoric stress gradients, J. Glaciol., 41, 331–344, 1995.
Brinkerhoff, D. J., Meierbachtol, T. W., Johnson, J. V., and Harper, J. T.: Sensitivity of the frozen/melted basal boundary to perturbations of basal traction and geothermal heat flux: Isunnguata Sermia, western Greenland, Ann. Glaciol., 52, 43–50, https://doi.org/10.3189/172756411799096330, 2011.
Brooks, A. N. and Hughes, T. J.: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Method. Appl. M., 32, 199–259, https://doi.org/10.1016/0045-7825(82)90071-8, 1982.
Bueler, E. and Brown, J.: Shallow shelf approximation as a "sliding law" in a thermomechanically coupled ice sheet model, J. Geophys. Res.-Earth, 114, F03008, https://doi.org/10.1029/2008JF001179, 2009.
Bueler, E., Lingle, C., Kallen-Brown, J., Covey, D., and Bowman, L.: Exact Solutions and Verification of Numerical Models of Isothermal Ice Sheets, J. Glaciol., 51, 291–306, 2005.
Colella, P., Graves, D. T., Keen, N., Ligocki, T. J., Martin, D. F., McCorquodale, P., Modiano, D., Schwartz, P., Sternberg, T., and Straalen, B. V.: Chombo Software Package for AMR Applications – Design Document, unpublished, 2000.
Cornford, S. L., Martin, D. F., Graves, D. T., Ranken, D. F., Brocq, A. M. L., Gladstone, R. M., Payne, A. J., Ng, E. G., and Lipscomb, W. H.: Adaptive mesh, finite volume modeling of marine ice sheets, J. Comput. Phys., 232, 529–549, https://doi.org/10.1016/j.jcp.2012.08.037, 2013.
Deuflhard, P.: Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, in: Springer Series in Computational Mathematics, vol. 35, Springer, Berlin, 2004.
Donea, J. and Huerta, A.: Finite element methods for flow problems, John Wiley and Sons, 2003.
Donea, J., Huerta, A., Ponthot, J., and Rodriguez-Ferran, A.: Arbitrary Lagrangian-Eulerian Methods, Encyclopedia of Computational Mechanics, 1, 2005.
Dukowicz, J. K.: Reformulating the full-Stokes ice sheet model for a more efficient computational solution, The Cryosphere, 6, 21–34, https://doi.org/10.5194/tc-6-21-2012, 2012.
Ettema, J., van den Broeke, M. R., van Meijgaard, E., van de Berg, W. J., Bamber, J. L., Box, J. E., and Bales, R. C.: Higher surface mass balance of the Greenland ice sheet revealed by high-resolution climate modeling, Geophys. Res. Lett., 36, L12501, https://doi.org/10.1029/2009GL038110, 2009.
Farrell, P. E., Ham, D. A., Funke, S. W., and Rognes, M. E.: Automated derivation of the adjoint of high-level transient finite element programs, arXiv:1204.5577, submitted, 2012.
Fausto, R., Ahlstrom, A., As, D., Boggild, C., and Johnsen, S.: A new present-day temperature parameterization for Greenland, J. Glaciol., 55, 95–105, 2009.
Favier, L., Gagliardini, O., Durand, G., and Zwinger, T.: A three-dimensional full Stokes model of the grounding line dynamics: effect of a pinning point beneath the ice shelf, The Cryosphere, 6, 101–112, https://doi.org/10.5194/tc-6-101-2012, 2012.
Gillet-Chaulet, F., Gagliardini, O., Seddik, H., Nodet, M., Durand, G., Ritz, C., Zwinger, T., Greve, R., and Vaughan, D. G.: Greenland ice sheet contribution to sea-level rise from a new-generation ice-sheet model, The Cryosphere, 6, 1561–1576, https://doi.org/10.5194/tc-6-1561-2012, 2012.
Glen, J. W.: The Creep of Polycrystalline Ice, P. Roy. Soc. Lond. A, 228, 519–538, 1955.
Goldberg, D. N. and Sergienko, O. V.: Data assimilation using a hybrid ice flow model, The Cryosphere, 5, 315–327, https://doi.org/10.5194/tc-5-315-2011, 2011.
Gottlieb, S. and Shu, C.: Total Variation Diminishing Runge-Kutta Schemes, Math. Comput., 67, 73–85, 1998.
Greve, R. and Hutter, K.: Polythermal three-dimensional modelling of the Greenland Ice Sheet with varied geothermal heat flux, Ann. Glaciol., 21, 8–12, 1995.
Gudmundsson, G. H. and Raymond, M.: On the limit to resolution and information on basal properties obtainable from surface data on ice streams, The Cryosphere, 2, 167–178, https://doi.org/10.5194/tc-2-167-2008, 2008.
Habashi, W. G., Dompierre, J., Bourgault, Y., Ait-Ali-Yahia, D., Fortin, M., and Vallet, M.-G.: Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles, Int. J. Numer. Meth. Fl., 32, 725–744, https://doi.org/10.1002/(SICI)1097-0363(20000330)32:6< 725::AID-FLD935> 3.0.CO;2-4, 2000.
Habermann, M., Maxwell, D., and Truffer, M.: Reconstruction of basal properties in ice sheets using iterative inverse methods, J. Glaciol., 58, 795–807, https://doi.org/10.3189/2012JoG11J168, 2012.
Heroux, M. A., Bartlett, R. A., Howle, V. E., Hoekstra, R. J., Hu, J. J., Kolda, T. G., Lehoucq, R. B., Long, K. R., Pawlowski, R. P., Phipps, E. T., Salinger, A. G., Thornquist, H. K., Tuminaro, R. S., Willenbring, J. M., Williams, A., and Stanley, K. S.: An overview of the Trilinos project, ACM Trans. Math. Softw., 31, 397–423, https://doi.org/10.1145/1089014.1089021, 2005.
Hutter, K.: A mathematical model of polythermal glaciers and ice sheets, Geophys. Astro. Fluid, 21, 201–224, https://doi.org/10.1080/03091928208209013, 1982.
Hutter, K.: Theoretical glaciology, Springer, 1983.
Johnson, J. V., Brinkerhoff, D. J., and Nowicki, S.: A novel mass onserving bed algorithm to estimate errors in bed elevation associated with flight line spacing, J. Geophys. Res., in review, 2013.
Joughin, I., Smith, B. E., Howat, I. M., Scambos, T., and Moon, T.: Greenland flow variability from ice-sheet-wide velocity mapping, J. Glaciol., 56, 415–430, https://doi.org/10.3189/002214310792447734, 2010.
Larour, E., Rignot, E., Joughin, I., and Aubry, D.: Rheology of the Ronne Ice Shelf, Antarctica, inferred from satellite radar interferometry data using an inverse control method, Geophys. Res. Lett., 32, L05503, https://doi.org/10.1029/2004GL021693, 2005.
Larour, E., Seroussi, H., Morlighem, M., and Rignot, E.: Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM), J. Geophys. Res.-Earth, 117, F01022, https://doi.org/10.1029/2011JF002140, 2012.
Leng, W., Ju, L., Gunzburger, M., Price, S., and Ringler, T.: A parallel high-order accurate finite element nonlinear Stokes ice sheet model and benchmark experiments, J. Geophys. Res.-Earth, 117, F01001, https://doi.org/10.1029/2011JF001962, 2012.
Leng, W., Ju, L., Gunzburger, M., and Price, S.: Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models, The Cryosphere, 7, 19–29, https://doi.org/10.5194/tc-7-19-2013, 2013.
Logg, A., Mardal, K.-A., and Wells, G. N., eds.: Automated Solution of Differential Equations by the Finite Element Method, Springer, New York, https://doi.org/10.1007/978-3-642-23099-8, 2012.
MacAyeal, D. R.: A Tutorial on the Use of Control Methods in Ice-Sheet Modeling, J. Glaciol., 39, 91–98, 1993.
Morlighem, M., Rignot, E., Seroussi, H., Larour, E., Ben Dhia, H., and Aubry, D.: Spatial patterns of basal drag inferred using control methods from a full-Stokes and simpler models for Pine Island Glacier, West Antarctica, Geophys. Res. Lett., 37, L14502, https://doi.org/10.1029/2010GL043853, 2010.
Morlighem, M., Rignot, E., Seroussi, H., Larour, E., Ben Dhia, H., and Aubry, D.: A mass conservation approach for mapping glacier ice thickness, Geophys. Res. Lett., 38, L19503, https://doi.org/10.1029/2011GL048659, 2011.
Nocedal, J. and Wright, S.: Numerical Optimization, Springer, USA, 2 Edn., 2000.
Nowicki, S. M. J.: Modelling the transition zone of marine ice sheets, Ph.D. thesis, University College London, 2007.
Pattyn, F.: A new three-dimensional higher-order thermomechanical ice-sheet model: basic sensitivity, ice-stream development and ice flow across subglacial lakes, J. Geophys. Res.-Sol. Ea., 108, 2382, https://doi.org/10.1029/2002JB002329, 2003.
Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson, G. H., Hindmarsh, R. C. A., Hubbard, A., Johnson, J. V., Kleiner, T., Konovalov, Y., Martin, C., Payne, A. J., Pollard, D., Price, S., Rückamp, M., Saito, F., Souček, O., Sugiyama, S., and Zwinger, T.: Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP-HOM), The Cryosphere, 2, 95–108, https://doi.org/10.5194/tc-2-95-2008, 2008.
Payne, A. J., Huybrechts, P., Abe-Oughi, A., Calov, J. L. F. R., Greve, R., Marshall, S. J., Marsiat, I., Ritz, C., Tarasov, L., and Thomassen, M. P. A.: Results from the EISMINT model intercomparison: the effect of thermomechanical coupling, J. Glaciol., 46, 227–238, 2000.
Pritchard, H. D., Arthern, R. J., Vaughan, D. G., and Edwards, L. A.: Extensive dynamic thinning on the margins of the Greenland and Antarctic ice sheets, Nature, 461, 971–975, https://doi.org/10.1038/nature08471, 2009.
Rutt, I. C., Hagdorn, M., Hulton, N. R. J., and Payne, A. J.: The Glimmer community ice sheet model, J. Geophys. Res., 114, F02004, https://doi.org/10.1029/2008JF001015, 2009.
Saito, F., Abe-Ouchi, A., and Blatter, H.: Effects of first-order stress gradients in an ice sheet evaluated by a three-dimensional thermomechanical coupled model, Ann. Glaciol., 37, 166–172, https://doi.org/10.3189/172756403781815645, 2003.
Saito, F., Abe-Ouchi, A., and Blatter, H.: European Ice Sheet Modelling Initiative (EISMINT) model intercomparison experiments with first-order mechanics, J. Geophys. Res.-Earth, 111, F02012, https://doi.org/10.1029/2004JF000273, 2006.
Salari, K. and Knupp, P.: Code Verification by the Method of Manufactured Solutions, Tech. rep., Sandia National Laboratory, 2000.
Sargent, A. and Fastook, J. L.: Manufactured analytical solutions for isothermal full-Stokes ice sheet models, The Cryosphere, 4, 285–311, https://doi.org/10.5194/tc-4-285-2010, 2010.
Schäfer, M., Gagliardini, O., Pattyn, F., and Le Meur, E.: Applicability of the Shallow Ice Approximation inferred from model inter-comparison using various glacier geometries, The Cryosphere Discuss., 2, 557–599, https://doi.org/10.5194/tcd-2-557-2008, 2008.
Schoof, C.: Variational methods for glacier flow over plastic till, J. Fluid Mech., 555, 299–320, https://doi.org/10.1017/S0022112006009104, 2006.
SeaRISE: SeaRISE website, available at: http://websrv.cs.umt.edu/isis/index.php/SeaRISE_Assessment, 2012.
Seddik, H., Greve, R., Zwinger, T., Gillet-Chaulet, F., and Gagliardini, O.: Simulations of the Greenland ice sheet 100 years into the future with the full Stokes model Elmer/Ice, J. Glaciol., 58, 427–440, 2012.
Shapiro, N. M. and Ritzwoller, M. H.: Inferring surface heat distributions guided by global seismic model: particular applications to Antarctica, Earth Planet. Sci. Lett., 223, 69–84,, 2004.
Weis, M., Greve, R., and Hutter, K.: Theory of shallow ice shelves, Continuum Mech. Therm., 11, 15–50, 1999.
Zwinger, T., Greve, R., Gagliardini, O., Shiraiwa, T., and Lyly, M.: A full Stokes-flow thermo-mechanical model for firn and ice applied to the Gorshkov crater glacier, Kamchatka, Ann. Glaciol., 45, 29–37, https://doi.org/10.3189/172756407782282543, 2007.
