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
Related authors
Douglas Brinkerhoff, Brandon Tober, Michael Daniel, Victor Devaux-Chupin, Michael Christoffersen, John W. Holt, Christopher F. Larsen, Mark Fahnestock, Michael G. Loso, Kristin M. F. Timm, Russell Mitchell, and Martin Truffer
EGUsphere, https://doi.org/10.5194/egusphere-2024-2354, https://doi.org/10.5194/egusphere-2024-2354, 2024
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
Short summary
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
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.
Douglas Brinkerhoff, Brandon Tober, Michael Daniel, Victor Devaux-Chupin, Michael Christoffersen, John W. Holt, Christopher F. Larsen, Mark Fahnestock, Michael G. Loso, Kristin M. F. Timm, Russell Mitchell, and Martin Truffer
EGUsphere, https://doi.org/10.5194/egusphere-2024-2354, https://doi.org/10.5194/egusphere-2024-2354, 2024
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
Short summary
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
Short summary
Short summary
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.
Related subject area
Numerical Modelling
A hybrid ice-mélange model based on particle and continuum methods
New glacier thickness and bed topography maps for Svalbard
Quantifying the buttressing contribution of landfast sea ice and melange to Crane Glacier, Antarctic Peninsula
Multi-physics ensemble modelling of Arctic tundra snowpack properties
Two-way coupling between ice flow and channelized subglacial drainage enhances modeled marine-ice-sheet retreat
Sensitivity of the future evolution of the Wilkes Subglacial Basin ice sheet to grounding-line melt parameterizations
Modelling snowpack on ice surfaces with the ORCHIDEE land surface model: application to the Greenland ice sheet
Application of a regularised Coulomb sliding law to Jakobshavn Isbræ, western Greenland
Brief communication: Stalagmite damage by cave ice flow quantitatively assessed by fluid–structure interaction simulations
Exploring the decision-making process in model development: focus on the Arctic snowpack
Exploring the potential of forest snow modeling at the tree and snowpack layer scale
Simulating lake ice phenology using a coupled atmosphere–lake model at Nam Co, a typical deep alpine lake on the Tibetan Plateau
Modelling the effect of free convection on permafrost melting rates in frozen rock clefts
How many parameters are needed to represent polar sea ice surface patterns and heterogeneity?
Antarctic sensitivity to oceanic melting parameterizations
Analytical solutions for the advective–diffusive ice column in the presence of strain heating
A minimal machine learning glacier mass balance model
Ice viscosity governs hydraulic fracture that causes rapid drainage of supraglacial lakes
Microstructure-based modelling of snow mechanics: experimental evaluation of the cone penetration test
Snow redistribution in an intermediate-complexity snow hydrology modelling framework
Increasing numerical stability of mountain valley glacier simulations: implementation and testing of free-surface stabilization in Elmer/Ice
Improving large-scale snow albedo modelling using a climatology of light-absorbing particle deposition
Analyzing the sensitivity of a blowing snow model (SnowPappus) to precipitation forcing, blowing snow, and spatial resolution
Exploring non-Gaussian sea ice characteristics via observing system simulation experiments
Past and future of the Arctic sea ice in High-Resolution Model Intercomparison Project (HighResMIP) climate models
Biases in ice sheet models from missing noise-induced drift
Quantifying radiative effects of light–absorbing particles deposition on snow at the SnowMIP sites
Present-day mass loss rates are a precursor for West Antarctic Ice Sheet collapse
A 3D glacier dynamics–line plume model to estimate the frontal ablation of Hansbreen, Svalbard
Data-driven surrogate modeling of high-resolution sea-ice thickness in the Arctic
Physically-based modelling of glacier evolution under climate change in the tropical Andes
Using Icepack to reproduce ice mass balance buoy observations in landfast ice: improvements from the mushy-layer thermodynamics
Modeling the timing of Patagonian Ice Sheet retreat in the Chilean Lake District from 22–10 ka
Understanding the influence of ocean waves on Arctic sea ice simulation: a modeling study with an atmosphere–ocean–wave–sea ice coupled model
Sea ice cover in the Copernicus Arctic Regional Reanalysis
Regime shifts in Arctic terrestrial hydrology manifested from impacts of climate warming
Smoothed particle hydrodynamics implementation of the standard viscous–plastic sea-ice model and validation in simple idealized experiments
Coupled thermo–geophysical inversion for permafrost monitoring
Using specularity content to evaluate eight geothermal heat flow maps of Totten Glacier
Surging of a Hudson Strait-scale ice stream: subglacial hydrology matters but the process details mostly do not
Impact of the Nares Strait sea ice arches on the long-term stability of the Petermann Glacier ice shelf
Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment
Quantifying the uncertainty in the Eurasian ice-sheet geometry at the Penultimate Glacial Maximum (Marine Isotope Stage 6)
Simulating ice segregation and thaw consolidation in permafrost environments with the CryoGrid community model
Reconciling ice dynamics and bed topography with a versatile and fast ice thickness inversion
The stability of present-day Antarctic grounding lines – Part 2: Onset of irreversible retreat of Amundsen Sea glaciers under current climate on centennial timescales cannot be excluded
The stability of present-day Antarctic grounding lines – Part 1: No indication of marine ice sheet instability in the current geometry
Phase-field models of floe fracture in sea ice
Exploring the ability of the variable-resolution Community Earth System Model to simulate cryospheric–hydrological variables in High Mountain Asia
Investigating the thermal state of permafrost with Bayesian inverse modeling of heat transfer
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
Marijn van der Meer, Harry Zekollari, Matthias Huss, Jordi Bolibar, Kamilla Hauknes Sjursen, and Daniel Farinotti
EGUsphere, https://doi.org/10.5194/egusphere-2024-2378, https://doi.org/10.5194/egusphere-2024-2378, 2024
Short summary
Short summary
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.–Febr.). Our model can accurately predict glacier mass from 1961–2021 but struggles for extreme years (2022 and 2023).
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
Manon Gaillard, Vincent Vionnet, Matthieu Lafaysse, Marie Dumont, and Paul Ginoux
EGUsphere, https://doi.org/10.5194/egusphere-2024-1795, https://doi.org/10.5194/egusphere-2024-1795, 2024
Short summary
Short summary
This study presents an efficient method to improve large-scale snow albedo simulations by considering the spatial variability of 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 ten global sites improved albedo predictions by 10 % on average and over 25 % in the Arctic. This method can also enhance other snow models' predictions without complex simulations.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
Enrico Zorzetto, Paul Ginoux, Sergey Malyshev, and Elena Shevliakova
EGUsphere, https://doi.org/10.5194/egusphere-2024-1258, https://doi.org/10.5194/egusphere-2024-1258, 2024
Short summary
Short summary
Light-absorbing particles (LAPs) deposition on snow leads to a darkening of the snow surface and can thus accelerate snow melt. Understanding to what extent different types of LAPs contribute to snow melt is important both to predict changes in water availability and for improving 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.
Tim van den Akker, William H. Lipscomb, Gunter R. Leguy, Jorjo Bernales, Constantijn Berends, Willem Jan van de Berg, and Roderik S. W. van de Wal
EGUsphere, https://doi.org/10.5194/egusphere-2024-851, https://doi.org/10.5194/egusphere-2024-851, 2024
Short summary
Short summary
In this study, we present an improved way of representing ice thickness change rates into an ice sheet model. We apply this method using two ice sheet models on the Antarctic Ice Sheet. We found that the two largest outlet glaciers on the Antarctic Ice Sheet, the 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 meters globally.
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
Short summary
Short summary
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
Short summary
Short summary
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.
Jonathan D. Mackay, Nicholas E. Barrand, David M. Hannah, Emily Potter, Nilton Montoya, and Wouter Buytaert
EGUsphere, https://doi.org/10.5194/egusphere-2024-863, https://doi.org/10.5194/egusphere-2024-863, 2024
Short summary
Short summary
Glaciers in the tropics are poorly-observed, making it difficult to predict how they will retreat in the future. Most computer models neglect important processes that control tropical glacier retreat. We combine two existing models to remedy this limitation. Our model replicates observed changes in glacier retreat and shows us where our process understanding limits the accuracy of predictions and which processes are less important than we previously thought, helping to direct future research.
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
Yan Huang, Liyun Zhao, Michael Wolovick, Yiliang Ma, and John C. Moore
The Cryosphere, 18, 103–119, https://doi.org/10.5194/tc-18-103-2024, https://doi.org/10.5194/tc-18-103-2024, 2024
Short summary
Short summary
Geothermal heat flux (GHF) is an important factor affecting the basal thermal environment of an ice sheet and crucial for its dynamics. But it is poorly defined for the Antarctic ice sheet. We simulate the basal temperature and basal melting rate with eight different GHF datasets. We use specularity content as a two-sided constraint to discriminate between local wet or dry basal conditions. Two medium-magnitude GHF distribution maps rank well, showing that most of the inland bed area is frozen.
Matthew Drew and Lev Tarasov
The Cryosphere, 17, 5391–5415, https://doi.org/10.5194/tc-17-5391-2023, https://doi.org/10.5194/tc-17-5391-2023, 2023
Short summary
Short summary
The interaction of fast-flowing regions of continental ice sheets with their beds governs how quickly they slide and therefore flow. The coupling of fast ice to its bed is controlled by the pressure of meltwater at its base. It is currently poorly understood how the physical details of these hydrologic systems affect ice speedup. Using numerical models we find, surprisingly, that they largely do not, except for the duration of the surge. This suggests that cheap models are sufficient.
Abhay Prakash, Qin Zhou, Tore Hattermann, and Nina Kirchner
The Cryosphere, 17, 5255–5281, https://doi.org/10.5194/tc-17-5255-2023, https://doi.org/10.5194/tc-17-5255-2023, 2023
Short summary
Short summary
Sea ice arch formation in the Nares Strait has shielded the Petermann Glacier ice shelf from enhanced basal melting. However, with the sustained decline of the Arctic sea ice predicted to continue, the ice shelf is likely to be exposed to a year-round mobile and thin sea ice cover. In such a scenario, our modelled results show that elevated temperatures, and more importantly, a stronger ocean circulation in the ice shelf cavity, could result in up to two-thirds increase in basal melt.
Michael Wolovick, Angelika Humbert, Thomas Kleiner, and Martin Rückamp
The Cryosphere, 17, 5027–5060, https://doi.org/10.5194/tc-17-5027-2023, https://doi.org/10.5194/tc-17-5027-2023, 2023
Short summary
Short summary
The friction underneath ice sheets can be inferred from observed velocity at the top, but this inference requires smoothing. The selection of smoothing has been highly variable in the literature. Here we show how to rigorously select the best smoothing, and we show that the inferred friction converges towards the best knowable field as model resolution improves. We use this to learn about the best description of basal friction and to formulate recommended best practices for other modelers.
Oliver G. Pollard, Natasha L. M. Barlow, Lauren J. Gregoire, Natalya Gomez, Víctor Cartelle, Jeremy C. Ely, and Lachlan C. Astfalck
The Cryosphere, 17, 4751–4777, https://doi.org/10.5194/tc-17-4751-2023, https://doi.org/10.5194/tc-17-4751-2023, 2023
Short summary
Short summary
We use advanced statistical techniques and a simple ice-sheet model to produce an ensemble of plausible 3D shapes of the ice sheet that once stretched across northern Europe during the previous glacial maximum (140,000 years ago). This new reconstruction, equivalent in volume to 48 ± 8 m of global mean sea-level rise, will improve the interpretation of high sea levels recorded from the Last Interglacial period (120 000 years ago) that provide a useful perspective on the future.
Juditha Aga, Julia Boike, Moritz Langer, Thomas Ingeman-Nielsen, and Sebastian Westermann
The Cryosphere, 17, 4179–4206, https://doi.org/10.5194/tc-17-4179-2023, https://doi.org/10.5194/tc-17-4179-2023, 2023
Short summary
Short summary
This study presents a new model scheme for simulating ice segregation and thaw consolidation in permafrost environments, depending on ground properties and climatic forcing. It is embedded in the CryoGrid community model, a land surface model for the terrestrial cryosphere. We describe the model physics and functionalities, followed by a model validation and a sensitivity study of controlling factors.
Thomas Frank, Ward J. J. van Pelt, and Jack Kohler
The Cryosphere, 17, 4021–4045, https://doi.org/10.5194/tc-17-4021-2023, https://doi.org/10.5194/tc-17-4021-2023, 2023
Short summary
Short summary
Since the ice thickness of most glaciers worldwide is unknown, and since it is not feasible to visit every glacier and observe their thickness directly, inverse modelling techniques are needed that can calculate ice thickness from abundant surface observations. Here, we present a new method for doing that. Our methodology relies on modelling the rate of surface elevation change for a given glacier, compare this with observations of the same quantity and change the bed until the two are in line.
Ronja Reese, Julius Garbe, Emily A. Hill, Benoît Urruty, Kaitlin A. Naughten, Olivier Gagliardini, Gaël Durand, Fabien Gillet-Chaulet, G. Hilmar Gudmundsson, David Chandler, Petra M. Langebroek, and Ricarda Winkelmann
The Cryosphere, 17, 3761–3783, https://doi.org/10.5194/tc-17-3761-2023, https://doi.org/10.5194/tc-17-3761-2023, 2023
Short summary
Short summary
We use an ice sheet model to test where current climate conditions in Antarctica might lead. We find that present-day ocean and atmosphere conditions might commit an irreversible collapse of parts of West Antarctica which evolves over centuries to millennia. Importantly, this collapse is not irreversible yet.
Emily A. Hill, Benoît Urruty, Ronja Reese, Julius Garbe, Olivier Gagliardini, Gaël Durand, Fabien Gillet-Chaulet, G. Hilmar Gudmundsson, Ricarda Winkelmann, Mondher Chekki, David Chandler, and Petra M. Langebroek
The Cryosphere, 17, 3739–3759, https://doi.org/10.5194/tc-17-3739-2023, https://doi.org/10.5194/tc-17-3739-2023, 2023
Short summary
Short summary
The grounding lines of the Antarctic Ice Sheet could enter phases of irreversible retreat or advance. We use three ice sheet models to show that the present-day locations of Antarctic grounding lines are reversible with respect to a small perturbation away from their current position. This indicates that present-day retreat of the grounding lines is not yet irreversible or self-enhancing.
Huy Dinh, Dimitrios Giannakis, Joanna Slawinska, and Georg Stadler
The Cryosphere, 17, 3883–3893, https://doi.org/10.5194/tc-17-3883-2023, https://doi.org/10.5194/tc-17-3883-2023, 2023
Short summary
Short summary
We develop a numerical method to simulate the fracture in kilometer-sized chunks of floating ice in the ocean. Our approach uses a mathematical model that balances deformation energy against the energy required for fracture. We study the strength of ice chunks that contain random impurities due to prior damage or refreezing and what types of fractures are likely to occur. Our model shows that crack direction critically depends on the orientation of impurities relative to surrounding forces.
René R. Wijngaard, Adam R. Herrington, William H. Lipscomb, Gunter R. Leguy, and Soon-Il An
The Cryosphere, 17, 3803–3828, https://doi.org/10.5194/tc-17-3803-2023, https://doi.org/10.5194/tc-17-3803-2023, 2023
Short summary
Short summary
We evaluate the ability of the Community Earth System Model (CESM2) to simulate cryospheric–hydrological variables, such as glacier surface mass balance (SMB), over High Mountain Asia (HMA) by using a global grid (~111 km) with regional refinement (~7 km) over HMA. Evaluations of two different simulations show that climatological biases are reduced, and glacier SMB is improved (but still too negative) by modifying the snow and glacier model and using an updated glacier cover dataset.
Brian Groenke, Moritz Langer, Jan Nitzbon, Sebastian Westermann, Guillermo Gallego, and Julia Boike
The Cryosphere, 17, 3505–3533, https://doi.org/10.5194/tc-17-3505-2023, https://doi.org/10.5194/tc-17-3505-2023, 2023
Short summary
Short summary
It is now well known from long-term temperature measurements that Arctic permafrost, i.e., ground that remains continuously frozen for at least 2 years, is warming in response to climate change. Temperature, however, only tells half of the story. In this study, we use computer modeling to better understand how the thawing and freezing of water in the ground affects the way permafrost responds to climate change and what temperature trends can and cannot tell us about how permafrost is changing.
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.
