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.
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
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.
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
Arctic sea ice mass balance in a new coupled ice–ocean model using a brittle rheology framework
Snow cover prediction in the Italian central Apennines using weather forecast and land surface numerical models
Geothermal heat flux is the dominant source of uncertainty in englacial-temperature-based dating of ice rise formation
Simulating the current and future northern limit of permafrost on the Qinghai–Tibet Plateau
Improving interpretation of sea-level projections through a machine-learning-based local explanation approach
Subglacial hydrology modulates basal sliding response of the Antarctic ice sheet to climate forcing
Thermal regime of the Grigoriev ice cap and the Sary-Tor glacier in the inner Tien Shan, Kyrgyzstan
Wave-triggered breakup in the marginal ice zone generates lognormal floe size distributions: a simulation study
Exploring the capabilities of electrical resistivity tomography to study subsea permafrost
The predictive power of ice sheet models and the regional sensitivity of ice loss to basal sliding parameterisations: a case study of Pine Island and Thwaites glaciers, West Antarctica
Evaluating simplifications of subsurface process representations for field-scale permafrost hydrology models
Simulations of firn processes over the Greenland and Antarctic ice sheets: 1980–2021
Evaluation of six geothermal heat flux maps for the Antarctic Lambert–Amery glacial system
Representation of soil hydrology in permafrost regions may explain large part of inter-model spread in simulated Arctic and subarctic climate
A data exploration tool for averaging and accessing large data sets of snow stratigraphy profiles useful for avalanche forecasting
Sea ice floe size: its impact on pan-Arctic and local ice mass and required model complexity
Land–atmosphere interactions in sub-polar and alpine climates in the CORDEX flagship pilot study Land Use and Climate Across Scales (LUCAS) models – Part 1: Evaluation of the snow-albedo effect
Impact of runoff temporal distribution on ice dynamics
Impact of atmospheric forcing uncertainties on Arctic and Antarctic sea ice simulation in CMIP6 OMIP
The stability of present-day Antarctic grounding lines – Part B: Possible commitment of regional collapse under current climate
Can changes in deformation regimes be inferred from crystallographic preferred orientations in polar ice?
Stabilizing effect of mélange buttressing on the marine ice-cliff instability of the West Antarctic Ice Sheet
A probabilistic seabed–ice keel interaction model
Modelling supraglacial debris-cover evolution from the single-glacier to the regional scale: an application to High Mountain Asia
The effect of changing sea ice on wave climate trends along Alaska's central Beaufort Sea coast
Strong increase in thawing of subsea permafrost in the 22nd century caused by anthropogenic climate change
Arctic sea ice anomalies during the MOSAiC winter 2019/20
Effective coefficient of diffusion and permeability of firn at Dome C and Lock In, Antarctica, and of various snow types – estimates over the 100–850 kg m−3 density range
Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes
The instantaneous impact of calving and thinning on the Larsen C Ice Shelf
Derivation of bedrock topography measurement requirements for the reduction of uncertainty in ice-sheet model projections of Thwaites Glacier
A comparison of the stability and performance of depth-integrated ice-dynamics solvers
A new vertically integrated MOno-Layer Higher-Order (MOLHO) ice flow model
On the contribution of grain boundary sliding type creep to firn densification – an assessment using an optimization approach
Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes
Assessment of neutrons from secondary cosmic rays at mountain altitudes – Geant4 simulations of environmental parameters including soil moisture and snow cover
A seasonal algorithm of the snow-covered area fraction for mountainous terrain
Edge displacement scores
The 21st-century fate of the Mocho-Choshuenco ice cap in southern Chile
Lateral thermokarst patterns in permafrost peat plateaus in northern Norway
Modelling steady states and the transient response of debris-covered glaciers
Marine ice sheet experiments with the Community Ice Sheet Model
Twentieth century global glacier mass change: an ensemble-based model reconstruction
A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation
The transferability of adjoint inversion products between different ice flow models
Inferring the basal sliding coefficient field for the Stokes ice sheet model under rheological uncertainty
The tipping points and early warning indicators for Pine Island Glacier, West Antarctica
Effects of multi-scale heterogeneity on the simulated evolution of ice-rich permafrost lowlands under a warming climate
Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations
Snow cover duration trends observed at sites and predicted by multiple models
Guillaume Boutin, Einar Ólason, Pierre Rampal, Heather Regan, Camille Lique, Claude Talandier, Laurent Brodeau, and Robert Ricker
The Cryosphere, 17, 617–638, https://doi.org/10.5194/tc-17-617-2023, https://doi.org/10.5194/tc-17-617-2023, 2023
Short summary
Short summary
Sea ice cover in the Arctic is full of cracks, which we call leads. We suspect that these leads play a role for atmosphere–ocean interactions in polar regions, but their importance remains challenging to estimate. We use a new ocean–sea ice model with an original way of representing sea ice dynamics to estimate their impact on winter sea ice production. This model successfully represents sea ice evolution from 2000 to 2018, and we find that about 30 % of ice production takes place in leads.
Edoardo Raparelli, Paolo Tuccella, Valentina Colaiuda, and Frank S. Marzano
The Cryosphere, 17, 519–538, https://doi.org/10.5194/tc-17-519-2023, https://doi.org/10.5194/tc-17-519-2023, 2023
Short summary
Short summary
We evaluate the skills of a single-layer (Noah) and a multi-layer (Alpine3D) snow model, forced with the Weather Research and Forecasting model, to reproduce snowpack properties observed in the Italian central Apennines. We found that Alpine3D reproduces the observed snow height and snow water equivalent better than Noah, while no particular model differences emerge on snow cover extent. Finally, we observed that snow settlement is mainly due to densification in Alpine3D and to melting in Noah.
Aleksandr Montelli and Jonathan Kingslake
The Cryosphere, 17, 195–210, https://doi.org/10.5194/tc-17-195-2023, https://doi.org/10.5194/tc-17-195-2023, 2023
Short summary
Short summary
Thermal modelling and Bayesian inversion techniques are used to evaluate the uncertainties inherent in inferences of ice-sheet evolution from borehole temperature measurements. We show that the same temperature profiles may result from a range of parameters, of which geothermal heat flux through underlying bedrock plays a key role. Careful model parameterisation and evaluation of heat flux are essential for inferring past ice-sheet evolution from englacial borehole thermometry.
Jianting Zhao, Lin Zhao, Zhe Sun, Fujun Niu, Guojie Hu, Defu Zou, Guangyue Liu, Erji Du, Chong Wang, Lingxiao Wang, Yongping Qiao, Jianzong Shi, Yuxin Zhang, Junqiang Gao, Yuanwei Wang, Yan Li, Wenjun Yu, Huayun Zhou, Zanpin Xing, Minxuan Xiao, Luhui Yin, and Shengfeng Wang
The Cryosphere, 16, 4823–4846, https://doi.org/10.5194/tc-16-4823-2022, https://doi.org/10.5194/tc-16-4823-2022, 2022
Short summary
Short summary
Permafrost has been warming and thawing globally; this is especially true in boundary regions. We focus on the changes and variability in permafrost distribution and thermal dynamics in the northern limit of permafrost on the Qinghai–Tibet Plateau (QTP) by applying a new permafrost model. Unlike previous papers on this topic, our findings highlight a slow, decaying process in the response of permafrost in the QTP to a warming climate, especially regarding areal extent.
Jeremy Rohmer, Remi Thieblemont, Goneri Le Cozannet, Heiko Goelzer, and Gael Durand
The Cryosphere, 16, 4637–4657, https://doi.org/10.5194/tc-16-4637-2022, https://doi.org/10.5194/tc-16-4637-2022, 2022
Short summary
Short summary
To improve the interpretability of process-based projections of the sea-level contribution from land ice components, we apply the machine-learning-based
SHapley Additive exPlanationsapproach to a subset of a multi-model ensemble study for the Greenland ice sheet. This allows us to quantify the influence of particular modelling decisions (related to numerical implementation, initial conditions, or parametrisation of ice-sheet processes) directly in terms of sea-level change contribution.
Elise Kazmierczak, Sainan Sun, Violaine Coulon, and Frank Pattyn
The Cryosphere, 16, 4537–4552, https://doi.org/10.5194/tc-16-4537-2022, https://doi.org/10.5194/tc-16-4537-2022, 2022
Short summary
Short summary
The water at the interface between ice sheets and underlying bedrock leads to lubrication between the ice and the bed. Due to a lack of direct observations, subglacial conditions beneath the Antarctic ice sheet are poorly understood. Here, we compare different approaches in which the subglacial water could influence sliding on the underlying bedrock and suggest that it modulates the Antarctic ice sheet response and increases uncertainties, especially in the context of global warming.
Lander Van Tricht and Philippe Huybrechts
The Cryosphere, 16, 4513–4535, https://doi.org/10.5194/tc-16-4513-2022, https://doi.org/10.5194/tc-16-4513-2022, 2022
Short summary
Short summary
We examine the thermal regime of the Grigoriev ice cap and the Sary-Tor glacier, both located in the inner Tien Shan in Kyrgyzstan. Our findings are important as the ice dynamics can only be understood and modelled precisely if ice temperature is considered correctly in ice flow models. The calibrated parameters of this study can be used in applications with ice flow models for individual ice masses as well as to optimise more general models for large-scale regional simulations.
Nicolas Guillaume Alexandre Mokus and Fabien Montiel
The Cryosphere, 16, 4447–4472, https://doi.org/10.5194/tc-16-4447-2022, https://doi.org/10.5194/tc-16-4447-2022, 2022
Short summary
Short summary
On the fringes of polar oceans, sea ice is easily broken by waves. As small pieces of ice, or floes, are more easily melted by the warming waters than a continuous ice cover, it is important to incorporate these floe sizes in climate models. These models simulate climate evolution at the century scale and are built by combining specialised modules. We study the statistical distribution of floe sizes under the impact of waves to better understand how to connect sea ice modules to wave modules.
Mauricio Arboleda-Zapata, Michael Angelopoulos, Pier Paul Overduin, Guido Grosse, Benjamin M. Jones, and Jens Tronicke
The Cryosphere, 16, 4423–4445, https://doi.org/10.5194/tc-16-4423-2022, https://doi.org/10.5194/tc-16-4423-2022, 2022
Short summary
Short summary
We demonstrate how we can reliably estimate the thawed–frozen permafrost interface with its associated uncertainties in subsea permafrost environments using 2D electrical resistivity tomography (ERT) data. In addition, we show how further analyses considering 1D inversion and sensitivity assessments can help quantify and better understand 2D ERT inversion results. Our results illustrate the capabilities of the ERT method to get insights into the development of the subsea permafrost.
Jowan M. Barnes and G. Hilmar Gudmundsson
The Cryosphere, 16, 4291–4304, https://doi.org/10.5194/tc-16-4291-2022, https://doi.org/10.5194/tc-16-4291-2022, 2022
Short summary
Short summary
Models must represent how glaciers slide along the bed, but there are many ways to do so. In this paper, several sliding laws are tested and found to affect different regions of the Antarctic Ice Sheet in different ways and at different speeds. However, the variability in ice volume loss due to sliding-law choices is low compared to other factors, so limited empirical knowledge of sliding does not prevent us from making predictions of how an ice sheet will evolve.
Bo Gao and Ethan T. Coon
The Cryosphere, 16, 4141–4162, https://doi.org/10.5194/tc-16-4141-2022, https://doi.org/10.5194/tc-16-4141-2022, 2022
Short summary
Short summary
Representing water at constant density, neglecting cryosuction, and neglecting heat advection are three commonly applied but not validated simplifications in permafrost models to reduce computation complexity at field scale. We investigated this problem numerically by Advanced Terrestrial Simulator and found that neglecting cryosuction can cause significant bias (10%–60%), constant density primarily affects predicting water saturation, and ignoring heat advection has the least impact.
Brooke Medley, Thomas A. Neumann, H. Jay Zwally, Benjamin E. Smith, and C. Max Stevens
The Cryosphere, 16, 3971–4011, https://doi.org/10.5194/tc-16-3971-2022, https://doi.org/10.5194/tc-16-3971-2022, 2022
Short summary
Short summary
Satellite altimeters measure the height or volume change over Earth's ice sheets, but in order to understand how that change translates into ice mass, we must account for various processes at the surface. Specifically, snowfall events generate large, transient increases in surface height, yet snow fall has a relatively low density, which means much of that height change is composed of air. This air signal must be removed from the observed height changes before we can assess ice mass change.
Haoran Kang, Liyun Zhao, Michael Wolovick, and John C. Moore
The Cryosphere, 16, 3619–3633, https://doi.org/10.5194/tc-16-3619-2022, https://doi.org/10.5194/tc-16-3619-2022, 2022
Short summary
Short summary
Basal thermal conditions are important to ice dynamics and sensitive to geothermal heat flux (GHF). We estimate basal thermal conditions of the Lambert–Amery Glacier system with six GHF maps. Recent GHFs inverted from aerial geomagnetic observations produce a larger warm-based area and match the observed subglacial lakes better than the other GHFs. The modelled basal melt rate is 10 to hundreds of millimetres per year in fast-flowing glaciers feeding the Amery Ice Shelf and smaller inland.
Philipp de Vrese, Goran Georgievski, Jesus Fidel Gonzalez Rouco, Dirk Notz, Tobias Stacke, Norman Julius Steinert, Stiig Wilkenskjeld, and Victor Brovkin
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-150, https://doi.org/10.5194/tc-2022-150, 2022
Revised manuscript accepted for TC
Short summary
Short summary
The current generation of Earth system models exhibits large inter-model differences in the simulated climate of the Arctic and subarctic zone. We used an adapted version of the MPI Earth System model to show that differences in the representation of the soil hydrology in permafrost-affected regions could help explain a large part of the inter-model spread in the Arctic and subarctic climate and also have pronounced impacts on important whether systems as far to the south as the tropics.
Florian Herla, Pascal Haegeli, and Patrick Mair
The Cryosphere, 16, 3149–3162, https://doi.org/10.5194/tc-16-3149-2022, https://doi.org/10.5194/tc-16-3149-2022, 2022
Short summary
Short summary
We present an averaging algorithm for multidimensional snow stratigraphy profiles that elicits the predominant snow layering among large numbers of profiles and allows for compiling of informative summary statistics and distributions of snowpack layer properties. This creates new opportunities for presenting and analyzing operational snowpack simulations in support of avalanche forecasting and may inspire new ways of processing profiles and time series in other geophysical contexts.
Adam William Bateson, Daniel L. Feltham, David Schröder, Yanan Wang, Byongjun Hwang, Jeff K. Ridley, and Yevgeny Aksenov
The Cryosphere, 16, 2565–2593, https://doi.org/10.5194/tc-16-2565-2022, https://doi.org/10.5194/tc-16-2565-2022, 2022
Short summary
Short summary
Numerical models are used to understand the mechanisms that drive the evolution of the Arctic sea ice cover. The sea ice cover is formed of pieces of ice called floes. Several recent studies have proposed variable floe size models to replace the standard model assumption of a fixed floe size. In this study we show the need to include floe fragmentation processes in these variable floe size models and demonstrate that model design can determine the impact of floe size on size ice evolution.
Anne Sophie Daloz, Clemens Schwingshackl, Priscilla Mooney, Susanna Strada, Diana Rechid, Edouard L. Davin, Eleni Katragkou, Nathalie de Noblet-Ducoudré, Michal Belda, Tomas Halenka, Marcus Breil, Rita M. Cardoso, Peter Hoffmann, Daniela C. A. Lima, Ronny Meier, Pedro M. M. Soares, Giannis Sofiadis, Gustav Strandberg, Merja H. Toelle, and Marianne T. Lund
The Cryosphere, 16, 2403–2419, https://doi.org/10.5194/tc-16-2403-2022, https://doi.org/10.5194/tc-16-2403-2022, 2022
Short summary
Short summary
Snow plays a major role in the regulation of the Earth's surface temperature. Together with climate change, rising temperatures are already altering snow in many ways. In this context, it is crucial to better understand the ability of climate models to represent snow and snow processes. This work focuses on Europe and shows that the melting season in spring still represents a challenge for climate models and that more work is needed to accurately simulate snow–atmosphere interactions.
Basile de Fleurian, Richard Davy, and Petra M. Langebroek
The Cryosphere, 16, 2265–2283, https://doi.org/10.5194/tc-16-2265-2022, https://doi.org/10.5194/tc-16-2265-2022, 2022
Short summary
Short summary
As temperature increases, more snow and ice melt at the surface of ice sheets. Here we use an ice dynamics and subglacial hydrology model with simplified geometry and climate forcing to study the impact of variations in meltwater on ice dynamics. We focus on the variations in length and intensity of the melt season. Our results show that a longer melt season leads to faster glaciers, but a more intense melt season reduces glaciers' seasonal velocities, albeit leading to higher peak velocities.
Xia Lin, François Massonnet, Thierry Fichefet, and Martin Vancoppenolle
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-110, https://doi.org/10.5194/tc-2022-110, 2022
Revised manuscript accepted for TC
Short summary
Short summary
This study provides clues on how improved atmospheric reanalysis products influence sea ice simulations in ocean-sea ice models. The summer ice concentration simulation in both hemispheres can be improved with changed surface heat fluxes. The winter Antarctic ice concentration and the Arctic drift speed near the ice edge and the ice velocity direction simulations are improved with changed wind stress. The radiation fluxes and winds in atmospheric reanalyses are crucial for sea ice simulation.
Ronja Reese, Julius Garbe, Emily A. Hill, Benoît Urruty, Kaitlin A. Naughten, Olivier Gagliardini, Gael Durand, Fabien Gillet-Chaulet, David Chandler, Petra M. Langebroek, and Ricarda Winkelmann
The Cryosphere Discuss., https://doi.org/10.5194/tc-2022-105, https://doi.org/10.5194/tc-2022-105, 2022
Revised manuscript accepted for TC
Short summary
Short summary
We use an ice sheet model to test where current climate conditions in Antarctica might lead. We find that, depending on model parameters, present-day ocean and atmosphere conditions might commit a collapse of parts of West Antarctica which evolves over centuries to millennia. Importantly, this collapse is not yet irreversible as shown in our accompanying study.
Maria-Gema Llorens, Albert Griera, Paul D. Bons, Ilka Weikusat, David J. Prior, Enrique Gomez-Rivas, Tamara de Riese, Ivone Jimenez-Munt, Daniel García-Castellanos, and Ricardo A. Lebensohn
The Cryosphere, 16, 2009–2024, https://doi.org/10.5194/tc-16-2009-2022, https://doi.org/10.5194/tc-16-2009-2022, 2022
Short summary
Short summary
Polar ice is formed by ice crystals, which form fabrics that are utilised to interpret how ice sheets flow. It is unclear whether fabrics result from the current flow regime or if they are inherited. To understand the extent to which ice crystals can be reoriented when ice flow conditions change, we simulate and evaluate multi-stage ice flow scenarios according to natural cases. We find that second deformation regimes normally overprint inherited fabrics, with a range of transitional fabrics.
Tanja Schlemm, Johannes Feldmann, Ricarda Winkelmann, and Anders Levermann
The Cryosphere, 16, 1979–1996, https://doi.org/10.5194/tc-16-1979-2022, https://doi.org/10.5194/tc-16-1979-2022, 2022
Short summary
Short summary
Marine cliff instability, if it exists, could dominate Antarctica's contribution to future sea-level rise. It is likely to speed up with ice thickness and thus would accelerate in most parts of Antarctica. Here, we investigate a possible mechanism that might stop cliff instability through cloaking by ice mélange. It is only a first step, but it shows that embayment geometry is, in principle, able to stop marine cliff instability in most parts of West Antarctica.
Frédéric Dupont, Dany Dumont, Jean-François Lemieux, Elie Dumas-Lefebvre, and Alain Caya
The Cryosphere, 16, 1963–1977, https://doi.org/10.5194/tc-16-1963-2022, https://doi.org/10.5194/tc-16-1963-2022, 2022
Short summary
Short summary
In some shallow seas, grounded ice ridges contribute to stabilizing and maintaining a landfast ice cover. A scheme has already proposed where the keel thickness varies linearly with the mean thickness. Here, we extend the approach by taking into account the ice thickness and bathymetry distributions. The probabilistic approach shows a reasonably good agreement with observations and previous grounding scheme while potentially offering more physical insights into the formation of landfast ice.
Loris Compagno, Matthias Huss, Evan Stewart Miles, Michael James McCarthy, Harry Zekollari, Amaury Dehecq, Francesca Pellicciotti, and Daniel Farinotti
The Cryosphere, 16, 1697–1718, https://doi.org/10.5194/tc-16-1697-2022, https://doi.org/10.5194/tc-16-1697-2022, 2022
Short summary
Short summary
We present a new approach for modelling debris area and thickness evolution. We implement the module into a combined mass-balance ice-flow model, and we apply it using different climate scenarios to project the future evolution of all glaciers in High Mountain Asia. We show that glacier geometry, volume, and flow velocity evolve differently when modelling explicitly debris cover compared to glacier evolution without the debris-cover module, demonstrating the importance of accounting for debris.
Kees Nederhoff, Li Erikson, Anita Engelstad, Peter Bieniek, and Jeremy Kasper
The Cryosphere, 16, 1609–1629, https://doi.org/10.5194/tc-16-1609-2022, https://doi.org/10.5194/tc-16-1609-2022, 2022
Short summary
Short summary
Diminishing sea ice is impacting waves across the Arctic region. Recent work shows the effect of the sea ice on offshore waves; however, effects within the nearshore are less known. This study characterizes the wave climate in the central Beaufort Sea coast of Alaska. We show that the reduction of sea ice correlates strongly with increases in the average and extreme waves. However, found trends deviate from offshore, since part of the increase in energy is dissipated before reaching the shore.
Stiig Wilkenskjeld, Frederieke Miesner, Paul P. Overduin, Matteo Puglini, and Victor Brovkin
The Cryosphere, 16, 1057–1069, https://doi.org/10.5194/tc-16-1057-2022, https://doi.org/10.5194/tc-16-1057-2022, 2022
Short summary
Short summary
Thawing permafrost releases carbon to the atmosphere, enhancing global warming. Part of the permafrost soils have been flooded by rising sea levels since the last ice age, becoming subsea permafrost (SSPF). The SSPF is less studied than the part on land. In this study we use a global model to obtain rates of thawing of SSPF under different future climate scenarios until the year 3000. After the year 2100 the scenarios strongly diverge, closely connected to the eventual disappearance of sea ice.
Klaus Dethloff, Wieslaw Maslowski, Stefan Hendricks, Younjoo J. Lee, Helge F. Goessling, Thomas Krumpen, Christian Haas, Dörthe Handorf, Robert Ricker, Vladimir Bessonov, John J. Cassano, Jaclyn Clement Kinney, Robert Osinski, Markus Rex, Annette Rinke, Julia Sokolova, and Anja Sommerfeld
The Cryosphere, 16, 981–1005, https://doi.org/10.5194/tc-16-981-2022, https://doi.org/10.5194/tc-16-981-2022, 2022
Short summary
Short summary
Sea ice thickness anomalies during the MOSAiC (Multidisciplinary drifting Observatory for the Study of Arctic Climate) winter in January, February and March 2020 were simulated with the coupled Regional Arctic climate System Model (RASM) and compared with CryoSat-2/SMOS satellite data. Hindcast and ensemble simulations indicate that the sea ice anomalies are driven by nonlinear interactions between ice growth processes and wind-driven sea-ice transports, with dynamics playing a dominant role.
Neige Calonne, Alexis Burr, Armelle Philip, Frédéric Flin, and Christian Geindreau
The Cryosphere, 16, 967–980, https://doi.org/10.5194/tc-16-967-2022, https://doi.org/10.5194/tc-16-967-2022, 2022
Short summary
Short summary
Modeling gas transport in ice sheets from surface to close-off is key to interpreting climate archives. Estimates of the diffusion coefficient and permeability of snow and firn are required but remain a large source of uncertainty. We present a new dataset of diffusion coefficients and permeability from 20 to 120 m depth at two Antarctic sites. We suggest predictive formulas to estimate both properties over the entire 100–850 kg m3 density range, i.e., anywhere within the ice sheet column.
Konstantin Schürholt, Julia Kowalski, and Henning Löwe
The Cryosphere, 16, 903–923, https://doi.org/10.5194/tc-16-903-2022, https://doi.org/10.5194/tc-16-903-2022, 2022
Short summary
Short summary
This companion paper deals with numerical particularities of partial differential equations underlying 1D snow models. In this first part we neglect mechanical settling and demonstrate that the nonlinear coupling between diffusive transport (heat and vapor), phase changes and ice mass conservation contains a wave instability that may be relevant for weak layer formation. Numerical requirements are discussed in view of the underlying homogenization scheme.
Tom Mitcham, G. Hilmar Gudmundsson, and Jonathan L. Bamber
The Cryosphere, 16, 883–901, https://doi.org/10.5194/tc-16-883-2022, https://doi.org/10.5194/tc-16-883-2022, 2022
Short summary
Short summary
We modelled the response of the Larsen C Ice Shelf (LCIS) and its tributary glaciers to the calving of the A68 iceberg and validated our results with observations. We found that the impact was limited, confirming that mostly passive ice was calved. Through further calving experiments we quantified the total buttressing provided by the LCIS and found that over 80 % of the buttressing capacity is generated in the first 5 km of the ice shelf downstream of the grounding line.
Blake A. Castleman, Nicole-Jeanne Schlegel, Lambert Caron, Eric Larour, and Ala Khazendar
The Cryosphere, 16, 761–778, https://doi.org/10.5194/tc-16-761-2022, https://doi.org/10.5194/tc-16-761-2022, 2022
Short summary
Short summary
In the described study, we derive an uncertainty range for global mean sea level rise (SLR) contribution from Thwaites Glacier in a 200-year period under an extreme ocean warming scenario. We derive the spatial and vertical resolutions needed for bedrock data acquisition missions in order to limit global mean SLR contribution from Thwaites Glacier to ±2 cm in a 200-year period. We conduct sensitivity experiments in order to present the locations of critical regions in need of accurate mapping.
Alexander Robinson, Daniel Goldberg, and William H. Lipscomb
The Cryosphere, 16, 689–709, https://doi.org/10.5194/tc-16-689-2022, https://doi.org/10.5194/tc-16-689-2022, 2022
Short summary
Short summary
Here we investigate the numerical stability of several commonly used methods in order to determine which of them are capable of resolving the complex physics of the ice flow and are also computationally efficient. We find that the so-called DIVA solver outperforms the others. Its representation of the physics is consistent with more complex methods, while it remains computationally efficient at high resolution.
Thiago Dias dos Santos, Mathieu Morlighem, and Douglas Brinkerhoff
The Cryosphere, 16, 179–195, https://doi.org/10.5194/tc-16-179-2022, https://doi.org/10.5194/tc-16-179-2022, 2022
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.
Timm Schultz, Ralf Müller, Dietmar Gross, and Angelika Humbert
The Cryosphere, 16, 143–158, https://doi.org/10.5194/tc-16-143-2022, https://doi.org/10.5194/tc-16-143-2022, 2022
Short summary
Short summary
Firn is the interstage product between snow and ice. Simulations describing the process of firn densification are used in the context of estimating mass changes of the ice sheets and past climate reconstructions. The first stage of firn densification takes place in the upper few meters of the firn column. We investigate how well a material law describing the process of grain boundary sliding works for the numerical simulation of firn densification in this stage.
Anna Simson, Henning Löwe, and Julia Kowalski
The Cryosphere, 15, 5423–5445, https://doi.org/10.5194/tc-15-5423-2021, https://doi.org/10.5194/tc-15-5423-2021, 2021
Short summary
Short summary
This companion paper deals with numerical particularities of partial differential equations underlying one-dimensional snow models. In this second part we include mechanical settling and develop a new hybrid (Eulerian–Lagrangian) method for solving the advection-dominated ice mass conservation on a moving mesh alongside Eulerian diffusion (heat and vapor) and phase changes. The scheme facilitates a modular and extendable solver strategy while retaining controls on numerical accuracy.
Thomas Brall, Vladimir Mares, Rolf Bütikofer, and Werner Rühm
The Cryosphere, 15, 4769–4780, https://doi.org/10.5194/tc-15-4769-2021, https://doi.org/10.5194/tc-15-4769-2021, 2021
Short summary
Short summary
Neutrons from secondary cosmic rays, measured at 2660 m a.s.l. at Zugspitze, Germany, are highly affected by the environment, in particular by snow, soil moisture, and mountain shielding. To quantify these effects, computer simulations were carried out, including a sensitivity analysis on snow depth and soil moisture. This provides a possibility for snow depth estimation based on the measured number of secondary neutrons. This method was applied at Zugspitze in 2018.
Nora Helbig, Michael Schirmer, Jan Magnusson, Flavia Mäder, Alec van Herwijnen, Louis Quéno, Yves Bühler, Jeff S. Deems, and Simon Gascoin
The Cryosphere, 15, 4607–4624, https://doi.org/10.5194/tc-15-4607-2021, https://doi.org/10.5194/tc-15-4607-2021, 2021
Short summary
Short summary
The snow cover spatial variability in mountains changes considerably over the course of a snow season. In applications such as weather, climate and hydrological predictions the fractional snow-covered area is therefore an essential parameter characterizing how much of the ground surface in a grid cell is currently covered by snow. We present a seasonal algorithm and a spatiotemporal evaluation suggesting that the algorithm can be applied in other geographic regions by any snow model application.
Arne Melsom
The Cryosphere, 15, 3785–3796, https://doi.org/10.5194/tc-15-3785-2021, https://doi.org/10.5194/tc-15-3785-2021, 2021
Short summary
Short summary
This study presents new methods to assess how well observations of sea ice expansion are reproduced by results from models. The aim is to provide information about the quality of forecasts for changes in the sea ice extent to operators in or near ice-infested waters. A test using 2 years of model results demonstrates the practical applicability and usefulness of the methods that are presented.
Matthias Scheiter, Marius Schaefer, Eduardo Flández, Deniz Bozkurt, and Ralf Greve
The Cryosphere, 15, 3637–3654, https://doi.org/10.5194/tc-15-3637-2021, https://doi.org/10.5194/tc-15-3637-2021, 2021
Short summary
Short summary
We simulate the current state and future evolution of the Mocho-Choshuenco ice cap in southern Chile (40°S, 72°W) with the ice-sheet model SICOPOLIS. Under different global warming scenarios, we project ice mass losses between 56 % and 97 % by the end of the 21st century. We quantify the uncertainties based on an ensemble of climate models and on the temperature dependence of the equilibrium line altitude. Our results suggest a considerable deglaciation in southern Chile in the next 80 years.
Léo C. P. Martin, Jan Nitzbon, Johanna Scheer, Kjetil S. Aas, Trond Eiken, Moritz Langer, Simon Filhol, Bernd Etzelmüller, and Sebastian Westermann
The Cryosphere, 15, 3423–3442, https://doi.org/10.5194/tc-15-3423-2021, https://doi.org/10.5194/tc-15-3423-2021, 2021
Short summary
Short summary
It is important to understand how permafrost landscapes respond to climate changes because their thaw can contribute to global warming. We investigate how a common permafrost morphology degrades using both field observations of the surface elevation and numerical modeling. We show that numerical models accounting for topographic changes related to permafrost degradation can reproduce the observed changes in nature and help us understand how parameters such as snow influence this phenomenon.
James C. Ferguson and Andreas Vieli
The Cryosphere, 15, 3377–3399, https://doi.org/10.5194/tc-15-3377-2021, https://doi.org/10.5194/tc-15-3377-2021, 2021
Short summary
Short summary
Debris-covered glaciers have a greater extent than their debris-free counterparts due to insulation from the debris cover. However, the transient response to climate change remains poorly understood. We use a numerical model that couples ice dynamics and debris transport and varies the climate signal. We find that debris cover delays the transient response, especially for the extent. However, adding cryokarst features near the terminus greatly enhances the response.
Gunter R. Leguy, William H. Lipscomb, and Xylar S. Asay-Davis
The Cryosphere, 15, 3229–3253, https://doi.org/10.5194/tc-15-3229-2021, https://doi.org/10.5194/tc-15-3229-2021, 2021
Short summary
Short summary
We present numerical features of the Community Ice Sheet Model in representing ocean termini glaciers. Using idealized test cases, we show that applying melt in a partly grounded cell is beneficial, in contrast to recent studies. We confirm that parameterizing partly grounded cells yields accurate ice sheet representation at a grid resolution of ~2 km (arguably 4 km), allowing ice sheet simulations at a continental scale. The choice of basal friction law also influences the ice flow.
Jan-Hendrik Malles and Ben Marzeion
The Cryosphere, 15, 3135–3157, https://doi.org/10.5194/tc-15-3135-2021, https://doi.org/10.5194/tc-15-3135-2021, 2021
Short summary
Short summary
To better estimate the uncertainty in glacier mass change modeling during the 20th century we ran an established model with an ensemble of meteorological data sets. We find that the total ensemble uncertainty, especially in the early 20th century, when glaciological and meteorological observations at glacier locations were sparse, increases considerably compared to individual ensemble runs. This stems from regions with a lot of ice mass but few observations (e.g., Greenland periphery).
Niccolò Tubini, Stephan Gruber, and Riccardo Rigon
The Cryosphere, 15, 2541–2568, https://doi.org/10.5194/tc-15-2541-2021, https://doi.org/10.5194/tc-15-2541-2021, 2021
Short summary
Short summary
We present a new method to compute temperature changes with melting and freezing – a fundamental challenge in cryosphere research – extremely efficiently and with guaranteed correctness of the energy balance for any time step size. This is a key feature since the integration time step can then be chosen according to the timescale of the processes to be studied, from seconds to days.
Jowan M. Barnes, Thiago Dias dos Santos, Daniel Goldberg, G. Hilmar Gudmundsson, Mathieu Morlighem, and Jan De Rydt
The Cryosphere, 15, 1975–2000, https://doi.org/10.5194/tc-15-1975-2021, https://doi.org/10.5194/tc-15-1975-2021, 2021
Short summary
Short summary
Some properties of ice flow models must be initialised using observed data before they can be used to produce reliable predictions of the future. Different models have different ways of doing this, and the process is generally seen as being specific to an individual model. We compare the methods used by three different models and show that they produce similar outputs. We also demonstrate that the outputs from one model can be used in other models without introducing large uncertainties.
Olalekan Babaniyi, Ruanui Nicholson, Umberto Villa, and Noémi Petra
The Cryosphere, 15, 1731–1750, https://doi.org/10.5194/tc-15-1731-2021, https://doi.org/10.5194/tc-15-1731-2021, 2021
Short summary
Short summary
We consider the problem of inferring unknown parameter fields under additional uncertainty for an ice sheet model from synthetic surface ice flow velocity measurements. Our results indicate that accounting for model uncertainty stemming from the presence of nuisance parameters is crucial. Namely our findings suggest that using nominal values for these parameters, as is often done in practice, without taking into account the resulting modeling error can lead to overconfident and biased results.
Sebastian H. R. Rosier, Ronja Reese, Jonathan F. Donges, Jan De Rydt, G. Hilmar Gudmundsson, and Ricarda Winkelmann
The Cryosphere, 15, 1501–1516, https://doi.org/10.5194/tc-15-1501-2021, https://doi.org/10.5194/tc-15-1501-2021, 2021
Short summary
Short summary
Pine Island Glacier has contributed more to sea-level rise over the past decades than any other glacier in Antarctica. Ice-flow modelling studies have shown that it can undergo periods of rapid mass loss, but no study has shown that these future changes could cross a tipping point and therefore be effectively irreversible. Here, we assess the stability of Pine Island Glacier, quantifying the changes in ocean temperatures required to cross future tipping points using statistical methods.
Jan Nitzbon, Moritz Langer, Léo C. P. Martin, Sebastian Westermann, Thomas Schneider von Deimling, and Julia Boike
The Cryosphere, 15, 1399–1422, https://doi.org/10.5194/tc-15-1399-2021, https://doi.org/10.5194/tc-15-1399-2021, 2021
Short summary
Short summary
We used a numerical model to investigate how small-scale landscape heterogeneities affect permafrost thaw under climate-warming scenarios. Our results show that representing small-scale heterogeneities in the model can decide whether a landscape is water-logged or well-drained in the future. This in turn affects how fast permafrost thaws under warming. Our research emphasizes the importance of considering small-scale processes in model assessments of permafrost thaw under climate change.
Gong Cheng, Nina Kirchner, and Per Lötstedt
The Cryosphere, 15, 715–742, https://doi.org/10.5194/tc-15-715-2021, https://doi.org/10.5194/tc-15-715-2021, 2021
Short summary
Short summary
We present an inverse modeling approach to improve the understanding of spatiotemporally variable processes at the inaccessible base of an ice sheet by determining the sensitivity of direct surface observations to perturbations of basal conditions. Time dependency is proved to be important in these types of problems. The effect of perturbations is analyzed based on analytical and numerical solutions.
Richard Essery, Hyungjun Kim, Libo Wang, Paul Bartlett, Aaron Boone, Claire Brutel-Vuilmet, Eleanor Burke, Matthias Cuntz, Bertrand Decharme, Emanuel Dutra, Xing Fang, Yeugeniy Gusev, Stefan Hagemann, Vanessa Haverd, Anna Kontu, Gerhard Krinner, Matthieu Lafaysse, Yves Lejeune, Thomas Marke, Danny Marks, Christoph Marty, Cecile B. Menard, Olga Nasonova, Tomoko Nitta, John Pomeroy, Gerd Schädler, Vladimir Semenov, Tatiana Smirnova, Sean Swenson, Dmitry Turkov, Nander Wever, and Hua Yuan
The Cryosphere, 14, 4687–4698, https://doi.org/10.5194/tc-14-4687-2020, https://doi.org/10.5194/tc-14-4687-2020, 2020
Short summary
Short summary
Climate models are uncertain in predicting how warming changes snow cover. This paper compares 22 snow models with the same meteorological inputs. Predicted trends agree with observations at four snow research sites: winter snow cover does not start later, but snow now melts earlier in spring than in the 1980s at two of the sites. Cold regions where snow can last until late summer are predicted to be particularly sensitive to warming because the snow then melts faster at warmer times of year.
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.