Articles | Volume 15, issue 2
https://doi.org/10.5194/tc-15-715-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/tc-15-715-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
15 Feb 2021
Research article |
| 15 Feb 2021
| 15 Feb 2021
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
Department of Information Technology, Uppsala University, P.O. Box 337, 751 05 Uppsala, Sweden
Nina Kirchner
Department of Physical Geography, Stockholm University, 106 91 Stockholm, Sweden
Bolin Centre for Climate Research, Stockholm University, 106 91 Stockholm, Sweden
Per Lötstedt
Department of Information Technology, Uppsala University, P.O. Box 337, 751 05 Uppsala, Sweden
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Gong Cheng, Mansa Krishna, and Mathieu Morlighem
EGUsphere, https://doi.org/10.5194/egusphere-2025-1188, https://doi.org/10.5194/egusphere-2025-1188, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
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Predicting ice sheet contributions to sea level rise is challenging due to limited data and uncertainties in key processes. Traditional models require complex methods that lack flexibility. We developed PINNICLE, an open-source Python library that integrates machine learning with physical laws to improve ice sheet modeling. By combining data and physics, PINNICLE enhances predictions and adaptability, providing a powerful tool for climate research and sea level rise projections.
Shfaqat A. Khan, Helene Seroussi, Mathieu Morlighem, William Colgan, Veit Helm, Gong Cheng, Danjal Berg, Valentina R. Barletta, Nicolaj K. Larsen, William Kochtitzky, Michiel van den Broeke, Kurt H. Kjær, Andy Aschwanden, Brice Noël, Jason E. Box, Joseph A. MacGregor, Robert S. Fausto, Kenneth D. Mankoff, Ian M. Howat, Kuba Oniszk, Dominik Fahrner, Anja Løkkegaard, Eigil Y. H. Lippert, and Javed Hassan
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-348, https://doi.org/10.5194/essd-2024-348, 2024
Revised manuscript accepted for ESSD
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The surface elevation of the Greenland Ice Sheet is changing due to surface mass balance processes and ice dynamics, each exhibiting distinct spatiotemporal patterns. Here, we employ satellite and airborne altimetry data with fine spatial (1 km) and temporal (monthly) resolutions to document this spatiotemporal evolution from 2003 to 2023. This dataset of fine-resolution altimetry data in both space and time will support studies of ice mass loss and useful for GIS ice sheet modelling.
Gong Cheng, Mathieu Morlighem, and G. Hilmar Gudmundsson
Geosci. Model Dev., 17, 6227–6247, https://doi.org/10.5194/gmd-17-6227-2024, https://doi.org/10.5194/gmd-17-6227-2024, 2024
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We conducted a comprehensive analysis of the stabilization and reinitialization techniques currently employed in ISSM and Úa for solving level-set equations, specifically those related to the dynamic representation of moving ice fronts within numerical ice sheet models. Our results demonstrate that the streamline upwind Petrov–Galerkin (SUPG) method outperforms the other approaches. We found that excessively frequent reinitialization can lead to exceptionally high errors in simulations.
Younghyun Koo, Gong Cheng, Mathieu Morlighem, and Maryam Rahnemoonfar
EGUsphere, https://doi.org/10.5194/egusphere-2024-1620, https://doi.org/10.5194/egusphere-2024-1620, 2024
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Calving, the breaking of ice bodies from the terminus of a glacier, plays an important role in the mass losses of Greenland ice sheets. However, calving parameters have been poorly understood because of the intensive computational demands of traditional numerical models. To address this issue and find the optimal calving parameter that best represents real observations, we develop deep-learning emulators based on graph neural network architectures.
Joel A. Wilner, Mathieu Morlighem, and Gong Cheng
The Cryosphere, 17, 4889–4901, https://doi.org/10.5194/tc-17-4889-2023, https://doi.org/10.5194/tc-17-4889-2023, 2023
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We use numerical modeling to study iceberg calving off of ice shelves in Antarctica. We examine four widely used mathematical descriptions of calving (
calving laws), under the assumption that Antarctic ice shelf front positions should be in steady state under the current climate forcing. We quantify how well each of these calving laws replicates the observed front positions. Our results suggest that the eigencalving and von Mises laws are most suitable for Antarctic ice shelves.
Gong Cheng, Per Lötstedt, and Lina von Sydow
Geosci. Model Dev., 13, 2245–2258, https://doi.org/10.5194/gmd-13-2245-2020, https://doi.org/10.5194/gmd-13-2245-2020, 2020
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A full Stokes subgrid scheme in two dimensions for the grounding line migration problem is presented in the open-source finite-element framework Elmer/ICE. This method can achieve comparable results to previous research using a more than 20 times larger mesh size, which can be used to improve the efficiency in marine ice sheet simulations.
Gong Cheng and Per Lötstedt
The Cryosphere, 14, 673–691, https://doi.org/10.5194/tc-14-673-2020, https://doi.org/10.5194/tc-14-673-2020, 2020
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We present a time-dependent inverse method for ice sheet modeling. By investigating the sensitivity of the observations of the velocity and the height at the surface to the basal conditions of the ice, we show that if the basal parameters are time dependent, then time cannot be ignored in the inversion. By looking at the numerical features, we conclude that adding the height information of an ice sheet in the velocity inversion procedure could improve the robustness of the inference.
Sergey Marchenko, Gong Cheng, Per Lötstedt, Veijo Pohjola, Rickard Pettersson, Ward van Pelt, and Carleen Reijmer
The Cryosphere, 13, 1843–1859, https://doi.org/10.5194/tc-13-1843-2019, https://doi.org/10.5194/tc-13-1843-2019, 2019
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Thermal conductivity (k) of firn at Lomonosovfonna, Svalbard, is estimated using measured temperature evolution and density. The optimized k values (0.2–1.6 W (m K)−1) increase downwards and over time and are most sensitive to systematic errors in measured temperature values and their depths, particularly in the lower part of the profile. Compared to the density-based parameterizations, derived k values are consistently larger, suggesting a faster conductive heat exchange in firn.
Eef C. H. van Dongen, Nina Kirchner, Martin B. van Gijzen, Roderik S. W. van de Wal, Thomas Zwinger, Gong Cheng, Per Lötstedt, and Lina von Sydow
Geosci. Model Dev., 11, 4563–4576, https://doi.org/10.5194/gmd-11-4563-2018, https://doi.org/10.5194/gmd-11-4563-2018, 2018
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Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve. Therefore, approximations to the FS equations are used, especially when modeling an ice sheet on long time spans. Here, we report a combination of an approximation with the FS equations that allows simulating the dynamics of ice sheets over long time spans without introducing artifacts caused by application of approximations in parts of the domain where they are not valid.
Gong Cheng, Mansa Krishna, and Mathieu Morlighem
EGUsphere, https://doi.org/10.5194/egusphere-2025-1188, https://doi.org/10.5194/egusphere-2025-1188, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
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Predicting ice sheet contributions to sea level rise is challenging due to limited data and uncertainties in key processes. Traditional models require complex methods that lack flexibility. We developed PINNICLE, an open-source Python library that integrates machine learning with physical laws to improve ice sheet modeling. By combining data and physics, PINNICLE enhances predictions and adaptability, providing a powerful tool for climate research and sea level rise projections.
Jamie Barnett, Felicity Alice Holmes, Joshua Cuzzone, Henning Åkesson, Mathieu Morlighem, Matt O'Regan, Johan Nilsson, Nina Kirchner, and Martin Jakobsson
EGUsphere, https://doi.org/10.5194/egusphere-2025-653, https://doi.org/10.5194/egusphere-2025-653, 2025
This preprint is open for discussion and under review for The Cryosphere (TC).
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Understanding how ice sheets have changed in the past can allow us to make better predictions for the future. By running a state-of-the-art model of Ryder Glacier, North Greenland, over the past 12,000 years we find that both a warming atmosphere and ocean play a key role in the evolution of the Glacier. Our conclusions stress that accurately quantifying the ice sheet’s interactions with the ocean are required to predict future changes and reliable sea level rise estimates.
Felicity Alice Holmes, Jamie Barnett, Henning Åkesson, Mathieu Morlighem, Johan Nilsson, Nina Kirchner, and Martin Jakobsson
EGUsphere, https://doi.org/10.5194/egusphere-2024-3839, https://doi.org/10.5194/egusphere-2024-3839, 2024
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Northern Greenland contains some of the ice sheet's last remaining glaciers with floating ice tongues. One of these is Ryder Glacier, which has been relatively stable in recent decades in contrast to nearby glaciers. Here, we use a computer model to simulate Ryder Glacier until 2300 under both a low and high emissions scenario. Very high levels of surface melt under a high emissions future leads to a sea-level rise contribution an order of magnitude higher than under a low emissions future.
Shfaqat A. Khan, Helene Seroussi, Mathieu Morlighem, William Colgan, Veit Helm, Gong Cheng, Danjal Berg, Valentina R. Barletta, Nicolaj K. Larsen, William Kochtitzky, Michiel van den Broeke, Kurt H. Kjær, Andy Aschwanden, Brice Noël, Jason E. Box, Joseph A. MacGregor, Robert S. Fausto, Kenneth D. Mankoff, Ian M. Howat, Kuba Oniszk, Dominik Fahrner, Anja Løkkegaard, Eigil Y. H. Lippert, and Javed Hassan
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-348, https://doi.org/10.5194/essd-2024-348, 2024
Revised manuscript accepted for ESSD
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The surface elevation of the Greenland Ice Sheet is changing due to surface mass balance processes and ice dynamics, each exhibiting distinct spatiotemporal patterns. Here, we employ satellite and airborne altimetry data with fine spatial (1 km) and temporal (monthly) resolutions to document this spatiotemporal evolution from 2003 to 2023. This dataset of fine-resolution altimetry data in both space and time will support studies of ice mass loss and useful for GIS ice sheet modelling.
Adrian Dye, Robert Bryant, Francesca Falcini, Joseph Mallalieu, Miles Dimbleby, Michael Beckwith, David Rippin, and Nina Kirchner
EGUsphere, https://doi.org/10.5194/egusphere-2024-2510, https://doi.org/10.5194/egusphere-2024-2510, 2024
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Thermal undercutting of the terminus has driven recent rapid retreat of an Arctic glacier. Water temperatures (~4 °C) at the ice front were warmer than previously assumed and thermal undercutting was over several metres deep. This triggered phases of high calving activity, playing a substantial role in the rapid retreat of Kaskasapakte glacier since 2012, with important implications for processes occurring at glacier-water contact points and implications for hydrology and ecology downstream.
Gong Cheng, Mathieu Morlighem, and G. Hilmar Gudmundsson
Geosci. Model Dev., 17, 6227–6247, https://doi.org/10.5194/gmd-17-6227-2024, https://doi.org/10.5194/gmd-17-6227-2024, 2024
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We conducted a comprehensive analysis of the stabilization and reinitialization techniques currently employed in ISSM and Úa for solving level-set equations, specifically those related to the dynamic representation of moving ice fronts within numerical ice sheet models. Our results demonstrate that the streamline upwind Petrov–Galerkin (SUPG) method outperforms the other approaches. We found that excessively frequent reinitialization can lead to exceptionally high errors in simulations.
Younghyun Koo, Gong Cheng, Mathieu Morlighem, and Maryam Rahnemoonfar
EGUsphere, https://doi.org/10.5194/egusphere-2024-1620, https://doi.org/10.5194/egusphere-2024-1620, 2024
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Calving, the breaking of ice bodies from the terminus of a glacier, plays an important role in the mass losses of Greenland ice sheets. However, calving parameters have been poorly understood because of the intensive computational demands of traditional numerical models. To address this issue and find the optimal calving parameter that best represents real observations, we develop deep-learning emulators based on graph neural network architectures.
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
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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.
Joel A. Wilner, Mathieu Morlighem, and Gong Cheng
The Cryosphere, 17, 4889–4901, https://doi.org/10.5194/tc-17-4889-2023, https://doi.org/10.5194/tc-17-4889-2023, 2023
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We use numerical modeling to study iceberg calving off of ice shelves in Antarctica. We examine four widely used mathematical descriptions of calving (
calving laws), under the assumption that Antarctic ice shelf front positions should be in steady state under the current climate forcing. We quantify how well each of these calving laws replicates the observed front positions. Our results suggest that the eigencalving and von Mises laws are most suitable for Antarctic ice shelves.
Felicity A. Holmes, Eef van Dongen, Riko Noormets, Michał Pętlicki, and Nina Kirchner
The Cryosphere, 17, 1853–1872, https://doi.org/10.5194/tc-17-1853-2023, https://doi.org/10.5194/tc-17-1853-2023, 2023
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Glaciers which end in bodies of water can lose mass through melting below the waterline, as well as by the breaking off of icebergs. We use a numerical model to simulate the breaking off of icebergs at Kronebreen, a glacier in Svalbard, and find that both melting below the waterline and tides are important for iceberg production. In addition, we compare the modelled glacier front to observations and show that melting below the waterline can lead to undercuts of up to around 25 m.
H. E. Markus Meier, Madline Kniebusch, Christian Dieterich, Matthias Gröger, Eduardo Zorita, Ragnar Elmgren, Kai Myrberg, Markus P. Ahola, Alena Bartosova, Erik Bonsdorff, Florian Börgel, Rene Capell, Ida Carlén, Thomas Carlund, Jacob Carstensen, Ole B. Christensen, Volker Dierschke, Claudia Frauen, Morten Frederiksen, Elie Gaget, Anders Galatius, Jari J. Haapala, Antti Halkka, Gustaf Hugelius, Birgit Hünicke, Jaak Jaagus, Mart Jüssi, Jukka Käyhkö, Nina Kirchner, Erik Kjellström, Karol Kulinski, Andreas Lehmann, Göran Lindström, Wilhelm May, Paul A. Miller, Volker Mohrholz, Bärbel Müller-Karulis, Diego Pavón-Jordán, Markus Quante, Marcus Reckermann, Anna Rutgersson, Oleg P. Savchuk, Martin Stendel, Laura Tuomi, Markku Viitasalo, Ralf Weisse, and Wenyan Zhang
Earth Syst. Dynam., 13, 457–593, https://doi.org/10.5194/esd-13-457-2022, https://doi.org/10.5194/esd-13-457-2022, 2022
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Based on the Baltic Earth Assessment Reports of this thematic issue in Earth System Dynamics and recent peer-reviewed literature, current knowledge about the effects of global warming on past and future changes in the climate of the Baltic Sea region is summarised and assessed. The study is an update of the Second Assessment of Climate Change (BACC II) published in 2015 and focuses on the atmosphere, land, cryosphere, ocean, sediments, and the terrestrial and marine biosphere.
Gong Cheng, Per Lötstedt, and Lina von Sydow
Geosci. Model Dev., 13, 2245–2258, https://doi.org/10.5194/gmd-13-2245-2020, https://doi.org/10.5194/gmd-13-2245-2020, 2020
Short summary
Short summary
A full Stokes subgrid scheme in two dimensions for the grounding line migration problem is presented in the open-source finite-element framework Elmer/ICE. This method can achieve comparable results to previous research using a more than 20 times larger mesh size, which can be used to improve the efficiency in marine ice sheet simulations.
Gong Cheng and Per Lötstedt
The Cryosphere, 14, 673–691, https://doi.org/10.5194/tc-14-673-2020, https://doi.org/10.5194/tc-14-673-2020, 2020
Short summary
Short summary
We present a time-dependent inverse method for ice sheet modeling. By investigating the sensitivity of the observations of the velocity and the height at the surface to the basal conditions of the ice, we show that if the basal parameters are time dependent, then time cannot be ignored in the inversion. By looking at the numerical features, we conclude that adding the height information of an ice sheet in the velocity inversion procedure could improve the robustness of the inference.
Sergey Marchenko, Gong Cheng, Per Lötstedt, Veijo Pohjola, Rickard Pettersson, Ward van Pelt, and Carleen Reijmer
The Cryosphere, 13, 1843–1859, https://doi.org/10.5194/tc-13-1843-2019, https://doi.org/10.5194/tc-13-1843-2019, 2019
Short summary
Short summary
Thermal conductivity (k) of firn at Lomonosovfonna, Svalbard, is estimated using measured temperature evolution and density. The optimized k values (0.2–1.6 W (m K)−1) increase downwards and over time and are most sensitive to systematic errors in measured temperature values and their depths, particularly in the lower part of the profile. Compared to the density-based parameterizations, derived k values are consistently larger, suggesting a faster conductive heat exchange in firn.
Eef C. H. van Dongen, Nina Kirchner, Martin B. van Gijzen, Roderik S. W. van de Wal, Thomas Zwinger, Gong Cheng, Per Lötstedt, and Lina von Sydow
Geosci. Model Dev., 11, 4563–4576, https://doi.org/10.5194/gmd-11-4563-2018, https://doi.org/10.5194/gmd-11-4563-2018, 2018
Short summary
Short summary
Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve. Therefore, approximations to the FS equations are used, especially when modeling an ice sheet on long time spans. Here, we report a combination of an approximation with the FS equations that allows simulating the dynamics of ice sheets over long time spans without introducing artifacts caused by application of approximations in parts of the domain where they are not valid.
Matt O'Regan, Jan Backman, Natalia Barrientos, Thomas M. Cronin, Laura Gemery, Nina Kirchner, Larry A. Mayer, Johan Nilsson, Riko Noormets, Christof Pearce, Igor Semiletov, Christian Stranne, and Martin Jakobsson
Clim. Past, 13, 1269–1284, https://doi.org/10.5194/cp-13-1269-2017, https://doi.org/10.5194/cp-13-1269-2017, 2017
Short summary
Short summary
Past glacial activity on the East Siberian continental margin is poorly known, partly due to the lack of geomorphological evidence. Here we present geophysical mapping and sediment coring data from the East Siberian shelf and slope revealing the presence of a glacially excavated cross-shelf trough reaching to the continental shelf edge north of the De Long Islands. The data provide direct evidence for extensive glacial activity on the Siberian shelf that predates the Last Glacial Maximum.
Johan Nilsson, Martin Jakobsson, Chris Borstad, Nina Kirchner, Göran Björk, Raymond T. Pierrehumbert, and Christian Stranne
The Cryosphere, 11, 1745–1765, https://doi.org/10.5194/tc-11-1745-2017, https://doi.org/10.5194/tc-11-1745-2017, 2017
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Recent data suggest that a 1 km thick ice shelf extended over the glacial Arctic Ocean during MIS 6, about 140 000 years ago. Here, we theoretically analyse the development and equilibrium features of such an ice shelf. The ice shelf was effectively dammed by the Fram Strait and the mean ice-shelf thickness was controlled primarily by the horizontally integrated mass balance. Our results can aid in resolving some outstanding questions of the state of the glacial Arctic Ocean.
J. Ahlkrona, N. Kirchner, and P. Lötstedt
Geosci. Model Dev., 6, 2135–2152, https://doi.org/10.5194/gmd-6-2135-2013, https://doi.org/10.5194/gmd-6-2135-2013, 2013
Related subject area
Discipline: Ice sheets | Subject: Numerical Modelling
Present-day mass loss rates are a precursor for West Antarctic Ice Sheet collapse
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
Calving from horizontal forces in a revised crevasse-depth framework
Antarctic sensitivity to oceanic melting parameterizations
Analytical solutions for the advective–diffusive ice column in the presence of strain heating
Ice viscosity governs hydraulic fracture that causes rapid drainage of supraglacial lakes
Glacier damage evolution over ice flow timescales
Improved basal drag of the West Antarctic Ice Sheet from L-curve analysis of inverse models utilizing subglacial hydrology simulations
Calibrated sea level contribution from the Amundsen Sea sector, West Antarctica, under RCP8.5 and Paris 2C scenarios
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Biases in ice sheet models from missing noise-induced drift
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The stability of present-day Antarctic grounding lines – Part 1: No indication of marine ice sheet instability in the current geometry
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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
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
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
Impact of runoff temporal distribution on ice dynamics
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Stabilizing effect of mélange buttressing on the marine ice-cliff instability of the West Antarctic Ice Sheet
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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
Marine ice sheet experiments with the Community Ice Sheet Model
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
Quantifying the effect of ocean bed properties on ice sheet geometry over 40 000 years with a full-Stokes model
Bayesian calibration of firn densification models
A kinematic formalism for tracking ice–ocean mass exchange on the Earth's surface and estimating sea-level change
Results of the third Marine Ice Sheet Model Intercomparison Project (MISMIP+)
Ocean-forced evolution of the Amundsen Sea catchment, West Antarctica, by 2100
Parameter sensitivity analysis of dynamic ice sheet models – numerical computations
Simulated retreat of Jakobshavn Isbræ during the 21st century
Development of physically based liquid water schemes for Greenland firn-densification models
Regional grid refinement in an Earth system model: impacts on the simulated Greenland surface mass balance
initMIP-Antarctica: an ice sheet model initialization experiment of ISMIP6
Modeling the response of northwest Greenland to enhanced ocean thermal forcing and subglacial discharge
Assessment of the Greenland ice sheet–atmosphere feedbacks for the next century with a regional atmospheric model coupled to an ice sheet model
Tim van den Akker, William H. Lipscomb, Gunter R. Leguy, Jorjo Bernales, Constantijn J. Berends, Willem Jan van de Berg, and Roderik S. W. van de Wal
The Cryosphere, 19, 283–301, https://doi.org/10.5194/tc-19-283-2025, https://doi.org/10.5194/tc-19-283-2025, 2025
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In this study, we present an improved way of representing ice thickness change rates in an ice sheet model. We apply this method using two ice sheet models of the Antarctic Ice Sheet. We found that the two largest outlet glaciers on the Antarctic Ice Sheet, Thwaites Glacier and Pine Island Glacier, will collapse without further warming on a timescale of centuries. This would cause a sea level rise of about 1.2 m globally.
George Lu and Jonathan Kingslake
The Cryosphere, 18, 5301–5321, https://doi.org/10.5194/tc-18-5301-2024, https://doi.org/10.5194/tc-18-5301-2024, 2024
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Water below ice sheets affects ice-sheet motion, while the evolution of ice sheets likewise affects the water below. We create a model that allows for water and ice to affect each other and use it to see how this coupling or lack thereof may impact ice-sheet retreat. We find that coupling an evolving water system with the ice sheet results in more retreat than if we assume unchanging conditions under the ice, which indicates a need to better represent the effects of water in ice-sheet models.
Yu Wang, Chen Zhao, Rupert Gladstone, Thomas Zwinger, Benjamin K. Galton-Fenzi, and Poul Christoffersen
The Cryosphere, 18, 5117–5137, https://doi.org/10.5194/tc-18-5117-2024, https://doi.org/10.5194/tc-18-5117-2024, 2024
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Our research delves into the future evolution of Antarctica's Wilkes Subglacial Basin (WSB) and its potential contribution to sea level rise, focusing on how basal melt is implemented at the grounding line in ice flow models. Our findings suggest that these implementation methods can significantly impact the magnitude of future ice loss projections. Under a high-emission scenario, the WSB ice sheet could undergo massive and rapid retreat between 2200 and 2300.
Donald A. Slater and Till J. W. Wagner
EGUsphere, https://doi.org/10.5194/egusphere-2024-2927, https://doi.org/10.5194/egusphere-2024-2927, 2024
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Calving is when icebergs break off glaciers and fall into the ocean. It is an important process determining how ice sheets will respond to change in climate, but it is currently poorly understood and hard to include in numerical models that are used for sea level projections. We revised an existing theory for how this process works, overcoming shortcomings of the existing theory and explaining observations showing that calving style depends on how thick the ice is.
Antonio Juarez-Martinez, Javier Blasco, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
The Cryosphere, 18, 4257–4283, https://doi.org/10.5194/tc-18-4257-2024, https://doi.org/10.5194/tc-18-4257-2024, 2024
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We present sea level projections for Antarctica in the context of ISMIP6-2300 with several forcings but extend the simulations to 2500, showing that more than 3 m of sea level contribution could be reached. We also test the sensitivity on a basal melting parameter and determine the timing of the loss of ice in the west region. All the simulations were carried out with the ice sheet model Yelmo.
Daniel Moreno-Parada, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
The Cryosphere, 18, 4215–4232, https://doi.org/10.5194/tc-18-4215-2024, https://doi.org/10.5194/tc-18-4215-2024, 2024
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Our study tries to understand how the ice temperature evolves in a large mass as in the case of Antarctica. We found a relation that tells us the ice temperature at any point. These results are important because they also determine how the ice moves. In general, ice moves due to slow deformation (as if pouring honey from a jar). Nevertheless, in some regions the ice base warms enough and melts. The liquid water then serves as lubricant and the ice slides and its velocity increases rapidly.
Tim Hageman, Jessica Mejía, Ravindra Duddu, and Emilio Martínez-Pañeda
The Cryosphere, 18, 3991–4009, https://doi.org/10.5194/tc-18-3991-2024, https://doi.org/10.5194/tc-18-3991-2024, 2024
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Due to surface melting, meltwater lakes seasonally form on the surface of glaciers. These lakes drive hydrofractures that rapidly transfer water to the base of ice sheets. This paper presents a computational method to capture the complicated hydrofracturing process. Our work reveals that viscous ice rheology has a great influence on the short-term propagation of fractures, enabling fast lake drainage, whereas thermal effects (frictional heating, conduction, and freezing) have little influence.
Meghana Ranganathan, Alexander A. Robel, Alexander Huth, and Ravindra Duddu
EGUsphere, https://doi.org/10.5194/egusphere-2024-1850, https://doi.org/10.5194/egusphere-2024-1850, 2024
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The rate of ice loss from ice sheets is controlled by the flow of ice from the center of the ice sheet and internal fracturing of the ice. These are coupled – fractures can reduce the viscosity of ice and enable more rapid flow, and rapid flow can cause fracturing of ice. We present a simplified way of representing damage that is applicable to long-timescale flow estimates. Using this model, we find that including fracturing into an ice sheet simulation can increase the loss of ice by 13–29 %.
Lea-Sophie Höyns, Thomas Kleiner, Andreas Rademacher, Martin Rückamp, Michael Wolovick, and Angelika Humbert
EGUsphere, https://doi.org/10.5194/egusphere-2024-1251, https://doi.org/10.5194/egusphere-2024-1251, 2024
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Glaciers' sliding over bedrock is governed by water pressure in the hydrological system underneath the glacier and the roughness of the land underneath the glacier. We estimate this roughness using a modelling approach, which optimises this unknown parameter. The water pressure is simulated, too, which improves the robustness of the computed drag at the ice sheet base. We provide this data to other modellers and scientists doing geophysical field observations.
Sebastian H. R. Rosier, G. Hilmar Gudmundsson, Adrian Jenkins, and Kaitlin A. Naughten
EGUsphere, https://doi.org/10.5194/egusphere-2024-1838, https://doi.org/10.5194/egusphere-2024-1838, 2024
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Glaciers in the Amundsen Sea region of Antarctica have been retreating and losing mass, but their future contribution to global sea level rise remains highly uncertain. We use an ice sheet model and uncertainty quantification methods to evaluate the probable range of mass loss from this region for two future climate scenarios and find that the rate of ice loss until 2100 will likely remain similar to present-day observations, with little sensitivity to climate scenario over this short timeframe.
Ziad Rashed, Alexander Robel, and Helene Seroussi
EGUsphere, https://doi.org/10.5194/egusphere-2024-1435, https://doi.org/10.5194/egusphere-2024-1435, 2024
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Sermeq Kujalleq, Greenland's largest glacier, has significantly retreated since the late 1990s in response to warming ocean temperatures. Using a large ensemble approach, our simulations show that the retreat is mainly initiated by the arrival of warm water but sustained and accelerated by the glacier's position over deeper bed troughs and vigorous calving. We highlight the need for models of ice mélange to project glacier behavior under rapid calving regimes.
Alexander A. Robel, Vincent Verjans, and Aminat A. Ambelorun
The Cryosphere, 18, 2613–2623, https://doi.org/10.5194/tc-18-2613-2024, https://doi.org/10.5194/tc-18-2613-2024, 2024
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The average size of many glaciers and ice sheets changes when noise is added to the system. The reasons for this drift in glacier state is intrinsic to the dynamics of how ice flows and the bumpiness of the Earth's surface. We argue that not including noise in projections of ice sheet evolution over coming decades and centuries is a pervasive source of bias in these computer models, and so realistic variability in glacier and climate processes must be included in models.
Joshua Cuzzone, Matias Romero, and Shaun A. Marcott
The Cryosphere, 18, 1381–1398, https://doi.org/10.5194/tc-18-1381-2024, https://doi.org/10.5194/tc-18-1381-2024, 2024
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We simulate the retreat history of the Patagonian Ice Sheet (PIS) across the Chilean Lake District from 22–10 ka. These results improve our understanding of the response of the PIS to deglacial warming and the patterns of deglacial ice margin retreat where gaps in the geologic record still exist, and they indicate that changes in large-scale precipitation during the last deglaciation played an important role in modulating the response of ice margin change across the PIS to deglacial warming.
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
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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
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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.
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
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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
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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.
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
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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
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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.
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
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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.
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
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To improve the interpretability of process-based projections of the sea-level contribution from land ice components, we apply the machine-learning-based
SHapley Additive 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
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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.
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
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Models must represent how glaciers slide along the bed, but there are many ways to do so. In this paper, several sliding laws are tested and found to affect different regions of the Antarctic Ice Sheet in different ways and at different speeds. However, the variability in ice volume loss due to sliding-law choices is low compared to other factors, so limited empirical knowledge of sliding does not prevent us from making predictions of how an ice sheet will evolve.
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
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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
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Basal thermal conditions are important to ice dynamics and sensitive to geothermal heat flux (GHF). We estimate basal thermal conditions of the Lambert–Amery Glacier system with six 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.
Basile de Fleurian, Richard Davy, and Petra M. Langebroek
The Cryosphere, 16, 2265–2283, https://doi.org/10.5194/tc-16-2265-2022, https://doi.org/10.5194/tc-16-2265-2022, 2022
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As temperature increases, more snow and ice melt at the surface of ice sheets. Here we use an ice dynamics and subglacial hydrology model with simplified geometry and climate forcing to study the impact of variations in meltwater on ice dynamics. We focus on the variations in length and intensity of the melt season. Our results show that a longer melt season leads to faster glaciers, but a more intense melt season reduces glaciers' seasonal velocities, albeit leading to higher peak velocities.
Maria-Gema Llorens, Albert Griera, Paul D. Bons, Ilka Weikusat, David J. Prior, Enrique Gomez-Rivas, Tamara de Riese, Ivone Jimenez-Munt, Daniel García-Castellanos, and Ricardo A. Lebensohn
The Cryosphere, 16, 2009–2024, https://doi.org/10.5194/tc-16-2009-2022, https://doi.org/10.5194/tc-16-2009-2022, 2022
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Polar ice is formed by ice crystals, which form fabrics that are utilised to interpret how ice sheets flow. It is unclear whether fabrics result from the current flow regime or if they are inherited. To understand the extent to which ice crystals can be reoriented when ice flow conditions change, we simulate and evaluate multi-stage ice flow scenarios according to natural cases. We find that second deformation regimes normally overprint inherited fabrics, with a range of transitional fabrics.
Tanja Schlemm, Johannes Feldmann, Ricarda Winkelmann, and Anders Levermann
The Cryosphere, 16, 1979–1996, https://doi.org/10.5194/tc-16-1979-2022, https://doi.org/10.5194/tc-16-1979-2022, 2022
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Marine cliff instability, if it exists, could dominate Antarctica's contribution to future sea-level rise. It is likely to speed up with ice thickness and thus would accelerate in most parts of Antarctica. Here, we investigate a possible mechanism that might stop cliff instability through cloaking by ice mélange. It is only a first step, but it shows that embayment geometry is, in principle, able to stop marine cliff instability in most parts of West Antarctica.
Neige Calonne, Alexis Burr, Armelle Philip, Frédéric Flin, and Christian Geindreau
The Cryosphere, 16, 967–980, https://doi.org/10.5194/tc-16-967-2022, https://doi.org/10.5194/tc-16-967-2022, 2022
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Modeling gas transport in ice sheets from surface to close-off is key to interpreting climate archives. Estimates of the diffusion coefficient and permeability of snow and firn are required but remain a large source of uncertainty. We present a new dataset of diffusion coefficients and permeability from 20 to 120 m depth at two Antarctic sites. We suggest predictive formulas to estimate both properties over the entire 100–850 kg m3 density range, i.e., anywhere within the ice sheet column.
Tom Mitcham, G. Hilmar Gudmundsson, and Jonathan L. Bamber
The Cryosphere, 16, 883–901, https://doi.org/10.5194/tc-16-883-2022, https://doi.org/10.5194/tc-16-883-2022, 2022
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We modelled the response of the Larsen C Ice Shelf (LCIS) and its tributary glaciers to the calving of the A68 iceberg and validated our results with observations. We found that the impact was limited, confirming that mostly passive ice was calved. Through further calving experiments we quantified the total buttressing provided by the LCIS and found that over 80 % of the buttressing capacity is generated in the first 5 km of the ice shelf downstream of the grounding line.
Blake A. Castleman, Nicole-Jeanne Schlegel, Lambert Caron, Eric Larour, and Ala Khazendar
The Cryosphere, 16, 761–778, https://doi.org/10.5194/tc-16-761-2022, https://doi.org/10.5194/tc-16-761-2022, 2022
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In the described study, we derive an uncertainty range for global mean sea level rise (SLR) contribution from Thwaites Glacier in a 200-year period under an extreme ocean warming scenario. We derive the spatial and vertical resolutions needed for bedrock data acquisition missions in order to limit global mean SLR contribution from Thwaites Glacier to ±2 cm in a 200-year period. We conduct sensitivity experiments in order to present the locations of critical regions in need of accurate mapping.
Alexander Robinson, Daniel Goldberg, and William H. Lipscomb
The Cryosphere, 16, 689–709, https://doi.org/10.5194/tc-16-689-2022, https://doi.org/10.5194/tc-16-689-2022, 2022
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Here we investigate the numerical stability of several commonly used methods in order to determine which of them are capable of resolving the complex physics of the ice flow and are also computationally efficient. We find that the so-called DIVA solver outperforms the others. Its representation of the physics is consistent with more complex methods, while it remains computationally efficient at high resolution.
Thiago Dias dos Santos, Mathieu Morlighem, and Douglas Brinkerhoff
The Cryosphere, 16, 179–195, https://doi.org/10.5194/tc-16-179-2022, https://doi.org/10.5194/tc-16-179-2022, 2022
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Projecting the future evolution of Greenland and Antarctica and their potential contribution to sea level rise often relies on computer simulations carried out by numerical ice sheet models. Here we present a new vertically integrated ice sheet model and assess its performance using different benchmarks. The new model shows results comparable to a three-dimensional model at relatively lower computational cost, suggesting that it is an excellent alternative for long-term simulations.
Timm Schultz, Ralf Müller, Dietmar Gross, and Angelika Humbert
The Cryosphere, 16, 143–158, https://doi.org/10.5194/tc-16-143-2022, https://doi.org/10.5194/tc-16-143-2022, 2022
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Firn is the interstage product between snow and ice. Simulations describing the process of firn densification are used in the context of estimating mass changes of the ice sheets and past climate reconstructions. The first stage of firn densification takes place in the upper few meters of the firn column. We investigate how well a material law describing the process of grain boundary sliding works for the numerical simulation of firn densification in this stage.
Gunter R. Leguy, William H. Lipscomb, and Xylar S. Asay-Davis
The Cryosphere, 15, 3229–3253, https://doi.org/10.5194/tc-15-3229-2021, https://doi.org/10.5194/tc-15-3229-2021, 2021
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We present numerical features of the Community Ice Sheet Model in representing ocean termini glaciers. Using idealized test cases, we show that applying melt in a partly grounded cell is beneficial, in contrast to recent studies. We confirm that parameterizing partly grounded cells yields accurate ice sheet representation at a grid resolution of ~2 km (arguably 4 km), allowing ice sheet simulations at a continental scale. The choice of basal friction law also influences the ice flow.
Jowan M. Barnes, Thiago Dias dos Santos, Daniel Goldberg, G. Hilmar Gudmundsson, Mathieu Morlighem, and Jan De Rydt
The Cryosphere, 15, 1975–2000, https://doi.org/10.5194/tc-15-1975-2021, https://doi.org/10.5194/tc-15-1975-2021, 2021
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Some properties of ice flow models must be initialised using observed data before they can be used to produce reliable predictions of the future. Different models have different ways of doing this, and the process is generally seen as being specific to an individual model. We compare the methods used by three different models and show that they produce similar outputs. We also demonstrate that the outputs from one model can be used in other models without introducing large uncertainties.
Olalekan Babaniyi, Ruanui Nicholson, Umberto Villa, and Noémi Petra
The Cryosphere, 15, 1731–1750, https://doi.org/10.5194/tc-15-1731-2021, https://doi.org/10.5194/tc-15-1731-2021, 2021
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We consider the problem of inferring unknown parameter fields under additional uncertainty for an ice sheet model from synthetic surface ice flow velocity measurements. Our results indicate that accounting for model uncertainty stemming from the presence of nuisance parameters is crucial. Namely our findings suggest that using nominal values for these parameters, as is often done in practice, without taking into account the resulting modeling error can lead to overconfident and biased results.
Sebastian H. R. Rosier, Ronja Reese, Jonathan F. Donges, Jan De Rydt, G. Hilmar Gudmundsson, and Ricarda Winkelmann
The Cryosphere, 15, 1501–1516, https://doi.org/10.5194/tc-15-1501-2021, https://doi.org/10.5194/tc-15-1501-2021, 2021
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Pine Island Glacier has contributed more to sea-level rise over the past decades than any other glacier in Antarctica. Ice-flow modelling studies have shown that it can undergo periods of rapid mass loss, but no study has shown that these future changes could cross a tipping point and therefore be effectively irreversible. Here, we assess the stability of Pine Island Glacier, quantifying the changes in ocean temperatures required to cross future tipping points using statistical methods.
Clemens Schannwell, Reinhard Drews, Todd A. Ehlers, Olaf Eisen, Christoph Mayer, Mika Malinen, Emma C. Smith, and Hannes Eisermann
The Cryosphere, 14, 3917–3934, https://doi.org/10.5194/tc-14-3917-2020, https://doi.org/10.5194/tc-14-3917-2020, 2020
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To reduce uncertainties associated with sea level rise projections, an accurate representation of ice flow is paramount. Most ice sheet models rely on simplified versions of the underlying ice flow equations. Due to the high computational costs, ice sheet models based on the complete ice flow equations have been restricted to < 1000 years. Here, we present a new model setup that extends the applicability of such models by an order of magnitude, permitting simulations of 40 000 years.
Vincent Verjans, Amber A. Leeson, Christopher Nemeth, C. Max Stevens, Peter Kuipers Munneke, Brice Noël, and Jan Melchior van Wessem
The Cryosphere, 14, 3017–3032, https://doi.org/10.5194/tc-14-3017-2020, https://doi.org/10.5194/tc-14-3017-2020, 2020
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Ice sheets are covered by a firn layer, which is the transition stage between fresh snow and ice. Accurate modelling of firn density properties is important in many glaciological aspects. Current models show disagreements, are mostly calibrated to match specific observations of firn density and lack thorough uncertainty analysis. We use a novel calibration method for firn models based on a Bayesian statistical framework, which results in improved model accuracy and in uncertainty evaluation.
Surendra Adhikari, Erik R. Ivins, Eric Larour, Lambert Caron, and Helene Seroussi
The Cryosphere, 14, 2819–2833, https://doi.org/10.5194/tc-14-2819-2020, https://doi.org/10.5194/tc-14-2819-2020, 2020
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The mathematical formalism presented in this paper aims at simplifying computational strategies for tracking ice–ocean mass exchange in the Earth system. To this end, we define a set of generic, and quite simple, descriptions of evolving land, ocean and ice interfaces and present a unified method to compute the sea-level contribution of evolving ice sheets. The formalism can be applied to arbitrary geometries and at all timescales.
Stephen L. Cornford, Helene Seroussi, Xylar S. Asay-Davis, G. Hilmar Gudmundsson, Rob Arthern, Chris Borstad, Julia Christmann, Thiago Dias dos Santos, Johannes Feldmann, Daniel Goldberg, Matthew J. Hoffman, Angelika Humbert, Thomas Kleiner, Gunter Leguy, William H. Lipscomb, Nacho Merino, Gaël Durand, Mathieu Morlighem, David Pollard, Martin Rückamp, C. Rosie Williams, and Hongju Yu
The Cryosphere, 14, 2283–2301, https://doi.org/10.5194/tc-14-2283-2020, https://doi.org/10.5194/tc-14-2283-2020, 2020
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We present the results of the third Marine Ice Sheet Intercomparison Project (MISMIP+). MISMIP+ is one in a series of exercises that test numerical models of ice sheet flow in simple situations. This particular exercise concentrates on the response of ice sheet models to the thinning of their floating ice shelves, which is of interest because numerical models are currently used to model the response to contemporary and near-future thinning in Antarctic ice shelves.
Alanna V. Alevropoulos-Borrill, Isabel J. Nias, Antony J. Payne, Nicholas R. Golledge, and Rory J. Bingham
The Cryosphere, 14, 1245–1258, https://doi.org/10.5194/tc-14-1245-2020, https://doi.org/10.5194/tc-14-1245-2020, 2020
Gong Cheng and Per Lötstedt
The Cryosphere, 14, 673–691, https://doi.org/10.5194/tc-14-673-2020, https://doi.org/10.5194/tc-14-673-2020, 2020
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We present a time-dependent inverse method for ice sheet modeling. By investigating the sensitivity of the observations of the velocity and the height at the surface to the basal conditions of the ice, we show that if the basal parameters are time dependent, then time cannot be ignored in the inversion. By looking at the numerical features, we conclude that adding the height information of an ice sheet in the velocity inversion procedure could improve the robustness of the inference.
Xiaoran Guo, Liyun Zhao, Rupert M. Gladstone, Sainan Sun, and John C. Moore
The Cryosphere, 13, 3139–3153, https://doi.org/10.5194/tc-13-3139-2019, https://doi.org/10.5194/tc-13-3139-2019, 2019
Vincent Verjans, Amber A. Leeson, C. Max Stevens, Michael MacFerrin, Brice Noël, and Michiel R. van den Broeke
The Cryosphere, 13, 1819–1842, https://doi.org/10.5194/tc-13-1819-2019, https://doi.org/10.5194/tc-13-1819-2019, 2019
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Firn models rely on empirical approaches for representing the percolation and refreezing of meltwater through the firn column. We develop liquid water schemes of different levels of complexity for firn models and compare their performances with respect to observations of density profiles from Greenland. Our results demonstrate that physically advanced water schemes do not lead to better agreement with density observations. Uncertainties in other processes contribute more to model discrepancy.
Leonardus van Kampenhout, Alan M. Rhoades, Adam R. Herrington, Colin M. Zarzycki, Jan T. M. Lenaerts, William J. Sacks, and Michiel R. van den Broeke
The Cryosphere, 13, 1547–1564, https://doi.org/10.5194/tc-13-1547-2019, https://doi.org/10.5194/tc-13-1547-2019, 2019
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A new tool is evaluated in which the climate and surface mass balance (SMB) of the Greenland ice sheet are resolved at 55 and 28 km resolution, while the rest of the globe is modelled at ~110 km. The local refinement of resolution leads to improved accumulation (SMB > 0) compared to observations; however ablation (SMB < 0) is deteriorated in some regions. This is attributed to changes in cloud cover and a reduced effectiveness of a model-specific vertical downscaling technique.
Hélène Seroussi, Sophie Nowicki, Erika Simon, Ayako Abe-Ouchi, Torsten Albrecht, Julien Brondex, Stephen Cornford, Christophe Dumas, Fabien Gillet-Chaulet, Heiko Goelzer, Nicholas R. Golledge, Jonathan M. Gregory, Ralf Greve, Matthew J. Hoffman, Angelika Humbert, Philippe Huybrechts, Thomas Kleiner, Eric Larour, Gunter Leguy, William H. Lipscomb, Daniel Lowry, Matthias Mengel, Mathieu Morlighem, Frank Pattyn, Anthony J. Payne, David Pollard, Stephen F. Price, Aurélien Quiquet, Thomas J. Reerink, Ronja Reese, Christian B. Rodehacke, Nicole-Jeanne Schlegel, Andrew Shepherd, Sainan Sun, Johannes Sutter, Jonas Van Breedam, Roderik S. W. van de Wal, Ricarda Winkelmann, and Tong Zhang
The Cryosphere, 13, 1441–1471, https://doi.org/10.5194/tc-13-1441-2019, https://doi.org/10.5194/tc-13-1441-2019, 2019
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We compare a wide range of Antarctic ice sheet simulations with varying initialization techniques and model parameters to understand the role they play on the projected evolution of this ice sheet under simple scenarios. Results are improved compared to previous assessments and show that continued improvements in the representation of the floating ice around Antarctica are critical to reduce the uncertainty in the future ice sheet contribution to sea level rise.
Mathieu Morlighem, Michael Wood, Hélène Seroussi, Youngmin Choi, and Eric Rignot
The Cryosphere, 13, 723–734, https://doi.org/10.5194/tc-13-723-2019, https://doi.org/10.5194/tc-13-723-2019, 2019
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Many glaciers along the coast of Greenland have been retreating. It has been suggested that this retreat is triggered by the presence of warm water in the fjords, and surface melt at the top of the ice sheet is exacerbating this problem. Here, we quantify the vulnerability of northwestern Greenland to further warming using a numerical model. We find that in current conditions, this sector alone will contribute more than 1 cm to sea rise level by 2100, and up to 3 cm in the most extreme scenario.
Sébastien Le clec'h, Sylvie Charbit, Aurélien Quiquet, Xavier Fettweis, Christophe Dumas, Masa Kageyama, Coraline Wyard, and Catherine Ritz
The Cryosphere, 13, 373–395, https://doi.org/10.5194/tc-13-373-2019, https://doi.org/10.5194/tc-13-373-2019, 2019
Short summary
Short summary
Quantifying the future contribution of the Greenland ice sheet (GrIS) to sea-level rise in response to atmospheric changes is important but remains challenging. For the first time a full representation of the feedbacks between a GrIS model and a regional atmospheric model was implemented. The authors highlight the fundamental need for representing the GrIS topography change feedbacks with respect to the atmospheric component face to the strong impact on the projected sea-level rise.
Cited articles
Ahlkrona, J., Lötstedt, P., Kirchner, N., and Zwinger, T.: Dynamically
coupling the non-linear Stokes equstions with the shallow ice approximation
in glaciology: Description and first applications of the ISCAL method,
J. Comput. Phys., 308, 1–19, 2016. a
Brondex, J., Gagliardini, O., Gillet-Chaulet, F., and Durand, G.: Sensitivity
of grounding line dynamics to the choice of the friction law, J. Glaciology,
63, 854–866, 2017. a
Brondex, J., Gillet-Chaulet, F., and Gagliardini, O.: Sensitivity of centennial mass loss projections of the Amundsen basin to the friction law, The Cryosphere, 13, 177–195, https://doi.org/10.5194/tc-13-177-2019, 2019. a
Cheng, G.: Numerical experiments for FS adjoint, Zenodo, https://doi.org/10.5281/zenodo.3611158,
2020a. a
Cheng, G.: Numerical experiments for SSA adjoint, Zenodo, https://doi.org/10.5281/zenodo.3611154,
2020b. a
Farinotti, D., Longuevergne, L., Moholdt, G., Duethmann, D., Mölg, T.,
Bolch, T., Vorogushyn, S., and Güntner, A.: Substantial glacier mass
loss in the Tien Shan over the past 50 years, Nat. Geosci., 8,
716–722, https://doi.org/10.1038/ngeo2513, 2015. a
Fisher, A. T., Mankoff, K. D., Tulaczyk, S. M., Tyler, S. W., and Foley, N.:
High geothermal heat flux measured below the West Antarctic Ice Sheet,
Science Advances, 1, e1500093, https://doi.org/10.1126/sciadv.1500093, 2015. a
Fowler, A. C.: Weertman, Lliboutry and the development of sliding theory,
J. Glaciol., 56, 965–972, https://doi.org/10.3189/002214311796406112, 2011. a
Gagliardini, O., Zwinger, T., Gillet-Chaulet, F., Durand, G., Favier, L., de Fleurian, B., Greve, R., Malinen, M., Martín, C., Råback, P., Ruokolainen, J., Sacchettini, M., Schäfer, M., Seddik, H., and Thies, J.: Capabilities and performance of Elmer/Ice, a new-generation ice sheet model, Geosci. Model Dev., 6, 1299–1318, https://doi.org/10.5194/gmd-6-1299-2013, 2013. a
Gladstone, R. M., Warner, R. C., Galton-Fenzi, B. K., Gagliardini, O., Zwinger, T., and Greve, R.: Marine ice sheet model performance depends on basal sliding physics and sub-shelf melting, The Cryosphere, 11, 319–329, https://doi.org/10.5194/tc-11-319-2017, 2017. a
Glen, J. W.: The creep of polycrystalline ice, P. Roy. Soc. Lond. A Mat., 228, 519–538, 1955. a
Goldberg, D. N., Heimbach, P., Joughin, I., and Smith, B.: Committed retreat of Smith, Pope, and Kohler Glaciers over the next 30 years inferred by transient model calibration, The Cryosphere, 9, 2429–2446, https://doi.org/10.5194/tc-9-2429-2015, 2015. a
Greve, R. and Blatter, H.: Dynamics of Ice Sheets and Glaciers,
Advances in Geophysical and Environmental Mechanics and Mathematics
(AGEM2), Springer, Berlin, 287 pp., https://doi.org/10.1007/978-3-642-03415-2, 2009. a, b, c, d
Gudmundsson, G. H.: Transmission of basal variability to glacier surface, J.
Geophys. Res., 108, 2253, https://doi.org/10.1029/2002JB002107, 2003. a
Heimbach, P. and Losch, M.: Adjoint sensitivities of sub-ice-shelf melt rates
to ocean circulation under the Pine Island Ice Shelf, West
Antarctica, Ann. Glaciol., 53, 59–69, 2012. a
Hutter, K.: Theoretical Glaciology, D. Reidel Publishing Company, Terra Scientific Publishing Company, Dordrecht, the Netherlands, https://doi.org/10.1007/978-94-015-1167-4, 510 pp., 1983. a, b
Iken, A.: The effect of the subglacial water pressure on the sliding velocity of a glacier in an idealized numerical model, J. Glaciol., 27,
407–421, https://doi.org/10.1017/S0022143000011448, 1981. a
Jay-Allemand, M., Gillet-Chaulet, F., Gagliardini, O., and Nodet, M.: Investigating changes in basal conditions of Variegated Glacier prior to and during its 1982–1983 surge, The Cryosphere, 5, 659–672, https://doi.org/10.5194/tc-5-659-2011, 2011. a, b
Key, K. and Siegfried, M. R.: The feasibility of imaging subglacial hydrology
beneath ice streams with ground-based electromagnetics,
J. Glaciol., 63, 755–771, https://doi.org/10.1017/jog.2017.36, 2017. a
Kyrke-Smith, T. M., Gudmundsson, G. H., and Farrell, P. E.: Relevance of detail in basal topography for basal slipperiness inversions: a case study on Pine Island Glacier, Antarctica, Frontiers Earth Sci., 6, 33, 2018. a
Lliboutry, L.: General Theory of Subglacial Cavitation and Sliding of
Temperate Glaciers, J. Glaciol., 7, 21–58,
https://doi.org/10.3189/s0022143000020396, 1968. a
Maier, N., Humphrey, N., Harper, J., and Meierbachtol, T.: Sliding dominates
slow-flowing margin regions, Greenland Ice Sheet, Science Advances, 5,
eaaw5406, https://doi.org/10.1126/sciadv.aaw5406, 2019. a
Martin, N. and Monnier, J.: Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface, The Cryosphere, 8, 721–741, https://doi.org/10.5194/tc-8-721-2014, 2014. a
Minchew, B., Simons, M., Björnsson, H., Pálsson, F., Morlighem, M.,
Seroussi, H., Larour, E., and Hensley, S.: Plastic bed beneath
Hofsjökull Ice Cap, central Iceland, and the sensitivity of ice
flow to surface meltwater flux, J. Glaciol., 62, 147–158, 2016. a
Minchew, B. M., Meyer, C. R., Pegler, S. S., Lipovsky, B. P., Rempel, A. W.,
Gudmundsson, G. H., and Iverson, N. R.: Comment on “Friction at the bed
does not control fast glacier flow”, Science, 363, eaau6055, https://doi.org/10.1126/science.aau6055, 2019. a
Monnier, J. and des Boscs, P.-E.: Inference of the bottom properties in shallow ice approximation models, Inverse Probl., 33, 115001, https://doi.org/10.1088/1361-6420/aa7b92, 2017. a
Morland, L. W.: Unconfined Ice-Shelf Flow, in: Dynamics of the West Antarctic
Ice Sheet, edited by: van der Veen, C. J. and Oerlemans, J., Springer, Netherlands, 99–116, 1987. a
Morlighem, M., Seroussi, H., Larour, E., and Rignot, E.: Inversion of basal
friction in Antarctica using exact and incomplete adjoints of a high-order
model, J. Geophys. Res.-Earth Surf., 118, 1–8, 2013. a
Mouginot, J., Rignot, E., Bjørk, A. A., van den Broeke, M., Millan, R.,
Morlighem, M., Noël, B., Scheuchl, B., and Wood, M.: Forty-six years
of Greenland Ice Sheet mass balance from 1972 to 2018, P. Natl. Acad. Sci. USA, 116, 9239–9244, https://doi.org/10.1073/pnas.1904242116, 2019. a
Nye, J. F.: The motion of ice sheets and glaciers, J. Glaciol., 3, 493–507, 1959. a
Nye, J. F.: A calculation on the sliding of ice over a wavy surface using a
Newtonian viscous approximation, P. R. Soc. A, 311, 445–467, 1969. a
Pattyn, F. and Morlighem, M.: The uncertain future of the Antarctic Ice
Sheet, Science, 367, 1331–1335, 2020. a
Pattyn, F., Schoof, C., Perichon, L., Hindmarsh, R. C. A., Bueler, E., de Fleurian, B., Durand, G., Gagliardini, O., Gladstone, R., Goldberg, D., Gudmundsson, G. H., Huybrechts, P., Lee, V., Nick, F. M., Payne, A. J., Pollard, D., Rybak, O., Saito, F., and Vieli, A.: Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP, The Cryosphere, 6, 573–588, https://doi.org/10.5194/tc-6-573-2012, 2012. a, b, c
Perego, M., Price, S. F., and Stadler, G.: Optimal initial conditions for
coupling ice sheet models to Earth system models, J. Geophys. Res.-Earth Surf., 119, 1894–1917, 2014. a
Petra, N., Martin, J., Stadler, G., and Ghattas, O.: A computational framework for infinite-dimensional Bayesian inverse problems, Part II: Newton MCMC with application to ice sheet flow inverse problems,
SIAM J. Sci. Comput., 36, A1525–A1555, 2014. a
Pörtner, H.-O., Roberts, D. C., Masson-Delmotte, V., Zhai, P., Poloczanska,
E., Mintenbeck, K., Tignor, M., Alegría, A., Nicolai, M., Okem, A.,
Petzold, J., Rama, B., and Weyer, N. M.: IPCC, 2019: Technical Summary,
in: IPCC Special Report on the Ocean and Cryosphere in a Changing
Climate, in press, 2019. a, b, c
Rignot, E., Mouginot, J., Scheuchl, B., van den Broeke, M., van Wessem,
M. J., and Morlighem, M.: Four decades of Antarctic ice sheet mass balance
from 1979–2017, P. Natl. Acad. Sci. USA, 116, 1095–1103, https://doi.org/10.1073/pnas.1812883116, 2019. a
Ritz, C., Edwards, T. L., Durand, G., Payne, A. J., Peyaud, V., and Hindmarsh, R. C.: Potential sea level rise from Antarctic ice-sheet instability constrained by observations, Nature, 528, 115–118, 2015. a
Schannwell, C., Drews, R., Ehlers, T. A., Eisen, O., Mayer, C., and Gillet-Chaulet, F.: Kinematic response of ice-rise divides to changes in ocean and atmosphere forcing, The Cryosphere, 13, 2673–2691, https://doi.org/10.5194/tc-13-2673-2019, 2019. a
Schoof, C.: The effect of cavitation on glacier sliding, P. R. Soc. A, 461, 609–627, 2005. a
Schoof, C.: Ice sheet grounding line dynamics: Steady states, stability and
hysteresis, J. Geophys. Res.-Earth Surf., 112, F03S28, https://doi.org/10.1029/2006JF000664, 2007. a, b
Schoof, C.: Ice-sheet acceleration driven by melt supply variability, Nature,
468, 803–806, 2010. a
Sergienko, O. and Hindmarsh, R. C. A.: Regular patterns in frictional
resistance of ice-stream beds seen by surface data inversion, Science, 342,
1086–1089, 2013. a
Seroussi, H., Morlighem, M., Larour, E., Rignot, E., and Khazendar, A.: Hydrostatic grounding line parameterization in ice sheet models, The Cryosphere, 8, 2075–2087, https://doi.org/10.5194/tc-8-2075-2014, 2014. a
Smith, R. C.: Uncertainty Quantification: Theory, Implementation, and
Applications, Society for Industrial and Applied Mathematics, Philadelphia,
ISBN 9781611973211, 382 pp., 2014. a
Sole, A. J., Mair, D. W. F., Nienow, P. W., Bartholomew, I. D., King, I. D.,
Burke, M. A., and Joughin, I.: Seasonal speedup of a Greenland
marine-terminating outlet glacier forced by surface melt-induced changes in
subglacial hydrology, J. Geophys. Res., 116, F03014, https://doi.org/10.1029/2010JF001948, 2011. a
Stearn, L. A. and van der Veen, C. J.: Friction at the bed does not control
fast glacier flow, Science, 361, 273–277, 2018. a
Steffen, W., Rockström, J., Richardson, K., Lenton, T. M., Folke, C.,
Liverman, D., Summerhayes, C. P., Barnosky, A. D., Cornell, S. E., Crucifix, M., Donges, J. F., Fetzer, I., Lade, S. J., Scheffer, M., Winkelmann, R., and Schellnhuber, H. J.: Trajectories of the Earth System in the Anthropocene,
P. Natl. Acad. Sci. USA, 115, 8252–8259, https://doi.org/10.1073/pnas.1810141115, 2018. a
Thorsteinsson, T., Raymond, C. F., Gudmundsson, G. H., Bindschadler, R. A.,
Vornberger, P., and Joughin, I.: Bed topography and lubrication inferred from surface measurements on fast-flowing ice streams, J. Glaciol., 49, 481–490, 2003. a
Tsai, V. C., Stewart, A. L., and Thompson, A. F.: Marine ice-sheet profiles and stability under Coulomb basal conditions, J. Glaciol., 61, 205–215, 2015. a
Vallot, D., Pettersson, R., Luckman, A., Benn, D. I., Zwinger, T., van Pelt, W. J. J., Kohler, J., Schäfer, M., Claremar, B., and Hulton, N. R. J.: Basal dynamics of Kronebreen, a fast-flowing tidewater glacier in Svalbard: non-local spatio-temporal response to water input, J. Glaciol., 11, 179–190, 2017. a
van der Veen, C. J.: Tidewater calving, J. Glaciol., 42, 375–385, 1996. a
van Pelt, W. J. J., Oerlemans, J., Reijmer, C. H., Pettersson, R., Pohjola, V. A., Isaksson, E., and Divine, D.: An iterative inverse method to estimate basal topography and initialize ice flow models, The Cryosphere, 7, 987–1006, https://doi.org/10.5194/tc-7-987-2013, 2013.
a
van Vuuren, D. P., Edmonds, J., Kainuma, M., Riahi, K., Thomson, A., Hibbard,
K., Hurtt, G. C., Kram, T., Krey, V., Lamarque, J.-F., Masui, T.,
Meinshausen, M., Nakicenovic, N., Smith, S. J., and Rose, S. K.: The
representative concentration pathways: an overview, Climatic Change, 109, 5, 2011. a
Weertman, J.: Equilibrium profile of ice caps, J. Glaciol., 3, 953–964, 1961. a
Wilkens, N., Behrens, J., Kleiner, T., Rippin, D., Rückamp, M., and Humbert, A.: Thermal structure and basal sliding parametrisation at Pine Island Glacier – a 3D full-Stokes model study, The Cryosphere, 9, 675–690, https://doi.org/10.5194/tc-9-675-2015, 2015. a
Yu, H., Rignot, E., Seroussi, H., and Morlighem, M.: Retreat of Thwaites Glacier, West Antarctica, over the next 100 years using various ice flow models, ice shelf melt scenarios and basal friction laws, The Cryosphere, 12, 3861–3876, https://doi.org/10.5194/tc-12-3861-2018, 2018. a
Zhu, H., Petra, N., Stadler, G., Isaac, T., Hughes, T. J. R., and Ghattas, O.: Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model, The Cryosphere, 10, 1477–1494, https://doi.org/10.5194/tc-10-1477-2016, 2016. a
Zoet, L. K. and Iverson, N. R.: A slip law for glaciers on deformable beds,
Science, 368, 76–78, 2020. a
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.
We present an inverse modeling approach to improve the understanding of spatiotemporally...
