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
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
Related authors
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
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.
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.
Abhay Prakash, Qin Zhou, Tore Hattermann, and Nina Kirchner
EGUsphere, https://doi.org/10.5194/egusphere-2023-73, https://doi.org/10.5194/egusphere-2023-73, 2023
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Seasonal 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 model results show that amplification of thermal driving and friction velocity in the ice shelf cavity driven by the surface forcing modulations amplify the basal melting.
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
Short summary
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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
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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
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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
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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
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Jeremy Rohmer, Remi Thieblemont, Goneri Le Cozannet, Heiko Goelzer, and Gael Durand
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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.
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
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We use an ice sheet model to test where current climate conditions in Antarctica might lead. We find that, depending on model parameters, present-day ocean and atmosphere conditions might commit a collapse of parts of West Antarctica which evolves over centuries to millennia. Importantly, this collapse is not yet irreversible as shown in our accompanying study.
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
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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.
Julien Brondex, Fabien Gillet-Chaulet, and Olivier Gagliardini
The Cryosphere, 13, 177–195, https://doi.org/10.5194/tc-13-177-2019, https://doi.org/10.5194/tc-13-177-2019, 2019
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Here, we apply a synthetic perturbation to the most active drainage basin of Antarctica and show that centennial mass loss projections obtained through ice flow models depend strongly on the implemented friction law, i.e. the mathematical relationship between basal drag and sliding velocities. In particular, the commonly used Weertman law considerably underestimates the sea-level contribution of this basin in comparison to two water pressure-dependent laws which rely on stronger physical bases.
Hongju Yu, Eric Rignot, Helene Seroussi, and Mathieu Morlighem
The Cryosphere, 12, 3861–3876, https://doi.org/10.5194/tc-12-3861-2018, https://doi.org/10.5194/tc-12-3861-2018, 2018
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Thwaites Glacier, West Antarctica, has experienced rapid grounding line retreat and mass loss in the past decades. In this study, we simulate the evolution of Thwaites Glacier over the next century using different model configurations. Overall, we estimate a 5 mm contribution to global sea level rise from Thwaites Glacier in the next 30 years. However, a 300 % uncertainty is found over the next 100 years, ranging from 14 to 42 mm, depending on the model setup.
Youngmin Choi, Mathieu Morlighem, Michael Wood, and Johannes H. Bondzio
The Cryosphere, 12, 3735–3746, https://doi.org/10.5194/tc-12-3735-2018, https://doi.org/10.5194/tc-12-3735-2018, 2018
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Calving is an important mechanism that controls the dynamics of Greenland outlet glaciers. We test and compare four calving laws and assess which calving law has better predictive abilities. Overall, the calving law based on von Mises stress is more satisfactory than other laws, but new parameterizations should be derived to better capture the detailed processes involved in calving.
Rupert M. Gladstone, Yuwei Xia, and John Moore
The Cryosphere, 12, 3605–3615, https://doi.org/10.5194/tc-12-3605-2018, https://doi.org/10.5194/tc-12-3605-2018, 2018
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Computer models for the simulation of marine ice sheets (ice sheets resting on bedrock below sea level) historically show poor numerical convergence for grounding line (the boundary between grounded and floating parts of the ice sheet) movement. We have further characterised the nature of the numerical problems leading to poor convergence and highlighted implications for the design of computer experiments that test grounding line movement.
Hélène Seroussi and Mathieu Morlighem
The Cryosphere, 12, 3085–3096, https://doi.org/10.5194/tc-12-3085-2018, https://doi.org/10.5194/tc-12-3085-2018, 2018
Michael J. Wolovick and John C. Moore
The Cryosphere, 12, 2955–2967, https://doi.org/10.5194/tc-12-2955-2018, https://doi.org/10.5194/tc-12-2955-2018, 2018
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In this paper, we explore the possibility of using locally targeted geoengineering to slow the rate of an ice sheet collapse. We find that an intervention as big as existing large civil engineering projects could have a 30 % probability of stopping an ice sheet collapse, while larger interventions have better odds of success. With more research to improve upon the simple designs we considered, it may be possible to perfect a design that was both achievable and had good odds of success.
Chen Zhao, Rupert M. Gladstone, Roland C. Warner, Matt A. King, Thomas Zwinger, and Mathieu Morlighem
The Cryosphere, 12, 2637–2652, https://doi.org/10.5194/tc-12-2637-2018, https://doi.org/10.5194/tc-12-2637-2018, 2018
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A combination of computer modelling and observational data were used to infer the resistance to ice flow at the bed of the Fleming Glacier on the Antarctic Peninsula. The model was also used to simulate the distribution of temperature within the ice, which governs the rate at which the ice can deform. This is especially important for glaciers like the Fleming Glacier, which has both regions of rapid deformation and regions of rapid sliding at the bed.
Chen Zhao, Rupert M. Gladstone, Roland C. Warner, Matt A. King, Thomas Zwinger, and Mathieu Morlighem
The Cryosphere, 12, 2653–2666, https://doi.org/10.5194/tc-12-2653-2018, https://doi.org/10.5194/tc-12-2653-2018, 2018
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A combination of computer modelling and observational data were used to infer the resistance to ice flow at the bed of the Fleming Glacier on the Antarctic Peninsula in both 2008 and 2015. The comparison suggests the grounding line retreated by ~ 9 km from 2008 to 2015. The retreat may be enhanced by a positive feedback between friction, melting and sliding at the glacier bed.
Lenneke M. Jong, Rupert M. Gladstone, Benjamin K. Galton-Fenzi, and Matt A. King
The Cryosphere, 12, 2425–2436, https://doi.org/10.5194/tc-12-2425-2018, https://doi.org/10.5194/tc-12-2425-2018, 2018
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We used an ice sheet model to simulate temporary regrounding of a marine ice sheet retreating across a retrograde bedrock slope. We show that a sliding relation incorporating water-filled cavities and the ice overburden pressure at the base allows the temporary regrounding to occur. This suggests that choice of basal sliding relation can be important when modelling grounding line behaviour of regions where potential ice rises and pinning points are present and regrounding could occur.
Clemens Schannwell, Stephen Cornford, David Pollard, and Nicholas E. Barrand
The Cryosphere, 12, 2307–2326, https://doi.org/10.5194/tc-12-2307-2018, https://doi.org/10.5194/tc-12-2307-2018, 2018
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Despite the speculation on the state and fate of Larsen C Ice Shelf, a key unknown factor remains: what would be the effects of ice-shelf collapse on upstream drainage basins and thus global sea levels? In our paper three state-of-the-art numerical ice-sheet models were used to simulate the volume evolution of the inland ice sheet to ice-shelf collapse at Larsen C and George VI ice shelves. Our results suggest sea-level rise of up to ~ 4 mm for Larsen C ice shelf and ~ 22 for George VI ice shelf.
Nadine Steiger, Kerim H. Nisancioglu, Henning Åkesson, Basile de Fleurian, and Faezeh M. Nick
The Cryosphere, 12, 2249–2266, https://doi.org/10.5194/tc-12-2249-2018, https://doi.org/10.5194/tc-12-2249-2018, 2018
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We use an ice flow model to reconstruct the retreat of Jakobshavn Isbræ since 1850, forced by increased ocean warming and calving. Fjord geometry governs locations of rapid retreat: narrow and shallow areas act as intermittent pinning points for decades, followed by delayed rapid retreat without additional climate warming. These areas may be used to locate potential moraine buildup. Evidently, historic retreat and geometric influences have to be analyzed individually for each glacier system.
Giri Gopalan, Birgir Hrafnkelsson, Guðfinna Aðalgeirsdóttir, Alexander H. Jarosch, and Finnur Pálsson
The Cryosphere, 12, 2229–2248, https://doi.org/10.5194/tc-12-2229-2018, https://doi.org/10.5194/tc-12-2229-2018, 2018
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Geophysical systems can often contain scientific parameters whose values are uncertain, complex underlying dynamics, and field measurements with errors. These components are naturally modeled together within what is known as a Bayesian hierarchical model (BHM). This paper constructs such a model for shallow glaciers based on an approximation of the underlying dynamics. The evaluation of this model is aided by the use of exact analytical solutions from the literature.
Olivier Passalacqua, Marie Cavitte, Olivier Gagliardini, Fabien Gillet-Chaulet, Frédéric Parrenin, Catherine Ritz, and Duncan Young
The Cryosphere, 12, 2167–2174, https://doi.org/10.5194/tc-12-2167-2018, https://doi.org/10.5194/tc-12-2167-2018, 2018
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Locating a suitable drill site is a key step in the Antarctic oldest-ice challenge. Here we have conducted a 3-D ice flow simulation in the region of Dome C using a refined bedrock description. Five selection criteria are computed that together provide an objective overview on the local ice flow conditions. We delineate kilometer-scale favorable areas that overlap with the ones recently proposed by another group. We propose a few drill sites that should be surveyed during the next field seasons.
Yongmei Gong, Thomas Zwinger, Jan Åström, Bas Altena, Thomas Schellenberger, Rupert Gladstone, and John C. Moore
The Cryosphere, 12, 1563–1577, https://doi.org/10.5194/tc-12-1563-2018, https://doi.org/10.5194/tc-12-1563-2018, 2018
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In this study we apply a discrete element model capable of simulating ice fracturing. A microscopic-scale discrete process is applied in addition to a continuum ice dynamics model to investigate the mechanisms facilitated by basal meltwater production, surface meltwater and ice crack opening, for the surge in Basin 3, Austfonna ice cap. The discrete element model is used to locate the ice cracks that can penetrate though the full thickness of the glacier and deliver surface water to the bed.
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...
