Articles | Volume 6, issue 6
https://doi.org/10.5194/gmd-6-2135-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/gmd-6-2135-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Model evaluation paper
| 
19 Dec 2013
Model evaluation paper |
| 19 Dec 2013
Accuracy of the zeroth- and second-order shallow-ice approximation – numerical and theoretical results
J. Ahlkrona
Division of Scientific Computing, Department of Information Technology, Uppsala University, Uppsala, Sweden
Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden
N. Kirchner
Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden
Department of Physical Geography and Quaternary Geology, Stockholm University, Stockholm, Sweden
P. Lötstedt
Division of Scientific Computing, Department of Information Technology, Uppsala University, Uppsala, Sweden
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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
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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.
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.
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.
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, Nina Kirchner, and Per Lötstedt
The Cryosphere, 15, 715–742, https://doi.org/10.5194/tc-15-715-2021, https://doi.org/10.5194/tc-15-715-2021, 2021
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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.
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.
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.
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Geosci. Model Dev., 18, 3635–3659, https://doi.org/10.5194/gmd-18-3635-2025, https://doi.org/10.5194/gmd-18-3635-2025, 2025
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Ice-sheet models are computer programs that can simulate how the Greenland and Antarctic ice sheets will evolve in the future. The accuracy of these models depends on their resolution: how small the details are that the model can resolve. We have created a model with a variable resolution that can resolve a lot of detail in areas where lots of changes happen in the ice and less detail in areas where the ice does not move so much. This makes the model both accurate and fast.
Richard Essery, Giulia Mazzotti, Sarah Barr, Tobias Jonas, Tristan Quaife, and Nick Rutter
Geosci. Model Dev., 18, 3583–3605, https://doi.org/10.5194/gmd-18-3583-2025, https://doi.org/10.5194/gmd-18-3583-2025, 2025
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How forests influence accumulation and melt of snow on the ground is of long-standing interest, but uncertainty remains in how best to model forest snow processes. We developed the Flexible Snow Model version 2 to quantify these uncertainties. In a first model demonstration, how unloading of intercepted snow from the forest canopy is represented is responsible for the largest uncertainty. Global mapping of forest distribution is also likely to be a large source of uncertainty in existing models.
Alex E. West and Edward W. Blockley
Geosci. Model Dev., 18, 3041–3064, https://doi.org/10.5194/gmd-18-3041-2025, https://doi.org/10.5194/gmd-18-3041-2025, 2025
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This study uses ice mass balance buoys – temperature- and height-measuring devices frozen into sea ice – to find how well climate models simulate (1) melt and growth of Arctic sea ice and (2) conduction of heat through Arctic sea ice. This may help understand why models produce varying amounts of sea ice in the present day. We find that models tend to show more melt, growth or conduction for a given ice thickness than the buoys, although the difference is smaller for models with more physically realistic thermodynamics.
Ole Richter, Ralph Timmermann, G. Hilmar Gudmundsson, and Jan De Rydt
Geosci. Model Dev., 18, 2945–2960, https://doi.org/10.5194/gmd-18-2945-2025, https://doi.org/10.5194/gmd-18-2945-2025, 2025
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The new coupled ice sheet–ocean model addresses challenges related to horizontal resolution through advanced mesh flexibility, enabled by the use of unstructured grids. We describe the new model, verify its functioning in an idealised setting and demonstrate its advantages in a global-ocean–Antarctic ice sheet domain. The results of this study comprise an important step towards improving predictions of the Antarctic contribution to sea level rise over centennial timescales.
Niccolò Maffezzoli, Eric Rignot, Carlo Barbante, Troels Petersen, and Sebastiano Vascon
Geosci. Model Dev., 18, 2545–2568, https://doi.org/10.5194/gmd-18-2545-2025, https://doi.org/10.5194/gmd-18-2545-2025, 2025
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In this work we introduce IceBoost, a machine learning framework to model the ice thickness distribution of all the world's glaciers with greater accuracy than state-of-the-art methods. The model is trained on 3.7 million measurements globally available and provides skilful estimates across all regions. This advancement will help in better assessing future sea level changes and freshwater resources, with significance for both the scientific community and society at large.
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
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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.
Jan Svoboda, Marc Ruesch, David Liechti, Corinne Jones, Michele Volpi, Michael Zehnder, and Jürg Schweizer
Geosci. Model Dev., 18, 1829–1849, https://doi.org/10.5194/gmd-18-1829-2025, https://doi.org/10.5194/gmd-18-1829-2025, 2025
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Accurately measuring snow height is key for modeling approaches in climate science, snow hydrology, and avalanche forecasting. Erroneous snow height measurements often occur when snow height is low or changes, for instance during snowfall in summer. We prepare a new benchmark dataset with annotated snow height data and demonstrate how to improve the measurement quality using modern deep-learning approaches. Our approach can be easily implemented in a data pipeline for snow modeling.
Alek Aaron Petty, Christopher Cardinale, and Madison Smith
EGUsphere, https://doi.org/10.5194/egusphere-2025-766, https://doi.org/10.5194/egusphere-2025-766, 2025
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We put global climate models to the test against NASA’s ICESat-2 satellite to see how well they simulate global sea ice cover. By adding fancy laser data from ICESat-2, we can better assess how well the models are performing compared to the standard assessments of sea ice area. Overall the models do a good job but there’s room for improvement, especially across the Southern Ocean. We should think a bit more about sea ice density if we want more reliable freeboard comparisons.
James W. Marschalek, Edward Gasson, Tina van de Flierdt, Claus-Dieter Hillenbrand, Martin J. Siegert, and Liam Holder
Geosci. Model Dev., 18, 1673–1708, https://doi.org/10.5194/gmd-18-1673-2025, https://doi.org/10.5194/gmd-18-1673-2025, 2025
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Ice sheet models can help predict how Antarctica's ice sheets respond to environmental change, and such models benefit from comparison to geological data. Here, we use an ice sheet model output and other data to predict the erosion of debris and trace its transport to where it is deposited on the ocean floor. This allows the results of ice sheet modelling to be directly and quantitively compared to real-world data, helping to reduce uncertainty regarding Antarctic sea level contribution.
Anton Korosov, Yue Ying, and Einar Ólason
Geosci. Model Dev., 18, 885–904, https://doi.org/10.5194/gmd-18-885-2025, https://doi.org/10.5194/gmd-18-885-2025, 2025
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We have developed a new method to improve the accuracy of sea ice models, which predict how ice moves and deforms due to wind and ocean currents. Traditional models use parameters that are often poorly defined. The new approach uses machine learning to fine-tune these parameters by comparing simulated ice drift with satellite data. The method identifies optimal settings for the model by analysing patterns in ice deformation. This results in more accurate simulations of sea ice drift forecasting.
Xia Wang, Tao Che, Xueyin Ruan, Shanna Yue, Jing Wang, Chun Zhao, and Lei Geng
Geosci. Model Dev., 18, 651–670, https://doi.org/10.5194/gmd-18-651-2025, https://doi.org/10.5194/gmd-18-651-2025, 2025
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We employed the WRF-Chem model to parameterize atmospheric nitrate deposition in snow and evaluate its performance in simulating snow cover, snow depth, and concentrations of dust and nitrate using new observations from northern China. The results generally exhibit reasonable agreement with field observations in northern China, demonstrating the model's capability to simulate snow properties, including concentrations of reservoir species.
Samar Minallah, William Lipscomb, Gunter Leguy, and Harry Zekollari
EGUsphere, https://doi.org/10.5194/egusphere-2024-4152, https://doi.org/10.5194/egusphere-2024-4152, 2025
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We implemented a new modeling framework within an Earth system model to study the evolution of mountain glaciers under different climate scenarios and applied it to the European Alps. Alpine glaciers will lose a large volume fraction under current temperatures, with near complete ice loss under warmer scenarios. This is the first use of a 3D, higher-order ice flow model for regional-scale glacier simulations that will enable assessments of coupled land ice and Earth system processes.
Simon Horton, Florian Herla, and Pascal Haegeli
Geosci. Model Dev., 18, 193–209, https://doi.org/10.5194/gmd-18-193-2025, https://doi.org/10.5194/gmd-18-193-2025, 2025
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We present a method for avalanche forecasters to analyze patterns in snowpack model simulations. It uses fuzzy clustering to group small regions into larger forecast areas based on snow characteristics, locations, and temporal history. Tested in the Columbia Mountains in two winter seasons, it closely matched real forecast regions regions and identified major avalanche hazard patterns. This approach simplifies complex model outputs, helping forecasters make informed decisions.
Adrien Michel, Johannes Aschauer, Tobias Jonas, Stefanie Gubler, Sven Kotlarski, and Christoph Marty
Geosci. Model Dev., 17, 8969–8988, https://doi.org/10.5194/gmd-17-8969-2024, https://doi.org/10.5194/gmd-17-8969-2024, 2024
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We present a method to correct snow cover maps (represented in terms of snow water equivalent) to match better-quality maps. The correction can then be extended backwards and forwards in time for periods when better-quality maps are not available. The method is fast and gives good results. It is then applied to obtain a climatology of the snow cover in Switzerland over the past 60 years at a resolution of 1 d and 1 km. This is the first time that such a dataset has been produced.
Ghislain Picard and Quentin Libois
Geosci. Model Dev., 17, 8927–8953, https://doi.org/10.5194/gmd-17-8927-2024, https://doi.org/10.5194/gmd-17-8927-2024, 2024
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The Two-streAm Radiative TransfEr in Snow (TARTES) is a radiative transfer model to compute snow albedo in the solar domain and the profiles of light and energy absorption in a multi-layered snowpack whose physical properties are user defined. It uniquely considers snow grain shape flexibly, based on recent insights showing that snow does not behave as a collection of ice spheres but instead as a random medium. TARTES is user-friendly yet performs comparably to more complex models.
Tim Hill, Derek Bingham, Gwenn E. Flowers, and Matthew J. Hoffman
EGUsphere, https://doi.org/10.22541/essoar.172736254.41350153/v2, https://doi.org/10.22541/essoar.172736254.41350153/v2, 2024
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Subglacial drainage models represent water flow beneath glaciers and ice sheets. Here, we train fast statistical models called Gaussian Process emulators to accelerate subglacial drainage modelling by ~1000 times. We use the fast emulator predictions to show that three of the model parameters are responsible for >90 % of the variance in model outputs. The fast GP emulators will enable future uncertainty quantification and calibration of these models.
Yoshihiro Nakayama, Alena Malyarenko, Hong Zhang, Ou Wang, Matthis Auger, Yafei Nie, Ian Fenty, Matthew Mazloff, Armin Köhl, and Dimitris Menemenlis
Geosci. Model Dev., 17, 8613–8638, https://doi.org/10.5194/gmd-17-8613-2024, https://doi.org/10.5194/gmd-17-8613-2024, 2024
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Global- and basin-scale ocean reanalyses are becoming easily accessible. However, such ocean reanalyses are optimized for their entire model domains and their ability to simulate the Southern Ocean requires evaluation. We conduct intercomparison analyses of Massachusetts Institute of Technology General Circulation Model (MITgcm)-based ocean reanalyses. They generally perform well for the open ocean, but open-ocean temporal variability and Antarctic continental shelves require improvements.
Diego Monteiro, Cécile Caillaud, Matthieu Lafaysse, Adrien Napoly, Mathieu Fructus, Antoinette Alias, and Samuel Morin
Geosci. Model Dev., 17, 7645–7677, https://doi.org/10.5194/gmd-17-7645-2024, https://doi.org/10.5194/gmd-17-7645-2024, 2024
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Modeling snow cover in climate and weather forecasting models is a challenge even for high-resolution models. Recent simulations with CNRM-AROME have shown difficulties when representing snow in the European Alps. Using remote sensing data and in situ observations, we evaluate modifications of the land surface configuration in order to improve it. We propose a new surface configuration, enabling a more realistic simulation of snow cover, relevant for climate and weather forecasting applications.
Alessandro Maissen, Frank Techel, and Michele Volpi
Geosci. Model Dev., 17, 7569–7593, https://doi.org/10.5194/gmd-17-7569-2024, https://doi.org/10.5194/gmd-17-7569-2024, 2024
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By harnessing AI models, this work enables processing large amounts of data, including weather conditions, snowpack characteristics, and historical avalanche data, to predict human-like avalanche forecasts in Switzerland. Our proposed model can significantly assist avalanche forecasters in their decision-making process, thereby facilitating more efficient and accurate predictions crucial for ensuring safety in Switzerland's avalanche-prone regions.
Davor Dundovic, Joseph G. Wallwork, Stephan C. Kramer, Fabien Gillet-Chaulet, Regine Hock, and Matthew D. Piggott
EGUsphere, https://doi.org/10.5194/egusphere-2024-2649, https://doi.org/10.5194/egusphere-2024-2649, 2024
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Accurate numerical studies of glaciers often require high-resolution simulations, which often prove too demanding even for modern computers. In this paper we develop a method that identifies whether different parts of a glacier require high or low resolution based on its physical features, such as its thickness and velocity. We show that by doing so we can achieve a more optimal simulation accuracy for the available computing resources compared to uniform resolution simulations.
Enrico Zorzetto, Sergey Malyshev, Paul Ginoux, and Elena Shevliakova
Geosci. Model Dev., 17, 7219–7244, https://doi.org/10.5194/gmd-17-7219-2024, https://doi.org/10.5194/gmd-17-7219-2024, 2024
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We describe a new snow scheme developed for use in global climate models, which simulates the interactions of snowpack with vegetation, atmosphere, and soil. We test the new snow model over a set of sites where in situ observations are available. We find that when compared to a simpler snow model, this model improves predictions of seasonal snow and of soil temperature under the snowpack, important variables for simulating both the hydrological cycle and the global climate system.
Therese Rieckh, Andreas Born, Alexander Robinson, Robert Law, and Gerrit Gülle
Geosci. Model Dev., 17, 6987–7000, https://doi.org/10.5194/gmd-17-6987-2024, https://doi.org/10.5194/gmd-17-6987-2024, 2024
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We present the open-source model ELSA, which simulates the internal age structure of large ice sheets. It creates layers of snow accumulation at fixed times during the simulation, which are used to model the internal stratification of the ice sheet. Together with reconstructed isochrones from radiostratigraphy data, ELSA can be used to assess ice sheet models and to improve their parameterization. ELSA can be used coupled to an ice sheet model or forced with its output.
Fu Zhao, Xi Liang, Zhongxiang Tian, Ming Li, Na Liu, and Chengyan Liu
Geosci. Model Dev., 17, 6867–6886, https://doi.org/10.5194/gmd-17-6867-2024, https://doi.org/10.5194/gmd-17-6867-2024, 2024
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In this work, we introduce a newly developed Antarctic sea ice forecasting system, namely the Southern Ocean Ice Prediction System (SOIPS). The system is based on a regional sea ice‒ocean‒ice shelf coupled model and can assimilate sea ice concentration observations. By assessing the system's performance in sea ice forecasts, we find that the system can provide reliable Antarctic sea ice forecasts for the next 7 d and has the potential to guide ship navigation in the Antarctic sea ice zone.
Chenhui Ning, Shiming Xu, Yan Zhang, Xuantong Wang, Zhihao Fan, and Jiping Liu
Geosci. Model Dev., 17, 6847–6866, https://doi.org/10.5194/gmd-17-6847-2024, https://doi.org/10.5194/gmd-17-6847-2024, 2024
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Sea ice models are mainly based on non-moving structured grids, which is different from buoy measurements that follow the ice drift. To facilitate Lagrangian analysis, we introduce online tracking of sea ice in Community Ice CodE (CICE). We validate the sea ice tracking with buoys and evaluate the sea ice deformation in high-resolution simulations, which show multi-fractal characteristics. The source code is openly available and can be used in various scientific and operational applications.
Ulrich Strasser, Michael Warscher, Erwin Rottler, and Florian Hanzer
Geosci. Model Dev., 17, 6775–6797, https://doi.org/10.5194/gmd-17-6775-2024, https://doi.org/10.5194/gmd-17-6775-2024, 2024
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openAMUNDSEN is a fully distributed open-source snow-hydrological model for mountain catchments. It includes process representations of an empirical, semi-empirical, and physical nature. It uses temperature, precipitation, humidity, radiation, and wind speed as forcing data and is computationally efficient, of a modular nature, and easily extendible. The Python code is available on GitHub (https://github.com/openamundsen/openamundsen), including documentation (https://doc.openamundsen.org).
Matthias Rauter and Julia Kowalski
Geosci. Model Dev., 17, 6545–6569, https://doi.org/10.5194/gmd-17-6545-2024, https://doi.org/10.5194/gmd-17-6545-2024, 2024
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Snow avalanches can form large powder clouds that substantially exceed the velocity and reach of the dense core. Only a few complex models exist to simulate this phenomenon, and the respective hazard is hard to predict. This work provides a novel flow model that focuses on simple relations while still encapsulating the significant behaviour. The model is applied to reconstruct two catastrophic powder snow avalanche events in Austria.
Till Andreas Soya Rasmussen, Jacob Poulsen, Mads Hvid Ribergaard, Ruchira Sasanka, Anthony P. Craig, Elizabeth C. Hunke, and Stefan Rethmeier
Geosci. Model Dev., 17, 6529–6544, https://doi.org/10.5194/gmd-17-6529-2024, https://doi.org/10.5194/gmd-17-6529-2024, 2024
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Earth system models (ESMs) today strive for better quality based on improved resolutions and improved physics. A limiting factor is the supercomputers at hand and how best to utilize them. This study focuses on the refactorization of one part of a sea ice model (CICE), namely the dynamics. It shows that the performance can be significantly improved, which means that one can either run the same simulations much cheaper or advance the system according to what is needed.
Iain Wheel, Douglas I. Benn, Anna J. Crawford, Joe Todd, and Thomas Zwinger
Geosci. Model Dev., 17, 5759–5777, https://doi.org/10.5194/gmd-17-5759-2024, https://doi.org/10.5194/gmd-17-5759-2024, 2024
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Calving, the detachment of large icebergs from glaciers, is one of the largest uncertainties in future sea level rise projections. This process is poorly understood, and there is an absence of detailed models capable of simulating calving. A new 3D calving model has been developed to better understand calving at glaciers where detailed modelling was previously limited. Importantly, the new model is very flexible. By allowing for unrestricted calving geometries, it can be applied at any location.
Kévin Fourteau, Julien Brondex, Fanny Brun, and Marie Dumont
Geosci. Model Dev., 17, 1903–1929, https://doi.org/10.5194/gmd-17-1903-2024, https://doi.org/10.5194/gmd-17-1903-2024, 2024
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In this paper, we provide a novel numerical implementation for solving the energy exchanges at the surface of snow and ice. By combining the strong points of previous models, our solution leads to more accurate and robust simulations of the energy exchanges, surface temperature, and melt while preserving a reasonable computation time.
Matthieu Baron, Ange Haddjeri, Matthieu Lafaysse, Louis Le Toumelin, Vincent Vionnet, and Mathieu Fructus
Geosci. Model Dev., 17, 1297–1326, https://doi.org/10.5194/gmd-17-1297-2024, https://doi.org/10.5194/gmd-17-1297-2024, 2024
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Increasing the spatial resolution of numerical systems simulating snowpack evolution in mountain areas requires representing small-scale processes such as wind-induced snow transport. We present SnowPappus, a simple scheme coupled with the Crocus snow model to compute blowing-snow fluxes and redistribute snow among grid points at 250 m resolution. In terms of numerical cost, it is suitable for large-scale applications. We present point-scale evaluations of fluxes and snow transport occurrence.
Lizz Ultee, Alexander A. Robel, and Stefano Castruccio
Geosci. Model Dev., 17, 1041–1057, https://doi.org/10.5194/gmd-17-1041-2024, https://doi.org/10.5194/gmd-17-1041-2024, 2024
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The surface mass balance (SMB) of an ice sheet describes the net gain or loss of mass from ice sheets (such as those in Greenland and Antarctica) through interaction with the atmosphere. We developed a statistical method to generate a wide range of SMB fields that reflect the best understanding of SMB processes. Efficiently sampling the variability of SMB will help us understand sources of uncertainty in ice sheet model projections.
Anjali Sandip, Ludovic Räss, and Mathieu Morlighem
Geosci. Model Dev., 17, 899–909, https://doi.org/10.5194/gmd-17-899-2024, https://doi.org/10.5194/gmd-17-899-2024, 2024
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We solve momentum balance for unstructured meshes to predict ice flow for real glaciers using a pseudo-transient method on graphics processing units (GPUs) and compare it to a standard central processing unit (CPU) implementation. We justify the GPU implementation by applying the price-to-performance metric for up to million-grid-point spatial resolutions. This study represents a first step toward leveraging GPU processing power, enabling more accurate polar ice discharge predictions.
Julien Brondex, Kévin Fourteau, Marie Dumont, Pascal Hagenmuller, Neige Calonne, François Tuzet, and Henning Löwe
Geosci. Model Dev., 16, 7075–7106, https://doi.org/10.5194/gmd-16-7075-2023, https://doi.org/10.5194/gmd-16-7075-2023, 2023
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Vapor diffusion is one of the main processes governing snowpack evolution, and it must be accounted for in models. Recent attempts to represent vapor diffusion in numerical models have faced several difficulties regarding computational cost and mass and energy conservation. Here, we develop our own finite-element software to explore numerical approaches and enable us to overcome these difficulties. We illustrate the capability of these approaches on established numerical benchmarks.
Daniel Moreno-Parada, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
EGUsphere, https://doi.org/10.5194/egusphere-2023-2690, https://doi.org/10.5194/egusphere-2023-2690, 2023
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We introduce Nix, an ice-sheet model designed for understanding how large masses of ice behave. Nix as a computer program that simulates the movement and temperature changes in ice sheets. Nix helps us study how ice sheets respond to changes in the atmosphere and ocean. We found that how fast ice melts under the shelves and how heat is exchanged, play a role in determining the future of ice sheets. Nix is a useful tool for learning more about how climate change affects polar ice sheets.
Matthias Tonnel, Anna Wirbel, Felix Oesterle, and Jan-Thomas Fischer
Geosci. Model Dev., 16, 7013–7035, https://doi.org/10.5194/gmd-16-7013-2023, https://doi.org/10.5194/gmd-16-7013-2023, 2023
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Avaframe - the open avalanche framework - provides open-source tools to simulate and investigate snow avalanches. It is utilized for multiple purposes, the two main applications being hazard mapping and scientific research of snow processes. We present the theory, conversion to a computer model, and testing for one of the core modules used for simulations of a particular type of avalanche, the so-called dense-flow avalanches. Tests check and confirm the applicability of the utilized method.
Jordi Bolibar, Facundo Sapienza, Fabien Maussion, Redouane Lguensat, Bert Wouters, and Fernando Pérez
Geosci. Model Dev., 16, 6671–6687, https://doi.org/10.5194/gmd-16-6671-2023, https://doi.org/10.5194/gmd-16-6671-2023, 2023
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We developed a new modelling framework combining numerical methods with machine learning. Using this approach, we focused on understanding how ice moves within glaciers, and we successfully learnt a prescribed law describing ice movement for 17 glaciers worldwide as a proof of concept. Our framework has the potential to discover important laws governing glacier processes, aiding our understanding of glacier physics and their contribution to water resources and sea-level rise.
Prateek Gantayat, Alison F. Banwell, Amber A. Leeson, James M. Lea, Dorthe Petersen, Noel Gourmelen, and Xavier Fettweis
Geosci. Model Dev., 16, 5803–5823, https://doi.org/10.5194/gmd-16-5803-2023, https://doi.org/10.5194/gmd-16-5803-2023, 2023
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We developed a new supraglacial hydrology model for the Greenland Ice Sheet. This model simulates surface meltwater routing, meltwater drainage, supraglacial lake (SGL) overflow, and formation of lake ice. The model was able to reproduce 80 % of observed lake locations and provides a good match between the observed and modelled temporal evolution of SGLs.
Kevin Hank, Lev Tarasov, and Elisa Mantelli
Geosci. Model Dev., 16, 5627–5652, https://doi.org/10.5194/gmd-16-5627-2023, https://doi.org/10.5194/gmd-16-5627-2023, 2023
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Physically meaningful modeling of geophysical system instabilities is numerically challenging, given the potential effects of purely numerical artifacts. Here we explore the sensitivity of ice stream surge activation to numerical and physical model aspects. We find that surge characteristics exhibit a resolution dependency but converge at higher horizontal grid resolutions and are significantly affected by the incorporation of bed thermal and sub-glacial hydrology models.
Yannic Fischler, Thomas Kleiner, Christian Bischof, Jeremie Schmiedel, Roiy Sayag, Raban Emunds, Lennart Frederik Oestreich, and Angelika Humbert
Geosci. Model Dev., 16, 5305–5322, https://doi.org/10.5194/gmd-16-5305-2023, https://doi.org/10.5194/gmd-16-5305-2023, 2023
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Water underneath ice sheets affects the motion of glaciers. This study presents a newly developed code, CUAS-MPI, that simulates subglacial hydrology. It is designed for supercomputers and is hence a parallelized code. We measure the performance of this code for simulations of the entire Greenland Ice Sheet and find that the code works efficiently. Moreover, we validated the code to ensure the correctness of the solution. CUAS-MPI opens new possibilities for simulations of ice sheet hydrology.
Julia Kaltenborn, Amy R. Macfarlane, Viviane Clay, and Martin Schneebeli
Geosci. Model Dev., 16, 4521–4550, https://doi.org/10.5194/gmd-16-4521-2023, https://doi.org/10.5194/gmd-16-4521-2023, 2023
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Snow layer segmentation and snow grain classification are essential diagnostic tasks for cryospheric applications. A SnowMicroPen (SMP) can be used to that end; however, the manual classification of its profiles becomes infeasible for large datasets. Here, we evaluate how well machine learning models automate this task. Of the 14 models trained on the MOSAiC SMP dataset, the long short-term memory model performed the best. The findings presented here facilitate and accelerate SMP data analysis.
Johannes Aschauer, Adrien Michel, Tobias Jonas, and Christoph Marty
Geosci. Model Dev., 16, 4063–4081, https://doi.org/10.5194/gmd-16-4063-2023, https://doi.org/10.5194/gmd-16-4063-2023, 2023
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Snow water equivalent is the mass of water stored in a snowpack. Based on exponential settling functions, the empirical snow density model SWE2HS is presented to convert time series of daily snow water equivalent into snow depth. The model has been calibrated with data from Switzerland and validated with independent data from the European Alps. A reference implementation of SWE2HS is available as a Python package.
Eric Keenan, Nander Wever, Jan T. M. Lenaerts, and Brooke Medley
Geosci. Model Dev., 16, 3203–3219, https://doi.org/10.5194/gmd-16-3203-2023, https://doi.org/10.5194/gmd-16-3203-2023, 2023
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Ice sheets gain mass via snowfall. However, snowfall is redistributed by the wind, resulting in accumulation differences of up to a factor of 5 over distances as short as 5 km. These differences complicate estimates of ice sheet contribution to sea level rise. For this reason, we have developed a new model for estimating wind-driven snow redistribution on ice sheets. We show that, over Pine Island Glacier in West Antarctica, the model improves estimates of snow accumulation variability.
Sebastian Westermann, Thomas Ingeman-Nielsen, Johanna Scheer, Kristoffer Aalstad, Juditha Aga, Nitin Chaudhary, Bernd Etzelmüller, Simon Filhol, Andreas Kääb, Cas Renette, Louise Steffensen Schmidt, Thomas Vikhamar Schuler, Robin B. Zweigel, Léo Martin, Sarah Morard, Matan Ben-Asher, Michael Angelopoulos, Julia Boike, Brian Groenke, Frederieke Miesner, Jan Nitzbon, Paul Overduin, Simone M. Stuenzi, and Moritz Langer
Geosci. Model Dev., 16, 2607–2647, https://doi.org/10.5194/gmd-16-2607-2023, https://doi.org/10.5194/gmd-16-2607-2023, 2023
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The CryoGrid community model is a new tool for simulating ground temperatures and the water and ice balance in cold regions. It is a modular design, which makes it possible to test different schemes to simulate, for example, permafrost ground in an efficient way. The model contains tools to simulate frozen and unfrozen ground, snow, glaciers, and other massive ice bodies, as well as water bodies.
Alex S. Gardner, Nicole-Jeanne Schlegel, and Eric Larour
Geosci. Model Dev., 16, 2277–2302, https://doi.org/10.5194/gmd-16-2277-2023, https://doi.org/10.5194/gmd-16-2277-2023, 2023
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This is the first description of the open-source Glacier Energy and Mass Balance (GEMB) model. GEMB models the ice sheet and glacier surface–atmospheric energy and mass exchange, as well as the firn state. The model is evaluated against the current state of the art and in situ observations and is shown to perform well.
Yafei Nie, Chengkun Li, Martin Vancoppenolle, Bin Cheng, Fabio Boeira Dias, Xianqing Lv, and Petteri Uotila
Geosci. Model Dev., 16, 1395–1425, https://doi.org/10.5194/gmd-16-1395-2023, https://doi.org/10.5194/gmd-16-1395-2023, 2023
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State-of-the-art Earth system models simulate the observed sea ice extent relatively well, but this is often due to errors in the dynamic and other processes in the simulated sea ice changes cancelling each other out. We assessed the sensitivity of these processes simulated by the coupled ocean–sea ice model NEMO4.0-SI3 to 18 parameters. The performance of the model in simulating sea ice change processes was ultimately improved by adjusting the three identified key parameters.
Varun Sharma, Franziska Gerber, and Michael Lehning
Geosci. Model Dev., 16, 719–749, https://doi.org/10.5194/gmd-16-719-2023, https://doi.org/10.5194/gmd-16-719-2023, 2023
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Most current generation climate and weather models have a relatively simplistic description of snow and snow–atmosphere interaction. One reason for this is the belief that including an advanced snow model would make the simulations too computationally demanding. In this study, we bring together two state-of-the-art models for atmosphere (WRF) and snow cover (SNOWPACK) and highlight both the feasibility and necessity of such coupled models to explore underexplored phenomena in the cryosphere.
Anne M. Felden, Daniel F. Martin, and Esmond G. Ng
Geosci. Model Dev., 16, 407–425, https://doi.org/10.5194/gmd-16-407-2023, https://doi.org/10.5194/gmd-16-407-2023, 2023
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We present and validate a novel subglacial hydrology model, SUHMO, based on an adaptive mesh refinement framework. We propose the addition of a pseudo-diffusion to recover the wall melting in channels. Computational performance analysis demonstrates the efficiency of adaptive mesh refinement on large-scale hydrologic problems. The adaptive mesh refinement approach will eventually enable better ice bed boundary conditions for ice sheet simulations at a reasonable computational cost.
Dalei Hao, Gautam Bisht, Karl Rittger, Edward Bair, Cenlin He, Huilin Huang, Cheng Dang, Timbo Stillinger, Yu Gu, Hailong Wang, Yun Qian, and L. Ruby Leung
Geosci. Model Dev., 16, 75–94, https://doi.org/10.5194/gmd-16-75-2023, https://doi.org/10.5194/gmd-16-75-2023, 2023
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Snow with the highest albedo of land surface plays a vital role in Earth’s surface energy budget and water cycle. This study accounts for the impacts of snow grain shape and mixing state of light-absorbing particles with snow on snow albedo in the E3SM land model. The findings advance our understanding of the role of snow grain shape and mixing state of LAP–snow in land surface processes and offer guidance for improving snow simulations and radiative forcing estimates in Earth system models.
Esteban Alonso-González, Kristoffer Aalstad, Mohamed Wassim Baba, Jesús Revuelto, Juan Ignacio López-Moreno, Joel Fiddes, Richard Essery, and Simon Gascoin
Geosci. Model Dev., 15, 9127–9155, https://doi.org/10.5194/gmd-15-9127-2022, https://doi.org/10.5194/gmd-15-9127-2022, 2022
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Snow cover plays an important role in many processes, but its monitoring is a challenging task. The alternative is usually to simulate the snowpack, and to improve these simulations one of the most promising options is to fuse simulations with available observations (data assimilation). In this paper we present MuSA, a data assimilation tool which facilitates the implementation of snow monitoring initiatives, allowing the assimilation of a wide variety of remotely sensed snow cover information.
Vincent Verjans, Alexander A. Robel, Helene Seroussi, Lizz Ultee, and Andrew F. Thompson
Geosci. Model Dev., 15, 8269–8293, https://doi.org/10.5194/gmd-15-8269-2022, https://doi.org/10.5194/gmd-15-8269-2022, 2022
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We describe the development of the first large-scale ice sheet model that accounts for stochasticity in a range of processes. Stochasticity allows the impacts of inherently uncertain processes on ice sheets to be represented. This includes climatic uncertainty, as the climate is inherently chaotic. Furthermore, stochastic capabilities also encompass poorly constrained glaciological processes that display strong variability at fine spatiotemporal scales. We present the model and test experiments.
Cited articles
Ahlkrona, J., Kirchner, N., and Lötstedt, P.: A numerical study of scaling relations for Non-Newtonian thin film flows with applications in ice sheet modelling, Quart. J. Mech. Appl. Math., 66, 417–435, 2013.
Baral, D. R.: Asymptotic theories of large scale motion, temperature and moisture distributions in land based polythermal ice shields and in floating ice shelves, a critical review and new developments, Ph. D. thesis, Department of Mechanics (III), Technical University Darmstadt, Darmstadt, Germany, 1999.
Baral, D. R., Hutter, K., and Greve, R.: Asymptotic theories of large-scale motion, temperature and moisture distribution in land-based polythermal ice sheets: a critical review and new developments, Appl. Mech. Rev., 54, 215–256, 2001.
Blatter, H.: Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients, J. Glaciol., 41, 333–344, 1995.
Calov, R., Greve, R., Abe-Ouchi, A., Bueler, E., Huybrechts, P., Johnson, J. V., Pattyn, F., Pollard, D., Ritz, C., Saito, F., and Tarasov, L.: R}esults of the Ice Sheet Model Intercomparison Project – Heinrich Event INtercOmparison, {(ISMIP HEINO), J. Glaciol., 56, 371–383, 2010.
Colbeck, S. C. and Evans, R. J.: A flow law for temperate glacier ice, J. Glaciol., 12, 71–86, 1973.
Egholm, D. L., Knudsen, M. F., Clark, C. D., and Lesemann, J. E.: Modeling the flow of glaciers in steep terrains: the integrated Second-Order Shallow-Ice Approximation (iSOSIA), J. Geophys. Res., 116, F02012, https://doi.org/10.1029/2010JF001900, 2011.
Fowler, A. C. and Larson, D. A.: On the flow of polythermal glaciers, I. Model and preliminary results, Proc. Roy. Soc. Lond. A, 363, 217–242, 1978.
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/gmdd-6-1689-2013, 2013.
Greve, R.: Thermomechanisches Verhalten polythermer Eisschilde – Theorie, Analytik, Numerik, Ph. D. thesis, Department of Mechanics (III), Technical Univeristy Darmstadt, Germany, 1995.
Greve, R.: A continuum-mechanical formulation for shallow polythermal ice sheets, Philos. T. Roy. Soc. A, 355, 921–974, 1997.
Greve, R. and Blatter, H.: Dynamics of Ice Sheets and Glaciers, Advances in Geophysical and Environmental Mechanics and Mathematics (AGEM2), Springer, Berlin, 2009.
Hutter, K.: Theoretical Glaciology, D. Reidel Publishing Company, Terra Scientific Publishing Company, Dordrecht, 1983.
Johnson, R. E. and McMeeking, R. M.: Near-surface flow in glaciers obeying Glen's law, Quart. J. Mech. Appl. Math., 7, 273–291, 1984.
Kirchner, N., Hutter, K., Jakobsson, M., and Gyllencreutz, R.: Capabilities and limitations of numerical ice sheet models: a discussion for Earth-scientists and modelers, Quaternary Sci. Rev., 30, 3691–3704, 2011.
Lliboutry, L. A.: The dynamics of temperate glaciers from the detailed viewpoint, J. Glaciol., 8, 185–205, 1969.
MacAyeal, D. R.: The basal stress distribution of I}ce Stream E, {Antarctica, inferred by control methods, J. Geophys. Res., 97, 595–603, 1992.
Mangeney, A. and Califano, F.: The shallow-ice approximation for anisotropic ice – Formulation and limits, J. Geophys. Res., 103, 691–705, 1998.
Morland, L. W.: Thermo–mechanical balances of ice sheet flows, Geophys. Astrophys. Fluid Dynam., 29, 237–266, 1984.
Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson, G. H., Hindmarsh, R. C. A., Hubbard, A., Johnson, J. V., Kleiner, T., Konovalov, Y., Martin, C., Payne, A. J., Pollard, D., Price, S., Rückamp, M., Saito, F., Souček, O., Sugiyama, S., and Zwinger, T.: Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP–HOM), The Cryosphere, 2, 95–108, https://doi.org/10.5194/tc-2-95-2008, 2008.
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.
Råback, P., Malinen, M., Ruokolainen, J., Pursula, A., and Zwinger, T.: Elmer Models Manual, CSC – IT Center for Science, Helsinki, Finland, 2013.
Schoof, C. and Hindmarsh, R.: Thin-film flows with wall slip: an asymptotic analysis of higher order glacier flow models, Quart. J. Mech. Appl. Math., 63, 73–114, 2010.
Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K., Tignor, M., and Miller, H.: The physical science basis, in: Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change 2007, Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2007.
Sou\v cek, O. and Martinec, Z.: Iterative improvement of the shallow-ice approximation, J. Glaciology, 54, 812–822, 2008.
