Articles | Volume 11, issue 1
https://doi.org/10.5194/tc-11-541-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/tc-11-541-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
15 Feb 2017
Research article |
| 15 Feb 2017
Models for polythermal ice sheets and glaciers
University of Oxford, Oxford, UK
Christian Schoof
University of British Columbia, BC, Canada
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Marianne Haseloff, Ian J. Hewitt, and Richard F. Katz
EGUsphere, https://doi.org/10.5194/egusphere-2025-204, https://doi.org/10.5194/egusphere-2025-204, 2025
This preprint is open for discussion and under review for The Cryosphere (TC).
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We combine models for marine ice sheets (which terminate in the ocean) and water flux at the ice-bed interface. The coupled system evolves dynamically due to a positive feedback between ice flow, heat dissipation at the ice stream bed, and basal lubrication. Our results show that depending on the hydraulic properties of the bed, distinct dynamic regimes can be identified. These regimes include steady streaming, hydraulically controlled surges, and thermally controlled oscillations.
Gabriel Cairns, Graham Benham, and Ian Hewitt
EGUsphere, https://doi.org/10.5194/egusphere-2024-2880, https://doi.org/10.5194/egusphere-2024-2880, 2024
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Thick layers of porous rock known as sedimentary basins lie underneath many glaciers in Antarctica that flow into the sea. These layers contain large amounts of groundwater, some of which is seawater. We use a mathematical model to predict how groundwater flows through these basins, finding that seawater can become trapped due to changes in the ice sheet over time. We also predict where water flows out of (or into) these basins, and we discuss possible implications for the glacier.
Tilly Woods and Ian J. Hewitt
The Cryosphere, 17, 1967–1987, https://doi.org/10.5194/tc-17-1967-2023, https://doi.org/10.5194/tc-17-1967-2023, 2023
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Solar radiation causes melting at and just below the surface of the Greenland ice sheet, forming a porous surface layer known as the weathering crust. The weathering crust is home to many microbes, and the growth of these microbes is linked to the melting of the weathering crust and vice versa. We use a mathematical model to investigate what controls the size and structure of the weathering crust, the number of microbes within it, and its sensitivity to climate change.
Barry Hankin, Ian Hewitt, Graham Sander, Federico Danieli, Giuseppe Formetta, Alissa Kamilova, Ann Kretzschmar, Kris Kiradjiev, Clint Wong, Sam Pegler, and Rob Lamb
Nat. Hazards Earth Syst. Sci., 20, 2567–2584, https://doi.org/10.5194/nhess-20-2567-2020, https://doi.org/10.5194/nhess-20-2567-2020, 2020
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With growing support for nature-based solutions to reduce flooding by local communities, government authorities and international organisations, it is still important to improve how we assess risk reduction. We demonstrate an efficient, simplified 1D network model that allows us to explore the
whole-systemresponse of numerous leaky barriers placed in different stream networks, whilst considering utilisation, synchronisation effects and cascade failure, and we provide advice on their siting.
Colin R. Meyer and Ian J. Hewitt
The Cryosphere, 11, 2799–2813, https://doi.org/10.5194/tc-11-2799-2017, https://doi.org/10.5194/tc-11-2799-2017, 2017
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We describe a new model for the evolution of snow temperature, density, and water content on the surface of glaciers and ice sheets. The model encompasses the surface hydrology of accumulation and ablation areas, allowing us to explore the transition from one to the other as thermal forcing varies. We predict year-round liquid water storage for intermediate values of the surface forcing. We also compare our model to data for the vertical percolation of meltwater in Greenland.
Marianne Haseloff, Ian J. Hewitt, and Richard F. Katz
EGUsphere, https://doi.org/10.5194/egusphere-2025-204, https://doi.org/10.5194/egusphere-2025-204, 2025
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Gabriel Cairns, Graham Benham, and Ian Hewitt
EGUsphere, https://doi.org/10.5194/egusphere-2024-2880, https://doi.org/10.5194/egusphere-2024-2880, 2024
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Thick layers of porous rock known as sedimentary basins lie underneath many glaciers in Antarctica that flow into the sea. These layers contain large amounts of groundwater, some of which is seawater. We use a mathematical model to predict how groundwater flows through these basins, finding that seawater can become trapped due to changes in the ice sheet over time. We also predict where water flows out of (or into) these basins, and we discuss possible implications for the glacier.
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The Cryosphere, 18, 3841–3856, https://doi.org/10.5194/tc-18-3841-2024, https://doi.org/10.5194/tc-18-3841-2024, 2024
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The objective of the study is to understand the interactions between surface and basal crevasses by conducting a stability analysis and addressing the implications of the findings for potential calving laws. The study's findings indicate that, while the propagation of one crack in the case of two aligned surface and basal crevasses does not significantly reinforce the propagation of the other, the presence of multiple crevasses on one side enhances stability and decreases crack propagation.
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EGUsphere, https://doi.org/10.5194/egusphere-2023-807, https://doi.org/10.5194/egusphere-2023-807, 2023
Preprint withdrawn
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We used a model to study how crevasses propagate in ice shelves. Our model combines a viscous model and a fracture mechanics model. We studied periodic crevasses on an ice shelf being stretched. We show that existing models based only on stress cannot fully explain how crevasses grow and lead to iceberg calving. This model can be a useful tool to train a low-dimensional representation calving law for an ice sheet model.
Tilly Woods and Ian J. Hewitt
The Cryosphere, 17, 1967–1987, https://doi.org/10.5194/tc-17-1967-2023, https://doi.org/10.5194/tc-17-1967-2023, 2023
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Solar radiation causes melting at and just below the surface of the Greenland ice sheet, forming a porous surface layer known as the weathering crust. The weathering crust is home to many microbes, and the growth of these microbes is linked to the melting of the weathering crust and vice versa. We use a mathematical model to investigate what controls the size and structure of the weathering crust, the number of microbes within it, and its sensitivity to climate change.
Maryam Zarrinderakht, Christian Schoof, and Anthony Peirce
The Cryosphere, 16, 4491–4512, https://doi.org/10.5194/tc-16-4491-2022, https://doi.org/10.5194/tc-16-4491-2022, 2022
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Iceberg calving is the reason for more than half of mass loss in both Greenland and Antarctica and indirectly contributes to sea-level rise. Our study models iceberg calving by linear elastic fracture mechanics and uses a boundary element method to compute crack tip propagation. This model handles the contact condition: preventing crack faces from penetrating into each other and enabling the derivation of calving laws for different forms of hydrological forcing.
Barry Hankin, Ian Hewitt, Graham Sander, Federico Danieli, Giuseppe Formetta, Alissa Kamilova, Ann Kretzschmar, Kris Kiradjiev, Clint Wong, Sam Pegler, and Rob Lamb
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Christian Schoof
The Cryosphere, 14, 3175–3194, https://doi.org/10.5194/tc-14-3175-2020, https://doi.org/10.5194/tc-14-3175-2020, 2020
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Glacier lake outburst floods are major glacial hazards in which ice-dammed reservoirs rapidly drain, often in a recurring fashion. The main flood phase typically involves a growing channel being eroded into ice by water flow. What is poorly understood is how that channel first comes into being. In this paper, I investigate how an under-ice drainage system composed of small, naturally occurring voids can turn into a channel and how this can explain the cyclical behaviour of outburst floods.
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We analyse a large glacier borehole pressure dataset and provide a holistic view of the observations, suggesting a consistent picture of the evolution of the subglacial drainage system. Some aspects are consistent with the established understanding and others ones are not. We propose that most of the inconsistencies arise from the capacity of some areas of the bed to become hydraulically isolated. We present an adaptation of an existing drainage model that incorporates this phenomena.
Marianne Haseloff, Christian Schoof, and Olivier Gagliardini
The Cryosphere, 12, 2545–2568, https://doi.org/10.5194/tc-12-2545-2018, https://doi.org/10.5194/tc-12-2545-2018, 2018
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Colin R. Meyer and Ian J. Hewitt
The Cryosphere, 11, 2799–2813, https://doi.org/10.5194/tc-11-2799-2017, https://doi.org/10.5194/tc-11-2799-2017, 2017
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We describe a new model for the evolution of snow temperature, density, and water content on the surface of glaciers and ice sheets. The model encompasses the surface hydrology of accumulation and ablation areas, allowing us to explore the transition from one to the other as thermal forcing varies. We predict year-round liquid water storage for intermediate values of the surface forcing. We also compare our model to data for the vertical percolation of meltwater in Greenland.
Christian Schoof, Andrew D. Davis, and Tiberiu V. Popa
The Cryosphere, 11, 2283–2303, https://doi.org/10.5194/tc-11-2283-2017, https://doi.org/10.5194/tc-11-2283-2017, 2017
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We show mathematically and computationally how discharge of ice from ocean-terminating glaciers is controlled by a combination of different forces acting on ice near the grounding line of a glacier and how that combination of forces is affected by the process of iceberg formation, which limits the length of floating ice tongues extending in front of the glacier. We show that a deeper fjord may lead to a longer ice tongue providing greater drag on the glacier, slowing the rate of ice discharge.
Alexander A. Robel, Christian Schoof, and Eli Tziperman
The Cryosphere, 10, 1883–1896, https://doi.org/10.5194/tc-10-1883-2016, https://doi.org/10.5194/tc-10-1883-2016, 2016
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Portions of the Antarctic Ice Sheet edge that rest on upward-sloping beds have the potential to collapse irreversibly and raise global sea level. Using a numerical model, we show that changes in the slipperiness of sediments beneath fast-flowing ice streams can cause them to persist on upward-sloping beds for hundreds to thousands of years before reversing direction. This type of behavior is important to consider as a possibility when interpreting observations of ongoing ice sheet change.
C. Schoof, C. A Rada, N. J. Wilson, G. E. Flowers, and M. Haseloff
The Cryosphere, 8, 959–976, https://doi.org/10.5194/tc-8-959-2014, https://doi.org/10.5194/tc-8-959-2014, 2014
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The Cryosphere, 7, 229–240, https://doi.org/10.5194/tc-7-229-2013, https://doi.org/10.5194/tc-7-229-2013, 2013
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Understanding the orientation of ice grains is key for predicting ice flow. We explore the evolution of these orientations using a new efficient model. We present an exploration of the patterns produced under a range of temperatures and 2D deformations, including for the first time a universal regime diagram. We do this for deformations relevant to ice sheets but not studied in experiments. These results can be used to understand drilled ice cores and improve future modelling of ice sheets.
Franz Lutz, David J. Prior, Holly Still, M. Hamish Bowman, Bia Boucinhas, Lisa Craw, Sheng Fan, Daeyeong Kim, Robert Mulvaney, Rilee E. Thomas, and Christina L. Hulbe
The Cryosphere, 16, 3313–3329, https://doi.org/10.5194/tc-16-3313-2022, https://doi.org/10.5194/tc-16-3313-2022, 2022
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Ice crystal alignment in the sheared margins of fast-flowing polar ice is important as it may control the ice sheet flow rate, from land to the ocean. Sampling shear margins is difficult because of logistical and safety considerations. We show that crystal alignments in a glacier shear margin in Antarctica can be measured using sound waves. Results from a seismic experiment on the 50 m scale and from ultrasonic experiments on the decimetre scale match ice crystal measurements from an ice core.
Falk M. Oraschewski and Aslak Grinsted
The Cryosphere, 16, 2683–2700, https://doi.org/10.5194/tc-16-2683-2022, https://doi.org/10.5194/tc-16-2683-2022, 2022
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Old snow (denoted as firn) accumulates in the interior of ice sheets and gets densified into glacial ice. Typically, this densification is assumed to only depend on temperature and accumulation rate. However, it has been observed that stretching of the firn by horizontal flow also enhances this process. Here, we show how to include this effect in classical firn models. With the model we confirm that softening of the firn controls firn densification in areas with strong horizontal stretching.
M. Reza Ershadi, Reinhard Drews, Carlos Martín, Olaf Eisen, Catherine Ritz, Hugh Corr, Julia Christmann, Ole Zeising, Angelika Humbert, and Robert Mulvaney
The Cryosphere, 16, 1719–1739, https://doi.org/10.5194/tc-16-1719-2022, https://doi.org/10.5194/tc-16-1719-2022, 2022
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Radio waves transmitted through ice split up and inform us about the ice sheet interior and orientation of single ice crystals. This can be used to infer how ice flows and improve projections on how it will evolve in the future. Here we used an inverse approach and developed a new algorithm to infer ice properties from observed radar data. We applied this technique to the radar data obtained at two EPICA drilling sites, where ice cores were used to validate our results.
Yu Wang, Chen Zhao, Rupert Gladstone, Ben Galton-Fenzi, and Roland Warner
The Cryosphere, 16, 1221–1245, https://doi.org/10.5194/tc-16-1221-2022, https://doi.org/10.5194/tc-16-1221-2022, 2022
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The thermal structure of the Amery Ice Shelf and its spatial pattern are evaluated and analysed through temperature observations from six boreholes and numerical simulations. The simulations demonstrate significant ice warming downstream along the ice flow and a great variation of the thermal structure across the ice flow. We suggest that the thermal structure of the Amery Ice Shelf is unlikely to be affected by current climate changes on decadal timescales.
Reza Zeinali-Torbati, Ian D. Turnbull, Rocky S. Taylor, and Derek Mueller
The Cryosphere, 15, 5601–5621, https://doi.org/10.5194/tc-15-5601-2021, https://doi.org/10.5194/tc-15-5601-2021, 2021
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Using the reanalysis datasets and the Canadian Ice Island Drift, Deterioration and Detection database, a probabilistic model was developed to quantify ice island fracture probability under various atmospheric and oceanic conditions. The model identified water temperature as the most dominant variable behind ice island fracture events, while ocean currents played a minor role. The developed model offers a predictive capability and could be of particular interest to offshore and marine activities.
Rowan Romeyn, Alfred Hanssen, Bent Ole Ruud, and Tor Arne Johansen
The Cryosphere, 15, 2939–2955, https://doi.org/10.5194/tc-15-2939-2021, https://doi.org/10.5194/tc-15-2939-2021, 2021
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Air-coupled flexural waves are produced by the interaction between pressure waves in air and bending waves in a floating ice sheet. The frequency of these waves is related to the physical properties of the ice sheet, specifically its thickness and rigidity. We demonstrate the usefulness of air-coupled flexural waves for estimating ice thickness and give a theoretical description of the governing physics that highlights their similarity to related phenomena in other fields.
Pavel Talalay, Yazhou Li, Laurent Augustin, Gary D. Clow, Jialin Hong, Eric Lefebvre, Alexey Markov, Hideaki Motoyama, and Catherine Ritz
The Cryosphere, 14, 4021–4037, https://doi.org/10.5194/tc-14-4021-2020, https://doi.org/10.5194/tc-14-4021-2020, 2020
Maria Zeitz, Anders Levermann, and Ricarda Winkelmann
The Cryosphere, 14, 3537–3550, https://doi.org/10.5194/tc-14-3537-2020, https://doi.org/10.5194/tc-14-3537-2020, 2020
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The flow of ice drives mass losses in the large ice sheets. Sea-level rise projections rely on ice-sheet models, solving the physics of ice flow and melt. Unfortunately the parameters in the physics of flow are uncertain. Here we show, in an idealized setup, that these uncertainties can double flow-driven mass losses within the possible range of parameters. It is possible that this uncertainty carries over to realistic sea-level rise projections.
Mingdong Wei, Arttu Polojärvi, David M. Cole, and Malith Prasanna
The Cryosphere, 14, 2849–2867, https://doi.org/10.5194/tc-14-2849-2020, https://doi.org/10.5194/tc-14-2849-2020, 2020
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Laboratory-scale work on saline ice is usually limited to the use of dry isothermal specimens. Here we developed techniques for conducting floating-ice experiments. The mechanical behavior of floating-ice specimens under cyclic compression was compared with that of dry specimens. Moreover, both of them were successfully analyzed using a theoretical model. Results demonstrate the importance of the work on warm and floating ice, increasingly existing in the polar regions due to climate change.
Martin Rongen, Ryan Carlton Bay, and Summer Blot
The Cryosphere, 14, 2537–2543, https://doi.org/10.5194/tc-14-2537-2020, https://doi.org/10.5194/tc-14-2537-2020, 2020
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We report on the observation of a directional anisotropy in the intensity of backscattered light. The measurement was performed using a laser dust logger in the SPC14 drill hole at the geographic South Pole. We find the anisotropy axis to be compatible with the ice flow direction. It is discussed in comparison to a similar anisotropy observed by the IceCube Neutrino Observatory. In future, the measurement principle may provide a continuous record of crystal properties along entire drill holes.
Ernst-Jan N. Kuiper, Ilka Weikusat, Johannes H. P. de Bresser, Daniela Jansen, Gill M. Pennock, and Martyn R. Drury
The Cryosphere, 14, 2429–2448, https://doi.org/10.5194/tc-14-2429-2020, https://doi.org/10.5194/tc-14-2429-2020, 2020
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A composite flow law model applied to crystal size distributions from the NEEM deep ice core predicts that fine-grained layers in ice from the last Glacial period localize deformation as internal shear zones in the Greenland ice sheet deforming by grain-size-sensitive creep. This prediction is consistent with microstructures in Glacial age ice.
Ernst-Jan N. Kuiper, Johannes H. P. de Bresser, Martyn R. Drury, Jan Eichler, Gill M. Pennock, and Ilka Weikusat
The Cryosphere, 14, 2449–2467, https://doi.org/10.5194/tc-14-2449-2020, https://doi.org/10.5194/tc-14-2449-2020, 2020
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Fast ice flow occurs in deeper parts of polar ice sheets, driven by high stress and high temperatures. Above 262 K ice flow is further enhanced, probably by the formation of thin melt layers between ice crystals. A model applying an experimentally derived composite flow law, using temperature and grain size values from the deepest 540 m of the NEEM ice core, predicts that flow in fine-grained layers is enhanced by a factor of 10 compared to coarse-grained layers in the Greenland ice sheet.
Christopher C. Schneck, Tadros R. Ghobrial, and Mark R. Loewen
The Cryosphere, 13, 2751–2769, https://doi.org/10.5194/tc-13-2751-2019, https://doi.org/10.5194/tc-13-2751-2019, 2019
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Properties of suspended frazil ice and flocs in water of different salinities were measured in the lab using high-resolution images. It was found that freshwater frazil particles and flocs were larger than in saline water by ~13 % and 75 %, respectively. Both the growth rate of particles and the porosity of flocs decreased with salinity and ranged between 0.174 and 0.024 mm min−1 and 86 % and 75 % for freshwater and 35 ‰ saline water, respectively.
Ľubica Vetráková, Vilém Neděla, Jiří Runštuk, and Dominik Heger
The Cryosphere, 13, 2385–2405, https://doi.org/10.5194/tc-13-2385-2019, https://doi.org/10.5194/tc-13-2385-2019, 2019
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We froze salty solutions to examine where and how the brine is distributed within the ice by using an environmental scanning electron microscope. The structures are highly heterogeneous, consisting of almost pure ice intertwined with brine, which can form lamellae, veins, or pools on the surface. Considering various concentrations and methods for laboratory ice preparation, we determined how the freezing technique influences the microstructure of the brine on and in the ice.
Alexander Meyer, Dmitry Eliseev, Dirk Heinen, Peter Linder, Franziska Scholz, Lars Steffen Weinstock, Christopher Wiebusch, and Simon Zierke
The Cryosphere, 13, 1381–1394, https://doi.org/10.5194/tc-13-1381-2019, https://doi.org/10.5194/tc-13-1381-2019, 2019
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The acoustic damping in natural glaciers is a largely unexplored physical property that has relevance for various applications particularly for the exploration of glaciers with probes. We present measurements of the attenuation of sound in situ on the Italian glacier Langenferner. The tested frequency ranges from 2 to 35 kHz. The attenuation length ranges between 13 m for low frequencies and 5 m for high frequencies.
Carie M. Frantz, Bonnie Light, Samuel M. Farley, Shelly Carpenter, Ross Lieblappen, Zoe Courville, Mónica V. Orellana, and Karen Junge
The Cryosphere, 13, 775–793, https://doi.org/10.5194/tc-13-775-2019, https://doi.org/10.5194/tc-13-775-2019, 2019
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This paper provides a characterization of the physical and optical properties of "rotten" Arctic sea ice collected in two field seasons from off the coast of Utqiaġvik (formerly Barrow), Alaska. Rotten ice is physically and optically distinct when compared to ice from earlier in the melt season. It is marked by large connected pores, has lost most of its brine content, and scatters more light. This fragile, permeable ice type may become increasingly important in a warming Arctic.
Chao Qi, David J. Prior, Lisa Craw, Sheng Fan, Maria-Gema Llorens, Albert Griera, Marianne Negrini, Paul D. Bons, and David L. Goldsby
The Cryosphere, 13, 351–371, https://doi.org/10.5194/tc-13-351-2019, https://doi.org/10.5194/tc-13-351-2019, 2019
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Ice deformed in nature develops crystallographic preferred orientations, CPOs, which induce an anisotropy in ice viscosity. Shear experiments of ice revealed a transition in CPO with changing temperature/strain, which is due to the change of dominant CPO-formation mechanism: strain-induced grain boundary migration dominates at higher temperatures and lower strains, while lattice rotation dominates at other conditions. Understanding these mechanisms aids the interpretation of CPOs in natural ice.
Marianne Haseloff, Christian Schoof, and Olivier Gagliardini
The Cryosphere, 12, 2545–2568, https://doi.org/10.5194/tc-12-2545-2018, https://doi.org/10.5194/tc-12-2545-2018, 2018
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The widths of the Siple Coast ice streams evolve on decadal to centennial timescales. We investigate how the rate of thermally driven ice stream widening depends on heat dissipation in the ice stream margin and at the bed, and on the inflow of cold ice from the ice ridge. As determining the migration rate requires resolving heat transfer processes on very small scales, we derive a parametrization of the migration rate in terms of parameters that are available from large-scale model outputs.
Johanna Kerch, Anja Diez, Ilka Weikusat, and Olaf Eisen
The Cryosphere, 12, 1715–1734, https://doi.org/10.5194/tc-12-1715-2018, https://doi.org/10.5194/tc-12-1715-2018, 2018
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We investigate the effect of crystal anisotropy on seismic velocities in glacier ice by calculating seismic phase velocities using the exact c axis angles to describe the crystal orientations in ice-core samples for an alpine and a polar ice core. Our results provide uncertainty estimates for earlier established approximative calculations. Additionally, our findings highlight the variation in seismic velocity at non-vertical incidence as a function of the horizontal azimuth of the seismic plane.
Johannes Feldmann and Anders Levermann
The Cryosphere, 11, 1913–1932, https://doi.org/10.5194/tc-11-1913-2017, https://doi.org/10.5194/tc-11-1913-2017, 2017
Adam J. Campbell, Betzalel Massarano, Edwin D. Waddington, and Stephen G. Warren
The Cryosphere, 11, 1141–1148, https://doi.org/10.5194/tc-11-1141-2017, https://doi.org/10.5194/tc-11-1141-2017, 2017
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How could plant life, that needs light to survive, live on a planet covered with ice? Such a situation is thought to have existed during what are called the Snowball Earth events over 600 million years ago. Here we find that
ice shadows, regions where ice has difficulty flowing into, may have a played a role in that survival of early plant life.
Matthew J. Vaughan, Kasper van Wijk, David J. Prior, and M. Hamish Bowman
The Cryosphere, 10, 2821–2829, https://doi.org/10.5194/tc-10-2821-2016, https://doi.org/10.5194/tc-10-2821-2016, 2016
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The physical properties of ice are of interest in the study of the dynamics of sea ice, glaciers, and ice sheets. We used resonant ultrasound spectroscopy to estimate the effects of temperature on the elastic and anelastic characteristics of polycrystalline ice, which control the propagation of sound waves. This information helps calibrate seismic data, in order to determine regional-scale ice properties, improving our ability to predict ice sheet behaviour in response to climate change.
J. Feldmann and A. Levermann
The Cryosphere, 9, 631–645, https://doi.org/10.5194/tc-9-631-2015, https://doi.org/10.5194/tc-9-631-2015, 2015
D. Besson and I. Kravchenko
The Cryosphere, 7, 855–866, https://doi.org/10.5194/tc-7-855-2013, https://doi.org/10.5194/tc-7-855-2013, 2013
D. N. Goldberg and O. V. Sergienko
The Cryosphere, 5, 315–327, https://doi.org/10.5194/tc-5-315-2011, https://doi.org/10.5194/tc-5-315-2011, 2011
H. Hausmann and M. Behm
The Cryosphere, 5, 329–340, https://doi.org/10.5194/tc-5-329-2011, https://doi.org/10.5194/tc-5-329-2011, 2011
Cited articles
Aschwanden, A., Bueler, E., Khroulev, C., and Blatter, H.: An enthalpy formulation for glaciers and ice sheets, J. Glaciol., 58, 441–457, 2012.
Bercovici, D., Ricard, Y., and Schubert, G.: A two-phase model for compaction and damage. 1. General Theory, J. Geophys. Res., 106, 8887–8906, 2001.
Blatter, H. and Greve, R.: Comparison and verification of enthalpy schemes for polythermal glaciers and ice sheets with a one-dimensional model, Polar Sci., 9, 197–207, 2015.
Brinkerhoff, D. J. and Johnson, J. V.: Data assimilation and prognostic whole ice sheet modelling with the variationally derived, higher order, open source, and fully parallel ice sheet model VarGlaS, The Cryosphere, 7, 1161–1184, https://doi.org/10.5194/tc-7-1161-2013, 2013.
Fountain, A. G. and Walder, J. S.: Water flow through temperate glaciers, Rev. Geophys., 36, 299–328, 1998.
Fowler, A. C.: On the transport of moisture in polythermal glaciers, Geophys. Astrophys. Fluid, 28, 99–140, 1984.
Fowler, A. C. and Larson, D. A.: On the flow of polythermal glaciers I. Model and preliminary analysis, Proc. R. Soc. Lon. Ser. A, 363, 217–242, 1978.
Greve, R.: A continuum-mechanical formulation for shallow polythermal ice sheets, Philos. Tr. R. Soc. A, 355, 921–974, 1997.
Greve, R. and Blatter, H.: Dynamics of Ice Sheets and Glaciers, Springer, Heidelberg, 2009.
Hutter, K.: A mathematical model of polythermal glaciers and ice sheets, Geophys. Astro. Fluid, 21, 201–224, 1982.
Kleiner, T., Rückamp, M., Bondzio, J. H., and Humbert, A.: Enthalpy benchmark experiments for numerical ice sheet models, The Cryosphere, 9, 217-228, https://doi.org/10.5194/tc-9-217-2015, 2015.
Lliboutry, L.: Permeability, brine content and temperature of temperate ice, J. Glaciol., 10, 15–29, 1971.
Lliboutry, L.: Temperate ice permeability, stability of water veins and percolation of internal meltwater, J. Glaciol., 42, 201–211, 1996.
McKenzie, D.: The generation and compaction of partially molten rock, J. Petrol., 25, 713–765, 1984.
Nye, J. and Mae, S.: The effect of non-hydrostatic stress on intergranular water veins and lenses in ice, J. Glaciol., 11, 81–101, 1972.
Nye, J. F.: The Flow law of ice from measurements in glacier tunnels, laboratory experiments and the Jungfraufirn borehole experiment, Proc. R. Soc. Lon. Ser. A, 219, 477–489, 1953.
Nye, J. F.: Water flow in Glaciers: Jökulhlaups, Tunnels and Veins, J. Glaciol., 17, 181–207, 1976.
Nye, J. F. and Frank, F. C.: Hydrology of the Intergranular veins in a temperate glacier, IASH, 95, 157–161, 1973.
Schoof, C. and Hewitt, I. J.: Ice-Sheet Dynamics, Annu. Rev. Fluid Mech., 45, 217–239, 2013.
Schoof, C. and Hewitt, I. J.: A model for polythermal ice incorporating gravity-driven moisture transport, J. Fluid Mech., 797, 504–535, https://doi.org/10.1017/jfm.2016.251, 2016.
Seroussi, H., Morlighem, M., Rignot, E., Khazendar, A., Larour, E., and Mouginot, J.: Dependence of century-scale projections of the Greenland ice sheet on its thermal regime, J. Glaciol., 59, 1024–1034, https://doi.org/10.3189/2013JoG13J054, 2013.
Wettlaufer, J. S. and Worster, M. G.: Premelting Dynamics, Annu. Rev. Fluid Mech., 38, 427–452, 2006.
Wilson, N. J. and Flowers, G. E.: Environmental controls on the thermal structure of alpine glaciers, The Cryosphere, 7, 167–182, https://doi.org/10.5194/tc-7-167-2013, 2013.
Short summary
Many glaciers contain ice both below and at the melting temperature. Predicting the evolution of temperature and water content in such ice masses is important because they exert a strong control on the flow of the ice. We present two new models to calculate these quantities, demonstrate a number of example numerical calculations, and compare the results with existing methods. The novelty of the new methods is the inclusion of gravity-driven water transport within the ice.
Many glaciers contain ice both below and at the melting temperature. Predicting the evolution...
