TY - JOUR A1 - Levermann, Anders A1 - Feldmann, Johannes T1 - Scaling of instability timescales of Antarctic outlet glaciers based on one-dimensional similitude analysis JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - Recent observations and ice-dynamic modeling suggest that a marine ice-sheet instability (MISI) might have been triggered in West Antarctica. The corresponding outlet glaciers, Pine Island Glacier (PIG) and Thwaites Glacier (TG), showed significant retreat during at least the last 2 decades. While other regions in Antarctica have the topographic predisposition for the same kind of instability, it is so far unclear how fast these instabilities would unfold if they were initiated. Here we employ the concept of similitude to estimate the characteristic timescales of several potentially MISI-prone outlet glaciers around the Antarctic coast. Our results suggest that TG and PIG have the fastest response time of all investigated outlets, with TG responding about 1.25 to 2 times as fast as PIG, while other outlets around Antarctica would be up to 10 times slower if destabilized. These results have to be viewed in light of the strong assumptions made in their derivation. These include the absence of ice-shelf buttressing, the one-dimensionality of the approach and the uncertainty of the available data. We argue however that the current topographic situation and the physical conditions of the MISI-prone outlet glaciers carry the information of their respective timescale and that this information can be partially extracted through a similitude analysis. Y1 - 2019 U6 - https://doi.org/10.5194/tc-13-1621-2019 SN - 1994-0416 SN - 1994-0424 VL - 13 IS - 6 SP - 1621 EP - 1633 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Mengel, Matthias A1 - Feldmann, Johannes A1 - Levermann, Anders T1 - Linear sea-level response to abrupt ocean warming of major West Antarctic ice basin JF - Nature climate change N2 - Antarctica’s contribution to global sea-level rise has recently been increasing1. Whether its ice discharge will become unstable and decouple from anthropogenic forcing2,3,4 or increase linearly with the warming of the surrounding ocean is of fundamental importance5. Under unabated greenhouse-gas emissions, ocean models indicate an abrupt intrusion of warm circumpolar deep water into the cavity below West Antarctica’s Filchner–Ronne ice shelf within the next two centuries6,7. The ice basin’s retrograde bed slope would allow for an unstable ice-sheet retreat8, but the buttressing of the large ice shelf and the narrow glacier troughs tend to inhibit such instability9,10,11. It is unclear whether future ice loss will be dominated by ice instability or anthropogenic forcing. Here we show in regional and continental-scale ice-sheet simulations, which are capable of resolving unstable grounding-line retreat, that the sea-level response of the Filchner–Ronne ice basin is not dominated by ice instability and follows the strength of the forcing quasi-linearly. We find that the ice loss reduces after each pulse of projected warm water intrusion. The long-term sea-level contribution is approximately proportional to the total shelf-ice melt. Although the local instabilities might dominate the ice loss for weak oceanic warming12, we find that the upper limit of ice discharge from the region is determined by the forcing and not by the marine ice-sheet instability. Y1 - 2016 U6 - https://doi.org/10.1038/NCLIMATE2808 SN - 1758-678X SN - 1758-6798 VL - 6 SP - 71 EP - + PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Feldmann, Johannes A1 - Levermann, Anders T1 - From cyclic ice streaming to Heinrich-like events: the grow-and-surge instability in the Parallel Ice Sheet Model JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - Here we report on a cyclic, physical ice-discharge instability in the Parallel Ice Sheet Model, simulating the flow of a three-dimensional, inherently buttressed ice-sheet-shelf system which periodically surges on a millennial timescale. The thermomechanically coupled model on 1 km horizontal resolution includes an enthalpy-based formulation of the thermodynamics, a nonlinear stress-balance-based sliding law and a very simple subglacial hydrology. The simulated unforced surging is characterized by rapid ice streaming through a bed trough, resulting in abrupt discharge of ice across the grounding line which is eventually calved into the ocean. We visualize the central feedbacks that dominate the subsequent phases of ice buildup, surge and stabilization which emerge from the interaction between ice dynamics, thermodynamics and the subglacial till layer. Results from the variation of surface mass balance and basal roughness suggest that ice sheets of medium thickness may be more susceptible to surging than relatively thin or thick ones for which the surge feedback loop is damped. We also investigate the influence of different basal sliding laws (ranging from purely plastic to nonlinear to linear) on possible surging. The presented mechanisms underlying our simulations of self-maintained, periodic ice growth and destabilization may play a role in large-scale ice-sheet surging, such as the surging of the Laurentide Ice Sheet, which is associated with Heinrich events, and ice-stream shutdown and reactivation, such as observed in the Siple Coast region of West Antarctica. Y1 - 2017 U6 - https://doi.org/10.5194/tc-11-1913-2017 SN - 1994-0416 SN - 1994-0424 VL - 11 SP - 1913 EP - 1932 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Feldmann, Johannes A1 - Levermann, Anders A1 - Mengel, Matthias T1 - Stabilizing the West Antarctic Ice Sheet by surface mass deposition JF - Science Advances N2 - There is evidence that a self-sustaining ice discharge from the West Antarctic Ice Sheet (WAIS) has started, potentially leading to its disintegration. The associated sea level rise of more than 3m would pose a serious challenge to highly populated areas including metropolises such as Calcutta, Shanghai, New York City, and Tokyo. Here, we show that the WAIS may be stabilized through mass deposition in coastal regions around Pine Island and Thwaites glaciers. In our numerical simulations, a minimum of 7400 Gt of additional snowfall stabilizes the flow if applied over a short period of 10 years onto the region (-2 mm year(-1) sea level equivalent). Mass deposition at a lower rate increases the intervention time and the required total amount of snow. We find that the precise conditions of such an operation are crucial, and potential benefits need to be weighed against environmental hazards, future risks, and enormous technical challenges. Y1 - 2019 U6 - https://doi.org/10.1126/sciadv.aaw4132 SN - 2375-2548 VL - 5 IS - 7 PB - American Assoc. for the Advancement of Science CY - Washington ER - TY - JOUR A1 - Feldmann, Johannes A1 - Levermann, Anders T1 - Interaction of marine ice-sheet instabilities in two drainage basins: simple scaling of geometry and transition time JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - The initiation of a marine ice-sheet instability (MISI) is generally discussed from the ocean side of the ice sheet. It has been shown that the reduction in ice-shelf buttressing and softening of the coastal ice can destabilize a marine ice sheet if the bedrock is sloping upward towards the ocean. Using a conceptional flow-line geometry, we investigate the possibility of whether a MISI can be triggered from the direction of the ice divide as opposed to coastal forcing and explore the interaction between connected basins. We find that the initiation of a MISI in one basin can induce a destabilization in the other. The underlying mechanism of basin interaction is based on dynamic thinning and a consecutive motion of the ice divide which induces a thinning in the adjacent basin and a successive initiation of the instability. Our simplified and symmetric topographic setup allows scaling both the geometry and the transition time between both instabilities. We find that the ice profile follows a universal shape that is scaled with the horizontal extent of the ice sheet and that the same exponent of 1/2 applies for the scaling relation between central surface elevation and horizontal extent as in the pure shallow ice approximation (Vialov profile). Altering the central bed elevation, we find that the extent of grounding-line retreat in one basin determines the degree of interaction with the other. Different scenarios of basin interaction are discussed based on our modeling results as well as on a conceptual flux-balance analysis. We conclude that for the three-dimensional case, the possibility of drainage basin interaction on timescales on the order of 1 kyr or larger cannot be excluded and hence needs further investigation. Y1 - 2015 U6 - https://doi.org/10.5194/tc-9-631-2015 SN - 1994-0416 SN - 1994-0424 VL - 9 IS - 2 SP - 631 EP - 645 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Feldmann, Johannes A1 - Levermann, Anders T1 - Collapse of the West Antarctic Ice Sheet after local destabilization of the Amundsen Basin JF - Proceedings of the National Academy of Sciences of the United States of America N2 - The future evolution of the Antarctic Ice Sheet represents the largest uncertainty in sea-level projections of this and upcoming centuries. Recently, satellite observations and high-resolution simulations have suggested the initiation of an ice-sheet instability in the Amundsen Sea sector of West Antarctica, caused by the last decades' enhanced basal ice-shelf melting. Whether this localized destabilization will yield a full discharge of marine ice from West Antarctica, associated with a global sea-level rise of more than 3 m, or whether the ice loss is limited by ice dynamics and topographic features, is unclear. Here we show that in the Parallel Ice Sheet Model, a local destabilization causes a complete disintegration of the marine ice in West Antarctica. In our simulations, at 5-km horizontal resolution, the region disequilibrates after 60 y of currently observed melt rates. Thereafter, the marine ice-sheet instability fully unfolds and is not halted by topographic features. In fact, the ice loss in Amundsen Sea sector shifts the catchment's ice divide toward the Filchner-Ronne and Ross ice shelves, which initiates grounding-line retreat there. Our simulations suggest that if a destabilization of Amundsen Sea sector has indeed been initiated, Antarctica will irrevocably contribute at least 3 m to global sea-level rise during the coming centuries to millennia. KW - West Antarctic Ice Sheet KW - sea-level rise KW - tipping point KW - instability KW - marine ice-sheet instability Y1 - 2015 U6 - https://doi.org/10.1073/pnas.1512482112 SN - 0027-8424 VL - 112 IS - 46 SP - 14191 EP - 14196 PB - National Acad. of Sciences CY - Washington ER - TY - GEN A1 - Feldmann, Johannes A1 - Levermann, Anders T1 - Similitude of ice dynamics against scaling of geometry and physical parameters T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - The concept of similitude is commonly employed in the fields of fluid dynamics and engineering but rarely used in cryospheric research. Here we apply this method to the problem of ice flow to examine the dynamic similitude of isothermal ice sheets in shallow-shelf approximation against the scaling of their geometry and physical parameters. Carrying out a dimensional analysis of the stress balance we obtain dimensionless numbers that characterize the flow. Requiring that these numbers remain the same under scaling we obtain conditions that relate the geometric scaling factors, the parameters for the ice softness, surface mass balance and basal friction as well as the ice-sheet intrinsic response time to each other. We demonstrate that these scaling laws are the same for both the (two-dimensional) flow-line case and the three-dimensional case. The theoretically predicted ice-sheet scaling behavior agrees with results from numerical simulations that we conduct in flow-line and three-dimensional conceptual setups. We further investigate analytically the implications of geometric scaling of ice sheets for their response time. With this study we provide a framework which, under several assumptions, allows for a fundamental comparison of the ice-dynamic behavior across different scales. It proves to be useful in the design of conceptual numerical model setups and could also be helpful for designing laboratory glacier experiments. The concept might also be applied to real-world systems, e.g., to examine the response times of glaciers, ice streams or ice sheets to climatic perturbations. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 564 KW - grounding line motion KW - full-stokes model KW - West Antarctica KW - sheet models KW - Pine Island KW - stream-B KW - shelf KW - flow KW - sensitivity KW - collapse Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-412441 SN - 1866-8372 IS - 564 SP - 1753 EP - 1769 ER - TY - GEN A1 - Feldmann, Johannes A1 - Levermann, Anders T1 - From cyclic ice streaming to Heinrich-like events BT - the grow-and-surge instability in the Parallel Ice Sheet Model T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - Here we report on a cyclic, physical ice-discharge instability in the Parallel Ice Sheet Model, simulating the flow of a three-dimensional, inherently buttressed ice-sheet-shelf system which periodically surges on a millennial timescale. The thermomechanically coupled model on 1 km horizontal resolution includes an enthalpy-based formulation of the thermodynamics, a nonlinear stress-balance-based sliding law and a very simple subglacial hydrology. The simulated unforced surging is characterized by rapid ice streaming through a bed trough, resulting in abrupt discharge of ice across the grounding line which is eventually calved into the ocean. We visualize the central feedbacks that dominate the subsequent phases of ice buildup, surge and stabilization which emerge from the interaction between ice dynamics, thermodynamics and the subglacial till layer. Results from the variation of surface mass balance and basal roughness suggest that ice sheets of medium thickness may be more susceptible to surging than relatively thin or thick ones for which the surge feedback loop is damped. We also investigate the influence of different basal sliding laws (ranging from purely plastic to nonlinear to linear) on possible surging. The presented mechanisms underlying our simulations of self-maintained, periodic ice growth and destabilization may play a role in large-scale ice-sheet surging, such as the surging of the Laurentide Ice Sheet, which is associated with Heinrich events, and ice-stream shutdown and reactivation, such as observed in the Siple Coast region of West Antarctica. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 652 KW - grounding-line migration KW - last glacial period KW - West Antarctica KW - North Atlantic KW - numerical simulations KW - iceberg discharges KW - creep stability KW - basal mechanics KW - climate KW - ocean Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-418777 SN - 1866-8372 IS - 652 ER - TY - GEN A1 - Feldmann, Johannes A1 - Levermann, Anders T1 - Interaction of marine ice-sheet instabilities in two drainage basins BT - simple scaling of geometry and transition time T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Universität N2 - The initiation of a marine ice-sheet instability (MISI) is generally discussed from the ocean side of the ice sheet. It has been shown that the reduction in ice-shelf buttressing and softening of the coastal ice can destabilize a marine ice sheet if the bedrock is sloping upward towards the ocean. Using a conceptional flow-line geometry, we investigate the possibility of whether a MISI can be triggered from the direction of the ice divide as opposed to coastal forcing and explore the interaction between connected basins. We find that the initiation of a MISI in one basin can induce a destabilization in the other. The underlying mechanism of basin interaction is based on dynamic thinning and a consecutive motion of the ice divide which induces a thinning in the adjacent basin and a successive initiation of the instability. Our simplified and symmetric topographic setup allows scaling both the geometry and the transition time between both instabilities. We find that the ice profile follows a universal shape that is scaled with the horizontal extent of the ice sheet and that the same exponent of 1/2 applies for the scaling relation between central surface elevation and horizontal extent as in the pure shallow ice approximation (Vialov profile). Altering the central bed elevation, we find that the extent of grounding-line retreat in one basin determines the degree of interaction with the other. Different scenarios of basin interaction are discussed based on our modeling results as well as on a conceptual flux-balance analysis. We conclude that for the three-dimensional case, the possibility of drainage basin interaction on timescales on the order of 1 kyr or larger cannot be excluded and hence needs further investigation. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 511 KW - Pine Island Glacier KW - model PISM-PIK KW - West Antarctica KW - grounding-line KW - Thwaites Glacier KW - divide position KW - part 1 KW - stability KW - shelf KW - accumulation Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-408903 SN - 1866-8372 IS - 511 ER - TY - JOUR A1 - Feldmann, Johannes A1 - Levermann, Anders T1 - Similitude of ice dynamics against scaling of geometry and physical parameters JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - The concept of similitude is commonly employed in the fields of fluid dynamics and engineering but rarely used in cryospheric research. Here we apply this method to the problem of ice flow to examine the dynamic similitude of isothermal ice sheets in shallow-shelf approximation against the scaling of their geometry and physical parameters. Carrying out a dimensional analysis of the stress balance we obtain dimensionless numbers that characterize the flow. Requiring that these numbers remain the same under scaling we obtain conditions that relate the geometric scaling factors, the parameters for the ice softness, surface mass balance and basal friction as well as the ice-sheet intrinsic response time to each other. We demonstrate that these scaling laws are the same for both the (two-dimensional) flow-line case and the three-dimensional case. The theoretically predicted ice-sheet scaling behavior agrees with results from numerical simulations that we conduct in flow-line and three-dimensional conceptual setups. We further investigate analytically the implications of geometric scaling of ice sheets for their response time. With this study we provide a framework which, under several assumptions, allows for a fundamental comparison of the ice-dynamic behavior across different scales. It proves to be useful in the design of conceptual numerical model setups and could also be helpful for designing laboratory glacier experiments. The concept might also be applied to real-world systems, e.g., to examine the response times of glaciers, ice streams or ice sheets to climatic perturbations. Y1 - 2016 U6 - https://doi.org/10.5194/tc-10-1753-2016 SN - 1994-0416 SN - 1994-0424 VL - 10 SP - 1753 EP - 1769 PB - Copernicus CY - Göttingen ER -