Articles | Volume 10, issue 4
https://doi.org/10.5194/tc-10-1799-2016
© Author(s) 2016. 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-10-1799-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
18 Aug 2016
Research article |
| 18 Aug 2016
A simple equation for the melt elevation feedback of ice sheets
Anders Levermann
CORRESPONDING AUTHOR
Potsdam Institute for Climate Impact Research, Potsdam, Germany
LDEO, Columbia University, NY, USA
Institute of Physics, Potsdam University, Potsdam, Germany
Ricarda Winkelmann
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Institute of Physics, Potsdam University, Potsdam, Germany
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48 citations as recorded by crossref.
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- Emergence of cascading dynamics in interacting tipping elements of ecology and climate A. Klose et al. 10.1098/rsos.200599
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- The hysteresis of the Antarctic Ice Sheet J. Garbe et al. 10.1038/s41586-020-2727-5
- A simple stress-based cliff-calving law T. Schlemm & A. Levermann 10.5194/tc-13-2475-2019
- AMOC Stabilization Under the Interaction With Tipping Polar Ice Sheets S. Sinet et al. 10.1029/2022GL100305
- Comparison and Synthesis of Sea‐Level and Deep‐Sea Temperature Variations Over the Past 40 Million Years E. Rohling et al. 10.1029/2022RG000775
- Rate-induced tipping cascades arising from interactions between the Greenland Ice Sheet and the Atlantic Meridional Overturning Circulation A. Klose et al. 10.5194/esd-15-635-2024
- Long‐term projections of sea‐level rise from ice sheets N. Golledge 10.1002/wcc.634
- Regime Shifts in Glacier and Ice Sheet Response to Climate Change: Examples From the Northern Hemisphere S. Marshall 10.3389/fclim.2021.702585
- Recent progress in understanding climate thresholds P. Good et al. 10.1177/0309133317751843
- A framework for automated supraglacial lake detection and depth retrieval in ICESat-2 photon data across the Greenland and Antarctic ice sheets P. Arndt & H. Fricker 10.5194/tc-18-5173-2024
- Global warming due to loss of large ice masses and Arctic summer sea ice N. Wunderling et al. 10.1038/s41467-020-18934-3
- Millennial-scale variability of the Antarctic ice sheet during the early Miocene N. Sullivan et al. 10.1073/pnas.2304152120
- Uncertainties too large to predict tipping times of major Earth system components from historical data M. Ben-Yami et al. 10.1126/sciadv.adl4841
- Mass loss of the Antarctic ice sheet until the year 3000 under a sustained late-21st-century climate C. Chambers et al. 10.1017/jog.2021.124
- Mean-field theory for double-well systems on degree-heterogeneous networks P. Kundu et al. 10.1098/rspa.2022.0350
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- Glacial erosion on a snowball Earth: testing for bias in flux balance, geographic setting, and tectonic regime P. Hoffman 10.1139/cjes-2022-0004
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- Projections of precipitation and temperatures in Greenland and the impact of spatially uniform anomalies on the evolution of the ice sheet N. Bochow et al. 10.5194/tc-18-5825-2024
- Constraining safe and unsafe overshoots in saddle-node bifurcations E. Enache et al. 10.1063/5.0197940
- A low climate threshold for south Greenland Ice Sheet demise during the Late Pleistocene N. Irvalı et al. 10.1073/pnas.1911902116
- Modeling Northern Hemispheric Ice Sheet Dynamics, Sea Level Change, and Solid Earth Deformation Through the Last Glacial Cycle H. Han et al. 10.1029/2020JF006040
- Sea-level response to melting of Antarctic ice shelves on multi-centennial timescales with the fast Elementary Thermomechanical Ice Sheet model (f.ETISh v1.0) F. Pattyn 10.5194/tc-11-1851-2017
- Projecting Antarctica's contribution to future sea level rise from basal ice shelf melt using linear response functions of 16 ice sheet models (LARMIP-2) A. Levermann et al. 10.5194/esd-11-35-2020
- Dynamics of tipping cascades on complex networks J. Krönke et al. 10.1103/PhysRevE.101.042311
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- Global warming overshoots increase risks of climate tipping cascades in a network model N. Wunderling et al. 10.1038/s41558-022-01545-9
- Monitoring the Multiple Stages of Climate Tipping Systems from Space: Do the GCOS Essential Climate Variables Meet the Needs? S. Loriani et al. 10.1007/s10712-024-09866-4
- Monsoon hysteresis reveals atmospheric memory A. Katzenberger & A. Levermann 10.1073/pnas.2418093122
- What do we mean, ‘tipping cascade’? A. Klose et al. 10.1088/1748-9326/ac3955
- Firn on ice sheets C. Amory et al. 10.1038/s43017-023-00507-9
- Interacting tipping elements increase risk of climate domino effects under global warming N. Wunderling et al. 10.5194/esd-12-601-2021
- Anticipation-induced social tipping: can the environment be stabilised by social dynamics? P. Müller et al. 10.1140/epjs/s11734-021-00011-5
- Anticipating critical transitions in multidimensional systems driven by time- and state-dependent noise A. Morr et al. 10.1103/PhysRevResearch.6.033251
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- Role of Snowfall Versus Air Temperatures for Greenland Ice Sheet Melt‐Albedo Feedbacks J. Ryan et al. 10.1029/2023EA003158
- Present‐Day Greenland Ice Sheet Climate and Surface Mass Balance in CESM2 L. van Kampenhout et al. 10.1029/2019JF005318
- Dynamic regimes of the Greenland Ice Sheet emerging from interacting melt–elevation and glacial isostatic adjustment feedbacks M. Zeitz et al. 10.5194/esd-13-1077-2022
48 citations as recorded by crossref.
- Modelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package N. Wunderling et al. 10.1140/epjs/s11734-021-00155-4
- Emergence of cascading dynamics in interacting tipping elements of ecology and climate A. Klose et al. 10.1098/rsos.200599
- Numerical reconstructions of the flow and basal conditions of the Rhine glacier, European Central Alps, at the Last Glacial Maximum D. Cohen et al. 10.5194/tc-12-2515-2018
- Overshooting the critical threshold for the Greenland ice sheet N. Bochow et al. 10.1038/s41586-023-06503-9
- The hysteresis of the Antarctic Ice Sheet J. Garbe et al. 10.1038/s41586-020-2727-5
- A simple stress-based cliff-calving law T. Schlemm & A. Levermann 10.5194/tc-13-2475-2019
- AMOC Stabilization Under the Interaction With Tipping Polar Ice Sheets S. Sinet et al. 10.1029/2022GL100305
- Comparison and Synthesis of Sea‐Level and Deep‐Sea Temperature Variations Over the Past 40 Million Years E. Rohling et al. 10.1029/2022RG000775
- Rate-induced tipping cascades arising from interactions between the Greenland Ice Sheet and the Atlantic Meridional Overturning Circulation A. Klose et al. 10.5194/esd-15-635-2024
- Long‐term projections of sea‐level rise from ice sheets N. Golledge 10.1002/wcc.634
- Regime Shifts in Glacier and Ice Sheet Response to Climate Change: Examples From the Northern Hemisphere S. Marshall 10.3389/fclim.2021.702585
- Recent progress in understanding climate thresholds P. Good et al. 10.1177/0309133317751843
- A framework for automated supraglacial lake detection and depth retrieval in ICESat-2 photon data across the Greenland and Antarctic ice sheets P. Arndt & H. Fricker 10.5194/tc-18-5173-2024
- Global warming due to loss of large ice masses and Arctic summer sea ice N. Wunderling et al. 10.1038/s41467-020-18934-3
- Millennial-scale variability of the Antarctic ice sheet during the early Miocene N. Sullivan et al. 10.1073/pnas.2304152120
- Uncertainties too large to predict tipping times of major Earth system components from historical data M. Ben-Yami et al. 10.1126/sciadv.adl4841
- Mass loss of the Antarctic ice sheet until the year 3000 under a sustained late-21st-century climate C. Chambers et al. 10.1017/jog.2021.124
- Mean-field theory for double-well systems on degree-heterogeneous networks P. Kundu et al. 10.1098/rspa.2022.0350
- Critical slowing down suggests that the western Greenland Ice Sheet is close to a tipping point N. Boers & M. Rypdal 10.1073/pnas.2024192118
- The evolution of future Antarctic surface melt using PISM-dEBM-simple J. Garbe et al. 10.5194/tc-17-4571-2023
- A simple parametrization of mélange buttressing for calving glaciers T. Schlemm & A. Levermann 10.5194/tc-15-531-2021
- Theoretical and paleoclimatic evidence for abrupt transitions in the Earth system N. Boers et al. 10.1088/1748-9326/ac8944
- Hysteresis and orbital pacing of the early Cenozoic Antarctic ice sheet J. Van Breedam et al. 10.5194/cp-19-2551-2023
- Sea Level Rise in Europe: Observations and projections A. Melet et al. 10.5194/sp-3-slre1-4-2024
- Towards the incorporation of tipping elements in global climate risk management: probability and potential impacts of passing a threshold Y. Iseri et al. 10.1007/s11625-018-0536-7
- Glacial erosion on a snowball Earth: testing for bias in flux balance, geographic setting, and tectonic regime P. Hoffman 10.1139/cjes-2022-0004
- Disentangling the drivers of future Antarctic ice loss with a historically calibrated ice-sheet model V. Coulon et al. 10.5194/tc-18-653-2024
- The long-term sea-level commitment from Antarctica A. Klose et al. 10.5194/tc-18-4463-2024
- Projections of precipitation and temperatures in Greenland and the impact of spatially uniform anomalies on the evolution of the ice sheet N. Bochow et al. 10.5194/tc-18-5825-2024
- Constraining safe and unsafe overshoots in saddle-node bifurcations E. Enache et al. 10.1063/5.0197940
- A low climate threshold for south Greenland Ice Sheet demise during the Late Pleistocene N. Irvalı et al. 10.1073/pnas.1911902116
- Modeling Northern Hemispheric Ice Sheet Dynamics, Sea Level Change, and Solid Earth Deformation Through the Last Glacial Cycle H. Han et al. 10.1029/2020JF006040
- Sea-level response to melting of Antarctic ice shelves on multi-centennial timescales with the fast Elementary Thermomechanical Ice Sheet model (f.ETISh v1.0) F. Pattyn 10.5194/tc-11-1851-2017
- Projecting Antarctica's contribution to future sea level rise from basal ice shelf melt using linear response functions of 16 ice sheet models (LARMIP-2) A. Levermann et al. 10.5194/esd-11-35-2020
- Dynamics of tipping cascades on complex networks J. Krönke et al. 10.1103/PhysRevE.101.042311
- No general stability conditions for marine ice-sheet grounding lines in the presence of feedbacks O. Sergienko 10.1038/s41467-022-29892-3
- Global warming overshoots increase risks of climate tipping cascades in a network model N. Wunderling et al. 10.1038/s41558-022-01545-9
- Monitoring the Multiple Stages of Climate Tipping Systems from Space: Do the GCOS Essential Climate Variables Meet the Needs? S. Loriani et al. 10.1007/s10712-024-09866-4
- Monsoon hysteresis reveals atmospheric memory A. Katzenberger & A. Levermann 10.1073/pnas.2418093122
- What do we mean, ‘tipping cascade’? A. Klose et al. 10.1088/1748-9326/ac3955
- Firn on ice sheets C. Amory et al. 10.1038/s43017-023-00507-9
- Interacting tipping elements increase risk of climate domino effects under global warming N. Wunderling et al. 10.5194/esd-12-601-2021
- Anticipation-induced social tipping: can the environment be stabilised by social dynamics? P. Müller et al. 10.1140/epjs/s11734-021-00011-5
- Anticipating critical transitions in multidimensional systems driven by time- and state-dependent noise A. Morr et al. 10.1103/PhysRevResearch.6.033251
- Basin stability and limit cycles in a conceptual model for climate tipping cascades N. Wunderling et al. 10.1088/1367-2630/abc98a
- Role of Snowfall Versus Air Temperatures for Greenland Ice Sheet Melt‐Albedo Feedbacks J. Ryan et al. 10.1029/2023EA003158
- Present‐Day Greenland Ice Sheet Climate and Surface Mass Balance in CESM2 L. van Kampenhout et al. 10.1029/2019JF005318
- Dynamic regimes of the Greenland Ice Sheet emerging from interacting melt–elevation and glacial isostatic adjustment feedbacks M. Zeitz et al. 10.5194/esd-13-1077-2022
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Short summary
In recent decades, the Greenland Ice Sheet has been losing mass and has thereby contributed to global sea-level rise. Here we derive the basic equations for the melt elevation feedback that can lead to self-amplifying melt of the Greenland Ice Sheet and ice sheets in general. The theory unifies the results of complex models when the feedback dominates the dynamics and it allows us to estimate the melt time of ice sheets from data in cases where ice dynamic loss can be neglected.
In recent decades, the Greenland Ice Sheet has been losing mass and has thereby contributed to...
