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Linear response functions to project contributions to future sea level

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Abstract

We propose linear response functions to separately estimate the sea-level contributions of thermal expansion and solid ice discharge from Greenland and Antarctica. The response function formalism introduces a time-dependence which allows for future rates of sea-level rise to be influenced by past climate variations. We find that this time-dependence is of the same functional type, R(t) ∼ t α, for each of the three subsystems considered here. The validity of the approach is assessed by comparing the sea-level estimates obtained via the response functions to projections from comprehensive models. The pure vertical diffusion case in one dimension, corresponding to α =  −0.5, is a valid approximation for thermal expansion within the ocean up to the middle of the twenty first century for all Representative Concentration Pathways. The approximation is significantly improved for α =  − 0.7. For the solid ice discharge from Greenland we find an optimal value of α =  −0.7. Different from earlier studies we conclude that solid ice discharge from Greenland due to dynamic thinning is bounded by 0.42 m sea-level equivalent. Ice discharge induced by surface warming on Antarctica is best captured by a positive value of α = 0.1 which reflects the fact that ice loss increases with the cumulative amount of heat available for softening the ice in our model.

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References

  • Allen MR, Frame DJ, Huntingford C, Jones CD, Lowe JA, Meinshausen M, Meinshausen N (2009) Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature 458:1163–1166. doi:10.1038/nature08019

    Article  Google Scholar 

  • Bueler E, Brown J (2009) The shallow shelf approximation as a sliding law in a thermomechanically coupled ice sheet model. J Geophys Res 114:F03008

    Article  Google Scholar 

  • Church J, Gregory J, Huybrechts P, Kuhn M, Lambeck K, Nhuan M, Qin D, Woodworth P (2001) Changes in sea level. In: Houghton J, Ding Y, Griggs D, Noguer M, Linden PV, Dai X, Maskell K, Johnson C (eds) Climate change 2001: the scientific basis: contribution of working group I to the third assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge, pp 639–694

    Google Scholar 

  • Church JA, White NJ, Konikow LF, Domingues CM, Cogley JG, Rignot E, Gregory JM, van den Broeke MR, Monaghan AJ, Velicogna I (2011) Revisiting the Earth’s sea-level and energy budgets from 1961 to 2008. Geophys Res Lett 38:L18601. doi:10.1029/2011GL048794

    Article  Google Scholar 

  • Frieler K, Meinshausen M, Mengel M, Braun N, Hare W (2011) A scaling approach to probabilistic assessment of regional climate change. J Clim. doi:10.1126/science.1070942

  • Gillett NP, Arora VK, Zickfeld K, Marshall SJ, Merryfield WJ (2011) Ongoing climate change following a complete cessation of carbon dioxide emissions. Nat Geosci 4:83–87. doi:10.1038/ngeo1047

    Article  Google Scholar 

  • Good P, Gregory JM, Lowe JA (2011) A step-response simple climate model to reconstruct and interpret AOGCM projections. Geophys Res Lett 38:L01703. doi:10.1029/2010GL045208

    Article  Google Scholar 

  • Hansen J, Ruedy R, Sato M, Imhoff M, Lawrence W, Easterling D, Peterson T, Karl T (2001) A closer look at United States and global surface temperature change. J Geophys Res 106:23947–23964. doi:10.1029/2001JD000354

    Article  Google Scholar 

  • Hooss G, Voss R, Hasselmann K, Maier-Reimer E, Joos F (2001) A nonlinear impulse response model of the coupled carbon cycle-climate system (NICCS). Clim Dyn 18:189–202. doi:10.1007/s003820100170

    Article  Google Scholar 

  • Huybrechts P, Goelzer H, Janssens I, Driesschaert E, Fichefet T, Goosse H, Loutre MF (2011) Response of the Greenland and Antarctic ice sheets to multi-millennial greenhouse warming in the earth system model of intermediate complexity LOVECLIM. Surv Geophys 32:397–416

    Article  Google Scholar 

  • Jevrejeva S, Moore JC, Grinsted A (2010) How will sea level respond to changes in natural and anthropogenic forcings by 2100? Geophys Res Lett 37:7703. doi:10.1029/2010GL042947

    Article  Google Scholar 

  • Martin MA, Winkelmann R, Haseloff M, Albrecht T, Bueler E, Khroulev C, Levermann A (2011) The Potsdam Parallel Ice Sheet Model (PISM-PIK) part 2: dynamic equilibrium simulation of the Antarctic ice sheet. The Cryosphere 5(3):727–740

    Article  Google Scholar 

  • Marčelja S (2010) The timescale and extent of thermal expansion of the global ocean due to climate change. Ocean Sci 6:179–184

    Article  Google Scholar 

  • Meier MF, Dyurgerov MB, Rick UK, ÓNeel S, Pfeffer WT, Anderson RS, Anderson SP, Glazovsky AF (2007) Glaciers dominate eustatic sea-level rise in the 21st century. Science 317:1064–1067. doi:10.1126/science.1143906

    Article  Google Scholar 

  • Meinshausen M, Smith S, Calvin K, Daniel J, Kainuma M, Lamarque JF, Matsumoto K, Montzka S, Raper S, Riahi K, Thomson A, Velders G, van Vuuren D (2011) The RCP greenhouse gas concentrations and their extensions from 1765 to 2300. Clim Chang 109:213–241. doi:10.1007/s10584-011-0156-z

    Article  Google Scholar 

  • Mikolajewicz U, Gröger M, Maier-Reimer E, Schurgers G, Vizcaíno M, Winguth AME (2007) Long-term effects of anthropogenic CO2 emissions simulated with a complex earth system model. Clim Dyn 28:599–633. doi:10.1007/s00382-006-0204-y

    Article  Google Scholar 

  • Montoya M, Griesel A, Levermann A, Mignot J, Hofmann M, Ganopolski A, Rahmstorf S (2005) The earth system model of intermediate complexity CLIM BER-3α. Part I: description and performance for present day conditions. Clim Dyn 25:237–263

    Article  Google Scholar 

  • Pfeffer WT, Harper JT, O’Neel S (2008) Kinematic constraints on glacier contributions to 21st-century sea-level rise. Science 321:1340–1343

    Article  Google Scholar 

  • Price SF, Payne AJ, Howat IM, Smith BE (2011) Committed sea-level rise for the next century from Greenland ice sheet dynamics during the past decade. Proc Natl Acad Sci 108:8978–8983

    Article  Google Scholar 

  • Rahmstorf S (2007) A semi-empirical approach to projecting future sea-level rise. Science 315:368–370

    Article  Google Scholar 

  • Riahi K, Grübler A, Nakicenovic N (2007) Scenarios of long-term socio-economic and environmental development under climate stabilization. Technol Forecast Soc Chang 74(7):887–935. doi:10.1016/j.techfore.2006.05.026

    Article  Google Scholar 

  • Ridley J, Gregory JM, Huybrechts P, Lowe JA (2010) Thresholds for irreversible decline of the greenland ice sheet. Clim Dyn 35:1049–1057. doi:10.1007/s00382-009-0646-0

    Article  Google Scholar 

  • Schewe J, Levermann A, Meinshausen M (2011) Climate change under a scenario near 1.5°C of global warming: monsoon intensification, ocean warming and steric sea level rise. Earth Syst Dyn 2(1):25–35. doi:10.5194/esd-2-25-2011

    Article  Google Scholar 

  • Solomon S, Plattner GK, Knutti R, Friedlingstein P (2009) Irreversible climate change due to carbon dioxide emissions. Proc Natl Acad Sci 106:1704–1709. doi:10.1073/pnas.0812721106

    Article  Google Scholar 

  • Swingedouw D, Fichefet T, Hybrechts P, Goosse H, Driesschaert E, Loutre MF (2008) Antarctic ice-sheet melting provides negative feedbacks on future climate warming. Geophys Res Lett 35:doi:10.1029/2008GL034,410

  • Vermeer M, Rahmstorf S (2009) Global sea level linked to global temperature. Proc Natl Acad Sci 106:21527–21532

    Article  Google Scholar 

  • Vizcaino M, Mikolajewicz U, Jungclaus J, Schurgers G (2010) Climate modification by future ice sheet changes and consequences for ice sheet mass balance. Clim Dyn 34:301–324

    Article  Google Scholar 

  • van Vuuren DP, Eickhout B, Lucas PL, den Elzen MGJ (2006) Long-term multi-gas scenarios to stabilise radiative forcing—exploring costs and benefits within an integrated assessment framework. The energy journal 27:201–233

    Google Scholar 

  • van Vuuren D, den Elzen M, Lucas P, Eickhout B, Strengers B, van Ruijven B, Wonink S, van Houdt R (2007) Stabilizing greenhouse gas concentrations at low levels: an assessment of reduction strategies and costs. Clim Chang 159:81–119

    Google Scholar 

  • Winguth A, Mikolajewicz U, Gröger M, Maier-Reimer E, Schurgers G, Vizcaíno M (2005) Centennial-scale interactions between the carbon cycle and anthropogenic climate change using a dynamic Earth system model. Geophys Res Lett 32:L23,714

    Article  Google Scholar 

  • Winkelmann R, Martin MA, Haseloff M, Albrecht T, Bueler E, Khroulev C, Levermann A (2011) The Potsdam Parallel Ice Sheet Model (PISM-PIK) part 1: model description. The Cryosphere 5(3):715–726. doi:10.5194/tc-5-715-2011

    Article  Google Scholar 

  • Winkelmann R, Levermann A, Frieler K, Martin MA (2012) Uncertainty in future solid ice discharge from Antarctica. The Cryosphere Discuss 6:673–714. doi:10.5194/tcd-6-673-2012

    Article  Google Scholar 

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Acknowledgments

This study was funded by the German Federal Ministry of Education and Research (BMBF). We would like to thank Stephen Price for sharing his data with us.

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Authors and Affiliations

  1. Potsdam Institute for Climate Impact Research, Potsdam, Germany

    Ricarda Winkelmann & Anders Levermann

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  1. Ricarda Winkelmann
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  2. Anders Levermann
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Correspondence to Ricarda Winkelmann.

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Winkelmann, R., Levermann, A. Linear response functions to project contributions to future sea level. Clim Dyn 40, 2579–2588 (2013). https://doi.org/10.1007/s00382-012-1471-4

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  • DOI: https://doi.org/10.1007/s00382-012-1471-4

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