Letter | Published:

Emergent constraint on equilibrium climate sensitivity from global temperature variability

Nature volume 553, pages 319322 (18 January 2018) | Download Citation


Equilibrium climate sensitivity (ECS) remains one of the most important unknowns in climate change science. ECS is defined as the global mean warming that would occur if the atmospheric carbon dioxide (CO2) concentration were instantly doubled and the climate were then brought to equilibrium with that new level of CO2. Despite its rather idealized definition, ECS has continuing relevance for international climate change agreements, which are often framed in terms of stabilization of global warming relative to the pre-industrial climate. However, the ‘likely’ range of ECS as stated by the Intergovernmental Panel on Climate Change (IPCC) has remained at 1.5–4.5 degrees Celsius for more than 25 years1. The possibility of a value of ECS towards the upper end of this range reduces the feasibility of avoiding 2 degrees Celsius of global warming, as required by the Paris Agreement. Here we present a new emergent constraint on ECS that yields a central estimate of 2.8 degrees Celsius with 66 per cent confidence limits (equivalent to the IPCC ‘likely’ range) of 2.2–3.4 degrees Celsius. Our approach is to focus on the variability of temperature about long-term historical warming, rather than on the warming trend itself. We use an ensemble of climate models to define an emergent relationship2 between ECS and a theoretically informed metric of global temperature variability. This metric of variability can also be calculated from observational records of global warming3, which enables tighter constraints to be placed on ECS, reducing the probability of ECS being less than 1.5 degrees Celsius to less than 3 per cent, and the probability of ECS exceeding 4.5 degrees Celsius to less than 1 per cent.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    et al. Long-term climate change: projections, commitments and irreversibility. In Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds et al.) Ch. 12 (Cambridge Univ. Press, 2013)

  2. 2.

    & Using the current seasonal cycle to constrain snow albedo feedback in future climate change. Geophys. Res. Lett. 33, L03502 (2006)

  3. 3.

    et al. Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: the HadCRUT4 dataset. J. Geophys. Res. 117, D08101 (2012)

  4. 4.

    et al. Beyond equilibrium climate sensitivity. Nat. Geosci. 10, 727–736 (2017)

  5. 5.

    et al. An observationally based estimate of the climate sensitivity. J. Clim. 15, 3117–3121 (2002)

  6. 6.

    et al. Evaluating adjusted forcing and model spread for historical and future scenarios in the CMIP5 generation of climate models. J. Geophys. Res. Atmos. 118, (2013)

  7. 7.

    & Variation in climate sensitivity and feedback parameters during the historical period. Geophys. Res. Lett. 43, 3911–3920 (2016)

  8. 8.

    Inference of climate sensitivity from analysis of Earth’s radiation budget. Ann. Rev. Earth Planet. Sci. 44, 85–106 (2016)

  9. 9.

    Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks. Nat. Clim. Chang. 7, 331–335 (2017)

  10. 10.

    & Using multiple observationally-based constraints to estimate climate sensitivity. Geophys. Res. Lett. 33, L06704 (2006)

  11. 11.

    et al. Sensitivity of tropical carbon to climate change constrained by carbon dioxide variability. Nature 494, 341–344 (2013)

  12. 12.

    et al. Projected land photosynthesis constrained by changes in the seasonal cycle of atmospheric CO2. Nature 538, 499–501 (2016)

  13. 13.

    Stochastic climate models. I. Theory. Tellus 28, 473–485 (1976)

  14. 14.

    et al. The frequency response of temperature and precipitation in a climate model. Geophys. Res. Lett. 38, L16711 (2011)

  15. 15.

    & Projections of the pace of warming following an abrupt increase in atmospheric carbon dioxide concentration. Environ. Res. Lett. 8, 034039 (2013)

  16. 16.

    et al. Transient climate response in a two-layer energy-balance model. Part I: Analytical solution and parameter calibration using CMIP5 AOGCM experiments. J. Clim. 26, 1841–1857 (2013)

  17. 17.

    et al. Evaluation of climate models. In Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds et al.) Ch. 9 (Cambridge Univ. Press, 2013)

  18. 18.

    Climate response and fluctuation dissipation. J. Atmos. Sci. 32, 2022–2026 (1975)

  19. 19.

    , & An overview of CMIP5 and the experiment design. Bull. Am. Meteorol. Soc. 93, 485–498 (2012)

  20. 20.

    et al. Forcing, feedbacks and climate sensitivity in CMIP5 coupled atmosphere-ocean models. Geophys. Res. Lett. 39, L09712 (2012)

  21. 21.

    Twentieth century climate model response and climate sensitivity. Geophys. Res. Lett. 34, L22710 (2007)

  22. 22.

    et al. Tipping elements in the Earth’s climate system. Proc. Natl Acad. Sci. USA 105, 1786–1793 (2008)

  23. 23.

    et al. Early-warning signals for critical transitions. Nature 461, 53–59 (2009)

  24. 24.

    et al. Energy budget constraints on climate response. Nat. Geosci. 6, 415–416 (2013)

  25. 25.

    & The implications for climate sensitivity of AR5 forcing and heat uptake estimates. Clim. Dyn. 45, 1009–1023 (2015)

  26. 26.

    et al. Implications for climate sensitivity from the response to individual forcings. Nat. Clim. Chang. 6, 386–389 (2015)

  27. 27.

    , & Spread in model climate sensitivity traced to atmospheric convective mixing. Nature 505, 37–42 (2014)

  28. 28.

    & Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends. Q. J. R. Meteorol. Soc. 140, 1935–1944 (2014)

Download references


This work was supported by the European Research Council (ERC) ECCLES project, grant agreement number 742472 (P.M.C.); the EU Horizon 2020 Research Programme CRESCENDO project, grant agreement number 641816 (P.M.C. and M.S.W.); the EPSRC-funded ReCoVER project (M.S.W.); and the NERC CEH National Capability fund (C.H.). We also acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups (listed in Extended Data Table 1 of this paper) for producing and making available their model output.

Author information


  1. College of Engineering, Mathematics and Physical Science, University of Exeter, Exeter EX4 4QF, UK

    • Peter M. Cox
    •  & Mark S. Williamson
  2. Centre for Ecology and Hydrology, Wallingford OX10 8BB, UK

    • Chris Huntingford


  1. Search for Peter M. Cox in:

  2. Search for Chris Huntingford in:

  3. Search for Mark S. Williamson in:


All authors collaboratively designed the study and contributed to the manuscript. P.M.C. led the study and drafted the manuscript. C.H. was the lead on the time-series data for the CMIP5 models. M.S.W. led on the theoretical analysis.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Peter M. Cox.

Reviewer Information Nature thanks P. Forster and T. Mauritsen for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

About this article

Publication history






Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.