Decadal global temperature variability increases strongly with climate sensitivity


Climate-related risks are dependent not only on the warming trend from GHGs, but also on the variability about the trend. However, assessment of the impacts of climate change tends to focus on the ultimate level of global warming1, only occasionally on the rate of global warming, and rarely on variability about the trend. Here we show that models that are more sensitive to GHGs emissions (that is, higher equilibrium climate sensitivity (ECS)) also have higher temperature variability on timescales of several years to several decades2. Counter-intuitively, high-sensitivity climates, as well as having a higher chance of rapid decadal warming, are also more likely to have had historical ‘hiatus’ periods than lower-sensitivity climates. Cooling or hiatus decades over the historical period, which have been relatively uncommon, are more than twice as likely in a high-ECS world (ECS = 4.5 K) compared with a low-ECS world (ECS = 1.5 K). As ECS also affects the background warming rate under future scenarios with unmitigated anthropogenic forcing, the probability of a hyper-warming decade—over ten times the mean rate of global warming for the twentieth century—is even more sensitive to ECS.

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Fig. 1: Decadal variability in global temperature.
Fig. 2: Emergent relationship between ECS and warming trends.
Fig. 3: Varying window lengths.
Fig. 4: Probability of warming and cooling.

Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

Code availability

The Python code used to produce the figures in this paper is available is available via Code Ocean28 at


  1. 1.

    United Nations Framework Convention on Climate Change (United Nations, 1992).

  2. 2.

    Lenton, T. M. Early warning of climate tipping points. Nat. Clim. Change 1, 201–209 (2011).

    Article  Google Scholar 

  3. 3.

    Taylor, K. E., Stouffer, R. J. & Meehl, G. A. An overview of CMIP5 and the experiment design. Bull. Am. Meteorol. Soc. 93, 485–498 (2012).

    Article  Google Scholar 

  4. 4.

    Stocker, T. F., Dahe, Q. & Plattner, G.-K. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) 82–85 (IPCC, Cambridge Univ. Press, 2013).

  5. 5.

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

    CAS  Article  Google Scholar 

  6. 6.

    Roe, G. Feedbacks, timescales, and seeing red. Annu. Rev. Earth Planet. Sci. 37, 93–115 (2009).

    CAS  Article  Google Scholar 

  7. 7.

    Strogatz, S. H. Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering (Westview, 2000).

  8. 8.

    Hasselmann, K. Stochastic models of climate extremes: theory and observations. Tellus 28, 473–485 (1976).

    Article  Google Scholar 

  9. 9.

    Wigley, T. M. L. & Raper, S. C. B. Natural variability of the climate system and detection of the greenhouse effect. Nature 344, 324–327 (1990).

    Article  Google Scholar 

  10. 10.

    Caldeira, K. & Myhrvold, N. P. Projections of the pace of warming following an abrupt increase in atmospheric carbon dioxide concentration. Environ. Res. Lett. 8, 34039–10 (2013).

    Article  Google Scholar 

  11. 11.

    Geoffroy, O. 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).

    Article  Google Scholar 

  12. 12.

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

    Article  Google Scholar 

  13. 13.

    Gottwald, G. A., Wormell, J. P. & Wouters, J. On spurious detection of linear response and misuse of the fluctuation–dissipation theorem in finite time series. Phys. D 331, 89–101 (2016).

    Article  Google Scholar 

  14. 14.

    Kubo, R. The fluctuation–dissipation theorem. Rep. Prog. Phys. 29, 255–284 (1966).

    CAS  Article  Google Scholar 

  15. 15.

    Lutsko, N. J. & Takahashi, K. What can the internal variability of CMIP5 models tell us about their climate sensitivity? J. Clim. 31, 5051–5069 (2018).

    Article  Google Scholar 

  16. 16.

    Caldwell, P. M., Zelinka, M. D. & Klein, S. A. Evaluating emergent constraints on equilibrium climate sensitivity. J. Clim. 31, 3921–3942 (2018).

    Article  Google Scholar 

  17. 17.

    Schwartz, S. E. Heat capacity, time constant, and sensitivity of Earth’s climate system. J. Geophys. Res. 112, 24–25 (2007).

    Article  Google Scholar 

  18. 18.

    Colman, R. & Power, S. B. What can decadal variability tell us about climate feedbacks and sensitivity? Clim. Dynam. 51, 3815–3828 (2018).

    Article  Google Scholar 

  19. 19.

    Nijsse, F. J. M. M. & Dijkstra, H. A. A mathematical approach to understanding emergent constraints. Earth Syst. Dynam. 9, 999–1012 (2018).

    Article  Google Scholar 

  20. 20.

    Roberts, C. D., Palmer, M. D., McNeall, D. & Collins, M. Quantifying the likelihood of a continued hiatus in global warming. Nat. Clim. Change 5, 337–342 (2015).

    Article  Google Scholar 

  21. 21.

    Smith, D. M. et al. Role of volcanic and anthropogenic aerosols in the recent global surface warming slowdown. Nat. Clim. Change 6, 936–940 (2016).

    CAS  Article  Google Scholar 

  22. 22.

    Medhaug, I., Stolpe, M. B., Fischer, E. M. & Knutti, R. Reconciling controversies about the ‘global warming hiatus’. Nature 545, 41–47 (2017).

    CAS  Article  Google Scholar 

  23. 23.

    Cox, P. M., Huntingford, C. & Williamson, M. S. Emergent constraint on equilibrium climate sensitivity from global temperature variability. Nature 553, 319–322 (2018).

    CAS  Article  Google Scholar 

  24. 24.

    Brown, P. T. & Caldeira, K. Greater future global warming inferred from Earth’s recent energy budget. Nature 552, 45–50 (2017).

    CAS  Article  Google Scholar 

  25. 25.

    Sherwood, S. C., Bony, S. & Dufresne, J. L. Spread in model climate sensitivity traced to atmospheric convective mixing. Nature 505, 37–42 (2014).

    Article  Google Scholar 

  26. 26.

    Stan Modeling Language Users Guide and Reference Manual Version 2.18.0 (Stan Development Team, 2018).

  27. 27.

    Williamson, M. S., Cox, P. M. & Nijsse, F. J. M. M. Theoretical foundations of emergent constraints: relationships between climate sensitivity and global temperature variability in conceptual models. Dynam. Stat. Clim. Syst. 3, dzy006 (2018).

    Google Scholar 

  28. 28.

    Nijsse, F. J. M. M., Cox, P. M., Huntingford, C. & Williamson, M. S. Decadal variability and climate sensitivity [Source Code]. (Code Ocean, 2019);

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This work was supported by the European Research Council ECCLES project, grant agreement number 742472 (F.J.M.M.N. and P.M.C.); the EU Horizon 2020 Research Programme CRESCENDO project, grant agreement number 641816 (P.M.C. and 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 Supplementary Table 1) for producing and making available their model output.

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All authors contributed towards the design of the study and aided in writing the manuscript. F.J.M.M.N. led on the theoretical analysis; C.H. led on the time-series data.

Corresponding author

Correspondence to Femke J. M. M. Nijsse.

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Peer review information: Nature Climate Change thanks Patrick Brown and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–5, Table 1 and references.

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Nijsse, F.J.M.M., Cox, P.M., Huntingford, C. et al. Decadal global temperature variability increases strongly with climate sensitivity. Nat. Clim. Chang. 9, 598–601 (2019).

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