Assumptions for emergent constraints

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Fig. 1: Analysis of simulated and observed time series using three methods to isolate unforced variability.
Fig. 2: Comparison of the central estimate and likely range of ECS for various methods and for four observational datasets.


  1. 1.

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

    ADS  CAS  Article  Google Scholar 

  2. 2.

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

    ADS  Article  Google Scholar 

  3. 3.

    Brockwell, P. J. R. A. D. Introduction to Time Series and Forecasting (Springer, Berlin, 1996).

    Google Scholar 

  4. 4.

    Wilks, D. S. Statistical Methods in the Atmospheric Sciences Vol. 100 (Elsevier, Amsterdam, 2011).

    Google Scholar 

  5. 5.

    Foster, G., Annan, J. D., Schmidt, G. A. & Mann, M. E. Comment on “Heat capacity, time constant, and sensitivity of Earth’s climate system” by S. E. Schwartz. J. Geophys. Res. 113, D15102 (2008).

    ADS  Article  Google Scholar 

  6. 6.

    Ting, M., Kushnir, Y., Seager, R. & Li, C. Forced and internal twentieth-century SST trends in the North Atlantic. J. Clim. 22, 1469–1481 (2009).

    ADS  Article  Google Scholar 

  7. 7.

    Mann, M. E., Steinman, B. A. & Miller, S. K. On forced temperature changes, internal variability and the AMO. Geophys. Res. Lett. 41, 3211–3219 (2014).

    ADS  Article  Google Scholar 

  8. 8.

    Cheung, A. H. et al. Comparison of low-frequency internal climate variability in CMIP5 models and observations. J. Clim. 30, 4763–4776 (2017).

    ADS  Article  Google Scholar 

  9. 9.

    Steinman, B. A., Mann, M. E. & Miller, S. K. Atlantic and Pacific multidecadal oscillations and Northern Hemisphere temperatures. Science 347, 988–991 (2015).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  10. 10.

    Frankcombe, L. M., England, M. H., Mann, M. E. & Steinman, B. A. Separating internal variability from the externally forced climate response. J. Clim. 28, 8184–8202 (2015).

    ADS  Article  Google Scholar 

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P.T.B. and M.B.S. performed the analysis. P.T.B. wrote an initial draft of the manuscript. All authors contributed to interpreting the results and refining the manuscript.

Corresponding author

Correspondence to Patrick T. Brown.

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Declared none.

Extended data figures and tables

Extended Data Fig. 1 Ψ metric of temperature variability versus time.

This figure is analogous to figure 2a in Cox et al.1, but without data from ACCESS1-0, inmcm4, IPSL-CM5B-LR, MPI-ESM-LR, GFDL-ESM2G, MIROC5 and bcc-csm1-1-m because not all required simulations were available for these models. Black lines correspond to Ψ calculated from the historical experiment, which includes all forcings. Blue lines correspond to Ψ calculated from the historical–natural experiment (‘historicalNat’), which includes only forcings from changes in incoming solar radiation and volcanic aerosols. Red lines correspond to Ψ calculated from the historical greenhouse gas experiment (‘historicalGHG’), which includes only forcing from well-mixed greenhouse gases (and ozone in some models). Thin lines are individual model-ensemble members (r1i1p1) and thick lines are multi-model means (MMMs). The data show that Ψ (as calculated by Cox et al.1) is non-stationary and inflated towards the end of the record, even in the case where models are forced by only greenhouse gases.

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Brown, P.T., Stolpe, M.B. & Caldeira, K. Assumptions for emergent constraints. Nature 563, E1–E3 (2018).

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  • Emergent Constraints
  • Equilibrium Climate Sensitivity (ECS)
  • Global Mean Temperature
  • External Impulsive Forces
  • NOAA Observations

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