Brief Communications Arising | Published:

Assumptions for emergent constraints

Naturevolume 563pagesE1E3 (2018) | Download Citation

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  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).

  2. 2.

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

  3. 3.

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

  4. 4.

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

  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).

  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).

  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).

  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).

  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).

  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).

Download references

Author information


  1. Department of Global Ecology, Carnegie Institution for Science, Stanford, CA, USA

    • Patrick T. Brown
    •  & Ken Caldeira
  2. Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland

    • Martin B. Stolpe


  1. Search for Patrick T. Brown in:

  2. Search for Martin B. Stolpe in:

  3. Search for Ken Caldeira in:


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.

Competing interests

Declared none.

Corresponding author

Correspondence to Patrick T. Brown.

Extended data figures and tables

  1. 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.

Supplementary information

  1. Supplementary Material

    This file contains assumptions for emergent constraints.

About this article

Publication history




Issue Date


Further reading

  • Cox et al. reply

    • Peter M. Cox
    • , Mark S. Williamson
    • , Femke J. M. M. Nijsse
    •  & Chris Huntingford

    Nature (2018)


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.