Brief Communications Arising | Published:

Cox et al. reply

Naturevolume 563pagesE10E15 (2018) | Download Citation

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Data availability

Relevant data are available from the corresponding author on reasonable request.


  1. 1.

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

  2. 2.

    Rypdal, M., Fredriksen, H.-B., Rypdal, K. & Steene, R. J. Emergent constraints on climate sensitivity. Nature 563, (2018).

  3. 3.

    Po-Chedley, S., Proistosescu, C., Armour, K. C. & Santer, B. D. Climate constraint reflects forced signal. Nature 563, (2018).

  4. 4.

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

  5. 5.

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

  6. 6.

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

  7. 7.

    Frost, C. & Thompson, S. G. Correcting for regression dilution bias: comparison of methods for a single predictor variable. J. R. Stat. Soc. Ser. A 163, 173–189 (2000).

  8. 8.

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

  9. 9.

    Williamson, M. S., Cox, P. M. & Nijsse, F. J. M. M. Theoretical foundation of emergent constraints: relationships between climate sensitivity and global temperature variability in conceptual models. Dyn. Stat. Clim. Syst. (in the press).

  10. 10.

    Meinshausen, M. et al. The RCP greenhouse gas concentrations and their extensions from 1765 to 2300. Clim. Change 109, 213 (2011).

Download references

Author information


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

    • Peter M. Cox
    • , Mark S. Williamson
    •  & Femke J. M. M. Nijsse
  2. Centre for Ecology and Hydrology, Wallingford, UK

    • Chris Huntingford


  1. Search for Peter M. Cox in:

  2. Search for Mark S. Williamson in:

  3. Search for Femke J. M. M. Nijsse in:

  4. Search for Chris Huntingford in:


The list of co-authors and their order are slightly different from the original study4. F.J.M.M.N. carried-out many statistical tests in response to the accompanying Comments, and has therefore been added to the author list for this Reply. Similarly, M.S.W. carried out substantial new work with simple models, and has therefore been moved to the second-author position. P.M.C. and M.S.W. drafted the response. C.H. provided the time-series data for the CMIP5 models. M.S.W. produced Fig. 1 and Extended Data Fig. 2 using the one- and two-box models. P.M.C. produced Fig. 2 and Extended Data Fig. 1 from the CMIP5 models. F.J.M.M.N. provided statistical expertise and analysed the impact of regression dilution. All authors contributed to the final version of the Reply.

Competing interests

Declared none.

Corresponding author

Correspondence to Peter M. Cox.

Extended data figures and tables

  1. Extended Data Fig. 1 Impact of de-trending on the ECS–Ψ relationship in CMIP5 models.

    a, Control runs linearly de-trended in a 55-year moving window (r = 0.75). b, Control runs without de-trending (r = 0.45).

  2. Extended Data Fig. 2 Typical results for experiments (i)–(iv) with the two-box model.

    As in Figs. 1 and 2, letters represent models given in extended data table 1 in Cox et al.4. Solid lines indicate the emergent relationship and dotted lines are the prediction error.

  3. Extended Data Table 1 Experiments with common models

About this article

Publication history




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.