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Cox et al. reply

Nature volume 563, pages E10–E15 (2018)Cite this article

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replying to P. T. Brown, M. B. Stolpe & K. Caldeira Nature 563, https://doi.org/10.1038/s41586-018-0638-5 (2018); M. Rypdal, H.-B. Fredriksen, K. Rypdal & R. J. Steene Nature 563, https://doi.org/10.1038/s41586-018-0639-4 (2018); S. Po-Chedley, C. Proistosescu, K. C. Armour & B. D. Santer Nature 563, https://doi.org/10.1038/s41586-018-0640-y (2018)

The accompanying Comments1,2,3 make several common points on our original study4, which we address here. The main point in all three Comments relates to the role of external forcing, with each assuming that external forcing contaminates our emergent constraint. Each Comment goes on to suggest alternative methods for removing external forcing, including using pre-industrial control runs1,3, using shorter periods of the historical record2,3 or de-trending using the CMIP5 model mean1. All of these alternative methods are reported to weaken our emergent constraint on equilibrium climate sensitivity (ECS)4. Here we show that these alternative methods are neither necessary nor justified. Although residual external forcing after de-trending affects the gradient of the linear relationship between ECS and our metric of global temperature variability (Ψ), it does not undermine our original emergent constraint, which depends on only the linear proportionality between Ψ and ECS. Using outputs from the CMIP5 models, as well as one-box5 and two-box6 conceptual models, we show that the linear ECS–Ψ relationship is not only present but also strengthened by the presence of residual external forcing, which therefore serves to usefully reduce the uncertainty in the resulting emergent constraint on ECS.

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Fig. 1: Typical results for experiments with the one-box Hasselmann model.
Fig. 2: Comparison of different emergent relationships.

Data availability

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

References

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Authors and Affiliations

  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

Authors
  1. Peter M. Cox
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  2. Mark S. Williamson
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  3. Femke J. M. M. Nijsse
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  4. Chris Huntingford
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Contributions

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.

Corresponding author

Correspondence to Peter M. Cox.

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Declared none.

Extended data figures and tables

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).

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.

Extended Data Table 1 Experiments with common models
Full size table

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Cox, P.M., Williamson, M.S., Nijsse, F.J.M.M. et al. Cox et al. reply. Nature 563, E10–E15 (2018). https://doi.org/10.1038/s41586-018-0641-x

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