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


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Author information

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.

Correspondence to Peter M. Cox.

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

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Fig. 1: Typical results for experiments with the one-box Hasselmann model.
Fig. 2: Comparison of different emergent relationships.
Extended Data Fig. 1: Impact of de-trending on the ECS–Ψ relationship in CMIP5 models.
Extended Data Fig. 2: Typical results for experiments (i)–(iv) with the two-box model.


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