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Ensemble reconstruction constraints on the global carbon cycle sensitivity to climate


The processes controlling the carbon flux and carbon storage of the atmosphere, ocean and terrestrial biosphere are temperature sensitive1,2,3,4 and are likely to provide a positive feedback leading to amplified anthropogenic warming3. Owing to this feedback, at timescales ranging from interannual to the 20–100-kyr cycles of Earth's orbital variations1,5,6,7, warming of the climate system causes a net release of CO2 into the atmosphere; this in turn amplifies warming. But the magnitude of the climate sensitivity of the global carbon cycle (termed γ), and thus of its positive feedback strength, is under debate, giving rise to large uncertainties in global warming projections8,9. Here we quantify the median γ as 7.7 p.p.m.v. CO2 per °C warming, with a likely range of 1.7–21.4 p.p.m.v. CO2 per °C. Sensitivity experiments exclude significant influence of pre-industrial land-use change on these estimates. Our results, based on the coupling of a probabilistic approach with an ensemble of proxy-based temperature reconstructions and pre-industrial CO2 data from three ice cores, provide robust constraints for γ on the policy-relevant multi-decadal to centennial timescales. By using an ensemble of >200,000 members, quantification of γ is not only improved, but also likelihoods can be assigned, thereby providing a benchmark for future model simulations. Although uncertainties do not at present allow exclusion of γ calculated from any of ten coupled carbon–climate models, we find that γ is about twice as likely to fall in the lowermost than in the uppermost quartile of their range. Our results are incompatibly lower (P < 0.05) than recent pre-industrial empirical estimates of 40 p.p.m.v. CO2 per °C (refs 6, 7), and correspondingly suggest 80% less potential amplification of ongoing global warming.

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Figure 1: Temperature and CO 2 variability over the past millennium.
Figure 2: Long-term temperature variation, amplitude and uncertainty.
Figure 3: Estimates for γ.
Figure 4: Sensitivity in empirical and model estimates of γ.


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We thank P. Friedlingstein, R. Knutti and T. Stocker for comments, the C4MIP consortium for use of their model output, and the Swiss National Science Foundation (NCCR-Climate) and the European Union projects Carbo-Extreme (226701) and Millennium (017008) for funding.

Author Contributions D.C.F., J.E., C.C.R. and F.J. designed the study, with input from U.B. and V.T. D.C.F. and C.C.R. performed the analysis with input from F.J. and J.E. B.S. provided and interpreted results for land-use sensitivity experiments. All authors contributed to discussion, interpretation and writing the paper.

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Correspondence to David C. Frank.

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Frank, D., Esper, J., Raible, C. et al. Ensemble reconstruction constraints on the global carbon cycle sensitivity to climate. Nature 463, 527–530 (2010).

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