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Warming caused by cumulative carbon emissions towards the trillionth tonne


Global efforts to mitigate climate change are guided by projections of future temperatures1. But the eventual equilibrium global mean temperature associated with a given stabilization level of atmospheric greenhouse gas concentrations remains uncertain1,2,3, complicating the setting of stabilization targets to avoid potentially dangerous levels of global warming4,5,6,7,8. Similar problems apply to the carbon cycle: observations currently provide only a weak constraint on the response to future emissions9,10,11. Here we use ensemble simulations of simple climate-carbon-cycle models constrained by observations and projections from more comprehensive models to simulate the temperature response to a broad range of carbon dioxide emission pathways. We find that the peak warming caused by a given cumulative carbon dioxide emission is better constrained than the warming response to a stabilization scenario. Furthermore, the relationship between cumulative emissions and peak warming is remarkably insensitive to the emission pathway (timing of emissions or peak emission rate). Hence policy targets based on limiting cumulative emissions of carbon dioxide are likely to be more robust to scientific uncertainty than emission-rate or concentration targets. Total anthropogenic emissions of one trillion tonnes of carbon (3.67 trillion tonnes of CO2), about half of which has already been emitted since industrialization began, results in a most likely peak carbon-dioxide-induced warming of 2 °C above pre-industrial temperatures, with a 5–95% confidence interval of 1.3–3.9 °C.

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Figure 1: Idealized carbon dioxide emission scenarios and response to benchmark scenario.
Figure 2: Peak CO 2 -induced warming as a function of total cumulative emissions 1750–2500 for 250 idealized emission scenarios.
Figure 3: Warming commitment for selected scenarios shownin Fig. 1a .


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We thank N. Gillett, K. Shine and T. Stocker for suggestions, P. Stott for estimates of twentieth-century-attributable warming, J. Welby for help calibrating the simple climate model. P. Friedlingstein and the C4MIP modelling community for model output and I. Tracey for help with the manuscript. M.R.A. and D.J.F. acknowledge support from NERC and the FP6 ENSEMBLES project. M.R.A. received additional support from the International Detection and Attribution Working Group (IDAG), supported by the DOE Office of Science, Office of Biological and Environmental Research and NOAA Climate Program Office, and from the British Council. C.H. acknowledges the CEH Science Budget Fund. C.D.J. and J.A.L. were supported by the Joint DECC, Defra and MoD Integrated Climate Programme (DECC/Defra GA01101; MoD CBC/2B/0417_Annex C5).

Author Contributions M.R.A. and D.J.F. designed, tested and ran the simple climate model. C.H., C.D.J. and J.A.L. developed and tuned HadSCCCM1 and C.H. and J.A.L. ran the simulations; M.M. ran the MAGICC model contributing to Fig. 3 and N.M. advised on statistical analysis. All authors contributed to writing the paper.

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Correspondence to Myles R. Allen.

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Allen, M., Frame, D., Huntingford, C. et al. Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature 458, 1163–1166 (2009).

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