1. Department of Physics, University of Oxford, OX1 3PU, UK
2. Smith School of Enterprise and the Environment, University of Oxford, OX1 2BQ, UK
3. Centre for Ecology and Hydrology, Wallingford, OX10 8BB, UK
4. Met Office Hadley Centre, FitzRoy Road, Exeter, EX1 3PB, UK
5. Met Office Hadley Centre (Reading Unit), Department of Meteorology, University of Reading, RG6 6BB, Reading, UK
6. Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany
7. Department of Statistics, University of Oxford, OX1 3TG, UK

Correspondence to: Myles R. Allen¹ Correspondence and requests for materials should be addressed to M.R.A. (Email: myles.allen@physics.ox.ac.uk).

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 uncertain^{1, 2, 3}, complicating the setting of stabilization targets to avoid potentially dangerous levels of global warming^{4, 5, 6, 7, 8}. Similar problems apply to the carbon cycle: observations currently provide only a weak constraint on the response to future emissions^{9, 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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