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Current level and rate of warming determine emissions budgets under ambitious mitigation


Some of the differences between recent estimates of the remaining budget of carbon dioxide (CO2) emissions consistent with limiting warming to 1.5 °C arise from different estimates of the level of warming to date relative to pre-industrial conditions, but not all. Here we show that, for simple geometrical reasons, the combination of both the level and rate of human-induced warming provides a remarkably accurate prediction of remaining emission budgets to peak warming across a broad range of scenarios, if budgets are expressed in terms of CO2-forcing-equivalent emissions. These in turn predict CO2 emissions budgets if (but only if) the fractional contribution of non-CO2 drivers to warming remains approximately unchanged, as it does in some ambitious mitigation scenarios, indicating a best-estimate remaining budget for 1.5 °C of about 22 years’ current emissions from mid-2017, with a ‘likely’ (1 standard error) range of 13–32 years. This provides a simple, transparent and model-independent metric of progress towards an ambitious temperature stabilization goal that could be used to inform the Paris Agreement stocktake process. It is less applicable to less ambitious goals. Alternative definitions of current warming and scenarios for non-CO2 drivers give lower 1.5 °C budgets. Lower budgets based on the MAGICC simple modelling system widely used in integrated assessment studies reflect its relatively high simulated current warming rates.

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Fig. 1: Emissions and temperatures in a 1.5 °C stabilization scenario.
Fig. 2: Current level and rate of warming constrain emission budgets to peak warming.
Fig. 3: Implications of current level and rate of warming for emissions budgets for 1.5 °C.

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  1. Millar, R. J. et al. Emission budgets and pathways consistent with limiting warming to 1.5 °C. Nat. Geosci. 10, 741–747 (2017).

    Article  Google Scholar 

  2. Goodwin, P. et al. Pathways to 1.5 °C and 2 °C warming based on observational and geological constraints. Nat. Geosci. 11, 102–107 (2018).

    Article  Google Scholar 

  3. Tokarska, K. B. & Gillett, N. P. Cumulative carbon emissions budgets consistent with 1.5 °C global warming. Nat. Clim. Change 8, 296–299 (2018).

    Article  Google Scholar 

  4. Mengis, N., Partanen, A.-I., Jalbert, J. & Matthews, H. D. 1.5 °C carbon budget dependent on carbon cycle uncertainty and future non-CO2 forcing. Sci. Rep. 8, 5831 (2018).

    Article  Google Scholar 

  5. Schurer, A. P., Mann, M. E., Hawkins, E., Hegerl, G. C. & Tett, S. F. B. Importance of the pre-Industrial baseline for likelihood of exceeding Paris goals. Nat. Clim. Change 7, 563–567 (2017).

    Article  Google Scholar 

  6. Schurer, A. P. et al. Interpretations of the Paris climate target. Nat. Geosci. 11, 220–221 (2018).

    Article  Google Scholar 

  7. Mauritsen, T. & Pincus, R. Committed warming inferred from observations. Nat. Clim. Change 7, 652–655 (2017).

    Article  Google Scholar 

  8. Rogelj, J., Schleussner, C.-F. & Hare, W. Getting it right matters: Temperature Goal Interpretations in Geoscience Research. Geophys. Res. Lett. 44, 10662–10665 (2017).

    Article  Google Scholar 

  9. Rogelj, J. et al. Paris Agreement climate proposals need a boost to keep warming well below 2 °C. Nature 534, 631–639 (2016).

    Article  Google Scholar 

  10. Hienola, A. et al. The impact of aerosol emissions on the 1.5 °C pathways. Environ. Res. Lett. 13, 044011 (2018).

    Article  Google Scholar 

  11. Meinshausen, M., Raper, S. C. B. & Wigley, T. M. L. Emulating coupled atmosphere–ocean and carbon cycle models with a simpler model, MAGICC6 – Part 1: Model description and calibration. Atmos. Chem. Phys. 11, 1417–1456 (2011).

    Article  Google Scholar 

  12. IPCC Climate Change 2014: Synthesis Report (eds Core Writing Team, Pachauri, R. K. & Meyer L. A.) (IPCC, 2015).

  13. Peters, G. P. Beyond carbon budgets. Nat. Geosci. 11, 378–380 (2018).

    Article  Google Scholar 

  14. Rogelj, J. et al. Differences between carbon budget estimates unraveled. Nat. Clim. Change 6, 245–252 (2016).

    Article  Google Scholar 

  15. Haustein, K. et al. A real-time global warming index. Sci. Rep. 7, 15417 (2017).

    Article  Google Scholar 

  16. Allen, M. R. & Stocker, T. M. Impact of delay in reducing carbon dioxide emissions. Nat. Clim. Change 4, 23–26 (2014).

    Article  Google Scholar 

  17. Otto, F. E., Frame, D. J., Otto, A. & Allen, M. R. Embracing uncertainty in climate change policy. Nat. Clim. Change 5, 917–920 (2015).

    Article  Google Scholar 

  18. Matthews, H. D. et al. Estimating carbon budgets for ambitious climate targets. Curr. Clim. Change Rep. 3, 69–77 (2017).

    Article  Google Scholar 

  19. Millar, R. J. & Friedlingstein, P. The utility of the historical record for assessing the transient climate response to cumulative emissions. Phil. Trans. R. Soc. Lond. A 376, 20160449 (2018).

    Article  Google Scholar 

  20. Van Vuuren, D. P. et al. Alternative pathways to the 1.5 °C target reduce the need for negative emission technologies. Nat. Clim. Change 8, 391–397 (2018).

    Article  Google Scholar 

  21. Shindell, D. et al. Simultaneously mitigating near-term climate change and improving human health and food security. Science 335, 183–189 (2012).

    Article  Google Scholar 

  22. Wigley, T. M. L. The Kyoto Protocol: CO2, CH4 and climate implications. Geophys. Res. Lett. 25, 2285–2288 (1998).

    Article  Google Scholar 

  23. Manning, M. & Reisinger, A. Broader perspectives for comparing different greenhouse gases. Phil. Trans. R. Soc. Lond. A 369, 1891–1905 (2011).

    Article  Google Scholar 

  24. Report on the Structured Expert Dialogue of the 2013–2015 Review FCCC/SB/2015/INF.1, paragraph 39 (UNFCCC, 2015).

  25. Bindhoff, N. L. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) Ch. 10 (IPCC, Cambridge Univ. Press, Cambridge, 2013).

  26. Millar, R. J. et al. Reply to ‘Interpretations of the Paris climate target’. Nat. Geosci. 11, 222 (2018).

    Article  Google Scholar 

  27. Rhode, R. et al. A new estimate of the average Earth surface land temperature spanning 1753–2011. Geoinfor. Geostat. (2013).

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

    Article  Google Scholar 

  29. Matthews, H. D., Gillett, N. P., Stott, P. A. & Zickfeld, K. The proportionality of global warming to cumulative carbon emissions. Nature 459, 829–832 (2009).

    Article  Google Scholar 

  30. Ricke, K. L. & Caldeira, K. Maximum warming occurs about one decade after a carbon dioxide emission. Environ. Res. Lett. 9, 124002 (2014).

    Article  Google Scholar 

  31. Zickfeld, K. et al. Setting cumulative emissions targets to reduce the risk of dangerous climate change. Proc. Natl Acad. Sci. USA 106, 16129–16134 (2009).

    Article  Google Scholar 

  32. Jenkins, S. et al. Framing climate goals in terms of cumulative CO2-forcing-equivalent emissions. Geophys. Res. Lett. 45, 2795–2804 (2018).

    Article  Google Scholar 

  33. Allen, M. R. et al. A solution to the misrepresentations of CO2-equivalent emissions of short-lived climate pollutants under ambitious mitigation. npj Climate Atmos. Sci. (in the press).

  34. MacDougall, A. H., Zickfeld, K., Knutti, R. & Matthews, H. D. Sensitivity of carbon budgets to permafrost carbon feedbacks and non-CO2 forcings. Environ. Res. Lett. 10, 125003 (2015).

    Article  Google Scholar 

  35. Millar, R. J., Nicholls, Z., Friedlingstein, P. & Allen, M. R. A modified impulse-response representation of the global near-surface air temperature and atmospheric concentration response to carbon dioxide emissions. Atmos. Chem. Phys. 17, 7213–7228 (2017).

    Article  Google Scholar 

  36. Clarke, L. et al. in Climate Change 2014: Mitigation of Climate Change (eds Edenhofer, O. et al.) Ch. 6 (IPCC, Cambridge Univ. Press, Cambridge, 2014).

  37. Kirtman, B. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) Ch. 11 (IPCC, Cambridge Univ. Press, Cambridge, 2013).

  38. Morice, C. P., Kennedy, J. J., Rayner, N. A. & Jones, P. D. Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: The HadCRUT4 data set. J. Geophys. Res. Atmos. 117, D08101 (2012).

    Article  Google Scholar 

  39. Foster, G. & Rahmstorf, S. Global temperature evolution 1979–2010. Environ. Res. Lett. 6, 044022 (2011).

    Article  Google Scholar 

  40. McGuire, A. D. et al. Dependence of the evolution of carbon dynamics in the northern permafrost region on the trajectory of climate change. Proc. Natl Acad. Sci. USA 115, 3882–3887 (2018).

    Article  Google Scholar 

  41. Ehlert, D. & Zickfeld, K. What determines the warming commitment after cessation of CO2 emissions? Environ. Res. Lett. 12, 015002 (2017).

    Article  Google Scholar 

  42. Myhre, G. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) Ch. 8 (IPCC, Cambridge Univ. Press, Cambridge, 2013).

  43. Le Queré, C. et al. Global carbon budget 2016. Earth Syst. Sci. Data 8, 605–649 (2016).

    Article  Google Scholar 

  44. Hoesly, R. M. et al. Historical (1750–2014) anthropogenic emissions of reactive gases and aerosols from the Community Emissions Data System (CEDS). Geosci. Model Dev. 11, 369–408 (2018).

    Article  Google Scholar 

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We would like to thank P. Forster for proving up-to-date forcing series for our analysis, and J. Rogelj for his helpful comments and advice on this study. N.J.L., S.J. and E.G. were supported by the NERC DTP, MOAP and ECI student placement schemes; R.J.M. and M.R.A. are supported by the Oxford Martin School and ECI; and K.H. is supported by the World Weather Attribution Project. We acknowledge the WCRP’s Working Group on Coupled Modelling and thank the climate modelling groups for producing and making available their model output.

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N.J.L., R.J.M. and M.R.A. conceived the study; N.J.L. produced all figures except Supplementary Fig. 4; K.H. provided updated estimates of human-induced warming and performed the analysis generating Supplementary Fig. 4; S.J. contributed code for the calculation of CO2-fe emissions and E.G. helped with the analysis and checking of the IIASA MAGICC simulations. N.J.L. and M.R.A. wrote the paper, with all authors contributing.

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Correspondence to Nicholas J. Leach.

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Leach, N.J., Millar, R.J., Haustein, K. et al. Current level and rate of warming determine emissions budgets under ambitious mitigation. Nature Geosci 11, 574–579 (2018).

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