Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Sensitivity of climate to cumulative carbon emissions due to compensation of ocean heat and carbon uptake

Nature Geoscience volume 8, pages 29–34 (2015)Cite this article

Subjects

Abstract

Climate model experiments reveal that transient global warming is nearly proportional to cumulative carbon emissions on multi-decadal to centennial timescales1,2,3,4,5. However, it is not quantitatively understood how this near-linear dependence between warming and cumulative carbon emissions arises in transient climate simulations6,7. Here, we present a theoretically derived equation of the dependence of global warming on cumulative carbon emissions over time. For an atmosphere–ocean system, our analysis identifies a surface warming response to cumulative carbon emissions of 1.5 ± 0.7 K for every 1,000 Pg of carbon emitted. This surface warming response is reduced by typically 10–20% by the end of the century and beyond. The climate response remains nearly constant on multi-decadal to centennial timescales as a result of partially opposing effects of oceanic uptake of heat and carbon8. The resulting warming then becomes proportional to cumulative carbon emissions after many centuries, as noted earlier9. When we incorporate estimates of terrestrial carbon uptake10, the surface warming response is reduced to 1.1 ± 0.5 K for every 1,000 Pg of carbon emitted, but this modification is unlikely to significantly affect how the climate response changes over time. We suggest that our theoretical framework may be used to diagnose the global warming response in climate models and mechanistically understand the differences between their projections.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Global surface warming versus cumulative carbon emissions.
Figure 2: Cumulative carbon emissions, cumulative ocean carbon undersaturation and Δln CO2 over time in our coupled atmosphere–ocean model (GENIE) for six twenty-first century emission scenarios23.
Figure 3: Thermal and carbon response to cumulative carbon emissions over 3,000 years for six emission scenarios23 in our coupled atmosphere–ocean model.
Figure 4: A schematic depiction of the ocean thermal and carbon response to anthropogenic carbon emissions.

Similar content being viewed by others

References

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Zickfield, K., Eby, M., Matthews, H. D. & Weaver, A. J. Setting cumulative emissions targets to reduce the risk of dangerous climate change. Proc. Natl Acad. Sci. USA 106, 16129–16134 (2009).

    Article  Google Scholar 

  4. Zickfield, K. et al. Long-term climate change commitment and reversibility: An EMIC intercomparison. J. Clim. 26, 5782–5809 (2013).

    Article  Google Scholar 

  5. Gillet, N. P., Arora, V. K., Matthews, D. & Allen, M. R. Constraining the ratio of global warming to cumulative CO2 emissions using CMIP5 simulations. J. Clim. 26, 6844–6858 (2013).

    Article  Google Scholar 

  6. IPCC, Climate Change 2013: The Physical Science Basis (eds Stocker, T. F.et al.) (Cambridge Univ. Press, 2013).

    Google Scholar 

  7. Collins, M. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F.et al.) Ch. 12 (IPCC, Cambridge Univ. Press, 2013).

    Google Scholar 

  8. Solomon, S., Plattner, G-K., Knutti, R. & Friedlingstein, P. Irreversible climate change due to carbon dioxide emissions. Proc. Natl Acad. Sci. USA 106, 1704–1709 (2009).

    Article  Google Scholar 

  9. Williams, R. G., Goodwin, P., Ridgwell, A. & Woodworth, P. L. How warming and steric sea level rise relate to cumulative carbon emissions. Geophys. Res. Lett. 39, L19715 (2012).

    Google Scholar 

  10. Friedlingstein, P. et al. Climate-carbon cycle feedback analysis: Result from the C4MIP model intercomparison. J. Clim. 19, 3337–3353 (2006).

    Article  Google Scholar 

  11. Winton, M., Takahashi, K. & Held, I. Importance of ocean heat uptake efficacy to transient climate change. J. Clim. 23, 2333–2344 (2010).

    Article  Google Scholar 

  12. Knutti, R. & Hergerl, G. C. The equilibrium sensitivity of the Earth’s temperature to radiation changes. Nature Geosci. 1, 735–743 (2008).

    Article  Google Scholar 

  13. Church, J. A. et al. Revisiting the Earth’s sea-level and energy budgets from 1961 to 2008. Geophys. Res. Lett. 38, L18601 (2011).

    Article  Google Scholar 

  14. Myhre, G., Highwood, E. J., Shine, K. P. & Stordal, F. New estimates of radiative forcing due to well mixed greenhouse gases. Geophys. Res. Lett. 25, 2715–2718 (1998).

    Article  Google Scholar 

  15. Pierrehumbert, R. T. Short-lived climate pollution. Annu. Rev. Earth Planet. Sci. 42, 341–379 (2014).

    Article  Google Scholar 

  16. Ciais, P. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F.et al.) Ch. 6 (IPCC, Cambridge Univ. Press, 2013).

    Google Scholar 

  17. Le Quéré, C. et al. Trends in the sources and sinks of carbon dioxide. Nature Geosci. 2, 831–836 (2009).

    Article  Google Scholar 

  18. Goodwin, P., Williams, R. G., Follows, M. J. & Dutkiewicz, S. Ocean-atmosphere partitioning of anthropogenic carbon dioxide on centennial timescales. Glob. Biogeochem. Cycles 21, GB1014 (2007).

    Article  Google Scholar 

  19. Goodwin, P., Williams, R. G., Ridgwell, A. & Follows, M. J. Climate sensitivity to the carbon cycle modulated by past and future changes to ocean chemistry. Nature Geosci. 2, 145–150 (2009).

    Article  Google Scholar 

  20. Zickfield, K., Arora, V. K. & Gillett, N. P. Is the climate response to CO2 emissions path dependent? Geophys. Res. Lett. 39, L05703 (2012).

    Google Scholar 

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

    Google Scholar 

  22. Ridgwell, A. et al. Marine geochemical data assimilation in an efficient Earth System Model of global biogeochemical cycling. Biogeosciences 4, 87–104 (2007).

    Article  Google Scholar 

  23. IPCC, Report on Emissions Scenarios (eds Nakicenovic, N. & Swart, R.) (Cambridge Univ. Press, 2000).

    Google Scholar 

  24. Krasting, J. P., Dunne, J. P., Shevliakova, E. & Stouffer, R. J. Trajectory sensitivity of the transient climate response to cumulative carbon emissions. Geophys. Res. Lett. 41, 2520–2527 (2014).

    Article  Google Scholar 

  25. Sabine, C. L. et al. The oceanic sink for anthropogenic CO2 . Science 305, 367–371 (2004).

    Article  Google Scholar 

  26. Li, C., von Storch, J-S. & Marotzke, J. Deep-ocean heat uptake and equilibrium climate response. Clim. Dynam. 40, 1071–1086 (2013).

    Article  Google Scholar 

  27. Frölicher, T. L., Winton, M. & Sarmiento, J. L. Continued global warming after CO2 emissions stoppage. Nature Clim. Change 4, 40–44 (2014).

    Article  Google Scholar 

  28. Winton, W., Griffies, S. M., Samuels, B. L., Sarmiento, J. L. & Frölicher, T. L. Connecting changing ocean circulation with changing climate. J. Clim. 26, 2268–2278 (2013).

    Article  Google Scholar 

  29. Goodwin, P. & Lenton, T. M. Quantifying the feedback between ocean heating and CO2 solubility as an equivalent carbon emission. Geophys. Res. Lett. 36, L15609 (2009).

    Article  Google Scholar 

  30. Archer, D. et al. Atmospheric lifetime of fossil-fuel carbon dioxide. Annu. Rev. Earth Planet. Sci. 37, 117–134 (2009).

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by UK NERC Postdoctoral Fellowship NE/I020725/2 and NERC grants NE/K012789/1 and NE/H017453/1.

Author information

Authors and Affiliations

  1. Department of Ocean and Earth Sciences, National Oceanography Centre Southampton, University of Southampton, Southampton SO14 3ZH, UK

    Philip Goodwin

  2. Department of Earth, Ocean and Ecological Sciences, School of Environmental Science, University of Liverpool, Liverpool L69 3GP, UK

    Richard G. Williams

  3. School of Geographical Science, University of Bristol, Bristol BS8 1SS, UK

    Andy Ridgwell

Authors
  1. Philip Goodwin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard G. Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andy Ridgwell
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

P.G. and R.G.W. provided the theory, with P.G. deriving the equations for the transient adjustment. A.R. conducted the supporting numerical modelling with GENIE. P.G. and R.G.W. led the writing of this study, and contributed equally, and A.R. provided comments on the manuscript.

Corresponding authors

Correspondence to Philip Goodwin or Richard G. Williams.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 571 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goodwin, P., Williams, R. & Ridgwell, A. Sensitivity of climate to cumulative carbon emissions due to compensation of ocean heat and carbon uptake. Nature Geosci 8, 29–34 (2015). https://doi.org/10.1038/ngeo2304

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/ngeo2304

This article is cited by

Search

Advanced search

Quick links

Nature Briefing Microbiology

Sign up for the Nature Briefing: Microbiology newsletter — what matters in microbiology research, free to your inbox weekly.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing: Microbiology