Skip to main content

Thank you for visiting 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.

Causal feedbacks in climate change



The statistical association between temperature and greenhouse gases over glacial cycles is well documented1, but causality behind this correlation remains difficult to extract directly from the data. A time lag of CO2 behind Antarctic temperature—originally thought to hint at a driving role for temperature2,3—is absent4,5 at the last deglaciation, but recently confirmed at the last ice age inception6 and the end of the earlier termination II (ref. 7). We show that such variable time lags are typical for complex nonlinear systems such as the climate, prohibiting straightforward use of correlation lags to infer causation. However, an insight from dynamical systems theory8 now allows us to circumvent the classical challenges of unravelling causation from multivariate time series. We build on this insight to demonstrate directly from ice-core data that, over glacial–interglacial timescales, climate dynamics are largely driven by internal Earth system mechanisms, including a marked positive feedback effect from temperature variability on greenhouse-gas concentrations.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



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

Figure 1: Causation inferred from time series of insolation, temperature and GHGs.
Figure 2: Correlation of cross-mapped versus observed values as a function of the length of the time series.
Figure 3: Time displacements maximizing CCM skill corresponding to causal relationships indicated above the bars.


  1. Petit, J. R. et al. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature 399, 429–436 (1999).

    Article  CAS  Google Scholar 

  2. Fischer, H., Wahlen, M., Smith, J., Mastroianni, D. & Deck, B. Ice core records of atmospheric CO2 around the last three glacial terminations. Science 283, 1712–1714 (1999).

    Article  CAS  Google Scholar 

  3. Shackleton, N. J. The 100,000-year ice-age cycle identified and found to lag temperature, carbon dioxide, and orbital eccentricity. Science 289, 1897–1902 (2000).

    Article  CAS  Google Scholar 

  4. Pedro, J. B., Rasmussen, S. O. & Van Ommen, T. D. Tightened constraints on the time-lag between Antarctic temperature and CO2 during the last deglaciation. Clim. Past 8, 1213–1221 (2012).

    Article  Google Scholar 

  5. Shakun, J. D. et al. Global warming preceded by increasing carbon dioxide concentrations during the last deglaciation. Nature 484, 49–54 (2012).

    Article  CAS  Google Scholar 

  6. Landais, A. et al. Two-phase change in CO2, Antarctic temperature and global climate during Termination II. Nature Geosci. 6, 1062–1065 (2013).

    Article  CAS  Google Scholar 

  7. Schneider, R., Schmitt, J., Köhler, P., Joos, F. & Fischer, H. A reconstruction of atmospheric carbon dioxide and its stable carbon isotopic composition from the penultimate glacial maximum to the last glacial inception. Clim. Past 9, 2507–2523 (2013).

    Article  Google Scholar 

  8. Sugihara, G. et al. Detecting causality in complex ecosystems. Science 338, 496–500 (2012).

    Article  CAS  Google Scholar 

  9. Le Treut, H. et al. in Climate Change 2007: The Physical Science Basis (eds Solomon, S. et al.) 93–127 (IPCC, Cambridge Univ. Press, 2007).

    Google Scholar 

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

    Article  Google Scholar 

  11. Cox, P. M., Betts, R. A., Jones, C. D., Spall, S. A. & Totterdell, I. J. Acceleration of global warming due to carbon-cycle feedbacks in a coupled climate model. Nature 408, 184–187 (2000).

    Article  CAS  Google Scholar 

  12. Friedlingstein, P., Dufresne, J. L., Cox, P. M. & Rayner, P. How positive is the feedback between climate change and the carbon cycle? Tellus B 55, 692–700 (2003).

    Article  Google Scholar 

  13. Cramer, W. et al. Global response of terrestrial ecosystem structure and function to CO2 and climate change: Results from six dynamic global vegetation models. Glob. Change Biol. 7, 357–373 (2001).

    Article  Google Scholar 

  14. Schuur, E. A. G. et al. The effect of permafrost thaw on old carbon release and net carbon exchange from tundra. Nature 459, 556–559 (2009).

    Article  CAS  Google Scholar 

  15. Archer, D. et al. The importance of ocean temperature to global biogeochemistry. Earth Planet. Sci. Lett. 222, 333–348 (2004).

    Article  CAS  Google Scholar 

  16. Archer, D., Buffett, B. & Brovkin, V. Ocean methane hydrates as a slow tipping point in the global carbon cycle. Proc. Natl Acad. Sci. USA 106, 20596–20601 (2009).

    Article  CAS  Google Scholar 

  17. Friedlingstein, P. et al. Positive feedback between future climate change and the carbon cycle. Geophys. Res. Lett. 28, 1543–1546 (2001).

    Article  CAS  Google Scholar 

  18. Prentice, I. C. et al. in Climate Change 2001: The Scientific Basis (eds Houghton, J. T. et al.) 183–238 (IPCC, Cambridge Univ. Press, 2001).

    Google Scholar 

  19. Hansen, J. et al. Climate change and trace gases. Phil. Trans. R. Soc. A 365, 1925–1954 (2007).

    Article  CAS  Google Scholar 

  20. Rosen, J. L. et al. An ice core record of near-synchronous global climate changes at the Bølling transition. Nature Geosci. 7, 459–463 (2014).

    Article  CAS  Google Scholar 

  21. Parrenin, F. et al. Synchronous change of atmospheric CO2 and Antarctic temperature during the last deglacial warming. Science 339, 1060–1063 (2013).

    Article  CAS  Google Scholar 

  22. Takens, F. in Symposium on Dynamical Systems and Turbulence (eds Young, L. S. & Rand, D. A.) 366–381 (Lecture Notes in Mathematics, Springer, 1981).

    Google Scholar 

  23. Deyle, E. R. & Sugihara, G. Generalized theorems for nonlinear state space reconstruction. PLoS ONE 6, e18295 (2011).

    Article  CAS  Google Scholar 

  24. Loulergue, L. et al. Orbital and millennial-scale features of atmospheric CH4 over the past 800,000 years. Nature 453, 383–386 (2008).

    Article  CAS  Google Scholar 

  25. Lüthi, D. et al. High-resolution carbon dioxide concentration record 650,000–800,000 years before present. Nature 453, 379–382 (2008).

    Article  Google Scholar 

  26. Hays, J. D., Imbrie, J. & Shackleton, N. J. Variations in the earth’s orbit: Pacemaker of the ice ages. Science 194, 1121–1132 (1976).

    Article  CAS  Google Scholar 

  27. Wolff, E. W. et al. Changes in environment over the last 800,000 years from chemical analysis of the EPICA Dome C ice core. Quat. Sci. Rev. 29, 285–295 (2010).

    Article  Google Scholar 

  28. Berger, A. & Loutre, M. F. Insolation values for the climate of the last 10 million years. Quat. Sci. Rev. 10, 297–317 (1991).

    Article  Google Scholar 

  29. Sugihara, G. & May, R. M. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734–741 (1990).

    Article  CAS  Google Scholar 

  30. Ebisuzaki, W. A method to estimate the statistical significance of a correlation when the data are serially correlated. J. Clim. 10, 2147–2153 (1997).

    Article  Google Scholar 

Download references


M.S. and E.H.v.N. are supported by an ERC advanced grant. This work was carried out under the program of the Netherlands Earth System Science Centre (NESSC). T.M.L. is supported by a Royal Society Wolfson Research Merit Award and the European Commission (ENB.2013.6.1-3) HELIX project. G.S. and H.Y. were supported by National Science Foundation (Grant No. DEB-1020372). E.D. and H.Y. are supported by National Science Foundation Graduate Research Fellowships and E.D. also by the Environmental Protection Agency Science to Achieve Results Fellowship. G.S. was further supported by NSF-NOAA Comparative Analysis of Marine Ecosystem Organization (CAMEO) program Grant NA08OAR4320894/CAMEO, by the Sugihara Family Trust, the Deutsche Bank-Jameson Complexity Studies Fund, the McQuown Chair in Natural Science, and DoD/SERDP.

Author information

Authors and Affiliations



M.S. and E.H.v.N. conceived the research. All authors contributed to the design of the research. E.H.v.N. and H.Y. analysed the data. All authors contributed to writing the manuscript.

Corresponding authors

Correspondence to Egbert H. van Nes or George Sugihara.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

van Nes, E., Scheffer, M., Brovkin, V. et al. Causal feedbacks in climate change. Nature Clim Change 5, 445–448 (2015).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

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