Causal feedbacks in climate change

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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.

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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


  1. Environmental Sciences Group, Wageningen University, NL-6700 AA Wageningen, the Netherlands

    • Egbert H. van Nes
    •  & Marten Scheffer
  2. Max Planck Institute for Meteorology, Bundesstraße 53, 20146 Hamburg, Hamburg, Germany

    • Victor Brovkin
  3. Earth System Science Group, College of Life and Environmental Sciences, University of Exeter, Exeter EX4 4QE, UK

    • Timothy M. Lenton
  4. Scripps Institution of Oceanography, University of California, California 92093, USA

    • Hao Ye
    • , Ethan Deyle
    •  & George Sugihara


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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.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Egbert H. van Nes or George Sugihara.

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