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Emergent constraints on Earth’s transient and equilibrium response to doubled CO2 from post-1970s global warming


Future global warming is determined by both greenhouse gas emission pathways and Earth’s transient and equilibrium climate response to doubled atmospheric CO2. Energy-balance inference from the instrumental record typically yields central estimates for the transient response of around 1.3 K and the equilibrium response of 1.5–2.0 K, which is at the lower end of those from contemporary climate models. Uncertainty arises primarily from poorly known aerosol-induced cooling since the early industrialization era and a temporary cooling induced by evolving sea surface temperature patterns. Here we present an emergent constraint on post-1970s warming, taking advantage of the weakly varying aerosol cooling during this period. We derive a relationship between the transient response and the post-1970s warming in Coupled Model Intercomparison Project Phase 5 (CMIP5) models. We thereby constrain, with the observations, the transient response to 1.67 K (1.17–2.16 K, 5–95th percentiles). This is a 20% increase relative to energy-balance inference stemming from previously neglected upper-ocean energy storage. For the equilibrium climate sensitivity we obtain a best estimate of 2.83 K (1.72–4.12 K) contingent on the temporary pattern effects exhibited by climate models. If the real world’s surface temperature pattern effects are substantially stronger, then the upper-bound equilibrium sensitivity may be higher than found here.

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Fig. 1: Emergent constraints based on the 1970–2005 warming.
Fig. 2: Probability distributions of the TCR.
Fig. 3: Comparison of the MPI-ESM-1.2-highECS model with observations.
Fig. 4: Probability distributions of the ECS.
Fig. 5: The impact of pattern effects.

Data availability

CMIP5 data can be accessed through ESGF nodes. HadCRUT4 data are provided by the UK Met Office Hadley Centre. The NOAA/OAR/ESRL PSD dataset website provided the NOAA GlobalTemp dataset as well as the GISTEMP dataset. BEST was downloaded from the Berkeley Earth website. The Cowtan and Way 2.0 dataset is available from the author’s website ( Forcing data comes from the IPCC AR5 WG1 report24.

Code availability

An archive with scripts to conduct the data download, preprocess the data, analyse them and obtain the figures supporting this study is archived by the Max Planck Institute for Meteorology and can be obtained by contacting either the corresponding author or


  1. 1.

    Hawkins, E. & Sutton, R. The potential to narrow uncertainty in regional climate predictions. Bull. Am. Meteorol. Soc. 90, 1095–1107 (2009).

    Article  Google Scholar 

  2. 2.

    Grose, M. R., Gregory, J., Colman, R. & Andrews, T. What climate sensitivity index is most useful for projections? Geophys. Res. Lett. 45, 1559–1566 (2018).

    Article  Google Scholar 

  3. 3.

    Rohling, E. J. et al. Making sense of palaeoclimate sensitivity. Nature 491, 683–691 (2012).

    Article  Google Scholar 

  4. 4.

    Gregory, J. M., Stouffer, R. J., Raper, S. C. B., Stott, P. A. & Rayner, N. A. An observationally based estimate of the climate sensitivity. J. Clim. 15, 3117–3121 (2002).

    Article  Google Scholar 

  5. 5.

    Otto, A. et al. Energy budget constraints on climate response. Nat. Geosci. 6, 415–416 (2013).

    Article  Google Scholar 

  6. 6.

    Lewis, N. & Curry, J. A. The implications for climate sensitivity of AR5 forcing and heat uptake estimates. Clim. Dynam. 45, 1009–1023 (2014).

    Article  Google Scholar 

  7. 7.

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

    Article  Google Scholar 

  8. 8.

    Johnson, G. C., Lyman, J. M. & Loeb, N. G. Improving estimates of Earth’s energy imbalance. Nat. Clim. Change 6, 639–640 (2016).

    Article  Google Scholar 

  9. 9.

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

    Article  Google Scholar 

  10. 10.

    Held, I. M. et al. Probing the fast and slow components of global warming by returning abruptly to preindustrial forcing. J. Clim. 23, 2418–2427 (2010).

    Article  Google Scholar 

  11. 11.

    Zhou, C., Zelinka, M. D. & Klein, S. A. Impact of decadal cloud variations on the Earth’s energy budget. Nat. Geosci. 9, 871–874 (2016).

    Article  Google Scholar 

  12. 12.

    Armour, K. C. Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks. Nat. Clim. Change 7, 331–335 (2017).

    Article  Google Scholar 

  13. 13.

    Andrews, T. et al. Accounting for changing temperature patterns increases historical estimates of climate sensitivity. Geophys. Res. Lett. 45, 8490–8499 (2018).

    Article  Google Scholar 

  14. 14.

    Kiehl, J. Twentieth century climate model response and climate sensitivity. Geophys. Res. Lett. 34, L22710 (2007).

    Article  Google Scholar 

  15. 15.

    Smith, S. J. et al. Anthropogenic sulfur dioxide emissions: 1850–2005. Atmos. Chem. Phys. 11, 1101–1116 (2011).

    Article  Google Scholar 

  16. 16.

    Stevens, B. Rethinking the lower bound on aerosol radiative forcing. J. Clim. 28, 4794–4819 (2015).

    Article  Google Scholar 

  17. 17.

    Fiedler, S., Stevens, B. & Mauritsen, T. On the sensitivity of anthropogenic aerosol forcing to model-internal variability and parameterizing a twomey effect. J. Adv. Model. Earth Syst. 9, 1325–1341 (2017).

    Article  Google Scholar 

  18. 18.

    Gregory, J. M. & Forster, P. M. Transient climate response estimated from radiative forcing and observed temperature change. J. Geophys. Res. Atmos. 113, D23105 (2008).

    Article  Google Scholar 

  19. 19.

    Bengtsson, L. & Schwartz, S. E. Determination of a lower bound on Earth’s climate sensitivity. Tellus B 65, 21533 (2013).

    Article  Google Scholar 

  20. 20.

    Forster, P. M. et al. Evaluating adjusted forcing and model spread for historical and future scenarios in the CMIP5 generation of climate models. J. Geophys. Res. Atmos. 118, 1139–1150 (2013).

    Article  Google Scholar 

  21. 21.

    Mauritsen, T. et al. Developments in the MPI-M earth system model version 1.2 (MPI-ESM1.2) and its response to increasing CO2. J. Adv. Model. Earth Syst. 11, 998–1038 (2018).

    Article  Google Scholar 

  22. 22.

    Gregory, J. M., Andrews, T. & Good, P. The inconstancy of the transient climate response parameter under increasing CO2. Phil. Trans. R. Soc. A 373, 20140417 (2015).

    Article  Google Scholar 

  23. 23.

    Gregory, J. M., Andrews, T., Good, P., Mauritsen, T. & Forster, P. M. Small global-mean cooling due to volcanic radiative forcing. Clim. Dynam. 47, 3979–3991 (2016).

    Article  Google Scholar 

  24. 24.

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

  25. 25.

    Shindell, D. T. et al. Radiative forcing in the ACCMIP historical and future climate simulations. Atmos. Chem. Phys. 13, 2939–2974 (2011).

    Article  Google Scholar 

  26. 26.

    Regayre, L. A. et al. Uncertainty in the magnitude of aerosol-cloud radiative forcing over recent decades. Geophys. Res. Lett. 41, 9040–9049 (2014).

    Article  Google Scholar 

  27. 27.

    Zhao, M. et al. The gfdl global atmosphere and land model am4.0/lm4.0: 1. simulation characteristics with prescribed SSTs. J. Adv. Model. Earth Syst. 10, 691–734 (2018).

    Article  Google Scholar 

  28. 28.

    Hansen, J. et al. Climate response times: Dependence on climate sensitivity and ocean mixing. Science 229, 857–859 (1985).

    Article  Google Scholar 

  29. 29.

    Geoffroy, O. et al. Transient climate response in a two-layer energy-balance model. part ii: representation of the efficacy of deep-ocean heat uptake and validation for CMIP5 AOGCMs. J. Clim. 26, 1859–1876 (2013).

    Article  Google Scholar 

  30. 30.

    Morice, C. P., Kennedy, J. J. & Rayner, N. A. 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 

  31. 31.

    Vose, R. S. et al. NOAA’s merged land–ocean surface temperature analysis. Bull. Am. Meteorol. Soc. 93, 1677–1685 (2012).

    Article  Google Scholar 

  32. 32.

    Hansen, J. E., Ruedy, R. A., Sato, M. & Lo, K.-W. K. Global surface temperature change. Rev. Geophys. 48, RG4004 (2010).

    Article  Google Scholar 

  33. 33.

    Rohde, R. et al. A new estimate of the average earth surface land temperature spanning 1753 to 2011. Geoinform. Geostat. 1, 1 (2013).

    Google Scholar 

  34. 34.

    Cowtan, K. & Way, R. G. Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends. Q. J. R. Meteorol. Soc. 140, 1935–1944 (2014).

    Article  Google Scholar 

  35. 35.

    Andrews, T., Gregory, J. M., Webb, M. J. & Taylor, K. E. Forcing, feedbacks and climate sensitivity in CMIP5 coupled atmosphere-ocean climate models. Geophys. Res. Lett. 39, L09712 (2012).

    Google Scholar 

  36. 36.

    Jones, C. et al. (eds) in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) Annex II (IPCC, Cambridge Univ. Press, 2013).

  37. 37.

    Boggs, P. T., Byrd, R. H. & Schnabel, R. B. A Stable and efficient algorithm for nonlinear orthogonal distance regression. SIAM J. Sci. Stat. Comput. 8, 1052–1078 (1987).

    Article  Google Scholar 

  38. 38.

    Sherwood, S. C., Bony, S. & Dufresne, J.-L. Spread in model climate sensitivity traced to atmospheric convective mixing. Nature 505, 37–42 (2014).

    Article  Google Scholar 

  39. 39.

    Brient, F. et al. Shallowness of tropical low clouds as a predictor of climate models’ response to warming. Clim. Dynam. 47, 433–449 (2016).

    Article  Google Scholar 

  40. 40.

    Stevens, B. et al. MACv2-SP: a parameterization of anthropogenic aerosol optical properties and an associated Twomey effect for use in CMIP6. Geosci. Model Dev. 10, 433–452 (2017).

    Article  Google Scholar 

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D.J.-d.-l.-C. and T.M. were supported by the Max-Planck-Gesellschaft, and T.M. received funding from European Research Council Consolidator Grant No. 770765 and European Union Horizon 2020 project no. 820829. The study benefitted from comments and input from K. Armour, S. Bühler, A. Dessler, S. Fiedler, P. Forster, R. Pincus, B. Stevens and M. Watanabe. Computational resources were made available by Deutsches Klimarechenzentrum through support from Bundesministerium für Bildung und Forschung.

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D.J.-d.-l.-C. and T.M. developed the methodology and wrote the manuscript.

Corresponding author

Correspondence to Diego Jiménez-de-la-Cuesta.

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The authors declare no competing interests.

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Jiménez-de-la-Cuesta, D., Mauritsen, T. Emergent constraints on Earth’s transient and equilibrium response to doubled CO2 from post-1970s global warming. Nat. Geosci. 12, 902–905 (2019).

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