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.

Progressing emergent constraints on future climate change


In recent years, an evaluation technique for Earth System Models (ESMs) has arisen—emergent constraints (ECs)—which rely on strong statistical relationships between aspects of current climate and future change across an ESM ensemble. Combining the EC relationship with observations could reduce uncertainty surrounding future change. Here, we articulate a framework to assess ECs, and provide indicators whereby a proposed EC may move from a strong statistical relationship to confirmation. The primary indicators are verified mechanisms and out-of-sample testing. Confirmed ECs have the potential to improve ESMs by focusing attention on the variables most relevant to climate projections. Looking forward, there may be undiscovered ECs for extremes and teleconnections, and ECs may help identify climate system tipping points.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: An illustration of the relationship between the emergent constraint approach and conventional climate model evaluation.
Fig. 2: Emergent relationships for two ECs relating to physical and biogeochemical components of the climate system.
Fig. 3: Illustration of the confirmation process for ECs.
Fig. 4: Four proposed ECs used to constrain Arctic sea ice projections in AR5.


  1. 1.

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

  2. 2.

    Taylor, K. E., Stouffer, R. J. & Meehl, G. A. An overview of CMIP5 and the experiment design. B. Am. Meteorol. Soc. 93, 485–498 (2012).

    Article  Google Scholar 

  3. 3.

    Hall, A. & Manabe, S. The role of water vapor feedback in unperturbed climate variability and global warming. J. Climate 12, 2327–2346 (1999).

    Article  Google Scholar 

  4. 4.

    Soden, B. J., Wetherald, R. T., Stenchikov, G. L. & Robock, A. Global cooling after the eruption of Mount Pinatubo: a test of climate feedback by water vapor. Science 296, 727–730 (2002).

    CAS  Article  Google Scholar 

  5. 5.

    Rind, D., Healy, R., Parkinson, C. & Martinson, D. The pole of sea-ice in 2x CO2 climate model sensitivity part 1: the total influence of sea-ice thickness and extent. J. Climate 8, 449–463 (1995).

    Article  Google Scholar 

  6. 6.

    Rind, D., Healy, R., Parkinson, C. & Martinson, D. The role of sea ice in 2xCO(2) climate model sensitivity part 2: hemispheric dependencies. Geophys. Res. Lett. 24, 1491–1494 (1997).

    CAS  Article  Google Scholar 

  7. 7.

    Ivanova, D. P., Gleckler, P. J., Taylor, K. E., Durack, P. J. & Marvel, K. D. Moving beyond the total sea ice extent in gauging model biases. J. Climate 29, 8965–8987 (2016).

    Article  Google Scholar 

  8. 8.

    Parkinson, C. L., Vinnikov, K. Y. & Cavalieri, D. J. Evaluation of the simulation of the annual cycle of Arctic and Antarctic sea ice coverages by 11 major global climate models. J. Geophys. Res. Oceans 111, 14 (2006).

    Google Scholar 

  9. 9.

    Gleckler, P. J., Taylor, K. E. & Doutriaux, C. Performance metrics for climate models. J. Geophys. Res. Atm. 113, 20 (2008).

    Article  Google Scholar 

  10. 10.

    Hall, A. & Qu, X. Using the current seasonal cycle to constrain snow albedo feedback in future climate change. Geophys. Res. Lett. 33, L03502 (2006).

    Google Scholar 

  11. 11.

    Cox, P. M. et al. Sensitivity of tropical carbon to climate change constrained by carbon dioxide variability. Nature 494, 341–344 (2013).

    CAS  Article  Google Scholar 

  12. 12.

    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).

    CAS  Article  Google Scholar 

  13. 13.

    Cox, P. M. et al. Amazonian forest dieback under climate-carbon cycle projections for the 21st century. Theor. Appl. Climatol. 78, 137–156 (2004).

    Article  Google Scholar 

  14. 14.

    Caldwell, P. M. et al. Statistical significance of climate sensitivity predictors obtained by data mining. Geophys. Res. Lett. 41, 1803–1808 (2014). This paper demonstrates that statistically significant, but physically meaningless, emergent relationships can be found in ESM ensembles, illustrating an important potential pitfall of the EC technique.

    Article  Google Scholar 

  15. 15.

    Kubo, R. The fluctuation-dissipation theorem. Rep. Prog. Phys 20, 255–284 (1966).

    Article  Google Scholar 

  16. 16.

    Lorenz, E. N. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963).

    Article  Google Scholar 

  17. 17.

    Kirk-Davidoff, D. B. On the diagnosis of climate sensitivity using observations of fluctuations. Atmos. Chem. Phys. 9, 813–822 (2009).

    CAS  Article  Google Scholar 

  18. 18.

    Majda, A. J., Abramov, R. & Gershgorin, B. High skill in low-frequency climate response through fluctuation dissipation theorems despite structural instability. Proc. Natl Acad. Sci. USA 107, 581–586 (2010).

    CAS  Article  Google Scholar 

  19. 19.

    Leith, C. E. Climate response and fluctuation dissipation. J. Atmos. Sci. 32, 2022–2026 (1975). The first suggestion to relate climate sensitivity to climate variability through the Fluctuation–Dissipation theorem.

    Article  Google Scholar 

  20. 20.

    Cox, P. M., Huntingford, C. & Williamson, M. S. Emergent constraint on equilibrium climate sensitivity from global temperature variability. Nature 553, 319–322 (2018). Emergent constraint on ECS from global temperature variability.

    CAS  Article  Google Scholar 

  21. 21.

    Wenzel, S., Cox, P. M., Eyring, V. & Friedlingstein, P. Emergent constraints on climate-carbon cycle feedbacks in the CMIP5 Earth system models. J. Geophys. Res. Biogeosci. 119, 794–807 (2014).

    CAS  Article  Google Scholar 

  22. 22.

    Williamson, M. S., Cox, P. M. & Nijsse, F. J. M. M. Theoretical foundation of emergent constraints: relationships between climate sensitivity and global temperature variability in conceptual models. Preprint at (2018).

  23. 23.

    Tian, B. J. Spread of model climate sensitivity linked to double-Intertropical Convergence Zone bias. Geophys. Res. Lett. 42, 4133–4141 (2015).

    Article  Google Scholar 

  24. 24.

    Gordon, N. D. & Klein, S. A. Low-cloud optical depth feedback in climate models. J. Geophys. Res. Atm. 119, 6052–6065 (2014). This is the earliest demonstration of an emergent constraint for the cloud optical-depth feedback.

    Article  Google Scholar 

  25. 25.

    Terai, C. R., Klein, S. A. & Zelinka, M. D. Constraining the low-cloud optical depth feedback at middle and high latitudes using satellite observations. J. Geophys. Res. Atm. 121, 9696–9716 (2016).

    Article  Google Scholar 

  26. 26.

    McCoy, D. T., Hartmann, D. L. & Grosvenor, D. P. Observed Southern Ocean cloud properties and shortwave reflection. Part II: phase changes and low cloud feedback. J. Climate 27, 8858–8868 (2014).

    Article  Google Scholar 

  27. 27.

    Senior, C. A. & Mitchell, J. F. B. Carbon-dioxide and climate: the impact of cloud parameterization. J. Climate 6, 393–418 (1993).

    Article  Google Scholar 

  28. 28.

    Tselioudis, G., Rossow, W. B. & Rind, D. Global patterns of cloud optical-thickness variation with temperature. J. Climate 5, 1484–1497 (1992).

    Article  Google Scholar 

  29. 29.

    Qu, X. & Hall, A. What controls the strength of snow-albedo feedback? J. Climate 20, 3971–3981 (2007). This paper documented the overwhelming similarities within ESMs between the seasonal cycle and future climate change versions of snow-albedo feedback, moving the snow-albedo feedback EC along in the confirmation process.

    Article  Google Scholar 

  30. 30.

    Qu, X. & Hall, A. On the persistent spread in snow-albedo feedback. Clim. Dynam. 42, 69–81 (2014).

    Article  Google Scholar 

  31. 31.

    Sanderson, B. M., Knutti, R. & Caldwell, P. A representative democracy to reduce interdependency in a multimodel ensemble. J. Climate 28, 5171–5194 (2015).

    Article  Google Scholar 

  32. 32.

    Annan, J. D. & Hargreaves, J. C. Reliability of the CMIP3 ensemble. Geophys. Res. Lett. 37, L02703 (2010).

    Article  Google Scholar 

  33. 33.

    Knutti, R., Masson, D. & Gettelman, A. Climate model genealogy: Generation CMIP5 and how we got there. Geophys. Res. Lett. 40, 1194–1199 (2013).

    Article  Google Scholar 

  34. 34.

    Pennell, C. & Reichler, T. On the effective number of climate models. J. Climate 24, 2358–2367 (2011).

    Article  Google Scholar 

  35. 35.

    Kamae, Y. et al. Lower-tropospheric mixing as a constraint on cloud feedback in a multiparameter multiphysics ensemble. J. Climate 29, 6259–6275 (2016).

    Article  Google Scholar 

  36. 36.

    Wagman, B. M. & Jackson, C. S. A test of emergent constraints on cloud feedback and climate sensitivity using a calibrated single-model ensemble. J. Climate 31, 7515–7532 (2018).

    Article  Google Scholar 

  37. 37.

    Caldwell, P. M., Zelinka, M. D. & Klein, S. A. Evaluating emergent constraints on equilibrium climate sensitivity. J. Climate 31, 3921–3942 (2018). This paper performed comparative analysis of the multiple ECs for climate sensitivity and offered techniques to assess the independence and confirm ECs for climate sensitivity.

    Article  Google Scholar 

  38. 38.

    Ceppi, P., Hartmann, D. L. & Webb, M. J. Mechanisms of the negative shortwave cloud feedback in middle to high latitudes. J. Climate 29, 139–157 (2016). This paper performed verification of the microphysical mechanism underlying the cloud optical-depth feedback, moving the cloud optical-depth feedback EC along in the confirmation process.

    Article  Google Scholar 

  39. 39.

    Adam, O., Schneider, T., Brient, F. & Bischoff, T. Relation of the double-ITCZ bias to the atmospheric energy budget in climate models. Geophys. Res. Lett. 43, 7670–7677 (2016).

    Article  Google Scholar 

  40. 40.

    Stroeve, J., Holland, M. M., Meier, W., Scambos, T. & Serreze, M. Arctic sea ice decline: faster than forecast. Geophys. Res. Lett. 34, L029703 (2007).

    Article  Google Scholar 

  41. 41.

    Boe, J. L., Hall, A. & Qu, X. September sea-ice cover in the Arctic Ocean projected to vanish by 2100. Nat. Geosci. 2, 341–343 (2009).

    CAS  Article  Google Scholar 

  42. 42.

    Mahlstein, I. & Knutti, R. September Arctic sea ice predicted to disappear near 2 degrees C global warming above present. J. Geophys. Res. Atm. 117, 11 (2012).

    Article  Google Scholar 

  43. 43.

    Collins, M. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) Ch. 12, 1029–1136 (Cambridge Univ. Press, 2013).

  44. 44.

    IPCC: Summary for Policymakers. In Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) 1–29 (Cambridge Univ. Press, 2013).

  45. 45.

    Bowman, K. W., Cressie, N., Qu, X. & Hall, A. A hierarchical statistical framework for emergent constraints: application to snow-albedo feedback. Geophys. Res. Lett. 45, L080082 (2018).

    Article  Google Scholar 

  46. 46.

    DeAngelis, A. M., Qu, X., Zelinka, M. D. & Hall, A. An observational radiative constraint on hydrologic cycle intensification. Nature 528, 249–253 (2015).

    CAS  Article  Google Scholar 

  47. 47.

    Thackeray, C. W., Qu, X. & Hall, A. Why do models produce spread in snow albedo feedback? Geophys. Res. Lett. 45, 6223–6231 (2018). An examination of how parameterization choices within ESMs lead to different magnitudes for snow-albedo feedback, a crucial step for model improvement in this feedback process.

    Article  Google Scholar 

  48. 48.

    McWilliams, J. C. Irreducible imprecision in atmospheric and oceanic simulations. Proc. Natl Acad. Sci. USA 104, 8709–8713 (2007).

    CAS  Article  Google Scholar 

  49. 49.

    Simpson, I. R. & Polvani, L. M. Revisiting the relationship between jet position, forced response, and annular mode variability in the southern midlatitudes. Geophys. Res. Lett. 43, 2896–2903 (2016).

    Article  Google Scholar 

  50. 50.

    Kidston, J. & Gerber, E. P. Intermodel variability of the poleward shift of the austral jet stream in the CMIP3 integrations linked to biases in 20th century climatology. Geophy. Res. Lett. 37, L042873 (2010).

    Google Scholar 

  51. 51.

    Li, G., Xie, S. P., He, C. & Chen, Z. S. Western Pacific emergent constraint lowers projected increase in Indian summer monsoon rainfall. Nat. Clim. Change 7, 708–712 (2017).

    Article  Google Scholar 

  52. 52.

    Dakos, V. et al. Slowing down as an early warning signal for abrupt climate change. Proc. Natl Acad. Sci. USA 105, 14308–14312 (2008).

    CAS  Article  Google Scholar 

  53. 53.

    Lucarini, V. & Sarno, S. A statistical mechanical approach for the computation of the climatic response to general forcings. Nonlinear Proc. Geoph. 18, 7–28 (2011).

    Article  Google Scholar 

  54. 54.

    Thompson, J. M. T. & Sieber, J. Climate tipping as a noisy bifurcation: a predictive technique. IMA J. Appl. Math. 76, 27–46 (2011).

    Article  Google Scholar 

  55. 55.

    Scheffer, M. et al. Early-warning signals for critical transitions. Nature 461, 53–59 (2009).

    CAS  Article  Google Scholar 

  56. 56.

    Drijfhout, S. et al. Catalogue of abrupt shifts in Intergovernmental Panel on Climate Change climate models. Proc. Natl Acad. Sci. USA 112, E5777–E5786 (2015).

    CAS  Article  Google Scholar 

  57. 57.

    Boulton, C. A., Good, P. & Lenton, T. M. Early warning signals of simulated Amazon rainforest dieback. Theor. Ecol. 6, 373–384 (2013).

    Article  Google Scholar 

  58. 58.

    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 

  59. 59.

    Brient, F. & Schneider, T. Constraints on climate sensitivity from space-based measurements of low-cloud reflection. J. Climate 29, 5821–5835 (2016).

    Article  Google Scholar 

  60. 60.

    Zhai, C. X., Jiang, J. H. & Su, H. Long-term cloud change imprinted in seasonal cloud variation: more evidence of high climate sensitivity. Geophys. Res. Lett. 42, 8729–8737 (2015).

    Article  Google Scholar 

  61. 61.

    Trenberth, K. E. & Fasullo, J. T. Simulation of present-day and twenty-first-century energy budgets of the southern cceans. J. Climate 23, 440–454 (2010).

    Article  Google Scholar 

  62. 62.

    Fasullo, J. T. & Trenberth, K. E. A less cloudy future: the role of subtropical subsidence in climate sensitivity. Science 338, 792–794 (2012).

    CAS  Article  Google Scholar 

  63. 63.

    Su, H. et al. Weakening and strengthening structures in the Hadley Circulation change under global warming and implications for cloud response and climate sensitivity. J. Geophys. Res. Atm. 119, 5787–5805 (2014).

    Article  Google Scholar 

  64. 64.

    Huber, M., Mahlstein, I., Wild, M., Fasullo, J. & Knutti, R. Constraints on climate sensitivity from radiation patterns in climate models. J. Climate 24, 1034–1052 (2011).

    Article  Google Scholar 

  65. 65.

    Tett, S. F. B., Rowlands, D. J., Mineter, M. J. & Cartis, C. Can top-of-atmosphere radiation measurements constrain climate predictions? Part II: climate sensitivity. J. Climate 26, 9367–9383 (2013).

    Article  Google Scholar 

  66. 66.

    Knutti, R., Meehl, G. A., Allen, M. R. & Stainforth, D. A. Constraining climate sensitivity from the seasonal cycle in surface temperature. J. Climate 19, 4224–4233 (2006).

    Article  Google Scholar 

  67. 67.

    Lutsko, N. J. & Takahashi, K. What can the internal variability of CMIP5 models tell us about their climate sensitivity? J. Climate 31, 5051–5069 (2018).

    Article  Google Scholar 

  68. 68.

    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 

  69. 69.

    Lipat, B. R., Tselioudis, G., Grise, K. M. & Polvani, L. M. CMIP5 models’ shortwave cloud radiative response and climate sensitivity linked to the climatological Hadley cell extent. Geophys. Res. Lett. 44, 5739–5748 (2017).

    Article  Google Scholar 

  70. 70.

    Volodin, E. M. Relation between temperature sensitivity to doubled carbon dioxide and the distribution of clouds in current climate models. Izv. Atmos. Ocean. Phys. 44, 288–299 (2008).

    Article  Google Scholar 

  71. 71.

    Siler, N., Po-Chedley, S. & Bretherton, C. S. Variability in modelled cloud feedback tied to differences in the climatological spatial pattern of clouds. Clim. Dynam. 50, 1209–1220 (2018).

    Article  Google Scholar 

  72. 72.

    Clement, A. C., Burgman, R. & Norris, J. R. Observational and model evidence for positive low-level cloud feedback. Science 325, 460–464 (2009).

    CAS  Article  Google Scholar 

  73. 73.

    Qu, X., Hall, A., Klein, S. A. & DeAngelis, A. M. Positive tropical marine low-cloud cover feedback inferred from cloud-controlling factors. Geophys. Res. Lett. 42, 7767–7775 (2015).

    Article  Google Scholar 

  74. 74.

    O’Gorman, P. A. Sensitivity of tropical precipitation extremes to climate change. Nat. Geosci. 5, 697–700 (2012). Emergent constraint on changing hydrologic extremes.

    Article  Google Scholar 

  75. 75.

    Lin, Y. L. et al. Causes of model dry and warm bias over central US and impact on climate projections. Nat. Commun. 8, 881 (2017).

    Article  Google Scholar 

  76. 76.

    Bowman, K. W. et al. Evaluation of ACCMIP outgoing longwave radiation from tropospheric ozone using TES satellite observations. Atmos. Chem. Phys. 13, 4057–4072 (2013).

    CAS  Article  Google Scholar 

  77. 77.

    Bracegirdle, T. J. & Stephenson, D. B. On the robustness of emergent constraints used in multimodel climate change projections of Arctic warming. J. Climate 26, 669–678 (2013).

    Article  Google Scholar 

  78. 78.

    Chadburn, S. E. et al. An observation-based constraint on permafrost loss as a function of global warming. Nat. Clim. Change 7, 340–344 (2017). Emergent constraint based on spatial rather than temporal variability.

    Article  Google Scholar 

  79. 79.

    Wenzel, S., Cox, P. M., Eyring, V. & Friedlingstein, P. Projected land photosynthesis constrained by changes in the seasonal cycle of atmospheric CO2. Nature 538, 499–501 (2016).

    Article  Google Scholar 

  80. 80.

    Kwiatkowski, L. et al. Emergent constraints on projections of declining primary production in the tropical oceans. Nat. Clim. Change 7, 355–358 (2017).

    CAS  Article  Google Scholar 

Download references


A.H. is supported by the National Science Foundation under Grant No. 1543268, and the U.S. Department of Energy Regional and Global Climate Modelling Program contract B618798:2. P.C. is supported by the European Research Council (ERC) ECCLES project (agreement number 742472) and the EU Horizon2020 CRESCENDO project (agreement number 641816). C.H. is supported by the NERC CEH National Capability Fund. S.K. is supported by the Regional and Global Climate Modelling Program of the Office of Science of the U.S. Department of Energy under the auspices of the U.S. DOE by LLNL under contract DE-AC52-07NA27344. This paper benefited from discussions at the Aspen Global Change Institute (AGCI) in 2017, during a model evaluation workshop that was attended by A.H., P.C. and S.K.

Author information




A.H. drafted large portions of the paper, informed by discussions with C.H., P.C., and S.K., and an earlier manuscript drafted mainly by C.H. C.H., P.C. and S.K. each also drafted pieces of the paper. AH revised the paper in response to reviewer comments, after gathering feedback from C.H., P.C., and S.K. C.H. managed the references throughout the drafting process.

Corresponding author

Correspondence to Alex Hall.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Journal peer review information: Nature Climate Change thanks Benjamin Sanderson and Tapio Schneider for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hall, A., Cox, P., Huntingford, C. et al. Progressing emergent constraints on future climate change. Nat. Clim. Chang. 9, 269–278 (2019).

Download citation

Further reading


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