Climatic Change

, Volume 119, Issue 3–4, pp 585–601 | Cite as

Disconcerting learning on climate sensitivity and the uncertain future of uncertainty

  • Alexis Hannart
  • Michael Ghil
  • Jean-Louis Dufresne
  • Philippe Naveau


How will our estimates of climate uncertainty evolve in the coming years, as new learning is acquired and climate research makes further progress? As a tentative contribution to this question, we argue here that the future path of climate uncertainty may itself be quite uncertain, and that our uncertainty is actually prone to increase even though we learn more about the climate system. We term disconcerting learning this somewhat counter-intuitive process in which improved knowledge generates higher uncertainty. After recalling some definitions, this concept is connected with the related concept of negative learning that was introduced earlier by Oppenheimer et al. (Clim Change 89:155–172, 2008). We illustrate disconcerting learning on several real-life examples and characterize mathematically certain general conditions for its occurrence. We show next that these conditions are met in the current state of our knowledge on climate sensitivity, and illustrate this situation based on an energy balance model of climate. We finally discuss the implications of these results on the development of adaptation and mitigation policy.


Probability Density Function Prior Distribution True Belief Climate Sensitivity Mitigation Policy 



The authors would like to thank the French Centre National de la Recherche Scientifique (CNRS) and the Argentinean CONICET for their support of this collaboration. MG’s work is partially supported by NSF grant DMS-0934426 and by US Department of Energy grant DE-SC0006694, while PN also acknowledges the ANR-funded AssimilEx and FP7 ACQWA projects. We thank Andres Farall for pointing out relevant references, and we are grateful to the Editor, to James Risbey and to two anonymous reviewers for their suggestions that helped us improve the original manuscript.

Supplementary material

10584_2013_770_MOESM1_ESM.pdf (634 kb)
(PDF 633 KB)


  1. Abbot DS, Silber M, Pierrehumbert RT (2011) Bifurcations leading to summer Arctic Sea ice loss. J Geophys Res 116:D19120CrossRefGoogle Scholar
  2. Allen MR, Andronova N, Booth B, Dessao S, Frame D et al (2006) Observational constraints on climate sensitivity. In: Schellnhuber HJ, Cramer W, Nakicenovic N, Wigley T, Yohen G (ed) Avoiding dangerous climate change. Cambridge University Press, Cambridge, pp 281–89Google Scholar
  3. Andronova NG, Schlesinger ME (2001) Objective estimation of the probability density function for climate sensitivity. J Geophys Res 106:22605–22611CrossRefGoogle Scholar
  4. Aristotle (1994) Posterior analytics, translated by J Barnes, 2nd edn. Clarendon Aristotle Series, Clarendon Press, UKGoogle Scholar
  5. Arrow RK, Fisher AC (1974) Environmental preservation, uncertainty and irreversibility. Q J Econ 88:312–319CrossRefGoogle Scholar
  6. Bacon F (2000) The Oxford Francis Bacon IV: the advancement of learning. Clarendon Press, UKGoogle Scholar
  7. Bagnoli M, Bergstrom T (2005) Log-concave probability and its applications. Econ Theory 26:455–469CrossRefGoogle Scholar
  8. Burdett K (1996) Truncated means and variances. Econ Lett 52:263–267CrossRefGoogle Scholar
  9. Chen J (2011) A partial order on uncertainty and information. J Theor Probab. doi: 10.1007/s10959-011-0375-2 Google Scholar
  10. Chen J, van Eeden C, Zidek JV (2010) Uncertainty and the conditional variance. Probab Stat Lett 80:1764–1770CrossRefGoogle Scholar
  11. Crutzen P, Oppenheimer M (2008) Learning about ozone depletion. Clim Change 64:1–10Google Scholar
  12. Darby MS, Mysak LA (1993) A Boolean delay equation model of an interdecadal Arctic climate cycle. Clim Dyn 8:241–246CrossRefGoogle Scholar
  13. Dijkstra HA, Ghil M (2005) Low-frequency variability of the large-scale ocean circulation: a dynamical systems approach. Rev Geophys 43:RG3002. doi: 10.1029/2002RG000122 CrossRefGoogle Scholar
  14. Dufresne JL, Bony S (2008) An assessment of the primary sources of spread of global warming estimates from coupled atmosphere-ocean models. J Climate 21:5135–5144CrossRefGoogle Scholar
  15. Forest DJ, Stone PH, Sokolov AP (2006) Estimated PDFs of climate system properties including natural and anthropogenic forcings. Geophys Res Lett 33:L01705Google Scholar
  16. Forster PMDF, Gregory JM (2006) The climate sensi-tivity and its components diagnosed from earth radiation budget data. J Clim 19:3952Google Scholar
  17. Frame DJ et al (2005) Constraining climate forecasts: the role of prior assumptions. Geophys Res Lett 32:L09702Google Scholar
  18. Ghil M (2001) Hilbert problems for the geosciences in the 21st century. Nonlin Processes Geophys 8:211–222CrossRefGoogle Scholar
  19. Ghil M, Mullhaupt AP, Pestiaux P (1987) Deep water formation and quaternary glaciations. Clim Dyn 2:1–10CrossRefGoogle Scholar
  20. Ghil M, Chekroun MD, Simonnet E (2008) Climate dynamics and fluid mechanics: natural variability and related uncertainties. Physica D 237:2111–2126. doi: 10.1016/j.physd.2008.03.036. CrossRefGoogle Scholar
  21. Gregory JM, et al (2002) An observationally based estimate of the climate sensitivity. J Clim 15(22):3117–3121Google Scholar
  22. Hannart A, Dufresne J-L, Naveau P (2009) Why climate sensitivity may not be so unpredictable. Geophys Res Lett 36:L16707CrossRefGoogle Scholar
  23. Hawkins E, Sutton R (2009) The potential to narrow uncertainty in regional climate predictions. Bull Am Meteorol Soc 90:1095–1107CrossRefGoogle Scholar
  24. Hegerl GC, Crowley T, Hyde WT, Frame D (2006) Constraints on climate sensitivity from temperature reconstructions of the past seven centuries. Nature 440Google Scholar
  25. Hillerbrand R, Ghil M (2008) Anthropogenic climate change: scientific uncertainties and moral dilemmas. Physica D 237:2132–2138. doi: 10.1016/j.physd.2008.02.015 CrossRefGoogle Scholar
  26. Humphrey LL, Helfand M, Chan BKS, Woolf SH (2002) Breast cancer screening: a summary of the evidence for the U.S. preventive services task force. Ann Intern Med 137:347–360CrossRefGoogle Scholar
  27. Keller K, Bolker BM, Bradford DF (2004) Uncertain climate thresholds and optimal economic growth. J Environ Econ Manag 48:723–741CrossRefGoogle Scholar
  28. Keller K, McInerney D (2007) The dynamics of learning about a climate threshold. Clim Dyn 30:321–332CrossRefGoogle Scholar
  29. Kelly DL, Kolstad CD (1999) Bayesian learning, growth and pollution. J Econ Dyn Control 23:491–518CrossRefGoogle Scholar
  30. Knutti R, Hegerl GC (2008) The equilibrium sensitivity of the Earth’s temperature to radiation changes. Nat Geosci 1:35–743CrossRefGoogle Scholar
  31. Knutti R, Stocker TF, Joos F, Plattner G-K (2002) Constraints on radiative forcing and future climate change from observations and climate model ensembles. Nature 416:719–723Google Scholar
  32. Kuhn TS (1962) The structure of scientific revolutions. University of Chicago Press, ChicagoGoogle Scholar
  33. Leach AJ (2007) The climate change learning curve. J Econ Dyn Control 31(5):1728–1752CrossRefGoogle Scholar
  34. Lenton TM et al (2008) Tipping elements in the Earth’s climate system. Proc Natl Acad Sci USA 105:1786–1793CrossRefGoogle Scholar
  35. Livina VN, Lenton TM (2012) A recent bifurcation in Arctic sea-ice cover. Cryosphere Discuss 6:2621–2651CrossRefGoogle Scholar
  36. O’Neill BC et al (2006) Learning and climate change. Clim Pol 6(5):585–589CrossRefGoogle Scholar
  37. Oppenheimer M, ONeill BC, Webster M (2008) Negative learning. Clim Change 89:155–172CrossRefGoogle Scholar
  38. Rahmstorf S (1999) Shifting seas in the greenhouse? Nature 399:523–524CrossRefGoogle Scholar
  39. Räisänen J (2005) Probability distributions of CO2-induced global warming as inferred directly from multimodel ensemble simulations. Geophysica 41:19–30Google Scholar
  40. Roe GH, Baker MB (2007) Why is climate sensitivity so unpre-dictable? Science 318:629–632Google Scholar
  41. Roe GH, Baker MB (2011) Comment on another look at climate sensitivity. Nonlinear Process Geophys 18:125–127CrossRefGoogle Scholar
  42. Soden BJ, Held IM (2006) An assessment of climate feedbacks in coupled ocean-atmosphere models. J Climate 19:3354CrossRefGoogle Scholar
  43. Solomon S et al eds (2007) Climate change 2007: the scientific basis. In: Contribution of working group I to the 4th assessment report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge/New YorkGoogle Scholar
  44. Stainforth DA et al (2005) Uncertainty in predictions of the climate response to rising levels of greenhouse gases. Nature 433:403–406CrossRefGoogle Scholar
  45. Stroeve JC, Kattsov V, Barrett AP, Serreze MC, Pavlova T, Holland MM, Meier WN (2012) Trends in Arctic sea ice extent from CMIP5, CMIP3 and observations. Geophys Res Lett 39:L16502CrossRefGoogle Scholar
  46. Tietsche S, Notz D, Jungclaus JH, Marotzke J (2011) Recovery mechanisms of Arctic summer sea ice. Geophys Res Lett 38(2):L02707CrossRefGoogle Scholar
  47. Tol RSJ (1997) On the optimal control of carbon dioxide emissions: an application of FUND. Environ Model Assess 2:151–163CrossRefGoogle Scholar
  48. Webster MD, Jakobovits L, Norton J (2008) Learning about climate change and implications for near-term policy. Clim Change 89:67–85CrossRefGoogle Scholar
  49. Zaliapin I, Ghil M (2010) Another look at climate sensitivity. Nonlin Processes Geophys 17:113–122CrossRefGoogle Scholar
  50. Zidek JV, van Eeden C (2003) Uncertainty, entropy, variance and the effect of partial information. In: Moore M, Froda S, Leger C (eds) Mathematical statistics and applications: Festschrift for Constance van Eeden. Lecture Notes–Monograph Series Institute of Mathematical Statistics, vol 42, pp 155–167Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Alexis Hannart
    • 1
  • Michael Ghil
    • 2
    • 3
  • Jean-Louis Dufresne
    • 4
  • Philippe Naveau
    • 5
  1. 1.Institut Franco-Argentin d’Etudes sur le Climat et ses ImpactsCNRS-CONICET-Universidad de Buenos AiresBuenos AiresArgentina
  2. 2.Geosciences DepartmentUCLALos AngelesUSA
  3. 3.Laboratoire de Météorologie DynamiqueEcole Normale SupérieureParisFrance
  4. 4.Laboratoire de Météorologie DynamiqueCNRS-Polytechnique-ENS-UPMCParisFrance
  5. 5.Laboratoire des Sciences du Climat et l’EnvironnementCNRS-CEAGif-sur-YvetteFrance

Personalised recommendations