Objectively combining AR5 instrumental period and paleoclimate climate sensitivity evidence

Article
  • 74 Downloads

Abstract

Combining instrumental period evidence regarding equilibrium climate sensitivity with largely independent paleoclimate proxy evidence should enable a more constrained sensitivity estimate to be obtained. Previous, subjective Bayesian approaches involved selection of a prior probability distribution reflecting the investigators’ beliefs about climate sensitivity. Here a recently developed approach employing two different statistical methods—objective Bayesian and frequentist likelihood-ratio—is used to combine instrumental period and paleoclimate evidence based on data presented and assessments made in the IPCC Fifth Assessment Report. Probabilistic estimates from each source of evidence are represented by posterior probability density functions (PDFs) of physically-appropriate form that can be uniquely factored into a likelihood function and a noninformative prior distribution. The three-parameter form is shown accurately to fit a wide range of estimated climate sensitivity PDFs. The likelihood functions relating to the probabilistic estimates from the two sources are multiplicatively combined and a prior is derived that is noninformative for inference from the combined evidence. A posterior PDF that incorporates the evidence from both sources is produced using a single-step approach, which avoids the order-dependency that would arise if Bayesian updating were used. Results are compared with an alternative approach using the frequentist signed root likelihood ratio method. Results from these two methods are effectively identical, and provide a 5–95% range for climate sensitivity of 1.1–4.05 K (median 1.87 K).

Keywords

Climate sensitivity Combining evidence Objective Bayesian Profile likelihood Bayesian updating AR5 

Supplementary material

382_2017_3744_MOESM1_ESM.pdf (364 kb)
Supplementary material 1 (PDF 363 KB)

References

  1. Aldrin M et al (2012) Bayesian estimation of climate sensitivity based on a simple climate model fitted to observations of hemispheric temperatures and global ocean heat content. Environmetrics 23:253–271CrossRefGoogle Scholar
  2. Allen MR, Frame DJ, Huntingford C, Jones CD, Lowe JA, Meinshausen M, Meinshausen N (2009) Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature 458:1163–1166CrossRefGoogle Scholar
  3. Andronova NG, Schlesinger ME (2001) Objective estimation of the probability density function for climate sensitivity. J Geophys Res 106(D19):22605–22611CrossRefGoogle Scholar
  4. Annan JD, Hargreaves JC (2006) Using multiple observationally-based constraints to estimate climate sensitivity. Geophys Res Lett 33:L06704CrossRefGoogle Scholar
  5. Annan JD, Hargreaves JC (2011) On the generation and interpretation of probabilistic estimates of climate sensitivity. Clim Change 104(3–4):423–436CrossRefGoogle Scholar
  6. Annan JD, Hargreaves JC (2013) A new global reconstruction of temperature changes at the Last Glacial Maximum. Clim Past 9:367–376CrossRefGoogle Scholar
  7. Annan JD, Hargreaves JC, Ohgaito R, Abe-Ouchi A, Emori S (2005) Efficiently constraining climate sensitivity with ensembles of paleoclimate simulations. Sci Online Lett Atmos 1:181–184Google Scholar
  8. Bayes T (1763) An essay towards solving a problem in the doctrine of chances. Philos Trans R Soc Lond 53:370–418 [54(1764):269–325. Reprinted in Biometrika 45(1958):293–315]CrossRefGoogle Scholar
  9. Berger J (2006) The case for objective Bayesian analysis. Bayesian Anal 1(3):385–402CrossRefGoogle Scholar
  10. Berger JO, Bernardo JM (1992) On the development of reference priors (with discussion). In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics 4. Oxford University Press, Oxford, pp 35–60Google Scholar
  11. Bernardo JM (1979) Reference posterior distributions for Bayesian inference (with discussion). J R Stat Soc Ser B 41:113–147Google Scholar
  12. Bernardo JM (2009) Modern Bayesian inference: foundations and objective methods. In: Bandyopadhyay P, Forster M (eds) Philosophy of statistics. North Holland, Oxford, pp 263–306Google Scholar
  13. Chylek P, Lohmann U (2008) Aerosol radiative forcing and climate sensitivity deduced from the last glacial maximum to Holocene transition. Geophys Res Lett 35:L04804Google Scholar
  14. Colman R, McAvaney B (2009) Climate feedbacks under a very broad range of forcing. Geophys Res Lett 36:L01702. doi:10.1029/2008GL036268 CrossRefGoogle Scholar
  15. Forest CE, Stone PH, Sokolov AP (2006) Estimated PDFs of climate system properties including natural and anthropogenic forcings. Geophys Res Lett 33:L01705. doi:10.1029/2005GL023977 CrossRefGoogle Scholar
  16. Forster de PMF, Gregory JM (2006) The climate sensitivity and its components diagnosed from earth radiation budget data. J Climate 19:39–52CrossRefGoogle Scholar
  17. Frame DJ, Booth BBB, Kettleborough JA, Stainforth DA, Gregory JM, Collins M, Allen MR (2005) Constraining climate forecasts: the role of prior assumptions. Geophys Res Lett 32:L09702. doi:10.1029/2004GL022241 CrossRefGoogle Scholar
  18. Fraser DAS, Reid N, Marras E, Yi GY (2010) Default priors for Bayesian and frequentist inference. J R Stat Soc B 72(5):631–654CrossRefGoogle Scholar
  19. Friedrich T et al (2016) Nonlinear climate sensitivity and its implications for future greenhouse warming. Sci Adv 2(11):e1501923CrossRefGoogle Scholar
  20. Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  21. Gregory J, Stouffer RJ, Raper SCB, Stott PA, Rayner NA (2002) An observationally based estimate of the climate sensitivity. J Climate 15:3117–3121CrossRefGoogle Scholar
  22. Grünwald (2007) The minimum description length principle. MIT Press, Cambridge, MAGoogle Scholar
  23. Hannart A, Ghil M, Dufresne J-L, Naveau P (2013) Disconcerting learning on climate sensitivity and the uncertain future of uncertainty. Clim Change 119:585–601CrossRefGoogle Scholar
  24. Hargreaves JC, Abe-Ouchi A, Annan JD (2007) Linking glacial and future climates through an ensemble of GCM simulations. Clim Past 3:77–87CrossRefGoogle Scholar
  25. Hargreaves JC, Annan JD, Yoshimori M, Abe-Ouchi A (2012) Can the Last Glacial Maximum constrain climate sensitivity? Geophys Res Lett 39:L24702CrossRefGoogle Scholar
  26. Hartigan JA (1965) The asymptotically unbiased prior distribution. Ann Math Stat 36(4):1137–1152CrossRefGoogle Scholar
  27. Hegerl G, Crowley TC, Hyde WT, Frame DJ (2006) Climate sensitivity constrained by temperature reconstructions over the past seven centuries. Nature 440:1029–1032. doi:10.1038/nature04679 CrossRefGoogle Scholar
  28. Holden PB, Edwards NR, Oliver KIC, Lenton TM, Wilkinson RD (2010) A probabilistic calibration of climate sensitivity and terrestrial carbon change in GENIE-1. Clim Dyn 35:785–806CrossRefGoogle Scholar
  29. Jeffreys H (1946) An invariant form for the prior probability in estimation problems. Proc R Soc A 186:453–461CrossRefGoogle Scholar
  30. Kass RE, Wasserman L (1996) The selection of prior distributions by formal rules. J Am Stat Assoc 91(435):1343–1370CrossRefGoogle Scholar
  31. Köhler P, Bintanja R, Fischer H, Joos F, Knutti R, Lohmann G, Masson-Delmotte V (2010) What caused Earth’s temperature variations during the last 800,000 years? Data-based evidence on radiative forcing and constraints on climate sensitivity. Quat Sci Rev 29:129–145CrossRefGoogle Scholar
  32. Lewis N (2013a) An objective Bayesian improved approach for applying optimal fingerprint techniques to estimate climate sensitivity. J Climate 26:7414–7429CrossRefGoogle Scholar
  33. Lewis N (2013b) Modification of Bayesian updating where continuous parameters have differing relationships with new and existing data. arXiv:1308.2791 [stat.ME]
  34. Lewis N (2014) Objective inference for climate parameters: Bayesian, transformation of variables and profile likelihood approaches. J Clim 27:7270–7284CrossRefGoogle Scholar
  35. Lewis N (2017) Combining independent Bayesian posteriors into a confidence distribution, with application to estimating climate sensitivity. J Stat Plan Inference (in press) Google Scholar
  36. Lewis N, Curry JA (2015) The implications for climate sensitivity of AR5 forcing and heat uptake estimates. Clim Dyn 45:1009–1023CrossRefGoogle Scholar
  37. Lindley DV (1958) Fiducial distributions and Bayes theorem. J R Stat Soc B 20(1):102–107Google Scholar
  38. Lindley DV (1972) Bayesian statistics: a review. Society for industrial and applied mathematics, PhiladelphiaCrossRefGoogle Scholar
  39. Martinez-Boti MA, Foster GL, Chalk TB, Rohling EJ, Sexton PF, Lunt DJ, Pancost RD, M.P.S. Badger, Schmidt DN (2015) Plio-Pleistocene climate sensitivity evaluated using high-resolution CO2 records. Nature 518:49–54CrossRefGoogle Scholar
  40. Morice CP, Kennedy JJ, Rayner NA, Jones PD (2012) Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: the HadCRUT4 data set. J Geophys Res 117:D08101. doi:10.1029/2011JD017187 CrossRefGoogle Scholar
  41. Otto A, Otto FEL, Boucher O, Church J, Hegerl G, Forster PM, Gillett NP, Gregory J, Johnson GC, Knutti R, Lewis N, Lohmann U, Marotzke J, Myhre G, Shindell D, Stevens B, Allen MR (2013) Energy budget constraints on climate response. Nat Geosci 6:415–416CrossRefGoogle Scholar
  42. Otto-Bliesner BL et al (2009) A comparison of PMIP2 model simulations and the MARGO proxy reconstruction for tropical sea surface temperatures at last glacial maximum. Clim Dyn 32:799–815CrossRefGoogle Scholar
  43. Palaeosens Project Members (2012) Making sense of palaeoclimate sensitivity. Nature 491:683–691CrossRefGoogle Scholar
  44. Pawitan Y, 2001: In all likelihood: statistical modeling and inference using likelihood Ch. 3.4. Oxford University Press, Oxford, 514Google Scholar
  45. Raftery AE, Schweder T (1993) Inference about the ratio of two parameters, with application to whale censusing. Am Stat 47(4):259–264Google Scholar
  46. Roe GH, Baker MB (2007) Why is climate sensitivity so unpredictable? Science 318(5850):629–632CrossRefGoogle Scholar
  47. Schmittner A et al (2012) Climate sensitivity estimated from temperature reconstructions of the last glacial maximum. Science, 334 (2011), 1385–1388; and Response to comment on “Climate sensitivity estimated from temperature reconstructions of the Last Glacial Maximum”. Science, 337(2012):1294CrossRefGoogle Scholar
  48. Seidenfeld T (1979) Why I am not an objective Bayesian; some reflections prompted by Rosenkrantz. Theory Decision 11(4):413–440CrossRefGoogle Scholar
  49. Snyder CW (2016) Evolution of global temperature over the past two million years. Nature 538:226–228CrossRefGoogle Scholar
  50. Stevens B, Sherwood SC, Bony S, Webb MJ (2016) Prospects for narrowing bounds on Earth’s equilibrium climate sensitivity. Earth’s Future 4:512–522CrossRefGoogle Scholar
  51. Szabó B, van der Vaart A, van Zanten H (2015) Frequentist coverage of adaptive nonparametric Bayesian credible sets. Ann Stat 43(4):1391–1428CrossRefGoogle Scholar
  52. von Deimling TS, Held H, Ganopolski A, Rahmstorf S (2006) Climate sensitivity estimated from ensemble simulations of glacial climate. Clim Dyn 27:149–163CrossRefGoogle Scholar
  53. Welch BL, Peers HW (1963) On formulae for confidence points based on integrals of weighted likelihoods. J R Soc Ser B 25:318–329Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.BathUK
  2. 2.CWI Amsterdam and Leiden UniversityAmsterdamThe Netherlands

Personalised recommendations