Allen, Myles R.

Booth, Ben B.B.

Collins, Matthew

Frame, David J.

Gregory, J.M.

Kettleborough, J.A.

Stainforth, D.A.

Geophysical Research Letters

Open Research Exeter

Correction to: “Constraining climate forecasts:The role of prior assumptions”D. J. Frame, B. Booth, J. A. Kettleborough, D. A. Stainforth, J. M. Gregory, M. Collins, and M. R. AllenIn the paper “Constraining climate forecasts: The role of prior assumptions” by Frame et al. (GeophysicalResearch Letters, 32, L09702, doi:10.1029/2004GL022241, 2005), the method used for the calculation of thelikelihood functions has been found to be incorrect. The error is best illustrated with the computation of thelikelihood function for climate system Effective Heat Capacity, or EHC. This is the ratio of two uncertainquantities: the amount of heat absorbed by the climate system over a given period and the surface warmingover the same period. If both of these quantities are assumed to be Gaussian, we can generate a large sampleand plot the likelihoods of the individual sample members as a function of their ratio, shown as the dots inthe ﬁgure.The appropriate likelihood proﬁle is shown by the solid line, obtained by taking the maximum of thelikelihoods as a function of EHC. In Frame et al. [2005], a sample histogram was taken instead, which gives thedashed line. This would coincide with the solid line if the distributions were Gaussian, but it is not. A similarerror was made in the interpretation of the likelihood proﬁle for attributable warming.In addition, we also misinterpreted the reported warming over 1955–1998 in Levitus et al. [2005] asrepresenting warming over the 39 year period between the centers of the ﬁrst and last 5 year averagingperiods. In fact, the ﬁgure pertains to warming over the full 44 year period. Correcting for this errorapproximately compensates for the other error in the EHC likelihood proﬁle, yielding the dash-dotted lineshown in the ﬁgure.Correcting all these errors, the upper bound of the 5–95% range for climate sensitivity under a uniform priorincreases from 11.6 to 14.5°C. Other reported upper bounds are affected by similar margins, with lowerbounds unaffected. In the context of other assumptions in the study, the impact of the error is modest, but itillustrates the importance of care in distinguishing likelihoods and probabilities in a Bayesian analysis.Subsequent papers [e.g., Allen et al., 2009] have used an explicit likelihood proﬁling approach for which thisissue did not arise.Figure 1. Likelihood proﬁles for climate system heat capacity as used in Frame et al. [2005]. Dots: likelihoods of a randomsample of ocean heat uptake and surface warming rates, plotted as a function of their ratio. Dashed line: likelihood incorrectlycalculated from a histogram of the dots, as in the original paper. Solid line: correctly calculated but still using the incorrectinterpretation of dates in Levitus et al. [2005]. Dash-dotted line: correctly calculated and also with the correct interpretation ofLevitus et al. [2005].FRAME ET AL. ©2014. American Geophysical Union. All Rights Reserved. 3257PUBLICATIONSGeophysical Research LettersCORRECTION10.1002/2014GL059853Citation:Frame, D. J., B. Booth, J. A.Kettleborough, D. A. Stainforth, J. M.Gregory, M. Collins, and M. R. Allen(2014), Correction to: “Constrainingclimate forecasts: The role of priorassumptions”, Geophys. Res. Lett., 41,3257–3258, doi:10.1002/2014GL059853.Received 7 MAR 2014Accepted article online 10 APR 2014Published online 2 MAY 2014Other studies [e.g., Domingues et al., 2008; Glecker et al., 2012] have indicated much larger revisions in rates ofocean heat uptake than the differences shown in the ﬁgure, so we do not think it is necessary for papersmaking use of the results of Frame et al. [2005] [e.g., Hegerl et al., 2006] to be reassessed. The centralconclusion of the paper, highlighting the important role of prior assumptions in explaining the markeddifferences in upper bounds on climate sensitivity being reported at the time, still stands.It is interesting that the “uniform sampling in observables” option as implemented by Frame et al. [2005]closely approximates the Jeffreys Prior [Lewis, 2013], but the arguments for and against the use of the JeffreysPrior in climate parameter estimation should be made on their own merits, unaffected by mistakes made inthe speciﬁcation of a likelihood function a decade ago.ReferencesAllen, M. R., D. J. Frame, C. Huntingford, C. D. Jones, J. A. Lowe, M. Meinshausen, and N. Meinshausen (2009), Warming caused by cumulativecarbon emissions towards the trillionth tonne, Nature, 458, 1163–1167.Domingues, C. M., J. A. Church, N. J. White, P. J. Gleckler, S. E. Wijffels, P. M. Barker, and J. R. Dunn (2008), Improved estimates of upper-oceanwarming and its contribution to multi-decadal sea level-rise, Nature, 453, 1090–1093, doi:10.1038/nature07080.Frame, D. J., B. B. B. Booth, J. A. Kettleborough, D. A. Stainforth, J. M. Gregory, M. Collins, and M. R. Allen (2005), Constraining climate forecasts:The role of prior assumptions, Geophys. Res. Lett., 32, L09702, doi:10.1029/2004GL022241.Glecker, P. J., et al. (2012), Human-induced global ocean warming on multidecadal timescales, Nat. Clim. Change, 2, 524–529.Hegerl, G. C., T. J. Crowley, W. T. Hyde, and D. J. Frame (2006), Climate sensitivity constrained by temperature reconstructions over the pastseven centuries, Nature, 440, 7087.Levitus, S., J. Antonov, and T. Boyer (2005), Warming of the world ocean, 1955–2003, Geophys. Res. Lett., 32, L02604, doi:10.1029/2004GL021592.Lewis, N. (2013), An objective Bayesian improved approach for applying optimal ﬁngerprint techniques to estimate climate sensitivity,J. Clim., 26(19), 7414–7429.AcknowledgmentWe are grateful to Nicholas Lewis fordrawing our attention to this error.Geophysical Research Letters 10.1002/2014GL059853FRAME ET AL. ©2014. American Geophysical Union. All Rights Reserved. 3258

Correction to: “Constraining climate forecasts: The role of prior assumptions”

Correction to: “Constraining climate forecasts: The role of prior assumptions”

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