Nic Lewis has a new post at Climate Audit that deals with some assumptions that went into IPCC AR4’s use of a uniform prior for estimating climate sensitivity.
He has shown it to be faulty, to the point that would normally be cause for a retraction, but this is Climate Science, where being wrong is simply a shade of grey, not black, nor white.
Frame and Allen’s original graph (Figure 1) showed that use of a uniform prior in ECS gives a very high 95% upper bound for climate sensitivity, whereas a uniform prior in Feedback strength (the reciprocal of ECS) – which declines with ECS squared – gives a low 95% bound. A uniform prior in the observable variables (AW and EHC) also gives a 95% bound under half that based on a uniform in ECS prior; using a prior that is uniform in transient climate response (TCR) rather than in AW, and is uniform in EHC, gives an almost identical PDF.
Figure 1: reproduction of Fig. (c) from Frame and Allen ‘Observational Constraints and Prior Assumptions on Climate Sensitivity’, 2004 IPCC Workshop on Climate Sensitivity. Vertical bars show 95% bounds.
However, the Frame et al 2005 claim that high sensitivity, high heat uptake cases cannot be ruled out is incorrect: such cases would give rise to excessive ocean warming relative to the observational uncertainty range. It follows that Frame and Allen’s proposal to use a uniform in ECS prior when it is ECS that is being estimated does not in fact answer the question they posed, as to what the study tells one about ECS given no prior knowledge about it. Of course, I am not the first person to point out that Frame and Allen’s proposal to use a uniform-in-ECS prior when estimating ECS makes no sense. James Annan and Julia Hargreaves did so years ago.
The noninformative prior used for method 2 is shown in Figure 3. The prior is very highly peaked the in low ECS, low Kv corner, and by an ECS of 5°C is, at mid-range Kv, under one-hundredth of its peak value . What climate scientist using a Subjective Bayesian approach would choose a joint prior for ECS and Kv looking like that, or even include any prior like it if exploring sensitivity to choice of priors? Most climate scientists would claim I had chosen a ridiculous prior that ruled out a priori the possibility of ECS being high. Yet, as I show in my paper, use of this prior produces identical results to those from applying the transformation of variables formula to the PDFs for AW and EHC that were derived in Frame et al 2005, and almost the same results as using the non-Bayesian profile likelihood method.
Figure 3: Noninformative Jeffreys’ prior for inferring ECS and Kv from the (AW, EHC) likelihood. (The fitted EHC distribution is parameterised differently here than in my paper, but the shape of the prior is almost identical.)
Whilst my paper was under review, the Frame et al 2005 authors arranged a corrigendum to Frame et al 2005 in GRL in relation to the likelihood function error and the miscalculation of the ocean heat content change. They did not take the opportunity to withdraw what they had originally written about choice of priors, or their claim about not being able to rule out high ECS values based on 20th century observations. My paper[v] is now available in Early Online Release form, here. The final submitted manuscript is available on my own webpage, here.
The complete Climate Audit post is here: http://climateaudit.org/2014/07/30/paper-justifying-ar4s-use-of-a-uniform-prior-for-estimating-climate-sensitivity-shown-to-be-faulty/