Thanks to Bill Shockley I’ve been made aware of new paper by James Annan about recent developments in Bayesian estimation of climate sensitivity. It covers many things I’ve been wondering about, so I found it very interesting. I don’t need to say much, since it’s pretty readable, but I’ll highlight a few things.
In Bayesian analysis one has to specify a prior, either a Subjective prior, or what is called an Objective prior. Early Bayesian analyses of climate sensitivity used uniform priors which were intended to be objective, but they gave unrealistically high weights to high climate sensitivities. There are other Objective priors (such as the Jeffrey’s prior used by Nic Lewis) and as James Annan’s paper says
[t]he priors used by [20–22] decay strongly for high values of S, and the resulting posterior pdfs have median estimates a little lower than 2oC with 5–95 % credible intervals that vary from about 1–3 to 1–4.5oC.
So, these newer Objective priors resolve the issue with the uniform priors, but bring the mediam estimate to below 2oC. However, as many have pointed out,
[w]hile these results are rather lower than many of those reported earlier in the literature (e.g. [10, 11]), they are not so dissimilar to recent results using the subjective paradigm [1, 17, 26, 30].
So, even the relatively low values returned by some Bayesian analyses using Objective priors, are not that different to results using more Subjective priors. Although James does discuss the problems with uniform priors, what would have been interesting would have seen some discussion of the other Objective priors, such as the Jeffreys’ prior used by Nic Lewis. This appears to peak at 0, which too seems physically implausible. It would be interesting to know more about the implications of this. Presumably, this could partly explain the difference between these results, and those using Subjective priors.
James’s paper also discusses the models that are normally used, which are pretty simply and – typically – assume that the feedback factor is constant. However,
[f]or many state of the art climate models, the “effective” feedback (that is, the value of () at a specific point in time) can change, typically (though not always) decreasing in standard scenarios of increasing greenhouse gas forcing [2,5]. A decrease in this feedback implies that the effective sensitivity early in the warming will be lower than the equilibrium sensitivity, and this suggests that methods which use the historical period for estimation may underestimate the true equilibrium sensitivity.
Hence, the assumption of a constant feedback factor may not be entirely realistic.
Also, if you combine other estimates, such as those from paleo-climatology and climate models, you get that
these two additional lines of argument both point to a sensitivity around the canonical value of 3oC —perhaps a little higher than estimates based on the observational warming, but certainly highly consistent with them—but each approach has significant uncertainties and inbuilt assumptions.
The paper ends with the following, which seems quite reasonable to me
While estimates based on the recent observational record are increasingly converging to a moderate value with a best estimate rarely far from 2 to 2.5oC, and a range which is confidently bounded between about 1 and 4.5oC (or less), these estimates are themselves conditional on approximations that are now recognised to introduce significant additional uncertainties (and perhapsa bias) into the results.
There’s more to it, but those are just some things that caught my eye. One comment I will make, is that if this was not such a contentious topic, that one can get reasonable agreement using various different estimates (some complex, some simple) would normally give some confidence that we’re in the right kind of ball park. However, since it is quite a contentious topic, the tendency is – unfortunately – to pick an estimate (and sometimes just a value) that suits the message that is being presented. Maybe, as James’s paper suggest, we should be considering the
possibility of synthesising different lines of research, all of which inform on the equilibrium sensitivity. Such an analysis has the potential for generating a more precise and credible result.