This is a guest posting by Nic Lewis. Nic has cross posted this to the comments at RC, with the normal style of response from Schmidt.
I am glad to see that my input into the Wall Street Journal op-ed pages has prompted a piece on climate sensitivity at RealClimate. I think that some comment on my energy balance based climate sensitivity estimate of 1.6–1.7°C (details at http://www.webcitation.org/6DNLRIeJH), which underpinned Matt Ridley's WSJ op-ed, would have been relevant and of interest.
You refer to the recent papers examining the transient constraint, and say "The most thorough is Aldrin et al (2012). … Aldrin et al produce a number of (explicitly Bayesian) estimates, their ‘main’ one with a range of 1.2°C to 3.5°C (mean 2.0°C) which assumes exactly zero indirect aerosol effects, and possibly a more realistic sensitivity test including a small Aerosol Indirect Effect of 1.2–4.8°C (mean 2.5°C)."
The mean is not a good central estimate for a parameter like climate sensitivity with a highly skewed distribution. The median or mode (most likely value) provide more appropriate estimates. Aldrin's main results mode for sensitivity is between 1.5 and 1.6°C; the median is about halfway between the mode and the mean.
I agree with you that Aldrin is the most thorough study, although its use of a uniform prior distribution for climate sensitivity will have pushed up the mean, mainly by making the upper tail of its estimate worse constrained than if an objective Bayesian method with a noninformative prior had been used.
It is not true that Aldrin assumes zero indirect aerosol effects. Table 1 and Figure 15 (2nd panel) of the Supplementary Material show that a wide prior extending from -0.3 to -1.8 W/m2 (corresponding to the AR4 estimated range) was used for indirect aerosol forcing. The (posterior) mean estimated by the study was circa -0.3 W/m2 for indirect aerosol forcing and -0.4 W/m2 for direct. The total of -0.7 W/m2 is the same as the best observational (satellite) total aerosol adjusted forcing estimate given in the leaked Second Order Draft of AR5 WG1, which includes cloud lifetime (2nd indirect) and other effects.
When Aldrin adds a fixed cloud lifetime effect of -0.25 W/m2 forcing on top of his variable parameter direct and (1st) indirect aerosol forcing, the mode of the sensitivity PDF increases from 1.6 to 1.8. The mean and the top of the range goes up a lot (to 2.5°C and 4.8°C, as you say) because the tail of the distribution becomes much fatter - a reflection of the distorting effect of using a uniform prior for ECS. But, given the revised aerosol forcing estimates given in the AR5 WG1 SOD, there is no justification at all for increasing the prior for aerosol indirect forcing prior by adding either -0.25 or -0.5 W/m2. On the contrary, it should be reduced, by adding something like +0.5 W/m2, to be consistent with the lower AR5 estimates.
It is rather surprising that adding cloud lifetime effect forcing makes any difference, insofar as Aldrin is estimating indirect and direct aerosol forcings as part of his Bayesian procedure. The reason is probably, because the normal/lognormal priors he is using for direct and indirect aerosol forcing aren't wide enough for the posterior mean fully to reflect what the model-observational data comparison is implying. When extra forcing of -0.25 or -0.5 W/m2 is added his prior mean total aerosol forcing is very substantially more negative than -0.7 W/m2 (the posterior mean without the extra indirect forcing). That results in the data maximum likelihoods for direct and indirect aerosol forcing being in the upper tails of the priors, biasing the aerosol forcing estimation to more negative values (and hence biasing ECS estimation to a higher value).
Ring et al. (2012) is another recent climate sensitivity study based on instrumental data. Using the current version, HadCRUT4, of the surface temperature dataset used in a predecessor study, it obtains central estimates for total aerosol forcing and climate sensitivity of respectively -0.5 W/m2 and 1.6 °C. This is a 0.9°C reduction from the sensitivity of 2.5°C estimated in that predecessor study, which used the same climate model. The reduction resulted from correcting a bug found in the climate model computer code. (Somewhat lower and higher estimates of aerosol forcing and sensitivity are found using other, arguably less reliable, temperature datasets.)