New(ish, but I'm just getting round to writing about it) review article by Knutti et al on climate sensitivity. The detailed review of published estimates is impressive, a lot of work must have gone into that. It has been spotted that the Callendar estimate is wrong: the value in the paper is about 1.8C for a doubling of CO2, which is rather lower than the value plotted in the figure. (This calculation ignores changes in clouds, so it's impressively close to what we would estimate today for the same processes).
Probably the most important aspect of the update, however, is summarised in the figure of how radiative imbalance changes with temperature as a model warms up (after an abrupt quadrupling of CO2). Simple linear first-order modelling of the energy balance would suggest that the points should lie on a straight line, with the intercepts on the y and x axes being the initial forcing and the equilibrium temperature change respectively (and these values can be halved to get those pertaining to a doubling of CO2). A handy consequence of this is that the equilibrium response could be estimated in a climate model, without the need to run the model to equilibrium. Based on this idea (often referred to as the “Gregory method ”), the equilibrium sensitivities of the CMIP models are typically estimated on the basis of a 150 year simulation following a quadrupling of CO2.
However models - and quite probably, the real world - doesn't behave like that. Instead, the points appear to cluster around a curve which implies the true equilibrium change is greater than that which would be estimated from analysis of an initial segment of the run.
I can't help wonder how rapidly and widely this method would have been accepted if it had been proposed by someone less eminent. I suspect there would be more of a “nice idea, but it doesn't really work that well”. Incidentally, the behaviour is nothing to do with quadrupling per se, you get similar results for greater and lesser forcing changes. I believe quadrupling was just chosen (rather than the more conventional doubling) to get a greater signal/noise ratio in the changes.