His numerical values for t and C are 5+-1, and 16.7+-7 respectively (with the uncertainties at one standard deviation). It is not entirely clear what he really intends these distributions to mean (itself a sign that he is a little out of his depth perhaps), but Ill interpret them in the only way I think reasonable in the context, as gaussian distributions for the parameters in question. He claims these values gives S equal to 0.3+-0.09, although he also writes 0.3+-0.14 elsewhere. This latter value works out at 1.1C+-0.5C for a doubling of CO2. But the quotient of two gaussians is not gaussian, or symmetric. I dont know how he did his calculation, but its clearly not right.
In fact, the 16%-84% probability interval (the standard central 68% probability interval corresponding to +- 1sd of a gaussian, and the IPPC likely) of this quotient distribution is really 0.18-0.52K/W/m^2 (0.7-1.9C per doubling) and the 2sd limit of 2.5% to 97.5% is 0.12-1.3K/W/m^2 (0.4-4.8C per doubling). While this range still focuses mostly on lower values than most analyses support, it also reaches the upper range that I (and perhaps increasingly many others) consider credible anyway. His 68% estimate of 0.6-1.6C per doubling is wrong to start with, and doubly misleading in the way that it conceals the long tail that naturally arises from his analysis.
He estimates a time constant which is supposed to characterise the response of the climate system to any perturbation. On the assumption that there is such a unique time constant, this value can apparently be estimated by some straightforward time series analysis - I havent checked this in any detail but the references he provides look solid enough. His estimate, based on observed 20th century temperature changes, comes out at 5y. However, he also notes that the literature shows that different analyses of models give wildly different indications of characteristic time scale, depending on what forcing is being considered - for example the response to volcanic perturbations has a dominant time scale of a couple of years, whereas the response to a steady increase in GHGs take decades to reach equilibrium. Unfortunately he does not draw the obvious conclusion from this - that there is no single time scale that completely characterises the climate system - but presses on regardless.
In fact there is an elementary physical explanation for this: the models (and the real climate system) exhibit a range of time scales, with the atmosphere responding very rapidly, the upper ocean taking substantially longer, and the deep ocean taking much longer still. When forced with rapid variations (such as volcanoes), the time series of atmospheric response will seem rapid, but in response to a steady forcing change, the system will take a long time to reach its new equilibrium. An exponential fit to the first few years of such an experiment will look like there is a purely rapid response, before the longer response of the deep ocean comes into play. This is trivial to demonstrate with simple 2-box models (upper and lower ocean) of the climate system.
Changing Schwartz 5y time scale into a more representative 15y would put his results slap bang in the middle of the IPCC range, and confirm the well-known fact that the 20th century warming does not by itself provide a very tight constraint on climate sensitivity. Its surprising that Schwartz didnt check his results with anyone working in the field, and disappointing that the editor in charge at JGR apparently couldnt find any competent referees to look at it.
