Via email, I hear that

this paper from

Stephen Schwartz is making a bit of a splash in the delusionosphere. In it, he purports to show that climate sensitivity is only about 1.1C, with rather small uncertainty bounds of +-0.5C.

Usually, I am happy to let RealClimate debunk the septic dross that still infects the media. In fact, since I have teased them about their zeal in the past, it may seem slightly hypocritical of me to bother with this. However, this specific paper is particularly close to my own field of research, and the author is also rather unusual in that he seems to be a respected atmospheric scientist with generally rather mainstream views on climate science (although perhaps a bit critical of the IPCC

here). However, his background is in aerosols, which suggests that he may have stumbled out of his field without quite realising what he is getting himself into.

Anyway, without further ado, on to the mistakes:

Mistake number 1 is a rather trivial mathematical error. He estimates sensitivity (K per W/m^2) via the equation

S=t/C

where C is the effective heat capacity (mostly ocean) and t is the time constant of the system (more on this later).

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 I'll 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 don't know how he did his calculation, but it's 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.

Mistake number 2 is more to do with the physics. In fact this is the big error, but I worked out the maths one first.

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 haven't 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.

Schwartz is, to be fair, admirably frank about the possibility that he is wrong:

This situation invites a scrutiny of the each of these findings for possible sources of error of interpretation in the present study.

He also says::

It might also prove valuable to apply the present analysis approach to the output of global climate models to ascertain the fidelity with which these models reproduce "whole Earth" properties of the climate system such as are empirically determined here.

Perhaps a better way of putting that would be to suggest applying the analysis to the output of computer models in order to test if the technique is capable of determining their (known) physical properties. Indeed, given the screwy results that Schwartz obtained, I would have thought this should be the first step, prior to his bothering to write it up into a paper. I have done this, by using his approach to estimate the "time scale" of a handful of GCMs based on their 20th century temperature time series. This took all of 5 minutes, and demonstrates unequivocally that the "time scale" exhibited through this analysis (which also comes out at about 5 years for the models I tested) does not represent the (known) multidecadal time scale of their response to a long-term forcing. In short, this method of analysis grossly underestimates the time scale of response of climate models to a long-term forcing change, so there is little reason to expect it to be valid when applied to the real system.

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. It's surprising that Schwartz didn't check his results with anyone working in the field, and disappointing that the editor in charge at JGR apparently couldn't find any competent referees to look at it.