From time to time I have been taking a look at the Stern Review. It seems so central to the cause of global warming alarmism, and while there's a lot to plough through this does at least mean that one may come across something new.

As part of my learning process, I have been enjoying some interesting exchanges with Chris Hope of the Judge Business School at Oxford Cambridge. Chris was responsible for the PAGE economic model, which underpinned Stern's work. The review was based on the 2002 version of the model, but a newer update - PAGE 2009 - has now appeared and I have been reading up about this from Chris's working papers, in particular this one, which looks at the social cost of carbon.

The first major variable discussed in the paper is, as you would expect, climate sensitivity. The Stern Review came out around the same time as the IPCC's Fourth Assessment Report and so we would expect the take on this most critical figure to be the same in the two documents, and indeed I have seen no sign that this isn't the case. Indeed the working paper notes that the mean is virtually unchanged between since the time of Stern.

The mean value is unchanged from the default PAGE2002 mean value of 3°C, but the range at the upper end is greater. In PAGE2002, the climate sensitivity was input as a triangular probability distribution, with a minimum value of 1.5°C and a maximum of 5°C.

The Fourth Assessment Report reviewed all the major studies on climate sensitivity at the time and reported them in a spaghetti graph, which I've redrawn below:

Don't worry for the minute which study is which. We can, for the minute, simply note the very wide range of estimates, with modes between 1 and 3°C (ignoring the rather wacky black line). We also see that the distributions are all skewed far to the right, suggesting median values that are several degrees higher.

In the next diagram I superimpose these values on top of the values used in the 2009 version of the PAGE model.

As you can see the PAGE model (in red) seems to pitch itself right in the middle of the range, its distribution seeming to leave out the territory covered by the cooler peaks at the left hand side as well as the catastrophic values at the right. So far, this appears at least defensible.

Chris Hope summarises his values as follows:

The lowest values are about 1.5 degC, there is a 5% chance that it will be below about 1.85 degC, the most likely value is about 2.5 degC, the mean value is about 3 degC, there is a 5% chance that it will be above 4.6 degC, and a long tail reaching out to nearly 7 degC. This distribution is consistent with the latest estimates from IPCC, 2007, which states that “equilibrium climate sensitivity is likely to be in the range 2°C to 4.5°C, with a best estimate value of about 3°C. It is very unlikely to be less than 1.5°C. Values substantially higher than 4.5°C cannot be excluded, but agreement with observations is not as good for those values. Probability density functions derived from different information and approaches generally tend to have a long tail towards high values exceeding 4.5°C. Analysis of climate and forcing evolution over previous centuries and model ensemble studies do not rule out climate sensitivity being as high as 6°C or more.” (IPCC, 2007, TS4.5)

However, now we hit what I think is a snag: not all all of the estimates of climate sensitivity are equal. Most of the studies published in the IPCC report were either entirely based on climate model output or relied upon it to some extent. In fact there was only one exception: the paper by Forster and Gregory, which is the only wholly empirical study in the corpus. I'll highlight that one in this next diagram.

Now the picture seems to look rather less satisfying. We can see that empirical measurement is suggesting a low climate sensitivity with the most likely value at around 1.5°C. Higher values are driven by the modelling studies. Moreover, we can see that large ranges of values of climate sensitivity as implied by the empirical measurements of Forster and Gregory are not covered by the PAGE model at all. The IPCC's suggestion – that climate sensitivity is most likely to be in the range 2–4.5°C – is shown to be barely supportable and then only by favouring computer simulations of the climate over empirical measurements. This seems to me to throw lesson one of the scientific method out of the classroom window. And I really do mean lesson one:

So an examination suggests that the values of climate sensitivity used in the PAGE model are highly debatable. But of course it's actually even worse than that (it usually is). Close followers of the climate debate will recall Nic Lewis's guest post at Prof Curry's blog last year, in which he noted that the "Forster and Gregory" values in the IPCC graph were not the values that were implicit in Forster and Gregory's published results - the IPCC had notoriously chosen to restate the findings in a way that gave a radically higher estimate of climate sensitivity.

So next I replot the IPCC figures, but using the real Forster and Gregory results rather than the "reworked" ones:

So now we see that there is very little overlap between climate sensitivity as used in the PAGE model and empirical measurement of that figure. If we look back to the IPCC narrative, their claim that

Values substantially higher than 4.5°C cannot be excluded, but agreement with observations is not as good for those values.

looks highly disingenuous. When they say the agreement with observations is "not as good", do they not mean that there is almost no agreement at all? And when they say that values above 4.5 degrees cannot be excluded, do they not mean that they must be excluded, because they are ruled out by empirical observation?

If Feynman is to be believed, the climate sensitivity values used in the Stern review are "wrong". Perhaps some of my more policy oriented readers can explain to me why the political process would want to use figures that are "wrong" instead of figures that are right.