The idea behind the method is that in equilibrium, there's a balance between radiation losses from the earth, and the radiation it absorbs from the sun. When something happens to disturb this balance - a forcing - the earth's surface temperature has to change to compensate - radiation increases with temperature. However, it will take some time for the earth to heat up (or cool down) to reach that temperature, in the meantime there will be a heat uptake which must be included in the calculation if one wants to use current data to estimate an equilibrium effect. One selects two time periods as far apart as practicable, takes an estimate of changes in the various forcings, subtracts an estimate of changes in heat uptake, and divides by the resulting temperature change to get the sensitivity to net forcing. Then one scales the result to the estimated change in forcing for a doubling of atmospheric carbon dioxide.
Lewis acknowledges in the comments under his article that this is estimating an Effective Climate Sensitivity rather than an Equilibrium Climate Sensitivity, but it's not clear to him or me why these should be much different (I could be wrong).
When Gregory tried this method, he got a median sensitivity of 6.1K, with a confidence interval stretching down to
The report gives the IPCC's current estimate of sensitivity: I quote from page SPM-11 of the Executive Summary (the whole leaked report can conveniently be accessed on scribd)
Equilibrium climate sensitivity is likely in the range 2°C–4.5°C, and very likely above 1.5°C. The most likely value is near 3°C. Equilibrium climate sensitivity greater than about 6°C–7°C is very unlikelySo Lewis's range overlaps a lot with the IPCC's range, albeit the range is obtained by allowing a model's parameters to vary within their individual error bounds, and the choices that give the low estimates in the IPCC's calculation may be inconsistent with the choices that give the high estimates in Lewis's.
I had a look at the parameters Lewis uses; one section in particular caught my eye, discussing the heat uptake parameter. (OHU is Ocean Heat Uptake, SOD is Second Order Draft - the leaked version.) To make it easier to read I've omitted the error analysis:
I estimate 2002–2011 OHU from a regression over 2002–2011 of 0–2000m pentadal ocean heat content estimate...the trend equates to 0.433 W/m², averaged over the Earth's surface...There is no alternative to using GCM-derived estimates of OHU for the 1871–1880 period, since there were no measurements then. I adopt the OHU estimate given in [Gregory 02] for the bracketing 1861–1900 period of 0.16 W/m², but deduct only 50% of it to compensate for the Levitus et al. (2012) regression trend implying a somewhat lower 2002-2011 OHU than is given in the SOD...That implies a change in OHU of 0.353 W/m²... Although Gregory 02 ignored non-ocean heat uptake, some allowance should be made for that and also for any increase in ocean heat content below 3000 m. The (slightly garbled) information in Section 3.2.5 of the SOD implies that 0–3000 m ocean warming accounts for 80–85% of the Earth's total heat uptake... Allowing for all components of the Earth's heat uptake implies an estimated change in total heat uptake of 0.43 W/m²...Natural variability in decadal OHU should be the counterpart of natural variability in decadal global surface temperature, so is not accounted for separately.The bit about deducting only 50% of the uptake in the reference period is hard to understand, and it's odd that he refers to the SOD value without specifying what it is. And Lewis doesn't say a word about disagreeing with SOD on this. So I went and looked up what SOD has to say. The relevant section is Box 3.1 on page 3-11 of Chapter 3:
It is virtually certain that Earth has gained substantial energy from 1971–2010 — an estimated first-difference change of 273 [194 to 353] ZJ (1 ZJ = 1021 J), with a rate of 213 TW from a linear fit over that time period (Box 3.1, Figure 1). From 1993–2010 the estimated energy gain is from a first difference is 163[125 to 200] ZJ with a linear rate estimate of 27 TW. Ocean warming dominates the total energy change inventory, accounting for roughly 93% on average from 1971–2010. Melting ice (including Arctic sea ice, ice sheets, and glaciers) accounts for 3% of the total, and warming of the continents 3%. Warming of the atmosphere makes up the remaining 1%. The ocean component of the 1993–2010 rate of energy gain is 257TW, equivalent to a global mean net air-sea heat flux of 0.71 W m–2, and that for 1971–2010 is 199 TW, implying a mean net air-sea heat flux of 0.55 W m–2The 27 TW given for the 1993-2010 rate is an obvious typo. It's easy to convert from joules to watts (a terawatt is 1012 watts): one divides by the number of years then divides by the number of seconds in a year. That tells me that the right number is 287 TW: I suppose the middle digit has somehow been dropped.
It's also easy to convert from watts to watts per square metre, taken over the whole of the earth's surface, by dividing by the earth's surface area. That gives 0.42 W m–2 as the average rate for 1971-2010, very close to Lewis's figure. But he ought to be using a figure for 2002-2011, and the rate has increased sharply during the period - I reproduce the chart from page 3-66 of SOD Chapter 3
My guess is that Lewis has tended to choose parameters which nudge his estimate downwards, and has been somewhat optimistic in his error estimates. But even with consensus parameters, this method will produce a significantly lower median estimate than the IPCC's. It seems worth seeking to understand why.
James Annan comments
I think a lot of what Nic Lewis says seems reasonable, though I also suspect that some of his choices will have served to underestimate sensitivity somewhat. Don't forget, "the ipcc" does no research to estimate sensitivity, they only summarise the literature which generally lags the latest evidence.