Even a 0.6C temperature rise was not enough. So the UN repealed a fundamental physical law. Buried in a sub-chapter in its 2001 report is a short but revealing section discussing “lambda” — the crucial factor converting radiant-energy forcings to temperature. The UN devoted several pages of its 2001 report to commenting on what it called the “remarkable” near-invariance of lambda at 0.5C per watt per square metre of direct forcing.

However, for the climatically-relevant range of temperatures, it is easy to verify that the Stefan-Boltzmann equation, which converts radiant energy to temperature, yields a near-linear temperature response to changes in radiant energy.

This law is as central to the thermodynamics of climate as Einstein’s later equation is to astrophysics. Like Einstein’s, it relates energy to the square of the speed of light, but by reference to temperature rather than mass. The UN plainly did not understand it.

The bigger the value of lambda, the bigger the temperature increase the UN could predict. Using the Stefan-Boltzmann law, the base value is just 0.22-0.3C per watt per square metre. In 1995 and again in 2001, the UN doubled lambda to 0.5C per watt, saying that feedbacks consequent on temperature increases were responsible for the extra. A bidding war began, involving the UN, its former climate-change chairman Sir John Houghton, and James Hansen, the scientist who had started the scare in 1988. Stern joined in. Table 1 shows just how little consensus there is about this key variable.

The IPCC (1995, 2001, 2007) has proposed three values, each higher than the last, but has corrected its definition of “lambda” for its next report. Hansen has also proposed three values, in a single paper (Hansen, 2006). Sir John Houghton (2002, 2006) has proposed two values. Stern (2006), here as elsewhere, is at the extreme high end of the table. Using his suggested 1.89C per watt means that 85% of the warming he thinks ought to have taken place in the 20^th century has disappeared into the oceans.

Even if Stern’s excitable estimate were right, the worst consequence would be the disappearance of the ice-cap at the North Pole during the summer. Polar bears would have to spend the summer in Greenland. The UN is about to concede that the ice-sheets in Greenland and Antarctica, which have been growing rapidly in the past 30 years (Greenland by an average of 2 inches a year) are not going to melt significantly, and that sea levels are not likely to rise all that much faster in the next century than in the past century.

The central problem with the UN’s calculations is that the computer models on which it heavily relies have consistently over-projected temperature, which has not risen as fast as the models had forecast. In 2000, the UK’s Hadley Centre solved the problem of over-projection by dividing its modelled output by three to “predict” 20^th-century temperature correctly.

Hansen (2006) now says the oceanic “flywheel effect” gives us extra time to act (always supposing that action is necessary). Therefore Stern’s alarmism is already outdated. However, provisional calculations — not yet verified or peer-reviewed — using the data and methods described in the UN’s forthcoming report suggest that the difference between the transient and equilibrium climate response to temperature is very small, and is probably intra-annual rather than supra-centennial — Table 2.

All of the principal processes and data relevant to projection of the temperature effects of radiative forcings are presented in a single table for the first time. The IPCC’s model-derived data and methodologies have been used to project temperature response to radiative forcings and consequent climate feedbacks between 1906 and 2006, and between 1906 and the point at which atmospheric CO₂ concentrations double. 1906 was selected as the base year because, unlike the IPCC’s base year 1750, it falls within the instrumental record. Also, it is the point at which both temperature and CO₂ concentrations began to rise appreciably (IPCC, 2007).

In addition to all of the anthropogenic and solar forcings tabulated in IPCC (2007), for each of which the IPCC’s central estimate is taken, Table 2 enumerates all climatic feedbacks except the CO2 feedback, which is most simply understood as bringing forward the moment when atmospheric CO₂ concentration will reach 556 ppmv, twice the pre-industrial 278 ppmv. The climate sensitivity event is likely to occur in 2100 at the latest.

The model produces outputs at the lower end of the range, partly because the effects of the CO₂ feedback are taken into account not as a temperature effect but as a time effect.

The projected temperature response to all climatic forcings and feedbacks in 2006 compared with the climatic state in 1906 is 0.8C, a little below the observed temperature increase of 0.84C (NCDC, 2006). At the climate-sensitivity event the temperature is projected to be 1.45C higher than in 1906, or ~ 0.6C warmer than the present.

These results from the simple model presented in Table 2 give no ground for supposing that any warming attributable to past forcings has not yet manifested itself fully in the temperature response, suggesting that both the duration and the amplitude of the difference between the transient and equilibrium climate responses may be small, and confirming the results of numerous climate-sensitivity studies following the eruption of Mount Pinatubo, Philippines, in June 1991.

Hansen et al. (1992) had proposed that the climate forcings and feedbacks following the Pinatubo eruption, though they were transient, would provide a benchmark for testing the AOGCMs’ ability to evaluate forcings and feedbacks correctly.

Sassen (1992) reported that cirrus clouds were produced during the eruption. Lindzen et al. (2001) proposed that cirrus clouds might provide a negative feedback partially counteracting the positive feedbacks, which the IPCC has now quantified (IPCC, 2007, ch.8), and further work continues on confirmation and quantification of this negative feedback. However, no allowance for this additional negative feedback has been made here.