**Here I demonstrate an error in the core scientific report (WGI) that came about through the IPCC’s alteration of a peer-reviewed result.**

The IPCC Fourth Assessment Report of 2007 (AR4) contained various errors, including the well publicised overestimate of the speed at which Himalayan glaciers would melt. However, the IPCC’s defenders point out that such errors were inadvertent and inconsequential: they did not undermine the scientific basis of AR4. Here I demonstrate an error in the core scientific report (WGI) that came about through the IPCC’s alteration of a peer-reviewed result. This error is highly consequential, since it involves the only instrumental evidence that is climate-model independent cited by the IPCC as to the probability distribution of climate sensitivity, and it substantially increases the apparent risk of high warming from increases in CO_{2} concentration.

In the Working Group 1: The Physical Science Basis Report of AR4 (“AR4:WG1″), various studies deriving estimates of equilibrium climate sensitivity from observational data are cited, and a comparison of the results of many of these studies is shown in Figure 9.20, reproduced below. In most cases, probability density functions (PDFs) of climate sensitivity are given, truncated over the range of 0°C to 10°C and scaled to give a cumulative distribution function (CDF) of 1 at 10°C.

Figure 1. IPCC AR4:WG1 Figure 9.20. [Hegerl et al, 2007] (click on figure to enlarge)

Of the eight studies for which PDFs are shown, only one – Forster/Gregory 06 [Forster and Gregory, 2006] – is based purely on observational evidence, with no dependence on any climate model simulations. Forster/Gregory 06 regressed changes in net radiative flux imbalance, less net radiative forcing, on changes in the global surface temperature, to obtain a direct measure of the overall climate response or feedback parameter (Y, units Wm^{-2} °C^{-1}). This parameter is the increase in net outgoing radiative flux, adjusted for any change in forcings, for each 1°C rise in the Earth’s mean surface temperature. Forster/Gregory 06 then derived an estimate of equilibrium climate sensitivity (hereafter “climate sensitivity”, with value denoted by S), the rise in surface temperature for a doubling of CO_{2} concentration, using the generally accepted relation S = 3.7/Y °C.

[–snip–]

The IPCC did not attempt, in the relevant part of AR4:WG1 (Chapter 9), any justification from statistical theory, or quote authority for, restating the results of Forster/Gregory 06 on the basis of a uniform prior in S. Nor did the IPCC challenge the Forster/Gregory 06 regression model, analysis of uncertainties or error assumptions. The IPCC simply relied on statements [Frame et al. 2005] that ‘advocate’ – without any justification from statistical theory – sampling a flat prior distribution in whatever is the target of the estimate – in this case, S. In fact, even Frame did not advocate use of a prior uniform distribution in S in a case like Forster/Gregory 06. Nevertheless, the IPCC concluded its discussion of the issue by simply stating that “uniform prior distributions for the target of the estimate [the climate sensitivity S] are used unless otherwise specified”.

The transformation effected by the IPCC, by recasting Forster/Gregory 06 in Bayesian terms and then restating its results using a prior distribution that is inconsistent with the regression model and error distributions used in the study, appears unjustifiable. In the circumstances, the transformed climate sensitivity PDF for Forster/Gregory 06 in the IPCC’s Figure 9.20 can only be seen as distorted and misleading.

The foregoing analysis demonstrates that the PDF for Forster/Gregory 06 in the IPCC’s Figure 9.20 is invalid. But the underlying issue, that Bayesian use of a uniform prior in S conveys a strong belief in climate sensitivity being high, prejudging the observational evidence, applies to almost all of the Figure 9.20 PDFs.