Part I: How the central estimate of global warming was exaggerated

By Christopher Monckton of Brenchley

In this new series, I propose to explore the sequence of errors, large and small, through which the climatological establishment has – until now – gotten away with greatly exaggerating climate sensitivity.

The errors have an unholy, cumulative effect, conspiring to bring about an exaggeration that is grievous.

The focus in this series will be on describing each error clearly, so that the commenters who have so vigorously had their say on my earlier descriptions of the current method of determining climate sensitivity can examine them and say whether they think the climatological establishment has come to the right conclusion.

I shall do my best to make it clear when I am describing the official position and when I am describing a proposed alternative view.

By all means criticize me if you think I am wrong about the errors I have identified, or if you think my description of the official position is wrong. But do not hold my feet to the fire for the official position itself: address your criticisms of it to the IPCC secretariat. I am here not to argue for the official position, but rather to raise certain very specific questions about it.

And please read these head posting carefully before you rush to comment. In my last posting, for instance, a commenter wrote that only at a late stage in the follow-up conversation had I introduced the notion that the emission temperature formed part of the basis for determining the reference sensitivity parameter λ 0 (see Fig. 2 for an illustration of how the official equation uses this parameter). In fact, the emission temperature had been explicitly determined in the head posting. There is a lot of detail in these postings. Read them carefully.

I shall not be considering the vexed question whether any or all of the errors the climatological establishment have insouciantly perpetrated and then sullenly perpetuated are deliberate, nor the related question of the extent to which certain leading members of that establishment know about the errors but find it socially convenient, politically expedient and, above all, financially profitable to look the other way. I shall merely report the errors as I find them, and invite your comments.

This is Part I of the series. In this first article, I shall describe a rather small error that arises from a consideration that will eventually be seen to have a very large influence on official exaggerations of predicted global warming. You may not think, at this stage, that it is really an error at all. Be patient. As this series unfolds, the full horror of what the climatological establishment has done will be exposed, step by ineluctable step.

Here and throughout the series, temperatures on the absolute or Kelvin scale will be given and anomalies stated in Celsius degrees will be presented as anomalies in Kelvin. Also, for simplicity, the IPCC’s Assessment Reports of 1990, 1995, 2001, 2007 and 2013 will be labeled AR1-5. The series will concern itself chiefly with equilibrium sensitivity.

Let us begin at the beginning. Almost 40 years ago, Charney (1979, p.2), in a report for the U.S. National Academy of Sciences, concluded: “We estimate the most probable global warming for a doubling of CO 2 to be near 3 [K], with a probable error of ± 1.5 [K].”

AR1 (p. xxv) concluded that “the models[’] results do not justify altering the previously accepted range of 1.5 to 4.5 [K]”, but added that, “Although scientists are reluctant to give a single best estimate in this range, … a value of climate sensitivity of 2.5 [K] has been chosen as the best estimate.”

AR2 (p. 34) and AR5 (p. 16) concurred, though AR5 declined to provide a central estimate.

Later in this series I shall address the remarkable fact that, after almost 40 years and tens of billions in taxpayers’ dollars, the climatological establishment has been unable (or unwilling) to narrow the interval of official global-warming predictions. So broad is the interval of those predictions that the “settled science” of how much global warming our sins of emission may cause is no more “settled” now than it was in 1979.

For now, however, let us focus on central estimates of climate sensitivity. Since there is now broad agreement among official circles that the radiative forcing in response to a CO 2 doubling is 3.7 Watts per square meter (an agreement that we shall in due course find unjustifiable, but that is not for today, so we shall accept it for now ad argumentum), the major reason for the large differences between models’ global-warming predictions is the great variation in estimates of temperature feedbacks – the additional forcing that are thought to arise as a result of the direct warming of the atmosphere caused by the original forcing and are expressed in Watts per square meter of the reference warming that triggered them.

Fig. 1 shows that indeed it is differences in feedbacks that are the cause of the broad interval of “settled-science” climate sensitivities. For climate sensitivities on 3.0 [1.5, 4.5] K imply unitless temperature-feedback factors f on 0.60 [0.23, 0.73] – an interval that is egregiously inconsistent with the remarkable near-thermostasis of the climate evidenced by the ice-cores over the past 810,000 years (see e.g. Jouzel et al., 2007).

The central feature of Fig. 1, for present purposes, is that the climate-sensitivity response ΔT to various values for the feedback factor f is very far from linear. This non-linearity will crop up again and again as this series unfolds, for the modelers, as will be seen in due course, understand it poorly.

Anyone who has ever built an operational-amplifier circuit intended to operate stably will know that a designed-in maximum feedback factor of not more than 0.1 (or 0.01 if possible) is desirable to ensure that anomalies in componentry, assembly, operation and ambient conditions do not induce unwanted runaway responses. The climate is remarkably stable: global temperatures have varied by little more than 3.3 K either side of the period mean for 810,000 years.

Given this near-perfect thermostasis, it is improbable a priori, and will later in this series be demonstrated to be impossible a posteriori, that true feedback values can fall anywhere in the zone marked “unstable” on the graph. The shaded zone, equivalent to an interval [1.5, 4.5] K for final or equilibrium climate sensitivity ΔT, is thus squarely in forbidden territory. But more of that another day.

Fig. 1 The response curve of equilibrium post-feedback climate sensitivity ΔT for feedback factors f on [–0.5, +2.0], showing the singularity at f = 1.0 and the design maximum at f = 0.1 generally adopted by process engineers for electronic circuits intended to perform stably. The shaded region covers the interval 0.60 [0.23, 0.73] of feedback factors f for AR5’s climate sensitivity ΔT on [1.5, 4.5] K, with the central estimate 3.0 K given in Charney (1979).

Back to today, when I am approaching the first little error toe-in-the-water [in passing, you will be delighted to know that the charming Latin adverb for “toe-in-the-water” is pedetemptim].

At present, official climatology tends to take the inter-model mean climate sensitivity as the central estimate of ΔT. However, as Fig. 1 shows, this approach implies a central estimate for the feedback factor f that is a great deal closer to the upper than to the lower bound of the interval of feedback factors f; and it is f that chiefly determines final sensitivity ΔT.

The correct approach, therefore, is to determine the inter-model mean feedback factor f and then to plug that value into the official climate-sensitivity equation (1), illuminated in Fig. 2, to determine the central estimate of final or equilibrium sensitivity.

In the current understanding, the pre-feedback or reference sensitivity determined from the left-hand or feedback part of (1), encompassed by the pale green brace, is 1.16 K. This, too, will turn out to be an exaggeration, but we shall deal with that in future articles.

Fig. 2 Illumination of the official climate-sensitivity equation (1)

From that value and from the predicted upper and lower bounds [1.5, 4.5] K of final or equilibrium climate sensitivity ΔT, it is a simple matter to rearrange the official equation to determine via (2) the feedback factors f corresponding with those bounds:

Thus, for ΔT on [1.5, 4.5] K, the feedback factor f falls on [0.23, 0.73]. The multi-model mean value of f will generally be close to the mean of the upper and lower bounds: thus, the central estimate of f will be about 0.48, from which (1) can be used to approximate the proper central estimate of climate sensitivity corresponding to the interval [1.5, 4.5] K, as (3) shows:

Charney’s central estimate ΔT = 3.0 K is more than one-third greater than this. The central estimate ΔT = 2.5 K in AR1, AR2 came closer to the true central estimate, but is still overstated by 12.5%, or one-eighth. As we say in Scotland, mony a mickle mak’s a muckle, and this apparently insignificant exaggeration is the beginning of the sequence of excesses that compound into a very large exaggeration indeed.

What of the vaunted ensembles of expensive models with which the climatological establishment has attempted to overcome the Lorenz constraint (Lorenz, 1963) on the reliable long-term prediction of future climate states that arises from the extreme sensitivity of the evolutionary path of objects such as the climate to very small variations in the initial conditions (AR3, §14.2.2.2)?

For the CMIP3 and CMIP5 model ensembles, the feedback sums c = Σ i c i , expressed in Watts per square meter per Kelvin, are illustrated graphically in AR5, fig. 9.43a, of which an enhanced detail is shown at Fig. 3.

Fig. 3 Feedback sums c = Σ i c i for CMIP5/AR5 and CMIP3/AR4

The published CMIP3 climate sensitivities are 3.3 [2.1, 4.4] K (AR5, p. 820, §9.7.3, for the bounds; AR5, p. 83, box TFE.6, for the central estimate). As Fig. 3 shows, the interval of feedback sums c in the CMIP3 ensemble was 1.93 [1.53, 2.35] W m–2 K–1. The product of the reference sensitivity parameter λ 0 = 0.312 K W–1 m2, determined as shown in Fig. 2, and these values of c is the interval 0.60 [0.48, 0.73] of feedback factors f. Then the final-gain factor G = (1 – f)–1, the ratio of final sensitivity ΔT to the reference sensitivity ΔT 0 , falls on 2.51 [1.91, 3.74], whereupon equilibrium post-feedback climate sensitivity ΔT = ΔT 0 G obtained using (1) accordingly falls on 2.9 [2.2, 4.3] K. The bounds are near-coextensive with those of the published CMIP3 equilibrium-sensitivity interval (assuming just a 3% variance in ΔT 0 they would be exact), but the published central estimate is shown to have been overstated by about one-eighth.

For the CMIP5 model ensemble for AR5, a similar analysis may be performed. The published CMIP5 equilibrium-sensitivity interval is 3.2 [2.1, 4.7] K (AR5, p. 83, box TFE.6). The interval of feedback sums c was 1.53 [1.00, 2.25] W m–2 K–1. The product of the reference sensitivity parameter λ 0 and these values gives the interval 0.48 [0.31, 0.70] of feedback factors f. Then the final-gain factor G = (1 – f)–1 falls on 1.91 [1.45, 3.35]. Vial et al. (2013, fig. 5a), the official paper analysing the CMIP5 models’ output for AR5, somewhat arbitrarily raises reference or pre-feedback sensitivity ΔT 0 from 1.16 to 1.42 K on the ground that some of the tropospheric changes caused by the CO 2 forcing do not affect sea surface temperatures and should thus be counted as part of the reference sensitivity. On this basis, equilibrium post-feedback climate sensitivity ΔT = ΔT 0 G obtained using (1) falls on 2.7 [2.1, 4.7] K. As with the CMIP3 models for AR3, the bounds determined from (1) are coextensive with the published CMIP5 equilibrium-sensitivity bounds, but the analysis shows the published central estimate to have been overstated by 18.5%.

Table 1 summarizes the overstatements of the central estimates of climate sensitivity:

Table 1 Exaggerated central climate-sensitivity estimates Official source Interval of ΔT Erroneous Corrected Exaggeration Charney (1979) [1.5, 4.5] K 3.0 K 2.2 K +35% AR1, AR2 [1.5, 4.5] K 2.5 K 2.2 K +12.5% CMIP3 for AR4 [2.1, 4.4] K 3.3 K 2.9 K +12.5% CMIP5 for AR5 [2.1, 4.7] K 3.2 K 2.7 K +18.5% AR5 [1.5, 4.5] K None 2.2 K n.a.

The official central estimates are exaggerated because the modelers have failed to take proper account of the exaggerated non-linearity of the temperature responses to linearly-increasing feedback sums. They have allowed that non-linearity to drag the central climate-sensitivity estimates erroneously upward by 12.5-35%.

Ø Next: How reference climate sensitivity ΔT 0 was exaggerated

References

Charney J (1979) Carbon Dioxide and Climate: A Scientific Assessment: Report of an Ad-Hoc Study Group on Carbon Dioxide and Climate, Climate Research Board, Assembly of Mathematical and Physical Sciences, National Research Council, Nat. Acad. Sci., Washington DC, July, pp. 22

IPCC (1990-2013) Assessment Reports AR1-5 are available from www.ipcc.ch

Lorenz EN (1963) Deterministic nonperiodic flow, J. Atmos. Sci. 20: 130-141.

Vial J, Dufresne J, Bony S (2013) On the interpretation of inter-model spread in CMIP5 climate sensitivity estimates, Clim Dyn 41: 3339, doi:10.1007/s00382-013-1725-9

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