Find out how to constrain unconstrained global-warming predictions – Watts Up With That?

By Christopher Monckton of Brenchley

Andy May’s splendid brace of articles about climate sensitivity, which gives a concise and elegant summary of close to half a century of scientific debate, concludes as follows:

“The ‘consensus’ estimates of the impact of greenhouse gases, especially CO2, on climate and global warming are the same as they were 42 years ago. The uncertainty has not narrowed. Observations invalidate the high IPCC modelled climate sensitivity today, just as they did for the National Research Council in 1979. …

“It is terribly sad that, after spending billions of dollars and untold man-hours, we have not narrowed the range of climate sensitivity to CO2 since 1979.”

In this essay, I propose to explain why it is that the range of predictions of future global warming remains so broad, and so excessive, and how it can be quite tightly constrained.

Andy’s words above echo those of the deputy director of the Russian Academy of Sciences, Academician Semenov, at a high-level meeting on climate sensitivity that I attended in Moscow at the invitation of the City Government two years ago. Academician Semenov opened the meeting by saying it was unsatisfactory that the interval of equilibrium sensitivities has remained as broad and as unconstrained as it is for as long as it has.

I replied that the reason why climate sensitivities had proven unconstrainable was the mistreatment of temperature feedback in climatology. Semenov drew me aside after the meeting, together with an IPCC representative, and I was asked to explain what I had meant.

Semenov, on hearing what I had to say, and on seeing that the IPCC representative could not refute it, called in the chief architect of the Russian climate model, who took careful notes.

Fig. 1. Rectangular-hyperbolic system response ECS to projected feedback fractions H > 0.5 entails excessive, ill-constrained ECS, while H < 0.25 constrains ECS well.

The problem is that unit feedback response (per degree of reference sensitivity), and hence the system-gain factor (the ratio of equilibrium sensitivity including feedback response to reference sensitivity excluding it), and hence equilibrium sensitivity itself, respond rectangular-hyperbolically to the feedback fraction (Fig. 1).

Because climatologists imagine (unjustifiably, as I shall show) that the feedback fraction is around 0.75, their predictions of global warming are both excessive and ill-constrained. The lack of constraint arises because the entire interval of overstated official global-warming predictions falls on the part of the rectangular hyperbola that soars away towards infinity.

I shall not be relying upon the climate models, because, as Pat Frank’s paper of 2019 on propagation of uncertainty in time-step models has definitively demonstrated, models cannot accurately predict global warming. They can tell us absolutely nothing – nothing at all – about how much warming we may cause. They may have many other purposes, but that is not one of them.

Pat – whose paper has not been refuted in the learned journals, though there have been one or two strikingly ignorant blog posts about it – has now written to draw the attention of the IPCC, via its error-reporting protocol, to its mistake in relying upon models for predicting future warming, For he has proven, using the standard validation technique of statistical propagation of uncertainty, that all the models’ predictions are no better than guesswork.

He has not received a reply, of course. For his paper – perhaps the most important ever to have been published in the field of climate-sensitivity studies – renders the entire basis for IPCC’s predictions, and for the pathetic pandemic of panic about warmer worldwide weather, null and void.

Instead, I shall use an earlier and inherently more reliable method of constraining equilibrium doubled-CO2 sensitivity (ECS), which is approximately equal to the entire all-causes anthropogenic warming over the 21st century (the two radiative forcings being about the same, at 3.5 Watts per square meter).

That powerful empirical constraint on equilibrium sensitivities outside GCMs, still deployed today, is apportionment of the total greenhouse effect between three quantities: direct warming by natural and anthropogenic greenhouse gases and feedback response –

“The strength of the greenhouse effect can be gauged by the difference between the effective emitting  temperature of the Earth as seen from space (about 255 K) and the globally-averaged surface temperature …” (IPCC 1990, p. 48).

Let us begin by agreeing some quantities. In my submission, the quantities in the following paragraphs are, broadly speaking, agreed by all sides in the climate debate.

First, as IPCC says above, the emission temperature that would prevail near the Earth’s surface in the total absence of greenhouse gases at the outset would be about 255 K.

As Professor Lindzen, the world’s foremost climatologist, said in a paper published in 1994, the true zero-feedback emission temperature, before allowing for any greenhouse-gas warming or feedback response, is more like 271 K once one has recalled that clouds would not be present in the absence of greenhouse gases. However, that is before allowing for Hölder’s inequalities between integrals, which might bring emission temperature back down to about 255 K.

As Professor Brown has written in these columns, establishing the true emission temperature is not a trivial problem. Here, ad argumentum, we shall consider an interval 255 [240, 270] K of emission temperature.

Today’s global mean surface temperature is about 288.5 K. Therefore, the midrange total greenhouse effect is 288.5 – 255, or 33.5 K. The 33.5 K greenhouse effect is the sum of three components: direct warming forced by preindustrial noncondensing greenhouse gases to 1850, before we had any significant influence on climate; direct warming forced by anthropogenic noncondensing greenhouse gases during the industrial era from 1850-2020; and feedback response.

Table 1. Preindustrial greenhouse-gas forcings

Table 1, based on concentrations of greenhouse gases in 1850 from Meinshausen+ (2017), gives the preindustrial radiative forcing to 1850 from the principal radiatively-active species. CFCs and HFCs are excluded because in 1850 their concentration was negligible.

Since the Planck sensitivity parameter (the first derivative of the Stefan-Boltzmann equation) is about 0.3 Kelvin per Watt per square meter, the direct warming by preindustrial greenhouse gases was 0.3 x 25.3, or 7.6 K.

Anthropogenic forcing from 1850-2020 was about 3.2 K (NOAA AGGI), with all non-greenhouse-gas anthropogenic forcings broadly self-canceling, so that direct period warming by anthropogenic greenhouse gases was about 0.9 K.

Therefore, the 33.5 K total greenhouse effect to date comprises 7.6 + 0.8 = 8.5 K direct greenhouse-gas warming, and 25 K feedback response.

We have also allowed for a 10% uncertainty (Cess et al. 1993) either side of the midrange 8.5 K estimate of total natural and anthropogenic reference sensitivity to date, and, simili modo, 10% either side of the midrange 1.06 K reference doubled-CO2 sensitivity (RCS: the product of the 0.3 K W–1 m2 Planck sensitivity parameter and the 3.52 W m–2 CMIP6 mean doubled-CO2 radiative forcing: Zelinka+ 2020).

Climatologists universally but erroneously assume that all of the 25 K feedback response to date must be feedback response to the 8.5 K direct warming by natural and anthropogenic greenhouse gases.

In logic, climatologists’ position cannot be correct. For the feedback processes that subsist at any given moment in a dynamical system such as the climate are inanimate. They have no freedom to decide that they will not respond at all to the first 29/30 of the 263.5 K total reference temperature in 2020, but that they will respond only, and suddenly, and very vigorously, to the final 1/30. Where is the sense in that?

Therefore, at any specified moment, such as the present, the feedback processes subsisting in the dynamical system of interest, the climate, must perforce respond equally to each degree of the 263.5 K total reference temperature.

The unit feedback response is, at that specified moment, applicable equally to each degree of reference temperature, without distinction. To the inanimate feedback processes, a Kelvin is a Kelvin is a Kelvin, regardless of its origin.

Therefore, the unit feedback response is not 25 / 8.5, or ~3, as climate scientists imagine. It is 25 / (255 + 8.5), or less than 0.1. Their implicit midrange unit feedback response is overstated by a factor 30.

Thus, the system-gain factor (just add 1 to the unit feedback response) is not 33.5 / 8.5, or ~4, as implied by the midrange CMIP6 ECS projection. It is (255 +33.5) / (255 + 8.5), or <1.1.

ECS, then, is not 4 times the 1.06 K RCS: after correction, it is <1.1 times RCS: i.e, more like 1.1-1.2 K. The currently-imagined ~4 K mean midrange ECS in the CMIP6 models is thus a near-fourfold overstatement – another reason why we do not concern ourselves with the models.

Table 2 shows that, though the current method of deriving ECS by apportionment of the total greenhouse effect is very sensitive to quite small uncertainties in emission temperature and in reference sensitivity to greenhouse gases, the corrected method is far less sensitive, for the dominance of emission temperature in the corrected equations calms everything down.

Table 2. ECS derived from current and corrected apportionments of the greenhouse effect

Sure enough, the use of mainstream, midrange data for the industrial era, making due allowance for the currently-estimated Earth energy imbalance, gives midrange ECS of 1.1 K, near-identical to the midrange 1.2 K obtained straightforwardly by correctly apportioning the total greenhouse effect.

At any moment, the feedback processes subsisting at that moment must necessarily respond equally and without discrimination to each degree of the then-subsisting total reference temperature. Therefore, at that moment, the magnitude of the feedback response to each component in that reference temperature is necessarily and strictly proportional to the magnitude of that component.

Thus, in the midrange case, the three components in the 263.5 K reference temperature are the 255 K emission temperature, the 7.6 K natural reference sensitivity and the 0.9 K anthropogenic reference sensitivity.

Therefore the three components in the 25 K total feedback response are the feedback responses of 24.2 K to emission temperature, 0.7 K to natural reference sensitivity and 0.1 K to anthropogenic reference sensitivity.

Note that this strictly-proportional apportionment at any given moment does not necessarily entail invariance of unit feedback response and consequently of the system-gain factor with temperature: it is simply an Augenblick of the position obtaining at that moment.

However, given that the 3.2 W m–2 total anthropogenic forcing to date is equivalent to 90% of the 3.52 W m–2 doubled-CO2 forcing, and given that RCS is little more than 1 K, it is scarcely credible that ECS will fall on the currently-implicit interval 4 [2, 6] K, for that would imply, per impossibile, that the doubled-CO2 unit feedback response 3 [1, 5] would exceed the industrial-era unit feedback response 1.1 – 1 = 0.1 by a factor 30 [10, 50].

Climatologists, by not realizing that emission temperature is by far the largest contributor to feedback response, mistakenly added the 24.2 K emission-temperature feedback response to, and miscounted it as though it were part of, the 0.8 K feedback response to direct warming forced by natural and anthropogenic greenhouse gases.

Thus, they exaggerated all the feedback-related quantities – including the unit feedback response (per degree of reference sensitivity), the feedback fraction (the fraction of equilibrium sensitivity represented by feedback response, and the system-gain factor. Table 3 shows the current and corrected calculations for these and other feedback-related quantities:

Table 3. Excess of current over corrected values of key feedback-related variables

There, then, is the answer to Andy May’s question. Suddenly, the hitherto-unconstrainable equilibrium sensitivities become constrained – and their entire interval turns out to be below the lower bound of the currently-imagined interval. Inserting the 255 K emission temperature in the equations for the relevant feedback-related variables calms the entire system down, and leads us to expect a small, slow, harmless, net-beneficial warming over the coming century.

Unless, that is, the solar grand minimum first adumbrated by Soon and Baliunas, Habibullo Abdussamatov, Valentina Zharkova, David Archibald, David Evans and others, and now beginning to be anticipated even by official climatology, cancels much or perhaps all of the 1.1-1.2 K 21st-century warming that is all that we can realistically hope for.


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