*By Christopher Monckton of Brenchley*

*Mainstream climate scientists have been busy in the last two years, publishing updated climatological data in time for IPCC’s forthcoming Sixth Assessment Report. The availability of those recent mainstream data provides an opportunity to derive from them the midrange equilibrium climate sensitivity to doubled CO_{2} (ECS) that IPCC ought to be predicting on the basis of those data.*

*As Monckton of Brenchley et al. (2015) pointed out in a paper for the Chinese Academy of Sciences in 2015, one does not need a complex, multi-billion-dollar computer model that gobbles up a small town’s-worth of electricity and topples a dozen polar bears every time it is turned on if all one wants to know is ECS. ECS is a useful standard yardstick because the doubled-CO_{2} forcing is roughly equal to the total anthropogenic forcing we might expect to see this century on a business-as-usual scenario. That paper, incidentally, has been downloaded from the Chinese Academy journal’s website more often than any other in its 60-year history, by an order of magnitude.*

*Here is a handy, do-it-yourself ECS calculator based on the latest data.*

*IPCC (1990) had predicted midrange medium-term anthropogenic warming equivalent to 0.34 K decade ^{–1}. In the real world, however, the least-squares trend over the 30 years 1991-2020 on the mean anomalies in two surface (GISS and HadCRUT) and two lower-troposphere (RSS and UAH) monthly temperature datasets is 0.2 K decade^{–1}, of which 70% (Wu et al. 2019), or 0.14 K, was down to us.*

*Therefore, IPCC’s original midrange medium-term lower-atmosphere warming has proven overstated 2.4 times over. John Christy (2021), in a fascinating online talk, has recently shown (Fig. 1) that the CMIP6 models have also overstated midrange mid-troposphere warming 2.4-fold.*

*One can gain a first ballpark estimate of midrange ECS by taking the CMIP6 mean 3.7 K ECS prediction (Meehl et al. 2020) and dividing it by 2.4. Answer: 1.5 K: not enough to worry about.*

*To derive ECS ΔE_{2} more precisely by developing the ideas in the Chinese Academy paper, just seven readily-obtainable and respectably-constrained mainstream midrange quantities are needed.*

**1: The Planck sensitivity parameter P **is the first derivative of the Stefan-Boltzmann equation: i.e., the ratio of surface temperature to 4 times the albedo-adjusted incoming top-of-atmosphere radiative flux density (Schlesinger 1988). Thus,

**= 288 / (4 x 241), or 0.3 K W**

*P*^{–1}m

^{2}. That uncontroversial value varies with surface temperature: but, from 1850 to doubled CO

_{2}compared with today’s temperature, it is close enough to 0.3 to make little difference.

**2: Doubled-CO**_{2}** radiative forcing Δ Q**

_{2}**was given as 3.45 W m**

^{–2}, the mean of 15 CMIP5 models, in Andrews (2012). For CMIP6, Zelinka et al. (2020) give 3.52 W m

^{–2}. Since we are using the latest mainstream data, we shall go with the latter value.

**3: The exponential-growth factor H **of unit feedback response with reference sensitivity is here taken, for caution, as equal to the 1.07 K

^{–1}given as the Clausius-Clapeyron increase in specific humidity with warming in Wentz (2007). This quantity, too, varies with temperature, but can safely be taken as constant over the narrow temperature interval of relevance here. In reality, the exponential growth in specific humidity is offset by the logarithmic temperature response to that growth, and IPCC (2013) estimates that at midrange all other feedbacks self-cancel. In reality, there is probably little or no growth in unit feedback response under today’s conditions. However, even if one were to assume

**= 1.2, well above reality, ECS would barely change.**

*H***4: Anthropogenic forcing Δ Q**

_{1}**from 1850-2020**was 2.9 W m

^{–2}, the sum of the 3.2 W m

^{–2}accumulated-greenhouse-gas forcing and the 0.4 W m

^{–2}ozone, –0.8 W m

^{–2}aerosol and 0.1 W m

^{–2}black-carbon forcings (NOAA AGGI; Gaudel+ 2020; Dittus+ 2020; IPCC 2001, p. 351).

**5: The anthropogenic fraction M **of warming and radiative imbalance from 1850-2020 was 0.7 (Wu et al., 2019; Scafetta 2021). The Wu paper has Gerald Meehl as a co-author.

**6: Transient warming T**

_{1}**from 1850-2020 was 1.07 K (HadCRUT5: Morice et al. 2020). Based on Wu et al., only 70% of this, or 0.75 K, was anthropogenic.**

**7: The Earth’s energy imbalance Δ N**

_{1}**from 1850-2020 takes account of delay in onset of warming after a forcing. Schuckmann et al. (2020) give the current mainstream midrange estimate 0.87 W m**

^{–2}.

*With these seven quantities (Fig. 2), all midrange, all up to date, all from mainstream climatological sources, one may not only derive a reliable midrange estimate of observational ECS directly without resorting to over-complex, insufficiently-falsifiable and error-prone computer models but also falsify the tenability of the currently-projected ECS interval 3.7 [2.0, 5.7] K (midrange Meehl et al., 2020; bounds Sherwood et al., 2020). Calculations are in Fig. 3. That simple table spells doom for the profiteers of doom.*

**How it works: **We have now influenced climate for 170 years since 1850. Before then, our influence was negligible. From the seven quantities in Fig. 2, a vital quantity is derivable – the unit feedback response, the additional warming from feedback per degree of reference sensitivity. With that, the unit feedback response for the period from now until doubled CO_{2} can be found with the help of the exponential-growth factor *H**, *whereupon ECS **Δ R**

**may bederived.**

_{1}**1850-2020: **The period unit feedback response ** U_{1}** is 1 less than the ratio of equilibrium sensitivity

**Δ**

*E***to reference sensitivity**

_{1}**Δ**

*R***: i.e., 1 less than the ratio of period warming including feedback response to period warming excluding feedback response).**

_{1}**Period reference sensitivity Δ R**

**, the direct warming before adding any feedback response, is 0.865 K, the product of the 0.3 K W**

_{1}^{–1}m

^{2}Planck parameter

**and the 2.9 W m**

*P*^{–2}period anthropogenic forcing

**Δ**

*Q***.**

_{1}**Period equilibrium sensitivity Δ E**

**, the eventual warming after all short-timescale feedbacks have acted and the climate has resettled to equilibrium, is a little more complicated. It is the product of two expressions: the anthropogenic fraction**

_{1}

*M***Δ**

*T***of observed period transient warming**

_{1}**Δ**

*T***and the energy-imbalance ratio.**

_{1}*The energy-imbalance ratio is the period anthropogenic forcing ΔQ_{1} divided by the difference between ΔQ_{1} and the anthropogenic fraction M ΔN_{1} of the period Earth energy imbalance ΔN_{1}. At equilibrium there would be no energy imbalance: the divisor and dividend would both be equal to ΔQ_{1}. In that event, ΔE_{1} would be equal to M ΔT_{1}. However, where (as at present) an energy imbalance subsists, further warming will occur even without further radiative forcing after 2020, so that ΔE_{1} is the product of M ΔT_{1} and the energy-imbalance ratio: i.e., 0.975 K.*

**The unit feedback response U**

**, the feedback response per degree of period reference sensitivity, i**

_{1}**s**1 less than the system-gain factor

**Δ**

*E***/**

_{1}**Δ**

*R***. It is just 0.127. Contrast this straightforward, real-world, observationally-derived midrange value with the 3.0 implicit in the following passage from Lacis et al. (2010), which encapsulates the erroneous official position:**

_{1}*“Noncondensing greenhouse gases, which account for 25% of the total terrestrial greenhouse effect, … provide the stable temperature structure that sustains the current levels of atmospheric water vapor and clouds via feedback processes that account for the remaining 75% of the greenhouse effect” (Lacis et al., 2010).*

**2020 to doubled CO**_{2}**: **As with 1850-2020, so with doubled CO_{2} concentration compared with the 415 ppmv in 2020, begin with –

**Period reference sensitivity Δ R**

**, the direct warming before adding any feedback response.**

_{2}**Δ**

*R***is 1.054 K. It is the product of the 0.3 K W**

_{2}^{–1}m

^{2}Planck parameter

**and the 3.52 W m**

*P*^{–2}period anthropogenic forcing

**Δ**

*Q***.**

_{2}*Next, feedback response is allowed for, so as to obtain ECS ΔE_{2}. The method is to increase the 1850-2020 unit feedback response U_{1} in line with the exponential-growth factor H.*

**The unit-feedback-response ratio X **is equal toexp(

*P***Δ**

*Q***ln**

_{2 }**), i.e., exp(**

*H***Δ**

*R***ln**

_{2}**), or, more simply, but offensively to math purists,**

*H*

*H*^{ΔR}**, which is 1.074.**

^{2}**The unit feedback response U**

**is the product of**

_{2}

*U***and**

_{1}**, i.e., 1.136.**

*X***ECS**** ****Δ E**

**is the product of reference sensitivity**

_{2}**Δ**

*E***to doubled CO**

_{2}_{2}and the system-gain factor

*U***+ 1: i.e., 1.2 K. Not 3.7 K (CMIP6: Meehl et al. 2020). Not 3.9 K (CMIP6: Zelinka et al. 2020). Just 1.2 K midrange anthropogenic global warming in response to doubled CO**

_{2}_{2}, or to all anthropogenic forcings across the entire 21

^{st}century. Not much of a “climate emergency”, then, is there?

**Falsifying ECS predictions via the response ratio X:** Knowing that the observationally-derived unit feedback response

*U***for 1850-2020 was 0.127, it is possible to derive the value of**

_{1}

*X***implicit in any ECS prediction**

_{P}**Δ**

*E***:**

_{2P}**= (**

*X*_{P}**Δ**

*E***/**

_{2P}**Δ**

*R***– 1). For instance, the 3.7 [2.0, 5.7] K ECS predicted by Meehl et al. (2020) and Sherwood et al. (2020) implies**

_{2}

*X***on 20 [7, 35]. Even the lower-bound**

_{P}

*X**=*7 would suggest, untenably, that the feedback response per degree of direct warming after 2020 was an absurd seven times the feedback response per degree before 2020. The high-end ECS of 10 K predicted in several extreme papers is still more impossible, implying

**= 67.**

*X***Uncertainties **are small, since by now climatology has settled on the values of the seven key parameters that are all that is needed to find ECS. If the 40 years’ rather more rapid warming from 1980-2020 were used as the basis for calculation, rather than 1850-2020, midrange ECS would rise to just 1.4 K. Even if all of the industrial-era warming were anthropogenic, ECS would be only 2 K, but it would no longer be midrange ECS based on current mainstream data.

**What they got wrong: **How, then, did climate scientists ever imagine that global warming would be about thrice as much as real-world observation reflected in Their latest midrange data would lead a dispassionate enquirer to expect?

*Climate models do not embody feedback formulism directly. However, their ECS predictions reflect the error in that they show 2.4 times as much medium-term midrange anthropogenic warming as has been observed over the past 30 years, and they are predicting 3 times the realistic midrange ECS.*

*In 2006, in preparation for my first article on global warming, I wrote to the late Sir John Houghton, then chairman of IPCC’s science working group, to ask why it was thought that eventual global warming would be about three times the direct warming. He replied that the natural greenhouse effect – the difference between the 255 K emission temperature without any greenhouse gases and the 287 K measured temperature in 1850 – comprised 8 K reference sensitivity to greenhouse gases and 24 K feedback response thereto.*

*It was this expectation of 3 K feedback response to every 1 K of direct warming, making 4 K eventual warming in all, that led the modelers to expect 3 or 4 K midrange ECS.*

*Climatologists had forgotten the Sun was shining (Fig. 4). What they had missed, when they borrowed feedback formulism from control theory in the mid-1980s, was that the 24 K preindustrial feedback response was not solely a response to the 8 K direct warming by greenhouse gases. A large fraction that 24 K of it was response to the 255 K emission temperature that would have obtained on Earth even without any greenhouse gases.*

*In reality, the preindustrial reference temperature was the sum of the 255 K emission temperature and the 8 K reference sensitivity to preindustrial greenhouse gases: i.e., somewhere in the region of 263 K. Given that the 255 K emission temperature is 32 times the 8 K preindustrial reference sensitivity to greenhouse gases, a substantial fraction of the 24 K total preindustrial feedback response was due to the former, correspondingly reducing the fraction due to the latter.*

*Feedback is a generally-applicable property of dynamical systems (systems that change their state over time), from electronic circuits to climate. If and only if the entire preindustrial reference temperature were 8 K, with no feedback response at all to emission temperature, would it be permissible to imagine that the unit feedback response was as great as 3. Even then, it would not follow automatically that today’s unit feedback response could be anything like as great as 3.*

*IPCC repeated the error in its 2013 Fifth Assessment Report and is about to do so again in its forthcoming Sixth Assessment Report. It defines “climate feedback” as responding only to perturbations (mentioned five times in the definition), but is silent on the far larger feedback response to emission temperature itself. It should replace its multi-thousand-page reports with the single monster equation (Fig. 5) that consolidates the stepwise calculations in Fig. 3:*

*Would you be willing to put your name to a report to IPCC, under its Error-Reporting Protocol, notifying it that ECS has been grossly overstated and requesting correction? If so, contact me via the first word of my surname [at] mail [dot] com and let me know. For the latest mainstream midrange data on which IPCC must perforce rely rule out the rapid, dangerous warming that it has so long, so confidently, so profitably but so misguidedly predicted.*

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