By Christopher Monckton of Brenchley | June 8, 2019

I am most grateful to Mr Stokes for his interesting recent posting in which he explains what he sees as the difference between official climatology’s implementation of feedback in deriving climate sensitivity and the approach taken by my co-authors and me.

The sheer quantity of the comments on these mathematical and physical discussions is an indication that getting down and dirty among the equations is of more than passing interest to the readership.

Let me begin this response to Mr Stokes by setting out, in round numbers and in the simplest possible terms, the difference between official climatology’s conclusion that feedback triples the direct or reference warming from greenhouse gases and our conclusion that, with remarkably little error, one can safely ignore feedback altogether in calculating equilibrium sensitivities.

In the CMIP5 models, the latest generation for which ensemble results have been published, the mean reference sensitivity to doubled CO_{2} – that is, the amount of warming that would occur in response to a doubling of the atmospheric concentration of CO_{2} if no temperature feedbacks were operating or if they were net-zero – is 1.05 Kelvin (based on Andrews 2012).

It is also currently thought (rightly or wrongly) that that value is very close to exact: the uncertainty is only 10% either way. Therefore, *ad argumentum, *we shall accept as canonical the fact that reference sensitivity to doubled CO_{2} before accounting for feedback is 1.05 K.

However, the same models give a mean Charney sensitivity – that is, the amount of warming that will occur after all sensitivity-altering temperature feedbacks have acted and the climate system has returned to equilibrium – of 3.35 K per CO_{2} doubling (based on Andrews, *op. cit*.)*.*

From these two canonical values, we know that official climatology reckons that the feedback response to doubled CO_{2} is 3.35 – 1.05, or a whopping 2.3 K, in response to a mere 1.05 K reference sensitivity. Recall that feedback represents the entire difference between reference sensitivity (before feedback) and equilibrium sensitivity (after feedback).

If official climatology were right, then the system-gain factor, which is the ratio of equilibrium to reference sensitivity, would be 3.35 / 1.05, or 3.2. Official climatology actually imagines that feedbacks multiply any directly-forced warming 3.2 times over.

Where does official climatology get this massive multiple 3.2 from? Here’s how. The emission temperature of the Earth is usually taken as about 255 K, and the reference sensitivity to the naturally-occurring, noncondensing greenhouse gases present in 1850 is taken as about 10 K (see e.g. Lacis+ 2010) so that the reference temperature in 1850 – the temperature that would have prevailed in the absence of feedback – is 265 K.

However, the measured temperature in 1850 was 287.5 K (HadCRUT4), and that was an equilibrium temperature (there would be no trend during the following 80 years). The difference between the emission temperature of 255 K and the measured temperature of 287.5 K in 1850 is 32.5 K. Divide the equilibrium sensitivity of 32.5 K by the reference sensitivity of 10 K and you get 3.25 – more or less exactly the system-gain factor that official climatology takes as its midrange estimate.

Thus, to IPCC *et hoc genus omne, *feedback is the big enchilada. It is imagined to account for between two-thirds and (in the sillier extremist papers, up to nine-tenths) of total global warming.* *

In official climatology, feedback not only accounts for up to 90% of total warming but also for up to 90% of the uncertainty in how much warming there will be. How settled is “settled science”, when after 40 years and trillions spent, the modelers still cannot constrain that vast interval? IPCC’s lower bound is 1.5 K Charney sensitivity; the CMIP5 models’ upper bound is 4.7 K. The usual suspects have no idea how much warming there is going to be.

My co-authors and I beg to differ. Feedback is not the big enchilada. Official climatology has – as far as we can discover – entirely neglected a central truth. That truth is that whatever feedback processes are present in the climate at any given moment must necessarily respond not merely to changes in the pre-existing temperature: they must respond to the entire reference temperature obtaining at that moment, specifically including the emission temperature that would be present even in the absence of any non-condensing greenhouse gases or of any feedbacks.

To see why this must be so, consider the following simple block diagram:

In the block diagram, emission temperature comes in at top left. Then (following the arrows) the reference sensitivities that occur over time, first natural and then anthropogenic, are successively added to it. Then the reference temperature, the sum of all these, passes to the input/output node and thence infinitely round and round the feedback loop, where the separately-powered feedback block (powered by the retention in the atmosphere of radiation that would, without feedback, have passed harmlessly out to space) adds a smidgin to the signal on each pass. The output signal is equilibrium temperature after feedback has acted.

Your mission, should you choose to accept it, is to try to find a respectable explanation for official climatology’s notion that the feedback loop, which receives as its input signal the entire reference temperature, can somehow magically decide that it will respond only to the perturbations of that reference temperature caused by the presence of natural and then also of anthropogenic noncondensing greenhouse gases, and yet that it will not also respond at all to the emission temperature, two orders of magnitude greater than the sensitivities.

No doubt one could devise an electronic circuit that would perform that feat. But the climate is not a circuit. The feedbacks that were present in 1850 must perforce have acted not only upon the greenhouse warming to that date but also upon the emission temperature that was there before any noncondensing greenhouse gases had made their presence felt.

Here, then, is the corrected calculation. The reference temperature in 1850, before feedback, was 265 K. In that year the equilibrium temperature, after feedback, was 287.5 K. So the system-gain factor that applied in 1850 was 287.5 / 265, or 1.085, about a third of climatology’s 3.2.

Now, if we multiply the 1.05 K reference sensitivity to doubled CO_{2} by the corrected system-gain factor 1.085, we get a Charney sensitivity not of 3.35 K, as official climatology does, but of just 1.15 K.

Ah, you may say, but perhaps the curve of equilibrium temperature as a response to reference temperature is nonlinear. Maybe it is, but it cannot be very nonlinear. Why not? Because the reference temperature in 1850 was more than 92% of equilibrium temperature.

Now, Mr Stokes’ article is correct as far as it goes. His central point is that if you are starting from an equilibrium, such as that which obtained in 1850, you don’t need to know how that equilibrium occurred: you can work out the system-gain factor simply as the ratio of equilibrium sensitivity to reference sensitivity in any period later than that equilibrium, rather than as the ratio of equilibrium temperature to reference temperature at the time of equilibrium.

So let’s do it climatology’s way, using official climatology’s own data to 2011, the year to which the figures were brought up to date in time for IPCC’s 2013 *Fifth Assessment Report. *

The net anthropogenic forcing from 1850 to 2011 was about 2.5 Watts per square meter. However, the heat capacity of the ocean introduces a delay in the equilibrium response. This delay is reflected in a radiative imbalance, thought to have been about 0.6 Watts per square meter to 2010 (Smith+ 2015).

Taking Smith as correct *ad argumentum*, climatology’s period system-gain factor derivable from the data for 1850-2011 is simply the ratio of 2.5 to (2.5 – 0.6), i.e. 1.315 (see Lewis & Curry 2018 for the equations). Then Charney sensitivity would be 1.315 x 1.05, or just 1.4 K, not the 3.35 K that official climatology would currently have us imagine.

Notice how much closer to our estimate 1.15 K is that real-world 1.4 K Charney sensitivity, based on official climatology’s own estimates of actual anthropogenic forcing and radiative imbalance, than it is to climatology’s midrange estimate 3.35 K.

Why is our estimate of midrange Charney sensitivity so very much closer to what is inferred from official, published estimates of forcing and radiative imbalance than official climatology’s midrange estimate?

The reason is that, unlike official climatology, we use all the available information, and specifically the information about the respective magnitudes, in 1850, of the reference temperature (265 K) and of the feedback response (22.5 K). The sum of these two was the observed surface equilibrium temperature in 1850.

Official climatology, which simply does not realize that feedbacks necessarily respond to the entire reference temperature that obtains at a given moment, is left with no choice but to throw that vital information away. Here is Mr Stokes doing that quite specifically:

“It is wrong to include variables from the original state equation [i.e., in 1850]. One reason is that they have been accounted for already in the balance of the state before perturbation. They don’t need to be balanced again. The other is that they aren’t proportional to the perturbation, so the results would make no sense. In the limit of small perturbation, you still have a big reference temperature term that won’t go away. No balance could be achieved.”

Now, Mr Stokes is quite right to say that there was a temperature equilibrium in 1850 and that, therefore, at that time the surface temperature of 287.5 K already included the various variables, i.e. the 255 K emission temperature, the 10 K reference sensitivity to the naturally-occurring noncondensing greenhouse gases present in 1850 and the 22.5 K feedback response to the 265 K reference temperature.

He is also right to say these variables “do not need to be balanced again”. But, and this is crucial, they do need to be taken into account in deriving the corrected system-gain factor of 287.5 / 265 and, from that, the corrected Charney sensitivity.

Climatology overlooks these values because it is unaware that at any given moment (such as 1850) feedbacks respond to the entire reference temperature that prevails at that time. Like Luther, they can do no other.

Mr Stokes is also right to say that the variables – in which I think he includes the feedback response – are “not proportional to the perturbation”. Here, he makes precisely our point. The feedback response in 1850 was, of course, necessarily and ineluctably proportional to the entire 265 K reference temperature, which is the sum of the 255 K emission temperature and the 10 K reference sensitivity to the natural forcings present in that year.

But climatology, in effect, takes the entire feedback response in 1850 to have been proportional solely to the 10 K natural perturbation of reference temperature. And there is its mistake. That is why its estimate of Charney sensitivity – and of all equilibrium sensitivities – is three times too big. It has, in effect, allocated to greenhouse gases the large feedback response that arises simply because the Sun is shining.

Yes, one can derive the system-gain factor as the ratio of sensitivities, just as we can derive it as the ratio of absolute temperatures. But the former approach, that of official climatology, is subject to vast uncertainty, while our approach, using those vital data from 1850 that climatology has for so long ignored in its sensitivity calculations, provides an interval of Charney sensitivities that is both accurate and well constrained.

To derive equilibrium temperature, one needs to know the reference temperature and *either *the feedback response *or *the system-gain factor. But we don’t know and cannot by any rational means determine how big the feedback response is by counting up the individual feedbacks, as climatology currently tries to do, because it is feedbacks that are the near-exclusive cause of the uncertainty in official climatology’s global-warming predictions.

No feedback can be quantified by direct measurement. Nor can any form of observation, however well-resolved, meticulous and honest, allow us to distinguish reliably, and quantitatively, between different individual feedbacks, or even between feedbacks and the forcings that engendered them.

Climatology cannot calculate Charney sensitivity reliably, because, though it knows that the reference sensitivity to doubled CO_{2} is 1.05 K, it cannot know the value of the feedbacks and it does not know the system-gain factor. It does not know this vital quantity because it has thrown away the information available at the one point – before any significant anthropogenic intervention – for which the data are quite well constrained, and from which it can be directly derived: i.e., 1850.

The data for 1850 are quite well constrained precisely because the entire equilibrium and reference temperatures in that year exceed by two orders of magnitude the tiny equilibrium and reference sensitivities that are the basis of climatology’s so-far-failed attempts to constrain the system-gain factor and hence the likely magnitude of future global warming.

We know quite reliably what the system-gain factor was in 1850. We also know that it is not going to be a whole lot different in 2100 from its value of 287.5 / 265, or 1.085, in 1850.

Why do we know this? Because the industrial-era anthropogenic reference sensitivity of just 0.75 K from 1850 to 2011 was so very small compared with the 265 K reference temperature already present in 1850. The climate has simply not changed enough to engender a major shift in the feedback regime that obtained in that year.

Even if such a major shift were to have occurred, the additional feedbacks would have responded not merely to our perturbation of emission temperature but to the entire reference temperature, including emission temperature. For one thing, the Great Pause of almost 19 years in global temperature up to 2015 could not possibly have occurred.

Therefore, we can be reasonably confident that Charney sensitivity – i.e. equilibrium sensitivity to doubled CO_{2} compared with 2011 – is not going to be very much different from 1.15 K. In fact, our professor of statistics, having gone through all the numbers in the most meticulous detail, has calculated that the corrected 95% confidence interval of Charney sensitivity is 1.09 to 1.23 K, an interval of just one-seventh of a Kelvin. Compare that with the 3.2 K interval of official Charney sensitivities, which range from 1.5 to 4.7 K.

Notice that we are only able to calculate the Charney sensitivity correctly because we already knew the system-gain factor. We knew it because we were able to derive it from the data that official climatology throws away because it does not know feedbacks respond to the entire reference temperature and not only to arbitrarily-chosen reference sensitivities.

Mr Stokes talks of the 255 K reference temperature in 1850 “not going away”. Precisely: it was then present, as was the additional 10 K in warming forced by the presence of the naturally-occurring noncondensing greenhouse gases in that year. Because it was present, it should have been taken into account. But it was not taken into account.

Since we know from theory, and from the block diagram, and from the test rig built by one of our co-authors, and from the more sophisticated rig built and operated for us by a government laboratory, that the feedbacks that were present in 1850 perforce acted upon the entire reference temperature that was present in that year, we can instantly and quite safely derive from that year’s data the system-gain factor and hence Charney sensitivity.

No need for vast, costly general-circulation models, if all you want to know is how much warming we may cause.

No need to know the value of any individual feedback.

Remarkably, no need even to take feedback into account in the calculation: the undershoot in Charney sensitivity that arises by ignoring feedback altogether is little more than a tenth of a Kelvin.

In our submission, this really is Game Over.