Feedback is not the big enchilada

By Christopher Monckton of Brenchley

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 CO2 – that is, the amount of warming that would occur in response to a doubling of the atmospheric concentration of CO2 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 CO2 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 CO2 doubling (based on Andrews, op. cit.).

From these two canonical values, we know that official climatology reckons that the feedback response to doubled CO2 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:

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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 CO2 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 CO2 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 CO2 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.

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349 thoughts on “Feedback is not the big enchilada

  1. Nick Stokes gets educated about climate – let’s resolve to not publish any more articles by Stokes
    on this subject.

    • Nick made some valid points – and preventing people from getting published and so denying public discussion is how the climate cult came to power

        • After what Griff did to Dr Crockford (accusation: not qualified to speak on polar bears) & Dr Curry (sold out to “warmists”), Griff qualifies as an anonymous, savage little cartoon character whose primary sources are London newspapers.

          I don’t support banning him, but it’s pretty obvious the WUWT audience understands what it’s dealing with.

    • Au contraire, mon ami. We do not want to create an echo chamber. Folks like Nick force us to keep on our game.

    • That would not reflect the spirit of this website. What makes this site different is that we have an actual debate, and Mr. Stokes is part of it. At least we have proper argument and counter argument here, and it shows that the science is far from settled.

      • While I very much appreciate Col Mosby’s support, I also welcome Mr Stokes’ willingness to engage in scientific debate. It is only the totalitarians who wish to shut all debate down and are therefore angry when there is any questioning of the Holy Books of IPeCaC.

        • When I have had discussions with Mr. Stokes via this blog he has always been honest and fair in his responses to me and I generally learn things from his comments, so I agree with Monckton of Brenchley, I welcome and appreciate Mr Stokes’ willingness to engage in scientific debate.

          • I actually agree with this assessment. He is knowledgeable, and brings forth many worthwhile points of view – and is largely polite, despite the sometimes impolite jabs directed at him. He’s the kind of person with whom debate is worthwhile.

    • Nick is a thoughtful and respectful member of the wuwt community and puts forward well thought out arguments. We may not agree with him but if we ignore his postings we become an echo chamber.

      Surely better to defeat his arguments with better arguments than to ban him?

      Tonyb

    • Absolutely and strongly disagree.
      We need more posts from “the dark side”, as some might view them.
      Don’t we want open and honest debate?
      The Manns and Gores and Gavins of the world would never dare to do what Nick did.

      • To clarify, disagree with ColMosby’s “let’s resolve to not publish any more articles by Stokes
        on this subject.”.

        • I think Mosby’s comment was a little tongue-in-cheek. The Dark Side’s modus operandii is to ban sceptics and prevent any opinion / paper in opposition to its dogma from being heard.

          • Agree — Anthony has never & won’t ever ban a “Stokes-like” commentator. Hasn’t banned anybody unless they became intolerably/personally abusive. This site’s owner has always been extremely tolerant compared to other sites.

      • The very concept of ‘Global Average Temperature’ measured to 0.1 degrees Celsius is dubious. Any claim based on the concept is equally dubious.

        We’ve had an article, recently, showing that the Global Average Temperature of recent years is merely an average of mid-ranges of daily highs and lows. This mid-range average would have a much higher error range than would an average of hourly readings. An world-wide average of hourly readings does not exist. Yet we find average temperature anomalies given to two decimal points.

        As for 1850, the idea of a Global Average Temperature for that time measured to 0.1 degrees Celsius is a fantasy. The Global Average Temperature of 1850 would be an entirely different beast to that of the modern variant and any attempt to harmonize them would be pure guesswork.

        We should have more articles emphasizing the dubiousness of the concept of Global Average Temperature. It is the starting point for any discussion of ‘climate change’, whatever that is.

        • I seem to remember that James Hansen himself has agreed that “global average temperature is not a useful metric”.

          I am neither a physicist nor a mathematician. My skill is with the use of words and my distrust of climatology stems from the climate science community’s dishonest use of language, either by stating things that are demonstrably not so, by “havering” (a good Scots word that implies a lot of “ums” and “ers” when challenged on any particular) and a retreat into obfuscation and “weasel words” patently designed to deflect attention from dubious conclusions.

          Nick Stokes does none of these things, no more does Monkton. Which doesn’t make either of them right but it does, in my book, make them honest which ought to mean in the fullness of time their deliberations and disagreements will drive this debate forward. We can ask for nothing more.

  2. Vastly improved explanation of the situation. WELL DONE!

    Is the simple way to put this that the standard approach is to say that because CO2 causes the temperature to be 10C warmer than it would be without CO2, and that because the world is 32C warmer than it would be if it were a perfectly conducting black body, that they say that because CO2 must be causing all the warming, that the 10C must be causing the total 32C and therefore the gain in the system must be ~3.2.

    If so, they are completely nuts and I’m surprised any serious scientist would listen to them.

    If CO2 went down to zero – there would still be water vapour in the air and there would still be clouds in the sky. These cause the temperature to be different irrespective of CO2. Indeed, because the effect of cloud’s is to reduce sunshine – it usually operates to reduce warming and causes the feedback to be much lower than it would be otherwise. So, we are almost certainly in a regime where if we increase CO2, the effect of doubling will not be 1.05C but less.

    • My good friend Mike Haseler has it exactly. Even if there were no noncondensing greenhouse gases, the Sun would still be shining, one-third of the dayside ocean would be open water, and the water vapor, cloud and ice-albedo feedbacks – the principal sensitivity-altering feedbacks – would all be operating at full chat.

      Therefore, either Mike is right and official climatology is, in effect, imagining that one multiplies the 10 K reference sensitivity to the naturally-occurring greenhouse gases by about 3.2 to get official climatology’s equilibrium sensitivity, or official climatology – despite its explicit statements that the climate sensitivity parameter that embodies the action of feedback is typically near-linear – is imagining a very nonlinear equilibrium response to temperature that has no physical warrant in the real climate.

      • Interesting! By implication, 10 K of warming is caused by 0.026 % CO2 in the atmospere. This leads to some intersting problems when considering Mars and Venus. For example the same cubic mtere of atmospere on venus contains ~350,000 times more CO2 than on earth (96.5% CO2 by volume and 93 bar). One wonders why Venus is only 462 C warmer? Mars by comaprison has a pressure of ~0.6 bar and 95.3% CO2 by volume, or to put it another way ~2,000 times the amount of CO2 per unit volume as compared to earth, yet has a temperature 0f ~ -60 Celcius. Both seem far to cold to support this value of 10K per 0.026% CO2.

        Happy for anyone to point out errors or expalin 🙂

    • “If so, they are completely nuts and I’m surprised any serious scientist would listen to them.”

      Well the climate changers do reckon the doomsday scenario all started with the Neolithic cooking fires and then the you know… like the Copper, Bronze and Iron Ages, etc, etc…
      https://www.msn.com/en-au/news/world/storm-hannah-unearths-sunken-forest-from-more-than-4500-years-ago/ar-AABVEuD
      Welcome to their salad days and no BBQs I suppose but then what’s the point of all their windmills solar panels and EVs you may well ask?

    • What baffles me is all this discussion over 10–15% of the energy budget and nothing about the huge heat engine of the water cycle that carries the other 85–90% of the solar input energy that arrives at Earth’s surface away from the surface by the convection of warm moist air and sends back down cool precipitation.

      This heat engine ramps up with warming and slows down with cooling and is a HUGE negative feedback that I see no one properly addressing. This is Trenberth’s missing energy that he would like to pretend is hiding in the ocean depths.

      Adding to this the fact that CO2 and water vapor are radiative gases that cool the planet after sundown and we have two mechanisms that more than compensate for any spurious, supposed greenhouse effect.

      • Ah, Mr Higley, haven’t you learned your lesson? (Total sarc)

        “Apparently you don’t realize that all this dynamic behaviour has been smoothed by averaging the temperature over as well the total surface of the earth as over a period of one year, resulting in one ( I repeat one!) variable, called global temperature.
        That gives the scientific right to consider the heat capacity of the atmosphere as one static parameter.”

        … ‘the license to indulge in magical thinking’ might be a more accurate description of the ‘smoothed by averaging’ process.

      • Better yet – the latent heat emitted by the water condensing / freezing is ‘corrected’ for temperature/altitude although I have yet to see any justification for varying latent heat of state change due to ambient temperatures. It seems like there is a misapplication of Stefan Boltzmann to emission of latent heat.

        However, there is very little explanation of how the latent heat leaves water molecules on condensation or freezing that does not involve hand-waving and claims of sensible heat that do not appear logical considering the amount of energy released.

    • So true. And painfully obvious.

      Systems with high sensitivity are unstable over long periods of time, and we know that the temperature of the Earth has remained within a fairly narrow range for millennia. Therefore, climate sensitivity must be very low.

      We’ve also run an experiment. Carbon dioxide concentrations have increased since 1950 from 311 ppm to 410 ppm, or 99 ppm, which is 32% of the first doubling. Ergo, assuming everything is proportional, the temperature increase to date should be 0.48 C with no climate sensitivity. With climate sensitivity in the range of the IPCC is should be 0.83 to 2.52 degrees. Okay, so how much actual warming have we observed since 1950? Around 0.60 degrees. Back calculating, that give a climate sensitivity number of 1.25.

      This suggests that climate sensitivity is low, likely close to zero.

      “the corrected 95% confidence interval of Charney sensitivity is 1.09 to 1.23 K.”

      Hey, wadda you know? Right on the button, imagine that.

      So we have three unrelated measurements of climate sensitivity. Chaotic system stability suggests that sensitivity of the climate to most inputs should be low, we have actual measurements of the response to date which suggests it is low, and we have the work presented here.

      When independent lines of evidence and deduction keep deriving the same answer, AND that answer correlates closely with reality, it suggests that the theory is correct.

      Thank you for your efforts Monckton of Brenchley. It is tough to go against the flow, but the truth is all that matters.

      • I am most grateful to Geoman for his kind comments. He makes an important point about the mutually-reinforcing coherence of both theoretical and empirical findings. Our theoretically-derived Charney-sensitivity interval is broadly consistent with observed warming to date, whether before or after the (probably exaggerated) radiative imbalance is taken into account.

        In the end, the point we are making is an extremely simple one. But simple does not mean wrong. We think we are right, and we think that, in the disciplined environment of peer review, eventually a journal is going to crack and do the decent thing and publish our result. Then there will be a flood of papers trying to tell us we are wrong: but climatology starts off on the back foot because the error of physics it has made is not an error of climatology but of control theory. The relevant science does not belong in the incestuous, very-tightly-controlled, Lysenkoist world of official climatology but in a different discipline altogether, and – though the Communist party line is ruthlessly enforced throughout the Western universities, official climatology’s current position is so obviously intellectually and scientifically untenable that in the end the orders will come down to shift to another method of shutting Capitalism and freedom down.

  3. Agreed. Some factors were producing climate in 1850, and unless there is some miraculous events taking place, the same factors are producing climate currently.
    It starts to look like homeopathy, where the drug has an effect even though it is no longer there, as the “water has a memory”. The IPCC models presume that anthropogenic GHGs “know” that they are anthropogenic, and behave in a different manner than “natural” GHGs.
    I stopped being that religious in Fourth grade.

    • That is one of the problems that gives the itch to many who have studied any geological history. The the best model of geological CO2 places it at over 20 times present levels roughly 550 MYA. It drop s more or less steadily (with various ups and downs until the Permian where it remains stable at present levels until the Permian Extinction and the Triassic. After that it climbs to the mid-Mesozoic reach about 10 times current levels before resuming a downward trend that has persisted to the Plestocene. So literally any effect prognosticated by a current climate model must have already happened more than once. Chemistry and physics do not alter locally over time, yet there is no geological evidence supporting any such patterrn.

  4. I was going to make a comment on Nick Stoke’s article, but Christopher Monckton has made it for me. It may help to look at it from signal to noise ratio standpoint.

    Everyone knows that the climate is a noisy system; after all, it is the system from which the science of chaos was first discovered, by Edward Lorenz. When dealing with noisy systems, it is difficult to determine characteristic things about it. My first introduction to the problem was trying to get high quality reel-to-reel tape recordings from early tube amplifier recorders.

    If you are trying to characterize a noisy system, the most effective way to do it is to raise the signal to noise ratio. With large signal, the true system characteristics can be determined.

    Using the input from the sun, and also the energy sink from outer space, allows one to apply a large signal into the system, so that the system noise is minor.

    -BillR

    • I am delighted at Mr Rostron’s distinguished contribution here. If he will be kind enough to email me his current email address, I shall be in touch with him directly.

    • Exactly. The “Noise,” also known as Natural Variation, as in Medieval Warm Period, Little Ice Age, Roman Warm Period, Holocene Optimum, is as large if not larger than the Signal, our dodgy temperature records. If the “Climate Scientists” say they are sure about this 1.05 K they are simply lying, as there is no basis to their assumption that ALL the warming since 1850, when we had temperature records from at least three places, is CAGW.

      Pseudo-science…

      • Michael Moon Re: “they are simply lying”
        Please do NOT pronounce actions to be immoral without strong evidence.
        “Do unto others what you would have them do to you.” Jesus
        Actions are often acting on what you have been trained in, based on the dominant culture, received wisdom, and understanding. e.g., the Aristotelians in Galileo’s time. Most may not have even examined the issue. See:

        “Out-of-date theories are not in principle unscientific because they have been discarded. That choice, however, makes it difficult to see scientific development as a process of accretion.” . . .
        “Scientific revolutions are inaugurated by a growing sense… that an existing paradigm has ceased to function adequately in the exploration of an aspect of nature to which that paradigm itself had previously led the way.”

        Thomas Kuhn The Structure of Scientific Revolutions. http://scihi.org/thomas-kuhn-scientific-revolutions/

        • One can lie intentionally with deceit or unknowingly. In the latter case, this might not be immoral.

  5. The lack of observation of the predicted mid-tropospheric tropical hotspot should be Game Over as well for the Climate Hustle, a hustle based on nothing but Cargo Cult-style modeling.

    • Mr O’Bryan is right: the absence of the tropical mid-troposphere “hot spot” (I had the honor to name it) does cast very grave doubt upon the models’ exaggerated estimates of equilibrium sensitivity, which depend in very large part on the tripling of directly-forced warming thanks to the water-vapor feedback, which, however, must be negligible in the absence of the hot spot.

      Our theoretical work demonstrates that the absence of the hot spot is a physical manifestation of the error of physics perpetrated by climatology in failing to take advantage of the fact that, in 1850, the feedbacks then present acted upon the entire reference temperature of 265 K, and not solely upon the reference sensitivity of just 10 K to the naturally-occurring, preindustrial, noncondensing greenhouse gases.

  6. I note that the term ‘non-condensing greenhouse gasses’ is very common. That neatly excludes water vapor from the discussion and water vapor is by far the most important greenhouse gas.

    The only way the increased level of CO2 becomes a problem is if it has an outsized effect on water vapor. It strikes me as passing strange to ignore water vapor.

    The other thing that strikes me as strange is to ignore stability. Stability analysis is part of any control system design. Certainly, in a system with significant positive feedback, a stability analysis should be mandatory. What does a quick google produce? … not much.

    An oft repeated criticism of positive feedback for the climate is that positive feedback systems are inherently unstable. Official climate science’s answer? … crickets.

    The claim that there is positive feedback should require exhaustive proof and an explanation of why we haven’t previously witnessed the kind of instability it would produce. … again, silence.

    Have there been any mathematically rigorous responses to CM’s observations on the misapplication of feedback theory? I’m not aware of any.

    I presented a simple explanation of why the reference level is crucial to the analysis of a feedback system. link As far as I can tell, Nick studiously ignored that part of my comment.

    Were it simply a scientific issue, CAGW should have been dead and buried a long time ago.

    • In response to CommieBob, the reason why official climatology draws a distinction between water vapor and the noncondensing greenhouse gases is that changes in the atmospheric burden of the former are treated as forcings and the consequent change in specific humidity, the atmospheric burden of water vapor, is treated as a feedback.

      This is a sensible enough distinction in the circumstances. But the problem is that official climatology accords too much influence to water vapor, rather than too little. It imagines that because the Clausius-Clapeyron relation allows the space occupied by the atmosphere to carry near-exponentially more water vapor as the temperature of that space rises, the atmosphere will actually carry that much more water vapor.

      Sure enough, near the surface it does so: the specific humidity is rising at the expected Clausius-Clapeyron rate of about 7% per Kelvin of atmospheric warming. However, additional water vapor near the surface doesn’t cause much warming, because the influence of water vapor is substantially overlain by that of clouds.

      It is in the tropical mid-troposphere that models calculate that water vapor feedback will be most influential, raising the temperature at that altitude by thrice the surface change. In reality, however, at that pressure altitude specific humidity has actually been declining with warming, inferentially due to subsidence drying (see e.g. Paltridge+ 2009). Therefore, the tropical mid-troposphere hot spot that all models confidently predict is not present in reality. And it is only if it were present that one could assume a strongly positive water vapor feedback.

      The absence of the hot spot, therefore, provides the physical observation that confirms our theoretical finding that the warming to be expected from our enrichment of the atmosphere with CO2 and other greenhouse gases will be small, slow, harmless and net-beneficial.

      • Indeed.

        It imagines that because the Clausius-Clapeyron relation allows the space occupied by the atmosphere to carry near-exponentially more water vapor as the temperature of that space rises, the atmosphere will actually carry that much more water vapor.

        As far as I can tell, it doesn’t account for the energy required to evaporate that much water.

        A serious problem with a simple linear model, such as that described by Hansen et al is that it ignores the power supply problem. ie. there is only finite energy in the climate system.

      • To Monckton of Brenchley, Christie et al refer to the scaling ratio (“What Do Observational Datasets Say about Modeled Tropospheric Temperature Trends since 1979?”, Remote Sensing, 2010). The article says: “We conclude that the lower tropospheric temperature (TLT) trend over these 31 years is +0.09 ± 0.03 °C decade−1. Given that the surface temperature (Tsfc) trends from three different groups agree extremely closely among themselves (~ +0.12 °C decade−1) this indicates that the ―scaling ratio‖ (SR, or ratio of atmospheric trend to surface trend: TLT/Tsfc) of the observations is ~0.8 ± 0.3. This is significantly different from the average SR calculated from the IPCC AR4 model simulations which is ~1.4. This result indicates the majority of AR4 simulations tend to portray significantly greater warming in the troposphere relative to the surface than is found in observations.”

        Temperature aloft was expected to be around 1.4-times surface, not thrice.

        To commieBob: positive feedback can be stable if the open-loop gain is less than 1.0 (the combined gain of the forward and feedback elements, if the link back to the summation point is broken). However, even if it is stable in the sense of bounded input results in bounded output, positive feedback tends to produce a fluctuating and horrendously “noisy” response to input.

        • But see IPCC’s hot-spot diagram, color-coded, which shows tropical mid-troposphere temperatures as about thrice the tropical surface temperatures. The quotation from Christie et al. refers to the whole atmosphere, not just the tropical atmosphere. But it is the tropical atmosphere that matters from the point of view of water-vapor feedback.

          • Christy et al examined trends in the tropical lower troposphere (TLT, 20°S–20°N). It’s not an examination of the whole of the atmosphere.

            You are correct that it is not the whole of the atmosphere that matters, and Christy is well aware of that. It would have been an error to examine the whole of the atmosphere when there is general agreement that the tropical region is the area of interest.

            Please just be cautioned that your claim of three times will be challenged.

          • Jordan is correct that Christy et al. were considering the tropical troposphere only (though their TLT refers to “Temperature lower troposphere”, not “Tropical lower troposphere”). However, IPCC and several others have published diagrams showing a tripling of the surface warming rate at altitude in the tropics.

      • It imagines that because the Clausius-Clapeyron relation allows the space occupied by the atmosphere to carry near-exponentially more water vapor as the temperature of that space rises, the atmosphere will actually carry that much more water vapor.“. I think you will find that “It” imagines correctly. The reason that water vapour does not provide as much positive feedback as the IPCC and others claim is that there is also proportionately more precipitation. Precipitation reduces the positive feedback, because it releases latent heat of evaporation at around cloud-top level, from whence much of it is lost to space.
        There are several papers that explore this. One, from memory, is by Susan Wuyffels et al.

        • Mike
          In the tropics a significant volume of that convection returns to ocean and land as warm rain water. What percentage of the original energy convection returns to the ocean.
          Regards

        • In response to Mr Jonas, the models all – and I mean all – get the predicted Clausius-Clapeyron increase in specific humidity in the crucial tropical mid-troposphere wrong. They all predict an increase, when in fact for 30 years and more there has actually been a decline, owing to subsidence drying (Paltridge+ 2009). Climatology, therefore, does not imagine correctly, except near the surface, where specific humidity is rising at the predicted 7% per Kelvin of warming, but where the spectral lines of water vapor overlie those of CO2.

        • Also note that once water vapor has condensed (or frozen) it is no longer a GHG but instead a blackbody radiator.

    • “It strikes me as passing strange to ignore water vapor.”
      It seems to me passing strange that this can be said under a post complaining that climate scientists treat it as the big enchilada. The point of “condensing” just refers to how it exercises its effect. CO2 is non-condensing, so if you put some in the air, it stays there for a long time. It is a forcing.

      But if you let off steam, it stays in the air for on average about 10 days. Then it returns to the sea, You can’t force anything that way. So how does it become the big enchilada? Evaporation from the sea, amounting to about a metre a year, balanced by an equal amount of rain. That is about 500,000 Gigatons per year. It completely dwarfs the flux changes of carbon. Because the rates are so high relative to the amount of water in the air, the latter is determined by those rates, which in turn are mainly determined by temperature. That is why it is a feedback and not a forcing.

      • Nick, it does not matter how long a gas stays in the atmosphere, only the average amount there over time. One molecule is the same as any other, and if the water vapor is continually replaced as fast as it is removed, the amount in the air is the issue , not the turnaround rate.

        • ” if the water vapor is continually replaced as fast as it is removed, the amount in the air is the issue , not the turnaround rate.”
          Yes. But in the case of water, it is the ratio of rates. Water in the air is in dynamic equilibrium. Law of mass action. You can say that because the rates are so fast compared with the amount present.

          In the case of CO2, you can’t. CO2 is not in dynamic equilibrium. The rate at which we are adding it exceeds the rates at which it can equilibrate with the sea. So the air concentration depends on the cumulative amount added, not a temperature-dependent exchange rate.

          • Interesting, this is what confuses me about all this talk about co2, excerpts of emphasis quoted below:

            3 paragraphs and then my novice interpretation..

            http://geocosmicrex.com/global-change/carboncycle/

            “You will note that the amount of carbon dioxide in the atmosphere is given as 750 gigatons. You will also note that 560 gigatons are consumed in the process of photosynthesis by land plants. Take special note of the amount in the ocean: 38,000 gigatons, or 50 times the amount in the atmosphere. The soil at any time stores about 1500 gigatons. In the ocean the CO2 is taken up by a variety of marine organisms that have the ability to precipitate calcium carbonate (CaCO3) from seawater. This calcium carbonate forms the shells, or exoskeletons, of creatures such as scallops, bryozoans, foraminifera and coccolithophores. When these creatures expire, their shells drift down and consolidate on the ocean floor where they are eventually lithified under pressure into limestone, chalk and marble, to become part of the lithosphere or rocky crust of the Earth.”

            “The next graphic also depicts the generalized global carbon cycle. It is reproduced from Botkin & Keller (2003) Environmental Science – Earth as a Living Planet; John Wiley & Sons, Inc. p. 63. It contains additional interesting details. Here fossil fuel burning accounts for 5.5 gigatons introduced into the atmosphere. This is one-half gigaton less than the preceding chart, presumably the one-half gigaton difference being the result of natural combustion and volcanism which is not included in this number. Storage in shallow ocean water is almost the same in both charts; fossil fuel deposits are shown to contain about 4000 gigatons of CO2 while the sedimentary rock reservoir contains upward of 100 million gigatons! This is truly a staggering amount of carbon dioxide, and all of it at one time passed through the global atmosphere before it was taken up by the oceans, converted into biogenic calcium carbonate, and locked up in the Earth’s crust. This is a clear implication that the ocean acts as a powerful pump, constantly extracting CO2 from the atmosphere and ultimately sequestering it into carbonate sedimentary rocks, where it remains for a very long time. The natural process of oceanic uptake, or absorption, is constantly depleting the Earth’s atmosphere of carbon dioxide, and if not replenished it would relatively quickly reduce the amount of CO2 to a concentration too low for effective photosynthesis.”

            “Finally, note that we have an additional interesting piece of information in the second graphic. The total amount of CO2 residing in the atmosphere is given as 750 gigatons (same as the first chart) along with an additional +3 gigatons per year due to burning of fossil fuels. Hopefully the reader is paying attention to the extent that they will see that this +3 gigatons is about half the amount initially introduced into the atmosphere due to fossil fuel combustion, given as 5.5 gigatons in this chart and 6 gigatons in the Raven & Berg chart. A substantial portion of the difference between CO2 released through combustion and the actual measured amount in the global atmosphere has been referred to as the “missing sink.”

            Humans are only contributing an extra 6 gigatons on top of attainted 750 gigatons circa 2004, but the oceans hold 38,000, and the proxy data is clear that when they do overlap, ocean temperature precedes co2 concentration.

            Nick states:
            “The rate at which we are adding it exceeds the rates at which it can equilibrate with the sea. ”

            Seems odd to me that nearly half of the 6/38000 gigatons is sequestered without fail, coupled with the insignificant addition per the ocean saturation.

            Seems like a mountain out of an ant hill. Any claims that it can’t keep up, when C3 and C4 plants thrive at 1000-1200ppm illustrate an profound lack of historical perspective. It is this lack of perspective and hyperbole that finally broke the spell for me as a true believer, to begin approaching this topic with clarity and reason.

            Nick, you are great with number crunching, but you have accepted a theory that is unfalsifiable, and you consistently dismiss the copious amount of historical and observational evidence (including defending all the dubious temperature adjustments) negating Co2 as a major player.

          • Also, the perspective that is constantly dismissed or at least clearly omitted, is the fact we had 2 miles of ice in North America just over 10,000 years ago with the global seas rising 400 feet in very short order. That’s a geological blip. A sneeze, and it was very recent. Those ice sheets extended down to Kentucky and Indiana.

            Moderate cold kills 20 times than moderate warmth. Every decline in human population, bubonic and Justinian plagues coincide with cooling, while the Renaissance, Roman rule, coincide with warming. Cathedrals building abruptly abandoned, grapes no longer growing in UK to compete with France, Greenland settlements dying off from encroaching ice.

            Nearly every single observable metric illustrates it is cooler now than the 1930s, and the trend is continuing to slightly cool. BOM has zero credibility, so that is unacceptable as a rebuttal. We’ve been down that road.

            F4 and F5 tornadoes declining
            SLR roughly linear for the last 10000 ish years

            Major hurricanes declining
            Days above 90 and 100 declining in the United States, with the supposed best historical land temperatures data

            Wettest and coldest overtime through May in untied started historical record 2018-2019

            180ppm (IIRC) dendrochronology established basement for plant life, with humans adding only approximately 1 in 10,000 since the onset of the industrial age

            Greening of the planet about 15% over the last 3 decades

            All you have is numbers on paper based off an erroneous, misanthropically founded, unfalsifiable theory with zero regard for perspective.

            All of this mumbo jumbo about ECR and other Charney and Feedback maths and Fritos and fruity loops is inconsequential. There observational data is clear:

            There is no catastrophe, except the possiblity of another cooling phase in the midst of leftist eugenics based hysterics forcing unreliable renewables and the costs on the citizens (see that disgusting governor and Democrats in my state of Colorado screwing over all the poor and middle class just recently)

            Co2 is logarithmic, and it’s inconsequential after the first few 100ppm, with only re-radiating outing lwir at 15 microns. It’s a big fat nothing burger.

            There hasn’t been a single downside from this warming, milder weather, slightly warmer evenings, and all this coming off the heels of the friggin little ice age!

            You are so focused on proving your faith the only truth, you’ve discounted the entire planets worth of evidence to the contrary

          • Good points, Matthew.

            It is of interest that they do the same thing with the carbon budget that MB indicates they are doing with ECS: take the equilibrium as a given, and then build the delta-budget on top of that as if the two systems were totally independent and decoupled.

        • Smack on. What is there is what counts towards forcing, not its derivative w. r. t. time

      • Nick,
        (1) I appreciate you are making a distinction between water vapour as a feedback and not a forcing.
        How does Schmidt et al 2010, “ Attribution of the present-day total greenhouse effect”, impact on all this?
        Does it not say that Greenhouse gases constitute about 1-2% of Earth’s atmosphere and of these water vapour and clouds cause at least 75% of greenhouse warming?
        Further only about 3% of the CO2 placed in the Earth’s atmosphere each year is from human emissions.
        So of the 25% of the greenhouse effect that is due to CO2 and methane, only 3% of this is due to manmade sources.
        That would suggest only a very small percent of the greenhouse effect is due to mankind.
        (2) Are Fischer et al (1999) and O. Humlum et al (2010) correct in stating that CO2 significantly lags temperature in the Ice Core records?

        • ” water vapour and clouds cause at least 75% of greenhouse warming”
          That is where the forcing issue comes in. Yes, they do, in the sense that without them and other GHG, the Earth would be about 33°C colder. But we aren’t forcing them. Insofar as their effect varies, it is through temperature, which changes the balance of evaporation and precipitation.

          “Further only about 3% of the CO2 placed in the Earth’s atmosphere each year is from human emissions.”
          That is a commonly quoted factoid. It is true that there is a big seasonal cycle. In summer
          plants store CO2 through photosynthesis, and the oceans emit CO2 because they get warmer, and CO2 is then less soluble. But the plant stored CO2 doesn’t stay stored; vegetation rots, or is eaten, or burnt in wildfire. And the ocean cycle is truly reversible. It gets cold again in the winter, and dissolves CO2 again. In fact, there are lots of arbitrary decisions in even summing this up. The plant and sea processes counter each other – do you take gross or net? And the hemispheres are out of phase.

          But the key thing is that that cycle, however you do the accounting, has been going on for millions of years and CO2 has not accumulated. But when we started baurning C on a grand scale, the amount in the air grew exponentially and about half the burning rate, consistently.

          “CO2 significantly lags temperature in the Ice Core records”
          Yes. Putting C directly in the air, from a new source, is a novelty. In the past, CO2 moved around passively, in response to temperature, which it lagged. Now it responds to a different stimulus – our mining.

    • “As far as I can tell, Nick studiously ignored that part”
      Not deliberately. But let me make amends. You wrote
      G = (T – offset) / (ip – ref)
      G being the gain. ip is the input signal, suggested as log(CO2). I am not sure why the denominator is written as a standard state difference with ref, which the corresponding term for T is described as offset. But the comment says that the offset is determined from the reference state, so it seems to be the same thing.

      Now I agree with that; it defines G as a rate, in a standard calculus way. Gain and feedback factors belong in the world of rates. Now what happens of you try to add something, reference temperature or whatever, into the numerator? It isn’t a difference, but will be treated as one. IOW, the gain will be calculated as if part of the change was a shift to the reference temperature from zero. And of course that is not true, but worse, it happens regardless of the smallness of the actual changes. The rate G is not a stable limit that you can put a number on, but goes to infinity.

      • The rate G is not a stable limit that you can put a number on, but goes to infinity.

        Not in the system as explained by Hansen et al. It is a constant. Indeed, if it is not a constant, then we are not dealing with a linear time invariant (LTI) system and the whole discussion is moot.

        The motivation for using linear approximations is to avoid intractable math. As long as we understand a system sufficiently, linear approximations are a valid and useful engineering tool. Anyway, that’s the approach Hansen used and that’s what we’re talking about.

  7. With this in the N.Stokes lead : “People outside climate science seem drawn to feedback analogies for climate behavior. Climate scientists sometimes make use of them too, although they are not part of GCMs.”

    That is a clear signal the feedback game is over, and will be consigned to the “never existed” bin with previous warming data (a rather stuffed cellar).

    It is a clear signal the climate game is not over, though – another meme is being cooked up (warmed over?).
    I’m just waiting to see the reworked IPCC recommendations, which are likely now being feverishly kneaded.

    The feedback battle may have been won, but not yet the war. Watch out!

    • Climate scientists sometimes make use of them (feedbacks) too, although they are not part of GCMs.

      Oh yes they are. link

      • “Oh yes they are.”

        The first sentence of the abstract of your link says otherwise:
        “A comparison is performed for water vapour, cloud, albedo and lapse rate feedbacks taken from published results of ‘offline’ feedback calculations for general circulation models (GCMs) with mixed layer oceans performing 2 · CO2 and solar perturbation experiments.”
        They do ‘offline’ calculations, because the GCMs do not themselves calculate feedbacks. They have no need to, and couldn’t usefully use such an averaged entity anyway. They solve local relations expressed by PDEs.

    • By far the strongest positive feedback, on average, isthat of water vapour (ranging from 1.1 Wm–2K–1to2.4 Wm–2K–1, with a mean value of 1.7 Wm–2K–1). Assuming a surface temperature feedback of –3.3 Wm–2K–1, the average model water vapour feedback acting alone is sufficient to double the 2·CO2warming, from1.2 K to 2.4 K. link

      This will take a lot more digging.

  8. The error that Monkton makes is to assume that the feedbacks are constant and act
    independent of the reference system. He needs to read the paper by Roe (“Feedbacks, Timescales, and Seeing Red”) which states “Gains and feedbacks calculated with respect to different reference systems cannot be directly compared.” Which is what Monkton is doing — trying to compare the feedbacks operating in one reference system (the one where the sun is not shining and thus turning it on makes a huge difference) to the standard reference system which is the earth in 1850. Roe
    as Nick Stokes mentioned has an entire section pointing out that feedbacks are just an alternative way of writing a Taylor series (to first order) and nobody should be surprised if the derivative of
    a function f(x) is different for different values of x. Knowing the slope of the function at one point does not allow you to estimate the slope at a very different point. The only function for which that is true is a straight line. So essentially what Monkton is claiming is that the temperature is a linear function of the forcing for all values of the forcing ranging from the sun being turned off to today. This is an astonishing claim and one for which there is no evidence.

    • “Izaak Walton” has perhaps not appreciated that at any given moment the feedback processes then subsisting must perforce act upon the entire reference signal. In climate, in 1850, that reference signal (a.k.a. reference or pre-feedback temperature) was the sum of the 255 K emission temperature and the 10 K directly-forced warming from naturally-occurring, noncondensing greenhouse gases: i.e., 265 K.

      But the output signal (a.k.a. equilibrium temperature after feedbacks have acted) was a measured 287.5 K. Therefore, in 1850, which is a long way from when the Sun was not shining and the Earth was without form and void, the feedback response was the difference between 287.5 and 265 K: i.e., 22.5 K. Now, climatology’s method in effect ascribes all of that feedback response to the 10 K reference sensitivity, which is plainly daft, because that leaves no room at all for any feedback response to the 255 K emission temperature.

      We are not dealing with multiple reference systems but with a single reference system. From 1850 to 2011, for instance, the reference temperature increased by a mere 0.75 K; and from 2011 to doubled CO2 compared with 2011 would add only another 1.05 K. These values are simply not large enough to engender major nonlinearities in the feedback regime. To make assurance doubly sure, we carefully considered each of the sensitivity-altering feedbacks, and none of them would suddenly account for a a tripling (or worse) of the feedback fraction between 1850 and doubled CO2 compared with 2011.

      It is blindingly obvious that climatology has made a large mistake.

      One can actually calculate the curve of, say, an exponential function provided that one has two points on the curve. We have (0, 0), the point through which all feedback response curves must pass, and (265, 287.5) in 1850. The exponent, then, is simply ln(287.5) / ln(265), which is just 1.0146, not greatly different from unity. To the nearest 20th of a Kelvin, the Charney sensitivity based on that exponent would be 1.15 K, just about identical to the linear case.

      Why is this so? Because, as the head posting points out, in 1850 the reference temperature was more than 92% of equilibrium temperature – which is much as one would expect in an essentially themostatic dynamical system (see e.g. Jouzel+ 2007, where it is demonstrated that in 800,000 years surface temperature has varied by little more than 3 K either side of the 800,000-year mean).

      • Again Mr. Monkton you need to read Roe. The feedbacks are defined in terms of the
        reference system. In the discussion it is clearly stated that:

        The very idea of a feedback implicitly partitions a system into a feedback process and a reference system on which that process acts. If you change the reference system, you change the feedback. Feedbacks can be meaningfully defined only when also accompanied by a choice and a clear definition of the reference system. In general, there is no single correct choice, and which one makes most sense depends on the problem. Loosely speaking, one possibility is to think of the reference system as containing the things that are known well, as in the case of choosing a blackbody planet as the reference for the climate system, and to think of the feedbacks as the things that are uncertain.
        Another possible partition is to regard the reference system as the things not being studied and to think of the feedbacks as the processes of interest. Here, though, it becomes important to appreciate that the expression for fi in Equation 19 depends on the reference state. When feedback processes are compared quantitatively, it is a requirement that they have been evaluated against the same reference system.

        What you are doing is trying to compare feedbacks for two different reference systems. Since the systems are
        different then the feedbacks are different as well. In the first system the reference system would appear to be the earth without the sun shining and then the feedbacks are the entire climate system. The second reference system is the earth and its climate in 1850 and hence the feedbacks are only the bits of the climate that change when you change the forcing. So when discussing the change in forcing from 1850 one doesn’t need to take
        into account the entire solar input since that is now part of the reference system and so all of the feedbacks
        operating have already been included.

        Again as Roe states in the discussion

        For example, the Stefan-Boltzman relation is often described as a negative climate feedback acting to regulate temperature anomalies. In fact, for a blackbody planet, which is the simplest imaginable reference system for the climate that is still meaningful, the Stefan- Boltzman relation is part of the reference system and therefore not a feedback at all. These are not semantic or esoteric issues—the quantitative intercomparison of different feedbacks can be done only when the reference system is defined and held constant.

        • The main feedback is stated as due to water vapor change due to temperature change engendered from a small CO2 induced change. If this is so, since seasonal temperature variation is very large compared to CO2 effects, where is the huge summer temperature increase due to feedback?

          • “where is the huge summer temperature increase due to feedback”
            Well, it does get warm in summer, and there probably is a component due to wv feedback; there is no easy way of telling. But the climate wv feedback applies to annually averaged temperature, at least, and globally averaged too.

        • “Izaak Walton” has misundertood Roe. The reference system we use is the pattern of temperatures or temperature changes in the absence of feedback. At any given moment, there is a reference temperature, before feedback acts, and an equilibrium temperature, after feedback acts (though not all of the equilibrium temperature necessarily comes though immediately).

          And our paper treats the SB law as part of the reference system, and not, as climatology does, as a feedback. On this, as on much else, we agree with Roe, whose paper we cite in ours.

          • It doesn’t seem to me logical that applying anything (in this case feedback) to a system can be done be selecting an arbitrary point (in this case 1850) and saying “everything starts from here”.

            If I understand the argument 1850 seems to have been chosen as some point at which the climate, or at least temperature, is considered to have been “stable”. But climate has never been stable and even if temperatures had been the same for several centuries that does not make them “stable”.

            At the risk of my looking an idiot (!) it appears to me that Nick is falling into the same trap as those who argue that 10°C is twice as warm as 5°C. The starting point for calculating feedbacks must surely by 0°K not whatever the temperature happens to have been in 1850, or 1750, or 45BC!

          • In response to Newminster, please refer to the block diagram in the head posting. All we are saying is that 1850 was a good year for doing calculations because there was a temperature equilibrium that year (the least-squares linear-regression trend on the HadCRUT4 dataset was zero for the next 80 years). Also, HadCRUT4 publishes the 2-sigma uncertainties as well as the mindrange estimate. By plotting the least-squares linear-regression trends on those uncertainties and on the midrange, we were able to determine that the uncertainty in 1850 in the HadCRUT4 data was less than 0.3 K either side of the midrange – and that is simply not a large enough error margin to have any appreciable effect on our calculations.

            It is also important to understand that in 1850 there were certain feedback processes operating; that they had perforce to respond to the entire reference temperature then prevalent; and that, therefore, the system-gain factor in 1850 (whatever may have happened before) was, at that time, 287.5 / 265, or 1.085. Since there was only 0.75 K reference warming from 1850-2011, far too small to engender a significant alteration in the feedback regime, one can take it that the system-gain factor is today about 1.085 and will remain close to that until all extractable coal, oil and gas have been extracted. That means just 1.15 K warming per CO2 doubling, not 3.35 K.

            It is a simple argument, but a sound one.

  9. LM- thank you for this. I’ve always wondered (thought) that if there is so much feedback on a temperature perturbation, then why hasn’t the temperature already gone berserk!

    • Mr Graney has captured the main point. The temperature would have to be about thrice what it is if official climatology’s implicit midrange estimate of the system-gain factor, i.e. 3.2, had any physical reality to it.

  10. Did anyone mention Gaia? I’d like to point out that a conference on Gaia will take place at the end of July in Exeter, UK. It is dedicated to the 100th birthday of James Lovelock, who will participate in a live event. Lovelock used to be a darling of the consensus but has fallen out of favor to some extent as he believes that global warming projections are exaggerated, among other politically incorrect positions. Make no mistake, however, as this conference will be warmist in nature.

    https://lovelockcentenary.info/

    • I’ve been telling James he’s wrong for 25 years. I thought when he moved to Dorset he’d conceded.

  11. Milord!

    That was like ‘climate feedback for dummies’. And that’s what we need. I would also append some kind of short vocabulary explaining terms used, as Charney sensitivity – means that, emission temperature – means this. Definitions of those bad boys are embedded in the main text but would be nice just quickly jump to the vocab. By the way, why ‘sensitivities’? Like ‘equilibrium sensitivity’ instead of just equilibrium?

    Under Nick’ text I asked him about this intriguing ‘big reference temperature term’ which ‘won’t go away’. He explained to me that it actually means something slightly different than it says it means – this big reference temperature should only be included in the first order terms and not included in higher order subsequent equations. Otherwise those higher order calculations go wrong.

  12. Hah! IPeCaC! You crack me up, my Lord.

    But seriously, your tireless efforts over the long years, characterized by scholarship, wit and humor, evidence your indefatigable nature. This article is another example of your clear reasoning and concise writing. I for one, salute you as one of our most intrepid warriors.

    • Many thanks to Mr Wilson for his very kind comments. I sense that we are getting close to slaying this particular dragon. If, as we find, equilibrium sensitivities are one-third of official climatology’s midrange estimate, then the climate “crisis” vanishes.

  13. I admit I’ve shifted thinking back and forth on the two presentations – Nick vs Lord M. It is a good debate. My problem with all of it is, if CO2 is the elephant in the room, what brought the climate down from another established data point – The Medieval Warm Period – to the depths of the Little Ice Age without anthropo help.

    I suggest there is another test that can be done to assess the consensus position. Assume CO2 is the control knob and calculate back what CO2 levels must have been in 1100AD to give us temperatures, as a secent approximation, very much as we have today. How does the derived CO2 compare with ice cores or other proxies. Since actual persisting anthropo CO2 is dwarfed by natural CO2 outgassing, most of the CO2 flux in the atmosphere is natural.

    • Gary

      The descent from MWP warmth to lia coldness was often sudden and happened more than once , so the lia could best be termed intermittent. What caused these fluctuations from warm to cold and back again?

      Climate variability is much greater than many realise. Dr Philip jones admitted this in his 2004 paper when examining CET during the 1730’s’ which had risen sharply from the tremendous cold of the 1690’s but was brought to a shuddering halt in the extremely severe winter of 1740.

      Incidentally the 1730’s were the warmest decade until the 1990’s. The period around 1540 was probably warmer still, but within a couple of decades we descended into the severest winters imaginable, depicted by Brueghel in his famous paintings..

    • This reminds me that the climate scientists are asking the wrong question. The question they should be asking and answering is: How has the climate been kept relatively stable (enough to allow life to evolve) for millions of years.

  14. “Mr Stokes is quite right to say that there was a temperature equilibrium in 1850”

    I have no idea when was the equilibrium, as far as I can see it could be at any time, at 1750 or 1950 or anywhere before, after or in between.
    Judging by the best long temperature records colected from a little patch of the globe (CET)
    http://www.vukcevic.co.uk/CET-SW.htm
    where almost all of the warming took place in the winter months, equilibrium appears to be at any summer of your choice. However the winter temperatures hardly show any equilibrium at any point in the 360 year long record.

    • In response to Vukcevik, in a dynamical system such as the climate, there is never really a true equilibrium: however, the least-squares linear-regression trend on the HadCRUT4 dataset shows no trend for 80 years after 1850, which makes the temperature of 287.5 K in 1850 a good enough equilibrium temperature for present purposes.

      Besides, one advantage of using entire reference and equilibrium temperatures is that even quite large uncertainty in their values leads to a small uncertainty in their ratio, the system-gain factor.

      • Lord Monckton
        Thank you for taking time to reply.
        Considering that some 70%+ of the globe is water and most of it in the South Hemisphere, I have strong doubts that any global temperature before 1940s could be considered reliable for purpose of equilibrium.
        Since there is no such a place which can be used as a representative of global temperatures, the next best is any place with a good and reasonably reliable record, the CET must be among the top few.
        http://www.vukcevic.co.uk/CET-2018.htm
        As it can be seen in the 80 years 1850-1930 temperatures are just unstable or even more so than anywhere between 1750-1990.
        I’m not entirely convinced by Mr Stokes argument about temperatures equilibrium around 1850 or at any other time within period of the instrumental records.

      • MOB
        By equilibrium I am to read, those values are recorded temperatures from a very few thermometers in the same location covering a relatively narrow latitude band, and the CO2 levels at that time. Temperature and CO2 values only?

        Is this correct.
        Regards

        • In response to Vukcevic and Mr Cropp, the HadCRUT4 dataset commendably publishes not only the midrange estimates but also the 2-sigma uncertainties for temperatures. In 1850, the 2-sigma uncertainties, calculated by reference to the least-squares linear-regression trends on the upper and lower bounds, were less than one third of a Kelvin either side of the midrange estimate. Since we accept all of official climatology except what we can demonstrate to be false, we take the midrange estimate for 1850 without demur. Other values might be chosen, but they would not much affect the calculation of the system-gain factor.

  15. Please mods, unflag my name and let my comments go if there is no “word” infractions. Otherwise it makes good, thoughtful and timely contributions impossible. I’ve been a commenter since 2007 and never been banned or even warned. My earliest comments may have deserved criticism, but, I believe, most of my stuff over the last few years has been temperate. I am an experienced geologist and engineer and have contributed considerable educational input. I even studied paleoclimatology as part of historical geology in the 1950s as most geo students did.

    • Comments seem to be updated once per hour ….
      hope this can be improved upon soon !

    • I don’t know if your name is flagged or not, but upstream IP issues can cause comments to go into the trash bin or otherwise awry. Mods basically check the “pending” folder randomly. No trend has been able to be determined for our moderating periodicity, despite extensive Monte Carlo simulations. In fact, coupled moderator-dynamics models are being generated by the Heartland Institute at this time to solve the puzzle. We expect to release projections (note: NOT forecasts) for moderator feedbacks in late 2020.

      :p

      rip

      • Thanks rip. Is it possible that anti WUWT persons could be gumming things up? It is after all the number one site globally for climate, much to the chagrin of post normal “progressive” globalists .

        • In response to Ripshin and Mr Pearse, because my head postings here pose (if correct) a fundamental challenge to the profits made by official climatology at the expense of the taxpayers who fund the governments they have panicked, some of the true-believers can become very angry and irrational. I have actually had hate-mail in my inbox from one troll. So the moderators are carefully reading everything, so as to keep the tone as far as possible within the bounds of civilized discourse. I, for one, have very good reason to be profoundly grateful for the trouble that they take on behalf of all of us, to keep the discussion on track and hence to provide one of the very, very few fora in which it is permissible for both sides to engage in discussion with one another at all on this subject.

          The moderators are to be warmly thanked and congratulated for their diligent and even-handed ministrations.

  16. See also Nickolov and Zeller. Atmospheric composition is irrelevant. Game over.

  17. See also Nickolov and Zeller. Atmospheric composition is irrelevant. Game over.

    • If only it were as Chaswarnertoo were correct. Unfortunately, however, Nikolov and Zeller had overlooked several key points in their analysis, not the least of which was that all their paper really does is to demonstrate empirically that, at any rate with respect to the half-dozen planetary bodies on which they based their analysis, the ideal-gas law is correct. They had not remembered that the surface atmospheric pressure, which they held out as the sole determinant of surface temperature (by a mechanism not satisfactorily described or demonstrated), is itself dependent upon the atmospheric composition, which of course includes the presence of greenhouse gases. Their argument was simply the wrong way round. In effect, they had perpetrated the logical fallacy of affirming the consequent.

      If only our universities still prevented anyone from studying there who had not mastered the elements of logic, how much more quickly we could all reach the truth on these climatological questions.

      • Milord, my understanding was that distance from the sun and albedo were also necessary information and yes, you are right, their surface pressure includes any greenhouse effect, dammit. I’ll need to read more.

    • Sorry Scotty, not meaning to rock your boat, but got to say…
      you still in the Planet B of some kind, as per Brexit, with Lord M as your guide there.

      Sorry again, but you know the North Korea is still a Democratic Republic…
      last I checked, still as such recognized…

      Enjoy the latest form of democracy, the 21st century British one, no much different than the N.K. at this point in time… politically dictated all way through…
      only responsive and accountable to political Machiavellian interests there, of the very few…

      It really matters not much if Brexit goes “yes” or “no”, because;
      what really matters is how it came to be, and how it ended up as a stagnating crises,
      for a country like UK…
      quite an expensive one…definitely not the fault of the people there, if you ask me.

      Many of you there, at this point want out, many of you also want still to stay in…
      and still you suppose to have a strong government and a strong Parliament to sort that out in and as per your behalf, as country in the whole.
      Still not fricking fracking happening one or the other yet, even after three years.

      You got a really really big mess there friends…

      cheers

  18. This all helps me to understand the Butterfly Effect that began in 1850 or the data artifact of it in the minds of modelers.

    Add that to the Butterfly Effect of the hanging chad in Al Gore’s trajectory through space-time and I am almost ready to move on to the connection between minute quantum fluctuations and the macro scale Big Bang.

  19. In response to Paramenter, who has taken a commendable interest in these threads and has been full of constructive comments, emission temperature is the temperature that would prevail on Earth in the absence of any non-condensing greenhouse gases and before any feedback had operated. Its official value is about 255 K.

    Charney sensitivity is equilibrium sensitivity to doubled CO2 after all sensitivity-altering feedbacks have operated and the climate has resettled to equilibrium. Official climatology estimates it at 3.35 K (midrange), but our midrange estimate is just 1.15 K.

    Equilibrium temperature is the sum of reference temperature (i.e.., the entire temperature at a given moment, before accounting for any feedback) and the feedback response.

    Yes Mr Stokes would prefer not to take account of reference temperature in 1850, but the ineluctable fact remains that the feedbacks present in 1850 had perforce to act upon and respond to that entire reference temperature, and not only to some part of it. Therefore, it should be taken into account in deriving the system-gain factor, and, if it is taken into account, it is obvious that Charney sensitivity is about a third of official climatology’s midrange estimate.

    • Milord,

      That’s quite interesting stuff, isn’t it? Initially I was sceptical about the idea that climatology could get basics so embarrassingly wrong. But as it stands I don’t see convincing refutation of your thesis. Your critics are talking about meaning of words, redefine some terms what feedback really means or what disturbance really means, use analogies and gedankenexperiments instead of direct evidence or exercise maths gymnastics with no clear linkage with the subject. Obvious signs that you and your co-authors may have hit a sweet spot.

      Yes Mr Stokes would prefer not to take account of reference temperature in 1850, but the ineluctable fact remains that the feedbacks present in 1850 had perforce to act upon and respond to that entire reference temperature, and not only to some part of it.

      I reckon Nick tries to hide this elephant by exploring concept of derivatives where original reference temperature has no place but that sounds very peculiar, at very least. Often in weighting contrary opinions consistency, coherence and clarity matter the most. Quick look on the feedback loop system diagram from a textbook tells more what constitutes the input and output signals than long and muddy reasoning.

      • OK, look at your system diagram. What comes out of the first adder? E, the error signal. What goes into the side branch? D, the disturbance variable. All products of the perturbation. Which embraces the ongoing emission temperature?

        • In the block diagram, emission temperature comes in at top left. Then just follow the arrows. The perturbation from the preindustrial naturally-occurring greenhouse gases is added to emission temperature. Then the anthropogenic reference sensitivity is added. At this point, then (let us call it 2011), the reference signal is the sum of emission temperature (255 K), the natural reference sensitivity (10 K) and the anthropogenic reference sensitivity (0.75 K). Total: 265.75 K referencve temperature. That reference temperature is fed to the feedback loop and, after modification by that loop, because the equilibrium temperature.

          In control theory, summative nodes marked “+” are simply additive: all temperatures entering such a node are summed and passed to the next node in sequence.

        • Hey Nick,

          OK, look at your system diagram.

          For me, it’s fairly straightforward. To the ‘main’ reference input (reference temperature) disturbances are added on later stages. Finally, such output, including reference temperature in it, is fed back as the input for the next iteration of the process.

          I think though that it may not be the ‘game over’, as our Lord indicated in his text, but rather ‘endgame’. If no serious scientific objections are raised against main thesis of this work I believe it will be eventually published. But because the weight it carries application of damage control tactics at the same time will be massive. First step it try to ignore and ridicule. If that does not work try to ‘fence’ those findings and minimise the impact. Looking forward to that!

  20. In the CMIP5 models, the latest generation for which ensemble results have been published, the mean reference sensitivity to doubled CO2 – that is, the amount of warming that would occur in response to a doubling of the atmospheric concentration of CO2 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 CO2 before accounting for feedback is 1.05 K.

    Two points:

    1. Just to point out that IPCC numbers as always are bumped up more, Hansen and Bony said 1.2 degrees:
    In the idealised situation that the climate response to a doubling of atmospheric CO2 consisted of a uniform temperature change only, with no feedbacks operating (but allowing for the enhanced radiative cooling resulting from the temperature increase), the global warming from GCMs would be around 1.2°C (Hansen et al., 1984; Bony et al., 2006).
    Column 2 page 631 IPCC Chapter 8

    2. Climate sensitivity of CO2 without feedbacks, can be used to figure out the amount of global warming other greenhouse gases would produce using the Global Warming Potential (GWP) numbers provided by the IPCC. The tables begin on page 731 same link as above, and what you will find is that Methane’s GWP of 85 works out to has a climate sensitivity of about 0.4°C per doubling and is on track to produce about 0.04°C of warming by 2100. Methane really isn’t 86 times more powerful than CO2, claiming it is, is just one of the many lies the IPCC promotes.

  21. “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”
    The feedback loop doesn’t decide. You decide, because you have chosen to analyse the differences between two states – say 1850 and now. This is then linearised so that the difference between states is set to a linear variation of the differences between variables – standard calculus as I described. In that environment of differences, you develop gains and feedback coefficients based on ratios of differences.

    “Mr Stokes talks of the 255 K reference temperature in 1850 “not going away”. Precisely: it was then present…”
    It was then present; it is now present. So it does not belong among the differences which are the material for perturbation analysis that yield gain and feedback. And if you try to include it, the arithmetic will treat it as a difference; in the case between its value and zero, and it becomes very large. Not only that, but it is insensitive to how close the states are. With a small or larger difference, you can work out gain and feedback in ratio. But if, no matter how small the difference, you add in the entire reference temperature, the ratios become meaningless.

    Let me illustrate with the beginning point of most calculus classes. You have a function f(x), just of 1 variable now. And you consider the effect of adding a small amount h to x. Newton says that the ratio
    (f(x+h)-f(x))/h
    tends to a constant – the derivative, also called rate or gradient. The ratio of differences.

    But then what happens if someone says that some part of f(x) (the state) should be added into the numerator. The ratio doesn’t tend to a constant any more, because the addendum was not proportional. It tends to infinity. And since most applications of calculus are made short of but near the limit, that is a big error.

    I used the common math terminology of zero order and first order. Here f(x) is zero order. The difference f(x+h)-f(x) is first order in h. You can analyse first order terms in ratio – Newton’s derivatives. But you must keep them separate from the zero order terms.

    • Precisely to avoid complications such as that which Mr Stokes attempts to advance, we built a test rig and found, not at all to our surprise, that the feedbacks present in the feedback block will act upon the entire reference temperature, and not merely upon some arbitrarily-selected fraction thereof.

      The head posting explicitly accepts that one can attempt to derive the system-gain factor as the ratio of equilibrium to reference sensitivities rather than as the ratio of entire equilibrium to reference temperatures. But that approach has not proven effective, because there is so much uncertainty as to the value of the individual temperature feedbacks, to say nothing of the uncertainty as to the interactions between them, and between them and the forcings.

      Given that our test rig shows very clearly that feedbacks respond to the entire reference temperature, no amount of sophistry will demonstrate that they do not. Mr Stokes, in failing to concede that such feedbacks as are present at a given moment will necessarily respond to the entire reference temperature present at that moment, is at odds with control theory.

      • “we built a test rig”
        Well, I don’t believe you can overturn climate science by building a test rig, but even less do I accept that you can overturn calculus. You are deducing rates of change (gain, feedback coefficients) by differencing things that became different because of the change, and taking ratios. Or should be. If you put in quantities themselves, rather than the amount they changed, then the rate calculation will treat them as if they changed from zero in one step. And the answer returned will be a very high rate indeed, and not approaching a limit with small change.

        • First of all, our test rig, and that constructed and operated under conditions of strict ambient-temperature control by a national laboratory, did not “overturn climate science”. It demonstrated that control theory is correct to find that the feedbacks operating in a dynamical system at any given moment must respond to the entire reference signal then obtaining, and not solely to a small and arbitrarily-chosen fraction thereof.

    • Nick Stokes –

      “In that environment of differences, you develop gains and feedback coefficients based on ratios of differences.”

      Those items must be consistent with what came before, though. If your gains and coefficients, applied to an earlier era, would produce results that are not in evidence in later data, then your estimates of these values are wrong.

  22. Temperature is not proportional to energy when the vast amount of water on the Earth must be taken into account. It takes substantially more energy to change water from 0 degrees to 1 degree than from 1 degree to 2 degrees. It takes even more energy to vaporize the water. https://www.britannica.com/science/latent-heat
    This is easily proven by dropping an ice cube into a cup of warm water. The ice cube with much less volume than the water can easily cool the warm water down. As long as there are huge masses of ice at the poles, it will require an enormous change in energy input to change temperatures significantly.
    The temperature changes that are seen are mostly caused by water currents moving warm water from the tropics to the poles and cold water back. The poles can quickly cool any warm water with only minimal ice melt. If less warm water makes its way to the poles, “average” temperatures can rise only because there are more non-polar temperature readings are used in calculating the average. This is seen in the temperature spikes caused by El Nino events. The total energy entering and leaving the Earth hasn’t changed, just it’s effect on local thermometers used to calculate an “average” temperature that has changed.

  23. CM’s approach to the problem is very similar to Salby’s analysis to the evolution of CO2 in the atmosphere and the conclusion that the Bern model is not physical because it removes CO2 when there is none left. See
    (https://edberry.com/blog/climate-physics/agw-hypothesis/what-is-really-behind-the-increase-in-atmospheric-co2/) at 58 min. If the problem is correctly framed the analysis can be decisive without quantifying things outside the frame. If the problem is framed poorly quantification of unobserved factors is necessary and the analysis becomes a guess.

  24. Here is what bothers me so much on this quote, from Nick Stokes article:

    “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.”

    That 1850 number is built on minimal data that covers maybe <1% of the planets surface, the rest of the world including 99.99% of the ocean water has ZERO temperature data to draw from

    This makes for a wild guess on what the temperature really was for that year. Too little data points with 99% of Southern Hemisphere without any data at all.

    Here is a post I made yesterday on this very point:

    http://www.politicalforum.com/index.php?threads/uncertainty-in-early-temp-records.551859/page-2#post-1070649639

    There are TWO NOAA charts for year 1900, showing how little of the planets surface have any daily temperature stations on it. Now imagine that 1850, with far less than that.

    • “this quote, from Nick Stokes article”
      It’s actually a quote from Lord M’s article. I’m getting lambasted for what is his choice of 1850. But I don’t disagree with it. On this point, it seems it is Lord M and I against the world.

    • In response to sunsettommy, the HadCRUT4 dataset, unlike most other datasets, takes care to publish not only the midrange estimate but also the 2-sigma (i.e., 95%) confidence interval, which, for 1850, was less than one-third of a Kelvin either side of the midrange estimate. That variability is too little to influence calculations based upon absolute reference and emission temperatures in 1850.

  25. The core point of disagreement is whether or not CO2 feedback is proportional to average temperature T in degrees Kelvin. Can someone please point us to a list of feedback mechanisms so that we can assess that they are all proportional to T ?

    I now understand Stokes’ argument to be: “we know that temperature was stable at 287.5 K; so feedback must go to zero at 287.5 deg K.” This certainly seems to suggest a non-linearity? Or am I missing something?

    • In response to boffin77, test apparatus constructed by one of my co-authors, and a further and more sophisticated apparatus built by a national laboratory, confirmed beyond all doubt that such feedback processes as subsist in a dynamical system at any given moment must perforce respond, at that moment, to the entire reference signal then obtaining, and not merely to some small and arbitrarily-chosen fraction of that reference signal. There is no doubt whatever about this. it is inherent in the equations, and, strictly speaking, did not need to be empirically verified, but we empirically verified it anyway, with a well designed experiment by a co-author and then with another well-designed experiment from a national laboratory.

      • Thanks for the quick reply. I agree completely (always have) that “such feedback processes as subsist in a dynamical system at any given moment must perforce respond, at that moment, to the entire reference signal.”

        My concern is that linear control systems with positive feedback don’t reach equilibrium. (Many of us know this from ancient school assemblies where the gain on the microphone was turned up too high and the room was immediately filled with an ear-splitting shriek.) In your simplified diagram (above) the “feedback fraction” [f_t] might be better written as [f * delta(t)] to indicate that the impact of feedback is very small over very short times, and grows with time. The fact that the impact is linear with time is an assumption you and I are making, not a requirement. Obviously, delta(t) = t – (t-1) and f will have units of inverse years.

        Given R(t-1) = temperature at time (t-1), the temperature at some new time t (which you call [E_t]) can be calculated as follows:
        E_t = R(t-1) / ( 1 – f * delta(t) ).
        This gives us what we expected: E_t gets larger as delta(t) gets positively larger.

        A key observation is that there is no equilibrium temperature under this model; T(t) will always rise with time t. I’m not sure why your diagram suggest it will reach equilibrium.

        I will add that I don’t think this is the correct model – runaway temperature feedback would have killed us all eons ago. However it might be an adequate model for estimating climate sensitivity, as you have done.

    • I now understand Stokes’ argument to be: “we know that temperature was stable at 287.5 K; so feedback must go to zero at 287.5 deg K.”

      Stokes? I’m trying to keep mouth shut in order to just appear stupid.

      • It is not clear why Boffin77 imagines that “linear control systems with positive feedback don’t reach equilibrium”. Of course they do, provided that the feedback fraction is well below unity. Just build a test rig and you can find this out. That’s what we did. Or you can just work the equations.

        Of course, some of the sillier extremist papers, predicting up to 11 K warming per CO2 doubling, are in effect assuming feedback fractions dangerously close to unity. But it was the observation that these absurdly high feedback fractions would lead to an instability not observed in the real world that led us to carry out our research in the first place.

        • Well I admit it has been many years since I designed control systems, but I did (long ago) build some that demonstrated what positive feedback does – and we all ducked for cover and pulled the plug.
          My analysis of the simplest case (the case where reference temperature Rt is constant) can be summarized non-mathematically as follows: Rt is being augmented by a feedback that gets larger with each passing year (such is the nature of positive feedback applied to a constant input). Your model is so admirably simple that nothing more needs to be said.
          Alarmists seem to think this will actually happen, but if it can happen now it must have happened in the past, in which case we would not be here to talk about it. Ergo it will not actually happen. Rather there must be, for example:
          – negative feedbacks that kick in at some temperature. or
          – non-linearities in the CO2 feedback.
          – or maybe the whole CO2 positive-feedback myth is inaccurate (and I know it is not your invention)

          I appreciate your educated and innovative and original approach to the investigation.

          • Boffin77 is incorrect to summarize by saying that reference temperature is augmented by a feedback that gets larger with each passing year, and wrong to suggest that such is the nature of a positive feedback applied to a constant input.

            He neglects to take account of the fact that a feedback is merely a radiative forcing whose magnitude is proportional to the temperature change driven by an original, direct forcing. Just like the direct forcing, the indirect forcing arising from temperature feedback is resolved by an increase in temperature, which restores radiative equilibrium.

          • Well these new comments make sense, though I can’t really match them up against the original diagram and text. So I’ll just say “thank you” for your patient replies to my comments, and best wishes for your radical critique of climate science.

          • In response to Boffin77, the block diagram in the head posting is standard fare. But one can only really understand how it works if one also has a grasp of the underlying mathematics. Briefly, the system-gain factor is equal to the reciprocal of (1 minus the feedback fraction), provided that the absolute value of the feedback fraction is less than 1. The reason why this is so goes back to the very first formal demonstration of the sum of an infinite convergent geometric series, some hundreds of years ago.

            Consider the block diagram. As the signal passes infinitely around the feedback loop, passing through the feedback block each time, an infinite series of successive powers of the feedback fraction arises. The sum of that series is 1 / (1 – f). In the long version of our paper that has been submitted to a journal, we have included the formal demonstration that this is the case, precisely to address the concerns of reviewers who might not otherwise realize that net-positive feedback does not necessarily entail a runaway response. Provided that the feedback fraction is safely below unity, there will be no runaway response.

            In practice, the feedback fraction (the fraction of equilibrium temperature represented by the feedback response) must be below 0.3, for otherwise the formidable stability of the temperature regime on Earth would be impossible. But official climatology imagines it must be about 0.6, and might even be very close to unity in some of the sillier, extremist papers, which is why it has been unable to constrain equilibrium sensitivity.

            The curve of 1 / (1 – f) is rectangular-hyperbolic, so that as f approaches unity the equilibrium sensitivity approaches infinity. It was our realization that this is the case that led us to begin examining what climatology was doing wrong.

  26. So, mathematically what is the sensitivity to a 38% increase in CO2? In 1850 CO2 was 300ppm and it is currently 415ppm. We have 169 years of observational evidence to work with. What does it tell us?

    • In response to artimms, it is implicit in the CMIP5 midrange estimates that reference sensitivity to a change in CO2 concentration is the Planck parameter 0.31 times the forcing coefficient 4.85 times the natural logarithm of the proportionate change in concentration. Thus, the reference sensitivity to a 38% increase in CO2 concentration is 4.85 x 0.31 x ln(1.38), or 0.5 K.

      Or one could take the entire net anthropogenic forcing of 2.5 Watts per square meter from 1850-2011. The reference sensitivity is then 2.5 times the Planck parameter: i.e., 0.75 K (which, coincidentally, is the actual least-squares linear regression trend on the HadCRUT4 temperature data from 1850-2011.

      To find out what the equilibrium sensitivity to the 2.5 Watts per square meter net period anthropogenic forcing would be were it not for a radiative imbalance of 0.6 Watts per square meter to 2010 (Smith+ 2015), one simply multiplies the 0.75 K directly-forced anthropogenic reference warming by 2.5 / (2.5 – 0.6), which means there should have been an equilibrium warming of 1 K by 2011, were it not for the time delay occasioned by the vast heat capacity of the oceans.

      The factor 2.5 / (2.5 – 0.6) is the period system-gain factor. But it is only 1.3, and not official climatology’s 3.2 – another sign that official climatology’s estimates of equilibrium sensitivity are about three times too big.

  27. “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)”
    That isn’t a gain. It is just saying that of the forcing, as proportion went into the sea. It is a correction that you might make to a gain for the shortfall from equilibrium. But it isn’t the gain.

    • Mr Stokes is wrong – or very largely so. The purpose of the radiative imbalance (it seems first to have been introduced to the literature by James Hansen in 2006 or thereby) is to correct for the timelag in the equilibrium-temperature response to radiative forcings and consequential feedbacks.

      The equilibrium sensitivity is derived from the sum of the direct forcings and the consequential forcings driven by temperature feedbacks (which are expressed as forcings denominated in Watts per square meter per Kelvin of the reference temperature, or sensitivity, that engendered the feedback response).

      Broadly speaking, the warming consequent upon the sum of the direct and feedback forcings is proportional to the magnitude of that sum, wherefore it follows that the ratio of the direct forcing to the difference between that forcing and the radiative imbalance is (or is very close to) the system-gain factor.

  28. It is of interest to note that,as Monckton states ,the feed back to CO2 is so small as to be immeasurable. It will be a surprise to most readers to see that the IPCC Summary for Policy Makers agrees with him see: https://climatesense-norpag.blogspot.com/2017/02/the-coming-cooling-usefully-accurate_17.html
    “Various approaches to improve the precision of multi-model projections have been explored, but there is still no agreed strategy for weighting the projections from different models based on their historical performance so that there is no direct means of translating quantitative measures of past performance into confident statements about fidelity of future climate projections. The use of a multi-model ensemble in the IPCC assessment reports is an attempt to characterize the impact of parameterization uncertainty on climate change predictions. The shortcomings in the modeling methods, and in the resulting estimates of confidence levels, make no allowance for these uncertainties in the models. In fact, the average of a multi-model ensemble has no physical correlate in the real world.
    The IPCC AR4 SPM report section 8.6 deals with forcing, feedbacks and climate sensitivity. It recognizes the shortcomings of the models. Section 8.6.4 concludes in paragraph 4 (4): “Moreover it is not yet clear which tests are critical for constraining the future projections, consequently a set of model metrics that might be used to narrow the range of plausible climate change feedbacks and climate sensitivity has yet to be developed”
    What could be clearer? The IPCC itself said in 2007 that it doesn’t even know what metrics to put into the models to test their reliability. That is, it doesn’t know what future temperatures will be and therefore can’t calculate the climate sensitivity to CO2. This also begs a further question of what erroneous assumptions (e.g., that CO2 is the main climate driver) went into the “plausible” models to be tested any way. The IPCC itself has now recognized this uncertainty in estimating CS – the AR5 SPM says in Footnote 16 page 16 (5): “No best estimate for equilibrium climate sensitivity can now be given because of a lack of agreement on values across assessed lines of evidence and studies.” Paradoxically the claim is still made that the UNFCCC Agenda 21 actions can dial up a desired temperature by controlling CO2 levels. This is cognitive dissonance so extreme as to be irrational. There is no empirical evidence which requires that anthropogenic CO2 has any significant effect on global temperatures.
    The climate model forecasts, on which the entire Catastrophic Anthropogenic Global Warming meme rests, are structured with no regard to the natural 60+/- year and, more importantly, 1,000 year periodicities that are so obvious in the temperature record. The modelers approach is simply a scientific disaster and lacks even average commonsense. It is exactly like taking the temperature trend from, say, February to July and projecting it ahead linearly for 20 years beyond an inversion point. The models are generally back-tuned for less than 150 years when the relevant time scale is millennial. The radiative forcings shown in Fig. 1 reflect the past assumptions. The IPCC future temperature projections depend in addition on the Representative Concentration Pathways (RCPs) chosen for analysis. The RCPs depend on highly speculative scenarios, principally population and energy source and price forecasts, dreamt up by sundry sources. The cost/benefit analysis of actions taken to limit CO2 levels depends on the discount rate used and allowances made, if any, for the positive future positive economic effects of CO2 production on agriculture and of fossil fuel based energy production. The structural uncertainties inherent in this phase of the temperature projections are clearly so large, especially when added to the uncertainties of the science already discussed, that the outcomes provide no basis for action or even rational discussion by government policymakers. The IPCC range of ECS estimates reflects merely the predilections of the modellers – a classic case of “Weapons of Math Destruction” (6).

    • ” … What could be clearer? The IPCC itself said in 2007 that it doesn’t even know what metrics to put into the models to test their reliability. That is, it doesn’t know what future temperatures will be and therefore can’t calculate the climate sensitivity to CO2. … ”
      >>

      Not to mention that such physical ‘testing’ would be non-helpful, when the testing time-scale is of the order of millennia.

      It’s thus not merely a “known unknown” but for practical purposes it’s an unknowable unknown, (unless you have a time-machine, and we don’t, but if we did we would already know when the next glacial commences, and intervening trend … plus have a record of the WX noise).

      This is the mother-of-all fool’s errands, but thank you for pointing out some within the IPCC’s publications agree with that.

  29. It is of interest to note that ,as Monckton says ,the effect of anthropogenic CO2 is too small to be measurable. Most readers will be surprised to learn that the IPCC Summaries for Policy Makers agree with him. See
    https://climatesense-norpag.blogspot.com/2017/02/the-coming-cooling-usefully-accurate_17.html
    “………The IPCC AR4 SPM report section 8.6 deals with forcing, feedbacks and climate sensitivity. It recognizes the shortcomings of the models. Section 8.6.4 concludes in paragraph 4 (4): “Moreover it is not yet clear which tests are critical for constraining the future projections, consequently a set of model metrics that might be used to narrow the range of plausible climate change feedbacks and climate sensitivity has yet to be developed”
    What could be clearer? The IPCC itself said in 2007 that it doesn’t even know what metrics to put into the models to test their reliability. That is, it doesn’t know what future temperatures will be and therefore can’t calculate the climate sensitivity to CO2. This also begs a further question of what erroneous assumptions (e.g., that CO2 is the main climate driver) went into the “plausible” models to be tested any way. The IPCC itself has now recognized this uncertainty in estimating CS – the AR5 SPM says in Footnote 16 page 16 (5): “No best estimate for equilibrium climate sensitivity can now be given because of a lack of agreement on values across assessed lines of evidence and studies.” Paradoxically the claim is still made that the UNFCCC Agenda 21 actions can dial up a desired temperature by controlling CO2 levels. This is cognitive dissonance so extreme as to be irrational. There is no empirical evidence which requires that anthropogenic CO2 has any significant effect on global temperatures. ………….Harrison and Stainforth 2009 say (7): “Reductionism argues that deterministic approaches to science and positivist views of causation are the appropriate methodologies for exploring complex, multivariate systems where the behavior of a complex system can be deduced from the fundamental reductionist understanding. Rather, large complex systems may be better understood, and perhaps only understood, in terms of observed, emergent behavior. The practical implication is that there exist system behaviors and structures that are not amenable to explanation or prediction by reductionist methodologies. The search for objective constraints with which to reduce the uncertainty in regional predictions has proven elusive. The problem of equifinality ……. that different model structures and different parameter sets of a model can produce similar observed behavior of the system under study – has rarely been addressed.” A new forecasting paradigm is required.

    • W.Elsasser addresses the limits of that reductionist paradigm, for biology.

      A Form of Logic Suited for Biology
      Walter M. Elsasser Department of Earth and Planetary Sciences The Johns Hopkins University Baltimore, Maryland http://www.nap.edu/readingroom/books/biomems/welsasser.htm

      The complexity of almost any living organism is beyond comprehension with a positivist approach. Still on a (discreet) continuum it might be possible to classify planetary climates. Zeller and Nikolev’s atmospheric pressure continuum points to another view.

  30. tony b and guy pearse discussed rapid cooling stops and starts in northern hemisphere temperatures -MWP, LIA and even current Arctic warming.

    Could the reason be Dansgaard-Oeschger events? Here is how I understand the causes of Arctic temperatures going up and down.

    Warm Gulf Stream waters flow upward past Greenland and Norway into the Arctic Ocean and under the sea ice;

    This warm saline water is found below cold saline covered by fresh water and in turn insulated by sea ice;

    Interestingly the cold periods last about 1000 years and the warm cycles a few decades defining D-O events;

    During the last Ice Age, Greenland’s average temperatures dramatically rose on average every 1500 years by 10°C (+/- 5°C) in a just matter of one or two decades, and then more gradually cooled;

    The cause of abrupt warming was the sudden removal of insulating sea ice that allowed ventilation of heat previously stored in the Arctic;

    70% of the D-O events occurred in times of CO2 indicating it not to be a factor in warming;

    When sea ice prevents heat ventilation, the inflow of warm and dense Atlantic water continues to store heat in the subsurface layers;

    The warm Atlantic water becomes more buoyant, upwells and melts the insulating ice cover; and,

    The loss of an insulating ice cover allows for the transfer of heat to the atmosphere causing a dramatic rise in surface temperatures to begin a D-O warm phase.

    Other studies show the Arctic Ocean has cooled since the early 1990’s and continues to cool as it seeks equilibrium with the atmosphere while transferring heat

    As quickly as the Arctic warmed occurred, cooling could be as abrupt and rapid returning to its normal cold state. The wobbly jet stream which has brought wide swings in weather would likely settle down and stabilize as the Arctic cools.

    Any opposition to these understandings?

    • Keith

      I obtained Hubert lambs records of wind direction back to around 1500 and tried to bring it up to date and then compared it to my reconstruction of CET back to 1540 . There is a close match most times showing how climate is affected by the direction of prevailing winds .

      Generally in this part of the world westerlies aRe warming, easterlies cold in winter and warm in summer etc. there was a preponderance of cold easterlies in the LIA and a surfeit of westerlies during the warm eras.

      our local abbey made windows smaller in the 1170’s as the climate cooled and the warm westerlies became much less common. Curiously the coldest eras also seem to be the wettest and stormiest which does not follow the general understanding that a warm atmosphere can contain more moisture

      The weather systems are driven by the meandering jet streams so rapid change from a cold to a warm state and back again seems to be the norm, but with protracted periods when winds from one direction or other predominate .

      So not disputing your comments and all we need is a few million in grants to carry out some more research

      Tonyb

      • TonyB
        There have been recent papers confirming Arctic heat ingress by wind. My own study of high latitude areas with high monthly temperature anomalies confirmed wind direction change.
        Regatds

        • tonyb and Martin Cropp both make good points about the influence of variability in wind direction on global mean surface temperatures. There are many such variable influences, such as the relative frequencies of el Nino and la Nina, for instance (and that, too, is partly influenced by wind direction).

        • “confirming Arctic heat ingress by wind”

          Is that just air heading up be cooled? Does it also imply cold air coming down be warmed?

      • Tonyb,
        That is extremely interesting. A very common unstated-but-implicit assumption in climate science is that energy can only enter or leave the climate system via radiative transfer. Some models do take into account some small geothermal effect as well, but generally it is assumed that all other methods of energy transfer in and out are negligible and can be safely ignored.

        One of the largely ignored mechanisms for transfer of energy is kinetic and heat energy addition/subtraction arising from momentum change. The “solid” Earth changes its axial rotation rate on a cyclic basis with periodicities ranging across all observable time scales from days to lunar cycle (weeks) to biannual to annual to multidecadal to multicentury. Measurements of the LOD (Length of Day which is inversely proportional to angular velocity) date back to the 17th century albeit with poor precision until the 20th century. Empirical Mode Decomposition or Fourier analysis of LOD records show identical frequency content to EMD or Fourier applied to the GMST series for multiannual periodicities. As the solid Earth spins faster or slower there is a frictional torque between the solid Earth and the hydrosphere and atmosphere which changes their angular momentum. Some of the variation is undoubtedly expliquable in terms of reditribution of surface masses. If there is no external driver for the variation in solid Earth angular velocity then we expect via conservation of angular momentum to see a clear correlation of Atmospheric Angular Momentum (AAM) and LOD, and indeed we do see a very strong correlation over periods of less than seven years. There is now general agreement that most of the changes in LOD on time scales from weeks to a few years are excited by changes in AAM – and vice versa. The atmosphere exchanges angular momentum with the solid Earth as expected. Because of the massive difference in moment of inertia, a very small change in LOD translates into a big change in AAM. This AAM to LOD correlation however shows a clear long-wavelength drift when longer periods are considered, which makes it highly likely that the solid Earth variation is subject to some “external” driver. “External” here means external to the climate system, so it could be a torque associated with variation in Earth’s liquid core or it could be external-to-Earth driven by orbital mechanics. Whatever the root cause, it has the effect of adding and subtracting about 4 x 10^22 joules of KE to the atmosphere every 60 years or so (full amplitude).
        Independently, there is also very strong evidence to suggest that the quasi-60 years cycles are forced cycles rather than any oscillation of ocean heat distribution. This comes from the relative phasing of net flux and temperature. If these cycles were caused by natural oscillations of heat distribution we would expect the temperature oscillation to be pi radians out of phase with the net flux oscillation; i.e. maximum surface temperature should yield maximum outgoing flux or cooling and minimum surface temperatures should encourage maximum incoming flux or warming. To the extent that we can estimate net flux phasing (from ocean heat estimates or from sea level rates historically) it does NOT exhibit this phasing. Instead, it shows a phasing which is entirely compatible with externally forced heating ( i.e. less than pi/2 phase separation) .
        So, in summary, we have a fairly substantial oscillation which is (a) probably externally forced and (b) of a magnitude which is too large to be explained by exchange of angular momentum as a sole cause and (c) cannot be explained by the current basket of external radiative drivers. We can add to this that the period between 1980 and 2000 during the most recent warm phase of the 60-year oscillation was driven by SW heating largely attributed to a major change in cloud albedo.

        The most dominant effect of the oscillation in LOD is its effect on the wind stress tensor. Primarily, it either strengthens or weakens the main east to west trade winds. This then changes both cloud fraction and distribution (which provides the missing energy in the net flux oscillation via SW). This also controls the likelihood of relative strength and frequency of ENSO events. In conclusion, I think that there is an oscillatory external torque, probably driven by orbital mechanics, which is responsible for the 60 year oscillation aka stadium wave via control of winds. The “missing” energy in this oscillation is determined by a parallel induced change in cloud fraction and distribution. Your observations fit into this hypothesis quite comfortably.

    • ” … As quickly as the Arctic warmed occurred, cooling could be as abrupt and rapid returning to its normal cold state. The wobbly jet stream which has brought wide swings in weather would likely settle down and stabilize as the Arctic cools. Any opposition to these understandings? … ‘
      >>

      That’s not what we see even via the annual seasonal change, colder season phase equates to faster and deeper jetstream flows that become closer to the equator as peak of cold approaches, and greater latitudinal excursion ‘wobble’ in general. So I see little reason to expect a general cooling phase to become more settled in time. In fact, such seems to correlate with greater storminess and variability.

    • Keith, my point was more that the descent from the MWP, which was much like the present warm period, to the cold depths of LIA occurred naturally without a connection to CO2, or any atmospheric drivers.

      Essentially, this is strong evidence that natural variations are the first order drivers of climate and that CO2 is at best a third order effect after water which is the source of multiple large effects: radiative; phase change enthalpies; convective heat transfer, albedo change from clouds, massive heat sink of the oceans, their heat transfer in ocean currents…

  31. Christopher Monckton,

    Very interesting work and I agree with others that your explanation in this post is the best yet.

    However, I have trouble understanding how the global mean surface air temperature could ever be at a steady “equilibrium” because it is constantly changing. For instance, there is an annual cycle in the global mean surface air temperature of about 4K, ranging from about 276K to about 285K to 289K (12C to 15C) in recent years as can be seen here:
    https://oz4caster.files.wordpress.com/2019/03/fig-1-ncar-r1-global-msat-1948-2019.gif

    And over longer time periods, our best proxies indicate more substantial variations of the annual average global mean surface air temperature in the past, as can be seen here:
    https://oz4caster.wordpress.com/paleo-climate/

    Maybe we could say “quasi-equilibrium” for an annual average?

    • “your explanation in this post is the best yet”

      It makes one think clear that before took some delving:

      “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.”

      That is indeed the basic arithmetic, and since that 1.085 factor is the ratio of two absolute temperatures in the climate ball park, it has to be close to 1, what ever observations or anything else say.

      But it isn’t justified here. In the first of this recent series it was, in a way. A function E(R) was defined, where E is actual surface temperature, and R is an imputed temperature that would exist without feedbacks. Now that does give a way forward; the sensitivity ECS could be written as response to forcing F:
      ECS = dE/dF = dE/dR dR/dF.
      But in the arithmetic here, dE/dR has been replaced by E/R. Joe Born has been focussing on that. Then why?

      The earlier paper did try to justify it by fitting various functions E(R) – linear, exponential etc. It didn’t make much difference, so let’s look at linear. The common requirement was that E(R) had to pass through (0,0) – ie E(0)=0. That is, 0K.

      But this is totally unphysical. For a start, air liquefies at about 80K. But you can’t sensibly extrapolate the properties of the atmosphere below about 200K. But it’s worse than that.

      E is not actually a function of R. They are related through the varying values of GHG. When GHGs go to zero, E and R both stand at about 255K. They can’t meaningfully go any lower, because there are no more GHGs to be removed. You certainly can’t say that there would be constant slope down to 0K.

      So if you want to make a gross linear approx, the point to relate to is (255,255), not (0,0). But that would be a gross approximation indeed. Even if you could reliably impute R over that range, the behaviour of the atmosphere changes radically. We are talking about snowball earth, after all. But if you did make that gross approx, the ratio would be something like
      (288-255)/(265-255)
      or about 3.3. Right in the IPCC range.

        • Bryan,
          “Do you have any thoughts on global mean surface air temperature “equilibrium”?”
          They would be considering at least an annual average, so that gets rid of the seasonal cycle. It hardly matters whether the system actually sat at equilibrium in 1850. You could have an amplifier sitting in a telecom network which is never at equilibrium. That doesn’t affect its ability to function as a linear amplifier. The key thing is that, over some range of perturbations, differences in states relate linearly to differences in state variables. If you imagine the results of a two variable system graphed, they would lie on a line, which is all that you need. The intercept at zero x (whatever you consider x) would be the notional equilibrium point, but it doesn’t matter whether you have data exactly there.

          People have odd ideas about Lord M’s starting point of 1850. It isn’t supposed to be a particularly perfect period. It is just one state; the present is another, and you can use differences between them to estimate rates. Both ends with have fluctuations due to cause other than the variables you are relating (noise). The criterion for choice are that you have a good period of separation, so that the differences you think are due to cause are large relative to the noise. On the other side, the start should not be so long ago that information is poor, and it should not create differences so large that the linear approximation is in doubt. Some might think 1850 fails the first – OK, choose a later period. Of course, the other criterion is that you should expect the cause that you are analysing should have been operating during the period. There is no point in including periods when it wasn’t; it will just add noise without information.

          • Nick thanks, your discussion makes good sense to me. It’s human nature to want to simplify problems in order to better address them and many times simplistic approaches that are not very accurate can work well enough for many purposes. My concern about climate science is that the numerous complex, chaotic, and interacting perturbations of varying magnitudes and durations that influence climate change introduce so much “noise” in the system that it is nearly impossible to accurately isolate the effect of a single perturbation like CO2, both for diagnostic and predictive purposes.

            I strongly suspect that many modelers are far too overconfident in their models, whether they be very simplistic or very complicated models. Until these models are validated with decades of future observations, I see little reason to have much confidence in them. At this point, they are little more than speculation. Because of all the parameterizations involved in the more complicated models, I suspect much iterative tweaking will be needed over many decades of comparing results to observations. Even then, because of the extreme complexity of the climate system, I have serious doubts that the current models will ever have enough skill to engender much confidence in their decadal to century scale predictive capabilities, especially on regional or local scales that are more important to most people. However, considering how much modeling has improved over the last 30 years, there could easily be unforeseen modifications that will improve model skill as has happened with short-term weather modeling. For that reason, I support both weather and climate modeling efforts, but strongly caution against unwarranted premature confidence.

      • Mr Stokes imagines, incorrectly, that at the emission temperature of 255 K there are no feedbacks. Perhaps he would care to calculate the temperature at the ocean surface directly beneath the zenith point, and think again. Or he may like to read Merlis+ (2010).

        He continues to fail to acknowledge that the feedback processes that were present in 1850 perforce responded to the entire temperature then prevalent, and not to some arbitrary and minuscule fraction thereof. In this, our professor of control theory is entirely clear: feedbacks respond to the entire reference signal, and not merely to some small fraction thereof.

        • “Mr Stokes imagines, incorrectly, that at the emission temperature of 255 K there are no feedbacks.”
          There are no GHG feedback fluxes, because there are no non-condensing GHGs. 255K is defined as the temperature when they have been removed. You’re trying to create the smile without the cat. In Lacis’ model I think there is still some water vapor at 255K. But it can’t provide feedback to GHG which aren’t there. And the wv certainly won’t be there at 200K.

          • In response to Mr Stokes, it is self-evident that there were no feedback responses to pre-industrial noncondensing greenhouse gases when there were no such gases in the atmosphere and the reference temperature comprised the 255 K emission temperature alone. However, that emission temperature on its own engendered a substantial temperature feedback response to precisely the same sensitivity-altering feedbacks as IPCC lists as driving the feedback response to the greenhouse gases.

            We have not at any stage suggested what Mr Stokes here implies we have suggested: namely that when there no greenhouse gases there was nevertheless a feedback response to the greenhouse gases.

            And, since the emission temperature is 255 K (actually, it’s probably about 10 K above that, once one has allowed for Hoelder’s inequalities between integrals, because one-third of the dayside would be open ocean), our current draft does not concern itself with what might have been the case if the Earth’s temperature were as low as 200 K.

          • “We have not at any stage suggested what Mr Stokes here implies we have suggested: namely that when there no greenhouse gases there was nevertheless a feedback response to the greenhouse gases.”
            Implies? Implies? From just the previous comment:
            “Mr Stokes imagines, incorrectly, that at the emission temperature of 255 K there are no feedbacks”

            “our current draft does not concern itself with what might have been the case if the Earth’s temperature were as low as 200 K.”
            The summary, from just a few days ago, was based heavily on the proposition that the E(R) function, of surface temperature vs imputed temperature without feedback, passed through (0,0), ie absolute zero 0K. That is the basis for expressing the gain as a ratio of absolute temperatures.

            In fact the lowest it can reach by reducing GHGs is a point near 255K where there are no GHGs and no feedback. And at that point E=R=255. And if you extend linearly to that point, you get a system gain, and hence sensitivity, of about 3K/doubling.

          • There are no GHG feedback fluxes, because there are no non-condensing GHGs. 255K is defined as the temperature when they have been removed.

            I don’t profess to know what magnitude any feedback at 255 K may have, but as a matter of theory I see no reason for your implied assumption that no greenhouse gas means no feedback.

            Let’s return to the physically more evocative feedback formulation T=g\cdot(F+\lambda T)—which Lord Monckton changed to his by replacing T with E, gF with R, and \lambda g with f. (Note here that I’m using the whole quantities rather than perturbation. That makes the use of a single forcing variable and addition problematic, but we’ll ignore that.) A temperature change initially resulting from a forcing \Delta F that represents, say, a dimming of the sun might have knock-on effects such as an albedo increase that further changes T.

            The feedback coefficient \lambda‘s value would reflect that temperature-caused albedo change. If you accept the possibility of such knock-on effects but don’t consider them feedback, then it seems to me your disagreement with Lord Monckton on that issue is merely semantic.

            Obviously, though, that albedo feedback’s magnitude is unlikely to be the same as, say, water-vapor or lapse-rate feedback’s at a higher temperature in the presence of greenhouses, so it is not unreasonable to entertain the notion that the feedback coefficient \lambda is highly dependent on temperature T and thus, contrary to what Lord Monckton thinks is dictated by feedback theory, that f is highly dependent on E: E is a significantly nonlinear function of R.

            I hasten to add that I have no idea whether the function actually is very nonlinear. But nothing in feedback theory rules that possibility out; a feedback-amplifier circuit could be built to model it.

          • “I see no reason for your implied assumption that no greenhouse gas means no feedback”
            I said there was no GHG feedback flux. It could of course be possible to have a feedback to some other heat source. But you can’t have feedback to GHG that aren’t there.

            The relevance is to Lord M’s function E(R), which you have been looking at. E is the surface temperature; R the temperature you would have with GHG forcing but no GHG feedback. As you remove GHG (in a thought experiment) the temperature drops until at 255K, they have all gone. E is then the temperature in the absence of GHG feedback (there are no GHGs). So E=R. The E(R) curve passes through that point.

            I don’t endorse Lord M’s practice of using the difference between such a point and present as the gradient for sensitivity purposes. I agree with you that it should be the local gradient at present climate. But if you do, then the system gain is (288-255)/(265-255)=3.3. Multiply by 1.05 to get the sensitivity.

          • Contrary to what I surmised, Mr. Stokes’ use of feedback seems to differ substantively from Lord Monckton’s, not merely semantically:

            R [is] the temperature you would have with GHG forcing but no GHG feedback.

            If I’m interpreting that correctly, Mr. Stokes doesn’t look upon R as what the temperature would be without any feedback to temperature at all. His version seems instead to include feedback to the entire temperature except the portion for which CO2 forcing is responsible. In contrast, Lord Monckton does seem to define R as excluding all feedback whatsoever.

            That substantive difference manifests itself in Mr. Stokes’ following statement:

            [I]f you [use Lord Monckton’s approach], then the system gain is (288-255)/(265-255)=3.3. Multiply by 1.05 to get the sensitivity

            That is, the two 255 K values imply that Mr. Stokes sees E(R) as passing through (R,E)=(T_E,T_E); there’s no CO2 forcing at the emission temperature T_E, so E has to equal R at that point.

            But emission temperature is based on today’s albedo and clouds, not on what they would be if the surface temperature equaled the emission temperature. This implies that, although Mr. Stokes’ version of R excludes some feedback, it includes any feedback that may occur at low temperatures through, say, the albedo-change mechanism.

            Since Lord Monckton’s version excludes all feedback, on the other hand, fT_E is non-zero and makes the (E,R) curve pass instead through some (T_E-fT_E, T_E). That puts the emission-temperature point to the left of where Mr. Stokes puts it, and Lord Monckton no doubt imagines it’s near the line from the origin to the (R,E) point that represents 1850’s conditions. If it is, then the resultant ECS estimate is much less than the one Mr. Stokes made for the sake of argument.

            So, as a high-ECS-value partisan, Mr. Stokes would seem to provide some support for Lord Monckton’s argument that in the view of “climatology” feedback “will not respond at all to the emission temperature.”

          • So, as a high-ECS-value partisan, Mr. Stokes would seem to provide some support for Lord Monckton’s argument that in the view of “climatology” feedback “will not respond at all to the emission temperature.”

            I’m afraid I overstated that. It’s not that Mr. Stokes believes there’s no feedback at all below the emission temperature. It’s merely that he ignored it in applying the hypothetical technique for the sake of argument.

          • “Contrary to what I surmised, Mr. Stokes’ use of feedback seems to differ substantively from Lord Monckton’s, not merely semantically:”

            I don’t think so. But it actually doesn’t matter. This whole discussion, based on what Lord M mostly says he does, has been totally off the beam relative to what he actually does, which is summarised in the post above:

            “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 CO2 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.”

            Two major things:
            1. There isn’t actually a feedback calculation at all, with or without emission temperature. If you think there is, then what is the feedback coefficient f?
            2. Nothing depends on the difference between 1850 and present. Only 1850 is used. The answer would be basically the same if only present were used (or 1950 etc).

            So back to basics. F is a forcing due to non-condensable GHG, expressed as equivalent CO2 in doublings (ie log_2(CO2)). E is surface temperature. The target is
            CS = dE/dF
            He introduces another quantity R, and writes, from calculus
            CS = dE/dR dR/dF
            and calls dE/dR system gain, and gets dR/dF from “official climatology” (OC) who get it from Soden and Held. And there is a generally agreed value of 1.05, which he used.

            So what is R? He uses the OC value, so it is whatever OC says it is. And that is the response to F that would occur without feedbacks. That is, feedback to F. Whenever you say feedback, it always has to be feedback to a defined signal.

            So then it is a matter of estimating dE/dR. In his first post of a week ago, he set out a lot of curve fitting options for the function E(R). He took Lacis’ estimate for present (E=287.5, R=265) as one point and he took E=0, R=0 as the other. A linear fit gives the ratio 287.5 / 265 cited here.

            But as I’ve objected above, 0K is nonsense here, and Lord M then said he didn’t do it (but he did). And I’ve said that a proper second point is E=R=255K. It could rather be Lacis’ 243K, resulting from progressively removing GHG. But the point is that at some temperature there, all non-condensable GHG’s have been removed. R is defined as the temperature you would have in the absence of feedback to those GHGs. No GHGs – no feedback. So at that point, certainly, E=R.

            And so if you put that into the linear fit, you would get not (287.5-0)/(265-0)=1.085, but
            (287.5-255)/(265-255)=3.25 as the system gain (a bit less if you use Lacis’ 243). That gives an ECS in the upper part of the IPCC range.

          • Mr Stokes continues to perpetrate elementary errors.

            1. Mr Stokes maintains that at the emission temperature of 255 K, in the absence of any noncondensing greenhouse gases, there would be no feedbacks – i.e., that the reference or pre-feedback emission temperature R_0 and the equilibrium or post-feedback temperature E_0 would be equal at 255 K. However, there would in fact be a large feedback, since one-third of the dayside (to first order) would be open ocean. Therefore, E_0 would be greater than R_0. Mr Stokes, like official climatology, fails to take account of that feedback to emission temperature – or, rather, he misallocates it to the preindustrial greenhouse gases.

            2. Mr Stokes seems to think that the calculations in the head posting (one of which he himself copies without acknowledgement and presents as a feedback calculation), are not feedback calculations. He may perhaps be unfamiliar with control theory and, therefore, unaware of the relationship between the system-gain factor and the feedback factor. Any textbook of control theory will enlighten him.

            3. Mr Stokes imagines that, because air becomes solid at well above 0 K, I am not permitted to point out that zero temperature entails zero feedback response. Again, any textbook of control theory will enlighten him. In the absence of an input signal or of any pre-feedback perturbation of that signal – in other words, if no signal enters the feedback loop by way of the summative input-output node – there will be a zero feedback response. One does not need to know anything about the state of a theoretically-impossible climate at 0 K to know that that is the case. Therefore, if one imagines that the equilibrium-temperature response function E(R) is exponential, one can derive the exponent from the point (0,0), which applies to all curves of temperature response to the action of feedback, and (265, 287.5), the quite well constrained values of reference and equilibrium sensitivity in 1850. The exponent is 1.0146 or thereby, which gives a curve that is vanishingly different from linear.

            4. In repeating (albeit without attribution) my calculation of official climatology’s system-gain factor 3.25 derivable from the position in 1850, Mr Stokes perpetrates the same mistake as official climatology itself: he assigns all of the feedback response to emission temperature to the preindustrial greenhouse gases – or, rather, he states that there would be no feedback response to emission temperature in the absence of greenhouse gases. A careful reading of the admittedly inspissate paper by Lacis+ (2010) would draw his attention to the fact that even they find a feedback response of about 10 K to emission temperature.

            5. Mr Stokes continues to fail to acknowledge the self-evident truth that the feedback processes that subsist in a dynamical object at any given moment must, at that moment, respond to the entire reference signal then obtaining. And he continues to fail to explain why he considers that truth not to be a truth. Since it is a truth, it follows that the 22.5 K feedback response, the difference between the reference temperature of (255 + 10) = 265 K and the observed equilibrium temperature of 287.5 K in 1850, is a feedback response not, as he tries to suggest, solely to the 10 K reference sensitivity to the preindustrial noncondensing greenhouse gases but to the entire reference temperature. Thus, 255/265 of that 22.5 K, i.e., 21.65 K, is feedback response to emission temperature, and only 0.85 K is feedback response to the 10 K reference sensitivity to the preindustrial noncondensers. Note that we do not need to know what the feedback response to emission temperature was in the absence of the noncondensing greenhouse gases: all we need to know is that not only the warming of 10 K forced by their presence but also the emission temperature was present in 1850 and that, therefore, at that time the feedbacks then present had to respond to both parts of the signal, and to respond proportionately to each part thereof.

            6. Mr Stokes imagines that deriving the system-gain factor as the ratio of sensitivities is preferable to deriving it as the ratio of entire reference signals. Of course, if we knew that the response curve was appreciably nonlinear (when in fact climatology finds it to be nearly linear), and if we had a sufficiently perfect knowledge either of the magnitudes of all sensitivity-altering feedbacks or of the system-gain factor, it would be best to concentrate on the most recent sensitivities: that goes without saying. However, the fact that the interval of Charney sensitivities has not budged for 40 years and is absurdly broad should have suggested to Mr Stokes’ mind, as it has to ours, that it is necessary to use the entire temperatures because they exceed the reference temperatures by two orders of magnitude and thus provide the opportunity to increase the signal-to-noise ratio dramatically.

            Mr Born continues to state the blindingly obvious – that, if one divorces a feedback calculation from any physical reality whatsoever, one can imagine any shape one wants for the response curve. However, as I have several times pointed out to him, we are not doing calculations in vacuo. The head posting demonstrates that official climatology regards – and treats – the climate-sensitivity parameter as near-invariant: calculations done on the basis of its error show that the system-gain factor in 1850 was 3.25 and the mean system-gain factor in response to doubled CO2 compared with today, as imagined by the CMIP5 ensemble (Andrews+ 2012), is 3.2. Looks pretty darn near-linear to me. Of course, the moment one corrects official climatology’s error in defining temperature feedback one observes an apparently extravagant nonlinearity if one takes official climatology’s interval of Charney sensitivities as canonical. But that nonlinearity is not only inconsistent with official climatology’s understanding that the climate-sensitivity parameter (and, therefore, the system-gain factor) is near-linear, but also inconsistent with physical reality. A careful examination of each of the sensitivity-altering temperature feedbacks shows that there is no physical basis for assuming the highly nonlinear equilibrium-temperature response curve imagined by Mr Born.

          • “In repeating (albeit without attribution)”
            How could the attribution be clearer? I said:
            “what he actually does, which is summarised in the post above:…”
            and quoted the words from it, in italics with quotation marks, as is my custom. If that isn’t clear, the authorship is unmistakeable by style.

            I’ll respond to other matters somewhat out of sequence:

            “Mr Stokes seems to think that the calculations in the head posting … are not feedback calculations”
            Yes, and I gave the test. If it is a feedback calculation, what is the feedback factor? Where is it derived?

            “A careful reading of the admittedly inspissate paper by Lacis+ (2010) would draw his attention to the fact that even they find a feedback response of about 10 K to emission temperature.”
            Lacis did an experiment with GISS Model E in which he removed all noncondensing GHGs, and followed events. After about 30 years, the surface temperature dropped to 265K and stayed there. Lacis didn’t make there a feedback attribution – GCMs do not deal with feedback, so you can’t experiment with removing it, only the gases. But arguing in reverse, one can say that the rise from 265K to 288K (putting the GHGs back) was due to the effect of both the GHGs directly and their feedbacks. You would probably wish to argue that the residual 10K is a feedback to emission temperature, but it makes no sense. 10K is simply the amount of warming relative to 255K that is created by the remaining water vapor when the non-condensing GHGs have been removed.

            In fact, Lacis et al wrote a more expansive paper in Tellus B, 2013 in which they do do feedback attribution (but not with GCM), see esp sec 6.6.

            “Therefore, E_0 would be greater than R_0. “
            In that “fraudulent practices” post of a week ago, in the section starting System Gain, it gives a value for R₀:
            “in 1850, R₀ + ΔR₀ = 265K, and ΔR₀ = 10K”.
            Clearly, there it is said that R₀ = 255K and that is with GHGs removed. The surface temperature E₀ with all GHGs (including water) removed is the emission temperature; E₀ = 255K.

            “Mr Stokes imagines that, because air becomes solid at well above 0 K, I am not permitted to point out that zero temperature entails zero feedback response.”

            What you actually say is that at R=0K, E=0K, and you use this as one of two fitting points for an inferred E(R) function, from which the CS was derived. Assuming that the function still applies after the atmosphere has solidified is, well, courageous. But even worse, it isn’t clear how the variables could even be defined there, or indeed how E(R) even makes sense as a functional relationship at any level. R is the notional limit after removing all non-condensing GHGs. So the addition of GHG since 1850 doesn’t change it, although it changes E. The removal process would just take them away the added GHG and still get down to 265K. I can’t see how it could actually take any other value. Certainly not values below 255K, when all GHGs have gone.

            “Therefore, E_0 would be greater than R_0. “
            In your “fraudulent practices” post of a week ago, in the section starting System Gain, it gives a value for R₀:
            “in 1850, R₀ + ΔR₀ = 265K, and ΔR₀ = 10K”.
            Clearly, there it is said that R₀ = 255K and that is with GHGs removed. The surface temperature E₀ with all GHGs (including water) removed is the emission temperature; E₀ = 255K.

            “Mr Stokes continues to fail to acknowledge the self-evident truth that the feedback processes that subsist in a dynamical object at any given moment must, at that moment, respond to the entire reference signal then obtaining.”
            Well, we’ve been through it many times. But again, amplification and feedback respond to proportionately to perturbation. The factor is called gain. You work out the output response by differencing the state variables. You can include constant factors like emission temperature if you really insist. But you must difference them as you do with other variables. And that, of course, yields zero.

            At least two commenters have sought to present a standard control diagram showing the whole state as input. An example is here. But in each case, as I point out, the very first thing done to that state is that it is passed into a differencer, which forms the difference with the output. What actually goes around the loop is not the state, but the error signal. Standard control terminology. That is the difference between the states. Anything that is constant between them will go to zero.

            “because they exceed the reference temperatures by two orders of magnitude and thus provide the opportunity to increase the signal-to-noise ratio dramatically”
            Well, you could add in the temperature of the sun. That would be even more dramatic. And just as devoid of meaning. Sensitivity represents the ratio of the change in one thing to the change in the other. If you add in something like emission temperature, it treats it as a change from zero, which of course is not what happened.

            Sensitivities are, well, sensitive. No use trying to eradicate noise.

          • Lord Monckton says he’s trained in formal logic, yet he seems congenitally incapable of following a logical argument.

            He contended that the E(R) curve couldn’t be very nonlinear, because it passes through (R, E) = (265 K, 287.5 K) (and, implicitly, through (0 K, 0 K)). (“[T]he curve of equilibrium temperature as a response to reference temperature . . . cannot be very nonlinear . . . [b]ecause the reference temperature [265 K] in 1850 was more than 92% of equilibrium temperature [287.5 K].”) So I showed him what shouldn’t have required demonstration: that a nearly cubic (and thus highly nonlinear) function could indeed pass through those points.

            First he denied that it could, then he falsely attributed a dreamed-up ratio to it, and now he runs away from his own test for function nonlinearity by saying I’ve shown only that “one can imagine any shape one wants for the response curve” if “one divorces a feedback calculation from any physical reality whatsoever.” He just throws random assertions against the wall in the hope that one will stick. But they rarely do.

            Among the other bases of his “mathematical proof” that E(R) is nearly linear is his notion of surpassing silliness that near linearity is established if the change in its average slope (“system gain factor”) is small over a small domain increment. Again, my simple power relationship demonstrated what should have been obvious without it: even a highly nonlinear function’s average slope needn’t change much over a small domain increment.

            Another basis is his nutty contention that, by referring to the small-signal equation’s feedback coefficient as a “near-invariant,” climatologists intended to say that E is a nearly linear function of R. Not only is such an interpretation inconsistent with the sensitivity he admits they estimate, but it would be wildly at odds with the way invariant is ordinarily used in control-systems contexts; in control systems the concept of invariance is typically orthogonal to that of linearity.

            I’m tempted use Lord Monckton’s own words and say that “any textbook of control theory will enlighten him” on this point. But in view of how woefully he misinterpreted Hendrik Bode’s work I doubt that he’d get much from consulting an authoritative text.

            Any lurker who thinks I’m judging Lord Monckton too harshly may be interested in reviewing how we got here. Lord Monckton now espouses applying to climate an equilibrium feedback equation seen more often in electronics and control systems. But that hasn’t always been his position.

            In publicity for a paper that he previously wrote about climate feedback he instead called it a “rogue equation.” In that paper he criticized the equation’s use in climate, saying of the closed-loop-gain-vs.-loop-gain hyperbola it produces that “in electronic circuits, the singularity at g_\infty=+1, where the voltage transits from the positive to the negative rail, has a physical meaning: in the climate, it has none.” The truth is that the hyperbola’s fourth-quadrant portion to which he thereby referred has nothing to do with a circuit’s “[transiting] from the positive to the negative rail.”

            I explained that to him, but rather than availing himself of an explanation from someone who’d begun studying the discipline half a century ago, he publicly disputed it. Without acknowledgement, though, he quietly dropped that “rogue equation” position—which he had previously propounded with just as much seeming authority as that with which he now characterizes (his misunderstanding of) that equation as universally applicable.

            Although he has now reversed his position he failed to comprehend my explanation’s implications; he now interprets that hyperbola’s fourth-quadrant portion as implying global cooling. Common sense tells us it implies no such thing, of course; if some positive feedback increases equilibrium temperature, more of it won’t do just the opposite. But common sense doesn’t seem to affect him.

            Now, he often invokes the authority of his “eminent”—albeit suspiciously absent—co-authors. But some of them were no doubt co-authors of that previous paper, too. And, although the previous paper’s central equation was a clear, fundamental error in linear-systems theory, none of those co-authors has so far as I’m aware retracted any aspect. So his co-authors’ authority doesn’t impress me.

            By my count this site has run something like ten of Lord Monckton’s head posts about his theory, and each one misled readers who lack the math and control-systems knowledge to see through it. Now, I can’t seriously fault the site’s personnel for failing to see how egregiously wrong that theory is; no one’s born knowing this stuff. But you’d think they’d have started to wonder after a claimed discovery that high sensitivity estimates have been based on “a fundamental error of physics” had persisted in attracting no support from any of the better-regarded skeptics.

          • Mr Stokes continues to double down on the elementary errors he makes.

            1. He says that he had cited me in italics on the following point from official climatology’s method:

            “So if you put that into the linear fit, you would get not

            (287.5-0)/(265-0)=1.085,

            but

            (287.5-255)/(265-255)=3.25

            as the system gain (a bit less if you use Lacis’ 243). That gives an ECS in the upper part of the IPCC range.”

            In fact, Mr Stokes had not put that quotation in italics: instead, he had presented it as though he were revealing something new. More importantly, he has failed to grasp the main point, which is that, since using climatology’s method as above gives a preindustrial system-gain factor 3.25 and since using the CMIP5 models’ estimated reference and equilibrium responses to doubled CO2 gives a predicted future system-gain factor 3.2, climatology indeed regards the climate-sensitivity parameter as near-linear, wherefore one may do the sensitivity calculation either climatology’s way using sensitivities or our way using the entire equilibrium and reference temperatures, and there will be very little difference in the answer either way – always provided that one has sufficient information to perform both calculations. But one does not have sufficient information to perform the calculation climatology’s way, since the uncertainties in the sensitivities on which it relies are so large in relation to the sensitivities themselves.

            2. Mr Stokes continues to fail to admit the truth that the feedbacks that subsist in the climate at any given moment must perforce respond to the entire reference temperature then present. That being the case, one can use the well constrained entire reference and equilibrium temperatures in 1850 as the necessary information to derive a far more reliable estimate of Charney sensitivity than if one uses the sensitivities, which are two orders of magnitude smaller. He seeks to argue that in an electronic circuit the input state is passed into a differencer and that what passes into the feedback loop is not the entire reference state but the error signal. But we are not dealing with an electronic circuit (though it was by reference to electronic circuits that the mathematics of feedback was first developed): we are dealing with the climate. Is Mr Stokes seriously seeking to maintain that, in 1850, the feedbacks then present were not responding to the entire reference temperature of 265 K? If he is, then perhaps he should approach a national laboratory, as we did, to build a test rig and see what happens. What happens is exactly what the equations predict will happen: the feedback processes will, like it or not, respond to the entire reference temperature.

            Mr Stokes

            3. Mr Stokes continues to pretend that he does not understand the relationship between the system-gain factor and the feedback fraction, so that he can maintain his silly pretence that the calculations we are discussing are not feedback calculations. Of course they are.

            4. Mr Stokes continues to pretend that in the absence of noncondensing greenhouse gases equilibrium temperature would be identical to reference temperature. This would not, however, be the case, because in the absence of the non-condensers about a third (to first order) of the dayside surface would be open water, so that water-vapor, cloud and (at that stage most importantly) ice-albedo feedbacks would be in operation. Even without noncondensers, therefore, there would be a substantial feedback response to emission temperature, wherefore E_0 would be almost 22 K greater than R_0.

            5. Mr Stokes continues to pretend that, because air becomes solid at well above 0 Kelvin, one cannot safely draw the conclusion that the feedback response to 0 Kelvin would be 0 Kelvin. That pretence is nonsense.

            6. Mr Stokes introduces a new and fatuous error: the suggestion that one might as well introduce the temperature of the Sun into the calculation. If he were to read any textbook of elementary celestial physics, he would learn that what is relevant to us here is the total incoming solar irradiance, which, owing to the distance of the Earth from the Sun, is more than somewhat smaller than the temperature of the Sun itself.

            7. Mr Stokes says it is “no use trying to eradicate noise”. If he will read an elementary textbook of control he will come to appreciate the advantage of increasing the signal-to-noise ratio, which our approach achieves.

            Then there is Mr Born. He continues to fail to understand that if a) the reference temperature in 1850 was 92% of the equilibrium temperature in that year and b) the climate-sensitivity parameter (which encompasses inter alia the effect of feedback) is near-linear, then functions such as his lead to spectacular and unphysical contradictions.

            His equivocation as to the meaning of “nonlinear” does not impress.

          • Monckton of Brenchley,

            Therefore, if one imagines that the equilibrium-temperature response function E(R) is exponential, one can derive the exponent from the point (0,0), which applies to all curves of temperature response to the action of feedback, and (265, 287.5), the quite well constrained values of reference and equilibrium sensitivity in 1850. The exponent is 1.0146 or thereby, which gives a curve that is vanishingly different from linear.

            Could you give the full formula for this exponential function, and explain how you derived a unique formula from two data points?

          • Bellman’s implicit objection is correct, of course: exponentials through those points are not unique.

            But one possible exponential through (0 K, 0 K) and (265 K, 287.5 K) is E=k\cdot(e^{aR}-1), where k= 19.35\,\mathrm{K} and a=0.0104\,\mathrm{K}^{-1}. That curve additionally passes through (266.05 K, 290.89 K) and thereby implies an ECS of 3.38 K.

          • That’s one objection.

            But I also suspect he’s not using an exponential function at all. I think he’s got a monomial, E = R^{1.0146}, which would explain why he thinks it is almost linear.

      • When GHGs go to zero, E and R both stand at about 255K.
        And that’s precisely where you go wrong. What makes you think think that there are no feedback effects unless there are greenhouse gases? You’re assuming your result.

    • In response to Bryan-oz4caster, in a multivariate dynamical system such as the climate, there is no such thing as a true equilibrium. However, if we are considering simply one variable – global mean surface temperature – we may look for a longish period during which, whatever the year-to-year fluctuations, the least-squares linear-regression trend is zero. For 80 years after 1850, the trend was zero. Therefore, it is respectable to take the temperature in 1850 as having been an equilibrium temperature.

      Of course, one should also allow for the uncertainty in that temperature measurement – but it was, if I remember correctly, only about 0.4 K either side of the midrange observation.

  32. Lord Monckton keeps repeating the same illogical arguments:

    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.

    That challenge has a false premise. Nothing in “official climatology” requires that “the feedback loop, which receives as its input signal the entire reference temperature . . . 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.”

    In particular, the high “system gain factor” that Lord Monckton attributes to “official climatology’s” estimate imposes no such requirement. To see this, consider the following equilibrium equation for a hypothetical correspondence between an “equilibrium temperature” E resulting from feedback in accordance with a feedback factor f and the “reference temperature” R that would have prevailed in the feedback’s absence:

    E=R+f(E)E

    That equation says f operates on the entire reference temperature. Here we’ve made f depend on temperature, as we would expect it to. If we pick, say, the following nonlinear dependence:

    f=1-CE^b,

    where b=-0.6586534 and C=38.37058\,\mathrm{K}^{-b}, then—even though, again, the feedback factor operates on the entire reference temperature—we get the “system gain factor” 3.2 that Lord Monckton says “official climatology” produces. So nothing about that high a value implies that the feedback doesn’t operate on the emission temperature.

    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.

    That doesn’t follow; the above-defined feedback-factor dependence does indeed cause a very nonlinear curve of equilibrium temperature as a response to reference temperature; it’s nearly cubic. Yet in that curve the ratio of 1850’s reference temperature 265 K to the corresponding equilibrium temperature 287.5 K. is 92%, which Lord Monckton implies is too high for a very nonlinear curve.

    Now, you may not think the real-life relationship is that nonlinear. Fine, neither do I. But Lord Monckton has not proven it isn’t. And he certainly hasn’t provided a “mathematical proof” that “official climatology” made a “grave error” in applying feedback theory.

    • Our mathematical model must mirror the real world, and not the other way round.

      If the model does not match, pitch it and start over.

    • Thanks Joe, I think this paragraph shows where CoB is going.

      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)

      So he seems to have missed the word noncondensing, ie water vapour : the most important GHG.
      He then goes on to compare calculations of the mean temperature calculated will all other GHG with actual recorded temperatures and cries : GOTCHA !

      His tortuous attempts at explaining what Nick Stokes explained so simply implies that either he does not understand it himself ( 90% confidence ) or he is simply trying to mislead and obfuscating to the point hardly anyone can follow it in an attempt to look learned and “baffle them with science”.

      • Greg may not, perhaps, appreciate that official climatology distinguishes between the noncondensing greenhouse gases, which, if their concentrations change, drive radiative forcings and the condensing greenhouse gas (water vapor), which, if its concentration changes, is responding to the change in temperature caused by the forcings from the noncondensing greenhouse gsaes.

        Since our approach is to adopt all of official climatology except what we can demonstrate to be false, we have adopted official climatology’s distinction between what is a forcing and what is a feedback consequential upon the warming caused by the forcing.

        Greg also seems unfamiliar with the notion of verifying a theoretical result empirically. Well, he’d better get over it: that, like it or not, is how science is done.

    • Mr Born, having been called out on his ridiculous function, merely repeats it. On his own admission, his function suggests that the feedback fraction in response to greenhouse-gas warming exceeds the feedback fraction in response to emission temperature by 1000%, spectacularly contrary not only to all that we know of feedbacks in the climate but also to official climatology’s view that the climate-sensitivity parameter, which embodies the entire action of feedback on temperature, is “a typically near-linear parameter”.

      It is only if one assumes that there is no feedback response to emission temperature that climatology’s system-gain factor gives a near-linear feedback response: i.e., in 1850 the equilibrium sensitivity of 32.5 K is about 3.2 times the reference sensitivity of 10 K, and in response to doubled CO2 the CMIP5 models’ midrange estimate is that the 3.35 K equilibrium sensitivity is about 3.2 times the 1.15 K reference sensitivity. The system gain factor is about 3.2 in both cases.

      It is only when one realizes that feedbacks in fact respond to the entire reference temperature and that, therefore, even in the absence of the naturally-occurring greenhouse gases the 255 K emission temperature itself induced a feedback that it becomes possible to realize that, though official climatology thinks it is treating feedback response as approximately linear it is in fact treating it – inadvertently – as so wildly nonlinear as to give rise to a readily-demonstrable contradiction whenever one assumes that any point on its interval of equilibrium sensitivities is correct.

      As our own illustration in the head posting demonstrated, the equilibrium warming of 1.4 K per CO2 doubling that is to be expected on the basis of the IPCC’s midrange estimate of net anthrogenic forcing to 2011 and official climatology’s estimate of the radiative imbalance to 2010 (Smit+ 2015) is in very much the same ballpark as our own estimate of 1.15 K, but falls a very long way short of the CMIP5 models’ imagined 3.35 K Charney sensitivity.

      Climatology has erred, and that is why it has not appreciated that, as Mr Born has noticed, its Charney-sensitivity estimates imply an extravagant nonlinearity in the equilibrium-temperature response curve that is wholly unwarranted in physical reality.

      • Priceless. I point out that Lord Monckton made three demonstrably false statements in a single comment, and he says I’m the one who’s been “called out.”

        Look, this is really simple. The conclusion of “climatology,” as Lord Moncton calls it, is that the equilibrium temperature with feedback is a very nonlinear function of what it would be without feedback. And despite all the logorrhea he uses to mask it, Lord Monckton’s “proof” boils down to little more than his bald assertion that the function can’t be very nonlinear.

        What’s his argument? The demonstrably false proposition that no function whose values are those he claims for the year 1850 could be very nonlinear:

        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.

        Yet he knew that argument was invalid when he made it, because only three days before, at https://wattsupwiththat.com/2019/06/05/the-moral-case-for-honest-and-competent-climate-science/#comment-2717128, I had showed him by example that a very nonlinear E(R) curve could indeed exhibit those values.

        But his response to that explanation was to make three demonstrably false statements: (1) that the E(R) curve I described was “exponential,” (2) that it had a y-intercept of 38 instead of the necessary zero, and (3) that its “feedback fraction f in response to greenhouse gases would be greater than the feedback fraction in response to emission temperature by a factor exceeding 80.”

        But substituting my example feedback-fraction expression f=CE^b into the relationship E=R/(1-f) implies the function’s form is E=kR^a, where a, b, C, and k are all constants: contrary to what Lord Monkton said, E is a power of R, not an exponential. Lord Monckton just seemed to say whatever came to mind, with no concern for whether it was true. But it didn’t matter, because his fanboys couldn’t tell the difference.

        And a power function clearly passes through the origin, so, again, despite what Lord Monckton said the function’s y-intercept is 0, not greater than 38. Lord Monckton just said whatever came to mind, with no concern for whether it was true. Because his fanboys couldn’t tell the difference.

        Moreover, by simply placing that function on a spreadsheet, anyone could have obtained the following values

        \begin{array}{lccc}  &\mathrm{R}&\mathrm{f}&\mathrm{E}\\  &&&\\  \mathrm{Abs. Zero}&0&-\infty&0\\  \mathrm{Emission}&255&0.0074&256.91\\  \mathrm{1850}&2655&0.0784&287.55\\  2\times\mathrm{CO}_2&265.05&0.0854&290.9  \end{array}

        and seen that the ratio 0.0854/0.0074 of f’s doubled-CO2 value to its emission-temperature value is only 11.5. So, when Lord Monckton said that the “feedback fraction f in response to greenhouse gases would be greater than the feedback fraction in response to emission temperature by a factor exceeding 80,” his statement was again demonstrably false.

        Three objectively, demonstrably, mathematically false statements in a single comment. That’s the way he operates: he just says whatever comes to mind, without regard to its truth, which his fanboys seem unable to recognize.

        And when I explained his errors to him, did he thank me for setting him straight? He did not. Instead he just denied: “On no evidence, the Born Liar maintains that the feedback-fraction ratio for Charney sensitivity of 3.35 K is 11 and not 80.” No evidence? The evidence was the incontrovertible math right in front of him. But his fanboys don’t do math, apparently, so he could make that claim with impunity.

        Now that he’s quietly discarded his ratio = 80 factoid in the face of my explanation, he presents the 11.5 value I showed him as though I’d made a grudging admission of some important point instead of having demonstrated that yet another of his pointless statements is erroneous: “On his own admission, his function suggests that the feedback fraction in response to greenhouse-gas warming exceeds the feedback fraction in response to emission temperature by 1000%.” The feedback fraction increased by 1000%? Of course it did; that’s just another way of saying the function is very nonlinear.

        So his whole theory boils down to his saying that the relationship can’t be very nonlinear because, well—then it would be very nonlinear. He’s saying climatology is wrong because it’s wrong. Apparently that’s what passes for reasoning in Lord Monckton’s circles.

        • Mr Born, in his increasing desperation to prove us wrong, continues to plug his dog of a function that entails a feedback fraction in response to greenhouse warming that is 11 times the feedback fraction in response to emission temperature in the absence of greenhouse gases. There is no physical basis for any such 1000% increase in the feedback fraction. And, however much he wrestles with the absurd over-predictions of official climatology, he will find that all of them lead to contradictions as absurd as his.

          As I have pointed out to him before, official climatology regards the climate-sensitivity parameter as “typically near-invariant”. Mr Born’s silly function is manifestly and egregiously at odds with that finding.

          Finally, he falsely asserts that I had said his function produces a feedback-fraction ratio of 80. No, I had said my illustrative exponential function had produced that ratio. He had written that “the example” had produced a ratio of 11, but he had written so confusingly that it was not clear he was talking of his example rather than mine.

          Be that as it may, official climatology regards the climate-sensitivity parameter and, therefore, the feedback fraction, as near-invariant, and it is demonstrable that – if one replicates official climatology’s error in failing to take account of the fact that feedback responds not only to some arbitrarily-chosen fraction of the reference temperature but to the entire reference temperature obtaining at a given moment – official climatology is indeed assuming the feedback fraction to be near-invariant. Let us do the math.

          The reference sensitivity to the pre-industrial greenhouse gases was 10 K or thereby. The equilibrium sensitivity was 287.5 – 255, or 32.5 K. The ratio of the equilibrium sensitivity to the reference sensitivity was thus about 3.25.

          The reference and equilibrium sensitivities in response to doubled CO2 concentration in the CMIP5 models are 1.05 K and 3.35 K respectively. The ratio of the equilibrium sensitivity to the reference sensitivity is thus predicted to be about 3.2 – not a whole lot different from the 3.25 that obtained in the pre-industrial era.

          That is how we know official climatology means what it says when it says the climate-sensitivity parameter is “typically near-invariant”.

          However, official climatology has not realized that feedback responds to the entire reference temperature. So the correct calculation for the preindustrial era is that the ratio of equilibrium to reference sensitivity was 287.5 / (255 + 10), or 1.085. But that is about a third of official climatology’s predicted midrange ratio 3.2.

          One should not jump, as Mr Born so eagerly does, into assuming that official climatology considers the climate-sensitivity parameter to be extravagantly nonlinear after all. The apparent nonlinearity arises from its fundamental error in defining temperature feedback.

        • Joe Born,
          The two points that you have been focused on (extrapolation from the origin vs use of local gradient and the lack of any general requirement for a feedback factor to be independent of the signal on which it operates) are well made. However, I can’t help thinking that the various hypothetical examples you are using to illustrate your maths points are by accident actually reinforcing one of the most egregious errors which Lord Monckton is making here – namely his assumption that there exists a feedback to temperature of an input temperature signal. This DOES NOT EXIST in climate science, either in the GCMs or in analytic application of energy balance models (EBMs). The feedbacks of most interest here are temperature-dependent feedbacks to net flux. There is no mechanism whereby a temperature input can induce any further change in temperature via feedback other than via a change in state-variables which then induces a change in net flux which then causes heating or cooling.

          This distinction is important. The input to this process is a flux forcing – a forced and sustained change in either incoming or outgoing flux – NOT a change in temperature. If a temperature perturbation is introduced into a system at steady-state by an internal redistribution of heat (eg an El Nino event) the feedbacks TO NET FLUX work to restore the flux balance and return the transient temperature to the same equilibrium temperature as before. The system equilibrium temperature remains unchanged throughout this process even though the transient temperature is varying. The equilibrium temperature cannot be changed without a forced change in either the incoming or the outgoing flux.

          Energy balance over a time period says that
          Energy accumulated = Energy entering – Energy leaving

          Differentiating the statement of energy balance (and dividing by global area to convert power to flux density), we obtain the instantaneous flux balance at TOA – expressed as an equation in surface temperature rather than brightness temperature: –
          Net Flux, N (positive downwards) = Incoming Flux – Outgoing Flux (1)

          Let us assume that we have a system in quasi steady-state in 1850 at time t= 0 and surface temperature, T0, which corresponds to the equilibrium surface temperature at that time. N must be equal to zero at t= 0 for steady-state. We now consider a forced constant step-change, F, to the incoming flux (positive downwards by convention).
          At time t, the incoming flux is equal to {Incoming flux at time t=0 + F} and the outgoing flux is equal to R(T) where T is the surface temperature at time t, and R is the temperature-dependent restorative flux. (As an aside, note that this restorative flux is a function of absolute temperature at this stage.)

          Eq (1) simply becomes N(t) = {Incoming flux at time t = 0} + F – R(T) (2)

          We don’t know the exact form of R(T) but we can perform a Taylor series expansion about the point T = T0. This yields:-
          R(T) = R(T0) + R'(T0) x (T – T0) + R”(T0) x (T – T0)^2 + higher order terms
          For small perturbations from T0, it is common but not compulsory to use just the first order approximation. Substituting this into Eq 2 yields:-

          N(t) = {Incoming flux at time t = 0} + F – { R(T0) + R'(T0) x (T – T0)} (3)
          We now note that at steady state at time t = 0, the incoming flux at time t=0 was equal to R(T0), the outgoing flux at time t = 0 . So we can write:-
          N(t) = F – R'(T0) x (T – T0) (4)

          Eq 4 is commonly called the “linear feedback equation”. R'(T0) is a constant in the above derivation, and it is positive, since it is dominated by the Planck response; i.e. the outgoing flux increases as temperature increases. The feedback to net flux is (therefore) unconditionally negative. If however you were to start at a different equilibrium temperature to derive Eq 4, R'(T0) would assume a very different value. If we assume that the only feedback in operation is the so-called “Planck response”, we can estimate its value by equating incoming radiation from Sol with outgoing radiation from Stefan-Boltzman and then consider the derivative of outgoing radiation with respect to temperature change. This yields a value of around 3.3 W/m^2/K – the Planck response. If the rest of the climatology is kept exactly the same, but we wish to consider a different equilibrium temperature, then this derivative term varies in proportion with the temperature derivative of Stefan-Boltzmann. In other words, it varies as the cube of the equilibrium temperature. So the point you make above about there being no justification for the assumption of constant feedback over a temperature range is completely correct. My main issue with your examples is that they give the impression that you have accepted Lord Monckton’s story that climate science recognises (or is founded on) a temperature feedback to temperature input as opposed to its recognition of a temperature-dependent feedback to net flux.

          We can eliminate N(t) from Eq 4 by postulating an ocean–heating model. In the simplest example – a single body model – we can replace N(t) with C dT/dt, the rate of energy gain with time, where C represents the heat capacity of the single body expressed in watt-years/m^2/k. I invite you to compare the form of the equations which you are using as examples against this new form of Eq 4. In this new form of Eq 4, it is the rate of change of temperature which receives the effect of feedback to net flux. Since we expect net flux to control the rate of heat gain, this seems eminently reasonable. In summary, and knowing that I am repeating myself, there is no direct feedback of temperature to temperature.

          Let us then briefly visit the question of the “gain associated with feedbacks”. This is not a gain associated with an input signal, as Lord Monckton wishes to treat it. It is a theoretical amplification factor expressed as the ratio of the predicted theoretical (non-physical) equilibrium temperature from all feedbacks relative to the predicted theoretical (non-physical) equilibrium temperature from just the Planck feedback, when both are predicted with the same flux forcing. The denominator is not an input signal to the numerator in any physical way.

          From Eq 4, the transient temperature must head for equilibrium temperature as t -> infinity and N(t) -> 0. As N(t) -> 0, we see that T -> F/ R'(T0)
          If we say that for the Planck response alone, R'(T0) = lambda(Planck)
          and that for the total feedback, R'(T0) = lambda(Planck) + lambda(other)
          then we see that the ratio of equilibrium temperature for all feedbacks to equilibrium temperature for Planck alone is just
          Amplification = lambda(Planck) / {lambda(Planck) + lambda(other))

          I have no problem with someone deciding to call this a “gain”. I do have a problem with someone declaring that they can prove the above basic maths is incorrect by declaring that it is based on the abuse of a control theory that it neither uses nor needs to use.

          • You’re absolutely correct about the “input temperature” and the risk that I’m reinforcing Lord Monckton’s misconception. Moreover, I’ll confess that I omitted any caveat even though I thought of that risk almost every time I commented on the subject.

            In my (partial) defense, though, I’m sure that commenters (maybe including me) brought that problem up more than once over a year ago, when Lord Monckton first unveiled his theory on this site. Since then, most of the knowledgeable commenters have drifted away in the face of Lord Monckton’s dishonest argumentation, and we now see mostly Monckton fanboys. So I’ve tried to make my comments as simple as possible.

            Also, complications arise from my attempt to give as fair a reading as possible to his contention 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.” As usual, his formulation is too vague to restrict itself to one interpretation. Rather than find fault with it, though, I’ve attempted to accord it a construction that is actually true.

            As I say, though, that causes complications. Surface temperature, for instance, ends up not being a single-valued function of forcing. Also, as we depart from small perturbations I feel increasingly queasy about combining the various forcings additively. So any treatment even nodding at rigor would demand more math tolerance of the reader than I’ve observed in this site’s regulars.

            Still, your criticism hasn’t be made often enough, so I’m glad you took the opportunity to make it now.

          • In response to Kribaez, one may derive the system-gain factor either as a secant slope, as climatology does, or simply as the ratio of equilibrium to reference sensitivities at a particular moment. The disadvantage of climatology’s approach is not, repeat not, that it is wrong, but that it is not useful: the very broad interval of equilibrium sensitivities to doubled CO2 concentration has not proven constrainable for 40 years.

            What is wrong is official climatology’s definition of feedback, which fails to encompass the fact that any feedback processes present in the climate at a given moment will respond not merely to changes in the input signal but also to the input signal itself. In the climate, the input signal is the 255 K emission temperature. Would that signal itself engender a feedback response, in the absence of any noncondensing greenhouse gases?
            The answer is Yes. Elementary calculations on annuli about the zenith point demonstrate that one-third of the dayside surface (to first order) would be ice-free, so that ice-albedo, water vapor and cloud feedbacks would operate.

            At present, however, as the head posting demonstrates, official climatology effectively misallocates all or most of the feedback response to emission temperature and attributes it to the naturally-occurring, noncondensing greenhouse gases that were present in 1850.

            With respect, therefore, Kribaez is wrong to state, in capitals at that, that the feedback response to the input temperature signal DOES NOT EXIST. It does exist, in physical reality. Just calculate the surface temperature at the zenith point in the absence of the noncondensing greenhouse gases, and the matter will become clearer.

            Kribaez maintains, in bold face, that the feedbacks of most interest are temperature-dependent feedbacks to net flux. He adds that “the input to this process is a flux foriing – a forced and sustained change in either incoming or outgoing flux – NOT a change in temperature.” However, in climatology feedbacks are denominated in Watts per square meter per Kelvin of the reference temperature (or, doing it climatology’s way, the reference sensitivity) that engendered them.

            His consideration of the Planck parameter as a feedback is one way of looking at it, but Roe (2009) prefers to treat that parameter as part of the reference system, expressing it in Kelvin per Watt per square meter rather than as though it were a feedback in Watts per square meter per Kelvin. Over the interval of interest – i.e., from 1850 via 2011 to a CO2 doubling compared with 2011 – the Planck parameter is near-invariant.

            Kribaez says I have told a “story that climate science recognises (or is founded on) a temperature feedback to temperature input as opposed to its recognition of a temperature-dependent feedback to net flux”. Surely I have made it plain enough that climate science does not at present define temperature feedback as responding, at any given moment, to the entire temperature then obtaining as well as to some arbitrarily-chosen fraction thereof.

            He ends by suggesting, in effect, that we ought not to be saying that the mathematical approach taken by official climatology in attempting to derive the system-gain factor from sensitivities rather than from entire temperatures is incorrect. But we do not say it is incorrect: merely that it is not useful. If it were useful, after 40 years and trillions spent, it would surely have been possible to constrain the interval of equilibrium sensitivities, but it has not been possible. It turns out to be more useful to derive the system-gain factor from the well-constrained reference and equilibrium temperatures that obtained in 1850. But climatology cannot do that, because its definition of feedback is defective in that it does not recognize that feedbacks respond to the entire temperature they find, specifically including emission temperature, to which, like it or not, there is a large feedback response.

            Mr Born continues to write in a characteristically malevolent, dishonest and bad-tempered fashion, adding heat but no light to the discussion.

            He professes to find it difficult to understand my statement 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.”

            Since nomenclature in feedback theory is not standardized, I shall clarify matters for Mr Born. The sensitivity-altering feedback processes present in the climate, which were acting in the absence of the noncondensing greenhouse gases and also act in their presence, are the water-vapor/lapse-rate, surface-albedo and cloud feedbacks. Broadly speaking, in official climatology’s understanding, all feedbacks except the water-vapor feedback self-cancel.

            The reference temperature at any given moment is the sum of the input temperature (emission temperature) and all subsequent perturbations thereof up to that moment.

            The feedback processes, being temperature-dependent (which is why they are called “temperature feedbacks” and are denominated in Watts per square meter per Kelvin of the reference temperature that engenders the feedback response to them) respond to the entire reference temperature.

            Though one can build an electronic feedback amplifier circuit with a differencer to permit the feedback loop to respond only to the perturbations of the input signal, in the climate there is no such differencer: the feedbacks, therefore, respond to the entire reference temperature.

            Mr Born is concerned about whether one should combine radiative forcings additively if one departs from small perturbations. But we know what the system-gain factor was in 1850, and all subsequent perturbations are small perturbations. In any event, we have simply adopted official climatology’s estimates of net radiative forcing in the industrial era: we have not combined them additively. And we have adopted official climatology’s estimate of reference sensitivity to doubled CO2.

            In general, we have followed an Occam’s-razor approach: essentia non sunt multiplicanda praeter necessitatem. Once it is recognized that feedbacks, being temperature-dependent, respond to the entire reference temperature and not merely to some arbitrary fraction thereof, and that reference temperature in 1850 was more than 92% of equilibrium temperature that year, and that the climate-sensitivity parameter is near-invariant, the derivation and constraint of equilibrium sensitivities becomes quite straightforward.

          • Lord Monckton,

            You should note that you can readily map from my equations to those of Roe 2009 with a simple change of variable definitions. [To confirm that my “gain” is entirely compatible with Roe’s, just redefine my variables as follows:-
            set my F = ΔRf from Roe
            set my lambda(Planck) = 1/λ0 from Roe (Yes, he uses an inverted form)
            set my lambda(other) = -c1 from Roe (His sign convention for non-Planck feedbacks is different from mine ]

            His Equation 4 – which is the only thing that looks like a temperature feedback to temperature input – is actually just a re-statement and rearrangement of the equilibrium temperature for all feedbacks i.e. ΔT = F/(lambda(Planck) + lambda(other)) using my variables, and leads to exactly the same “amplification” which I defined above. But note that I did not use Control Theory in any shape or form to arrive at estimates of climate sensitivity. Nor did I need Control Theory to define the “amplification”. As I have said before, it is very difficult to abuse Control Theory when it is neither used nor necessary.

            It is also worth noting that Roe’s work is looking strictly at a change in temperature from one equilibrium state to another, not transient temperatures. The change of state is brought about by a flux forcing, not a temperature input. Moreover, the only physical feedback in his equations is temperature-dependent feedback to net flux, a point which he himself makes several times.

            “The major feedbacks in the climate system are well known: For example,
            a positive radiative forcing such as that due to an increase in CO2 tends to increase temperatures, which tends to increase water vapor, which, in turn, produces a perturbation in the downwelling longwave radiation that amplifies the original forcing… When a feedback process is included in the system, the radiative perturbation to the system gets an additional nudge (either positive or negative) that is a function of the system response. The simplest representation is that this radiative nudge is linearly proportional to the system response, c1ΔT, where c1 is a constant…”

            The “amplification” which I define above and which is identical to that found by Roe is NOT the gain of a physical system driven by temperature input, as my derivation should demonstrate if you follow it carefully. There is only a temperature-dependent feedback to net flux arising as the result of a forced perturbation to net flux, something that Roe and I are apparently agreed on.

            On a second point, you wrote:-
            ” Surely I have made it plain enough that climate science does not at present define temperature feedback as responding, at any given moment, to the entire temperature then obtaining as well as to some arbitrarily-chosen fraction thereof.”

            There are a number of ways of arriving at Eq (4) in my post above, the linear feedback equation. I chose to show this particular method specifically to demonstrate the point that the feedbacks in EBMs use the absolute temperature as the relevant state variable, and not the incremental temperature – despite any appearances to the contrary. The restorative flux in my derivation, R(T), is by definition the outgoing flux at the absolute temperature T. If we apply a Taylor series expansion about the equilibrium temperature T0, then the full Taylor series expansion reproduces R(T) exactly; there is no estimation. The only approximation I then made was to drop higher order terms and use the first order approximation R(T) = R(T0) + R'(T0) (T-T0) . Note that this is STILL an estimate of the restorative flux at the absolute temperature, not incremental temperature. The fact that R(T0) can subsequently be eliminated does not mean that only incremental temperatures have been or are being considered! What it is actually telling us is that for a calculation of the temperature-dependent feedback to net flux, the most important thing to know is the local rate of change of the restorative flux (i.e. in the vicinity of T0) with respect to temperature change, which seems eminently reasonable. And although R'(T0) may be assumed to be constant for small perturbations from today’s temperatures, it would certainly have to be replaced if one wanted to initialise a model with a very different absolute temperature or if a very large temperature range was to be modelled.

            The AOGCMs, on the other hand, work strictly on absolute temperature field which is updated like all state variables at the end of every time-step. So both EBMs and AOGCMs do recognise absolute temperatures for estimation of feedbacks. It is certainly true that they do not recognise your “reference temperature” approach, but on the basis of the above, I can still not see any good reason or justification for trying to partition an equilibrium temperature as you wish to do, since the reference temperature you seek is at best a mathematical construct and not a driver of feedback in a physical sense. And if such good reason exists, it still seems to me to be an impossible task to do unambiguously, given that you have to “make a planet’s climatology” by assumption.

            Lastly, the fact that AOGCMs run hot, over-estimate climate sensitivity and still exhibit a very wide range of sensitivites says that they are not useful as predictors but does not per se provide any evidential support for your methodology. This is a post hoc ergo propter hoc fallacy.

          • Erratum:-
            In my response to Joe Born above, I derived the linear feedback equation typically used in EBMs. However, one of the paragraphs reflects the fact that I forgot my own variable definition in the text, which is never a great idea. Specifically, I frgot briefly that I was using T to denote an absolute temperature rather than a change in temperature.

            The original paragraph read:-
            “From Eq 4, the transient temperature must head for equilibrium temperature as t -> infinity and N(t) -> 0. As N(t) -> 0, we see that T -> F/ R'(T0)
            If we say that for the Planck response alone, R'(T0) = lambda(Planck)
            and that for the total feedback, R'(T0) = lambda(Planck) + lambda(other)
            then we see that the ratio of equilibrium temperature for all feedbacks to equilibrium temperature for Planck alone is just
            Amplification = lambda(Planck) / {lambda(Planck) + lambda(other))”

            This should have read:-
            “From Eq 4, the transient temperature must head for equilibrium temperature as t -> infinity and N(t) -> 0. As N(t) -> 0, we see that T-T0 -> F/ R'(T0)
            If we say that for the Planck response alone, R'(T0) = lambda(Planck)
            and that for the total feedback, R'(T0) = lambda(Planck) + lambda(other)
            then we see that the ratio of temperature change to equilibrium temperature for all feedbacks divided by temperature change to equilibrium temperature for Planck alone is just
            Amplification = lambda(Planck) / {lambda(Planck) + lambda(other))”
            In all subsequent discussion, including the comparison with Roe 2009, the maths is correct and compatible with this textual correction.
            Mea culpa. (It is amusingly strange how much Latin appears in responses to Lord Monckton.)

          • In response to Kribaez, I do not disagree with him that one may represent the Planck “feedback” as a true feedback. However, as Roe (2009) points out, it is more useful to treat it as part of the reference system, for then it can be used to derive both reference sensitivities and feedback responses. Nothing injurious to our result turns on this point.

  33. Dear Lord Monckton,
    it grieves me to see your valuable time wasted with those climate sensitivity assessments…..
    This sensitivity value is an entire hoax value, please check the authors Gerhard Gerlich and Gerhard Kramm (today in Fairbanks).
    Today a Willis article is out, setting the sensitivity to only 0.38 C for CO2 doubling, please check this article.
    ….. Let me explain the following: All those atmospheric sensitivity “calculations” contain the major error that they neglect/negate/omit/ignore decadal and centennial Earth orbit variations or orbital perturbations.
    [This has nothing to do with Milankovitch ,which is multi-millenial stuff (19-100 thou. years).]
    The warming since 1850, in fact, since the 17. century, is clearly due to variations in the Earth orbit, which were clearly and unrefutably calculated.
    Those orbital perturbations must be, and therefore are ignored on purpose, by all those atmospherical “experts”, because their entire calculations DEPEND on that all warming BELONGS to atmospherical/tropospherical “variables” and that orbital variables are kept constant by the method of ignoring them.
    If you do not get into the orbital perturbations theme, you will not be able to resolve global warming and make an accurate forecast.
    If you are able to understand/computer translate German, the perturbation literature is:
    Joachim Seifert: Das Ende der globalen Erwärmung, Berechnung des Klimawandels” (2010)
    ….otherwise see http://www.knowledgeminer.eu/climate-papers.html and in this case “Climate pattern Recognition,Part 8, 1600 – 2050 and part 1 to understand the orbital perturbation cycle development.
    JS.

    • Mr Seifert may not have noticed that the approach we are taking is to accept ad argumentum all of official climatology except what we can formally demonstrate to be false. When I say “demonstrate” I mean “prove formally by logic and beyond doubt”.

      Therefore, solely for the sake of argument, we accept – and in the head posting we explicitly state that we accept – that the reference sensitivity to doubled CO2 (i.e., the sensitivity before accounting for any temperature feedback) is 1.05 K. We think it possible that reference sensitivity is less than 1.05 K, but we cannot prove it and nor, with the best will in the world, can Mr Eschenbach or anyone else, given the present state of climate science.

      So we go with the official value because we cannot disprove it and do not propose to waste anyone’s time trying. Instead, we are able to demonstrate that official climatology, but not realizing that the feedback processes that existed in the climate in 1850 must have responded not only to the 10 K reference warming from greenhouse gases but also to the 255 K pre-existing emission temperature caused by the fact that the Sun is shining, has denied itself the opportunity to obtain quite a reliable and well-constrained value of equilibrium sensitivity to doubled CO2.

      The point is that we can prove what we assert, and we can confirm it not only by experimentation on a co-author’s test apparatus but also on the test apparatus constructed for us by a scientist at a government laboratory (who was promoted shortly thereafter, thanks to the quality of his work).

      We have also confirmed our result by performing calculations based on ten distinct, authoritative, published estimates of net anthropogenic radiative forcing over various periods.

      The kind of monkeying about that we have endured at the hands of reviewers to date is not acceptable and will no longer be tolerated. We are going to get our work properly reviewed. if the reviews find genuine defects, then that will be that. At least we tried. But if not, make no mistake about it – this is the end of the global warming scare. Climatology’s error is a large one. And millions are dying every year in consequence. The deaths have to stop, so we have to get the science right, notwithstanding the attempts of numerous vested interests to stop us.

      • Dear Lord Monckton,
        thank you for your kind reply! I appreciate your work, your fight for truth in science, actions in many parts of the world – I read all articles of yours, as soon as they come up at Anthonys. You are one of the major good players in climate science.
        However, the fact still remains that the Profs. Gerhard Gerlich and Gerhard Kramm entirely rebutted the climate sensitivity concept (just google), a scientific swindle, revealed in their detailed physical calculations.
        The other fact is that the climate sensitivity concept ignores all Earth orbital perturbations, which in reality cause climate warming and climate cooling, due to their varying of distances between Sun and Earth.
        Remaining within the atmosphere with whatever atmospherical concept and sensitivities, excludes the
        true Earth orbital climate drivers, variables, that govern the climate on Earth.

        • In response to Mr Seifert, official climatology has not accepted that Gerlich and Tscheuschner, or Gerlich and Dlugi, have proven that there is no such thing as climate sensitivity. And our approach is to focus the discussion on the topic of the head posting, which is feedback, and, therefore, to accept all of official climatology except what we can demonstrate to be false.

          We can demonstrate that official climatology’s definition of feedback is erroneous. That, and that alone, is the focus of the head posting. If, per impossibile, there were no greenhouse effect, then our conclusion that global warming will be small, slow, harmless and net-beneficial is demonstrated a fortiori.

  34. As a layman with limited math ability, would the following analogy be correct?

    Water from various sources is combined and then fed into a heater and the output water is hotter Than the input temperature. If we then feed some of the output back to the input, it would have a heating action on the entirety of the input water temperature.

    If we change the temperature of one of the input water sources, the feedback can still only effect the combined water temperature. If by some magical process, the feedback only effected the comment of water that changed temperature, It would soon mix in with the rest of the water.

    Not sure if this is relevant, but in the above analogy, the amount of feedback can be regulated with a valve in the feedback line and so the feedback can be made variable.

    Is the above anology correct?

    • Peter’s analogy is almost correct. What we are saying is that if water from various sources is combined, the warmth of all of that water, and not just of some small, arbitrarily-chosen fraction thereof, is what is fed to the feedback loop. The magnitude of the feedback response, therefore, is determined not merely by the small fraction but by the entire body of water.

  35. >>
    ” … 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. …”
    >>

    >>
    ” … 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. … ”
    >>

    >>
    ” … Compare that with the 3.2 K interval of official Charney sensitivities, which range from 1.5 to 4.7 K. …”,
    >>

    * Hence why the models run hotter than reality (and also do not account for a ‘hiatus’ occurring … ‘forcing’ apparently lacks the vital ingredient of a force vector).

    >>
    ” … 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. …”
    >>

    * In which case, how does a real-world hiatus even occur? The models don’t do hiatus, but the real world does. So even the prevailing feedbacks that should have occurred didn’t respond as “expected” in the real world.

    So how the heck can current models and “expected” future climate evolution behavior be useful for generating conclusions for policy implementations and with massive global economic and social implications?

    I don’t see anything ‘settled’ here, and it isn’t science either, as reality is the test of that, and the models consistently fail that test, yet we’re supposed to intellectually genuflect to this assertion that this is ‘scientific’, let alone that it’s a ‘settled science’?

    Elaborate garbage in still equates to detailed useless garbage coming out.

    What we are left with, at present, is another cyclic multi-decadal warming in recent decades, just like numerous other temporary warmings before it, and the absence of any anthropogenic differentiation of this multi-decadal warming from all of the other prior warmings, coolings and past approximations to a ‘hiatus’ condition interval, between such cyclic trend oscillations.

    Hence no detectable climate-change signal or even irregularity is present today (especially once you discount the corrupt endless adjustments and interpolation practices of systematic data corruption by ideologically undermined an apparently anti-scientific weather agencies).

    Same-Same.

    In other words, ” … 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. …”.

    Time for a pitifully childish humanity to get over its imaginary scary-monster under the collective united nations bed.

    And time for this writhing Medusa of what now passes for some sort of variety of ‘Climatology’, to have its head cut off before it can do more harm .

    And thank you Lord Monckton for coming back with such a damning reply to this prevailing ‘climate-sciencey-ness’ complacency, that’s so evident in the obvious need to constantly fudge the sensitivity, but to still get it completely out of whack with observed reality, even then.

    The ardent stubborn ‘belief’ is thus demonstrably a discontinuity in a ‘sensitivity’ that’s not actually physically present.

    That’s not science, it’s ignorance claiming ‘victory’, via style over substance, to make a nothing look like it’s something.

    As we say here, “Pull the other leg”, which was once something one did to make the person swimming around in front of you to image a shark may have bit their foot. When they don’t buy it, it is time to pull on the other leg even harder. And it seems we’ve all had our legs repeatedly over-extended by this ridiculous style-over-substance routine of the UN IPCC jiggery-pokery machine and the mass-media’s fish-‘n-chip wrapper production over-capacity.

    • Well said but the bewildering irony with the jiggery-pokery machine is it’s the surplus value of fossil fuels that has fostered and fed the monstrous style over substance edifice and yet they want to chop off the very hand that feeds it. That will be their undoing as the feedback effects are swift acting and obvious. Democratic majority trumps elite consensus any day.

    • I am grateful to WXCycles and to Observa for their kind comments. We shall persist in our research until either we are published or we are given proper scientific reviews, by reviewers who have actually read our paper and are willing to review it and can demonstrate in their reviews that we are incorrect. That is how science is supposed to work. Is it really unreasonable for us to ask for that?

      If, for instance, there is a fundamental and obvious error in our work, a competent reviewer expert in the field will be able to demonstrate the error in a few lines, and to the entire satisfaction of my expert colleagues. If not, then that is the end of the global warming scare.

  36. “It is wrong to include variables from the original state equation. One reason is that the have been accounted for already in the balance of the state before perturbation.”

    I can’t follow the math from either side. Take a balance sheet. That’s 1850. An income statement from that point on, makes no reference to that balance sheet. (This is a simplification.) You need to track inputs and outputs to get an income statement. You don’t say, we lost money, but look at the beginning balance sheet from 1850. That’s a distraction. We aren’t interested in the beginning or ending balance sheets as much as we are the income statement. The income statements drive the various balance sheets from different dates. Not the other way around. (This is a simplification.)

    Balance sheets are still important. If you have a lot of money, you can lose money for a long time. The thermal mass of all the oceans are like a huge amount of cash on a balance sheet. Which means you can add a lot of CO2 before those change a lot. So, we should give the correct amount of weight to each thing. The balance sheets and the income statements.

    • Yes, that is a reasonable analogy. If you think of total growth of wealth, you might include capital appreciation. Value of asset after, compared with before. All these go into a rate of change (income) statement.

      But you would put in the difference of asset values. What Lord M is doing, in effect, is adding total asset values in as income.

      • No Lord M is saying the interest rate return applies to the total retained capital, the base plus retaining earnings.

      • No, Lord M. is saying that the annual interest return on investment applies to the total capital, which is the base capital plus retained earnings. That is after all how an investment yielding 10% annually doubles in 7 years not 10.

  37. See Willis post about measuring temperature against total surface flux absorbed. He ended up with a increase of 0.38C for a 3.7 W/m^2 because of CO2 doubling. Because clouds are 85% of the DWIR , this is the reason why the 0.38C is so low. The CO2 ppm in 1850 was 285ppm . That means at present day of 413ppm there is a difference of 128ppm which represents only a 45 % increase.

    Therefore we have with the 5.35 Ln 2((CO2b-CO2a)/CO2a)) formula we obtain 1.66 W/m^2 . Now because of Holders inequality we cannot simply plug this into the Stefan_Boltzmann equation . Even if we did the increase in temperature would be no different from 1K. We are a long way from doubling CO2.

    Let us take the old 1974 produced NCAR graph of temperature for 1870 (I strongly suspect that the NASA graph has been doctored twice, once in 2000 and again 18 years later). The NCAR graph shows 1870 as 0.2 warmer than 1882. However that was northern hemisphere only.

    In any case for 1970 it shows 0.12 warm anomaly whereas the NASA graph shows 0. Because UAH shows 0.4 for 2019 that would mean only a difference of 0.28 from NCAR in 1970 to UAH today. Going backward on the NCAR graph to the start of 1870 we get 0.2 as per the above , so comparing that to UAH we get only a 0.2 C increase in 150 years. Since we have had only a 128ppm increase since 1850, that would explain the small increase of 0.4 from 1882 to now or the even smaller increase of 0.2C from 1870 to now. Since the LIA ended in 1850 I suspect that from 1850 to 1870 it was all warming , so let us say that 1850 temperature was probably close to the 1882 temperature which represents a total of 0.4C increase for 170 years. That is more in line with the 128 ppm increase since that time, if CO2 is the cause of warming (which I doubt anyway). So the 0.8C which the IPCC comes up with is double the increase in temperature which is all based on a faulty NASA temperature graph. The NCAR graph that was produced in 1974 had no agenda and can be believed. https://twitter.com/ATomalty/status/1136879230074130432

    • I got stuck on your first calculation. Why use a difference in the numerator?

      If the doubled-CO2 forcing increase is given by \Delta F_{2\times}=3.7\,\mathrm{W/m}^2 and the pre-industrial and current CO2 concentrations are given by \rho_1=285\,\mathrm{ppm} and \rho_2=413\,\mathrm{ppm}, I would have thought the current forcing would be given by \Delta F_{2\times}\log_2\left(\frac{\rho_2}{\rho_1}\right)=1.98\,\mathrm{W/m}^2. Note that this formula yields 3.7\,\mathrm{W/m}^2, as expected, for doubled CO2, i.e., for \rho_2/rho_1=2.

      Still, I’m not sure it makes much difference—except to a reader trying to follow the math.

      • Hi Joel,
        As a person that struggles with math. I am trying to follow the math. Even when most of it goes over may head. I still push the understanding peanut ahead, a bit at least. If we’re not following the math? Using it to make a prediction. What are we doing?

  38. Though I find Monckton’s presentation Byzantine and confused, I think his manuscript should get published or at least refused with well documented and objective reasons. Not “because I don’t like what it implies” rejection.

    That way it can be refuted thoroughly and officially if there is anything wrong with it.

    That is the way peer review and scientific discussion is supposed to work.

    I strongly suspect those reviewers who have rejected it so far were not able to follow it either and rejected out of ignorance they did not want to admit.

    • I think his manuscript should get published or at least refused with well documented and objective reasons. . . .That way it can be refuted thoroughly and officially if there is anything wrong with it.

      I agree with your general view, but you may be optimistic about the “refuted thoroughly” part. His writing is so impressionistic and his terminology so idiosyncratic that he can respond to any interpretation the critic gives by contending that he actually meant something else.

      Moreover, reviewer quality is an issue. I was appalled at how superficial the Richardson et al. rebuttal to his “irreducibly simple model” paper was; it missed the fundamental linear-systems error in the paper’s central equation, namely, that it purported to calculate a system’s response as the product of its stimulus and its step response. Similarly, Judith Curry hosted a Rud Istvan piece that pronounced the math “impeccable.” Yet simply applying Lord Moncton’s “simple model” to the historical numbers in the IPCCs Representative Concentration Pathways would have demonstrated how erroneous it is.

      This is basic, fundamental stuff that every undergraduate electrical-engineering major should have mastered by the time he graduated, but even among the commenters here who profess to be EEs there are many who seem unable to grasp such concepts.

    • In response to Greg, unfortunately most people find control theory Byzantine and confused. If we argue it with equations, people say there are too many equations. If we simplify the equations, people say there are too few equations. If we use practically no equations at all and explain the main points in the simplest English, as in the current head posting, those who genuinely want to understand us will say – as many kindly have – that the exposition is clear. But there will always be those who simply lack the necessary background expertise to comprehend the point being made, and there are those who very much want us to fail, for various reasons, especially if we are right.

      Mr Born is, regrettably, in the last category. He continues, with increasing desperation, to fire off a scatter-gun farrago of nonsense dressed up as though it meant something, and professes to substitute his zero qualifications and expertise in control theory for that of our tenured professor int he subject. He attempts to provide detailed criticism of a paper he has not even read, and refuses even to look up references demonstrating that what he says is nonsense, on the aprioristic ground that because I have cited the references I must have misunderstood them.

      I agree with Greg that our paper should now be subjected to proper peer review, rather than the pathetic and flagrantly dishonest pantomime to which it has been subjected so far. I have some reason to hope that we shall now get a proper review. If not, the police will be watching.

      • In response to Greg, unfortunately most people find control theory Byzantine and confused. If we argue it with equations, people say there are too many equations. If we simplify the equations, people say there are too few equations.

        I reckon two versions should be prepared: one formal and exact (as I’m sure in your submitted paper) and second ‘for dummies’, in order to facilitate dissemination of this precious knowledge. So at least folks with different technical backgrounds may access and evaluate those finding by themselves.

        • In response to Paramenter, the formal version of our paper has indeed been submitted, and we have received the usual automated acknowledgement. A simpler account is in the head posting.

          • Milord,

            In response to Paramenter, the formal version of our paper has indeed been submitted, and we have received the usual automated acknowledgement.

            Good stuff! All the best in this errand. Hopefully soon we will hear glorious and victorious announcement that the paper has been published. I’m sure it will draw lots of attention.

          • In response to Paramenter, I don’t suppose it will be as easy as all that. Official climatology simply does not realize that the feedback processes present at any moment must respond not merely to some small and arbitrarily-defined fraction of the reference signal but to the entire signal, which of course includes the 255 K emission temperature as well as the 10 K reference sensitivity to the preindustrial noncondensing greenhouse gases present in the atmosphere in 1850. Reviewers tend to be shocked by this suggestion, so we have had to provide a lengthy and tedious formal demonstration of the obvious. But, like one or two here, even with formal and unassailable proof – for the theory of feedback was established almost a century ago, and we couldn’t have gotten to the Moon without getting it right – the reviewers and editors can be expected to wriggle like stuck pigs, and duck and dive and dodge and weave. In the end, though, the truth will out.

  39. This whole exposition seems hopelessly muddled. What Monckton calls “reference sensitivity to doubled CO2” is literally the result of feedback – the outgoing radiation of the surface is intercepted by GHGs and “fed back'” to the Earth. This is textbook feedback, but Monckton’s analysis doesn’t treat it as such; he somehow interprets this physical feedback process as an open-loop gain, i.e. gain without feedback. Ironically, the “feedback” equations given in the post are what mathematically should result in his assumed 1.05K base sensitivity. Adding more GHGs just increases the value of the feedback fraction by intercepting more radiation that would otherwise escape to space and re-radiating it downward towards the surface.

    What “Monckton calls “feedback” (and I don’t blame him for this since this is what climate scientists inappropriately call it) is just a loose analogy to feedback, but not true feedback. It is not properly modeled by the equations and drawings he gives. For example, Monckton states 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.” The first problem with this statement is that what Monckton considers “feedback” is not “present in the climate at any given moment.” Consider, for example, the hypothesis that methane released from permafrost present in certain locations of the world will act as a feedback mechanism. Obviously, this feedback is only triggered once those particular locations have risen to the temperature where they start thawing; in the distant past, if temperatures were much cooler, incremental warming would not trigger this proposed feedback. Hence, it is not “present at any given moment.”

    The second problem is that physically, temperature cannot act as a feedback; it’s radiation that is emitted, and is therefore what has to fed back to become an input. Temperature is just a state variable, it can’t be moved around and “fed back.” What climate scientists call “feedback” does not reroute a portion of an output and turn it into an input; it’s always some other natural process with hypothesized intermediate steps, like receiving radiation as an input, which warms snow and ice, which melts, which causes more radiation to be absorbed, and so forth. But ice melting to increase the Earth’s albedo is not a feedback process because no output (outgoing radiation) is being directly rerouted to become an input (more radiation). It’s the input that drives this entire process, not the output. The equations Monckton cites therefore do not mathematically describe the way that this physical process (ice melting) operates.

    • A principal problem in many of these expositions, including your comment here, and indeed my comment here, is using English where mathematics is needed. One needs unambiguously defined variables with values. To be fair, Lord Monckton does sometimes do that.

      Your first paragraph points out the need to elucidate “feedback”. Radiative back scattering from CO2 is generally not thought of as a feedback, but a principal forcing from CO2. “Feedback” is usually taken to refer to the various effects of consequent changes to H2O: if absolute humidity increases then water vapour GHG effect increases, and if ice melts then the albedo decreases, leading to Earth absorbing more warming rays of the Sun.

      I agree with your comment that temperature cannot feed back on itself. Bear in mind though, that LM only assumes that because mainstream climate claptrap does, and he wants to prove them wrong at their own game. I mentioned in a comment below that I have a model of T = f(F), F=g(T), where T is absolute temperature, F is radiative forcing, and f and g are functions. f() is a standard function, and g() includes all the normal forcings plus H2O feedbacks. I can do quite neat things with these equations, and get a wide range of sensitivities (S) to doubled CO2, dependent on the gradient g'(T). A 2004 paper on the annual variation of g allows me to extrapolate to get S = 2.1K (higher than Monckton, lower than IPCC). The validity of the extrapolation is the greatest concern.

      I can locally (in the mathematical sense) turn these into a linear feedback, but that is pretty irrelevant.

      • “I agree with your comment that temperature cannot feed back on itself. Bear in mind though, that LM only assumes that because mainstream climate claptrap does,”

        Eh!
        No “mainstrean” science doesn’t assume anything of the sort!

        In fact it beyond illogical to think that an equilibrium (ref temp) can have a feedback.
        Quite obviously it cannot, else the climate would be forever under a forcing that would be acting to move it away from that equilibrium.
        A deltaT caused by a deltaF is what creates feedback.
        The classics educated/journalist snake-oil seller’s torchured writing and specious replies have sold many bottles of the said oil to gullible people.
        Look up Potholer54 (Peter Hadfield) videos, or his failure to answer his rebuttals of the efficacy of the snake-oil he markets on this very website.

        • Mr Banton, having been outed, now at last publishes here under his own name rather than under a furtive pseudonym. But he is as poisonously intemperate as ever. He resorts to the usual climate-Communist device of not dealing with the subject at hand but instead referring readers to another climate Communist’s ill-informed and profoundly prejudiced comments on matters entirely separate from the current discussion. That is the argumentum ad hominem, which has no place in true science but is widely adopted on the climate-Communist hard Left.

          He appears unaware that official climatology denominates feedback in Watts per square meter of the reference temperature (or sensitivity) that engendered it. The hint is in the name “temperature feedback”.

      • It’s absolutely true that Moncton’s analysis simply follows the nomenclature that climate scientists use. But my point is that, regardless of the terminology used, the mathematical calculations he uses don’t match the physical behavior of the system. Even though radiative capture and emission from CO2 is called forcing instead of feedback, in reality it acts as textbook feedback, and if you’re going to model it you have to treat it as it is – as feedback. Similarly, the things climate scientists call “feedback” cannot be accurately modeled by the equations Monckton uses because these processes do not involve directly feeding an output back to add to the input. Climate scientists just call them “feedback” because they believe that they are mechanisms other than CO2 by which some warming begets more warming and so forth.

        • Kurt’s insistence that direct forcings from changes in the concentration of greenhouse gases is at odds with official climatology, and he should take the matter up with the IPCC and not with me. The focus of the present paper is not on the direct forcings but upon official climatology’s overstatement of the consequential forcings that are known as feedbacks.

    • In reply to Kurt, our concept is by no means muddled. Understanding it, though, does require some knowledge of elementary methods in climatology. If one adds greenhouse gases to the atmosphere, one inhibits outgoing radiation and turns on the gas molecules so that they oscillate at the quantum level in their respective vibrational modes (with CO2 it is the bending mode), and that oscillation is, by definition, heat. This, therefore, is treated (and appropriately treated) by climatology as a forcing.

      Then various changes occur as a result of the fact that the space occupied by the atmosphere has become warmer in consequence of the forcing. These changes are appropriately treated as temperature feedbacks – in other words, they are denominated in Watts per square meter per Kelvin of reference temperature (if one does things our way) or of reference sensitivity (if one does things climatology’s way). It is a true feedback, for the mathematics of feedback is applicable mutatis mutandis to any dynamical system moderated by feedback. The climate is one such system.

      Kurt is perhaps not aware that the principal sensitivity-altering feedbacks, the ones that IPCC and the CMIP5 models use as the basis for converting reference sensitivity (sensitivity before accounting for feedback) to equilibrium sensitivity (sensitivity after allowing for feedback) are all short-acting – on timescales typically of hours, days, weeks or months – years at most. The only feedback that actually matters (because, broadly speaking, all others self-cancel) is the water vapor feedback. That feedback operates on a timescale of hours to days. So time-delay is not, after all, an issue as far as the feedbacks are concerned.

      However, one must cautiously allow for the fact that not all of the warming we engender will come through as sensible heat in the atmosphere, owing to the time-delay caused by the very large heat capacity of the oceans. We allow appropriately for this time-delay by taking account of the estimated radiative imbalance that was thought to subsist in 2010 (Smith+ 2015), as explained in the head posting.

      Contrary to what Kurt imagines, temperature can and does act as a feedback, which is precisely why feedbacks are denominated in Watts per square meter per Kelvin of the directly-forced reference temperature (or sensitivity) that engendered them. Feedbacks are, in effect, additional forcings whose magnitude is proportional to the reference temperature (or sensitivity).

      Again contrary to what Kurt imagines, the surface albedo feedback is indeed a feedback in official climatology’s understanding. If he wishes to argue against its being a feedback, his quarrel is not with me but with the IPCC. We don’t mind either way, because IPCC considers that, at midrange estimates, all feedbacks other than that of water vapor self-cancel, so the point is moot.

      • I certainly do not fault you for adopting climatology’s “feedback” terminology. In this respect, you pretty much have to take what you are given. But I made two main points in my post above, only one of which you seem to be responding to. Your mathematical analysis uses textbook engineering feedback expressions to try to model the Earth’s response to GHG emissions. But these models and equations physically represent only the process that occurs when GHGs intercept outgoing radiation and send half of what is intercepted back to the surface. Rather than mathematically treating this process as “feedback” (which it is) your exposition treats it as the “gain” of the climate system absent feedback. Granted, climate scientists do not refer to this process as “feedback” but this is irrelevant to my point, which is that your mathematics does not match the physical process you are modeling.

        The flip side of this same error is that you are using textbook feedback analysis to describe processes that in the real world don’t act the way your math describes. This has nothing to do with a time lag; even if the process were instantaneous, for example, melting ice to increase albedo is not a feedback process – it physically operates entirely as a result of the input radiation. Climate scientists call this “feedback” as a loose analogy, but that does not mean that it is appropriate to mathematically express it using the equations you do.

        As far as temperature ostensibly being feedback, temperature is a state variable that characterizes the heat content and thermal capacity of a specific material. Temperature can’t be moved around or “fed back.” A temperature determines the amount an object radiates and that radiation can be fed back towards the object, but I don’t see how the mathematical expressions you use are going to be applicable with temperatures as an input signal and as a feedback signal.

        • In response to Kurt, my original reply had in fact described, in some detail, the reasons why official climatology treats the forcings from changes in greenhouse-gas concentrations as forcings and the consequential forcings that arise from the temperature change engendered by the original forcings as feedbacks.

          if Kurt wishes to argue the toss on these definitions, his argument lies not with me but with the IPCC secretariat as the mouthpiece of official climatology. Our approach is to accept all of official climatology except what we can demonstrate to be false. Kurt’s attempt to define radiative forcings from changes in greenhouse-gas concentrations is idiosyncratic and inconsistent with official climatology: therefore, it is a distraction from the focus of our paper, which is exclusively on that fraction of predicted global warming that is contributed by what official climatology defines as feedback.

  40. Although I have studied and criticized this linear feedback stuff for the sake of argument, a year ago I derived a model wherein feeback is a function of temperature which is a function of forcing (which includes feedback). This is very incestuous, i.e. one gets an implicit equation rather than an explicit one. Nevertheless it can be solved numerically and sensitivity derived algebraically. The bottom line is that sensitivity depends on the gradient of H2O feedback relative to CO2 forcing.

    But I’ll need to get it published to get any traction, I suppose!

    Rich.

  41. The Sun started out only 70% as luminous as it is now 4.6 billion years ago. Despite that, there have been liquid oceans and life on Earth for about 4 billion years. There may be positive feedback over short temperature ranges, but in the LONG run, feedbacks are consistently large and negative. Else the oceans and life wouldn’t have lasted for 4 billion years.

  42. The Sun started out only 70% as luminous as it is now 4.6 billion years ago. Despite that fact, there have been liquid oceans and life on Earth for 4 billion years.

    There may be positive or zero feedback over short timescales and temperature ranges, but in the LONG run, feedback must be both large and negative to maintain those oceans and life over long periods. I suspect that most of the feedback comes from water in all of its phases.

    • In response to Mr McIntyre, in IPCC’s understanding all feedbacks other than that of water vapor self-cancel, so he is right that most of the feedback comes from water vapor. But that feedback is not reliably quantifiable by observation: nor can it be derived by any theoretical method. It is really guesswork. That is why we took an approach that did not require knowledge of the magnitude of any individual feedback.

  43. I am reminded of a Gary Larson cartoon where scientists in white lab coats stand in front of a chalkboard full of equations while engaged in a heated debate over a mathematical model of the elephant.

    Anyway, back in 2010, I asked Dr. Dimitri Koutsoyiannis (‘A Random Walk on Water’) if it might be possible to directly observe and characterize the postulated water vapor feedback mechanism in real time while it is operating in the earth’s atmosphere, using instrumentation systems and data collection systems designed specifically for that purpose.

    Paraphrasing Dr. Koutsoyiannis’ response, this is what he said:

    Owing to the magnitude of the problem, it is not possible at the current state of science to do these kinds of direct, real-time observations. Proof of the existence of the postulated feedback mechanism can only be gathered inferentially through a complicated process of examining and analyzing other lines of evidence.

    My question is this:

    If we can’t observe the feedback mechanism directly — assuming it actually exists — then what specifically are those other lines of evidence needed to inferentially characterize and quantify the postulated mechanism? What would a comprehensive list of these other lines of evidence look like?

    Moreover, how should these other lines of evidence, whatever the comprehensive list contains, be assembled and organized so that a knowledge base is available for reference and citation by each opposing side of the debate?

    A caveat to my question:

    Be careful what you ask for. If they choose to do so, whoever controls the knowledge base can also control the progress and outcome of the debate through selective choice of the information and the data the knowledge base contains. In other words, let the buyer beware.

    • In response to Beta Blocker, our method requires no knowledge of the magnitude of any individual feedback. The system-gain factor is at or very close to the available equilibrium and reference temperatures in 1850: i.e., 287.5 / 265, or 1.085. That system-gain factor embodies the entire influence of feedback on reference temperature.

      There is no reliable method of deriving the value of any temperature feedback by measurement. The uncertainties are too great.

      • Lord Monckton, so far you have not replied to Anthony Banton’s comment on my own. I hope you will, because I think you are better placed to set the picture straight than I am.

        • CO2rich should refer to my comment in response to the characteristically discourteous contribution from the dreadful Mr Banton, who, as usual, brings more heat than light, more prejudice than knowledge, more fiction than fact to the discussion.

  44. Since we seem to be having commentators with quite different perspectives on what feedback means and how it applies, I suppose I can try for some insight here, and support a certain way of looking at the matter with a couple of quick web links?

    Basically, I am taking the view that Lord Monckton has the whole matter of feedback *and* it’s plausible relevance to the most usefully idealized climate models *correct*. So the implication is that Nick Stokes and some others, call them “climate conventional theorists”, are either getting it wrong, or else they are applying a more or less odd or eclectic view of the basic idea of feedback (at least at those times when the conventional climatists deem that feedback is a useful concept, which strangely enough, they don’t always seem to). The thing to note here, right away, is that feedback is, in itself a “large” topic, easy for even experts to misapply or make over complicated, if they aren’t careful! I myself am layman enough to mess things up quite easily, I’m sure, so I’m not here to critique Mr. Stokes or anyone else line by line exactly.

    What I want to do here is, I only want to throw in a couple of relevant Control Theory web references, just put a couple of examples into this discussion, to help illustrate the basics of how feedbacks ought to work (at least in any regular DC amplifier or DC regulator kind of scenario).

    Now my initial “kick off”, or inspiration for digging out a couple of web links on this, was my reading of Stokes vs. Monckton back a bit in the current discussion. This was when Lord Monckton was supporting his idea by referencing the success of his op-amp based test rig for feedback (using voltage as the analog for earth average temperature). Mr. Stokes then said, in essence, that instead of using *that* sort of DC level feedback, or DC gain rig as a model, modellers should instead be using calculus for “deducing rates of change” (said rates of change would be amplified and/or integrated so as to give more of a “slope boost” effect to the idea of feedback as such)? Note that “slope boost” is my term here, not Stokes’ (I am honestly struggling, trying to visualize what he means).

    Thus, I refer to Web Link #1 (of 2 links):

    https://www.maplesoft.com/content/EngineeringFundamentals/11/MapleDocument_11/Block%20Diagrams,%20Feedback%20and%20Transient%20Response%20Specifications.pdf

    The above is a primer on “Block Diagrams, Feedback and Transient Response .. ” for understanding how to model such things on Maplesoft math software. The thing to notice here is that right away they give a couple of block diagrams, one for a “household heating system”, then a very slightly more generalized version of the same thing, the ” System plant” block feedback diagram. This is then followed by a still more abstract “Fig. 3: Block diagram with feedback” diagram. So they are going carefully “step by step” on the abstraction, you see, like “techno nerd” babytalk (I really like that, myself).

    The thing is, if you follow the diagrams and the bits of math below, you wind up at a “Fig. 8: Equivalent system diagram”, where the situation is very much as Lord M. would have the idea of feedback working all along! The only distinction is that the formula here is the one for negative feedback as opposed to positive (a very minor distinction, if you like, you can just change the sign in the denominator and that will give you the positive feedback version of things, i.e., just by flipping the ‘+” sign in the denominator over to a ‘-‘ you can get the positive feedback formula). So since the initial example being used here is a heating system, you have the temperature reference going *in*, the “heating system modified” temperature coming *out*, with no special amplification of slopes as such, or anything like that.

    Now if the above reference isn’t quite technical enough, I will also offer the following,
    Web Link #2 of 2:

    http://www.ti.com/lit/an/slva947/slva947.pdf

    My link number 2, above, is an interesting description of a certain kind of voltage regulator device (Texas Instruments device, the paper here gets quite technical on frequency response and how the device can be stable despite having *positive* feedback on some frequencies and *negative* feedback on others). Note carefully the technicality here, that even though the device operates on DC levels and is, in fact, a DC voltage regulator, the use of AC test signals is still considered vital for proving that the gadget as such is stable!
    The reason they are so careful about testing at different frequencies, is that even a system whose whole intent is to modulate DC (i.e., it’s not a signal amplifer in the radio or audio amp sense), even *there* it is important that the gadget should not go wild in some way when it is switched on, or when there is some other transient change. Transients imply frequency components, *then* you have to consider those separately if you want stability, and *so* maybe this is where you get some of the confusion that we’re seeing?

    The simpler discussion in this TI paper is really about the two kinds of feedback, positive and negative, being *not much different* at low feedback values (and therefore stable at low values of feedback factor)! Why, that just sounds a *lot* like the point that Christopher Monckton has been making all along, about low feedback being what it takes to have a stable system!

    So make of this what you will, all, the above is about as “feedback theory” as I am likely to want to get, for now anyway.

    • Mr Blenkinsop has been uncommonly diligent in chasing down primers on feedback theory that are available on the web. I am delighted, but not surprised, that these references seem to support our stance. I am not surprised because we get our feedback theory not from me (I am no expert) but from a tenured professor of control theory, a man of more than usual ability and determination, together with not one but two experienced, hands-on control engineers, one of whom built and ran our test rig, and an eminent scientist at a national laboratory who also built and ran a test rig for us. It is of course possible that all of us could be wrong, but consider the following facts:

      1. The world is warming at only one-third of the officially-predicted medium-term rate.
      2. Two-thirds of the warming predicted by official climatology comes from feedbacks.
      3. The error we have identified, once corrected, leaves very little influence for feedback: one can ignore it altogether without much error in deriving equilibrium sensitivities.
      4. The direct warming to be expected in the absence of any feedback and the direct warming that has been observed since 1850 are more or less identical.

      This coherence of several lines of evidence suggests at least the possibility that we may be on to something. If we are right, that is the end of the climate scare.

    • “The above is a primer on “Block Diagrams, Feedback and Transient Response .. ””
      It’s right there in the title – transient response. It does not include things that do not change. If you look at fig 4, it starts with a differencer, where you subtract the output from the reference signal to get the error signal. It is that difference which is then passed through the feedback apparatus to tell the plant what change it should make. The only thing that enters the loop is the difference. Eq 4 (with Fig 7) spells that out very explicitly. Lord M is trying to smuggle something past the differencer.

      If you read further, you might get excited where it introduces K, which it calls the DC gain. But it isn’t amplifying an unchanging input. Instead it is the response to a step change as an input signal.

      AS for Fig 8, that actually merely writes down Laplace transforms. But a Laplace transform is inherently of a transient signal; it can’t deal with one that never changes. It integrates only forward from a zero time; the quantity (integrand) before that was zero. The Laplace transform of 1 is actually the Laplace transform of a step change at t=0.

      • Well, OK, so in mentioning “K … the DC gain”, you’ve made my point, and in the graph in the article immediately following the heading “DC Gain, K” this graph clearly shows that the system output approaches the steady state (or DC) gain as the time variable approaches infinity (of course the practical amount of time for a system to settle to steady state will be something less than infinity).

        So, the basic feedback formula doesn’t just apply to AC Laplace domain calculations, it also applies to long term steady state output levels as well, in any continuous feedback situation (where the system steadily feeds back some part of the output level). Heck, they even define the practical timing or Settling Time in terms of the DC (steady state) output value (therefore necessarily factoring in the K factor as such, everything is defined using that). To quote the Settling Time definition given:

        “The settling time is defined as the time after which the output is within a specified band around the steady state value.
        The specified band is usually plus or minus 1% or plus or minus 5% of the steady state value.”

        • “So, the basic feedback formula doesn’t just apply to AC Laplace domain calculations, it also applies to long term steady state output levels as well”
          No, it doesn’t. A step change is not a steady state. It is a change. It is a difference between a before and after state. But Lord M’s emission temperature always has been and will be. He doesn’t take the difference of before and after.

          He could. It would actually be valid to include emission temperature on that basis. But the difference is zero.

          But mainly you haven’t dealt with the key ingredient in your control diagrams. It is the initial differencer. The system explicitly computes, and amplifies with feedback, the error signal. The difference between before and after. It does not feed back the state.

          • Aren’t we in danger of confusing or conflating about three somewhat different issues here, even if all three issues come from essentially the same block diagram?
            For instance the Mathsoft primer I referenced talks about a “home heating system” as it’s initial example, but the concept pictured isn’t like any real home heating system I ever saw (not when it comes right down to it)!
            I mean, the block diagrams there are of continuously controlled flow systems,
            so there is no mercury switch, no furnace lighting up, no running for a while, shutting down again, etc.
            I submit that in a *continuous flow* version of a heating system, there would be no actual “difference detector”,so nothing like a mercury switch banging on in response to a “zero difference”, and no “error detection” in that sense. At least I think there won’t be anything very meaningful as “error” in the time domain anyway!
            So, what I’m saying, I think there’s a potential confusion between on/off type systems, and also a confusing conflation of terminologies.
            I don’t know the history of referring to combined inputs as “error”, but maybe that is only helpful when looking at the Laplace domain, or AC response as such?

            To see what I mean here, imagine something that *is* patently a continuous flow controller, such as, say, an old fashioned centrifugal ball governor on a steam engine.
            The ball governor controls a valve, with the opening of the valve directly driven by the result you want to get out of this machine, i.e., the valve is closed or the valve inlet narrowed directly according to the speed in rpm’s of the engine drive shaft.
            Further, let’s say it is a given that the shaft speed is proportional to the steam flow rate through the valve, so if you cut down on the steam flow by 10 per cent, the shaft is sure to turn at only 90 percent of the rpm’s you had originally.

            Now in this situation, we may not be happy with just letting the steam through from our boiler direct into the piston chamber – ?
            If, say, a nominal calculation says we’ve got 5 kilograms per second of flow available, for 1000 rpm on the shaft, but for some reason we think that might cause problems?
            So, we go ahead, put the governor in place, and set the linkages involved so that we have a shaft speed signal feedback fraction (negative feedback) of 0.20, or 20 percent.
            Nothing tricky about that, right, we could do that?
            The (very simplistic) implication here is that we’ve now limited the flow to 4 kilos per second, and we’ve limited the speed to 800 rpm.
            All this hopefully with an advantage in greater stability, such as not allowing the boiler to go cold through expelling too much steam!

            Now, the point that must not be missed here is that we *are dealing with a live system, an energetic flow system, so control theory has to cut in here, telling us that the engine will react and actually produce more output than the most simple minded physics scaling would have said!
            The block gain on this situation is, I believe, 1/1.2, so the system will end up running at 83 percent of the nominal “straight through” capacity. so the output is 833 rpm,
            not 800 rpm as I scaled it initially!

            My point is, what does this have to do with making the ‘plus’ versus the ‘minus’ on a block diagram input into a “difference error”?
            In this example you’ve got 1000 rpm on the “plus” of the summation element going in, then you’ve got (nominally) 200 rpm on the ‘minus’ of the summation, followed by 833 rpm output!
            This most basic result is a steady state or “DC” output in principle — it has nothing to do with trying to subtract one thousand from one thousand to get zero, or whatever.

            Now, I just know someone is going to say that I’ve violated a conservation law somehow, so I’m going to finish up by quickly pointing out that the “feedback fraction” is specified as 0.2 here, so we are only subtracting *0.2 times* the 833 ending output (i.e., we are subtracting only 167 rpm off the 1000 rpm that we count as reference signal input). So the signals in this example *do* balance, and again, we’re *never* trying to subtract 1000 from 1000 !

          • Mr Blenkinsop will find the regulation mechanism he seeks in the fact that where a radiative imbalance occurs it is in due course resolved by an increase in temperature, which restores the balance.

            Mr Stokes continues to have difficulty in admitting what the simplest of test rigs would demonstrate – namely, that the feedback block present at any given moment will perforce modify the entire signal that has entered the summative input-output node of the feedback loop. Elementary control theory establishes that this is the case; the elementary equations of control theory demonstrate that it is the case; and test rigs built both by a co-author and by a government laboratory demonstrate that it is the case.

          • “test rigs built both by a co-author and by a government laboratory demonstrate that it is the case”
            We keep hearing this, when other arguments fail, but never get to see what the rig even is or does, let alone how it can possibly demonstrate what is claimed.

          • We . . . never get to see what the rig even is or does, let alone how it can possibly demonstrate what is claimed.

            Oh, I think we know generally what it is, and I’m sure it will indeed demonstrate that—at least according to some interpretation of Lord Monckton’s awkward phrasing—that “the feedback block present at any given moment will perforce modify the entire signal that has entered the summative input-output node of the feedback loop.”

            But it will also demonstrate the validity of Mr. Stokes approach to calculating the output by perturbations.

            Both things can be true.

          • The test apparatus demonstrated many things, not the least of which was that feedback responds not merely to some arbitrarily-selected fraction of the reference temperature but to the entire reference temperature, in which the largest element is the 255 K emission temperature.

            As the head posting states, one can do climate-sensitivity calculations either by using sensitivities or by using absolute temperatures. But if one uses the former, as official climatology does, even a small uncertainty in the value of the sensitivities entails a large uncertainty in their ratio, the system-gain factor, while using the latter, which are two orders of magnitude greater than the former, even quite large uncertainties in the value of the temperatures entails only a small uncertainty in their ratio, the corrected system-gain factor. As Bill Rostron has pointed out earlier in this thread, using absolute tempeatures – which is of course permissible, contrary to the impression Mr Stokes has been giving – increases the signal-to-noise ratio considerably, and that makes reliable derivation and constraint of equilibrium sensitivities a whole lot easier.

  45. Here is the weakness of both the Lord Monckton and Stokes analysis:

    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.

    Why should the 255+32.5K reference condtion be treated as invariant? While indeed there is data to show the condtion to be steady (or more likely steady state) over an 80 year period of time, that is not the same as invariant.

    That assumption needs to examined quite closely. If one assumes the reference condition to be invariant (and thus decoupled from post 1850 changes in climate conditions of solar radiation, atmospheric gases, ocean temperatures, etc.), then whatever calculation of the system gain is solely attributed to the proposed transfer function (CO&#8322 in the current work) elements. This simplification is rather hard to swallow regardless of how one goes about calibrating the transfer function.

    Consequently, the argument that the feedback contribution is small falls short of being totally convincing because one can mathematically postulate that elements of the feedback transfer function are working to suppress atmospheric warming (some kind of global thermal moderator) resulting in a net slight feedback signal. Consequently, the thermal forcing of green house gases is massively deadly, but for now the planetary climate machine is holding back the tide.

    One can correctly point-out that the T/CO&#8322 relationship is exhibiting an agreeably low system gain factor over the intervening years. That’s dandy, but one can then counter that we’re reaching the limits of what the global thermal moderator can stand and we’re nearing the tipping point. You argue that the system must be linear because of the disproportinate contribution of the reference signal. I cannot disprove that argument, but one can equally argue that the end of that linearity approaches. Anything here sound regretably familiar?

    Why I consider your proposed proof to fall short of convincing is as follows. All the parties have chosen to simplfy a complex system with many factors (or state variables in control-speak) to an input reference condition and a CO&#8322 forcing transfer function. One then calibrates that multi-variable transfer function from that output/input ratio. That could be correct. It could be incorrect. The mathematical pitfall is considered observability and controlability in state-variable control analysis (The Broom Balancer is considered the classic state variable control problem.) In short, one may not be able to predict (observe) or influence (control) a multi-variable system based on a reduced set of inputs and/or outputs. The problem become more peculiar if one considers sampled-data system (z-transform math) versus analogue data signals (Laplace transforms). Since the majority of the historical data is either daily averages or hourly readings, we’re embracing sampled-data analysis.

    Thus, while I appreciate your effort and acknowledge that you have put your finger on a problem with the prior analysis, you cannot quite reach your proof as a more appropriate calibration of a flawed approach is still flawed.

    • Master of the Obvious

      I quite like your observability point. Because if you are right, you are saying the enhanced greenhouse effect cannot observed (in the sense that we cannot confirm all of the relevant state variables) and therefore the scientific argument faces an intractable problem in providing relevant measurements to construct a supportable link to CO2 as a cause of warming.

      And by extension, you have destroyed your suggestion that “the thermal forcing of green house gases is massively deadly, but for now the planetary climate machine is holding back the tide”. And certainly no way to assert “one can then counter that we’re reaching the limits of what the global thermal moderator can stand and we’re nearing the tipping point”.

      Likewise, I quite like your consequential controllability argument as the unobservable state variables (according to your position) will frustrate any case to manage human emissions of CO2 in order to deliver some desired outcome with respect to future average temperatures (a measure which lacks physical meaning).

      Why should we assume the elements of the transfer function are small? I can offer two reasons. The first is to assume the atmospheric climate system is passive (it has no energy supply to call upon in order to amplify any of its variables) and open loop gain must therefore be less than unity. The second (which supports the first) is to observe that the climate is a stable system and this is also a characteristic of the same open loop gain.

      If you think the climate will reach some tipping point (amplification of any of its variables), you must argue that it will behave as an active system (has an energy source which will support amplification of the relevant variables) and show that this behaviour accords with conservation of energy.

      • “Jordan June 9, 2019 at 1:44 pm

        If you think the climate will reach some tipping point (amplification of any of its variables), you must argue that it will behave as an active system (has an energy source which will support amplification of the relevant variables) and show that this behaviour accords with conservation of energy.”

        I am not any good with words however, this perfectly explains the point I have been trying to make for sometime (Not always at WUWT). So, thank you Jordan. Where does the extra energy come from is my point?

        • The Sun you i***t!

          If we wanted to heat the Earth up dramatically, all we would have to do would be to eliminate all the ice and all the clouds, to lower the albedo. Oh, that’s quite hard I suppose. But that is where the extra energy comes from, by not reflecting it back to space.

          • See – owe to Rich

            Except you have overlooked angle of incidence. Its cold at the poles because incident sunlight is non existent for half the year, and the angle of incidence has its greatest impact at the solstice when the Earth’s tilt is at 23 degrees.

            To evaluate the ice albedo feedback, you have to focus your attention at the edge of the ice. As the ice retreats, the incident power of sunlight declines because the Earth is not a flat object, but the exposed surface radiate outward into the hemisphere above it at “local temperature”. This is a process which must cease at the point where the (reducing) incoming solar power can no longer melt any more ice. It is a saturated process (zero gain). Things are a bit more complicated than this because of the seasonal variation, but that’s just detail.

            The reason why there is ice at the poles is simply because there is no incoming sunlight there. Ice albedo feedback only exists in the imagination of people who have nothing better to worry about.

          • The Sun, NOT CO2 and positive feed-backs?

            Thanks!

            If you read the posts by the resident solar expert, he says there isn’t enough energy to do that.

          • Patrick MJD: yes, the Sun, but via positive feedbacks from melting ice and (supposedly) increasing water vapour.

            Jordan: I agree that the picture is complicated by angles of incidence, but right now the Sun is 23 degrees above the North Pole, which is the same as at midday in London in mid February. I can assure you that even with the air temperature around freezing, the Sun at that angle has plenty of power to melt snow and ice. Currently that pole has ice, but if it should ever be ice free there will be more absorption of sunlight.

            You talk about the edge of the ice, and there the Antarctic is more important because the edge is at lower latitudes than in the Arctic.

            The Antar

          • “See – owe to Rich June 11, 2019 at 1:35 am”

            Where are these feedbacks? Where is the extra energy?

            If there were such a feedback, there would be linear warming (Due to CO2 increase and “warming”). There isn’t.

      • If you think the climate will reach some tipping point (amplification of any of its variables), you must argue that it will behave as an active system (has an energy source which will support amplification of the relevant variables) and show that this behaviour accords with conservation of energy.

        Just for clarity, I am not arguing for this point; rather, arguing that utilizing transfer function mathematics will not settle the question in either direction. I’m going to presume that you meant “one” where the comment addressed “you”.

        The energy source can be postulated to be the sun; thus, under (admittedly questionable) assumptions of feedback gain, it could achieve the results proposed by some. I do not discount the arguments that experience suggests the thermal regulator to be more robust such that we’re unlikely to “tip” over the edge into a thermal runaway based on greenhouse gases. If I were the betting type, that is where I would place my money.

        However, Lord Monckton decried the lack of meaningful peer review of his work. He is now certainly getting it. Consequently, I will challenge his methods so he may improve his arguments. A combination of “open loop”, “passive” and (in Lord Monckton’s words) “typically near-invariant” are nice arguments and perhaps even the close to reality; but, it is not proof of reality (as science rarely achieves that exalted pinnacle).

        The work raises very salient questions about the nature of the transfer function climate models and their calibration. However, there is a limit to how far the argument can be taken. In particular, one cannot argue that since the net feedback signal is low, that the contributing signals are also low. That is a non-sequitur. Examination of even a single state-variable model can have large terms in the feedback transfer function that subsequently net near-zero. In the more likely multi-state-variable case, the math of observability renders discering the behavior of the state variables from the limited selection of input/output data rather doubtful.

        Now, do I believe that the individual terms are massively high and we’re all living on the edge? I do not for the reason that such a system would be (in my experience) rather twitchy and unstable. While the planet has exhibited variation in climate behavior on a long-term time scale, it has not shown the behavior of a high-gain system with under-damped response.

        However, if one is trying to argue by examination of transfer function models that there is no boogy-man lurking out there just around the CO2 corner, then the argument fails as one (not necessarily me) can arrange the transfer functions to fit any narrative one cares to concoct. Does that exercise make the assertion correct? Certainly not; however, the climate debate has not been a bastion of clear logic and consistent argument.

        So, if I were refereeing this paper, I would recomend it for publication with some comments back to the editor about the feedback assertion. It meets the criteria of raising good questions about the prior art and has well-constructed arguments. I would suggest being more clear about postulating the low feedback condition as being based on an examination of individual contributors and some analysis of the damping behavior of historical climate/temperature data. Preponderance of evidence is not proof, but it can be good argument.

    • “Master of the obvious” has not, perhaps, understood that the term “invariant” is not applicable to single points on a curve, such as that which obtained in 1850, where reference temperature (before accounting for feedback) was 265 K and equilibrium temperature was observed to be 287.5 K. The ratio of these two values, 287.5 / 265, was the system-gain factor applicable at that moment.

      The question is whether the curve of the system-gain factor over time is invariant or nearly so. Official climatology describes the climate-sensitivity parameter, which encompasses the influences of forcings and of feedbacks, as “typically near-invariant”. Since we accept all of official climatology except what we can disprove, we accept that the climate-sensitivity parameter, and therefore the curve of the system-gain factor over time, to be invariant or nearly so.

      But our paper also examines all of the sensitivity-altering feedbacks in detail, concluding that none of them could, under anything like modern conditions, give rise to a pronouncedly invariant response curve. Put simply, all sensitivity-altering feedbacks self-cancel except that of water vapor.

      By the Clausius-Clapeyron relation, specific humidity – the atmospheric burden of water vapor – is supposed to increase near-exponentially at about 7% per Kelvin (Wentz+ 2007) as the space occupied by the atmosphere warms. However, two considerations prevent the water vapor feedback from being anything like as strong as 7% per Kelvin. First, the temperature response to the water-vapor feedback forcing is approximately logarithmic, roughly canceling the exponentiality of the increase in specific humidity. Secondly, the specific humidity is not increasing at all in the crucial tropical mid-troposphere: it is declining, contrary to the predictions of all the models.

      Therefore, there is no good reason in atmospheric physics to expect a strongly nonlinear temperature response due to feedback. And that is why official climatology’s system-gain factors both for the preindustrial era to 1850 and for a subsequent doubling of CO2 concentration work out at about 3.2. This, at least, is consistent with the statement in IPCC (2001, ch. 6.1) that the climate-sensitivity parameter is “a typically near-invariant parameter”.

      What official climatology has not appreciated is that, once one takes into account the undeniable fact that such feedback processes as subsist in the climate at a given moment must act upon the entire temperature obtaining at that moment, and not merely to some arbitrarily-specified small fraction of that temperature, it is in fact predicting such wildly-exaggerated warming as to be strongly nonlinear, directly contrary to its finding that the climate-sensitivity parameter is “typically near-invariant”.

      Since there are good physical reasons to suppose that the climate-sensitivity parameter is indeed near-invariant, the system-gain factor over the geologically minuscule period from 1850 to a doubling of CO2 concentration compared with 2011 is scarcely going to change much. That is why we are reasonably confident that Charney sensitivity is not 3.35 K, as imagined by the CMIP5 models, but only 1.15 K, ending the climate “crisis”. That “crisis” arose solely from official climatology’s elementary error of physics in not appeciating that feedbacks act upon the entire reference signal they find, and not merely upon some fraction thereof.

      • That “crisis” arose solely from official climatology’s elementary error of physics in not appeciating that feedbacks act upon the entire reference signal they find, and not merely upon some fraction thereof.

        I will agree that you make many good arguments for that case; however, a preponderance of evidence does not disprove an assertion that a CO2 menance lurks in the near future.

        The models presented are of the form:

        T(lots_of_stuff@1850) + T(much_less_stuff@since 1850) = T(@today)

        Run a system gain calculation of T/CO2 and one now has the greatest menance to human survival since the Black Death. I reject that construct for the following reasons:

        (1) By tucking much of the climate mechanisms into the 1850 reference signal results in a model with all positive gain (post 1850) and no balancing negative gain. Such a supposition is dubious.

        (2) If one adopts the supposition that our climatic system has mechanisms to both capture heat (least we have moon-like temperatures at night) and ultimately loose that heat (as the sun sends more everyday), then the post-1850 transfer function should feature at least a good sub-set of the mechanisms present in the 1850 reference signal. The narrow choice of mechanisms in the post 1850 signal is doubtful.

        Consequently, I reject the T_reference invarance on first principals as I find the inherient assumptions indefensible. The proper form of the transfer function should be:

        T(still_lots_of_stuff@today) + T(much_less_stuff@today) = T(@today).

        You make arguments for the near invariance of the 1850 reference signal so that the model can be simplied to the previous form. Not an unreasonable approach. You offer analysis of various candidate mechanisms. But, you invoke Wentz et al., note the variation between predicted water vapor (based on equilibrium of a reversible, closed system) and observations while passing lightly over the mechanisms responsible for the variance.

        I agree with the analysis that solar radiance is the main signal input and should be properly accounted in the calibration. Bravo. However, your assertion that the climate system must be linear does not hold-up. You offer much evidence and analysis, but can you definitely account for why atmospheric moisture is almost never in equilbrium with the liquid state (per Clausius-Clapeyron)? If those mechanisms have slipped your dragnet, then what else have you missed?

        All the reasons that a climate feedback model fails to convice me of the CO2 menance still apply to your model. So, I can’t go that last step with you. Your preponderance of evidence makes a strong case, but I part company with reverse engineering a transfer function to predict individual elements (including CO2 effect). As I detailed for Jordan (vide supra), the math can be conveniently (and improperly) construed to fit whatever narrative one cares to propose.

        You have certainly cut the menance down to size. You make some good arguments for a stable climatic system which I believe to be a more fruitful narrative than trying to disprove things that go bump in the night. My suggestion is be ruthless on what you can prove/disprove and pick defensible positions.

        • “Master of the Obvious” appears very confused. Though I have patiently explained to him that describing a signal at a single moment as “near-invariant” is inappropriate (the signal is what it is), he continues as though this had not been explained to him.

          He says I “make arguments for the near-invariance of the 1850 reference signal”. I do no such thing. I assert that the reference temperature in 1850 was about 265 K.

          Official climatology asserts that the climate-sensitivity parameter – the quantum of warming to be expected at equilibrium per unit radiative forcing – is “a typically near-invariant parameter”. If “Master of the Obvious” considers that it is not near-invariant, then his quarrel is not with us but with official climatology. He should direct his concerns to the Secretariat of the IPCC, which will give him short shrift.

          • “Official climatology asserts that the climate-sensitivity parameter – the quantum of warming to be expected at equilibrium per unit radiative forcing – is “a typically near-invariant parameter”.”

            To be honest, I have no idea what this is supposed to mean.

            If it is saying that climate sensitivity is stationary, it could just say it in those well-understood terms.

            Or if the phrase “invariant” means something other than “stationary”, could you please just tell me what you are trying to say.

          • If my comments rankle due to my attempt to pin-down your claims, I do ask your forebearance but offer no apology. In your postings, you claimed to have “ended the ‘crisis'” and that it is “game over”. As many have noted, extrodinary claims require extrodinary proof. I applaud you for having stepped into the arena, but you are the one who set the bar quite high.

            This forum will offer you the fairest hearing you’ll get. One need only look at the treatment consciencious workers like Kidd and Pielke received for a preview of what lies ahead.

            I will offer an apology if I have become confused. As I both read and write dense technical documents and am also quite versant professionally in thermodynamics, equilibrium and transfer function mathematics (both s- and z-domain), I will politely suggest that some editting could facilitate readers of varying levels of experience in understanding your arguments. I have often found my own writing wonderfully clear. I rely heavily on outside review and editing to make sure my arguments are actually clear, cogent and (where achievable) concise.

            Here is the source of the confusion:

            Since there are good physical reasons to suppose that the climate-sensitivity parameter is indeed near-invariant, the system-gain factor over the geologically minuscule period from 1850 to a doubling of CO2 concentration compared with 2011 is scarcely going to change much.

            You also previously wrote:

            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.

            If you postulate near-invariance from 1850 onwards, then the refernence condition should also be near-invariant. If I have construed your concepts incorrectly, then some clarification would be useful.

            The 1850 reference temperature is a resonable estimate based on physical principals. I have no argument with that. However, that reference temperature is inheriently valid for calcuations concerning other signals only in 1850. The moment one utilizes that value in a calculation involving a signal from another time period (as in over a time interval), an implicit assumption of invariance has been embraced. Might be a good approximation, might not. in either case, it is yours to defend. I do sincerely apologize if I was unclear.

            However, please anticipate that any deficiency or even legitimate disagreement with any one argument/assertion will be mercilessly exploited in attempt to invalidate all of your arguments. Highly unfair and unscientific? You bet, but it’s the order of the day.

            In short, be your own harshest critic. If you pass on that opportunity, there are many volunteers who will gladly step into that role. You should be able to slice and dice my questions and not merely assert that I don’t get it. Yes, it is a tall order.

          • In response to “Master of the Obvious”, who praises himself for the clarity of his technical writing, I am not as incautious as to make the same claim for my own technical writing, because technical writing is difficult. It may be helpful if I explain that the system-gain factor is simply the ratio of equilibrium temperature (after feedback has acted) to reference temperature (before feedback acts) at a given moment.

            Therefore, if the system-gain factor is near-invariant over time, as official climatology finds it is (and in this I do not disagree), then it is the ratio that is near-invariant. There is nothing to stop the reference temperature from increasing over time, provided that the equilibrium temperature correspondingly increases so as to leave the ratio of equilibrium to reference temperature near-invariant.

            The reference temperature in 1850 was 265 K or thereby. It was the value at that point in time. “Master of the Obvious” had previously written that I was not correct in stating that the reference temperature on that date was near-invariant. But I had written no such thing: for a value at a particular time is what it is, and the term “near-invariant” is simply not applicable to it at all.

            The reference temperature in 2011 exceeded the reference temperature in 1850 by 0.75 K, and the reference temperature in response to a doubling of CO2 concentration compared with 1850 would add another 1.05 K to the reference temperature. But the system-gain factor, being near-invariant, will remain at or close to the ratio of equilibrium to reference temperature as it was in 1850: i.e., 287.5 /265, or 1.085.

  46. Simple climate sensitivity equations based on data

    Climate sensitivity is the warming from two times CO2. Only one basic parameter is needed: The temperature response factor, K, estimated from data.
    Basic relationship: Surface temperature rise from CO2 follows a log function of CO2 ppm changes.
    Tr = Klog(C2/C1)

    Where Tr = the global temperature rise over a time period.
    C1 and C2 are the CO2 ppm values at the beginning and end of the period.
    Solving for K gives: K = Tr/log(C2/C1)
    And climate sensitivity, CS = KLog(2)

    Example
    Christopher Monckton, et. al, published a paper in the 2015 Science China Press titled. “Why models run hot: results from an irreducibly simple climate model”. Using the temperature vs. time plot on page 2, Fig. 1, of the paper for the years from 1990 to 2015 shows a temperature rise of 0.34 C. Average CO2 ppm for these years is reported from Mauna Lao data are 354 and 401 ppm.

    Using the above equations, we get:
    Temperature response factor, K = 0.34/log(401/354) = 2.727
    Climate sensitivity = 2.727 x log(2) = 1.89 C

    Much less than the IPCC 4.5 value.

    Using other sources of temperature dates give the following:

    Dates Temp Rise C C1 ppm C2 ppm K = Tr/log(C2/C1) CS = Klog(2)
    1880 to 1944 0.24 283 310 2.63 1.82
    1944 to 2014 0.65 310 399 2.58 1.79
    1880 to 2014 0.94 283 399 2.74 1.89
    Average – – – 2.65 1.83

    Of course, the above must assume the temperature data is correct and temperature increases are all due to CO2. The reduction of the temperature slope due to ocean heat storage is mostly gone in about 20 years depending on the depth of the mixing layer.

    Note: The above is taken from part of a submission to this a website that was not used.

    • “Much less than the IPCC 4.5 value.”
      That is the upper extreme. The IPCC range is 1.5 to 4.5, so this estimate is within it. But it is also right outside of Lord M’s 1.09 to 1.23 range (calculated by a professor of statistics).

      • My estimates, based on data, include the urban heat effect that some feel is significant and other factors that I have no way of knowing. So my estimates could be high. But still much less that what most of the dire predictions are based on. This is coupled with estimates that assume all emission increases end up as more CO2 rather than much being absorbed, further increasing estimates of future warming.

    • That is a completely different approach to Lord Monckton’s, and it has its merits. Its demerits, however, are first the choice of endpoints, second the assumption that all other things are equal, and third that it gives Transient Climate Response which is generally thought to be less than Equilibrium Climate Sensitivity.

      Despite all that, I agree that your data support an ECS of below 2.5K.

      • Note my last sentence: “The reduction of the temperature slope due to ocean heat storage is mostly gone in about 20 years depending on the depth of the mixing layer.”

        In other words, the transient and equilibrium temperature responses are now basically equal for rates of temperature increases.

        The primary difference in transient and equilibrium temperature responses to a doubling of CO2 (a step function) is the delay because of heat absorption on the oceans. And any positive feedback will increase this delay. However, the temperature data usually taken is the rate of warming, such as degrees/decade. This value trends to be constant with an exponential increase of CO2 combined with a log response of temperature to CO2 content (a ramp function of temperature vs. time). I have done modeling with both step and ramp functions of input heat forcing to the ocean and heat loss to the atmosphere with a typical mixing layer of 50 meters (a large heat capacitor) and a variable number mixing layers down to 1000 meters, each layer with a thermal resistance and heat capacity that together cause delay and attenuation of the heat absorption.

        When the heat input ramp begins, the temperature rise rate after about 20 years is nearly the same as if there was no heat absorbed by the ocean. Since the ramp of CO2 increase is now at least 60 years old, the transient and equilibrium temperature responses for rate of temperature increases are nearly the same for a constant rate of CO2 increase.

    • To Richard P.:
      “”All warming due to CO2” – as assumption! This is important. Because it is a wrong assumption. The warming is a result of Earth orbital oscillations.
      See: http://www.knowledgeminer.eu/climate-papers.html, Climate Recognition Paper part 8, 1600-2050.

      Furthermore: The climate sensitivity value was developped by Schneider and Maas. This value is entirely
      wrong, based on physical grounds. See G. Kramm and G.Gerlich, explained in detail.

      As all warming is wrongly attributed to CO2, then, logically, it is waste of time calculating further into this assumed sensitivity direction.

    • I think this is estimating TCR, not ECS.

      The IPCC says that TCR is likely to be between 1°C and 2.5°C, so your estimates are pretty much in the center of that range.

        • Claes Johnson remains for me the leading voice on the Climate Modelling question along with Geoffrey Glassman.
          https://claesjohnson.blogspot.com/2011/01/greenhouse-effect-debate.html

          MÅNDAG 31 JANUARI 2011
          Greenhouse Effect Debate
          Judy Curry has opened a debate on the book Slaying the Sky Dragon: Death of the Greenhouse Gas Theory, focussing on my two chapters
          Computational Blackbody Radiation
          Climate Thermodynamics
          I look forward to a hopefully constructive lively discussion. Science does not thrive under dead
          silence. In particular, I hope that Spencer, Lord Monckton, Lindzen and other leading skeptics will give the debate some attention.

          My perspective is mathematical including both mathematical modeling and computation. I believe that physics must be expressed in mathematical terms, typically as differential equations, to have a precise meaning, and that understanding physics basically boils down to understanding mathematical models of different physical real phenomena, in the spirit of Dijkstra.

          I give different presentations of the underlying idea of computation of finite precision in posts on thermodynamics, blackbody radiation, greenhouse effect and climate on this blog and in My Book of Knols and under “books” on my home page.

          I repeat that I do not say “that there is no greenhouse effect” since the “greenhouse effect” is not well described in the literature. So anyone preparing to accuse me of “denying the greenhouse effect” should also prepare to tell me what sort of “greenhouse effect” I am supposed to deny. “Greenhouse effect denier” has the same value as “climate change denier”.

          What I am saying is that there is no backradiation, because that would correspond to an unstable physical phenomenon, as unstable and unphysical as “backdiffusion” or “backconduction”.

          What I am saying is that radiation alone without thermodynamics cannot tell anything meaningful about climate. A no-feedback sensitivity of + 1 C is just a formality or definition without any connection to reality, as non-informative as the statement that there are 100 centimeters on a meter, with its nature of definition signified by the message that it is “unassailable”. Anything “unassailable” is a definition and a definition carries no information about reality. This is important to understand for both CO2 alarmists and skeptics, since CO2 alarmism starts with the basic postulate of a no-feedback climate sensitivity of + 1 C, which is then jacked up to + 3 C by positive feedback. Without the + 1 to start from, CO2 alarmism has to start feedbacks from 0, which is a completely open game with not even the sign being known.

          Review of the debate after 83 comments Jan 31:
          None of the big skeptics has had anything to say. Only Judy Curry who agrees that something is wrong with the Kiehl-Trenberth energy budget, but does not want to tell what.
          Of course Monckton and Spencer do not want to answer any of my questions, or Lindzen…
          If you are a skeptic then you pose questions, and of course do not answer any, just like a professional journalist or Freudian therapist. But scientists need to answer questions.
          Mostly confusing remarks as if my message has not be absorbed at all. Absorbitivity = 0.
          The “greenhouse effect” is strong and healthy science, although the equations are missing.
          Judy Curry clarifies and says that the KT budget with backradiation is basically correct.
          Summary of my position Febr 1:
          Radiative heat transfer is carried by electromagnetic waves described by Maxwell’s equations. The starting point of a scientific discussion of radiation should better start with Maxwell’s equations than with some simplistic ad hoc model like the ones typically referred to in climate science with ad hoc invented “back radiation” of heat energy. If there is anything like “backradiation” it must be possible to find it in Maxwell’s wave equations. In my analysis I use a version of Maxwell’s wave equations and show that there is no backradiation, because that would correspond to an unstable phenomenon and unstable physics does not persist over time.
          Climate results from thermodynamics with radiative forcing, and radiation alone cannot tell anything of real significance, such as the effect of changing the atmospheric radiative properties a little: It is not clear if more clouds orwater vapour will cause global cooling or warming, or the effect of a small change of CO2. Climate CO2 alarmism is based on a postulate of a climate sensitivity of + 1 C which is a formality without known real significance.
          I welcome specific comments on these two points.

          • This appears to be yet another tiresome attempt to flog the dead horse “There is no greenhouse effect”. Time and time again it is explained to those who flog that dead horse that the greenhouse effect does not, repeat not, repeat not operate by way of back-radiation. It operates at the quantum level when a photon in one of the absorption bands of CO2 interacts with a CO2 molecule. The collision induces a quantum oscillation in the bending vibrational mode of the molecule (which, due to the disposition of its atoms, does not in itself possess a dipole moment), and that oscillation is by definition heat.

            As Professor Christopher Essex puts it, it is like switching on trillions of tiny radiators, which emit heat in all directions. By processes that are near-exclusively non-radiative – e.g. subsidence and precipitation – the heat from some of these collisions is transferred throughout the atmosphere. Maundering on about “back-radiation” is, therefore, off the point.

            It is also off topic. Here, we are considering not the directly-forced warming but the consequential feedbacks.

  47. Saturation of the CO2 reflection bands by water vapor destroys the whole exercise. A saturated system has zero gain (or very close to zero).

    • In response to Mr Simon, the saturation only obtains at or near the surface. Higher up, where the atmosphere is drier, there is no saturation. However, in the tropical mid-troposphere, where the bulk of the warming caused by the water-vapor feedback is supposed to originate, there has been a decline, rather than the predicted strong increase, in specific humidity, greatly reducing the impact of the imagined (and largely imaginary) water vapor feedback.

  48. A lot has already been discussed but I’ll add my few observations.

    First, I can usually best any typical warmist but when I come to this site I can find some who I would have difficulty arguing with, Nick being one of them.
    So I was intrigued when I saw his post and read it. I got lost quickly as I’ve never had calculus but this is what I surmised from the article: All things that go into temperature outside of CO2 can be considered “noise” or a set of variables that don’t matter much. And so a linear equation can be used to show that if CO2 increases so does the temperature.

    That is what Nick’s post boiled down to me. And as having studied astronomy and having some science background I felt this was a very simplistic view that doesn’t account for any other variables such as the sun. I want to thank Christopher Monckton as I was at least able to follow the logic of his thought. I have been a skeptic for a long time, since the change from global cooling to warming I realized they had no idea of what they were talking about. Then following the subject for years and reading that, during the period when they were saying our ice cap was shrinking it was also noted that the ice cap on Mars was shrinking, hmmm, maybe it has nothing to do with CO2 I thought but maybe the sun? Then reading about ice core samples that showed CO2 PPM in the 3000-5000 ranges during periods where it was estimated were colder than current, hmmm, maybe CO2 has little to do with our temperature, maybe it is more driven by solar radiation?

    Anyway, I want to thank both Nick and Christopher for the lively back and forth as I enjoy reading this site even if the math and science goes beyond my understanding. 🙂

    • Many thanks to Mr Capricci for his kind comments. Unfortunately, feedback theory is not at all easy to understand, which is why – in our submission – climate science has gotten it so wrong for so long. It will be good to get proper peer review of our paper, so that we can see who is right. And I hope that, now it is becoming known that the police are beginning to take an interest in those aspects of the global-warming case that are fraudulent, those who have by their action or inaction perpetrated and perpetuated the fraud will think twice and thrice before continuing to do so.

  49. Lord Monckton is correct to identify a big error in climatology’s treatment of feedbacks.
    However the next step is to realise that feedbacks in a dissipative open chaotic system lead to complex oscillatory behaviour. As Lorenz showed in 1961 (Deterministic Nonperiodic Flow).
    Miskolczi grasped this, that the atmosphere chaotically selfregulates and overall radiative balance is maintained regardless of small increases in trace gasses.

    Miskolczi’s analysis based on actual radiosonde atmospheric data, showed that at present CO2 concentrations, the radiative warming effect is saturated, because the atmospheric heat engine is always striving to maximize the dissipation of surface heat into space. In the present circumstance, any additional input of heat produces a reaction of additional evaporation or convection to restore the energy balance. Radiative equilibrium is not disturbed, as shown by the stability of the optical depth in the upper troposphere.

    Miskolczi’s insigt means that the land-sea surface heats the atmosphere only by evaporation, conduction, and subsequent convection, not by radiation. The layer of air in contact with the surface is in radiative equilibrium, so that warming and cooling of the surface is matched by the immediate air. The land-sea surface does not cool by radiation to the atmosphere, nor is it warmed by “back-radiation.”

    Above the surface-air boundary, heat exchanges between layers of air do include radiative activity, and at the TOA it is all radiation into space. The dissipative-nonlinear climate system makes regulatory adjustment to compensate for changes in CO2 with changes in humidity and clouds, in order to most efficiently convert short wave incoming solar energy, into long wave outgoing energy. With warming and cooling periods, the proportions of H20 and CO2 at the TOA have fluctuated, but the combined optical depth has been stable over the last 60 years.

    • Mr Salmon has rightly identified the key evidence for Miskolczi’s case, which is that the optical depth – as far as we can measure it – has remained stable, when theory dictates that it should decrease with warming. However, it is difficult to prove Miskolczi’s case due to uncertainties in measurement. That is why we have adopted the theoretical approach of demonstrating that official climatology has incorrectly defined temperature feedback, and that, in consequence, the global warming predicted by the models is thrice what is occurring, and thrice what the corrected theoretical approach would lead us to expect.

    • Thanks, that’s a helpful clarification. Are people still making radiosonde measurements in an attempt to confirm or disprove Miskolczi?

      BTW I attended a Prep School near Bath, UK called Monkton Combe Junior School, in Combe Down. Is your title linked to that Monkton, or a different one (containing a “c”)?

  50. https://claesjohnson.blogspot.com/2013/11/standard-calculus-as-ill-posed-unstable.html

    Standard Calculus as Ill-Posed Unstable Backward Magic

    Jacques Hadamard (1865-1963) was a gentle man with strong opinions on mathematics.

    Previous posts on the Fundamental Theorem of Calculus have exposed two approaches to the connection between primitive function/integral x(t), derivative Dx=dxdt and integrand v(t) connected by the equations:
    Dx(t)=v(t)
    x(t)=∫t0v(s)ds.
    In the standard approach as presented in e.g. the standard text book Calculus: A Complete Course by Adams and Essex, the integral x(t) as an area under the graph t→v(t) is the primary given object and the proof of the Fundamental Theorem consists of showing that x(t) satisfies the differential equation Dx=v.
    https://claesjohnson.blogspot.com/2013/11/standard-calculus-as-ill-posed-unstable.html
    Claes always seemed to have rather a good point with this.

  51. https://claesjohnson.blogspot.com/2013/11/standard-calculus-as-ill-posed-unstable.html

    Standard Calculus as Ill-Posed Unstable Backward Magic

    Jacques Hadamard (1865-1963) was a gentle man with strong opinions on mathematics.

    Previous posts on the Fundamental Theorem of Calculus have exposed two approaches to the connection between primitive function/integral x(t), derivative Dx=dxdt and integrand v(t) connected by the equations:
    Dx(t)=v(t)
    x(t)=∫t0v(s)ds.
    In the standard approach as presented in e.g. the standard text book Calculus: A Complete Course by Adams and Essex, the integral x(t) as an area under the graph t→v(t) is the primary given object and the proof of the Fundamental Theorem consists of showing that x(t) satisfies the differential equation Dx=v.
    https://claesjohnson.blogspot.com/2013/11/standard-calculus-as-ill-posed-unstable.html
    Claes always seemed to have rather a good point with this.
    Certainty about uncertainties

    What of the uncertainties in our result? Some of the official input values on which we have relied are subject to quite wide error margins. However, because our mid-range estimate of Charney sensitivity is low, occurring at the left-hand end of the rectangular-hyperbolic curve of Charney sensitivities in response to various values of the feedback fraction, the interval of plausible sensitivities is nothing like as broad as the official interval, which I shall now demonstrate to be a hilarious fiction.

    clip_image004

    The Charney report of 1979, echoed by several IPCC Assessment Reports, gives a Charney-sensitivity interval 3.0 [1.5, 4.5] K. The 2013 Fifth Assessment Report retains the bounds but no longer dares to state the mid-range estimate, for a reason that I shall now reveal.
    is it only me that sees Claes observation to the general Mathematics and the specifics in Image oo4 above?

  52. Milord,

    In response to Paramenter, I don’t suppose it will be as easy as all that. Official climatology simply does not realize that the feedback processes present at any moment must respond not merely to some small and arbitrarily-defined fraction of the reference signal but to the entire signal […]

    Sooner or later they start to realise that. This truth will be also leaking into the public domain, even without formal article published (this blog may plays small role in this). I know that getting your article publish will be a mammoth task. We’re dealing with determined and ruthless defenders of the party line. I’m afraid some of them share Pilate worldview (‘what is the truth?’) what won’t make things easier. Still, good to know that you’re pursuing!

  53. Dear Lord Monckton,
    I see that you defend well your analysis of feedback and climate sensitivity, showing that in official climatology their calculations were done with numerous errors.
    I hope that you succeed in this undertaking and that a revision of official numbers will be the result of your efforts.
    I therefore understand that you leave the question whether climate sensitivity does exist or not aside and rather concentrate onto the errors in official sensitivity and feedback calculations.
    This post should, however, also be taken as opportunity to point to additional directions in research.
    According to Gerlich, Kramm et. al., the climate sensitivity is based onto the formula proposed by Schneider and Maas, and this formula is plainly wrong. And therefore all subsequent calculations with a wrong root MUST therefore also be wrong, and even increase in wrongness. And there is no such thing as an accumulation of “wrong” to make one “right”, no matter the amount of calculations done with 10, 30, 50% wrongness subtracted or added.
    To my research: Earth orbital perturbations in decadal/centennial size, which can eactly be calculated, are the true cause of the the temperature increase in the past. The low point was in 1610, with the Sun-Earth distance largest at the both ends of the minor [not major! axis, which is constant], therefore the coldest decades in the 17. century. The high temperature peak will be 439 years later, at 2049, with the shortest Sun-Earth distance at both ends of the minor axis of the Earth orbit. And the temperature increase since the 17. century is exactly in size what the orbital values demand. Therefore, there is NO place for CO2 and NO warming effects caused by CO2. All warming is entirely covered by the Earth orbital perturbations.
    At the moment, we are entering a warming temperature plateau for the next 30 years until the peak in 2049, with an average temperature level of 0.25 – 0.30 C above the 30 year running mean. See for yourself: The temperatures in the coming years will remain plateau and not increase.
    The literature see http://www.knowledgeminer.eu/climate-papers.html,
    Climate pattern recognition,PART 8, also PART 1-7 for covering the entire Holocene.
    The scientific temperature calculations are given in a separate booklet.
    best regards JS.

  54. I’m not going to respond to Lord Monckton’s most-recent distortion of what I’ve said. But for the sake of any lurkers I’ll make one observation.

    A recent addition to his arguments for near linearity is the IPCC’s statement that certain parameters are “nearly invariant.” But that statement neither intentionally nor accidentally implies linearity. The IPCC was merely saying that the temperature a given model says is caused by a given increment of forcing seems not to depend on whether that forcing increment results from a change in, say, albedo instead of greenhouse-gas concentration. Furthermore, the IPCC was probably focusing only on small forcing increments that occur in a global-average-surface temperature regime within a few degrees of those that prevail now.

    Independently of whether that was its focus, though, there’s no reason to interpret “nearly invariant” as meaning that all modes’ common incremental response could not be very different at much lower temperatures; as I explained to him before, invariance is orthogonal to linearity. Lord Monckton’s failure to grasp this concept, which at least as to time invariance is among control-systems theory’s most basic, shows yet again how woefully unqualified he is to pontificate as he endlessly does about that discipline.

    I might add in passing that this isn’t his first invariance problem. In his execrable paper “Why Models Run Hot: Results from an Irreducibly Simple Climate Model” the central equation’s fundamental error was to treat a time-invariant system that has memory as though it were a memoryless time-variant system. So far as I can tell he’s learned nothing in the four years since.

    • Joe,
      I say with the greatest respect that I would strongly recommend that you tone down the personal content. While I can sympathise with the frustration you are feeling, and I recognise that some/many of your responses are reactive, your venting your frustration in intemperate personal insults serves no useful purpose. Please think about what you are trying to achieve. The anger in your posts positively inhibits your ability to convince any readers of the validity of your views – and I do accept the validity of most of your mathematical arguments – and it only serves to evoke a bad response from Lord Monckton. (Please don’t tell me you believe that you have just cause. That is really not the issue.)

      I would also invite you to consider the likelihood that Lord Monckton is honestly presenting his beliefs, and that the biggest problem is that you are talking past each other using quite different languages which just happen to look like English.

      On a different point, as a result of your comment about “Why models Run Hot…”, I took a look at the paper for the first time. Yes, you are correct that the paper is founded on a memoryless model (which is difficult to support). It requires a convolution or superposition formulation to calculate transient temperatures from the arbitrary forcing series used as input, and not a rescaling of a linear relationship between forcing and temperature – which I understand to be your main point. Secondly, the “transience fraction” has to do a lot of work to try to make the linear relationship between temperature and forcing look like the convolution solution. In particular, it is not just a function of time and total feedback; it is a strong function of ocean heat capacity and the rate of heat exchange with the deep ocean – which are not parameterised in the base equations and which were not investigated in the text. Thirdly, I can see no benefit in expressing the total feedback as a gain term. The authors would have got the same results, all else being equal, if they had just left the total feedback term in their base Eq 1, without expressing it as a factor of a reference feedback. However, this third point did give me what I hope is insight into where Lord Monckton is coming from and how he got to where he is. I may yet be able to change his paradigm.

      • “I would also invite you to consider the likelihood that Lord Monckton is honestly presenting his beliefs.”

        Believe me, I have considered that possibility. And I think that to a degree he actually does believe he knows what he’s talking about. He would be far from the only person who honestly thinks his talent for rapidly regurgitating facts is the same as being good at understanding their implications. Moreover, I’ll admit that I’m not as innately patient with such people as I wish I were.

        Still, in most contexts I make an honest, and I believe usually successful, attempt to combat that impatience by regularly calling to mind Max Ehrmann’s advice that we “listen to others, even the dull and the ignorant; they too have their story.” Indeed, for years I attempted despite Lord Monckton’s vitriol to nudge him gently toward more-rational views—to the extent that it was remarked upon at the time: https://wattsupwiththat.com/2013/11/21/on-co2-residence-times-the-chicken-or-the-egg/#comment-1142100.

        But he has evaded and mischaracterized my arguments so consistently for so long that there’s no chance he’s being honest in his arguments. A few examples of how evasive and deceptive his responses have been are found at https://wattsupwiththat.com/2015/03/16/where-the-complex-climate-models-go-wrong/ and https://wattsupwiththat.com/2015/04/05/a-reply-to-born-how-to-represent-temperature-feedbacks-in-a-simple-model/.

        Despite that I might have persisted in biting my tongue if there weren’t another factor. It has become apparent that at this site there are very few people who, like you and Greg, can comprehend much about feedback. Indeed, few seem to have patience with even a single algebraic equation, much less calculus or differential equations (which, fortunately, haven’t come into play here).

        So the majority of this site’s readers are completely vulnerable to being swayed by atmospherics. Many are accordingly being badly misled; some have offered Lord Monckton financial support. Since objective facts and incontrovertible math therefore have little effect, the best I can do for them is express how outrageously wrong his theory is and hope that the scales fall from the eyes of one or two readers at least.

        I appreciate your thoughts. And in your position I might have thought the same thing—had my experience with him had not been so extensive and so uniformly unedifying. (If I recall, in fact, I myself may once have suggested overlooking his lack of courtesy.)

        Under the circumstances, though, I think I’ll continue to be plain about his evasiveness, dishonesty, and lack of knowledge.

        • Sorry to break this to you Joe but nothing that you or anyone that you know has ever written on climate feedbacks is worth the paper it’s printed on or the thumb-ATP consumed posting it. It all assumes linearity and equilibrium. The climate is a nonlinear far from equilibrium system. In such a system the role and effect of feedbacks is fundamentally different. Negative feedbacks exert friction and cause complex emergent pattern. Positive feedbacks cause collapse of such patterns and monotonic oscillations. Consider their role for example in the monotonic oscillation of Cepheid variable stars.

          Everything written on climate dynamics that is not built on the understanding that it is a dissipative periodically forced nonlinear chaotic system is irrelevant fiction. Probably a few million years of wasted human effort. A good point to go back to would be Ilya Prigogine’s nonlinear thermodynamics, and then, if you have the stomach for it, Miskolczi.

          • Sorry folks, you all are wrong! Why? Because the Earth orbit perturbations are entirely omitted in
            proposed calculations. The Earth´s flight around the Sun is a screw-type, spiral advance on its
            elliptic path, which means that Earth constantly deviates to either left, right, above and below
            the calculated elliptic path. And this shortens and lengthens on decadal and centennial scale the
            distance Sun-Earth, thus increasing and decreasing temperatures on Earth. And this on significant
            scale, see temp increase from the 17 to the 21st century (here: distance shortening).
            And this temperature increase caused by distance shortening is by collution kept under the table, in in order
            to attribute the observed warming to atmospheric feedbacks and sensitivities, on which you
            all waste your time trying to derive a correct calculation approach, which is futile because of
            omission of major climate variables od the Earths flight,
            More on this, see http://www.Climate Pattern Recognition, part 8 and also 1, here empirically
            derived over 10,000 years of the entire Holocene.
            f

          • In response to Mr Seifert, there are many things wrong with official climatology’s approach, but the focus of the head posting was on just one of these things: the incorrect definition of temperature feedback in official climatology.

            If Mr Seifert can refer me to peer-reviewed papers in respected astronomical journals quantifying the influence on terrestrial temperature of the Milankovich cycles – and specifically the variations in the eccentricity of the Earth’s orbit, which seem to be his present focus – I should be most grateful.

            From my recollection, though, the Milonkovic cycles operate on timescales of thousands of years: therefore, they are not good for explaining the short-term temperature fluctuations with which we are at present concerned.

          • Dear Lord Monckton,

            the literature question was just explained by me as a separate comment, instead of
            a reply comment within the Salmon comment.
            And, as I read your questions once more over: The osculating Earth orbital flight has nothing to do with eccentricity changes. Eccentricity of the orbit is uninteresting for the osculating Earth flight advance, because eccentricity changes are millenium- scale thus too small for a centennialscale and do not affect the spiral orbital flight.

        • Joe
          I went too far in my language in the above post which I regret. I sometimes over-react when someone I admire is attacked.

          However I strongly believe there is an issue here which goes beyond the climate and CO2 debate. It’s about how the global scientific community has absorbed – or failed to absorb – the discoveries and new theoretic paradigm of chaos and nonlinearity. For various reasons many fields of research have ignored chaos and nonlinear dynamics, to their detriment.

          Imagine the following.
          the scientific community superficially accept discoveries by Galileo, Kepler et al., that the earth is not static and orbits the sun. However, despite this, researchers continue to work on epicycles and a geocentric model of astronomy.
          Or that the discovery of chemical elements and Mendeleev’s periodic table is accepted; but that there is no pause in research into alchemy and the attempts via physical and chemical methods – with a little sorcery added – to transmute lead into gold.
          Or alternatively, while the proof of former ice ages, by Agassis and others, and the discovery by geology of rock strata showing the age of earth to be billions of years, are accepted, there is no interruption in research into Noah’s flood as a cause of present day geography.

          Something similar to this has happened in regard to the discoveries by Mandelbrot, Turing, Feigenbaum, Lorenz and many others concerning the role of chaos and edge-of-chaos nonlinear pattern formation in many natural processes as well as living organisms. Superficial acceptance is given to these discoveries. But fields of research such as climate, whose complex systems are grounded on such chaos-related phenomena, are proceeding as if chaos and nonlinearity did not exist. Only a few restricted fields such as chemical engineering and population ecology actually accept chaos and nonlinear dynamics at the heart, not the periphery, of what they are studying.

          Feedbacks are fundamental to spontaneous nonlinear pattern formation in a far-from-equilibrium system. And the paradigm and body of theory of dynamic feedbacks is totally different for such quasi-chaotic systems compared to linear systems at equilibrium. This affects how we interpret feedbacks in the chaotically churning atmosphere-ocean climate system.

          I get the feeling that science as a whole exerts a continual selection, perhaps unknowingly, where they confine their efforts to linear and equilibrium approximations of complex systems and choose research projects where they don’t have to invoke chaos/nonlinear dynamics. And often chaotic theory is wrongly excluded where it is at the heart of how a particular system behaves.

          Part of this is linked to a separation of mathematics and physics, politically and culturally, that took place during the 20th century. This is described nicely in James Gleik’s book “Chaos”.

          For example, if there had been a proper appreciation of chaotic dynamics in the climate system, especially the ocean, then the correlation of rising temperature and rising CO2 in the 20th century would not have been uncritically accepted as proof of CO2 forcing of climate. The concept of the null hypothesis together with an understanding of chaotic ocean dynamics, might have prompted a much more serious evaluation of whether the 20th century climate oscillations were not of the same natural kind that have always been continually happening, unrelated to CO2.

    • Mr Born imagines that IPCC’s account of the near-invariance of the climate-sensitivity parameter, and, therefore, of the system-gain factor and the feedback fraction does not also encompass near-linearity in the response function. However, the approximate value of that parameter is stated as about 0.5 Watts per square meter per Kelvin, which would not make a whole lot of sense if the parameter were to vary significantly over time.

      Exegesis of the inspissate holy books of IPeCaC is far from easy, so the approach we took was to take forcings and temperature changes every decade in the two growth scenarios – RCP6.0 and 8.5 – and calculate therefrom the feedback fractions for successive 30-year periods fro 2010-2040 to 2070-2100. The feedback fractions varied only from 0.41 to 0.55. From this it follows that official climatology does indeed expect the response function to be near-linear, as one would deduce from the fact that the climate-sensitivity parameter is near-invariant.

      • … and calculate therefrom the feedback fractions for successive 30-year periods fro 2010-2040 to 2070-2100. From this it follows that official climatology does indeed expect the response function to be near-linear, as one would deduce from the fact that the climate-sensitivity parameter is near-invariant.

        But isn’t there a difference between expecting something to be near-linear over a range of a few degrees, and being near linear from 0 – 265K?

        • In response to Bellman, we have assumed that emission temperature is 255 K (our calculations lead us to suspect it is actually more like 276 K once Hoelder’s inequalities between integrals have been allowed for). We have also taken 10 K as the directly-forced warming from the noncondensing greenhouse gases present in 1850. Therefore, the reference temperature in that year – i.e., the temperature that would then have obtained in the absence of temperature feedback – was 265 K. However, the observed equilibrium temperature was 287.5 K. The entire difference between these two values is attributable to feedback.

          Official climatology imagines that the entire 22.5 K feedback response in 1850 was driven by the 10 K warming forced noncondensing greenhouse gases, and that none of it was driven by the 255 K emission temperature (which, once one allows for Hoelder’s inequalities between integrals, is actually more like 276 K).

          The simplest approach is to recognize that the ratio of equilibrium to reference temperature in 1850 was incontrovertibly 287.5 / 265, or 1.085. We need not concern ourselves with what might have happened at 0 K, for two reasons: first, the values of reference and equilibrium temperature in 1850 are known and quite well constrained, so we know what the system-gain factor was in that year; and secondly, at 0 K temperature the feedback response would also be 0 K, for that is a characteristic of feedback response curves, for rather obvious reasons.

          The feedbacks present in 1850 operated in proportion to the respective contributions to reference temperature of emission temperature and of the warming forced by the pre-industrial noncondensing greenhouse gases.

          Now, since the climate-sensitivity parameter is near-invariant, it follows that the curve of the equilibrium-temperature response function is near-linear. From that, we infer – legitimately – that the equilibrium sensitivity to doubled CO2 will be the product of the reference sensitivity thereto, which is 1.05 K, and the system-gain factor 1.085 that obtained in 1850. The system-gain factor will not have changed much since then.

          We calibrated that result in two ways. First, we noted that the industrial-era net anthropogenic forcing to 2011 was about 2.5 Watts per square meter and the radiative imbalance due to the large heat capacity of the ocean was about 0.6 Watts per square meter. The system-gain factor in 2011, on the basis of these published estimates, is simply 2.5 / (2.5 – 0.6), or 1.316, quite close to our 1.085 and not at all close to official climatology’s imagined 3.2.

          Then we calculated the system-gain factors for successive 30-year periods from 2010-2040 to 2070-2100, based on predicted RCP6.0 and RCP8.5 forcings and temperature responses. The typical value was around 2.0, implying Charney sensitivity of about 2.1 K, which is right at the bottom of the CMIP5 interval.

          All of these considerations rule out the high sensitivities on which the current genocidal climate mitigation policies are based.

          • Thanks for the reply. For the sake of your figures might I suggest you don’t have to repeat all your calculations for each response.

            My question was about why your assumption of a linear relationship between feedback processes over a range from 0K to 256K, and I don’t think you really address that issue beyond repeating that assertion.

            The simplest approach is to recognize that the ratio of equilibrium to reference temperature in 1850 was incontrovertibly 287.5 / 265, or 1.085. We need not concern ourselves with what might have happened at 0 K, for two reasons: first, the values of reference and equilibrium temperature in 1850 are known and quite well constrained, so we know what the system-gain factor was in that year; and secondly, at 0 K temperature the feedback response would also be 0 K, for that is a characteristic of feedback response curves, for rather obvious reasons.

            So you have two points, (0,0) and (265, 287.5) and can fit an infinite number of curves through those points. But you assert that only near-linear curves are valid.

            To me, with no specialist knowledge, it just seems unlikely that feedback processes would follow a simple curve, let alone a straight line.

            The feedbacks present in 1850 operated in proportion to the respective contributions to reference temperature of emission temperature and of the warming forced by the pre-industrial noncondensing greenhouse gases.

            You are again asserting that feedback operated “in proportion”, without explaining why.

            Now, since the climate-sensitivity parameter is near-invariant, it follows that the curve of the equilibrium-temperature response function is near-linear.

            Again, an assertion that the climate-sensitivity is near-invariant. As I originally asked, why assume that near-invariant over a range of a few K, under real world conditions, must mean near-invariant between 0K and 255K?

            The system-gain factor will not have changed much since then.

            Why not?

            I find it difficult to believe that the various feedback processes would behave in the same way at say 100K, as they do at 256K.

            The system-gain factor in 2011, on the basis of these published estimates, is simply 2.5 / (2.5 – 0.6), or 1.316, quite close to our 1.085 and not at all close to official climatology’s imagined 3.2.

            I can’t say if this is correct, but the fact that by 2011 you’ve quadrupled the feedback value doesn’t suggest it’s near-linear.

            The typical value was around 2.0, implying Charney sensitivity of about 2.1 K, which is right at the bottom of the CMIP5 interval.

            But 2.1 K is well outside your ECS interval of [1.09, 1.23].

          • In response to Bellman, it should now be clear 1) that the system-gain factor in 1850 was 1.085; 2) that the feedbacks then present, which acted upon the entire reference temperature, acted proportionately at that moment, so that close to 22 K of the feedback response to reference temperature was response to the 255 K emission temperature, and less than 1 K was response to the preindustrial greenhouse-gas warming of 10 K (this is an elementary consequence of the fact that the feedback loop responds to the entire reference temperature); 3) that, on the generous assumption that IPCC’s midrange estimate of net anthropogenic radiative forcing to 2011 was 2.5 Watts per square meter, and that the radiative imbalance was as much as 0.6, the implicit system-gain factor was only 1.316, closer to our 1.085 than to the predicted midrange estimate 3.35 K in the CMIP5 ensemble; 4) that IPCC considers the climate-sensitivity parameter to be near-invariant, which necessarily implies that the equilibrium-sensitivity response function is near-linear; 5) that IPCC’s exaggerated predictions of 21st-century warming demonstrate a very near-linear evolution of the system-gain factor; 6) that even those exaggerated predictions only imply a 2.1 K Charney sensitivity, at the very bottom end of the CMIP5 predicted range, though the system-gain factor cannot have been as high as 2 because the equilibrium temperature in 2011 would then have been greater than 530 K, which it was not; 7) that it does not matter what happened at 0 K or 100 K, because we know what happened at 265 K, and official climatology assumes that the evolution of the response function since then is near-linear; 8) that the system-gain factor for 2011 cannot have have as high as the 1.316 implicit in IPCC’s midrange estimate of net anthropogenic forcing to that year because 1.316 times the reference temperature of 265.75 K in 2011 is approaching 350 K, and the Earth is nothing like that hot.

          • 7) that it does not matter what happened at 0 K or 100 K, because we know what happened at 265 K, and official climatology assumes that the evolution of the response function since then is near-linear;

            This is the nub of the problem. I, and others who have raised the problem before, think it does matter what would have happened at 100K. Your argument for a feedback of 0.085K for each K rise in reference temperature is based on averaging the warming caused by feedbacks in 1850 by the entire 256K of reference temperature. This makes the implicit assumption that the feedback responses are identical across all temperatures from 0K on.

            If in reality there would not be 8.5K of feedback warming with a reference temperature of 100K, then it follows the average is not meaningful across the temperature spectrum and you cannot deduce from it how much feedback response there will be when going from say 265K to 266K.

            As you demonstrate in points 6 and 8, the assumption of a linear feedback response for all temperatures leads to absurdities. Much more plausible to my mind to accept that the feedback response at 265K is different to the average.

          • Bellman has not, perhaps, understood that, since the usual value of the emission temperature that would have obtained in the absence of any feedback is 255 K, and the usual value of the warming occasioned by the presence of the preindustrial noncondensing greenhouse gases to 1850 is 10 K (giving a reference or pre-feedback temperature of 265 K in 1850), and since the equilibrium temperature in 1850 was measured as 287.5 K, it follows that in 1850 the ratio of equilibrium to reference temperature – the system-gain factor – was 287.5 / 265, or 1.085. No ifs, no buts, no maybes: that’s what it was.

            The only way to dispute that fact is to assert that 255 K, 10 K and 287.5 K are incorrect values. If they are accepted as correct, than the system-gain factor was 1.085.

            Next, it is necessary to address the question whether the system-gain factor is likely to prove invariant over the next two or three degrees of global warming. The answer is Yes, because official climatology finds the climate-sensitivity parameter to be near-invariant (see IPCC 2007 ch. 6 passim, or notice that the ratio of predicted transient warming to predicted net anthropogenic radiative forcing in the RCP6.0 and 8.5 scenarios for 30-year or 60-year periods throughout the 21st century from 2010-2100 is near-invariant), from which it necessarily follows that the system-gain factor is near-invariant.

            Accordingly, Charney sensitivity is simply the product of the 1.05 K reference sensitivity to doubled CO2 and the system-gain factor 1.085, giving 1.15 K, or thereby.

            It simply does not matter what might have happened at 0 K or 100 K or 200 K or some other arbitrarily-chosen value <255 K. What we are concerned with are the feedback processes that obtained from 1850 onward, in the industrial era. All that is necessary to establish Charney sensitivity is knowledge of the well-constrained values of reference and equilibrium temperatures in 1850 and knowledge of the 1.05 K reference sensitivity to doubled CO2, whereupon Charney sensitivity is equal to 1.05 x 287.5 / 265, or about 1.15 K. And that's a wrap.

          • It simply does not matter what might have happened at 0 K or 100 K or 200 K or some other arbitrarily-chosen value <255 K. What we are concerned with are the feedback processes that obtained from 1850 onward, in the industrial era.

            If it doesn’t matter how feedback processes respond below 255K, then what’s the point of your 287.5 / 265 formula? You are claiming you can predict how feedbacks will respond to post 1850 warming by taking an average over all temperature responses from 0K to 265K, and assuming the same average increase will happen over the next few degrees increase. If you accept that feedback processes might not have caused a proportionate response at 100K then why would you assume an increase from 265K to 266K will be equal to the average?

            Next, it is necessary to address the question whether the system-gain factor is likely to prove invariant over the next two or three degrees of global warming. The answer is Yes…

            And as I said at the start, even if the system-gain factor is invariant over the next two or three degrees, it does not follow that it is the same as the factor from 0K to 256K.

            … because official climatology finds the climate-sensitivity parameter to be near-invariant (see IPCC 2007 ch. 6 passim…

            I think you mean IPCC 2001, but no matter. As I keep saying I doubt the IPCC means that the parameter is near constant for all radiative forcings, rather than the range of forcings that the earth will actually experience.They also explain that the value is only used for a first order estimation. It seems strange to insist on the idea that \lambda must be invariant for all time and temperatures, whilst insisting it doesn’t matter what it’s real value would be below 255K.

        • Bellman asks: If it doesn’t matter how feedback processes respond below the emission temperature of 255 K, then what’s the point of deriving the system-gain factor that converts reference temperatures (before feedback acts) to equilibrium temperatures (after feedback has acted and the climate has resettled to equilibrium) as the ratio of the 287.5 K observed equilibrium temperature in 1850 to the reference temperature of 265 K that obtained that year?

          The trivial answer to Bellman’s question is that, since the reference temperature in 1850 was 10 K above the 255 K emission temperature (the 10 K being reference sensitivity to the presence of the preindustrial noncondensing greenhouse gases), it was not a temperature below 255 K.

          A more detailed answer is that Bellman has not, perhaps, understood (and, in this, he stands alongside the whole of official climatology) that the system-gain factor A – the ratio of equilibrium temperature E to reference temperature R – is not, repeat not, the secant slope of the curve of the equilibrium-temperature response function E(R). It is simply the ratio of E to R at a given moment of interest.

          Because this error is so widespread, the long version of our paper actually takes the trouble to prove what we might legitimately have simply left as a matter of definition. Briefly, the proof consists in demonstrating that the system-gain factor A is equal to 1 / (1 – f), where f is the feedback fraction (i.e., the fraction of E represented by the feedback response b), and then in formally demonstrating that, since the signal passes around the feedback loop an infinite number of times, multiplying itself by f each time, the system-gain factor A is the sum of the infinite convergent geometric series {f^0 + f^1 +f^2 + … + f^infinity} under the convergence criterion | f | < 1. Now, the sum of that power series is 1 / (1 – f). The proof that this is the case long predates the dismal science of climatology: it is, in fact, the oldest of all the proofs of the sums of infinite geometric series. However, climatologists are not necessarily familiar with the elements of number theory, which is why one of my co-authors asked me to prove the sum of the series. Once I had proven it, another co-author then asked why the proof was so detailed. I explained that the detail was necessary to establish the proposition rigorously.

          Once it is accepted – as in our submission it must be accepted – that A = 1 / (1 – f), it follows that, if for any year in the modern era we know the well-constrained values of E and R, as we do for 1850, we may at once derive the system-gain factor A that then obtained: A is simply E/R.

          What is more, if we also know that the climate-sensitivity parameter (the ratio of period equilibrium sensitivity to net period anthropogenic forcing for any given period in the industrial era) is near-invariant, without error we may state that A is the system-gain factor that will apply – say – to a CO2 doubling compared with 2011, the year to which sensitivity-relevant data for IPCC (2013) were brought up to date.

          That consideration answers Bellman's next point. He says it does not follow that, just because the system-gain factor A is invariant over the next two or three degrees' warming, A will be the same as "the factor from 0 K to 265 K". The point here is that A is not, repeat not, repeat not, the secant slope of the curve of E(R). It is not even the point slope of that curve either. It is simply the ratio of E to R at any point of interest on the curve – in the present instance, in 1850. We know the equilibrium temperature was then 287.5 K because we measured it. We know that the reference temperature was the sum of the 255 K emission temperature and the 10 K reference sensitivity to the pre-industrial noncondensing greenhouse gases. So we know their ratio. In 1850, that ratio was, as a matter of fact, 1.085, or very close thereto.

          Finally, Bellman says he doubts whether IPCC, in ch. 6.1 of its 2001 Third Assessment Report (I apologize for having inadvertently referred to the 2007 report when I meant 2001 in my earlier reply), meant that the climate-sensitivity parameter is near-constant for all radiative forcings, rather than for the range of forcings that the Earth will actually experience. If he will read the chapter carefully, he will find that it is both. The chapter is indeed principally concerned with demonstrating the utility of the concept of radiative forcing: however, an approximate value 0.5 is given for the system-gain factor. It is also true that IPCC cites some authors who say that in some circumstances and for some forcings the climate-sensitivity parameter may not necessarily be close to invariant. So we tested the values of reference sensitivity to net projected anthropogenic forcings against those of projected transient sensitivities in IPCC's Fifth Assessment Report (2013) and found that, for successive 30-year and 60-year periods in the 21st century, the system-gain factor was indeed remarkably near-invariant. In addition, we examined each of the sensitivity-relevant temperature feedbacks individually, including the Planck "feedback" that has caused some commenters here a good deal of difficulty, and found no reason to imagine that any of these feedbacks – most notably the water-vapor feedback – would be at all likely to contribute to an appreciably nonlinear feedback response.

          Bellman says: "It seems stange to insist on the idea that the climate-sensitivity parameter must be invariant for all time and temperatures while insisting it does not matter what its real value would be below 255 K. Here, he may have failed to recall that, since official climatology has hitherto unwisely confined its analysis to reference and equilibrium sensitivities to net anthropogenic forcings rather than to entire reference temperatures, when it talks of the near-invariance of the climate-sensitivity parameter it is talking only of the industrial era, and not of any period before 1850. And, as we have explained. we, too, are only concerning ourselves with the period from 1850 onward: we are not, repeat not, repeat not, repeating official climatology's mistake in assuming that the system-gain factor is the secant-slope of some segment of the equilibrium-temperature response curve E(R).

          It is quite possible – though not at all easy to demonstrate – that the system-gain factor that would obtain in the absence of the pre-industrial noncondensing greenhouse gases and, therefore, purely in response to the 255 K emission temperature is quite close to that which has obtained since 1850. The reason is that at 255 K approximately one-third of the dayside of the Earth would be ice-free, allowing all of the sensitivity-altering feedbacks listed in IPCC (2013) to operate. The water-vapor feedback would be somewhat less than at present, but the ice-albedo feedback would be quite a bit greater than at present. It is also possible that the evolution of E(R) follows an epidemic curve, and that we are now approaching the asymptote.

          Be that as it may, for present purposes it is necessary for us to demonstrate no more than that the system-gain factor A in 1850 was 1.085, that official climatology, both in theory and in its modeled predictions, treats it as near-invariant, and that it considers the reference sensitivity to doubled CO2 to be 1.05 K. From these facts, it follows that the midrange estimate of Charney sensitivity – equilibrium sensitivity to doubled CO2 – is 1.15 K.

          If Bellman considers that official climatology ought not to have relied upon a near-invariant climate-sensitivity parameter in its derivation of the equilibrium-sensitivity response curve shown in its 2013 report, he should address his concerns not to me but to the IPCC Secretariat. Our approach has been to adopt all of official climatology except what we can demonstrate to be erroneous. Our investigations of the question of nonlinearity, which were detailed and time-consuming, have led us to conclude that official climatology is right to treat the climate-sensitivity parameter as near-invariant, from which it follows that the system-gain factor will also be near-invariant.

          And this consideration answers Bellman's next point, which is that even if the A

          • The last part-sentence of my reply to Bellman, “And this consideration … “, should be delete.

          • A more detailed answer is that Bellman has not, perhaps, understood (and, in this, he stands alongside the whole of official climatology) that the system-gain factor A – the ratio of equilibrium temperature E to reference temperature R – is not, repeat not, the secant slope of the curve of the equilibrium-temperature response function E(R). It is simply the ratio of E to R at a given moment of interest.

            Regardless of how you derived the system-gain factor, you still require the function to be near-linear back to 0K. If not it’s strange how much time you’ve devoted to claiming that the curve of the response function must be near-linear and pass through (0,0).

            Your claim is that the feedback loop responds to all emission temperatures, not just to increases, so the question is do you regard the feedback fraction to be constant over all temperatures?

            If yes then it requires E(R) to be linear. If not you cannot assume that f_{265} = f_{266}, and in that case you cannot use the results from 1850 to determine ECS.

            You only need small changes in the actual feedback fraction to get very different rates of warming, so however correct you derivation might be mathematically, I don’t see how it can be useful in calculating true climate sensitivity.

            Suppose hypothetically that temperatures in the real world did rise by 3.5K after a doubling of CO2, so that at some point in the future reference temperature was 266.05K and equilibrium temperature was 291K. Your argument would be that the system gain factor would be 291 / 266.05 = 1.094. By your logic Charney sensitivity would then be 1.15K, despite the fact that observations show 3.5K warming.

          • Bellman asks whether we require the equilibrium-temperature response function to be near-linear across all temperatures. The answer is that we do not require it to be anything. However, since official climatology finds the climate-sensitivity parameter to be near-linear across the interval of interest, in the industrial era, so that the system-gain factor is also near-linear across that interval, after much investigation we agree with official climatology on that point.

            The advantage of our method is that it makes use of information discarded by official climatology in its derivation of equilibrium sensitivities: namely, the information that the system-gain factor expressed as the ratio of entire equilibrium to reference temperatures in 1850 was only 1.085, and not the 3.25 implicit in official climatology’s method.

            Bellman’s example, like all such examples that have been presented here, entails a manifest and physically-impossible contradiction. He posits official climatology’s midrange Charney and reference sensitivities respectively as 3.5 and 1.05 K. The implication is that the feedback response is the difference between these two values: i.e., 2.45 K. But then, using official climatology’s method, the feedback fraction – the ratio of the feedback response to equilibrium sensitivity – will be 2.45 / 3.5, or 0.7. Yet the feedback fraction in 1850 was only 0.08. By what physical process does he imagine that a mere doubling of CO2 concentration will engender a feedback fraction an order of magnitude greater than that which obtained in 1850?

          • As to the observations about the IPCC reports, I suppose the question I should ask is why are you referring to a 20 year old report as “official climatology”? AR5 makes no mention of the climate sensitivity parameter as being near-invariant or linear as far as I can see.

            Be that as it may, for present purposes it is necessary for us to demonstrate no more than that the system-gain factor A in 1850 was 1.085, that official climatology, both in theory and in its modeled predictions, treats it as near-invariant, and that it considers the reference sensitivity to doubled CO2 to be 1.05 K.

            Again, how can “official climatology” treat the system-gain factor as near-invariant when by your own definition “official climatology” doesn’t understand the system-gain factor. The climate sensitivity parameter that TAR describes as near-invariant is not the same thing as your system-gain factor.

            This matters because a small change to the near-invariant climate sensitivity parameter will have a proportionate effect on the climate sensitivity, but the same change to your parameter will result in a huge change to climate sensitivity.

          • Bellman:

            Suppose hypothetically that temperatures in the real world did rise by 3.5K after a doubling of CO2, so that at some point in the future reference temperature was 266.05K and equilibrium temperature was 291K. Your argument would be that the system gain factor would be 291 / 266.05 = 1.094. By your logic Charney sensitivity would then be 1.15K, despite the fact that observations show 3.5K warming.

            Well said; you put it better than I did. For anyone who can follow a logical argument, your explanation should be the end of Lord Monckton’s theory.

            Let me just add, though, that the cause of my morbid fascination isn’t that Lord Monckton nonetheless remains unpersuaded; we encounter folks all the time who display no reasoning ability. No, the thing that’s remarkable to me is how many of this site’s visitors are swayed by an argument so bereft of logic–even though many have physical-science backgrounds.

            I’ve speculated that much of the reason is his use of ambiguous formulations and idiosyncratic terminology; they mask his lack of logic. Although they make it inconvenient for people to really follow what he’s saying, readers just assume his conclusions follow from the welter of background facts that readers often recognize as true.

            As you’ve discovered, they don’t.

          • Bellman’s example, like all such examples that have been presented here, entails a manifest and physically-impossible contradiction.

            I don’t posit anything. I was trying to provide a simple example that illustrates the problem with your derivation of sensitivity. The same logic that says that it’s physically impossible for there to be 3.5K of warming after doubling of CO2 would also have to conclude that the response has to be linear since 0K.

            But then, using official climatology’s method, the feedback fraction – the ratio of the feedback response to equilibrium sensitivity – will be 2.45 / 3.5, or 0.7. Yet the feedback fraction in 1850 was only 0.08. By what physical process does he imagine that a mere doubling of CO2 concentration will engender a feedback fraction an order of magnitude greater than that which obtained in 1850?

            You’re comparing two different derivations of the feedback fraction, one of which you think is completely wrong and wonder why they are different. Applying your own derivation of the feedback fraction, the value in 1850 was 0.078, after my hypothetical 3.5K rise the fraction would be 0.086. An increase of about 10%, you could almost say near-invariant.

          • Bellman might like to explain in what respects he considers IPCC reports not to be official climatology. And, as I have explained to him before, the Fifth Assessment Report (2013) treats the climate-sensitivity parameter – the ratio of equilibrium sensitivity to radiative forcing – as near-invariant, as one may deduce from the evolution of the published values for the RCP6.0 and 8.5 scenarios (the other two scenarios find sensitivity low, as we do).

            Bellman asks how official climatology treats the system-gain factor as near-invariant, when by our definition it does not understand the system-gain factor. He is perhaps unaware that if the system-gain factor is near-invariant the values derived by our method using entire temperatures and by official climatology using sensitivities only will be near-identical.

            He also says that the climate-sensitivity parameter is not the same thing as the system-gain factor. He has not, however, spotted that if the climate-sensitivity parameter as defined above is near-invariant then official climatology’s system-gain factor must also be near-invariant, whereupon our system-gain factor will be near-invariant a fortiori because it is the ratio of temperatures that exceed by two orders of magnitude the sensitivities whose ratio is official climatology’s system-gain factor.

            Bellman says that a small change to the near-invariant climate sensitivity parameter will have a proportionate effect on climate sensitivity as derived by official climatology, but the same small change to our system-gain factor will result in a huge change to climate sensitivity. So let us do the math. We know that the system-gain factor at the equilibrium in 1850, derived by our method as the ratio of the entire equilibrium to reference temperatures in that year, was 1.085. We also know that, since the system was then in equilibrium, official climatology’s system-gain factor was also 1.085.

            Now, official climatology says that the midrange net industrial-era anthropogenic radiative forcing to 2011 was 2.5 Watts per square meter, or thereby, and that in 2010 there subsisted a radiative imbalance of 0.6 Watts per square meter, implying that climatology’s period system-gain factor was 2.5 / (2.5 – 0.6), or 1.316, implying a feedback fraction 0.240, three times the 0.078 that obtained in 1850.

            What, then, is our system-gain factor for 2011 under these circumstances? It is (287.5+1.0) / (265+0.75), or 1.0856, barely changed since 1850. However, there is no plausible physical process by which climatology’s period system-gain factor could be anything like as much as thrice the system-gain factor that prevailed at the equilibrium in 1850, and such a result would also fall foul of official climatology’s current understanding that the climate-sensitivity parameter, and therefore both climatology’s and our system-gain factors, is near-invariant.

            And even if, per impossibile, official climatology’s midrange period system-gain factor 1.316 were correct, Charney sensitivity would be only 1.316 times the 1.05 K reference sensitivity to doubled CO2 – i.e., less than 1.4 K, a result a great deal closer to our 1.15 K than to the CMIP5 models’ midrange 3.35 K.

          • A further clarification for Bellman: where the climate-sensitivity parameter is near-invariant, the values of the system-gain factor expressed as the ratio of entire equilibrium to reference temperatures and the proxy system-gain factor expressed as the secant-slope between two moments of interest [the secant slope is only equal to the system-gain factor where the curve is precisely linear] will not only be near-invariant, as explained in my earlier answer: they will also be near-identical.

          • I presume, “official climatology” means the most up-to-date science on the subject. Therefore the IPCC report from 203 is more “official” than one from 20 years ago.

            I see nothing to suggest the climate-sensitivity parameter to be near-invariant in AR5 – most of the chapter is explaining the complexity of forcings and feedbacks, and suggests that feedbacks respond differently to different forcings.
            The fact that you say two of the scenarios show lower sensitivity than the other two would suggest to me that the parameter is not invariant.

            You say that if the climate-sensitivity parameter being constant would imply that the system-gain factor must be constant. This is only true if it is constant for all temperatures back to 0K. Say, hypothetically there were no feedbacks until forcings were equal to 250K, and then where near-invariant for all forcings above this. The IPCC’s climate sensitivity parameter would be invariant, but your system-gain factor would be increasing as the forcings increased.

            I’m not sure what your point was with all the math at the end. It seems to confirm my point that local climate sensitivity is sensitive to very small changes in your definition of system-gain, but then you just say it’s impossible. You again seem to be comparing official climatology’s definition of feedback with your own and saying the fact that a feedback based on local changes is larger than the own based on your definition proves that the official one is impossible.

          • Bellman may like to investigate the ratios of output to reference sensitivity on the RCP6.0 and 8.5 scenarios, which – though he may perhaps not have realized this – were not in AR3 but in AR5, IPCC’s latest assessment report. The system-gain factors that are thus derivable are near-identical in both scenarios, and change very little over time.

            I do not require the curve of the equilibrium-temperature response function to be near-linear all the way to zero Kelvin. That may or may not be the case. All I need to demonstrate is that, in 1850, the system-gain factor derived as the ratio of equilibrium to reference temperatures was 1.085; that official climatology’s secant-slope proxy for the system-gain factor is near-invariant; that, therefore, our system-gain factor is near-invariant a fortiori, and that, in consequence, Charney sensitivity is 1.085 times the 1.05 K reference sensitivity to doubled CO2: i.e., 1.15 K or thereby.

            Recall that official climatology’s secant-slope proxy for the system-gain factor is obtained via a localized linearization in the form of a leading-order Taylor-series expansion. If one centers the linearization about 1850, then one has no need to concern oneself about what might have happened if the Sun were not shining and the preindustrial greenhouse gases were not present. All we are concerned with are modern conditions.

            Bellman’s suggestion that “You only need small changes in the actual feedback fraction to get very different rates of warming, so however correct you derivation might be mathematically, I don’t see how it can be useful in calculating true climate sensitivity” is only true for feedback fractions >0.3, for the curve of equilibrium-temperature response to feedback fractions is a rectangular hyperbola with its singularity at f = 1.0. That is the reason why some of the sillier extremist papers on climate sensitivity find it possible for Charney sensitivity to reach 10 K. However, since we know that the system-gain factor in 1850 was 1.085, it follows that the feedback fraction is 1 – 1 / 1.085, or only 0.078.

            The point here, illustrated by the math at the end of my previous response to Bellman, is that, since the system-gain factor is near-invariant, the curve of the response function is near-linear. Therefore, the proxy system-gain factor used by official climatology is, in 1850, just about identical to our system-gain factor. Now, climatology’s system-gain factor may grow by, say, 15% over the period 1850 to 2011 (though there is no particular reason to suppose that it will), but the corresponding growth in our system-gain factor will be negligible, because the entire temperatures of which our system-gain factor is the ratio exceed the tiny sensitivities posited by official climatology by two orders of magnitude.

          • I do not require the curve of the equilibrium-temperature response function to be near-linear all the way to zero Kelvin.

            And I disagree, so we are back to square one.

            Firstly, though you say here you don’t require it to be near linear, but your head post says “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.”, and you say the same and the end of this comment – ” since the system-gain factor is near-invariant, the curve of the response function is near-linear.”. So I’m still puzzled whether you think the response curve is near-liear or not, and why you keep emphasizing the near-linearity of it when you don’t require it.

            Secondly, if you accept the feedback factor might have been different, possibly much lower, below 255K, you have to accept it is increasing at a relatively fast rate after 255K. You simply cannot predict what the feedback factor will mean for future warming based on the factor in 1850, unless you assume a very near-invariant value.

            All I need to demonstrate is that, in 1850, the system-gain factor derived as the ratio of equilibrium to reference temperatures was 1.085; that official climatology’s secant-slope proxy for the system-gain factor is near-invariant; that, therefore, our system-gain factor is near-invariant a fortiori…

            And there’s your big mistake – that last statement does not follow at all from the first two, let alone a fortiori.

            If one centers the linearization about 1850, then one has no need to concern oneself about what might have happened if the Sun were not shining and the preindustrial greenhouse gases were not present. All we are concerned with are modern conditions.

            Your complaint was that modern climatology forgot the sun was shining, which I take to mean they start their calculations at a point where the sun is shining – say 255K. You insist that you have to consider the whole range of temperatures. So your feedback fraction acts on 265K of temperature, which includes the 255K when the sun wasn’t shining.

            If, say for the sake of argument, there were no feedbacks until the sun started shining, your definition still effectively spreads the feedback fraction across the whole range of temperature starting at absolute zero.

            I think this argument should be obvious, but lets spell out what happens in the hypothetical scenario of feedbacks only operating when temperatures are above 255K. At 0K there are zero feedbacks – your system gain factor tends to 1. At 255K there are zero feedbacks, and your system gain factor is still 1. When the refence temperature is 265K the actual temperature is 287.5K. Your system gain factor is 287.5 / 265 = 1.085.

            Now suppose the “official” version is correct and the climate sensitivity parameter is near-invariant. They only calculate the parameter as a delta, so the parameter is (287.5 – 255) / (265 – 255) = 32.5 / 10 = 3.25.

            So now what happens when the reference temperature rises to 266K? The “official” version says there will be a 1 degree rise that has to be multiplied by the near-invariant climate sensitivity parameter of 3.25, given around 3.25 degrees of total warming. By contrast your prediction is that at 266K reference temperature the actual temperature becomes 266 \times 1.085 = 288.61, that is 1.085 degrees of warming. But if the official parameter is correct the temperature is 287.5 + 3.25 = 290.75K, and your system gain factor becomes 290.75 / 266 = 1.093.

            Hence an invariant climate sensitivity parameter does not imply an invariant system gain factor.

            Bellman’s suggestion that “You only need small changes in the actual feedback fraction to get very different rates of warming, so however correct you derivation might be mathematically, I don’t see how it can be useful in calculating true climate sensitivity” is only true for feedback fractions \gt 0.3, for the curve of equilibrium-temperature response to feedback fractions is a rectangular hyperbola with its singularity at f = 1.0.

            I’m not sure if you are following my point – I’m sorry if I wasn’t clear. It’s true that small changes to the feedback fraction will only result in small changes to the system gain factor, but my point is small changes to the system gain factor will result in big temperature changes. This follows simply from the fact that any system gain has to be multiped by the absolute temperature. As absolute temperature are two orders of magnitude bigger than the temperature changes we are interested in it follows that a small change in the feedback fraction or system gain factor will have a large effect on the temperature change. Every 0.01 added to the system gain factor will be adding 2.6K to the temperature.

            You should understand this, because you make the same point in the head posting and even at the end of this current comment, when you say

            Now, climatology’s system-gain factor may grow by, say, 15% over the period 1850 to 2011 (though there is no particular reason to suppose that it will), but the corresponding growth in our system-gain factor will be negligible, because the entire temperatures of which our system-gain factor is the ratio exceed the tiny sensitivities posited by official climatology by two orders of magnitude.

          • Bellman says that if the curve of the equilibrium-temperature response function is near-linear across the interval of interest – i.e., from 1850 via 2011 to a CO2 doubling compared with 2011 – it must be near-linear all the way from zero Kelvin. He does not, however, adduce any argument in support of this proposition. I have already explained to him that official climatology’s climate-sensitivity parameter, and hence the system-gain factor, is near-invariant across the interval of interest, so that the response curve is near-linear across that interval.

            Bellman thinks that if the system-gain factor was much lower below than above the 255 K emission temperature than above it, we must accept that it is increasing at a relatively fast rate above 255 K. Yet, as I have explained to him, we know what the system-gain factor was in 1850, so we do not know at what rate it was rising.

            Bellman says one cannot predict what the system-gain factor will mean for future warming based on the factor in 1850, unless one assumes a near-invariant value. Official climatology, however, assumes and states just that, and we have accepted its finding.

            Bellman disagrees with my statement that if in 1850 the system-gain factor was 1.085 and if official climatology’s secant-slope proxy for the system-gain factor is near-invariant, it follows that our system-gain factor is near-invariant a fortiori. The reason why this statement is self-evidently true is that at the equilibrium temperature in 1850 the two system-gain factors – ours and official climatology’s – were identical. If, therefore, official climatology’s system-gain factor were to rise by, say 15% compared with 1850 by 2100, then our system-gain factor would rise by a far lesser percentage because entire temperatures exceed official climatology’s sensitivities by two orders of magnitude.

            Bellman says we insist we must consider the whole range of temperatures. No: we say that the system-gain factor acts on 265 K of temperature, which includes the 255K emission temperature that would obtain in the absence of any forcings or feedbacks, merely because the Sun is shining.

            Bellman imagines that if there were no feedbacks until the sun started shining, our definition effectively spreads the system-gain factor across the whole range of temperature starting at absolute zero. No: all we say is that the feedback processes present in the atmosphere in 1850 were bound to act on the entire reference temperature then obtaining. That statement says nothing about what might have been: what the feedbacks respond to is the temperature they find at a particular moment.

            Bellman says that, since at 0 K there are zero feedbacks, ur system gain factor tends to 1. No: it is undefined.

            Bellman says that at 255 K there are zero feedbacks. However, I have on repeated occasions explained that, to first order, one-third of the dayside of the Earth would be open water at 255 K, wherefore all of the sensitivity-altering feedbacks listed by IPCC would be operating.

            Bellman says that official climatology’s system-gain factor is only calculated as a delta, so the parameter is (287.5 – 255) / (265 – 255) = 32.5 / 10 = 3.25, and so that when the temperature rises to 265.75 K there will be a 0.75 K reference sensitivity that must be multiplied by 3.25, giving 2.45 K equilibrium sensitivity. But the midrange equilibrium sensitivity to the 0.75 K warming from 1850-2011 is 0.75 x 2.5 / (2.5 06) = 1.00 K, not 2.45 K. The system-gain factor 3.25 is far too large because official climatology makes Bellman’s mistake of assuming that at the 255 K emission temperature there are no feedbacks in operation.

            Bellman imagines that, though small changes to the feedback fraction will only result in small changes to the system gain factor, small changes to the system gain factor will result in big temperature changes. He has not understood that it is climatology’s system-gain factor that is near-invariant, changing the equilibrium sensitivity by a smallish fraction, and accordingly changing the equilibrium temperature by a very much smaller fraction, which is why our system-gain factor barely changes when official climatology’s system-gain factor changes.

          • Bellman says that if the curve of the equilibrium-temperature response function is near-linear across the interval of interest – i.e., from 1850 via 2011 to a CO2 doubling compared with 2011 – it must be near-linear all the way from zero Kelvin. He does not, however, adduce any argument in support of this proposition.

            If I said that, I wasn’t speaking clearly. It’s been my contention that a curve can be near linear across the interval of interest, but not very linear back to 0K. I rather thought it was your argument that any curve meeting the points (0, 0) and (265, 287.5) must be near linear. For example in a comment above you state:

            One can actually calculate the curve of, say, an exponential function provided that one has two points on the curve. We have (0, 0), the point through which all feedback response curves must pass, and (265, 287.5) in 1850. The exponent, then, is simply ln(287.5) / ln(265), which is just 1.0146, not greatly different from unity. To the nearest 20th of a Kelvin, the Charney sensitivity based on that exponent would be 1.15 K, just about identical to the linear case.

            There you are saying even an exponential function must be near linear all the way from zero Kelvin. (Incidentally you are not describing an exponential function there but a monomial, and your derivation of an exponent cannot be correct as you cannot have ln(0).)

            The reason why this statement is self-evidently true is that at the equilibrium temperature in 1850 the two system-gain factors – ours and official climatology’s – were identical.

            You need to explain to me why the two system-gain factors are identical in 1850. I note a comment above where talk about a proxy system-gain factor as being the gradient between two points of interest, but I’m completely lost as to why this must be the same as your system-gain factor.

            Bellman says we insist we must consider the whole range of temperatures. No …

            I’m probably not making myself clear. When I say you consider the whole range of temperatures I’m simply stating what you do when you derive the system-gain factor with respect to the absolute temperature – this inevitably means considering all the temperature resulting from the sun shining.

            Bellman imagines that if there were no feedbacks until the sun started shining, our definition effectively spreads the system-gain factor across the whole range of temperature starting at absolute zero.

            I’m not sure how your definition could do anything else. There are 22.5K of feedbacks in your scenario and you divide them by the absolute temperature 265K. I am not saying that this means that actual feedback response would be proportionate at all sub 255K temperatures – on the contrary I’m suggesting they won’t be. I expect feedbacks don’t really kick in until much warmer temperatures, but if they do your definition which requires feedbacks to respond to the entire reference temperature is not going to be very useful.

            Bellman says that, since at 0 K there are zero feedbacks, ur system gain factor tends to 1. No: it is undefined.

            Yes, I meant to say that. That’s why I meant it would trend to 1, unfortunately I mistyped this as “tend”.

            Bellman says that at 255 K there are zero feedbacks.

            No, I said if hypothetically there were no feedbacks at 255K. It was a thought experiment to demonstrate the difference between your system-gain factor and the IPCC’s climate sensitivity parameter, and to demonstrate that near-invariance in one does not imply near-invariance in the other.

            However, even if you are correct that the feedback fraction was a strong at 255K as it was at 265K, you still have to decide if there wasn’t some magical point below which feedbacks were either non-existent or at least much smaller than they now are. Either the function E(R) is near-linear or it isn’t.

  55. Lord Monckton,

    In light of the exchange we had upthread and my perusal of your paper “Why models run hot, results from an irreducibly simple climate model”, I think that at last I might have some insight into the source of some of your misconceptions. I was particularly struck by something which appeared in Figure 3 of that paper, which you or a co- author had referenced as having been “adapted” from an AR5 figure. Someone (you, perhaps?) had written in the textual subtitle for the figure:-
    “The Planck value shown as a ‘‘feedback’’ is not a true feedback, but a part of the climatic reference system.”

    I am 97% certain that this was an addition by you or one of your co-authors, rather than anything in the IPCC report, since the IPCC, as well as every climate scientist I know, explicitly recognises Planck as one of the atmospheric feedbacks.
    Your comment raises some interesting questions. Does the Planck feedback actually know that it is not a member of the feedback club? Did the other members actually advise it that it was no longer a member? I ask this because it continues to turn up for membership meetings. And who decided on its appointment to the Climatic Reference Council (CRC)? Can any of the other members of the atmospheric feedbacks join the CRC? Who gets to decide?

    I will return to these questions shortly, but first I want to show you a magic trick.

    Any screaming capitals below are for emphasis only.

    In my post upthread, I set out the (conventional) derivation of the linear feedback equation. I will continue to use the same variable names and definitions, but will eventually convert them into the form used by Roe 2009 with which you are obviously familiar so that you can confirm that changing the definitions of the constants has no impact on the results or inferences.

    The solution of the linear feedback equation for a constant step-forcing at infinite time yields:-
    T-T0 = F/lambda (i)
    where lambda = the total feedback (including the Planck response) Not Controversial.

    If we partition the total feedback into just two parts – the Planck response and “other”, we can write:-
    T-T0 = F/{lambda(Planck) + lambda(other)} (ii)
    Note that the variable T here is NOT a transient temperature; it is the equilibrium temperature achieved at infinite time in response to the constant step-forcing F.
    I will set T-T0 equal to ΔTall, defined as the expected change in temperature from the previous equilibrium state at T0 to the new equilibrium state induced by a flux forcing, F.
    We now obtain:-
    ΔTall = F/{lambda(Planck) + lambda(other)} (iii)
    The following are just mathematical re-arrangements of (iii) in slow motion.
    {lambda(Planck) + lambda(other)}xΔTall = F
    lambda(Planck)xΔTall = F – lambda(other)xΔTall
    ΔTall = 1/lambda(Planck) x (F – lambda(other)xΔTall) (iv)

    You see what I did there? I ask you to note that Eq (iv) looks remarkably like a temperature to temperature feedback! Moreover, if we expand the brackets, we see that the first term = F/lambda(Planck), which is the change in temperature at infinite time for a system which only has Planck as a feedback. [ Let me convert the variables (actually constants) to those used by Roe 2009. The ruleset that I offered previously was:-
    “set my F = ΔRf from Roe
    set my lambda(Planck) = 1/λ0 from Roe (Yes, he uses an inverted form)
    set my lambda(other) = -c1 from Roe (His sign convention for non-Planck feedbacks is different from mine ”
    Equation (iv) then becomes:-
    ΔTall = λ0 x (ΔRf +c1xΔTall) (v) ]

    Yep. You can verify that this equation is identical to Eq 4 in Roe 2009, which I suspect has sourced much of your paradigm.

    But now consider what I have just done with this magic trick. I have taken a mathematical IDENTITY, Equation (iii), which represents the equilibrium temperature solution (at infinite time) to the EBM or “linear feedback equation” in this instance, and solely by re-arranging the expression, I have magically produced what looks like a temperature feedback to temperature – still translated always via a net flux feedback, you might note. In so doing, we have now promoted the Planck-only temperature response at equilibrium into being a member of your Climate Reference Council, and taken it out of the feedback member’s enclosure. It looks like an input before feedback. Does this imply that this is then a physical input? In fact, does it imply that it is any type of input signal to the climate system? We started with an identity and we must end with an identity barring algebraic error. This expression comes from a stopped clock which is correct not twice a day but only once – at the equilibrium state.

    Now let us consider the question of membership of the Climate Reference Council.
    If I repartition lambda(other) into its constituent parts, then it might look something like:-

    lambda(other) = lambda(LapseRate) + lambda(WV) + lambda(surface albedo) + lambda(clouds)

    So now consider what happens if instead of choosing to separate out lambda(Planck) in the above magic trick, I separate out lambda(Planck) plus lambda(LapseRate). When modified Eq (iv) has similar form except that we have now promoted lambda(LapseRate) into being a member of the Climate Reference Council, and it has lost its membership of the feedback club. The “input temperature signal” has now become F/(lambda(Planck) + lambda(LapseRate)). Is this now the new physical input to the system? How can you have these two inputs to the system at the same time if they represent physical inputs?

    Earlier, in response to my assertion that there were no direct feedbacks to temperature in conventional climate science, only “temperature-dependent feedbacks to net flux”, you wrote:-

    ” In the climate, the input signal is the 255 K emission temperature. Would that signal itself engender a feedback response, in the absence of any noncondensing greenhouse gases?
    The answer is Yes. …
    With respect, therefore, Kribaez is wrong to state, in capitals at that, that the feedback response to the input temperature signal DOES NOT EXIST. It does exist, in physical reality.”

    OK, then let us consider in a bit more detail your chosen reference input temperature signal – which you have defined in line with Roe as the theoretical response of the system to just the Planck response. Using my nomenclature, AT EQUILIBRIUM this is :-
    ΔTplanck = F/lambda(Planck) (vi)

    ΔTplanck, like ΔTall refers to a change in temperature from the previous equilibrium state to the present theoretical equilibrium state, the latter being under the assumption that only Planck feedback is operating.

    In Roe nomenclature, Eq (vi) can be restated as ΔTplanck = Fxλ0 (vii)
    Mathematically, I can trivially take the ratio of ΔTall/ΔTplanck to yield an amplification or gain. It yields the same as Roe’s result or your own.

    I would first ask you to note that (a) ALL OF THE MATHS ABOVE RELATE TO A CHANGE FROM ONE EQUILIBRIUM CONDITION TO ANOTHER FORCED BY A FLUX FORCING ; THEY HAVE NOTHING TO DO WITH ANY DYNAMIC SYSTEM (b) the only reference temperature which is actually real is the previous equilibrium temperature, T0 (C) I can arbitrarily change the “input reference signal” without changing the physical system in any way; does that sound like a physical signal or an abstraction? (d) The only signal actually seen by the climate is the (real) temperature field. How does the climate know how to find your physical underlying reference signal which it is supposed to be responding to?

    You are, I’m afraid, hunting a snark, but you need to convince yourself of that.

    • Krib
      All the feedbacks (they are legion) in the earth’s climate operate in an open dissipative system which is chaotic-nonlinear, and in such a system, it is the feedbacks, specifically the interplay between the positive (excitability) and negative (friction) ones which determine the nature of the emergent spontaneous pattern formation by which the system as a whole exports entropy.

      All your equations assume linearity. And equilibrium. They are thus irrelevant. Climate is nonlinear and always far from equilibrium.

    • It is because the climate is a far-from-equilibrium system that Monckton is right and you are wrong. There can be no component of feedback that operates on “departure from equilibrium” only, because there is no equilibrium. Feedbacks operate at all points in the multi-dimensional phase space and probabilistic landscape.

      • Phil,
        You have read the first page of a book and then jumped to the last page without reading any of the pages in between. I explained upthread that the GCMs and the EBMs (which is what Lord Monckton’s formulation derives from) both already do apply feedbacks to the entire temperature.

        That is already a given. The comment that you are responding to is my attempt to get Lord Monckton to convince himself that the input signal on which he is basing his calculations is not physical and not an input signal at all. At any point in time, the climate system can only see one input signal and that is the actual temperature expressed in absolute terms. Lord Monckton believes that it is responding in a physical way to some mystical underlying temperature signal. The formulation above that you are responding to so negatively is actually the basis for Lord Monckton’s assertion of the existence of a physical reference input signal based on the Planck response alone. I am merely trying to show that it cannot possibly exist as a physical input and that his reference signal which derives from Roe 2009 is actually an arbitrary choice.

    • Kribaez,
      Not disagreeing on anything, and I treat Planck as a feedback, but just an observation.

      The closed-loop gain is often written
      CG=OG/(1+f*OG)
      where OG is the openloop gain and f could be a sum of feedback coefficients. That could be written
      CG=1/(1/OG+f)
      Then you could say that 1/OG is also a member of the club. It behaves just like another member of the f club.

      This has practical consequences, which I was thinking of when I wrote my feedback article. I used a finite gain transistor rather than an op amp. An op amp with feedback could have emulated the transistor. Then the feedback would have entered the arithmetic in exactly the place of 1/OG.

      Climate analogies are usually like that. The emulation could either be an infinite OG with Planck feedback, or a finite OG based on Planck. Both ways work. In the latter case, Planck is not in the club.

      • Nick,
        The main point I was trying to make is that the choice of “reference system” here is essentially arbitrary. My main aim is to get Lord Monckton to recognise that the reference system response is not a physical input; he has repeated several times that he believes that it is. In your universe, you are recognising (at least) that it is a choice made by the analyst – a mathematical abstraction.

        The subsidiary point is that this CG calculation so far at least is only justified to work between two equilibrium states, and is abstracted from a known result. It cannot generate that result. It is ironic that, on the one hand, Lord Monckton has claimed several times that Official Climatology does not recognise absolute temperatures, when in reality both GCMs and EBMs use real (absolute) temperatures as state variables, and, on the other hand, the derivation of the CG can be shown to be only legitimate for a ratio of temperature increments measured between two Equilibrium states.
        As an aside, you wrote:- “The emulation could either be an infinite OG with Planck feedback, or a finite OG based on Planck. Both ways work.” While I understand your comment in the context of the choice of a reference response, I invite you to try running either approach on a dynamic (i.e. transient) dataset, and you will find that neither approach works, or at least not without a reverse calculation after solving the EBM equations. To emulate an arbitrary forcing series (i.e. real life), a superposition or convolution approach is required. Temperature-dependent feedbacks all actuate net flux changes, which can take centuries to millenia to stabilise even for a fixed step-forcing. Prior to that, these “gains” are functions of time and ocean model characteristics, notably heat capacities and heatflow characterisation. This probably explains why nobody has tried to use a Control Box for dynamic emulation in CliSci.

    • Kribaez is of course correct that one can treat the Planck parameter as either a feedback or a part of the reference system. The caption complained of was unsatisfactorily worded. However, we agree with Roe that it matters to treat it as part of the reference system. Over the interval of interest, from 1850 via 2011 to a CO2 doubling compared with 2011, the Planck parameter (expressed as the Schlesinger ratio) does not change significantly, so the point is largely moot.

      And of course one can do feedback calculations between one equilibrium state and the next, using the secant slope of the response function as a proxy for the system-gain factor. If one had a sufficiently perfect knowledge of the magnitudes and interactions of the various forcings and feedbacks, that would of course be preferable in a sufficiently nonlinear response curve.

      However, climatology regards the response curve as near-linear, in which event the position in 1850, for instance, is of more than passing interest. The emission temperature before allowing for any forcing or feedback is 255 K, and the reference sensitivity (before accounting for any feedback) to the noncondensing greenhouse gases present in 1850 is 10 K. Of the 287.5 K equilibrium temperature in 1850, 265 K would, therefore, have obtained in the absence of temperature feedback. The remaining 22.5 K is attributable to feedback.

      Climatology imagines that the whole of that 22.5 K arises in response to the warming forced by the presence of the preindustrial noncondensing greenhouse gases. However, in the absence of those gases a third of the dayside of the Earth would be open water, and all the sensitivity-altering feedbacks now in operation would be operating. Climatology takes no account of the consequent (and large) feedback response, instead attributing all of it to the preindustrial noncondensers.

      • Lord Monckton,
        Thank you for this. It demonstrates some advance in your thinking, I hope.

        Can we now agree on the following facts:-

        a) “Atmospheric Feedbacks” in GCMs and EBMs are all temperature-dependent feedbacks to net flux. There are no direct feedbacks to an “input” temperature anywhere in the real system.
        b) The feedbacks in GCMs and EBMs translate into the partial derivatives of TOA flux with respect to temperature at the absolute temperature prevailing at that time.
        c) The choice of temperature response to Planck alone as a reference against which to quantify a temperature amplification or gain is a discretionary choice of the analyst. It is not founded on a physical input.
        d) The derivation of amplification or gain outlined in Roe 2009, based on (c) above applies strictly between two equilibrium points.

        If we can clear the above deadwood out of the way, then we can take a forensic trip backwards in time and in temperature to consider different ways of viewing your assumed equilibrium state in 1850. If, on the other hand, you are still resistant to any of the above, then please highlight which of them you do not accept.

        • In response to Kribaez, I have no particular interest in how the models currently arrive at their estimates of equilibrium sensitivity to radiative forcing, since those models have for 40 years failed utterly to constrain the very broad interval of Charney sensitivities first published in 1979. The models do not explicitly represent feedbacks at all. But, whatever they are doing, our result shows they must be doing it wrong.

          It is official climatology that denominates temperature feedbacks in Watts per square meter per Kelvin of the temperature change that arises from a direct radiative forcing (i.e., per Kelvin of the reference sensitivity). Our approach is to accept all of official climatology except what we can disprove. Since official climatology, supported explicitly by Roe (2009), accordingly treats the Planck sensitivity parameter as part of the reference system so that the reference sensitivity to radiative forcings can be calculated, we have adopted official climatology’s approach in this respect. Therefore, if Kribaez wishes to argue with that methodology, his argument is not with us but with official climatology and he should address his concern to the IPCC Secretariat.

          We have at no time cited Roe (2009) as authority for our result. We can find no paper in climatology that acknowledges the fact that any feedback processes operating at a given moment must respond not solely to the reference sensitivity but to the entire reference temperature. Our experiments at a national laboratory left us in no doubt about this fact, which is also self-evident in the governing equations of control theory, which are set out and formally proven in the long version of our paper.

          To establish that midrange Charney sensitivity is 1.15 K, all we need to do is to establish three propositions.

          First, that the reference sensitivity to doubled CO2 is 1.05 K. We do this with data from Andrews+ (2012).

          Secondly, that the system-gain factor in 1850, derived as the ratio of the 287.5 K equilibrium temperature to the 265 K reference temperature then obtaining, is 1.085.

          Thirdly, that official climatology regards the climate-sensitivity parameter as near-invariant (IPCC, 2007, ch. 6) and, therefore, that the curve of the equilibrium-temperature response function E(R) is near-linear. We modeled various nonlinear curves, all of which produced impossible contradictions. We also derived the system-gain factor 2.5 / (2.5 – 0.6) = 1.316 as the system-gain factor implicit in the finding in IPCC (2013) that there had been about 2.5 Watts per square meter of net anthropogenic radiative forcing to 2011 and that to the previous year there had been a radiative imbalance of 0.6 Watts per square meter (Smith 2015). And we carried out further tests on both the RCP6.0 and the RCP8.5 datasets to establish that the ratio of transient sensitivity to net anthropogenic forcing over successive 30-year and 60-year periods from 2010-2100 is near-invariant.

          If these three propositions are agreed – as, in our submission, they must be – then midrange Charney sensitivity is 1.05 x 1.085, or 1.15 K.

          • Lord Monckton,

            “The models do not explicitly represent feedbacks at all. But, whatever they are doing, our result shows they must be doing it wrong.”
            The GCMs do not have feedbacks as inputs, but they do simulate a feedback process to net flux; net flux is calculated on the then-current state-variables (which includes the absolute temperature field), which are updated every time-step. Post hoc evaluations of atmospheric feedbacks seek to estimate the rate of change of net flux with respect to surface temperature. The EBMs, on the other hand, explicitly represent feedbacks to net flux. In both instances, the calculations are based on absolute temperatures. There are numerous genuine reasons why GCMs are running hot and why they should not be deemed fit to inform decision-making. Your explanation is not one of them. Post hoc ergo propter hoc fallacy.

            Your propositions which “must be accepted”:-
            “First, that the reference sensitivity to doubled CO2 is 1.05 K. We do this with data from Andrews+ (2012). ” The more generally accepted median estimate is a little higher, but OK, accepted ad argumentum.

            “Secondly, that the system-gain factor in 1850, derived as the ratio of the 287.5 K equilibrium temperature to the 265 K reference temperature then obtaining, is 1.085. ” There is no “reference temperature” without your defining one as a mathematical abstraction. At the aggregate level you are working at, there is an average surface temperature and there is an average emission temperature or brightness temperature, which can be back-calculated from S-B. If you would take the trouble to understand that the feedbacks are not “temperature feedbacks” but “temperature-dependent feeedbacks to net flux”, then you would understand more clearly why it makes little sense to attempt to partition an absolute temperature.

            “Thirdly, that official climatology regards the climate-sensitivity parameter as near-invariant (IPCC, 2007, ch. 6) and, therefore, that the curve of the equilibrium-temperature response function E(R) is near-linear. ” While it may be valid to assume that feedbacks are invariant if we are considering only small changes to temperature and climatology, it is patently and demonstrably invalid to assume that they remain invariant over very large temperature ranges or when you start playing with major changes in the climatology. I invite you to try calculating the surface temperature and the feedback values if you eliminate clouds and water vapour from your construct climatology.

            ” We also derived the system-gain factor 2.5 / (2.5 – 0.6) = 1.316 as the system-gain factor implicit in the finding in IPCC (2013) that there had been about 2.5 Watts per square meter of net anthropogenic radiative forcing to 2011 and that to the previous year there had been a radiative imbalance of 0.6 Watts per square meter (Smith 2015). ”
            Your description of this 1.316 value as a “system gain factor” is different from your other uses of the term. This value, as you calculate it, is (unambiguously) an estimate of the ratio of temperature change to equilibrium divided by a single point estimate of transient temperature change (evaluated in 2011), under the assumption that the total forcing level is held constant at its 2011 value and that a constant linear feedback is in operation. It may be compared directly with the estimate from Lewis and Curry which can be found here:- https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=13&cad=rja&uact=8&ved=2ahUKEwiBhLqVgvXiAhWGTcAKHWEDCtEQFjAMegQIBhAC&url=https%3A%2F%2Fniclewis.files.wordpress.com%2F2014%2F09%2Flewiscurry_ar5-energy-budget-climate-sensitivity_clim-dyn2014_accepted-reformatted-edited.pdf&usg=AOvVaw2xGESkvk_ppHwtK4DxuxPp

            The equivalent value from Lewis and Curry is 1.98/(1.98 – 0.36) = 1.22 (dimensionless)

            Note that your estimate is higher than L&C because you assumed that 1850 was in equilibrium, whereas L&C accounted for change from non-zero initial forcing and heat uptake levels.

            L&C used an estimate of temperature change of 0.71K from base period (1859-1882) to final period (1985-2011). From the L&C values, you can obtain:-

            Projected change to equilibrium temperature at Forcing of 1.98 W/m2/K = 1.22*0.71 = 0.87K
            Projected change to equilibrium temperature for a 2xCO2 forcing of 3.7
            = 1.22*0.71*3.7/1.98 = 1.62K for a doubling of CO2. (L&C actually report a median value of 1.64K ECS for a doubling of CO2. )

            Now let us repeat the calculation for your values.
            I will use the same estimate of temperature change as in L&C i.e. 0.71K
            Projected change to equilibrium temperature at 2011 Forcing of 2.5 W/m2/K = 1.316*0.71 = 0.93 K
            Projected change to equilibrium temperature for a 2xCO2 forcing of 3.7
            = 1.316*0.71*3.7/2.5 = 1.38K for a doubling of CO2.

            Your estimated midrange Charney sensitivity is 1.15K. So, if I accept one of the three propositions you suggest must be agreed, it is incompatible with the other two. You may think that this difference is small, but given that the assumptive basis is identical, the key question from a forensic point of view is: why is this difference there at all?

            Let us re-do the calculation a different way. We will do it forwards from 1850.
            Your idiosyncratically-defined reference temperature is 265K. You define the (constant) Planck response as 1.05K/W/m2 to equilibrium. For your estimated forcing of 2.5 W/m2, your reference temperature therefore achieves, at the new equilibrium, a value of
            265 + 1.05*2.5 = 267.6k. Given that your estimated ratio of surface temperature equilibrium to reference temperature equilibrium of 1.085 is “invariant”, then we can now estimate your new surface temperature equilibrium value from the new reference temperature value using this ratio. We obtain for the new surface equilibrium temperature (all feedbacks) 1.085 * 267.6 = 290.4K. Since your previous 1850 equilibrium temperature was 287.5K, then this represents a change of (290.4-287.5) or 2.9K . This equilibrium, however, using your data, relates to a forcing of (only) 2.5 W/m^2. To project this to a doubling of CO2 at 3.7W/m2 forcing, we need to scale this up by 3.7/2.5, which yields your new estimate of ECS for a doubling of CO2 of 4.25K. Whoops! Even you must see that this is not consistent with the 1.38K ECS you derive from the incremental calculation based on your chosen values.

          • First, Kribaez says that my explanation of the agreed fact that the models are predicting twice or thrice the warming that is occurring – i.e., that the models’ error lies in their implementation of feedback – is an instance of the post hoc ergo propter hoc fallacy. It is no such thing. Official climatology, all of whose tenets we accept ad argumentum except to the extent that we can demonstrate that they are false, says that the uncertainty in the directly-forced warming from CO2 is 10% – i.e., plus or minus about 0.l K. Yet the uncertainty in the equilibrium warming is plus or minus about 1.5-1.6 K. From these values, it is inescapable that the only part of the calculation in which a large enough error to account for the large overshoot in predicted against observed temperatures is the feedback part.

            Next, Kribaez says he accepts ad argumentum that the CMIP5 models’ mean reference sensitivity to doubled CO2 is 1.05 K: yet, a few paragraphs later, he presents a calculation implying that it is 0.71 x 3.7 / 1.98, or 1.33 K.

            Then Kribaez repeats that there is no physical meaning to our statement that in 1850 the reference temperature – i.e., the temperature that would have obtained that year in the absence of feedback – was the sum of the 255 K emission temperature and the 10 K reference sensitivity to the preindustrial noncondensing greenhouse gases. He says these values are “idiosyncratic”, when in fact they are warranted in the peer-reviewed journals. Here, as so often, his dispute is not with us but with official climatology, whose tenets in this respect we have accepted ad argumentum.

            In the same vein, he jibs at our description of temperature feedbacks as “temperature feedbacks”. Again, his quarrel is not with us but with official climatology, which describes temperature feedbacks as “temperature feedbacks”. For good measure, it denominates them and lists them in Watts per square meter per Kelvin of the reference sensitivity (not a change in flux density, but a temperature change) to which they are responding. It is a truism that the reference sensitivity is itself driven by a forcing – i.e., a change in flux density, but, given the near-invariance of the Planck parameter over the period of interest, calculation on the basis of fluxes only will not in itself give a result that differs from a result obtained by doing things official climatology’s way in this respect.

            He then says it makes no sense to partition an absolute temperature. Here again he is at odds with official climatology, which partitions the absolute temperature that would prevail at equilibrium after a perturbation into a) the reference temperature before feedback has acted and b) the feedback response. Likewise, control theory partitions the output signal into the reference signal and the feedback response. And it is perfectly permissible to partition the reference signal into the input signal and as many subsequent perturbations as may have occurred at the moment of interest.

            He says there is no such thing as a reference temperature. Here his quarrel is not only with official climatology but also with control theory and, for good measure, with elementary logic. He accepts that in the absence of temperature feedback the reference sensitivity to doubled CO2 – and the reference sensitivity is a change in temperature – is about 1.05 K. He accepts that after accounting for temperature feedback the equilibrium sensitivity to doubled CO2 – and the equilibrium sensitivity is also a change in temperature – has a value higher than 1.05 K. From this it follows that he accepts that the difference between the equilibrium and reference sensitivities – also a change in temperature – is the feedback response. By the same token, there is an entire reference temperature in, say, 1850: that reference temperature is the sum of the emission temperature that would obtain without forcing or feedback and the reference sensitivity to the preindustrial noncondensing greenhouse gases. In effect, Kribaez is trying to say there is no such thing as a feedback response: for if there is one it is inescapable that the equilibrium temperature (or sensitivity) will comprise the sum of the reference temperature (or sensitivity) and the feedback response.

            Next, Kribaez quibbles about our derivation of the (excessive) system-gain factor derivable from official climatology’s estimate that there had been 2.5 Watts per square meter of net anthropogenic radiative forcing to 2011, at which time there also subsisted a radiative imbalance of 0.6 Watts per square meter. The system-gain factor thus derived (which is not ours but that of IPCC) is simply 2.5 / (2.5 – 0.6), or 1.316.

            But Kribaez says that Lewis & Curry 2018 (who used data and timescales that differed somewhat from those of IPCC 2013) found the period reference sensitivity since was 0.71 K (IPCC data implies 0.75 K); that the secant-slope system-gain factor was 1.22 (IPCC data implies 1.32); that period equilibrium sensitivity was 0.87 K (IPCC data implies 1.00 K); and that Charney sensitivity was 1.62 K (IPCC data implies 1.40 K). Therefore, there is not much difference between L&C’s result and the result derivable from IPCC data.

            Next, Kribaez asks why the secant-slope system-gain factor derivable from IPCC data to 2011 differs from our system-gain factor. It would be much more apposite to ask why the system-gain factor derivable from IPCC data or from L&C 2018 is so close to our system-gain factor and so far from the models’ midrange system-gain factor.

            Nevertheless, it is easy to answer his question. There is very little uncertainty as to the value of our system-gain factor, since it is derived from two well-constrained quantities that obtained in 1850. There is considerably greater uncertainty as to the secant-slope proxy system-gain factor derivable from IPCC forcings and from official climatology’s estimate of the radiative imbalance from 1850-2011, because there is uncertainty as to the magnitude of the net anthropogenic forcing and still more uncertainty as to the magnitude of the radiative imbalance, and because – as I have tried to explain to Kribaez before – the sensitivities whose ratio is official climatology’s secant-slope proxy for the system-gain factor are smaller than the entire temperatures whose ratio is our system-gain factor by two orders of magnitude: therefore, even small uncertainties in those sensitivities entail a large uncertainty in the secant-slope system-gain factor, while even large uncertainties in entire temperatures entail a small uncertainty in our system-gain factor.

            Next, Kribaez says we define the Planck response as 1.05 K to equilibrium. No: as we have repeatedly stated, we have taken the mean of the values from the 15 CMIP5 models given in Andrews 2012, and we have taken the 1.05 K value as near-invariant because, across the interval of interest, from 1850 via 2011 to a CO2 doubling compared with 2011, the Schlesinger ratio, a good approximation for the Planck parameter (see Schlesinger 1985) is near-perfectly invariant.

            Kribaez then performs a calculation forward from 1850 that appears erroneous. The correct calculation is as follows: The reference temperature owing to the Sun shining is 255 K; the reference sensitivity to the preindustrial noncondensing greenhouse gases is 10 K; the reference sensitivity to the industrial-era anthropogenic noncondensing greenhouse gases to 2011 is 0.75 K; and the reference sensitivity to a CO2 doubling compared with 2011 is 1.05 K. Therefore, the reference temperature at the moment of CO2 doubling compared with 2011 is the sum of these four values: i.e., 266.8 K. Since the system-gain factor is near-invariant at 1.085, the equilibrium temperature at the moment of CO2 doubling compared with the 2011 concentration is about 289.6 K, compared with 287.5 K in 1850. This approximately 2.1 K warming is the sum of the 1 K equilibrium sensitivity to the industrial-era noncondensing greenhouse gases from 1850 to 2011 and the 1.15 K equilibrium sensitivity to doubled CO2 thereafter.

            But I am most grateful to Kribaez for the trouble he is taking. It is very difficult for any one person to hold in mind all the various branches of science upon which our result depends, which is why I have an army of co-authors and pre-submission reviewers at my back. And I am always happy to try to explain what we are up to, and to listen carefully to any concerns that may be raised.

  56. Dear Lord Monckton,

    You asked me about astronomical literature on the influence of the Earth orbit onto the terrestrial climate.

    At first: ALL text connected with Milankovitch are Cycles on the scale of minimum 19,000 to maximum 100,000 years. Therefore NOT relevant for ANY climate changes on Earth on decadal and centennial scale, therefore: Lets forget everything connected with Milankovitch to explain global warming and global cooling on centennial scale, and the recent global warming, which occurred since the 17th century.
    We therefore have to focus onto Earth orbital features and their annual/decadal/centennial variations.
    To the literature: There is a literature scarcity on this astronomical matter, because astronomists for quite some time look into the depths of the universe and there is no new papers about the old, long explored Earth orbit around the Sun. All astronomers know the orbital basics: The Earth advance is NOT like an airplane advance, but screws around this advance line in a spiral fashion. In fact, a lot of advances in space are spiral movements, as the solar system spirals forward in space, as the planets spiral around the Sun, as does Earth, the Moon spirals around Earth in its daily flight line and even new lanched satellites start to spiral in their flight around Earth, which has to be compensated, for instance in GPS data. The spiralling flight is called an “osculating forward movement” – with deviations from the flight line to the left/right/up/down….. therefore the stars in large distance “jump up and down”, as so-called “osculating elements”, jumping along the up-down movement of Earth depending on its spiral position. This is general astronomical knowledge. The authors for the earth orbital osculating flight is Isaak Newton (he fought long with Leibniz on the shape and number of osculations – Leibniz counted five) and then Carl Gauss, he tried to derive a formula for the Earth´s flight, observed the sky 4 years, could not complete the formula and invented the Least Squares Method based on his astronomical measurements. Exact details and calculations you will find in my booklet: J.S.: Das Ende der globalen Erwärmung, Berechnung des Klimawandels” – have it machine translated, all relevant orbital features are understandably explained, this saves you quite a lot of time to comprehend the orbital subject, new to almost everyone.
    Also see: http://www.Climate Patter Recognition, Part 8, and Part 1, the orbital movement is derived empirically out of GISP2 temperature variations over the entire Holocene, the calculation method is explained. Here you can see that global Earth temperature is a product of the Sun-Earth distance. The Climate Pattern Recognition series needed 8 parts, for analyzing each and every temperature spike since 8,500 BC, thus over 10,000 years.
    The Earth orbital data is all known in JPL Pasadena, but kept under table, because they are NASA GISS and
    orbital data, which clearly MUST have an effect on the Earth temperature is kept out of public observations.
    And if none mentions the Earth orbit, then all climate forcings “are atmospherical” and the climate scientists may say: ALL forcing belongs to manmade CO2, BECAUSE WE DO NOT KNOW OF ANY OTHER FORCING since 1850. And thats what they need, keeping the orbit out of public focus andthat is what they colluded on in 2006 in preparation of AR4-
    Any questions welcome on weltklima at gmail.point com

    • It appears that there is no peer-reviewed paper establishing what Mr Seifert says. Without it, his theory will not be easily accepted.

      • Dear Lord Monckton,
        I reckon that there is astronomical literature covering the details and osculations of the Earth orbit somewhere, because these are no secrets on this and the osculation data is used in the JPL star positioning programs….
        The measurements, carried out by Issak Newton himself, which I employed in my texts, should suffice to provide a lot credibility, much more than in todays climate science peer/pal warmist reviewed papers.
        No-one would doubt the greatest mathematicien of the world.
        The measurements are given in Newtons major solar system calculation book.
        General details of the orbit I took from encyclopedias, which I found in the London British Library.
        To: “Not easily accepted”: The Earth orbital path and Issak Newton´s measurements would by endorsed by any knowledgable astronomer.
        Sufficient is the fact that orbital perpetuations exist due to the spiral flight shape, causing deviations from the elliptical flight line. And those, therefore, must be INCLUDED in climate forcing calculations, as well as resulting climatic effects, caused by increasing/decreasing the distances Sun-Earth, increasing/decreasing global temperatures.
        To abate the doubt, I recommend a consultation of a knowledgable astronomer concerning the osculating spiral flight of Earth: He will agree, and therefore flight path deviations/perturbations exist, with resulting climatic effects.

        • Solar System 2.0 – the helical model

          https://www.youtube.com/watch?v=mvgaxQGPg7I

          CRITIC/INSTRUCTOR – RHYS TAYLOR
          Here we have the rare individual who is both a scientist, critic and yet not above being an educator/instructor. Mr. Smith and Mr. Plait could learn much from Mr. Taylor (post-doctorate in astrophysics).
          Mr. Taylor wrote a few articles here, here and here. What sets him off from Mr. Plait and Mr. Smith is two-fold:
          He understands that DjSadhu’s first couple of videos have scientific errors, yet the basicpremise of the solar system moving through space in a helical motion is for the most part correct.
          He takes a constructive win-win approach and works in a positive manner with DjSadhu to fix the errors in an attempt to produce a more accurate video than the original two.

          https://longhairedmusings.wordpress.com/2017/09/07/social-conditioning-and-conventional-pieties-conspiracy-hypothesis-theory-crime-statecrimesagainstdemocracy-scads-conspiracy-of-context/

        • J.Seifert,

          Nicola Scafetta has been trying for many years to convince people that climate oscillations are caused by orbital effects. Like you, he points to the coincidence of certain celestial/orbital frequencies with climate cycle frequencies. You might find it interesting to Google some of his publications.

          His views have received only limited acceptance, and that is largely, I believe, because of his inability to propose a credible physical mechanism to relate climate effects to planetary influence. I believe that there does exist a possible mechanism, (as I explained somewhere up-thread in response to a comment from Tonyb about the correlation between winds and temperatures), but at the moment this exists as a poorly quantifiable hypothesis.

          I would also note that NASA JPL a few years ago were working on a similar hypothesis – wind variation arising from induced changes in atmospheric angular momentum. However, they were postulating that the external torque which was controlling changes in angular velocity of the surface of the Earth was exerted by inertial changes in Earth’s liquid core. Again, you might find it interesting to Google some of their findings.

          • To kribaez:
            I read all the Scafetta literature. He dedicates himself to the influence/effects/interactions of the OTHER solar planetary orbits onto Earth. Now a new paper is out, trying to prove that sunspot cycles are caused by planetary orbiting.
            Myself, I am not on this line, only the Earth orbit and its detailed perturbations, which can be recognized in the Earth´s climate, are my focus. Those effects are numbers larger than effects of other planets onto Earth.
            You can check my papers: http://www.climate pattern recognition, Part 8 and Part1 are the most important.

          • J Seifert,
            Your lonk takes me to a digital farming site with no pointers to your articles.

      • https://rwer.wordpress.com/2019/06/15/atmospheric-co2-concentration-year-1-to-2018/

        This Bed Wetting post appeared in my feed from “The Real Economics Blog”, Its an interesting read often with some good articles on the “Dismal Science”, It took your Good Name in Vain, and I had to point out the Absurd Axis employed by the Bed Wetting Graff (Brian Cox).

        June 16, 2019 at 1:30 pm
        Monckton is a Lord of the British Realm, he does not sit in the now Re constituted House of Lords, that does not make him an Imposter.
        Secondly Regarding Monckton’s paper on the errors in basic Climate modelling his Status as a British Peer of the realm has nothing to do with the mathematics of modelling feedbacks.
        Finally, perhaps William Happer or Freeman Dyson will tick more of your boxes for an appropriate expert qualified opinion.

        https://www.youtube.com/watch?v=YKBwoO8DOPw

        A Good Frolly video, there that should do it.

  57. I asked Mr Seifert for peer-reviewed and published evidence of the effect of orbital variability on the Earth’s climate. All he has offered is peer-reviewed and published evidence of the Earth’s orbital characteristics. I am already familiar with that. I do not need it: I need the peer-reviewed and published evidence of the effect of those orbital variations on variations in global mean surface temperature.

    However, all of this is off topic. The present focus is on the influence of temperature feedbacks on global temperature.

    • Dear Lord Monckton,
      The effect of Earth orbital oscillations can clearly be detected and proven in global annual temperatures on a weekly scale. A paper on this will abate the talk of a CO2-effect and the talk of climate being chaotic only and nothing can be revealed, which is a meme of those who understand nothing.

      I aim at publishing it peer reviewed over 2020. So you just need to wait and I will inform you on the progress in this matter in time.The orbital topic was on my backburner because I am dedicated to reveal the climatic effects of meteor impacts on Earth, which is at present my major concern. See my papers. For this reason, the “orbit paper delay”..

      • On looking at the astronomical tables, it is not clear to me that the variability in the Sun-Earth distance over the past century has any correlation with the variability in global mean surface temperature. There is, however, a correlation between the quantum of sunlight reaching the ground and variability in regional mean surface temperature. But there appears to be no correlation between global warming and the variability in the extent of global (and particularly tropical) cloud cover that governs the quantum of sunlight reaching the surface.

        In any event, all of this is off topic. Here, we are discussing the magnitude of the feedback response to radiative forcings.

        • Dear Lord Monckton,
          Let us agree on this: If not all variables are included, and major variables are missing then all calculations with the remaining, uncomplete variables must be faulty. I am sure we agree on that, and that is why I insist on my approach.
          Secondly, to “looking at tables”. An eye-balling needs the additional background of the
          matter, particularly when not generally known.
          Lets then leave the astronomical topic aside for now. once my peer-reviewed paper is at hand, I will inform you in time. I thank you for your appreciated time and conversation.
          Best regards, J.S,

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