Answer to a whigmaleerie about temperature feedback

By Christopher Monckton of Brenchley

Some days ago, a prolix, inspissate whigmaleerie was posted here – a gaseous halation, an unwholesome effluvium, an interminable and obscurantist expatiation purporting to cast doubt upon my team’s conclusion that official climatology has misdefined and misapplied feedback and has thus made a mountain out of a molehill, approximately tripling the true midrange rate of global warming we can expect our sins of emission to engender.

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We define emission temperature R0 as the 255 K global mean surface temperature that would obtain on Earth at today’s solar irradiance and albedo but before any greenhouse gases have entered the atmosphere and before any feedback begins to operate; B0 as the feedback response in Kelvin to R0; E0, the sum of R0 and B0, as the equilibrium temperature that would prevail after feedback has responded to emission temperature; ΔR0 as the 10 K reference sensitivity to the naturally-occurring, noncondensing, preindustrial greenhouse gases; ΔB0 as the feedback response to B0; ΔE0, the sum of ΔR0 and ΔB0, as the equilibrium sensitivity to the preindustrial noncondensing greenhouse gases present in 1850; R1, the 265 K sum of R0 and ΔR0, as the reference temperature (not including feedback responses) in 1850; B1, the sum of B0 and ΔB0, as the total feedback response to 1850; and E1, the sum of R1 and B1, as the observed equilibrium temperature (including feedback responses) in 1850. The graph above, a detail from Fig. 1 of the whigmaleerie, shows B0 as 5 K and ΔE0 as 28 K, implying that ΔB0 is 18 K or thereby.

Relationships between this gallimaufry of variables constituting the equilibrium global mean surface temperature in 1850 are shown below, where a0, the ratio of ΔE0 to ΔR0, is the system-gain factor or closed-loop gain that transforms reference sensitivity ΔR0 before feedback to equilibrium sensitivity ΔR0 after feedback.

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We define the unit feedback response as the ratio of the feedback response to the reference temperature or sensitivity that triggered it: or, in plain English, the amount of feedback-driven temperature or warming per degree of the pre-feedback temperature or warming.

The implication of the whigmaleerie’s Fig. 1 is that the unit feedback response ΔB0 / ΔR0 to the greenhouse warming to 1850 is 18/ 10, or 1.8, while the unit feedback response B0 / R0 to emission temperature is 5 / 255, or 0.02. The implication is that, in the widdershins world of the whigmaleerie, feedbacks are imagined – per impossibile – to respond 90 times more energetically to each degree of greenhouse-gas warming than to each degree of emission temperature. Nothing more need be said of the whigmaleerie, whose author had known of this central defect in his argument in advance, for I had explicitly drawn his attention to it before.

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I shall leave the reader to work out the relationship between the feedback impact ratio X, defined in the above equation, and various real or imagined values of the system-gain factor a0. In that revealing relationship between the X factor and a0, the reader will discern why it is that the high equilibrium sensitivities profitably imagined by official climatology, which had erroneously defined feedback and had consequently not understood that feedback responds to equilibrium temperature, are untenable. Or watch the video of my lunchtime keynote at the forthcoming Heartland Climate Conference in Washington DC. It will blow your socks off.

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242 thoughts on “Answer to a whigmaleerie about temperature feedback

  1. Lord Monckton, I do see your basic argument, that GHGs were producing an effect in 1850, resulting in that temperature. Therefore, counting the whole effect, including the changes since 1850, is an entirely reasonable method of calculating the effects of GHGs.
    However, the slithy toves were a bit much.

    • Do I understand correctly that that the calculations include natural variability including albedo, Milankovitch cycles, etc., and perhaps pixy dust in addition to GHG either natural or anthropogenic; in other words, the whole shebang. And that feedback may be either positive or negative.

      • No, from the original post, just an attempt to quantify the effect of GHGs. I would put it as the maximum effect.

        • Mr Halla is right: not only were GHGs present in 1850, accounting for a directly-forced warming, before feedback, of about 10 K (see e.g. Lacis+ 2010), but emission temperature was present too, and the feedback processes then subsisting (the same processes as today) had perforce to respond to emission temperature as well as to the preindustrial GHGs. He is also correct that we had no need to take account of variability in albedo, and still less of Milankovich cycles, which do not cause change over policy-relevant timescales.

          • we had no need to take account of variability in albedo

            Cloud is a significant part of albedo. Changes in cloud due to natural variability and as feedback to any changes due to warming ( natural or otherwise ) are key factors in understanding climate and climate feedbacks.

            ΔR0 as the 10 K reference sensitivity to the naturally-occurring, noncondensing, preindustrial greenhouse gases;

            Again you slip in the “noncondensing” exception as though it is the most obvious and necessary thing to do, without the slightest explanation of why. Water vapour is the most significant GHG by far. If you are going to exclude it you need to say more than just “noncondensing” .

            Also trying to impress everyone with your knowledge of obscure words from the paleo record of the English language is not a very convincing way to prove you know about physics and feedbacks.

          • Greg must be an unhappy soul: all he does is whine about everything. The reason why we had no need to take account of variability in albedo in arriving at emission temperature is that that quantity is canonically defined as the temperature that would prevail at the Earth’s surface in the absence of any greenhouse gases or feedbacks. Clouds are a form of water vapor, which is a greenhouse gas. That is why they are left out of account in deriving the emission temperature.

            And the reason for distinguishing between the noncondensing greenhouse gases such as CO2 or methane and the condensing greenhouse gas water vapor is that changes in the concentration of the former are treated by official climatology as forcings and changes in the concentration of the latter are treated as feedbacks. Since we accept all of official climatology except what we can prove to be false, we have retained that crucial and long-established distinction. if Greg wishes to argue against that, then he should address his concerns not to me but to the IPCC secretariat.

            It is interesting that all the regular trolls who infest threads such as this whine about inconsequentialities such as my occasional use of words with which their education has somehow not acquainted them. But they are outvoted by those who are delighted to extend their vocabularies. And why this distinction? Because the trolls see it as their sullen, boring mission merely to adhere to and to rebarbatively regurgitate the Party Line, whereas everyone else here enjoys learning something new.

          • Greg, “Cloud is a significant part of albedo. Changes in cloud due to natural variability and as feedback to any changes due to warming ( natural or otherwise ) are key factors in understanding climate and climate feedbacks.”

            So non condensing trace gases are never filtered out of the atmosphere by natural means, only by chemical processes.

            On the other hand non condensing gases don’t contribute to cloud formation so how can they interfere with climate / weather.

          • “On the other hand non condensing gases don’t contribute to cloud formation so how can they interfere with climate / weather.”

            As Greg stated, as feedbacks to changes in the total amount of climate forcing.

          • The changes to CO2 forcings are immeasurable, as are its impacts. “It’s models all the way down.”

        • I understand all of Monckton’s English without reaching for a dictionary. There was a time when I thought it was clever to write that way. Now I try to communicate effectively.

          • Quelgeek: The language has come down a long way in my lifetime. My generation was the last to have latin as a common highschool course (early 50s, Winnipeg). I met a lady in of about 50 recently who had a degree in English lit who told me that she hadn’t taken the ‘Shakspeare option”! I had Shakespeare starting in grade six and was obliged to study it again in the prescribed course in first year science at university and I’m a mere geologist and mining engineer. Heck, my father took both latin and Shakespeare in a one room schoolhouse on the Canadian Prairies that he rode to on horseback.

            Winston Churchill had an enormous vocabulary. He wrote a 4 vol history of the first world war, a 6 vol one on the second and a 4 vol “History of the English Speaking Peoples” starting from the Roman invasion through the the colonial period and, of course, the history of the British Isles.

            A colleague of mine in Winnipeg took his PhD in Chemistry at Oxford where he was also obliged to study remedial English and to ‘repair’ his accent on orientation exercises!! He, too, had studied latin and Shakespeare as a boy.

            CM of B is a graduate of Oxford and I have no doubt about his easy mastery of a much bigger vocabulary than I have (he was also a research guy and speechwriter for Prime Minister Thatcher). Re Winston C., did you know he won a Nobel Prize for Literature?You are probably aware that the founding fathers of the USA had British accents and als huge vocabularies.

          • Good for Gary Pearse! He is one of the majority here who enjoy coming across previously-undiscovered corners of the English language. But o how the trolls hate it! They are not here to learn or to enjoy, but merely to discombobulate.

          • Gary, America has come a long way (not saying which way) since the Enlightenment. Schools have replaced Latin/Shakespeare with Ebonics.

    • From my down to earth position in the wabe I can see that the Gaussian distribution curve for English encompasses, within those outer fringes of 2 SD`s, version spoken by Americans, Australians , Irish, Scottish etc etc etc, although I notice that Pidgin is further out, but still near the mean if measured in their own subset.

      as they say :- variety is the spice of life

      • No no no no. On one hand there is English as it is spoken by the Queen, and on the other there are mistakes.

  2. While there are many errors in how linear feedback amplifier analysis was misapplied incrementally in the formulation of climate feedback analysis, the esoteric concept of feedback is too complicated for most people to wrap their heads around, thus deferring to authority is pretty much a necessity which makes convincing others of the errors far more difficult especially since the errors have been improperly canonized as settled science for decades. An energy analysis would be far easier for more people to understand.

    The Earth receives 240 W/m^2 of post albedo input from the Sun whose equivalent temperature is about 255K. The net energy emitted by the surface are the SB Emissions of the surface at its temperature. Since only radiation can leave the planet, all of the non radiant energy entering the atmosphere (latent heat and convection) can only be returned to the surface thus have a zero sum influence on the net radiant emissions by the surface. The average net emissions are about 390 W/m^2 for an equivalent average temperature of about 288K. This means that the average W/m^2 from the Sun contributes about 1.62 W/m^2 to the surface emissions.

    One W/m^2 of forcing is defined as increasing the 240 W/m^2 of post albedo solar power up to 241 W/m^2 which is predicted to increase the average surface temperature from 288K to 288.8K requiring the net surface emissions to increase by about 4.4 W/m^2.

    The planet has no way to distinguish the next W/m^2 from the average W/m^2 concurrently arriving from the Sun, so it’s an obvious violation of COE if the average W/m^2 contributes 1.62 W/m^2 to the average emissions while the next W/m^2 contributes 4.4 W/m^2 to that average. Feedback can’t do this either, as W/m^2 of feedback are linear to W/m^2 of net emissions and feedback can’t tell one W/m^2 from any other either. In principle, the feedback power is the power returning to the surface from the atmosphere and that offsets emissions above and beyond what the arriving solar power can do in the absence of GHG’s and clouds providing that feedback. It’s magnitude is about 620 mw per W/m^2 of forcing making the 3.8 W/m^2 of feedback required by the IPCC obviously impossible.

    • Actually, the feedback is less than that. The Earth receives about 324 watts/m² from the Sun. Part of that is reflected thanks to negative feedback from clouds- that’s where we get the 240 watts.

      An additional 100 watts /meter² or so is dissipated in convection and in the latent heat of vaporization of water.

      390/241 gives a magnification of 1.618 in the greenhouse effect.
      Actual magnification is
      490/324 = 1.512, a lot less.

      • The convection and latent heat are not dissipated and whatever effect that energy, plus it’s offsetting return to the surface has on the surface temperature, is already manifested by the surface temperature and its corresponding radiant emissions quantified by the SB Law.

        While it’s true that some of the solar energy is reflected by clouds and ice contributing about 2/3 of the albedo, the surface power gain corresponding to the IPCC’s definition of the sensitivity is about 1.62 because only non reflected solar power contributes to the surface emissions (temperature). This adjustment in their definition allows them to hide the negative feedback like effect from albedo.

        BTW, clouds contribute more than half of the warming beyond what solar energy can do on its own, so the ‘feedback’ contribution from GHG’s is less than 300 mw per W/m^2. Only about 1/3 of this is from CO2, thus the total effect of CO2 is only about 100 mw per W/m^2. Even if the contribution from CO2 was to double, the result would be 1.72 W/m^2 of surface emissions per W/m^2 of forcing which is still far less than the 4.4 W/m^2 per W/m^2 of forcing predicted by the claimed nominal ECS.

        • How can you apply the Stephan Boltzmann equation and have 240 W/m^2(after subtracting 100 W/m^2 of reflection) as input at TOA and then calculate a temperature from that and say that is the temperature of a surface without an atmosphere after you have already used the atmosphere to reflect the 100W/m^2?

          • Very good question! Answer: You do it because (a) your EEG flatlined; (b) if you took a class in logic, you failed the class; (c) personal considerations make it dangerous to challenge the AGW orthodoxy; (d) at a social gathering of your fellow flatliners you want to be a part of the majority; (e) some combination of the above.

          • Alan,

            You can’t and it’s disingenuous to do so, but that’s the convention established by the IPCC’s self serving consensus when they consider the 255K equivalent temperature of 240 W/m^2 as the ‘pre feedback’, or open loop response. Without GHG’s and clouds, the albedo would be the same 0.11 as the Moon and the average surface temperature would be a degree or so below freezing. The consensus doesn’t like to acknowledge this because the claimed 33C ‘warming’ caused by GHG’s (most of which comes from clouds anyway), is only about 16C and doesn’t seem as important.

            The only legitimate open loop gain for the climate system is the behavior of an ideal BB which in the steady state emits 1 Joule for each Joule it absorbs which when expressed in terms of a rate density, emits 1 W/m^2 per W/m^2 it’s absorbing. The 1 W/m^2 of emissions per Wm^2 of forcing of the no feedback response becomes 1.62 W/m^2 per W/m^2 of forcing when all possible ‘feedbacks’, positive, negative, known and unknown have had their effect on the result.

          • https://link.springer.com/article/10.1007/s00704-016-1732-y

            I came across this paper published in 2016 that appears to be the hymn book that all alarmists preach from. Since it has been shown that downward backward IR has not been increasing even though all GHG’s have been increasing in atmosphere, the alarmists have had to switch their theories. Now their main premise as you know, is that as CO2 increases, it “pushes” the largest GHG emission height higher so that there is more emissions at a higher level than before. Left unsaid is the implication that because there is more emissions from a greater height, then that means there is more trapping of heat. Another interpretation of this is that because the greatest emission level has been pushed higher there is less radiation to space because the higher level will be colder. But this interpretation already assumed that the temperature of the lower level of emission has now been transformed to the temperature of the higher level. So this makes no sense because a new level can’ t both be colder and hotter at the same time. Both interpretations are nonsense of course. The key is to take this paper apart point by point so that the alarmists have no theory of the GHE to work with.

    • “…all of the non radiant energy entering the atmosphere (latent heat and convection) can only be returned to the surface thus have a zero sum influence on the net radiant emissions by the surface. “

      Mmm, no. Thermalization can pass that heat to radiating constituents, which can then send it fleeing to space.

    • Co2isnotevil

      I am answering separately from Alan and the others because my point is different.

      You touched well on the point that the effect of GHG’s is to drive up the surface temperature in order to “get the energy” past the atmosphere into space. That is the greenhouse effect. However there are two considerations which have not been well acknowledged and must be.

      The measure of concern is not the surface temperature (as if the Earth had no atmosphere) but the temperature of the air about two metres above the surface – what is being reported as the temperature in common parlance. The root of this error is the IPCC comparing the temperature of the Earth having a GHG-containing atmosphere with the Moon, instead of with the Earth with a GHG-free atmosphere, where the only variable is the GHG concentration.

      The second consideration is that there are two mechanisms for warming the air just above the surface, not one: back radiation as highlighted and calculated by Monckton, and convective heat transfer from the surface (which you estimate at about 100 Watts, value of which is unimportant to the principle I will hopefully highlight).

      Anything that takes heat from the surface and puts it into the atmosphere affects the ground temperature. Radiation and convection both do this, and some (or all) of that energy is conveyed back to the surface by either radiation or convection. As a result, as you correctly stated, the surface must perforce, increase in temperature to shed enough energy to space to bring the system into balance.

      Consider the extreme condition when there are no GHG’s in the atmosphere. The convective heat transfer will double due to stronger direct heating (there being no intervening GHG’s) and the atmosphere will be heated more by this mechanism than in their presence. The only means of transferring that heat back to the surface is that same mechanism: convective heat transfer at night when the surface has cooled radiatively.

      In this scenario the same insulating conditions prevail: the air warmer than the surface at night and is re-heated by the surface during the day. The surface must be warmer than it would be in the absence of an atmosphere, again in order to push the net incoming energy out to balance the equation. In short, a non-radiative atmosphere is not cooler than the surface at all times. Well…it is on paper if, like the IPCC, one ignores a physical mechanism that is always present.

      This understanding of convective heat transfer impacts any claimed temperature feedback from GHG’s.

      The standard arguments revert, after a radiation-only explanation of the surface temperature, to discussing the air temperature! The 1850 air temperature is suddenly the metric choice, and all warming attributed to radiative effects.

      Adding GHG’s to an atmosphere (condensing or not) increases its ability to lose heat so that not just the surface is involved. It is broadly accepted that GHG’s cool the atmosphere and increase the surface temperature. Fine. But it is not true that the warming of the atmosphere is cause by radiation alone. Therefore the ECS with respect to GHG’s cannot account for all atmospheric heating, because attempting to do so requires ignoring the convective heat transfer that exists in the absence of GHG’s and which brings the air temperature higher than the theoretical black body temperature. Discussing radiative heating only from a BB temperature will give the wrong GHG ECS.

      Monckton correctly discusses feedbacks, and correctly discusses what the radiative contribution to the air temperature would be if there was no convective heat transfer to the atmosphere from the surface. But there is.

      Some of the air temperature difference between a BB and 1850 comes from convective heat transfer therefore the ECS to GHG’s is lower than is calculated by the IPCC and Monckton.

  3. Christopher I appreciate your wit, have you ever considered taking up where George McDonald Fraser left off with the ‘Flashman’ novels? 😉
    Or perhaps a new Flashman type character in a series of AGWA related skulduggery ?

  4. What fun!
    I haven’t looked up so many words from one document since High School some forty plus years ago.
    Gallimaufry, snicker.

    A wonderful fun read!

    Have a wonderful visit to Washington DC and an excellent reception to your Lunch Keynote. I’m only a few miles away and unable to be there.

      • After Thursday, the pork-barrel climate extremists will have a lot to beef about, poor lambs!

        • Good luck but I humbly submit the biggest problem with the argument is forgetting to simplify the equation.

          No voter uses the IPCC math. They use grade school math and may recall the outcome when numerators outweigh denominators

          (Cars+Heat+Co2) ÷ Polar Bears = polar bears squashed by the top of the equation.

          They know blankets warm the user.
          Cars in the sun get hot. Insulating the attic lowers the bill.

          Until AGW refutation can be similarly distilled:

          (Hair Dryer + Bathtub) = Cold Bath

          there’ll be little persuasive turnover amongst barmates or soccer mom’s.

          • “(Hair Dryer + Bathtub) = Cold Bath” ??????????????
            Be careful you don’t electrocute yourself.

          • Alan Tomalty,

            Thanks for the peer review. Updated accordingly

            In all Cases Where a GFCI Is Not Installed:

            Bathtub + (Hair Dryer x Green Power) = Just as Cold Water

            That surely makes it safer, but distracts from my idea that people intuitively know you can’t heat the bathwater by blowing hot air at the surface.

            It’s an open source analogy, have at it.

    • In response to Ken, a thesaurus is a useful tool for those who need it. I don’t. Me, I read.

      • CMB – I’m looking for, and very much value, good reading/learning materials. If you have time, I would appreciate a recommended short-list, so that I, too, may eloquently express that which matters most.

        Much appreciated!

        • In response to Nigel in California, start with J.R.R. Tolkien’s Lord of the Rings: it’s a beautiful piece of modern English. Then (continuing in Oxford) read the Screwtape Letters by C.S. Lewis, the most accessible of theologians. Then, for sheer writing style, Gibbon’s Decline and Fall of the Roman Empire and Macaulay’s History of England (Hugh Trevor-Roper, when he was Professor of History at Oxford, made all undergraduates read these two in their first term). To pick up the Scottish words I’m fond of using, read the novels of John Buchan, of which the most entertaining is John Macnab. You should also read The Thirty-Nine Steps, Prester John and, to get something of the southern upland Scots, The Blanket of the Dark. Read one or two of Congreve’s plays. When you’ve got through that lot, come back to me: there are plenty more books on my list.

        • A further couple of important items for Nigel in California: the works of Shakespeare and the King James version of the Bible. He may also like to read the series of lectures on the glories of English literature by Sir Arthur Quiller-Couch, a minor poet from Fowey in Cornwall, whom the then Liberal Government appointed as Regius Professor of English at Oxford. Those lectures will give him plenty more ideas. Interestingly, Q (as he was known) devoted most of two lectures to the King James Version, which has had a far greater impact on the language than those who have never read it could possibly appreciate.

          • Thank you, Lord Monckton!

            I have a couple of these on the shelf (Gibbon’s, King James Bible). I shall look into the other’s at the local library. If you are interested in some religious history, and inspirational, good writing, I highly recommend “God Passes By” by Shoghi Effendi. He carried around a copy of Gibbon and attended Balliol College, Oxford from 1920-21. You can read it online here:

            http://www.bahai.org/r/690642564

            Again, many thanks for taking the time to put together the above list. I respect your efforts, and will put forth an honest effort to improve my English using the above recommendations.

  5. We should not lose sight of the fact that positive feedback was invoked by Dr. Hansen to transform a limited and, on the whole, beneficial warming into something catastrophic.

    CM did not start that nonsense. He merely pointed out that Hansen has misapplied a feedback analysis that Hansen, apparently, did not fully understand.

    • Yup. By ignoring negative feedbacks and exaggerating positive, Hansen managed to turn one degree of mild beneficial warming (plus yet more salubrious planetary greening) into a scary four degrees of heat per doubling of vital trace gas plant food in the air.

      On our self-regulating water world, negative feedbacks should always dominate, keeping it from runaway cooling or heating. Although we did suffer long periods of near freezing to death in the Paleoproterozoic and Neoproterozoic Eons, when the sun’s power was weaker.

      Runaway heating, not so much. As in never. Yet. In five billion years, yeah, probably or at least possibly. The sun gains one percent in power every 110 million years, then it will go red giant.

    • “We should not lose sight of the fact that positive feedback was invoked by Dr. Hansen to transform”
      That mis-states what he did. It’s true that he was lead author on one paper in 1984 which has been mentioned in recent discussions. But he didn’t really follow up much that line. The 1984 paper was titled: “CLIMATE SENSITIVITY: ANALYSIS OF FEEDBACK MECHANISMS”
      and it was introduced thus:
      “We study climate sensitivity and feedback processes in three independent ways : (1) by using a three dimensional (3-D) global climate model for experiments in which solar irradiance So is increased 2 percent or C02 is doubled, (2) by using the CLIMAP climate boundary conditions to analyze the contributions of different physical processes to the cooling of the last ice age (18K years ago), and (3) by using estimated changes in global temperature and the abundance of atmospheric greenhouse gases to deduce an empirical climate sensitivity for the period 1850-1980”

      His primary basis for sensitivity estimation, then and since, has been his 3D GCM. Like other GCMs, it makes no use of feedback ideas (it can’t). His specific section on feedback was titled
      “1-D Analysis of Feedbacks in 3-D Experiments”
      And that is the proper status of feedback here, as a post-hoc diagnostic, to interpret model output. You can use it if it helps you; Hansen later seems to have found that it mostly didn’t.

      Hansen’s actual feedback analysis was perfectly correct.

      • Thank God that American policy makers have ignored their preposterously faulty results.

      • B.S., Nick. Your model “emergent” feedbacks are a result of UN IPCC CMIP and other modelers’ adjustment of parameters to get an ECS that “seems about right,” in their words. If, and only if, models were purely first-principle exercises one might, and just might, get some idea of feedbacks in the climate system. Everything else is salesmanship; propaganda by those with a vested interest.

        Hansen started with the assumption of a 4X ECS. His patron, Sen. Wirth, demanded such results.

        • I once asked David Evans, who has four degrees in control theory and related subjects, to tell me what he thought of Hansen’s feedback paper of 1984 (an appropriate year). He said it was so full of errors that he would not have allowed it to pass peer review.

          • Hansen used Bode’s feedback analysis based on a 1945 paper. By the time Hansen wrote his paper, undergraduate textbooks presented a simple analysis that didn’t make the implicit reference level assumption made by Bode.

            It seems to me that Hansen knew less about feedback than a community college electronics student.

          • Spot on Milord.
            Back to the CO2. Seems to me partial pressure of CO2 is negligable so composition of atmosphere IS irrelevant, except for H2O.

          • “He said it was so full of errors that he would not have allowed it to pass peer review.”

            That was my assessment as well when I reviewed Hansen’s feedback paper nearly 2 decades ago. It was also my assessment of the follow on paper by Schlesinger which ostensibly corrected some of Hansen’s errors, but did so by introducing even more errors. These 2 papers combined comprised the only theoretical support in AR1 for an ECS large enough to be a potential concern and the many errors were subsequently canonized as settled science.

            Roe’s 2009 paper was a rehash of the Schlesinger’s paper, contained the same errors and should not have gotten past peer review either.

          • “that didn’t make the implicit reference level assumption made by Bode”
            Would you care to identify Hansen’s reference level assumption?

            Hansen, like Bode, is simply doing linear algebra with his variables. And despite the criticism, no-one has shown any point at which that algebra goes wrong.

          • Nick,

            Hansen cited Bode and then declared without showing his work, ‘it follows that’, f = 1/(1 – g). The proper equation is g = 1/(1 – f) which can derived from the gain equation, 1/Go = 1/g + f, setting the open loop gain to 1 and solving for g. Thereafter, the rest of his paper was moot.

            This error was indeed noticed by Schlesinger who ‘corrected’ it by showing some work deriving an apparently proper gain equation. Schlesinger’s derivation assumed Go was not a dimensionless 1, but an unknown ‘gain’ that converts a change in W/m^2 of input into a change in temperature output which Schlesinger improperly referred to as the open loop gain. He then assumed that the feedback factor, f*Go was the feedback fraction, f, which is only the case when Go = 1 and the result was what he claimed to be the open loop gain cancelled out. In other words, he undid the fake ‘amplification’ by Go before calculating the fraction of the gin block output to be added to the forcing input.

            You can see the error in this figure from his paper:

            http://www.palisad.com/co2/fb/sh1.png

            He claims f = GoF and that this is the dimensionless ‘f’ in the gain equation which is only true when the proper dimensionless Go is 1. His Go had units and his F undid those units.

            Both Hansen and Schlesinger assumed that the average input was the power supply and the incremental input was the forcing, which is absolutely incorrect and inconsistent with Bode’s preconditions of strict linearity and an infinite, implicit source of Joules supplying the output power. The solar input power can’t be both the forcing and the implicit power supply and it incremental solar input is considered forcing, all of the solar input must also be considered forcing.

            You can’t separate the average W/m^2 from the next W/m^2 as both necessarily have the same effect on the ultimate output, which can only be W/m^2, as only a dimensionless fraction, f, of an output in W/m^2 can be legitimately added to W/m^2 of solar forcing.

          • “The solar input power can’t be both the forcing and the implicit power supply and it incremental solar input is considered forcing, all of the solar input must also be considered forcing.”

            +1

          • George,
            “then declared without showing his work, ‘it follows that’, f = 1/(1 – g)”
            He did show his work. It is trivial linear algebra. His basic equation is actually (6):
            ΔTeq = ΔTₒ + ΔTfeedbacks (6)
            He defines f (feedback factor) and g (system gain) by:
            ΔTeq = f ΔTₒ (4) and
            ΔTfeedbacks = g ΔTeq (6)
            Substituting in (6):
            f ΔTₒ = ΔTₒ + g ΔTeq = ΔTₒ + g f ΔTₒ
            or
            f = 1 + g f
            f (1 – g) = 1
            f = 1/(1-g) (7)
            He’s writing in a scientific journal. You don’t need to spell out every step of high school algebra.

            You are using a different kind of g, which is actually 1-g in Hansen’s terms.

            “The solar input power can’t be both the forcing and the implicit power supply and it incremental solar input is considered forcing, all of the solar input must also be considered forcing.”
            Complete nonsense. Firstly, Hansen is mainly looking at GHG forcing, which doesn’t involve varying solar input. But your dogma just has no foundation. If you have mains hum in your power supply, that is a nuisance, and will show up as signal. It doesn’t mean that the whole power supply must be considered signal, or that you don’t have a power supply any more. All power supplies have some degree of hum.

          • Nick,
            Read Schlesinger’s paper where he even points out this specific error in Hansen’s paper.

            Examine your equations in more detail. The definition of the system gain as what you multiply the output by to get the feed back contribution is actually the dimensionless fraction of the output returned to the input as feedback. The definition of the feedback factor as what you multiply the input by to get the output is actually the closed loop gain.

            You then repeated Schlesinger’s faulty derivation while reversing f and g, where he assumed that g*f is the dimensionless fraction of the output added to the input which makes the same mistake of conflating the feedback fraction with the feedback factor. The feedback factor is Go*f, where Go is the dimensionless open loop gain and f is the dimensionless fraction of the output returned to the input as feedback. The feedback factor and feedback fraction are only the same when the open loop gain is 1.

            Delta T in and delta T out is no more linear than delta W/m^2 in and delta T out. The ONLY relationship linear enough to be considered representative of the closed look gain in a liner feedback amplifier is the ratio between the average W/m^2 of input from the Sun and the average W/m^2 of SB emissions by the surface consequential to its temperature.

          • “Read Schlesinger’s paper where he even points out this specific error in Hansen’s paper”
            There is no error. Schlesinger does not say there is an error. He simply points out that Hansen is using a different convention. Hansen is consistent, so there is no problem. Your objections are not pointing out errors. You are just saying that he should have used different conventions. But it is all just elementary linear algebra, and there is no obligation to do it your way. His way is fine.

          • All the math in the world fails when it does not represent reality. The world (atmosphere) is not warming in accordance with a 3X gain, feedback, or whatever term you want to arm-wave.

          • Nick,

            If the open loop surface power gain is not 1 W/m^2 of surface emissions per W/m^2 of forcing, what do you think it is and how can you justify that value?

            The surface power gain metric is very simple to understand and quantifies the W/m^2 change in surface emissions equivalent to a specified change in the surface temperature said to from from 1 W/m^2 of incremental input power (forcing), starting from the emissions corresponding to the current average temperature. It an equivalent metric to the IPCC’s sensitivity factor whose claimed nominal value is 0.8C per W/m^2 and which when converted into am EQUIVALENT surface power gain becomes 4.4 W/m^2 of surface emissions per W/m^2 of forcing.

            Do you deny the errors because you can’t possibly justify amplifying 1 W/m^2 of surface emissions per W/m^2 of forcing into the 4.4 W/m^2 of surface emissions per W/m^2 of forcing required to support the IPCC’s nominal ECS?

            To achieve this much surface power gain, the 3.4 W/m^2 of feedback power required is greater than the forcing casing it, which is an obvious violation of COE. If every W/m^2 from the Sun resulted in this much feedback power, the surface emissions would correspond to a temperature close to the boiling point of water. For this not to be the case, the climate must distinguish the next Joule from the average Joule and thus far after numerous requests, you’ve been unable to explain how the climate system can make this distinction, yet you stubbornly hold on to your position that requires this distinction to occur.

          • Nick,

            With no feedback in the system, Hansen states:

            ∆Teq = f ∆To

            ∆Teq cannot be equal to the feedback factor times the input. This means although Hansen used the label “f”, usually understood to be the feedback factor, this label is actually the closed loop gain of the system.

            g = ∆Tfeedbacks∕ ∆Teq

            The change in the output, ∆Teq, is the change in the input, ∆Tfeedback, multiplied by the closed loop gain of the system. This formula should be

            g = ∆Teq/∆Tfeedback, i.e. (∆Tfeedback) * g = ∆Teq

            The only other interpretation is that g is actually the feedback factor meaning:

            ∆Tfeedback = g * (∆Teq)

            ∆Teq = ∆To + ∆Tfeedback

            This is can only be correct if f = 1, i.e. the gain of the system = 1.

            So, yes, the math is correct but the interpretation of the formula is not what most people would understand from the labels used!

            The general equation, using Hansen’s labels would be

            ∆Teq = f * (∆To + ∆Tfeedback))

            or by substituting (1) above:

            ∆Teq = ∆To + g * (∆Te)

            Rearranging terms gives:

            ∆Teq- g * (∆Te) = ∆To , (1-g)∆Teq= ∆To or

            ∆Teq= ∆To / (1-g)

            This is the very definition of the closed-loop gain of a feedback system where g is the feedback factor.

            Now, Hansen states later in the article:

            “The feedback factor f provides an intuitive quantification of the strength of feedbacks”

            In other words, Hansen changes from using “f” as the closed loop gain of the system to using it as the feedback factor. A total inversion of how the math was actually written.

            Hansen’s math and his labeling is so confusing that the entire section becomes meaningless.

          • Tim,
            If ∆Teq = f ∆To is before feedback, then f represents the open loop gain, not the closed loop gain. Of course, since ∆To is not the input, but considered to be the zero feedback response to an unspecified input, the equation itself has no correspondence to anything having to do with the climate sensitivity which Hansen is attempting to quantify.

          • co2,

            Thanks for catching my error on the gain classification! He is still using “f” as a gain, not as a feedback factor.

            Regarding ∆To, Hansen uses the formula:
            ∆Teq = ∆To + ∆Tfeedback

            As I pointed out the general form should be: ∆Teq = f * (∆To + ∆Tfeedback)

            For a gain “f” to be applied that has to mean that (∆To + ∆Tfeedback) is an input. Otherwise his first formula would have to be ∆Teq = ∆To with no f.

            As I said, this whole section is so confused because of inconsistencies that it is meaningless.

          • haha X factor david evans
            Lord M now appeals to busted authorities.

            Evans ( along with Monckton) is one of the skeptics who refused to share code and data
            when requested

            Mini Manns

      • Like other GCMs, [Hansen’s model] makes no use of feedback ideas (it can’t).“.
        Nick Stokes, I think you need to explain yourself a bit here. The GCMs can only obtain their overestimates of warming by using unrealistically high feedback. How can they do that without using any feedback ideas?

        I think your answer will be that GCMs operate only from known physics, and the physics of feedbacks is not known, therefore it has to be parameterised. But parameterisation of feedback must use feedback ideas. Mustn’t it?

        • Mike,
          “The GCMs can only obtain their overestimates of warming by using unrealistically high feedback. How can they do that without using any feedback ideas?”
          Just not true. They don’t use high feedback. They don’t use feedback at all.

          The reason that they can’t is that they solve pde’s for the physics. That is, they divide the region up into millions of cells, and account for mass, momentum and energy transfer between cells. This is done over timesteps of a half hour or so, and the answer is whatever emerges. Feedback only makes sense on a global or other very large scale, with spatial and time averages. You can’t fit such global constraints into this cell scale arithmetic. For the same reason, they don’t use global scale forcings as input. They can’t. Forcings and feedback are what you can deduce from the arithmetic. They can’t be part of it.

          • Nick, this comment is very misleading. The physics of many climate processes are not known with precision such that models are able to calculate their values; thus modelers’ parameterizations of various climate metrics. It is these parameterizations that allow the many and varied outcomes of the various models, including ECSs. They also get to play with the values of historically unmeasured quantities such as aerosols.

            The modelers admit they “tune” their models to get ECSs that “seem about right.” It is not “just the physics,” as you and others claim. It is with much humor that I point out that it is a Russian model that comes closest to replicating the various measured climate metrics.

          • But you can by making certain assumptions as to increasing CO2 concentrations leading to increased temperatures leading to increased water vapor leading to increased temperatures, ….. Your whole shtick on feedbacks ignores the role “tuning” plays in generating desired model ECSs which leads everyone to talk about feedbacks. Quit playing hide-the-pea, Nick

      • “The temperature increase believed to have occurred in the past 130 years (approximately 0.5°C) is also found to imply a climate sensitivity of 2.5–5°C for doubled C02 (f = 2–4), if (1) the temperature increase is due to the added greenhouse gases…” – Climate Sensitivity: Analysis of Feedback Mechanisms – Hansen, Lacis – 1984

        Recall Lewis and Curry on Sensitivity. Hansen & Lacis used three methods, one of which is the above in quotes.

        Speaking of Lewis and Curry, what assumptions and methods did they use for determining climate sensitivity? Tell them they were wrong.

        • “Tell them they were wrong.”
          Well, it’s Lord M who is telling them that they, like all other scientists, are wrong. They are making the same alleged “grave error” of not feeding back “emission temperature”. This last has the effect of feeding back a number which the arithmetic treats as a change from absolute zero since 1850. Naturally the result is that, if such a change produced only a degree or so of warming, then the system must have no sensitivity to feedback at all.. But L&C found a sensitivity in the normal way. It’s at the low end of the IPCC range, but not totally fixed like Lord M’s.

          • Nick,

            It’s not at the low end of the IPCC’s range, but less than half of it. But it’s using the 1.1C anchor point which is not even correct, so it’s even lower than 0.7C in reality. We’ll be lucky if the ECS is even 0.5C.

            co2isnotevil’s heuristic minimizing and macro-averaging techniques suggest a best estimate ECS of only about 0.35C. Interestingly, his methods produce the same feedback factor as L&C.

    • Hansen’s paper was considered the holy grail theory supporting a high enough ECS to justify the formation of the IPCC and UNFCCC which started around the time his paper was published. Hansen made a critical error that was easy to spot and would have undermined the agenda if it had been scrutinized, especially as it comprised the theoretical foundation. He cited Bode as the feedback reference and then after the dubious phrase, ‘it follows that’, he presented a gain equation that assumed unit open loop gain and swapped the gain and feedback terms. He then came up with a set of presumed feedback coefficients that were consistent with his error, but meaningless none the less.

      Unfortunately, the error wasn’t detected, I believe by Schlesinger, until the process of forming the IPCC and UNFCCC had already gained critical mass around ‘science’ based on amplification by positive feedback. Schlesinger wrote a paper correcting Hansen’s error in time for AR1 by deriving an apparently correct gain equation starting with an apparent non unit open loop gain that converts W/m^2 into degrees. His derivation had another error of conflating the feedback fraction with the feedback factor which are only the same when the open loop gain is unity. In effect, what he considered to be the open loop gain was improperly canceled out of the derived gain equation. He then came up with another set of equally meaningless feedback coefficients. Schlesinger’s paper was then cited along with Hansen’s paper in AR1 as the theoretical basis for how feedback results in a large enough sensitivity to cause alarm and which has subsequently been canonized.

      • “Hansen’s paper was considered the holy grail theory supporting a high enough ECS “
        If there is any holy grail, it is Arrhenius’ paper of 1896, which got very similar ECS without using any Bode theory. In fact, of course, Hansen’s ECS, as he says, came from the results of his GCM.

        • Nick,
          Arrhenius assumed all the increase that was not due to water vapor was caused by CO2, when more than half is the consequence of clouds. which while GHG’s are narrow band absorbers and emitters of LWIR photons, the water in clouds is a broad band absorber and emitter of LWIR photons. His coefficients that led to his modeled (calculated) average of about 5F per doubling (2.8C) were also sketchily defined. The actual uncertainty in the Arrhenius calculation of the effect is even larger than the +/- 50% uncertainty in the ‘settled’ value of the ECS.

          The Arrhenius paper supplied the idea of a possibility while the Hansen paper supplied the feedback theory to support it. This is what makes confirmation bias so dangerous for the truth.

  6. “Whigmaliere: Any fantastical ornament; a trinket; a knickknack; also, a whim or crotchet. Also used attributively.”

    I do so love a thorough smack down. And the Brits do it the best.

  7. Ma Lord … I haven’t a clue what all this is about, but iffin I’m understanding this right, you are dividing the greenhouse response Bo of 5 K by the 255 K that gave rise to the signal acting upon the greenhouse gases, thus coming up with a factor per degree ….yes?

    A Question. Would it not be reasonable to assume that GHGs can only operate above their freezing temps? Thus, … the water vapor GHG effect would have to operate at temps above 273 K, and CO2 GHG effect would operate above 193 K. Thus, the entirety of GHG effect at 255 K would appear to be coming from CO2, at a rate of 5/62K setting the ECS of the Climate to CO2 at around 0.08 K/degree above 193 K (assuming a linear response for which I know is false).

    Of course, I see the flaw of my own argument, that being that the “globe” is NOT 288K, but is considerably hotter at the tropics, and colder at the poles …. thus rendering any attempts to model climate on a global scale a complete waste of time. And given the movement of energy throughout the system, I’m not sure we have the computer power to solve that problem using the current radiation approach.

    OTOH …. I’ve been meaning to model the earths climate using a completely different approach. … but … I don’t seem to have the time to do it. There is this thing in my field called a physiological based pharmacokinetic model … it essentially models the absorption, distribution and elimination of substances in a body. Unlike all this radiation crap, a PBPK model would account for the energy stored in all media, as well as the movement of energy through the system. Using energy instead of a substance, and accounting for all the energy sinks, and changes to input at steady state, I think there is a possibility a person of blowing the entire climate debate wide open. Such a system would be much more accurate in pinpointing sources of change, as it accounts for ALL energy, not just radiation.

    Anyway, keep up the good fight! Cheers.

  8. “We define emission temperature R0 as the 255 K global mean surface temperature that would obtain on Earth at today’s solar irradiance and albedo but before any greenhouse gases have entered the atmosphere and before any feedback begins to operate;”

    What bogusity!!

    Refer to the Dutton/Brune Penn State METEO 300 chapter 7.2: These two professors quite clearly assume/state that the earth’s current 0.3 albedo would remain even if the atmosphere were gone or if the atmosphere were 100 % nitrogen, i.e. at an average 240 W/m^2 OLR and an average S-B temperature of 255 K.

    That is just flat ridiculous.

    NOAA says that without an atmosphere the earth would be a -430 F frozen ice-covered ball.

    That is just flat ridiculous^2.

    Without the atmosphere or with 100% nitrogen (zero GHGs) there would be no liquid water or water vapor, no vegetation, no clouds, no snow, no ice, no oceans and no longer a 0.3 albedo. The earth would get blasted by the full 394 K, 121 C, 250 F solar wind.

    That is to say: the w/ atmosphere/albedo cools the earth compared to w/o and RGHE goes kerbluey.

    FEEDBACK

    DOES

    NOT

    EXIST!!!

    The surface is warmer than ToA per Q = 1/R * A * dT (warmer – colder) same as a insulated house.

    The sans atmosphere albedo might be similar to the moon’s as listed in NASA’s planetary data lists, a lunarific 0.11, 390 K on the lit side, 95 K on the dark. Nikolov and Kramm suggested the same.

    And the naked, barren, zero water w/o atmosphere earth would receive 27% to 43% more kJ/h of solar energy and as a result would be 19 to 33 C hotter not 33 C colder, a direct refutation of the greenhouse effect theory and most certainly NOT a near absolute zero frozen ball of ice.

    Nick S.

    https://sos.noaa.gov/Education/script_docs/SCRIPTWhat-makes-Earth-habitable.pdf
    (slide 14)

    ISR
    With 30 % albedo: 957.6 W/m^2, 360.5 K, 87.5 C, 189.5 F

    With 11% albedo: 1,217.5 W/m^2 (27.1%), 383.2 K, 109.8 C (22.3), 223.8 F

    With 0% albedo: 1,367.5 W/m^2 (42.8%), 394.0 K, 121.0 C (33.5), 250.0 F

    • You have the correct idea. Energy leaving earth is slowed, just like an insulated house, thereby raising the instant measurement of temperature. If energy was truly trapped in a feedback loop, each day would be hotter than the previous day with no way out.

      • Jim.,

        Energy is not “slowed.” The rate must remain the same, the temperature rise changes with the resistance.

        • “Energy is not “slowed.” The rate must remain the same, the temperature rise changes with the resistance.”

          The rate at which energy is lost is slowed. It’s just like in your house. The furnace comes on and injects heat into the house. The insulation in the house causes the heat to be lost at a slower rate than the furnace put it in. The energy is still lost to the external environment.

      • Jim,

        It’s tough to have a conversation in text boxes.

        Q = 1/R aka U * A * dT (Hot – Cold)

        Q = Btu/h – rate of energy flow – This changes w/ the thermostat setting or the solar constant or the albedo and w/ constant R and ToA cold when Q changes so does the hot surface T.

        R = thermal resistance – 1/R = U conductivity – ALL of the heat transfer mechanisms – conduction, convection, advection, latent and radiation contribute to/resist/promote the movement of energy, i.e. heat, from hot to cold. More R, more dT hotter, less R less dT colder.

        A = area – generally a constant. The area/volume ratio of a house can affect.

        Hot – surface/inside temperature

        Cold ToA/outside temperature – where the molecules stop and 100% radiation takes over – 32 km.

        This equation describes the atmosphere w/o any GHG or LWIR hocus pocus.

        The bogus feedback theory exists to explain how the atmosphere warms the earth. The atmosphere does not do that.

        As ISR and albedo go up and down so does the surface temperature.

    • In response to Mr Schroeder, yes, there are feedback processes operating in the climate. And yes, those feedbacks respond to emission temperature.

      Since emission temperature is canonically calculated assuming today’s insolation and albedo, lunar albedo is irrelevant, though we did use it to calibrate our method of deriving emission temperature against the measured lunar-surface temperatures from the Diviner satellite.

      We have used the canonical 255 K as the value of emission temperature; and, to first order, if one starts with an ice-planet with the same albedo as Europa and applies today’s insolation, one ends up – even before accounting for feedback or for any greenhouse-gas warming – with an albedo of about 0.3, which is today’s albedo. There would be more ice on Earth than now, but 75% of the ocean would be ice-free and, of course, before feedback there would be no clouds.

        • Mr Schroeder should not describe our calculations as hand-waving. Hand-waving is what happens when people don’t do calculations.

          Like it or not, the canonical value of emission temperature is 255 K. And our approach is to accept all of official climatology except what we can prove to be false. When we started with an ice-planet of the same albedo as Europa, applied today’s insolation to it and rotated it, we found that the albedo would be about 0.3 – which is exactly the value on the basis of which emission temperature is currently calculated. There would be no clouds, but more ice, so the albedo would be much the same as today’s. So, in the end, we decided there was no mileage in complicating our central argument by pointing out, for instance, that the canonical derivation of emission temperature makes no allowance for Hoelder’s inequalities between integrals, no allowance for latitudinal variation in insolation and albedo, and no allowance for the fact that, without greenhouse gases, there would be no clouds in the atmosphere. Coincidentally, then, the wildly incorrect method used by official climatology to derive emission temperature happens to come up with something very like the right answer, albeit by the wrong methods. Now, hand-wave your way out of that.

          • Greenhouse theory assumes that surrounding space is cold, that the naked earth would radiate at 240 W/m^2 and 255 K and the atmosphere “warms” the earth to 288 K.

            ALL of that is incorrect, but what is the alleged mechanism?

            The GHG molecular feedback loop absorbs, “traps” some kind of “extra” energy and “back” radiates warming the earth and atmosphere.

            There is absolutely zero thermodynamics for “trapping” and “back” radiation and “extra” energy violates conservation.

            But where do these GHGs get this “extra” (333 W/m^2) energy to absorb and trap?

            The surface radiates as an ideal black body at 289 K and 396 W/m^2.

            Because of the contiguous participating media, i.e. air molecules, such BB upwelling energy does not exist as demonstrated by experiment in the grand scientific tradition.

            https://principia-scientific.org/debunking-the-greenhouse-gas-theory-with-a-boiling-water-pot/

      • “There would be more ice on Earth than now, but 75% of the ocean would be ice-free and, of course, before feedback there would be no clouds.”

        Why would there be no clouds? Surely there would be evaporation from the ice-free oceans which would continuously put H2O into the atmosphere. At some point that evaporating H2O would saturate the atmosphere causing clouds to form, and eventually H2O would be returned to the oceans in the form of rain.

        What am I missing?

        • What Mr Gorman is missing is that clouds comprise water vapor, a greenhouse gas, but emission temperature is calculated on the basis that there are no greenhouse gases yet in the atmosphere.

          • You stated “There would be no clouds, but more ice, so the albedo would be much the same as today’s.”

            I asked “Why would there be no clouds?”

            And you answer “What Mr Gorman is missing is that clouds comprise water vapor”

            I specifically said there would be water vapor in the atmosphere from the unfrozen part of the ocean so there *would* be clouds. That water vapor would primarily be over the oceans that are not frozen. So there would be no increase or decrease in the amount of ice on the earth. The albedo contribution from clouds caused by that water vapor would *add* to the albedo, it wouldn’t substitute for contributions from ice.

            How much water vapor exists in the atmosphere of Europa? Probably very little. Any water vapor that escapes into the atmosphere is probably quickly returned to the surface as ice or snow. That is not the case for the Earth. In addition, Europa is almost 100% covered in ice. As far as I know that has never been the case for the Earth.

            Assumption 1: Europa’s and Earth’s albedo are the same
            Assumption 2: There is no water vapor in the atmosphere of Earth

            Once again it seems like a lot of magic thinking going on here!

        • Water vapor is a GHG. It’s GONE! ALL OF IT!!!!

          Atmospheric pressure keeps water liquid. No atmosphere, no pressure, no water – PERIOD!!

          Just like the moon!!

        • What you’re really missing is that they are arguing with hypothetical situations that in reality would never exist.
          Both sides of this argument are pretending there is a magical thermodynamic effect from certain gases inappropriately named greenhouse gases, it’s kind of amusing.

          • In response to Mr Turner, I am trained in Classical logic. One of the basics is Socratic elenchus, which specifically requires the arguer to accept at least one proposition advanced by his interlocutor. Then the arguer invites the interlocutor to agree a proposition of his own. Once that proposition is agreed, the arguer draws conclusions from each of the two propositions, and invites the interlocutor to agree that the conclusions are properly drawn. Then the arguer demonstrates that one of the conclusions from the interlocutor’s proposition is at odds with one of the conclusions from his own proposition. If he has done this right, the interlocutor is compelled to abandon his original proposition.

            It is for this reason that we have adopted the simple approach of accepting all of official climatology except what we can prove to be false. We cannot prove that there is no such thing as the greenhouse effect, for it can be demonstrated quite easily in the laboratory, and was first thus demonstrated at the Royal Institution, just down the road from m’ club, in 1851. The mechanism of the greenhouse effect is understood down to the quantum level, so denying its existence is unlikely to be regarded as an acceptable proposition by our interlocutors.

            Instead, we have accepted that the greenhouse effect exists, but we dispute the magnitude of its influence on global temperature. Our particular point of dispute concerns the knock-on effects known as temperature feedbacks. We are now able to demonstrate that the feedback response to greenhouse gases has been unduly inflated, because hitherto official climatology has not accepted that quite a large fraction of the feedback response that they assign to the greenhouse gases is actually a feedback response to emission temperature – a feedback response, if you like, to the fact that the Sun is shining.

  9. Lord Monckton, I could never aspire to your level of derogatory eloquence. But no matter.

    I have spent the past few weeks aiding/editing another PhD’s mathematical critique of your most recent views related to absolute temperature and fundamental feedback errors. It concerns an interesting mathematical detail your draft paper and related blog posts have overlooked.

    Recall, we most recently mathematically jousted over at Judith Curry’s Climate Etc some years ago on your previous ‘irreducible equation’ posts, which I showed rigorously were further mathematically reducible, and which when further properly reduced and plugged into reasonable assumptions that you provided, produced an ECS equivalent to that observed empirically by Lewis and Curry energy budget methods. Meaning your equations as critiqued were mathematically ‘right’ but their applied math used as you advertised wasn’t. All here can revisit that kerfuffle using CE search terms.

    The current post delay hang up (weeks prior to this post of yours) is WP equation subscripts. I have suggested the work around that Dr. Curry and I used previously. CtM has found another. So you should have a multipart substantive response from a fellow skeptic soonish. I cannot say more, since is not my post. But I did provide CtM a possibly elucidating WUWT foreword

    I look forward to engaging all substantively once the new post series (not from me) appears.

    • I look forward to the contribution from Mr Istvan and his colleagues. Meanwhile, the simplest way to deal with equations in the clunky Wor-depress interface is to do them in LaTex or Word’s dreadful equation writer, take a screen capture and insert the equation into the word file as an image. That’s what I did in the head posting, which makes life a lot easier for those editing it for posting.

      But it might be worth your while to wait until you’ve seen my presentation of our result at the Heartland conference. We’ve found a very explicit and simple and, we think, robust way to constrain high-end equilibrium sensitivity, which very greatly simplifies the argument and increases its rigor.

  10. I could never aspire to your level of derogatory eloquence. But no matter.

    I have spent the past few weeks aiding/editing another PhD’s mathematical critique of your most recent views related to absolute temperature and fundamental feedback errors. It concerns an interesting mathematical detail your draft paper and related blog posts have overlooked.

    Recall, we most recently mathematically jousted over at Judith Curry’s Climate Etc some years ago on your previous ‘irreducible equation’ posts, which I showed rigorously were further mathematically reducible, and which when further properly reduced and plugged into reasonable assumptions that you provided, produced an ECS equivalent to that observed empirically by Lewis and Curry energy budget methods. Meaning your equations as critiqued were mathematically ‘right’ but their applied math used as you advertised wasn’t. All here can revisit that kerfuffle using CE search terms.

    The current post delay hang up (weeks prior to this post of yours) is WP equation subscripts. I have suggested the work around that Dr. Curry and I used previously. CtM has found another. So you should have a multipart substantive response from a fellow skeptic soonish. I cannot say more, since is not my post. But I did provide CtM a possibly elucidating WUWT foreword

    I look forward to engaging all substantively once the new post series (not from me) appears.

  11. I think Tom Halla got it right with the first comment above. The effect of all the GHGs before is X. The effect of all the GHGs after is X + Y. That isn’t the question. The question is, what happens when CO2 increases from before? The question is, What does a change to Y do to the GSMT? We don’t say X did all this before and is really big and responsible for so much. It’s all those things. But the question is, What does a change to Y do to the GSMT?

    • Hallelujah

      How many times do we read even on here about CO2 being a radiative gas, and all about it’s properties and blah blah effing blah, thereby addressing the wrong question.

      Assuming that preindustrial CO2 was 280 ppm, then it’s what happens above 280 that matters, and even some of that (net) is from ocean outgassing. Say hello to the stable convection, clouds and water vapor at 30- 40,000 ppm (amongst many other things) you fossil-fuel derived Beer-Lambert Law-eviscerated little rascal.

      I got tired of posting comments like this about 5 years ago. Thanks for the reminder (Tom and Lord Monckton too). Apologies for only being able to come up with the word “rascal”, but I am a chemist.

    • Ragnaar’s question amounts to this: what is the local secant slope of the equilibrium-sensitivity response function? To answer that question, it is helpful to know what the slope was in 1850. To answer that question, it is helpful to have some idea of how much more energetically feedback responded to the naturally-occurring greenhouse gases in 1850 than it would have responded to the 255 K emission temperature without greenhouse gases.

  12. I am by no means an expert on feedback, but I do recall being taught in math class that feedback systems can lead to chaotic behavior. Chaos theory is hard, if not impossible to fully analyze. This is one reason I’m doubtful of climate models.

    • I’m doubtful of “climate models” because none of them are models… they’re simple linear progressions.

      “penny yesterday, two pennies today means four pennies tomorrow…”

  13. Monckton is just plain wrong and is trying to hide the fact behind overly complicated language.
    The definition of feedback used by most people is characterised by Roe in “Feedbacks, timescales and
    seeing red” published in 2009. In it he shows that the feedback is just a first order Taylor series expansion.
    Hence it depends on the instantaneous slope rather than the average slope.

    • Yes.
      Average slope = Average tax rate
      Instantaneous slope = Marginal tax rate
      The average tax rate will be sluggish and dampen itself to small changes. The marginal tax can be agile responding to the now, and not the history so much, in general.

    • Are you just fishing again Izaak?

      I’d like to see your maths on this one if you don’t mind. I don’t have time to read Roe. Keep it simple, but show why Lord Monckton is plain wrong.

      • The furtively pseudonymous “Izaak Walton” is indeed fishing. The fact that one can attempt to model feedback response as a leading-order Taylor-series expansion does not in any way invalidate our approach.

      • Hi Phil,
        The maths is simple but formatting it is very hard due to wordpress not liking equations.
        And Roe does a much better job than I would do in explaining it. But I can try.
        Suppose that the temperature T of the earth is a function of the solar forcing R. We can
        write that as:
        T=f(R)
        where f is the unknown function. Now we choose a particular value of R say R0 then we get
        the temperature T0 which satisfies
        T0=f(R0)
        Now we ask how does the temperature change if the radiative forcing goes from R0 to R0+dR
        where dR is a small change. Expanding the first equation as a Taylor series gives:
        T=f(R0)+ (df/dR)*dR
        where the derivative df/dR is evaluated at R=R0. We can then write T=T0+dT to get
        dT= (df/dR)*dR
        No what Roe does is he states that we do not know the function f so we approximate it by
        the Stefan Boltzman relationship (lets call it S) and through in a constant of proportionality
        giving
        dT= alpha (dS/dR)*dR
        now Roe then writes alpha=1/(1-f) and (dS/dR)*dR as Delta T to get
        dT= 1/(1-f) Delta T
        which is the standard feedback equation with a feedback value of ‘f’ which we have just
        derived as an alternative form of a Taylor series expansion.

        This analysis is valid for any function ‘f’ and relies on the fact that although we do not know the
        explicit form of ‘f’ we do now an explicit form for a similar function S. It is also obviously only valid
        for small changes in forcing since we have started with a first order Taylor series expansion. The other
        thing that it clearly shows is that if we choose a different reference point R0 or a different function S
        we would get a different value for the feedback fraction ‘f’ since the value of the derivative would be different.

        What Monckton does is start with the equation
        dT=1/(1-f) Delta T
        and then assumes with no justification that the same equation is valid for arbitrary large values of Delta T
        giving
        T=1/(1-f) T*
        where T* is his reference temperature. This is not valid from a mathematical viewpoint since it is only
        true for straight lines and most functions are not straight lines. Nor is there any physical justification for
        suggesting that the climate behaves in a linear fashion. Certainly the Stefan-Boltzman equation has a T^4
        term and therefore even a blackbody would not obey his feedback equation.

        • Yes, yes, we all know how one can linearize a possibly nonlinear curve in the region of a point of interest on that curve by way of a leading-order Taylor-series expansion, and we all know that adding terms to the expansion would gradually reproduce the underlying curve more and more precisely. If it were really as simple as that, official climatology would have had some scintilla of success in constraining the interval of Charney sensitivities, which, however, remains at [1.5, 4.5] K, exactly as it was in the Charney report 40 years ago. Billions spent, nothing changed. That ought to have suggested two things to Mr “Walton” : that the data to make the Taylor-series approach work are inadequate, and that official climatology’s chosen interval owes more to politics and profit than to mathematics and science.

          The use of Taylor series to represent the region very close to a point of interest on a curve is merely a mathematical tool which, with adequate underlying data, may be of value. Since the data are not adequate, the argument that one can express the relevant portion of the curve of the equilibrium-sensitivity response function by way of a leading-order Taylor-series expansion cannot and does not invalidate our approach.

          Mr “Walton” seems to imagine that we are assuming that the unit feedback response is invariant. No: we think it is near-invariant across the small interval from 255 to 290 K that is of interest, but we have explicitly considered the question whether it is appreciably variant. There is only one equation in the entire head posting: and that equation explicitly allows for variance in the unit feedback response.

          Mr “Walton”, before shooting his mouth off, may care to conduct the exercise suggested at the end of the head posting. And he may care to explain by what real-world physical process or processes the unit feedback response to the preindustrial greenhouse-gas warming exceeds the unit feedback response to emission temperature by a factor 140, as Fig. 1 of the whigmaleerie had carelessly implied.

        • The bottom line is that no approach conforms to the preconditions for using Bode’s linear feedback amplifier analysis since W/m^2 can’t be scaled by a dimensionless constant to arrive at degrees of temperature. First, the dimensions don’t work since by definition, the open loop gain is dimensionless. Second, even if you assigned units to the open loop gain, the relationship between W/m^2 and degrees is not linear and by definition, the input and output of the gain block must be linearly related to each other across all possible inputs and outputs.

          The linear amplifier feedback analysis being applied to the climate has no relationship to how the climate actually worlks. The climate system is not an active feedback control system, but is a passive feed-forward system where some fraction of the surface output is delayed and combined with future solar forcing, rather then emitted into space, and which replenishes emissions above and beyond what the solar forcing can replace on its own. More than half of this returned power comes from cloud emissions and the remaining arrives as GHG molecules relax to a lower energy state and emit photons directed at the surface.

          Some attributes of the system have a temperature dependence, but this isn’t characterizable as feedback and would be more properly characterized in the same manner as the temperature coefficient of a resistor.

    • No. The Taylor series expansion assumes an infinite power supply. Roe just rehashed Schlesinger’s paper and made the same mistakes in the derivation of the gain equation, that is, assuming unit open loop gain in one place and a non unit open loop gain in another that ‘amplifies’ W/m^2 into degrees. This mistake was made for the same reason which was conflating the feedback factor with the feedback fraction. The mistakes of assuming an infinite, implicit power supply and that approximate linearity around the mean is sufficient for applying feedback analysis incrementally were made by Hansen and never corrected by anyone, including Roe.

      Hence it depends directly on the absolute surface emissions and is completely independent of any rate of change in the forcing. Consider that the rate of change between night and day overwhelms seasonal variability which itself overwhelms the insignificant rate of change due to CO2 emissions.

      • No. A Taylor series expansion assumes that changes are small. If it assumed an
        infinite power supply (whatever that actually means) then presumably all Taylor
        series would be invalid. Rather than have a limited region of convergence. As
        anyone with a knowledge of complex analysis could tell you.

        • Izaak,

          Given the small change where the effect of the first term on the surface emissions is less than a percent of the baseline emissions, the second term is less than a percent of less than a percent. The only way that the second and subsequent terms can be large enough to matter is if power magically appears in the system.

          Consider that instantly doubling CO2 increases absorption by about 4 W/m^2 where 2 W/m^2 are returned to the surface. These 2 extra W/m^2 are about half a percent of the 390 W/m^2 baseline surface emissions which from the baseline ‘amplification’ from existing clouds and GHG’s contributes 2*1.62=3.2 W/m^2 to the surface emissions. The second term becomes half a percent of 3.2 W/m^2 or about 16 mw which when’amplified by 1.62 become 26 mw which is negligible and can be safely ignored.

          Note that only the incremental effects should appear in the Taylor series where the baseline effect is accounted for by the baseline ‘amplification’ of 1.62 W/m^2 of surface emissions per W/m^2 of forcing.

    • Izaak,

      Every time I read one of these papers I get totally confused. For example, from the paper you referenced:

      “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.”

      Where is this “amplifying” perturbation determined? How do we know it is “amplifying”? Water vapor also shields the Earth from the sun. How do we know that the net process impact of the increased water vapor is to “amplify” the original forcing? The net process impact may very well be net negative.

      Here’s another: “For f ≥ 1, G is undefined.”

      For f to be greater than one there would have to be some kind of active element in the feedback loop, i.e. energy would have to be created inside the feedback loop. I’m not sure how that would be possible in nature. It is actually “f” that is undefined for values greater than one.

      Or take this: “Note also that the not-uncommon misconception that a positive feedback automatically implies a runaway feedback is not true.”

      This is a misstatement of what the common perception is. The common perception is not that the feedback will automatically run away, the common perception is that the process being controlled by the feedback will run away! The author states elsewhere: ” in other words, some fraction of the output is fed back into the input (Figure 2b).” If the feedback is positive, i.e. it adds at the input, then the output will increase by some amount (the system gain times the amount being fed back) . And as the output increases then the amount being fed back will increase as well thus leading to the output increasing even more. It forms a race condition where the output just keeps going up until a physical limit is reached.

      I haven’t had time to get much past these obvious issues at the very start of the paper.

      • Tim,
        Taking water vapour feedback to be negative if you like. It doesn’t change the maths or
        the validity of the approach.

        The fact that having a feedback ‘f’ greater than 1 implies an external energy supply means
        that such a value is unphysical not mathematically undefined. G in contrast becomes ill-defined
        mathematically in that case. You are confusing mathematically possible values with physically
        possibly ones.

        The last comment appears to be simply a gripe about the language that Roe uses. Plus you
        appear to be suggesting that an infinite sum of positive numbers converges to infinity when
        in fact it can converge to a finite sum. Consider a hypothetical amplifier that has a gain of 1
        and you feedback 50% of the output to the input. Then if you input a signal of amplitude 1 you
        would get a output of 2 (50% of 2 is 1, add that to the 1 from the input to get 2 so which is the
        output so that is the final answer). So a positive feedback does not always lead to run-away
        answers.

        • “Taking water vapour feedback to be negative if you like. It doesn’t change the maths or the validity of the approach.”

          Ummmmm, doesn’t it change which side of the vertical axis you operating on in Fig 3?

          “G in contrast becomes ill-defined”

          It does? Mathematically the function has a discontinuity a f=1 but it certainly has a value for f>1. You’ve left off half of the graph! Your graph actually describes the real world since it shows nothing for f>1! It is f>1 that is undefined, not G.

          “Consider a hypothetical amplifier that has a gain of 1 and you feedback 50% of the output to the input”

          A gain of one implies that there is no feedback! If 1/(1-x) = 1 then x must be zero! If your feedback fraction then becomes 50% (i.e. f=0.5) then the gain becomes 2, it doesn’t remain at one. Thus 1.5 for an input becomes an output of 3. 50% of 3 becomes a feedback of 1.5. Thus the input becomes 2.5. Double this and you get an output of 5! You have just built a system with positive feedback and it is running away with you!

          • Except that you are failing to account for COE between the input and output of the gain block. Bode’s linear feedback amplifier analysis assumes that the output power originates from an implicit power supply thus this simplifying assumption allows COE to be ignored between the input and output of the gain block, while for the climate system, the output power originates from the input power (the forcing) and COE between the input and output can no longer be ignored.

            For the climate system the output power of the gain block can be either the output power of the system or feedback power, but not both. Bode assumes that the feedback term is measured by the gain block to determine how much power to deliver to the output from its implicit power supply while for the climate model, the feedback term is actually consumed to provide the output power of the gain block.

            Your runaway analysis assumes the existence of an implicit power supply that can provide an infinite about of output power.

          • “Your runaway analysis assumes the existence of an implicit power supply that can provide an infinite about of output power.”

            I agree. I was only following the math being used which, as you say, assumes an implicit power supply.

          • Tim,
            G becomes ill defined when f>1 since it becomes negative and the system would
            start to oscillate. Thus there is no way to define G. And while oscillating systems
            are perfectly possible (e.g. a laser) they do not have a well defined Gain.

            Also you are confusing the gain of the whole system with feedback and the gain
            of the amplifier inside the feedback system in my example. Within the feedback
            loop there is an amplifier with gain 1 but if you consider the entire system as a
            blackbox then it looks like an amplifier with gain 2. Positive feedback does not
            always induce run-away processes as my example shows.

          • “G becomes ill defined when f>1 since it becomes negative and the system would start to oscillate.”

            Why would the system start to oscillate? What is negative gain? If it is merely a 180deg change of the phase of the input signal then all of a sudden you start to feedback a negative value, i.e. the feedback is subtracted from the signal. This is classic “negative” feedback which prevents runaway. Or is negative gain merely attenuation? If it is attenuation of the input signal then the feedback becomes less and less and the output goes to zero. Pick your poison.

            “Also you are confusing the gain of the whole system with feedback and the gain of the amplifier inside the feedback system in my example. Within the feedback loop there is an amplifier with gain 1 but if you consider the entire system as a blackbox then it looks like an amplifier with gain 2. Positive feedback does not always induce run-away processes as my example shows.”

            I’m not confusing anything. If the feedback loop has a gain of 1 then in essence you have connected the output of the system to the input of the system. With no active element in the feedback loop that is the largest positive feedback you can have. And it is a surefire setup for runaway. It is the situation where f=1.

            Your gain equation is for the entire system. 1/(1-f) Meaning the only way you can have a system gain of 2 is for f to equal 0.5. And the system *will* runaway as that output continues to grow while the amount being fed back grows.

  14. Sadly, today we also suffer from torymaleerie, labourmaleerie, liberaldemocrat(ex-Whig)maleerie, scottishnationalsocialistmaleerie and of course greenmaleerie. Only the Brexit Party eschews maleerie in all its baleful, antihuman forms.

    It is after all a Scotsism, one of the many so beloved of Scrabble players.

  15. I understand feed backs in electronics, these types of feed backs have limits based on Voltage etc, the feed back does not continue increasing forever it stops at some point due to inherent limits.

    We all know the climate feed back has limits, we can see those limits in the temp records (ice core etc), sure we may not be able to explain why in detail and depth but we know they are there.

    Problem is for some this lack of knowledge is enough to pretend those limits dont exist so they exploit the situation to stoke fear among the people…they are sociopaths nothing more

    • Isn’t the mass of the oceans coupled in with those feedbacks too? Seems to me that would be adding a huge capacitance somewhere.

      • The oceans’ heat capacity introduces a time-delay before equilibrium is reached in response to forced warming as amplified by feedback. But, by doing all calculations on an equilibrium basis, one does not need to worry about the time-delay provided that the equilibrium sensitivity is small enough.

  16. Heartland Climate Conference . . . is a seating block reserved for the climate establishment?
    Would be fun to prominently display each name on a pole placard:
    – Michael Mann
    – Phil Jones
    – Gavin Schmidt
    – James Hansen
    Could be a Great Twitter pic.

  17. My Dear Lord Monckton,

    I fear you have fallen into grievous error in your calculations. One that could have calamatous impact upon your otherwise eloquent and cogent argumentitives.

    We no longer function in a “Closed Loop”! As was recently celeberated here in the Colonies, 50 years ago, we broke free from our fetid Terran chains, and reached out and beyond the Aether! We OPENED THE LOOP! Do you know how Calamatous that could be? We keep punching holes in our Ozone Aethersphere at our Peril!

    I fear we shall all rue the day when the mighty Sol figures this out, and smites us all for our pugnatiousness.

    Good day, Sir!

    • Let us not be argumentative or pugnacious about supposedly calamitous global warming.

      • I do apologize for the flippant nature of my comment, it was in jest, I assure you, but like all good humor, the kernel of truth in it does point to a question that has a difficult answer – to whit, where can one draw the line? Beyond what point “lie dragons” as it were? Forces outside our atmosphere work upon it, but trying to convince some who have fallen prey to the sirens call of the rapscullions who would blame man for everything?

        Many thanks, and kindest regards of the day.

        • Ah, you rapscallion, you did not notice that in my previous short comment I had corrected three spelling mistakes in your previous comment – and now I’ve corrected another one.

  18. As CO2isnotevil says above, feedback is a difficult concept to comprehend. A guest blog of mine ( MODTRAN ) from about a month ago touched upon the subject briefly. At the risk of getting stuck in this controversy, let me demonstrate a couple of points we might all agree upon.

    First, that the average response to the first 240 \, W/m^2 of solar irradiance has little bearing on the issue of what the response will be in stepping from 240 to 241 \, W/m^2. If the process is continuous the more pertinent question is what was the response in stepping from 239 to 240? The response of the next unit of irradiance is probably (as long as we are not near a bifurcation or “tipping point”) very similar to the response of the previous step in irradiance. To try to apply the average response over a broad range of previous inputs is to average the response of a system that was over some parts of this broad input range in irradiance quite different from current conditions; and to apply such an average could be very much in error.

    Second, to have an average response of 1.62 \, W/m^2 upward emitted power per unit of solar irradiance from the first 240 \, W/m^2; and then note a needed 4.4 \, W/m^2 of emitted power to step from 240 to 241 does not suggest a violation of conservation of energy. The problem here is that the situation is very different at the Earth’s surface than it is at the top of the atmosphere. At the top of the atmosphere one new \, W/m^2 of irradiance has to be match eventually by a new \, W/m^2 of emitted power if equilibrium is to ever re-establish itself. At the Earth’s surface however, something different happens.

    To return to my example in the MODTRAN blog, when CO2 concentration is suddenly doubled what occurs first is new absorption of emitted LW power in the atmosphere. This is manifest initially by a decrease in emitted power at the top of the atmosphere. This new absorption leads to some new increment of emitted power from within the atmosphere. Some of this is absorbed at the surface, which warms, which in turn emits some smaller-yet increment of emitted power which must travel through the atmosphere, which in turn absorbs some of it. This process repeats ad infinitum. What we are dealing with is an infinite series. It will eventually converge. When it does equilibrium is again established at the top of the atmosphere, the surface is warmer by some amount and will have an augmented emitted power, and the atmosphere itself is warmer and has enhanced emitted power also. Other feedbacks can intervene and modify this story, of course, but in the absence of anything but new CO2 in the atmosphere this is what will occur.

    The infinite series I described above is the feedback; and if it is a geometric series (which seems reasonable) then it will sum to something like \frac{1}{1-\lambda x}, in which the feedback factor is apparent.

    What Joe Born in his guest blog of last week hoped to illustrate is that there is no “theorem” that can prove what the feedback factor is, let alone prove that a large feedback factor is wrong. I do not believe that positive feedback is large, but the only way to determine that this is so is by measuring it (not simulating it) and we have at present few instances of excursions from equilibrium in climate for which we have observations capable of calculating feedback factor or climate sensitivity through inversion.

    • In response to Mr Kilty, the task of science is to constrain uncertainty, particularly where – as in the climate – the underlying data are uncertain and no feedback can be quantified by measurement. Mr Kilty may care to watch my Heartland presentation, where sufficient details will be given to allow him to see how it is that we are able to demonstrate that the high equilibrium sensitivities imagined by official climatology are untenable.

      • Thanks for your response. I see that your presentation is on July 25th sometime between 12:45 and 14:30 EDT. I will set some notification to either look for it live, or look for it on some delayed feed. Your talks, of which I have seen a few, are always entertaining and thought provoking.

        However, I still maintain that what we need to settle this debate are a sufficiently large group of actual measurements of climate sensitivity provided by disruptions of various sorts–we are just not there yet.

        • In case you missed it, his talk can be found at https://www.youtube.com/watch?v=xUT4vzprlCA, with his explanation of the “X factor” beginning at 5:09:33 and his “money graph” at 5:10:25. I’m sure you will recognize that three problems afflict it:

          First, his interpretation of the X factor confuses small- with large-signal versions of what he calls “unit feedback response” and thereby overstates the variation in that quantity. Second, since the “unit feedback response” relates feedback to input rather than output, it’s based on a fundamental misunderstanding of how feedback operates.

          And in the speech he compounds these inherent X-factor errors by, third, using an unreliable technique to infer the X factors in his “money graph” from ECS.

          Together these errors can result in overstating the feedback-response variation’s size by over two orders of magnitude and even getting its sign wrong. I accordingly offered WUWT a post dismantling the X factor, but, like my others that criticized Lord Monckton’s theories too directly, it was rejected. (I was actually surprised that I succeeded by couching that last one as an expansion of Nick Stokes’ piece.)

    • Kevin,

      When you get to the second term in the sequence, it’s already insignificant relative to the first term which itself is barely significant relative to the baseline. For example, consider the incremental absorption from instantaneously doubling CO2 to be 4 W/m^2. Each W/m^2 of absorption must contribute equally up and down, so half a Joule is returned to the surface for each Joule absorbed by the atmosphere and half a Joule is emitted into space. This makes the fractional effect of the first term on the baseline 2/390 or about half a percent. The fractional effect of the second term relative to the baseline is half a percent of half a percent which is already insignificant.

      If the 4 W/m^2 claimed was after half of the incremental absorption was emitted into space, then the second term effect relative to the baseline is one percent of one percent, which is also insignificant.

      I stand by my assertion that the required 4.4 W/m^2 increase in the average surface emissions from the next W/m^2 of solar forcing is indeed a violation of COE when the average W/m^2 from the Sun contributes only 1.62 W/m^2 to the average surface emissions. Whatever difference is happening at the surface relative to TOA affects each W/m^2 uniformly.

      The COE violation is the requirement that the surface must be able to distinguish the next W/m^2 of forcing from the average W/m^2 of forcing relative to the work it takes to warm the surface. Keep in mind that Joules are the units of work and Watts are a rate of Joules while W/m^2 are a rate density of Joules. It’s perfectly valid to geometrically average rate densities of Joules to establish the average rate density of Joules which can be converted into an EQUIVALENT average temperature.

      • I agree with you that the effect is small. In my doubling of CO2 scenario, with all other things remaining the same, surface temperature must rise only 0.75 ^\circ C and surface emission rise by 4 \, W/m^2 to reach a net of zero at the top of atmosphere and restore energy balance. Moreover, this is an upper bound because as the surface temperature rises there will be heat transfer by convection and latent energy which are impossible to calculate with the necessary precision to make any sort of convincing argument.

        In engineering we would never try to design something by calculating all of this to the sorts of precision people claim in climate science. Instead, we would calculate a design that we figure is \pm 20 \% correct , then build a prototype and make design adjustments until measurements showed we achieved our goal.

        I still don’t see the violation of conservation of energy you discuss in your final two paragraphs, because it looks like a comparison of apples to oranges sort of argument. Why compare the tangent at 240 \, W/m^2 with the secant from zero to 240, rather than compare secant from zero to 240 to the secant from zero to 241?

        • Kevin,

          The .75C for doubling CO2 is about right.

          The COE violation is because the surface power gain is demonstrable constant, that is, the limit of 1.62 W/m^2 of surface emissions per W/m^2 of forcing is independent of the temperature, the emissions or the forcing. The supporting data is presented here as a scatter plot:

          http://www.palisad.com/co2/tp/fig1.png

          The X axis is the average emissions at TOA and the Y axis is the average surface temperature. Each small red dot is the average for 1 month of data for each 2.5 degree slice of the planet. The larger dark dots are the averages for each slice across all 3 decades of the same weather satellite data. The data comes from the ISCCP data set supplied by GISS.

          The average temperature is calculated by converting the reported temperatures per cell into emissions using SB, geometrically averaging emissions across each cell in a slice and then converting the result back into an equivalent temperature using the inverse of the SB Law. The average emissions at TOA are calculated based on applying HITRAN derived radiant transfer models to surface emissions and cloud emissions based on the reported fraction of clouds, cloud optical depths, surface temperatures and cloud temperatures per cell and geometrically averaging the resulting emissions.

          The green line is the prediction of a gray body whose emissivity is 1/1.62 = 0.62, where T is along Y and the emissions are along X. To the extent that this relationship holds, then the ratio between the surface emissions as a BB at the reported temperature, T, and the emissions at TOA is a constant 1.62.

          Each slice receives a different amount of solar forcing and has a different average temperature and it’s quite clear that this average emissions ratio of 1.62 is independent of either. To the extent that this ratio is independent of the state (temperature) or the forcing, it must also apply to the next W/m^2 increasing the surface emissions by 1.62 W/m^2 and not 4.4 W/m^2 as the IPCC’s ECS predicts. Anything more than 1.62 requires energy to literally appear out of thin air.

          Even more interesting is to superimpose the relationship between the solar input and the surface temperature per slice. In this plot, the X axis is also the average solar input power per slice which is trivially calculated based on the reported reflectivity per cell. The slope of this relationship is 1 W/m^2 of surface emissions per W/m^2 of forcing biased up by half of the average atmospheric absorption, which is the prediction of the magenta line in this scatter plot. The prediction is based on the hypothesis that changes in entropy are minimized as the input changes when the output changes by the same amount.

          http://www.palisad.com/tp/fig2.png

          Where the green line prediction of the behavior along the output path from the surface to space as a gray body whose emissivity is 0.62 intersects with the magenta line prediction of the entropy minimizing behavior along the input path from space to the surface of 1 W/m^2 of surface emissions per W/m^2 of forcing defines the steady state average. Sure enough, the data confirms all of the predictions.

          While I can’t prove it yet, I have reasons to suspect that the 1.62 could actually be the golden ratio of 1.61803… One reason is that this ratio frequently occurs in other self organized systems that chaotically converge to an entropy minimizing steady state.

          • I have no idea if anyone still haunts this thread or if this comment will make its way to CO2isnotevil, but I am playing the part of a brutal skeptic here. Statements made by CO2isnotevil are italicized; my responses are in block Latin letters.

            Kevin,
            The .75C for doubling CO2 is about right.
            The COE violation is because the surface power gain is demonstrable constant, that is, the limit of 1.62 W/m^2 of surface emissions per W/m^2 of forcing is independent of the temperature, the emissions or the forcing. The supporting data is presented here as a scatter plot:
            http://www.palisad.com/co2/tp/fig1.png
            The X axis is the average emissions at TOA and the Y axis is the average surface temperature. Each small red dot is the average for 1 month of data for each 2.5 degree sliceof the planet. The larger dark dots are the averages for each slice across all 3 decades of the same weather satellite data. The data comes from the ISCCP data set supplied by GISS.

            I am not familiar with this data, but I see there is a blizzard of products available. Which specifically are you using?

            The average temperature is calculated by converting the reported temperatures per cell into emissions using SB, geometrically averaging emissions across each cell in a slice and then converting the result back into an equivalent temperature using the inverse of the SB Law.

            If the derived temperatures you are using from this data set are like those for GEOS data, then these temperatures do not correspond to the surface unless the sky is clear. You are getting some of these temperatures from cloud tops. Moreover in the GEOS data there are assumptions made about water vapor in order to arrive at surface radiance. In other words there is some potential for circularity here. I just don’t know until I understand what specific products you are using, and then go look at the technical documents for those data.

            The average emissions at TOA are calculated based on applying HITRAN derived radiant transfer models to surface emissions and cloud emissions based on the reported fraction of clouds, cloud optical depths, surface temperatures and cloud temperatures per cell and geometrically averaging the resulting emissions.

            What is “geometrical” averaging? Are you using MODTRAN to do these calculations, or do you have access to a copy of HITRAN? Or do you have access to a copy of MODTRAN independent of the UofChicago wrapper?

            The green line is the prediction of a gray body whose emissivity is 1/1.62 = 0.62, where T is along Y and the emissions are along X. To the extent that this relationship holds, then the ratio between the surface emissions as a BB at the reported temperature, T, and the emissions at TOA is a constant 1.62.

            I am playing devil’s advocate here. Let’s think about what the emissivity of a gray atmosphere has to depend upon. Why is the atmosphere gray in the first place? Well, because it contains IR active gasses. Thus the grayness must depend on the concentrations of these gasses at the very least. But you don’t even put any of these parameters into your calculation. Thus, an emissivity of 0.62 in your view applies to dry air like that above a place like Sante Fe or a wet place like Houston, and even above the cloud tops. It is just a constant? That is pretty hard to accept.
            In fact go to MODTRAN use a tropical atmosphere model. At a surface temperature of 299.7K you have an IR flux at TOA of 298.52; so your ratio is now 1.53, not 1.62. Change the surface temp by -12C. Thus drops the whole atmosphere by 12 degrees, perhaps unknowingly to the user, and creates a litany of errors also not presented to the user, because that is how the wrapper operates, but now your ratio is 1.57. Go to a midlatitude summer atmosphere with ground temperature of 294.2K and you will find a ratio of 1.47. Midlatitude winter you get 1.32 and so on.

            Each slice receives a different amount of solar forcing and has a different average temperature and it’s quite clear that this average emissions ratio of 1.62 is independent of either. To the extent that this ratio is independent of the state (temperature) or the forcing, it must also apply to the next W/m^2 increasing the surface emissions by 1.62 W/m^2 and not 4.4 W/m^2 as the IPCC’s ECS predicts. Anything more than 1.62 requires energy to literally appear out of thin air.

            No, all it requires is a greater flux up and down within the atmosphere as the concentration of IR active components increase.
            At this point my suspicion is that what you have done is calculate an average earth temperature and average Earth irradiance at TOA to arrive at the effective emissivity of 0.62.

            Even more interesting is to superimpose the relationship between the solar input and the surface temperature per slice. In this plot, the X axis is also the average solar input power per slice which is trivially calculated based on the reported reflectivity per cell. The slope of this relationship is 1 W/m^2 of surface emissions per W/m^2 of forcing biased up by half of the average atmospheric absorption, which is the prediction of the magenta line in this scatter plot. The prediction is based on the hypothesis that changes in entropy are minimized as the input changes when the output changes by the same amount.

            In one of Judith Curry’s blog posts, back in 2012 or so, she commented that entropy is very difficult to apply to weather and climate. I agree. One has to be very careful.

            Entropy increases during spontaneous processes. There is no physical principle holding that changes in entropy are minimized, or maximized for that matter. In fact minimizing entropy requires that the process you are contemplating be reversible and there is nothing reversible about heat transfer; minimizing in this context sounds like a way to violate the second law. There is that theorem due to Prigogine indicating that entropy rates of production are minimized when a process is so close to equilibrium that linear constitutive relationships hold, but I know of no others. What is it that “changes” related to entropy? More pertinently, how are you calculating entropy? Or are you?

            http://www.palisad.com/tp/fig2.png
            Where the green line prediction of the behavior along the output path from the surface to space as a gray body whose emissivity is 0.62 intersects with the magenta line prediction of the entropy minimizing behavior along the input path from space to the surface of 1 W/m^2 of surface emissions per W/m^2 of forcing defines the steady state average. Sure enough, the data confirms all of the predictions.

            I have no idea what this plot is telling me. You have a cloud of data points and a bunch of curves passing through them. I do not see a confirmation of predictions–i don’t even see any predictions.

            While I can’t prove it yet, I have reasons to suspect that the 1.62 could actually be the golden ratio of 1.61803… One reason is that this ratio frequently occurs in other self organized systems that chaotically converge to an entropy minimizing steady state.

            Sometimes argumentation by analogy is insightful; sometimes it is misleading. What specifically is your reason?

        • Kevin,

          I’m still listening …

          “I am not familiar with this data”

          https://isccp.giss.nasa.gov/

          ” … then these temperatures do not correspond to the surface unless the sky is clear.”

          Correct. I use the emissivity of the clouds reverse engineered from the optical depth (based on Rossow’s documentation) combined with radiant transfer models to determine the emissions at TOA from clouds, those originating from the surface and those originating from GHGs. The output emissions are a complicated calculation taking many factors into account, yet the relationship between the calculated values and the surface temperature is the most tightly regulated ratio among all other pairs of variables many of which are plotted and can be accessed from this link (pay special attention to the non linear relationships between cloud coverage and other attributes, including water vapor content!):

          http://www.palisad.com/co2/sens

          “What is “geometrical” averaging?”

          Averaging W/m^2 of emissions based on the area it’s being emitted by. For example, relative to the whole, the emissions from a 2.5 degree slice in Canada has less weight than the emissions from a 2.5 degree slice at the equator. Relative to the equal area cells in a slice, they’re all weighted equally when calculating the average emissions of a slice.

          ” … because it contains IR active gasses.”

          Clouds have a larger effect on the ‘grayness’ of the atmosphere. The relevant point is that the T^4 relationship between temperature and emissions is immutable and the only way to modify the relationship between the emissions of matter and its EQUIVALENT temperature is by applying a non unit emissivity.

          “Are you using MODTRAN …”

          I’m using something similar that I wrote myself which is also based on HITRAN absorption data and has been cross checked against MODTRAN. My algorithm is intrinsically much faster. easier to trade off accuracy for time and memory and the overall algorithm accounts for the effects of clouds, whose attributes come from the ISCCP cloud data product.

          “No, all it requires is a greater flux up and down within the atmosphere as the concentration of IR active components increase.”

          The geometry of the atmosphere precludes this. Energy leaves the atmosphere over twice the area (to surface and to space) it arrives from (the surface). This ratio does chaotically vary a little but, but only by a few percent on either side of 50/50 and the average is pretty constant. The specific density profile of the GHG distribution has no effect on the relevant geometry.

          “Entropy …”

          Entropy can be considered deviations from ideal. In this context, ideal is either the ideal behavior of a BB of 1 W/m^2 of surface emissions per W/m^2 of forcing or the behavior of an ideal gray body which is really a non ideal black body, but is none the less ideally quantifiable.

          The output path seems to be converging to the ideal behavior of a gray body whose emissivity is 0.62 (1/golden_ratio) while the input path converges to an incremental emissions sensitivity of 1 W/m^2 per W/m^2 of forcing, or about 0.19C per W/m^2 at the current average temperature and 4*.19 = 0.76C for doubling CO2 when considering that doubling CO2 is EQUIVALENT to 4 W/m^2 of incremental solar forcing.

          “There is no physical principle holding that changes in entropy are minimized”

          It can be considered an effect of the ‘Minimum Energy Principle” which is a consequence of the Second Law. But, as I said, this is a hypothesis whose predictions I’ve tested.

          “I have no idea what this plot is telling me.”

          http://www.palisad.com/co2/tp/fig2.png

          What this plot shows are two superimposed scatter plots of the data on top of the predictions made by my hypothesis. The magenta line is my prediction of the average relationship between the solar input and surface temperature. The small red dots are measurements of the monthly averages of the data being predicted and the larger dots centered on the small red dots are the 3 decade average of the relationship for each 2.5 degree slice of latitude.

          The green line is my prediction of the average relationship between the surface temperature and the emissions at TOA. Where the green line intersects the magenta line defines the steady state.

          The small yellow dots represent 3 decades of monthly measurements of the average surface temperature vs. the average emissions at TOA for each 2.5 degree slice from pole to pole, where the larger dots centered within the cloud of small yellow dots are the 3 decade averages for each slice.

          “What specifically is your reason?”

          My understanding of chaos theory and the results of some modeling I’ve been doing. In addition, the average amount of clouds vs. the temperature is counter intuitive (looks like the response of a tunnel diode) and is otherwise unpredictable unless there’s a hidden goal to maintain a constant average ratio between the NET average surface emissions and the average planet emissions.

          FYI, one of my email addresses is co2isnotevil at my domain which you can get from one of the links I supplied.

    • Darn it. I missed a closing $ on the latex markup. The series should sum to
      \frac{1}{1-\lambda x}

      [fixed~ctm]

  19. The implication is that, in the widdershins world of the whigmaleerie, feedbacks are imagined – per impossibile – to respond 140 times more energetically to each degree of greenhouse-gas warming than to each degree of emission temperature.

    As i see it, this is only impossible if you believe that feedbacks have to respond equally at all temperatures from 0K onward. It has nothing to do with the cause of the temperature, just the possibility that some feedbacks are going to respond more at 265K than they do at 200K. Just asserting that it’s impossible is not a valid argument.

    • Bellman gets the prize for identifying the main point of the head posting, which was that Fig. 1 of the whigmaleerie implies that feedbacks respond 140 times more energetically to each degree of greenhouse-gas warming than to each degree of emission temperature.

      The calculation does not in any way depend on imagining that feedbacks respond equally at all temperatures from 0 K onward. Our calculations begin at 255 degrees, because that is the rather rough and ready canonical value of the emission temperature that would prevail at the surface in the absence of greenhouse gases or feedbacks.

      Likewise, the calculation explicitly does not assume that feedbacks respond equally at different surface temperatures.

      Perhaps Bellman would like to suggest a plausible physical mechanism by which feedbacks can respond ten times as vigorously to greenhouse gases as to emission temperature, let alone 140 times as vigorously.

      • Likewise, the calculation explicitly does not assume that feedbacks respond equally at different surface temperatures.

        I don’t see that. If you argue that the feedback response can be derived from the temperature at 265K, and that this can be used to calculate ECS, you are implicitly assuming the response will be the same at 266.05K.

        Perhaps Bellman would like to suggest a plausible physical mechanism by which feedbacks can respond ten times as vigorously to greenhouse gases as to emission temperature, let alone 140 times as vigorously.

        A bit late in the day to be worrying about physical mechanisms when your argument has been to model the entirety of such mechanisms by a single linear equation. I couldn’t give you specific figures, but common sense tells me many physical mechanisms will only have an effect above certain temperatures. For example, the feedback caused by melting ice can only have an effect once global temperatures are sufficiently warm for ice to melt. Using your definitions it should be quite easy to see how the response averaged over the whole range of temperatures from 0K onward can be much small than the response averaged over a small change in temperature.

        It isn’t a question of the feedbacks responding more energetically to greenhouse-induced warming, it’s just the difference in the response to different temperature ranges.

        The calculation does not in any way depend on imagining that feedbacks respond equally at all temperatures from 0 K onward.

        I asked you this before, but if you don’t depend on that, why spend so much time in your original paper claiming that the function must be near-linear?

        Our calculations begin at 255 degrees…

        As far as I understand it, your calulations begin and end at 265K.

        • Bellman should work through the problem I have set for the reader at the end of the head posting. Then he will come to understand why there is a limit to the growth in feedback response over time. And there is no need to go back to 0 Kelvin: as any control theorist will tell you, the feedback loop modifies the entire reference temperature it receives, and not just any arbitrarily selected fraction thereof: therefore, even without greenhouse gases or feedbacks there woiuld be a feedback response to emission temperature. At today’s insolation and albedo, even if one starts with an ice-planet with the same albedo as Nasa assigns to the Jovian ice-satellite Europa, even without greenhouse gases or feedback the mean planetary temperature will be about 255 K. Or one can do what climatology does, and simply assume an albedo of 0.3, in which event most of the planet will be ice-free, so there is no need to wait till “temperatures are sufficiently warm for ice to melt”.

          The problem for the climate extremists is that they have implicitly assumed till now that the feedback response to the 255 K emission temperature is zero, while the feedback response to the 10 K reference sensitivity to the preindustrial greenhouse gases is 23 K (in round numbers). That won’t do.

          The question is this: how much more energetically do feedbacks respond to the 10 K of greenhouse warming than they did to the previous 255 K, per Kelvin? What should the feedback responses to these two quantities be? It’s a zero-sum game: we know the emisison temperature in 1850 was about 288 K, so the question is how to distribute the 23 K feedback response as between emission temperature and the 10 K greenhouse warming. But, if you play this game, you must have some reason for your choice: you must not simply choose values that happen to imply a large equilibrium sensitivity.

          Yes, we did some calculations going back to 0 K, just to see what happened. What happened was that the exercise smoked out the implicit imbalance between climatology’s imagined unit feedback response to emission temperature and its unit feedback response to greenhouse gases. Having smoked that out, we do not any longer need to go back to 0 K.

          Bellman asks where the calculations begin. They begin at 255 K, the emission temperature that would obtain at the surface in the absence of greenhouse gases or of feedback.

          • There is the matter of large signal and small signal analysis. The magnitudes of the various feedbacks vary with temperature. For example, warming the Earth from 76K (the approximate vaporization temperature of Earth’s main non-GHG atmospheric gases) to 100K would not cause any significant change in its atmosphere, clouds, ice cover, etc. so there won’t be any significant feedbacks. On the other hand, changing the Earth’s average surface temperature from 278 to 288 K causes a large decrease in ice cover, so the surface magnitude feedback is great in this temperature range, or at least part of it. The Earth or large regions of it may even have had unstable climate at times during some of the advances and retreats of Pleistocene glaciations, as advance or retreat of an ice sheet greatly reinforced a regional change in absorption of sunlight that was started by one of the Milankovitch oscillations.

            The biggest issue I see with determining the magnitudes of the various feedbacks in the post-1850 world is that this has mostly been done with climate models, whose calibration is questionable. Many of these models, especially the bulk of the CMIP5 ones, were selected/tuned to hindcast what happened before 2006, and mostly with concentration on the 1975-2005 period. It has been noted what variable factors have been considered by these models: Manmade change of greenhouse gases, atmospheric aerosols including those from volcanoes, solar variation. Are there any I missed? Not considered by these models: Multidecadal oscillations. They were swinging together in a direction of warming the world during most of the time from 1975 to 2005. I have an estimate (from using Fourier on HadCRUT3) that this caused about .2 degree C of the warming from 1975 to 2005, and the climate models attributed that to manmade increase of GHGs instead. So, if the climate models are adjusted or selected to model .2 degree C less warming than they do now during 1975-2005 from the manmade increase of GHGs that happened during 1975-2005, then I think they’ll give much more accurate magnitudes of climate sensitivity, and much more accurate forecasts for global temperature and temperature in various parts of the globe and the atmosphere.

          • But the calculation does not begin at 76 K: it begins at 255 K, with an albedo of 0.3: i.e, with almost as much open ocean as today, and all the feedbacks operating at full chat. That there may be some increase in the unit feedback response as surface temperature rises from 255 to 288 K is possible: that there will be an increase large enough to give an X factor of 90 is impossible in the real climate.

          • At today’s insolation and albedo, even if one starts with an ice-planet with the same albedo as Nasa assigns to the Jovian ice-satellite Europa, even without greenhouse gases or feedback the mean planetary temperature will be about 255 K.

            But the problem is you don’t know how fast the feedback is responding. You cannot divide the response by 255 and claim that’s how fast will respond to temperatures above 255K.

            The problem for the climate extremists is that they have implicitly assumed till now that the feedback response to the 255 K emission temperature is zero, while the feedback response to the 10 K reference sensitivity to the preindustrial greenhouse gases is 23 K (in round numbers). That won’t do.

            I’ve no idea if “extremists” have made such an assumption, but merely asserting that it won’t do is not a valid argument.

            we know the emission temperature in 1850 was about 288 K, so the question is how to distribute the 23 K feedback response as between emission temperature and the 10 K greenhouse warming.

            Yes, that’s my point.

            But, if you play this game, you must have some reason for your choice: you must not simply choose values that happen to imply a large equilibrium sensitivity.

            But you haven’t provided any reason why you think they have to be evenly distributed across all temperatures.

            Yes, we did some calculations going back to 0 K, just to see what happened. What happened was that the exercise smoked out the implicit imbalance between climatology’s imagined unit feedback response to emission temperature and its unit feedback response to greenhouse gases. Having smoked that out, we do not any longer need to go back to 0 K.

            So, having made it a major part of your original paper, you no longer think that the response function has to be near-linear?

            The trouble as I see it is you now have a function that is only based on a single point, which means it could be going in any direction and so have no way of using it to predict future feedback responses.

            Or as you suggest in the next paragraph you have two points, one at 255K and one at 265K. But you don’t say where the point at 255K is. You dismiss the idea that it might be at (255, 260) as impossible, so what is the point at 255K, and how do you determine it without assuming a linear function.

          • Bellman should work through the problem I have set for the reader at the end of the head posting.

            OK, (Apologies in advance for any \LaTeX issues).

            R_0 = 255 is the global temperature sans Greenhouse gases and feedbacks, and B_0 = 5 the imagined temperature increase at 255K caused by feedbacks.

            \frac{B_0}{R_0} = \frac{5}{255} \approx  0.02

            This 0.02 is the value to which you attach great importance, but what does it represent? It’s just one number divided by another number. The 5K of feedbacks divided by the entirety of K from 0 – 255.

            You then contrast this with the local rise,

            \frac{\Delta B_0}{\Delta R_0} = \frac{28}{10} = 2.8.

            This value has more meaning. It represents the average unit feedback response to a change in temperature, over a short range of values where feedbacks might be expected to be operating most vigorously.

            You seem to be astonished and claim it is impossible that the second value is bigger than the first, and I find it puzzling you cannot see why the difference is not impossible. But you were asking about X, and what it’s relationship with a_0, where

            a_0 = \frac{\Delta R_0 + \Delta B_0}{\Delta R_0} = 1 + \frac{\Delta B_0}{\Delta R_0}

            So,

            X = \frac{\Delta B_0 / \Delta R_0}{B_0 / R_0} = \frac{a_0 - 1}{B_0 / R_0}

            I’m not sure what that is meant to prove, over than if B_0 / R_0 is small, X will be large.

            Imagine a car is stuck in a traffic jam and only moves 1km in 5 hours. Its average speed is 0.2km per hour. Then it gets out of its jam and drives 50km in the next hour, at an average speed of 50 km per hour. Would you compare the ratio of these two values, 50 / 0.2 = 250 and conclude this was impossible?

  20. Perhaps it takes a whigmaleerie to know a whigmaleerie? Certainly it does take skill to obfuscate an interminable and obscurantist expatiation into even deeper impenetrability.

    • “Certainly it does take skill to obfuscate an interminable and obscurantist expatiation into even deeper impenetrability.”

      Global Warming…Climate Change….Climate whatever Charlatans own this in spades

    • What is not to understand about an imagined unit feedback response to greenhouse-gas warming that exceeds the unit feedback response to emission temperature by an order of magnitude? If Mr Foley would like to propose a physical process that could cause such a disparity in unit feedback responses in the real world, I’m listening. Or, as the French curtly say, j’ecoute.

      • I am somewhat at a disadvantage when it comes to proposing such a physical process, by not having a team of physicists and climatologists to help me out. So any debate between us would be unequal. However I am sceptical of the analyses by all sides of the climate debate, in particular with regard to this post, those based on the use of a mean temperature for the entire earth.

  21. The climate system obviously has hard limits to the “feedback” proposed by some, we can see that in ice core and similar measurements. Its never become too hot nor too cold for life to be maintained ergo if anyone tells you the temp will rise by 6-8-10 C by year 20XX then feel sorry for them as they are but simpletons fooled by the socialistic sociopaths who want to rule the world through fear and intimidation.

    What causes these hard limits in the “feedback” i dont know and prefer to listen to the likes of CMoB for a more detailed explanation. Be wary of snake oil salesmen comparing the climate feedback to the feedback in a microphone, what they fail to mention (through lack of knowledge i suspect) is the microphone analogy only explains positive feedback because thats the way a microphone is designed to amplify (positive feed back) there is no negative feedback in that analogy and therefore in their simplistic minds there is no negative feedback in the climate system.

    • “….. microphone is designed to amplify…” Sorry, that is just wrong. Disconnect the lead from the microphone to the amplifier and what happens, no feedback. Disconnect the power supply to the amplifier, no feedback. If you want to increase the sound of the feedback coming out of the speakers, when the proper connections are made, someone (external energy spent) must turn the volume control up.
      Look at it this way. You go to a live stage play. The sound of the actor’s voice reaching you depends of the energy of the actor and the design the the theater. The alarmist would have us believe there must be a speaker system someplace in the theater with something the controlling volume because you could “hear a pin drop”.

      • Really? I am wrong because if you unplug the power it no longer amplifies so sad, so very sad

  22. In redrawing the graph put up by Joe Born in his “Remystifying Climate Feedback” article, Christopher Monckton humorously makes the point that this “whigmaleerie” of a graph could be taken to imply that feedbacks are supposed to respond “140 times more energetically” than they really should! Actually if I try to follow Lord M’s formula on this exactly, it comes out “18/10” divided by “5/255”, so 90 times or so, not “140”, but I’m being picky there, since the graph is just someone else’s “whigmaleerie” anyway.

    What I really want to observe, is that the number “5” mentioned above, the 5 degree K value for “B zero” (the most basic feedback number in the “whig-a mc-craperie” thing or whatever), *that* number is just unrealistically small as compared to any other reading I’ve done of Lord M’s ideas. I mean, water vapour based temperature feed back is supposed to be able to happen even without any CO2 as such to help it, right, the feedback is supposed to operate most basically on the total energy flow going through the system (sunshine based power flow)? So you get more than just 5 degrees out of this, maybe as much as 30 degrees or so, even.

    In any case, good luck with your upcoming presentation, Lord M.! Continue to master the mcallagufferies, and subdue all those who would magnify the imagined “climate crisis” with each little tweak of the temperature sensitivity delta!

    • Congratulations to Mt Blenkinsop on having found an error in the head posting. His calculation is correct: I had carelessly put 28/10 when I should have put 18/10. But the conclusion is the same: there is no physical process that I can think of which would allow feedback to respond 90 times more energetically to the pre-industrial greenhouse-gas warming than to emission temperature.

      Many thanks to Mr Blenkinsop for his good wishes. He will enjoy my Heartland presentation, where the full significance of the X factor will be revealed. It is indeed a very powerful constraint ruling out the high equilibrium sensitivities currently imagined by official climatology.

      Moderators, please correct “28/10” to read “18/10” and “140” to read “90” in the head posting. Many thanks.

      (Corrections made as requested, also changed the 2.8 to 1.8) SUNMOD

    • Most grateful to Adrian for his kind words. I get a lot of my Scottish vocabulary from reading John Buchan, the inventor of the modern adventure novel, and my English vocabulary from reading Sir Walter Scott.

    • Many thanks for your kind words. What a joy is the English language: it has a vast and expressive vocabulary, and yet is almost as concise and clear as Latin.

  23. This is possibly a stupid question…what I’ve never understood about this “moisture feedback” is why does H2O only feedback heat absorbed by CO2? How does the H2O molecule know to feedback only radiation absorbed by CO2 and not the much greater amount of heat absorbed by other H2O molecules? If there is a “moisture feedback” wouldn’t the feedback cause “run-away warming” in the absence of CO2 by the presence of H2O alone? And if the “moisture feedback” is working on the H2O heat, than why would a ppm increase in CO2 overwhelm the more important feedback for the part per hundred H2O?….again, possibly stupid questions

    • tom,

      not stupid questions. For example, lots of the literature assumes that some of the IR radiation from the Earth towards space gets absorbed by the CO2 and then gets re-radiated back toward the Earth and is “trapped” somehow. How does the Earth tell CO2 IR from the IR in the Sun’s radiation? Why would the Earth radiate the IR from the sun back toward space but not the CO2 IR?

      If the IR from the sun is not radiated toward space by the Earth then it must be stored somehow. The storage of IR energy over millions of years should have us living on a molten rock! When you raise this issue all you get for an answer is that it is magic!

  24. To become the Prime Minister of climate science you must communicate effectively with the entire electorate, not merely those like unaccountable and unrepresentative Permanent Secretaries who delude themselves that using obscure expressions in over elaborate windbaggery is a sign of superiority.

    Mercifully, as Monckton would have to emulate Viscount Stansgate to have a chance of becoming Prime Minister, and furthermore as it is highly likely that AWB was not on his list of political heroes, he can sleep easy knowing that he is arguing at Nicea rather than standing for high political office…..

    • In response to Mr Jagger, one of our most eloquent politicians was Enoch Powell. He always included one or two words of Latin or Greek and one or two long or rare words of English in any speech he made. For he, like me, had had a Classical training, and he knew that the Greek speech coaches who trained the likes of Cicero taught them always to include one or two such words to intrigue the audience and to introduce them to a wider vocabulary.

  25. Whigmaleerie?

    Dagnabbit, Monckton, you sent me off to Roget and Frontistery to find things again! Kudos to you. Please do more! I needed a good laugh this morning and you gave me one. Thank you!

    • It’s a pleasure! Scottish has its own wonderful vocabulary, which deserves to be better known.

    • Where do I get a thesaurus????? I already have the Scottish Gaelic/English dictionary, but “whigmaleerie” will stick with me for eternity now!

  26. Interesting article, but vis a vis prolix, isn’t the pot calling the kettle black?

    • in answer to Greg in Houston, my head posting was two A4 pages in length, including the diagrams. The whigmaleerie to which I was replying was at least five times longer, and the whole foofaraw of tarradiddle was predicated on a silly mistake.

      • I’ll admit that the post of mine criticized by the head post here was longer than I would have preferred; the posts that I proposed to target Lord Monckton’s theory more directly were spiked, so to get one published I had to couch it as a discourse on equilibrium nonlinear feedback.

        Still, my post was roughly only the size of the first of the series of more than ten Christopher Monckton head posts on the same theory that this site alone has run, and those were on top of at least a hundred minutes of videos and whatever posts he ran on other sites.

        Also, I’ll call attention to one of Lord Monckton’s typical tactics: he says my post “was predicated on a silly mistake,” yet he is unable to identify clearly what that “mistake” was or provide a logical explanation of why it might indeed be a mistake. He only goes on about his made-up X-factor, which proves nothing.

        • The mistake perpetrated by the author of the whigmaleerie was not to realize that his diagram implied that the unit feedback response to greenhouse-gas warming was 90 times the unit feedback response to emission temperature. He has had this point explained to him many times, and has no answer to it.

        • The author of the whigmaleerie made a careless error by furnishing a diagram whose implication was that the unit feedback response to greenhouse-gas warming was 90 times the unit feedback response to emissiont emperature. No such feedback-impact ratio is credible, because there is no plausible physical process in the climate that could cause so large a ratio.

  27. It’s good the internet gives you access to the Oxford Dictionary for those colonials of us that did not receive a proper English education.

  28. Monckton
    Your opening remarks are obviously having fun with words.
    But it gives impetus to my long-running drive to “Eradicate Sesquipedelianism”.
    When I first started the movement it was “Stamp Out Sesquideliansim”, but perhaps you will agree that using a longer word adds considerable tone.
    I’m sure you will join the movement and welcome you to the ranks of now a two-person crowd.
    When you spoke to a group in Vancouver some ten years ago, I presented you with a framed cartoon.
    The image was of a business-man seeking wisdom from a guru on a mountaintop. The response was:
    “The karma of geophysics will soon overwhelm the dogma of global warming religions”.”
    –Bob

    • I do remember the Guru cartoon, with much pleasure.

      I am as much at ease with short words as with long. I use both short and long. Most here like that. Some don’t. They’re sour. Tough luck!

  29. The great Bard , Robert Burns :

    The best-laid schemes o’ Mice an’ Men
    Gang aft agley,
    An’ lea’e us nought but grief an’ pain,
    For promis’d joy!

    Urgently required reading for all CO2 schemers!

  30. M’Lord,
    If you wish to really challenge the magnitude of feedback, here is a little secret: increased atmospheric absorption of surface flux can only occur at the expense of the atmospheric window. And atmospheric partitioning of absorbed radiation limits the surface flux. I will leave the calculations as an exercise for you.

    • No: let Neogene Geo do the calculations for himself and get them peer-reviewed and published. We are addressing one particular defect in this series: there may be others, but they are beyond our ken.

  31. A sure sign that an advocate has a bad case is that he runs away from it. In the head post Lord Monckton does that by arguing against something that my post—the one he refers to as “a prolix, inspissate whigmaleerie”—never contended.

    Stripped of its sesquipedalianism, the head post above boils one simple thing: Lord Monckton doesn’t think equilibrium temperature E as a function of the value R it would have had without feedback is as nonlinear as implied by high equilibrium-climate-sensitivity (“ECS”) values. But neither do I. And my post didn’t contend otherwise. My post instead focused on Lord Monckton’s theory.

    His theory isn’t merely that ECS is low—a proposition I’ve never argued against—but rather that a low ECS value is mathematically implied by his entire-signal rule, which is that “such feedbacks as may subsist in a dynamical system at any given moment must perforce respond to the entire reference signal then obtaining, and not merely to some arbitrarily-selected fraction thereof.” As he stated it, “Once that point—which is well established in control theory but has, as far as we can discover, hitherto entirely escaped the attention of climatology—is conceded, as it must be, then it follows that equilibrium sensitivity to doubled CO2 must be low.”

    What my post did was show that the low-ECS conclusion he urged doesn’t at all follow from the entire-signal rule he postulated. As my post demonstrated, a feedback function that complies with his entire-signal rule can indeed result in ECS values as high as “official climatology” contends.

    Again, his case isn’t merely that ECS is low; others had argued for low ECS values already. But he dismissed such arguments as mere conjecture. Previous workers like Lindzen & Choi, he said, “can’t absolutely prove that they’re right.”

    In contrast, he said, “we think that what we’ve done here is to absolutely prove that we are right.” And an absolute proof, he said, is a “way to compel the assent” of those who would otherwise believe ECS is high—and thus that E(R) is significantly nonlinear, presumably because feedbacks aren’t very strong until temperatures approach water’s phase-change levels.

    As a consequence of his supposedly monumental achievement:

    —The Heartland Institute had him present his theory at the 12th International Conference on Climate Change.

    —In his presentation he implied that someone who’s now a member of the National Security Council commented on it favorably.

    —A YouTube video of his presentation was billed as “Monckton’s Mathematical Proof; Climate Sensitivity Is Low.”

    —In another YouTube video the editor of The New American magazine introduced his theory as “an incredible new development” and a “game changer” that “is going to make a huge difference in everything we know about climate change.”

    —There was a call for crowdfunding support of legal action against scientific journals’ refusal to publish his theory.

    —This site dedicated no fewer than ten head posts to his theory and was so taken in by it that it spiked (1) a proposed post showing by diagrams that his theory boils down to bad extrapolation and (2) a proposed post in which simulation of a “test rig” showed that his conclusion doesn’t follow as he says it does from “the mathematics of feedback in all dynamical systems, including the climate,” which “comes from electronic circuitry.”

    —He is to give a “lunchtime keynote at the forthcoming Heartland Climate Conference in Washington DC.”

    In short, he has managed to distract a great many skeptics from the yawning logical chasm between his entire-signal-rule premise and his low-ECS conclusion. As a skeptic myself, I find this troubling.

    • I should add that Lord Monckton’s way of saying he doesn’t think E(R) is linear is to say that “feedbacks are imagined – per impossibile – to respond [90] times more energetically to each degree of greenhouse-gas warming than to each degree of emission temperature.”

      As is his wont, that is, he compares the small-signal quantity at one point in the function domain with the large-signal quantity at another. Adepts in electronic circuitry, from which “the mathematics of feedback in all dynamical systems, including the climate, comes,” will no doubt recognize that physical systems routinely exhibit ratios that are as high as—and often orders of magnitude higher than—the one at which he directed the gratuitous Latin.

      Now, “there is no physical process that I can think of,” he says, “which would allow feedback to respond 90 times more energetically to the pre-industrial greenhouse-gas warming than to emission temperature.” But high-ECS proponents would presumably counter that there are more physical processes in heaven and earth, Lord Monckton, than you can think of.

      • Well, yes, the 255 K emission temperature that would obtain at the Earth’s surface in the absence of forcings or feedbacks is a large signal. No getting away from it. All subsequent signals are indeed small signals. But it is not plausible that the feedback response per Kelvin of the original large signal will be as much as 90 times the feedback response per Kelvin of the small subsequent open-loop gain of just 10 K – less than one-twenty-fifth of the 255 K large signal.

        Hand-waving about large closed-loop gains in other dynamical systems won’t do: one must propose a physically-based argument, in the climate, for the X-factor of 90 implicit in Fig. 1 of the whigmaleerie.

        And don’t whinge about Latin – to do so is racialist. We Europeans are proud of our linguistic heritage and at ease with using it.

        • “[O]ne must propose a physically-based argument, in the climate, for the X-factor of 90 implicit in Fig. 1”

          For someone who goes on so about his training formal logic, Lord Monckton has an exceedingly tenuous purchase on how to apply it.

          No, I needn’t propose a “physically-based argument” for the proposition that ECS is high enough to cause such an “X-factor”; I’ve never contended that it is high. If all Lord Monckton had said was that he doesn’t believe it’s that high, we wouldn’t be having this discussion.

          Instead, he contended that his entire-signal rule would “absolutely prove” that ECS is low and thereby “force the assent” of high-ECS partisans. So a mere assertion that so high an ECS is implausible or would result from “no physical process that [he] can think of” just won’t do.

          • Mr Born admits defeat. He is incapable of coming up with any plausible physical reason why the unit feedback response to greenhouse gases should exceed the unit feedback responsse to emission temperature by one or two orders of magnitude.

  32. Assume for purposes of argument that Soden & Held’s water vapor feedback mechanism does in fact exist, as described in their 2006 paper.

    Assume further that other kinds of processes not associated with the continuous addition of CO2 and methane to the atmosphere — processes which can cause an increase in warming at the surface — will cause their postulated feedback mechanism to become active.

    For background on this topic, please see this discussion among myself, Joe Born, Nick Stokes, and Tim Gorman here: https://wattsupwiththat.com/2019/07/16/remystifying-feedback/#comment-2747126

    The state of science is such that it is currently impossible to directly observe a feedback process operating in real time inside the earth’s atmosphere, in the same way we would observe a feedback process operating inside an electronic circuit on a test bed in a laboratory.

    The presence and characteristics of such atmospheric feedback processes, if they actually exist, must be inferred from other kinds of observations. Everyone is free to pick a set of observations, a theory to explain those observations, and a mathematical representation of the theory to describe its operational characteristics.

    Since 1880, the earth’s global mean temperature has risen approximately 1C, more or less, depending upon which temperature history you choose to believe — HadCRUT4, Best, whatever you like.

    If Soden & Held’s water vapor feedback mechanism does in fact exist, but sources of the rise in surface temperature other than CO2 and methane can in fact cause it to become active, then what are the most obvious questions which follow?

    Suppose for purposes of argument that 0.3C of that 1C rise is arbitrarily assigned to natural variation, with the bulk of that allocation assigned to the time period of from 1880 to 1945. It seems to me that these implications follow from that initial assumption:

    — If the Soden & Held amplification factor is 2, then does it not follow that 0.6C of the 1C rise between 1880 and 2018 might possibly have been a consequence of natural variation?

    — If the Soden & Held amplification factor is 3, then does it not follow that 0.9C of the 1C rise between 1880 and 2018 might possibly have been a consequence of natural variation?

    If, for purposes of argument, we choose to work within the Soden & Held feedback model and to accept its basic tenets, then we have to ask the question: Does the continuous addition of CO2 and methane to the atmosphere have a unique ability to drive Soden & Held’s water vapor feedback mechanism, as opposed to other kinds of processes which might produce an equivalent result?

    • Does the continuous addition of CO2 and methane to the atmosphere have a unique ability to drive Soden & Held’s water vapor feedback mechanism, as opposed to other kinds of processes which might produce an equivalent result?

      No, of course it doesn’t. No-one says it does. All rises in temperature are what allegedly cause the feedback. In which case the question is, looking historically, what the evidence about the timing and extent of previous rises tell us about the parameters of any feedback mechanism.

      They seem to suggest that if rises have any feedback effect in them, (i) its small (ii) its self limiting (iii) its self reversing. Otherwise, why was the MWP succeeded by the LIA?

      It would be interesting to hear from Nick Stokes why this argument is invalid.

      • I like your approach, Michel. Has any group of scientists explained the physical processes involved in the decreasing temperatures (and its associated ups and downs) since the Holocene Optimum? What the hell has been going on with historical climatic changes and how does that information (or lack thereof) affect our current arguments? Climate change did not begin in 1850.

        Making mathematical calculations and running computer programs if fun. But if one doesn’t understand the underlying fundamental dynamics, one is substituting conjecture for fact. The AR5 report’s running of UN IPCC climate models with assumed anthropogenic forcings and comparing that to runs without such forcing in order to “prove” everything is explained by Man’s actions is scientific fraud.

        • I don’t think they have (explained it). No-one seems to be interested in why, after the rises of the RWP and MWP, there was cooling.

          We have had the argument over whether earlier CO2 rises preceded warming or followed it. There the argument was that an initial period of warming may have preceded the CO2 rise and perhaps caused it, but then the CO2 rise drove the subsequent phase of increase.

          Yes, and now show us what caused the fall in temps afterwards. Was that caused by a fall on the CO2 levels? Did that fall precede or follow the fall in temps? What led to it, if so? Is there any feedback loop in the falling process?

          You have to explain both the previous rises and the falls. You have to be able to explain why they happen at all, and why they are of the size and duration they have, and why they reversed as they did. And your explanation has to be consistent with a full account of any feedbacks you claim exist.

          We may not be able to measure climate feedback in action, but we can certainly observe its effects and thereby estimate the magnitude and characteristic of any feedbacks we claim to have found.

          • Well, the data indicate the world is cooling over the last few thousand years. Are we heading into a glacial period on any reasonable planning period?

            The alarmists use a 300-year period to calculate the social cost of carbon. Could we be in Little Ice Age conditions within that period? I don’t know and nobody else does either.

      • “All rises in temperature are what allegedly cause the feedback.”
        Occasionally a better informed commenter here will note that you can’t infer feedback just from amplifier performance. In the usual expression for gain with feedback, g/(1-f), you just get a single number out, and there is a range of gain/feedback options that could have produced it.

        The fact that past events have been modest doesn’t prove there was little feedback; it could, and probably does, just mean that there wasn’t much happening before feedback.

        • “The fact that past events have been modest doesn’t prove there was little feedback; it could, and probably does, just mean that there wasn’t much happening before feedback.”

          Nick, this is absolute nonsense. You need to identify: 1) The referenced past events; 2) In what respect were they modest; 3) What does any of that have to do with the existence or magnitude of feedbacks; and 4) What the hell do you mean that “there wasn’t much happening before feedback.”

          Just what are you trying to prove here?

          • The matter is simple. Michel is trying to argue that because some past events had modest effect, therefore there can’t be much feedback. But you don’t know what the original forcing was. It may have been small, and so still modest after significant feedback. There is no way of telling just from observing the response.

          • Again, Nick, you need to describe the events and their effects. What responses are you talking about?

    • BB,
      Final question is a good one for the lateral thinker.
      Sadly, my hands-on involvement in physical sciences has lapsed for so long that I cannot provide a quantitative answer.
      Geoff S

  33. This is getting tedious. Christopher needs to just calmly argue his point, if he has one, and stop with the cjhildish and self indulgent bluster and verbiage. After the opening sentence I stopped reading. I am sure many others did too.

    If he wants to be taken seriously and to persuade, just make the point simply and clearly. Read the first sentence of this and you know immediately that you are reading something by a charlatan.

    I did by the way read, and read carefully, the earlier pieces on this subject. I thought they too were mistaken and unnecessarily complicated and obscurely worded, but OK, it was possible to disentangle a fairly simple argument and agree or disagree with it. But this stuff? Its horse manure.

    The point Christopher is trying to make can be made in a few sentences. its wrong, but its nothing like as complicated as his rhetoric would have you believe.

    Drop it. No-one is listening any more. They know that no serious person addresses these issues in this way.

    • And yet …. the validity of Soden & Held’s 2006 paper and their subsequent theoretical writings is of central importance to the question of how AGW’s alleged future impacts will affect mankind.

      The state of science is such that it is currently impossible to directly observe a temperature feedback process operating in real time inside the earth’s atmosphere, in the same way we would observe a feedback process operating inside an electronic circuit on a test bed in a laboratory.

      If Lord Monckton’s refutation of the Soden & Held feedback mechanism is to be persuasive from a scientific perspective — as opposed to being little more than a series of assertions made to a pop science audience — can his refutation be any less complicated in its verbiage and any less extensive in its mathematics than is Soden & Held’s own theoretical work?

      The answer is no, it can’t be simpler than what Monckton is now making of it. We don’t yet have the observational tools and the analytical techniques which could make a simpler refutation possible while still employing a disciplined, science based approach.

      • In response to Beta Blocker, there is indeed a certain minimum of mathematics and physics in our paper, and I don’t think it could be compressed much more than we have already done.

        The advantage of having been given the lunchtime keynote at the Heartland Conference is that there will be very many highly competent and highly skeptical climate scientists present, and they will not be slow in coming forward if our analysis is insufficiently scientific, or if it is just plain wrong.

        But the author of the whigmaleerie has plainly been taken more than somewhat aback at the news that his Fig. 1 implies 90 times more feedback response per Kelvin of preindustrial greenhouse-gas warming than per Kelvin of emission temperature.

        He had previously produced a curve that implied an X-factor of 11, and that had no physical justification either.

        Once the Heartland audience see how very slowly the system-gain factor (the closed-loop gain) grows with the X-factor, they will see what we see, and they well tell us whether they think it has the significance we think it has. This will be the toughest but fairest peer review we have ever faced: and we welcome that. If we’ve missed something important, we’d like to know.

        • “But the author of the whigmaleerie has plainly been taken more than somewhat aback at the news that his Fig. 1 implies 90 times more feedback response per Kelvin of preindustrial greenhouse-gas warming than per Kelvin of emission temperature.”

          Hardly. I was well of aware of that meaningless point before I wrote the post; Lord Monckton had brought it up before. The world is full of feedback mechanisms whose (conjured-up-by-Lord-Monckton) “X-factors” are that high. A control-systems text in front of me right now gives an example in which it’s infinite at some output values.

          Lord Monckton spews obscure nomenclature to frighten the natives. My guess is that he’ll pull the wool over the eyes of the Heartland Conference audience this time just as he apparently did last time. They won’t quite understand everything he says, but the conclusion will seem right and he’ll use a lot of technical terms, so they won’t think too critically about his logic.

          • Dave Fair:

            No, it wouldn’t be helpful.

            Lord Monckton is doing what he always does: he’s misrepresenting what I’ve said. I won’t show that his “X-factor” 90, because I don’t think it is 90 and have never said it was. What my post said instead is that I do not—repeat, do not—believe that ECS has a value that would imply “X-factor”of 90 but that such a value, which “official climatology” does believe, would not be inconsistent with his entire-signal rule.

            With all due respect, please don’t let Lord Monckton lead you around by the nose. That 90-times business he’s talking about it merely another way of saying that ECS is as high as he says “official climatology” says it is. For many reasons, I don’t think “official climatology” is right. Among them is work by researchers such as Lindzen & Choi and Lewis & Curry.

            So, contrary to the impression he repeatedly gives, I don’t think the “X-factor” he goes on about is 90, and neither do those researchers (or, at least they wouldn’t if they’d ever heard of it and accepted for the sake of argument all Lord Monckton’s numbers he bases it on). But Lord Monckton dismisses our opinions—i.e., our reasons for believing that ECS is low and that his “X-factor” accordingly is not 90—as mere conjectures.

            In contrast to our mere conjectures about ECS, he says, his theory absolutely proves that ECS is low. Specifically, he contends that a low ECS necessarily follows from the entire-signal rule he’s postulated.

            I’ve shown that it doesn’t, and he’s been unable to demonstrate otherwise. So he misrepresents my position and argues against what I didn’t say. Read my post and comments. You’ll see you’ve been misled about my position. And keep in mind that his “X-factor” business is just an obscure way of saying high ECS.

            Such obfuscation is Lord Monckton’s stock in trade. He is not an honest disputant.

    • If it’s getting tedious, you don’t have to read it. But a lot of people enjoy it. Don’t spoil their fun by being sour.

      • The above two comments were addressed to the unfortunate Michel, who is not enjoying himself here, and not to Beta Blocker, whose comment is sensible and constructive. Weirdpress has a funny way of deciding where in a thread a comment appears. Apologies to Beta Blocker if I had inadvertently appeared churlish.

        • Michel will come around once he recognizes that the context in which an argument is being made supplies details to that argument which may not be immediately obvious to someone who is reading an analysis without mentally imposing a prior frame of reference.

          Either their own contextual frame of reference, or someone else’s.

          For example, the contextual frame of reference for Soden & Held’s postulated feedback mechanism is a need to explain how an increase in surface temperature of 1C to 1.5C over some period of time can be amplified into a projected 2.5C to 3C increase, thus turning an uncomfortable outcome into a disastrous outcome for the earth and for all humanity.

          The base process being investigated through Soden & Held’s writings is the continuous addition of CO2 and methane to the atmosphere. The Soden & Held paper would not have been written had there not been a need to explain how CO2’s basic impact of a 1C to 1.5C rise can be amplified into a projected 2.5C to 3C rise over the next one-hundred years.

          Most everyone who examines Soden & Held’s work in detail, either to support it or to refute it, understands what contextual frame of reference is being applied when defending or criticizing the scientific arguments.

          Given it is impossible at the current state of science to directly observe the water vapor feedback process in operation, and given that the process can only be characterized and quantified by indirect means, then everyone who defends or refutes the Soden & Held feedback mechanism must play by the same set of rules, if they are to be taken seriously.

          This means that every line of inquiry which is pertinent to examining the postulated feedback mechanism is fair game for discussion — if the line of inquiry is being honestly pursued, and if the questions being asked have a direct bearing on the validity, or the lack thereof, of the postulated theory.

          • Actually, IIRC, water vapor changes in the atmosphere have been measured. Such measured values don’t comport with those used by the UN IPCC computer modelers and report authors.

          • Dave Fair: “Actually, IIRC, water vapor changes in the atmosphere have been measured. Such measured values don’t comport with those used by the UN IPCC computer modelers and report authors.”

            It would be very useful if someone having extensive knowledge of how the IPCC climate models are written could explain to us how Soden & Held’s feedback mechanism is being incorporated into the model designs. Are there substantive differences from one model to the next in how the postulated feedback mechanism is being handled?

    • Agreed.

      If you have a point to make and your real goal is to have your audience understand it, make it in as plain language as possible. Technical and Business writing are rarely, if ever, improved by injecting verbalistic geegaws.

      When a reader needs to resort to a dictionary or glossary it should be because the word in question has a more precise and context-appropriate meaning than a more familiar synonym.

      • My misson here, in reply to Mr Werner, is to inform, to educate and to entertain. The number of spontaneous comments from those who enjoy learning new words far outstrips those who are sour about it. Live a little!

        • Fair enough.
          Perhaps on your side of ‘the pond’ there is a different attitude about what we call ten-dollar words.

  34. While I can cope with the logical reasoning, I still have to object the premises. There simply is no GHE of a 33K.

    If we take a step back, we might easily agree on the “global warming” narrative failing at a lot of instances. Whether it is dubious temperature records, islands which refuse to sink, or polar bears failing to extinct. However all these questions are indeed “feedbacks” to the very foundations of a theory, and as much as they might be proven wrong, they will not do away with the foundation. The analogy here is not a Jabberwocky, but a Hydra.

    What hurts in this regard is the concession to the validity of the GHE, in order to possible cut a single head off the Hydra. Even if the reasoning was ever acknowledged (and it likely never will), it would only be a small Phyrric victory. As long as “climate criticists” support the ill fated theory of the GHE (or badly fail to falsify it), they are all just feeding the troll.

    For that reason my humble falsification of the GHE is so important.

    https://www.scribd.com/document/414175992/CO21

  35. Michel
    This is getting tedious. Christopher needs to just calmly argue his point, if he has one, and stop with the cjhildish and self indulgent bluster and verbiage.

    Or maybe not. Yes it has become customary to write scientific text in emotionally sterile text with a logical rigour and apparent complexity which convey mild intimidation. This is necessary to some extent. But human nature being what it is, science-speak ends up becoming the equivalent of medieval Ecclesiastical Latin in simply shutting out outsiders. And what is more pleasant to the human soul than membership of an elite and shutting out outsiders?

    Thus instead of asking the question “how long would it take a single aphid to eat all the vegetation on earth?”, the career scientist would dignify the otherwise frivolous sounding question by framing it as “Individual component of global macrophytophagy in Mysus persicae.”

    We are all here because in practice, emotionless technical language has not in practice safeguarded sound and effective science. The field of climate science, under an intolerable pressure of politics and conflicts of interest of cosmological proportions, has succumbed to group think, circular logic (tautology), confirmation bias and outright corruption (“hide the decline”). Beyond climate in wider science there is the growing scandal of non-reproducibility (not being able to get the same answer twice). Because fortress mentality defends conflict of interest.

    This site and many other science blogs have shown that it is possible to convey precise and important scientific arguments in normal human language. Contributors such as Christopher Monckton, Willis Eschenbach, Kip Hansen, Jim Steele, David Middleton and David Archibald, to name just a few, show that highly individual and expressive styles do not obstruct communication of real and important science.

    In short, a bit of tolerance and broad mindedness is no bad thing in scientific discussion as in life in general. Live and let live.

  36. We define emission temperature R0 as the 255 K global mean surface temperature that would obtain on Earth at today’s solar irradiance and albedo but before any greenhouse gases have entered the atmosphere and before any feedback begins to operate;

    Its easy to show that all things being equal with two black bodies except the spread of temperatures – one being 90 to 390K as seen at the equator of the moon and the other 275 to 303 K, the spread of sea surface temperatures on Earth, that you get the same sum of T^4 and mean T very close to the means observed for the Moon (eq) and the Earth (SST).

    Surely the first thing to do is account for this 30K effect.

    • You are perfectly right. The weighted (or geometric) average surface temperature of the moon is about 276K. That of Earth without GHGs, aerosols and clouds would be about 278K, which can well be derived from Fresnel equations with the proper refractive indices of water with regard to visible light and LWIR (N2 = 1.33 and 1.27 respectively).

  37. Although the head post is less internally inconsistent than most of Lord Monckton’s, his comments include a good example of how deceptive he is:

    “The author of the whigmaleerie made a careless error by furnishing a diagram whose implication was that the unit feedback response to greenhouse-gas warming was 90 times the unit feedback response to emission temperature.”

    The truth is that Lord Monckton has identified no error, careless or otherwise. And a less-deceptive description of that diagram’s actual implication is instead that the “unit feedback response” after greenhouse-gas warming at the pre-feedback temperature, 265 K, was less than 2.3 times the unit feedback response to warming at the emission temperature, 265 K.

    Now, I don’t think the actual climate exhibits a ratio even that high. As Bellman correctly observed, though, “[C]ommon sense tells me many physical mechanisms will only have an effect above certain temperatures. For example, the feedback caused by melting ice can only have an effect once global temperatures are sufficiently warm for ice to melt.” And 265 K is more than twice as close to the melting temperature as 255 K is. Add in effects like polar amplification, the further warming from feedback, and whatever difference there is between different cloud types’ unknown but undoubtedly nonlinear positive- and negative-feedback effects, and Lord Monckton’s basis for calling (what is actually) a ratio of 2.3 “impossible” is far from self-evident.

    Much less did that unsupported assertion of impossibility “absolutely prove,” as he claimed he could, that ECS is low. And, remember, his theory’s being an absolute proof is the advantage he claimed over other researchers, such as Lindzen & Choi, whose work he dismissed as mere “conjecture.” If he hadn’t made that claim, we wouldn’t be discussing this.

    To distract this site’s readership from his failure, he returned to the tactic he’s used repeatedly: he deceptively conflated large-and small-signal quantities. As my post showed by juxtaposing large-and small-signal quantities in its Figs. 3, 5, 6, 9, 11, and 13, large-and small-signal quantities are different animals, and it’s the small-signal quantity that’s most meaningful for most purposes. As Nick Stokes’ post said, “You can’t mix them.”

    But Lord Monckton did mix them. And he so chose his words as to blur the mixing. Specifically, he defined unit feedback response as “the ratio of the feedback response to the reference temperature or sensitivity that triggered it: or, in plain English, the amount of feedback-driven temperature or warming per degree of the pre-feedback temperature or warming.”

    Note that he twice used “temperature or warming” (emphasis added). By “temperature or” he not only included the large-signal quantity as well as the more-meaningful small-signal quantity but also lay the groundwork for distracting the WUWT readership’s attention with talk of his meaningless, made-up “feedback impact ratio X.”

    He defined that—oh, what to call it—whigmaleerie not as a small-signal quantity, not as a large-signal quantity, and not even as the (already meaningless) ratio of some temperature’s small-signal quantity to its large-signal quantity. He defined it instead as the ratio that (an approximation to) one temperature’s small-signal quantity bears to a lower temperature’s large-signal quantity. The only possible reason for creating the resultant meaningless ratio is to inflate the ratio by more than thirty times and thereby distract the WUWT readership from the fact that his theory had been completely dismantled.

    His theory is that a low ECS value is mathematically implied by his entire-signal rule, which is that “such feedbacks as may subsist in a dynamical system at any given moment must perforce respond to the entire reference signal then obtaining, and not merely to some arbitrarily-selected fraction thereof.” As he stated it, “Once that point—which is well established in control theory but has, as far as we can discover, hitherto entirely escaped the attention of climatology—is conceded, as it must be, then it follows that equilibrium sensitivity to doubled CO2 must be low.”

    By using his own “whigmaleerie,” he has distracted attention from the fact that, on the contrary, we’ve shown a high ECS value to be entirely consistent with the entire-signal rule he postulated. His theory has no merit.

    • Joe Born,

      I think the problem here (i.e. your problem) basically boils down to 2 simple things:

      1) The concept of the climate having a temperature, and more specifically there being an equilibrium starting temperature is NOT valid. In fact, the concept of there being a steady-state temperature in the climate is not even valid either. The entire system is perpetually oscillating. Yes, the perpetual oscillation can be averaged to a specific temperature and that average temperature can be modeled as being equivalent to a static average in equilibrium, but it never actually is in such a state.

      2) You apparently do NOT understand the difference between a system based theoretical error and an error at the raw physical principle level. They’re not the same thing. Monckton’s claimed error is of the former, not the latter. This distinction is crucial to the whole argument.

      Yourself (and Nick Stokes and Roy Spencer) apparently think that because the derived equations that generically describe and quantify a thermodynamic response to a temperature change have no imposed constraints or established bounds from the equations themselves, it invalidates Monckton’s whole thing and all other misunderstandings concerning how feedback is being applied to the climate system.

      Of course, this is not the line of argument (against it) being made at all, and the fact that one can devise equations that can describe a thermodynamic response to a temperature change of essentially unlimited magnitude or proportion is absolutely meaningless, and says nothing about whether any such response is even possible, let alone feasible and/or logical in a particular system.

      Remember also, Monckton is stipulating ‘in dynamical systems’, which also means systems that are perpetually oscillating as I’ve described above. This is a key distinction and stipulation in all of this.

      Now, maybe Monckton and his team could do a better job laying all of this out and making their case, but if you can’t understand the difference between a system based theoretical error and an error at the raw physical principle level, then this is just going to keep going around and around in circles forever.

      On another thread, I offered another way of systematically laying out the error that I think hones in on it perhaps better than Monckton and his team have.

      • So now all you need is for Monckton to explain what scientific method he uses when he determines that all feedbacks work equally across all temperature ranges. I’m not claiming my intuition is correct. The only justification I’ve seen him use have all been based on intuition; that a physical property cannot know it has to act differently at different temperatures, or that all feedbacks should act like electrical circuits.

    • RW
      1) The concept of the climate having a temperature, and more specifically there being an equilibrium starting temperature is NOT valid. In fact, the concept of there being a steady-state temperature in the climate is not even valid either. The entire system is perpetually oscillating. Yes, the perpetual oscillation can be averaged to a specific temperature and that average temperature can be modeled as being equivalent to a static average in equilibrium, but it never actually is in such a state.

      True.
      Climate is a far-from-equilibrium open and dissipative system containing feedbacks.
      Therefore the paradigm needed to study its behaviour is chaotic-nonlinear dynamics, emergent nonlinear pattern formation and attractor landscape analysis.
      Ed Lorenz’ discovery of “deterministic nonperiodic flow” in 1962 showed that there is no equilibrium, no stable plateau and in fact, in the strict sense – no climate!
      Talk of equilibrium temperatures exists only within a fantastical La-La-LinearLand, somewhere over the rainbow.
      Talk of equilibrium temperature

      • Yes, and this is what apparently Joe Born and Nick Stokes (and so many others) can’t understand even if their lives depended on it. They also can’t understand the difference between a system based theoretical error and an error at the raw physical principle level. It’s truly bizarre, in my opinion.

        But maybe Monckton and his team need to do a better job explaining all of this. I even suggested to him that perhaps he needs a separate paper addressing the two kinds of errors and how they relate to all of this. Without clarification, this is just going to go around in circles forever.

        • Wouldn’t these arguments be better addressed to Monckton? He’s the one claiming that all feedbacks can be reduced to a simple linear equation, with almost no uncertainty. The IPCC in contrast only limits ECS to a rather wide range of possible values – in part because the effects of feedbacks are uncertain.

          • Monckton’s team is essentially claiming feedbacks have already physically manifested bounds in the system, and given what’s accepted, i.e what they accept regarding everything else, the sensitivity should only be about 1C. These are approximate bounds on the sensitivity from the feedbacks — not a precise measure of it.

            But even this is too high because the 1C of intrinsic warming from 2xCO2 is not correct, has nothing to do with GHE warming of the surface, and something like around 0.5C of intrinsic effect is probably more accurate. This implies with net negative feedback (a near certainty), that the actual sensitivity is under 0.5C.

        • ‘RW’ said:

          “They also can’t understand the difference between a system based theoretical error and an error at the raw physical principle level. It’s truly bizarre, in my opinion.

          But maybe Monckton and his team need to do a better job explaining all of this .. ”

          Your distinction between theoretical error and literal physical error seems to resonate with me, come to think of it! Is your idea of theoretical system error like the difference between ideal open loop or “non-feedback” speed for an idealized steam engine vs the actual running speed of the engine, as in the very ideal or hypothetical example that I outlined back in a previous discussion — link for this is at:

          https://wattsupwiththat.com/2019/06/08/feedback-is-not-the-big-enchilada/#comment-2720047

          (This was a “negative feedback” proportional control example, since the assumption of ‘negative’ feedback just seemed more plausible than the ‘positive’ type of feedback, for a steam engine example as such)

          Now my point here is that while the output speed of my example engine *was* assumed to be a real physical thing, and the *feedback* based on this speed (for manipulating the control valve setting) was also truly physical in principle, what happens is that the *reference* speed (the ‘1000 rpm’ in my example) is not actually “right there” physically, not even in principle really! In the example, the 1000 rpm reference is more strictly a mathematical convenience, a hypothetical thing built into the most straightforward calculation of how the feedback works overall. This “1000 rpm” is similar in principle, it seems to me, to the “snowball earth” reference temperature that Christopher Monckton uses in his climate model — that reference temperature is not in itself supposed to be something you can measure or confirm directly by experiment, right? The difference between actual temperature and the reference is then, as you say, a “theoretical error”, not a “raw physical” one?

          Could this more or less elementary point really be a confusion for some people? I know that I reacted skeptically when I first heard of conventional theorists calculating how cold the planet ought to be if someone were to suck all the Greenhouse Gases out of the atmosphere!

          It occurs to me here that maybe even some of the “pro” climate modelers may take these reference points as an actual prediction, or as a built in reality of sorts! Wouldn’t looking at such references as a mere ‘formula parameters’ be the better way to picture it?

  38. One can have a great deal of fun with this feedback model, but all of the above posts are making an assumption which is not valid, and that is that the open loop gain is infinite. In a common electronic circuit the open loop gain will be designed to be high (as an approximation to infinite), and the circuit response will be close to that from the usual equation. However if the open loop gain is fairly low the response will be much less than expected, and the feedback factors will not really be in useful control of the design.

    Whilst I am in general agreement with Lord Monckton’s analysis, those suggesting that the response may be very high cannot be correct unless they can identify the source of the high open loop gain. The Bode analysis of the circuit requires that both open loop gain is available and that the output may receive power from an external (not the input) source. It also requires that the output is linearly connected to the inputs and feedbacks (although the feedback may be via a non-linear element) and that the gain element is entirely linear. I would like to suggest that no one has yet explained any of these necessities in “atmospheric” terms!

    The feedback amplifier may be a useful model of the atmosphere, but its characteristics cannot be given “magical” properties in order to explain warming, or anything else. Feedbacks, both positive or negative, must precisely obey the model rules, as must the open loop gain availability and mechanism. Please enlighten me as to how these work with atmospheric physics.

  39. There’s the complex planetary process of thermalization of cloud-modulated insolation by matter of starkly different thermal capcitance, followed by chaotic energy transfer between variously-coupled heat reservoirs, eventually resulting in the inevitable radiative loss to space through a semi-transparent atmosphere–all operating under the entropy-maximizing principle of thermodynamics. And there’s the simple conceptual model of a single-element “feedback” process that involves nothing more than high-school algebra to compute a static-gain. That the former can be meaningfully represented by the latter is an attempt to do geophysics on the cheap. The public pretense that this succeeds constitutes the undying hoax of “climate science”

  40. Returning to some points I’ve made earlier …..

    The state of science is such that it is currently impossible to directly observe a temperature feedback mechanism operating in real time inside the earth’s atmosphere, in the same way we would observe a feedback mechanism operating inside an electronic circuit on a test bed in a laboratory.

    The presence and characteristics of such atmospheric feedback mechanisms, if they actually exist, must be inferred from other kinds of observations.

    Topic #1:

    Soden & Held’s postulated feedback mechanism serves a need to explain how an increase in surface temperature of 1C to 1.5C over some period of time can be amplified into a projected 2.5C to 3C increase, thus turning an uncomfortable outcome into a disastrous outcome for the earth and for all humanity.

    Because their postulated feedback mechanism cannot be observed directly, Soden and Held use output from the climate models as one source of data among several in quantifying the theoretical sensitivity of earth’s climate system to the continuous addition of CO2 and methane to the atmosphere.

    That Soden and Held take this approach raises another obvious question.

    If the climate models take account of their postulated feedback mechanism, either directly or indirectly — and if Soden and Held are using model outputs as inputs into their sensitivity analysis — then is circular logic being used in characterizing and quantifying their theoretical mechanism?

    If Soden and Held’s feedback mechanism is being incorporated into the IPCC models in some way, either directly or indirectly, then how is this being done?

    Is it being accomplished directly through inclusion of feedback modeling algorithms operating within the main model’s dynamic core, or is it being done indirectly through the choice of values being assumed for the model’s physical parameterizations?

    If it being accomplished directly through inclusion of feedback modeling algorithms operating within the main model’s dynamic core, then on what basis in atmospheric physics is the algorithm being formulated?

    On the other hand, if it is being done indirectly through the choice of values being assumed for the model’s physical parameterizations, then on what basis are the assumed values being chosen?

    Topic #2:

    Let’s get back to another issue I raised earlier: the possible existence of processes other than the continuous addition of CO2 and methane to the atmosphere which can raise the temperature at the earth’s surface and thus activate a positive water vapor feedback mechanism.

    Both Joe Born and Nick Stokes say that Soden and Held’s postulated mechanism can be activated by other processes which can raise the surface temperature.

    If Soden & Held’s water vapor feedback mechanism does in fact exist, but sources of a rise in surface temperature other than CO2 and methane can in fact cause it to become active, then what are the implications for the IPCC models if positive feedback amplification can be activated by natural processes?

    For one example, if the addition of CO2 and methane to atmosphere is amplifying water vapor’s GHG effects, and if some natural process is also amplifying those GHG effects at the same time, then on what basis does one quantify and allocate the respective effects of each possible source?

    Summing up:

    It would be very useful if someone having extensive knowledge of how the IPCC climate models are designed and written could explain to us how Soden & Held’s feedback mechanism is being incorporated into the model designs, and also how that incorporation is being accomplished; i.e., through direct or indirect means, or possibly through some combination of the two.

    • You’re right that in general Lord Monckton’s temperature-addition step is problematic, but the particular curve you see above doesn’t suffer from that defect. It wasn’t generated by Lord Monckton’s approach.

      As the post he criticizes explains, forcings rather than temperatures were the quantities that got added in my calculations. It’s only after the addition that the forcings were converted to Lord Monckton’s temperature quantities.

      Rather than represent temperature additions, therefore, all the drawing above shows is differences between the resultant equilibrium temperatures and the values they’d have had without feedback. Lord Monckton is employing those differences in a gimmick, but in this case the problem isn’t that he’s using temperature addition.

      Incidentally, just using without-feedback temperature is problematic, too, as kribaez’s comments on the previous threads explain. But I averted my eyes from that and several other errors to focus on the logical gap between Lord Monckton’s entire-signal postulate and his low-ECS conclusion.

    • Goodness sakes! So when ‘conventional’ theorists (like, say, Arrhenius in his day) added a certain global temperature increase due to a doubling of CO2, and they add that 1.5 degrees C (or 2 degrees or whatever), it is improper just to add like that? Temperature is immune to the use of arithmetic?

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