Feet of clay: The official errors that exaggerated global warming – part 3

Part III: How the feedback factor f was exaggerated

By Christopher Monckton of Brenchley

In this series (Part 1 and Part 2) I am exploring the cumulative errors, large and small, through which the climatological establishment has succeeded in greatly exaggerating climate sensitivity. Since the series concerns itself chiefly with equilibrium sensitivity, time-dependencies, including those arising from non-linear feedbacks, are irrelevant.

So far, it has been established that the models’ failure to determine the central estimate of equilibrium or final climate sensitivity ΔT from their central estimate of the unitless feedback factor f (see Part I of this series) combined with their erroneous official mixing of surface temperature and emission-altitude flux in the Stefan-Boltzmann equation to generate an excessive value for the climate-sensitivity parameter λ0 (see Part II) had led to a 40% exaggeration of the central estimates of the reference pre-feedback sensitivity ΔT0 and hence of final sensitivity ΔT in the CMIP5 ensemble of general-circulation climate models.

Part III will consider a further effect of the official exaggeration of λ0 on climate sensitivity –the overstatement of the temperature feedback factor f.

The official equation (1) of climate sensitivity as it now stands, which was well calibrated against the outputs of both the CMIP3 and CMIP5 model ensembles in Part I, is –

(1) clip_image002

where clip_image004

clip_image006

Fig. 1 Illumination of the official climate-sensitivity equation (1)

Fig. 1 illuminates the interrelation between the various terms in (1). We shall now determine equilibrium sensitivity stepwise, making corrections for the errors identified in Parts I and II along the way and, this time, also correcting the value of the feedback factor f.

The net incoming flux density F0, at the emission altitude about 5 km above ground level depends solely on the total solar irradiance S0 = 1361 W m–2 and on the mean albedo or reflectance α = 0.3, thus: F0 = S0(1 – α) / 4 = 238.175 W m–2. From the fundamental equation of radiative transfer, assuming emission-altitude emissivity ε0 = 1 and the Stefan-Boltzmann constant σ = 5.67 x 10–8 W m–2 K–4, emission temperature T0 = [F0 / (ε0 σ)]1/4 = 254.578 K.

Add the CO2 radiative forcing ΔF0 = 5.35 ln(2) = 3.708 W m–2 to obtain the pre-feedback or reference flux density Fμ = 241.883 W m–2, from which the Stefan-Boltzmann equation gives Tμ = 255.563 K, so that reference sensitivity ΔT0 = Tμ T0 = 0.985 K.

With these preliminaries, we begin the consideration of temperature feedbacks, which are additional forcings ci, summing to c = Σi ci, expressed in Watts per square meter per Kelvin of the reference warming ΔT0 that triggered them. This time, we shall concentrate only on the central estimate of climate sensitivity. In the next article, we shall examine the upper and lower bounds, for the hitherto poorly-constrained breadth of the climate-sensitivity interval arises chiefly from variations in temperature feedbacks between models.

IPCC’s interval of climate sensitivities in AR5 is [1.5, 4.5] K, just as it was in the Charney report for the National Academy of Sciences in 1979. Where λ0 is the official reference-sensitivity parameter 3.2–1 K W–1 m2, the ratios G of these bounds to IPCC’s estimate ΔT0 = λ0ΔF0 = 1.159 K of reference sensitivity fall on [1.294, 3.883], implying [0.227, 0.742] as the bounds of the interval of feedback factors f = 1 – 1 / G. The central estimate of f is here taken simply as (0.227 + 0.742) / 2 = 0.485, implying a feedback sum c = f / λ0 = 1.550 W m–2 K–1.

At this stage we are not going to challenge IPCC’s implicit central estimate of the feedback sum. If we were to retain IPCC’s concept and estimate of λ0, and consequently its estimate of reference sensitivity ΔT0, then the central estimate of equilibrium sensitivity based on the feedback sum c = 1.550 W m–2 K–1 would be 2.2 K, as Fig. (1) shows.

Fig. 1 shows a stable, an unstable and a climate-unphysical region. The stable region, where the feedback factor is either negative or at most 0.1 (and preferably little more than 0.01), reflects the fact that process engineers designing electronic circuits designed to perform stably even where the reliability of componentry and the stability of ambient operating conditions cannot be guaranteed often use a rule-of-thumb maximum design value for feedbacks, since any value above the maximum may lead to unwanted instability.

Why is the operation of feedbacks in electronic circuits of interest when looking at the climate? The answer is that the mathematics of feedback amplification was originally developed for electronic circuits, typically amplifiers, and that the two papers that between them established the present mathematical approach to feedbacks in the climate – Hansen (1984) and Schlesinger (1985) – refer back specifically to the treatment of feedbacks in electronic circuits as the origin of and justification for the method they proposed.

clip_image008

Fig. 1 The rectangular-hyperbolic curve of equilibrium climate sensitivity ΔT in response to the feedback factor f = λ0Σici, based on the official method of determining climate sensitivity, showing that implicit official final sensitivity in response to the central estimate f = 0.485 is 2.2 K.

Now, the mere fact that process engineers often try to impose an upper bound on feedback where it might lead to instability does not prove that climate feedbacks in the region shown in Fig. 1 as unstable are impossible. However, it suggests that they are unlikely; and, in the next article, we shall demonstrate that, in the climate, feedbacks do not occur in that region, and that they only appear to do so owing to a substantial error in climate feedback analysis.

For now, we shall take IPCC’s implicit central estimate of the feedback sum c = 1.550 W m–2 K–1 and use it as the basis for determining the central estimate of climate sensitivity, but without using the defective official quantity λ0.

Instead, we shall redetermine the unitless feedback factor f as the product of c and the first derivative of the Stefan-Boltzmann equation at the emission altitude after taking into account the pre-feedback increase in radiative flux density at that altitude, thus:

(2) clip_image010 1.550 clip_image012 0.409.

From this value, the final gain factor G = 1 / (1 – f ) = 1.693. The product of G and ΔF0 gives the final flux change ΔF, so that the final flux density F = F0 + ΔF = 244.454 W m–2, whereupon the final temperature T is 256.239 K, and the final sensitivity ΔT = TT0 < 1.7 K.

Charney (1979) gave the central estimate of ΔT as 3.0 K. The CMIP5 models’ value is 3.2 K, which is a 92.5% exaggeration compared with the value 1.661 K found here. As we shall see later in the series, even this corrected central estimate is substantially too high.

Table 1 summarizes the calculations in this article.

Determination of the central estimate of final climate sensitivity
Variable Derivation Value Units
2 x CO2 forcing ΔF0 5.35 ln (2) 3.708 W m–2
Emission flux density F0 S0 (1 – α) / 4 238.175 W m–2
Amplified flux density Fμ F0 + ΔF0 241.883 W m–2
Amplified temperature Tμ (Fμ / σ)1/4 255.563 K
Emission temperature T0 (F0 / σ)1/4 254.578 K
Reference sensitivity ΔT0 Tμ – T0 0.985 K
Official feedback factor foff (0.227 + 0.742) / 2 0.485 Unitless
Implicit feedback sum c foff / λ0 | λ0 = 3.2–1 1.550 W m–2 K–1
Corrected feedback factor f c Tμ / (4Fμ) 0.409 Unitless
Final gain factor G (1 – f )–1 1.693 Unitless
Final flux change ΔF G ΔF0 6.279 W m–2
Final flux density F F0 + ΔF 244.454 W m–2
Final temperature T (F / σ)1/4 256.239 K
Final sensitivity ΔT T T0 1.661 K

Ø Next: How the breadth of the climate-sensitivity interval was exaggerated.

References

Charney J (1979) Carbon Dioxide and Climate: A Scientific Assessment: Report of an Ad-Hoc Study Group on Carbon Dioxide and Climate, Climate Research Board, Assembly of Mathematical and Physical Sciences, National Research Council, Nat. Acad. Sci., Washington DC, July, pp. 22

Hansen J, Lacis A, Rind D, Russell G, Stone P, Fung I, Ruedy R, Lerner J (1984) Climate sensitivity: analysis of feedback mechanisms. Meteorol. Monographs 29:130–163

IPCC (1990-2013) Assessment Reports AR1-5 are available from www.ipcc.ch

Schlesinger ME (1985) Quantitative analysis of feedbacks in climate models simulations of CO2-induced warming. In: Physically-Based Modelling and Simulation of Climate and Climatic Change – Part II (Schlesinger ME, ed.), Kluwer Acad. Pubrs. Dordrecht, Netherlands, 1988, 653-735.

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332 thoughts on “Feet of clay: The official errors that exaggerated global warming – part 3

  1. If you look on the home page, the lead-in says, ” How the feedback factor f was exaggerated By Christopher Monckton of Brenchley. Made me laugh.

    • EXTREME TROLL WARNING!

      There are more imbecilic comments here than I have ever seen before.on WUWT.

      The Klimate Inquisition is on steroids today.

      • Peter, notice they never talk about it when the CO2 levels in the atmosphere were over 1,500 ppm for millions of years,How come it didn’t go into run away warming then?

        Here is my simple consideration:

        I see a lot of discussion going on here about sensitivity. The maths long as my arm,and some of it not precise numbers, to make a concluding argument, that sensitivity is really much smaller than what the IPCC thinks it is.

        What I am more interested in, is past climate history,showing any indication of any minor instability ever going into the major run away instability phase. The IPCC never seem to point out a time out of the past 1.5 Billion years to show evidence of prolonged instability, that would support their claim.It is a fatal weakness because there is strong evidence based on several published papers that CO2 in the atmosphere has been Much,much higher than today, WITHOUT that much babbled about run away instability ever occurring, they think is probably going to happen in the near future with only a meager 500 ppm of CO2 hanging around in the air.

        Frankly, it never happened when the CO2 level was over 4,000 ppm,for MILLIONS of years,what make you think it will happen with 500-700 ppm,in the near future?

      • Peter, I always take the large number of trolls turning up to oppose, muddle or derail the conversation thread following Christopher Monckton’s articles as a sure sign that what he produces is extremely important. Clearly the alarmists think so too, or they wouldn’t try nearly so hard.

        :)

  2. There is nothing left of AGW and yet it just keeps rolling on BBC and the Guardian and CNN like a zombie out of control. Things will change if Trump gets in I imagine.

    • Guess again. Trump has belittled AGW when asked about it, but I wouldn’t expect him to devote much energy against it as President, since so few voters consider it a priority. My hunch is that, if he actually wins election, he will also have a strong majority in the Senate. But would he be willing to challenge and defang EPA, to stop their insane tilting at windmills? I doubt it.

      • Actually, even if Trump should win, the GOP majority in the Senate is liable to shrink, at best. Republicans are defending too many shaky seats this year against too many strong Democrat candidates to expect to increase their majority.

      • –But would he be willing to challenge and defang EPA, to stop their insane tilting at windmills? I doubt it.–
        The question is would Trump veto a bill which defunds the federal EPA. Or simply reduce it’s budget
        significantly, 8 billion now, so next have it 6 billion, then 4 billion, etc.
        And the 6 billion you give it, can have requirements of having EPA do cost estimate on all existing environmental regulations, with a warning of failing to adequately do this assessment properly and timing fashion will result in more dramatic budget cut and eventual elimination of agency- which would proven it’s too incompetent- or not having any benefit associated with it’s existence. The bill should also tell the agency it should everything possible of refraining from causing pollution in the future:
        http://www.newsweek.com/epa-causes-massive-colorado-spill-1-million-gallons-mining-waste-turns-river-361019

  3. I am not good at maths ( really I am not )
    I remember just before I was introduced to arithmetic my joy at observing the natural world, all the insects and other creatures I could approach and examine.
    So when somebody told me to look for a pattern, this plus this equals this, to find recognizable truths I instinctively said, No it is not like that.

  4. We have 4.5 billion years of observational evidence wherein the climate has NEVER driven into the unstable region. Monckton should take credit for that.

      • His Lordship is responsible for all kinds of things, besides exaggerating the climate feedback factor.

        He should never be left alone with an unguarded open microphone at his elbow.

        And if you see him on an aeroplane wearing a parachute, just check that you are not flying over any stadiums or stadia or public gatherings of any kind.

        LMofB is very resourceful !

        G

    • “, the mere fact that process engineers often try to impose an upper bound on feedback where it might lead to instability does not prove that climate feedbacks in the region shown in Fig. 1 as unstable are impossible.”

      No but, 4.5 billion years of stable operation has to lead you think that the feedback is more likely negative than positive. In this, as in all inquiries the null hypothesis must be that the feed back is 0.

      I am not a mathematician, but, it is intuitively obvious that, if the feedback in any system is positive, the system must be liable to excursions outside of its operating parameters. In the system of earth’s climate, we must believe that if the feedbacks are positive, the planet would have gone Venus at least once. There is of course no evidence that such a disaster ever happened. Ergo, the system cannot have net positive feed back. Indeed, the feedback is most likely net negative.

      • Mr Sobchack is, of course, right: positive feedback factors sufficiently close to unity must indeed expose the system to the risk of an unstable response. It is not that one cannot construct a circuit with, say, a feedback factor +0.5 that will never be stable. One can. However, one needs to have very good control of the componentry and of the operating conditions. Where there is doubt about either, and where stability is a requirement, process engineers will try to avoid positive feedback altogehter, and will certainly seek to limit it to 0.1, or 0.01 if at all possible.

        To anyone with a sufficiently open mind, the notion that in a climate not under the fingertip control of its designers, and subject to substantial endogenous as well as exogenous variability, feedback factors as very high as those imagined by official climatology are consistent with the observed stability is self-evidently questionable, to say the least.

        As it turns out, feedbacks are not in the zone of instability shown in the diagram. All will be revealed in the next part of this series.

      • To follow up on Monckton’s reply (below) “To anyone with a sufficiently open mind, the notion that in a climate not under the fingertip control of its designers, and subject to substantial endogenous as well as exogenous variability, feedback factors as very high as those imagined by official climatology are consistent with the observed stability is self-evidently questionable, to say the least.” \

        I”d like to extend upon his remarks to indicate that “endogenous and exogenous variability includes various and sundry asteroid impacts, the Deccan Traps, Snowball Earth, this list of largest volcanic eruptions (https://en.wikipedia.org/wiki/List_of_largest_volcanic_eruptions), multiple ice ages, etc… None of which were able to budge the Earths climate towards Venus or Mars’.

        Ergo, the climate system must be extremely stable.

      • Monckton of Brenchley said in part September 6, 2016 at 4:45 pm:

        …..”It is not that one cannot construct a circuit with, say, a feedback factor +0.5 that will never be stable. One can. However, one needs to have very good control of the componentry and of the operating conditions…..”

        I am FRANKLY unsure if he meant to say “stable” or “unstable” here. The second part of the sentence only makes sense if he meant to say unstable.

        But his “componentry” considerations are covered in engineering by our “Classical Sensitivity” as I discussed below with the circuit diagram. One need not hide shaking in the corner, sucking ones “Rules of Thumb” if one can do real engineering.

      • Mr Hutchins, who continues to be discourteous, has still not learned the wisdom and common sense of waiting up until I have deployed the full argument on temperature feedbacks before trying to criticise it. He has a very poor understanding and a still poorer method of conducting an argument. He is out of his depth and should really desist.

      • Monckton of Brenchley said in part: September 6, 2016 at 6:21 pm
        “……Mr Hutchins, who continues to be discourteous,…..

        Could Monckton perhaps have the courtesy to say if he meant to say “unstable” (which makes sense) instead of “stable” which he wrote (which is nonsense). I would like to suppose he misspoke.

      • “The stable region, where the feedback factor is either negative or at most 0.1 (and preferably little more than 0.01)”

        Maybe he was getting confused with resistor tolerance?

      • ulriclyons September 6, 2016 at 6:56 pm:
        ” Maybe he was getting confused with resistor tolerance?”

        Thanks for that.

        I think Monckton misspoke and meant to say you COULD use f=+0.5 but needed to do so with great care less such things as resistor tolerance, temperature drift., etc. eat your lunch on you. I think the “not”, the “cannot” and the “never” tripped him up. What could “not that one cannot construct a circuit with, say, a feedback factor +0.5 that will never be stable” possibly mean? Why not just say you tripped over your tongue? He avoided the invitation to clarify.

        Good engineering takes care of this, easily.

        Bernie

      • co2isnotevil September 6, 2016 at 1:00 pm below. Took the scales away from eyes. The entire analysis of climate as an amplifier is inapt. Amplifiers have external sources of energy. The climate system has no source of energy other than the sun.

      • So Walter; is the sun simply the source of energy as you suggest; with good cause ??

        Or is the sun the REAL input signal to the climate system, so the real source of energy may in fact be the charged battery that we call Earth (and its oceans).

        Planet earth stores an astronomical amount of energy in a variety of forms; including that garbage can form of energy that we call “HEAT” (noun).

        As a system at a Temperature higher than zero K, the system must be; according to our laws of physics, be losing energy in the form of thermal radiation, which depends pretty much only on the Temperature of the Earth or its components.

        But then there is that big orange ball up there that continues to pour energy in a nearly constant but variable amount down upon us at a annual mean rate of 1362 ish W/m^2, to recharge the battery.

        Which is pretty much what it does, since most of that solar energy simply goes right into deep ocean storage.

        So maybe Planet earth is the source of energy that powers the climate, and the sun is merely the battery charger, and is only loosely coupled to the climate, which I think is about what Dr. Leif Svalgaard seems to suggest. (I say seems, since I am not certain of that).

        G

      • “So maybe Planet earth is the source of energy that powers the climate”

        No, but it is the repository of energy that builds up when the instantaneous input power from the Sun exceeds the instantaneous emissions of the planet and is the source of extra power when the outgoing power exceeds the incoming power. This is basically the same thing for any black body and a massless black body will not emit anything as it has no stored energy to emit.

        The source is the stimulus which is energy from the Sun and the average temperature of the mass storing solar energy is proportional to the stored energy (i.e. 1 calorie, 1 cc H20, 1C) where this stored energy is a consequence of the balance between the incoming rate of energy absorbed by the mass (mostly ocean) and the emissions by it consequential to its temperature per the Stefan-Boltzmann Law.

        If anything is ‘powered’, its the weather, whose source of joules is primary the latent heat of evaporation brought up from the surface. Of course, weather is not climate and the source of the energy evaporating the water is still the Sun.

      • Monckton of Brenchley: It is not that one cannot construct a circuit with, say, a feedback factor +0.5 that will never be stable.

        Does that not make more sense if written this way? It is not that one cannot construct a circuit with, say, a feedback factor +0.5 that will be stable.

        or One can construct a circuit with, say, a feedback factor +0.5 that will be stable.

        Then: One can. However, one needs to have very good control of the componentry and of the operating conditions. etc

      • matthewrmarler –

        What he said made NO sense, as you say. Monckton tripped over the, not, cannot, never, and stable. But I guess if you have “Lord” before your name, it is discourteous to point out such flubs. At least I was, as well as “out of [my] depth” (see above). He accepts neither criticism nor lifelines.

        You fixed it. Wonder what invective you will be rewarded with!

      • Mr Hutchins, inadequate and desperately out of his depth here, is again reduced to sniveling about futile semantics. Don’t whine.

      • Monckton apparently fails to recognize that I have never said anything against his calculations as applied to climate. I spoke ONLY of electronics and his co-option and misappropriations of what he supposes practitioners know and do. He knows more about climate than I do, so I have said NOTING about climate except to say that he is likely RIGHT about overstated sensitivity.

        I do however know a LOT more about electronic circuitry than he does (as do many here), so I have noted several of the uninformed things about which he screws up and stubbornly still insists he does understand. He presumes to speak for a community (design engineers) of which he is not a member, gets the principles wrong, and then keeps digging deeper. He doesn’t choose to learn, or to accept help.

        (1) Here we have a good example and I challenge him. He said: “It is not that one cannot construct a circuit with, say, a feedback factor +0.5 that will never be stable.” Does he stick by this, as is, or does he admit that he should have said “unstable”.

        (2) Further: where specifically did he get the notion (like a reference or a name) that circuit design engineers who use op-amps restrict positive feedbacks to less than f=0.1?

        He has been asked these EASY TO ANSWER questions by me and by others, but only evades and insults.

  5. You forgot to mention several other problems with the feedback model used by climate science.
    1) Passive systems like the climate are unconditionally stable, where passive, per Bode means no internal sources of energy.
    2) Bode assumes input to output linearity and an input of forcing and output of temperature are certainly not linearly related to each other.
    3) The reference 255K is too far from the average surface temperature of 287K for the assumption of approximate linearity to be approximately true. (Yes, I know you think that the model is not modelling the surface temperature, but on that point you are incorrect, its actually not modelling anything of any relevance to the climate sensitivity).
    4) Hansen confused the feedback fraction with the otherwise useless attribute called the ‘feedback factor’
    5) The current model assumes an open loop gain of 1
    6) The lambda0 is essentially a constant that multiplies the output of the unit gain feedback loop whose only purpose is to adjust the units.
    7) The so called pre-feedback sensitivity is actually the post feedback sensitivity and this is what the empirical constant multiplying the 255K pre-feedback sensitivity is adjusting for.
    8) The closed loop gain (system gain per Roe) is the ratio of 2 gains. This only appears to work out because of the assumption of unit open loop gain and dividing the closed loop gain by 1 results in the closed loop gain. The real closed loop gain per Bode is the post feedback sensitivity or the ratio between the output and input of the model.

    • co2isnotevil – I’d like to add that it seems rather strange to calculate an equilibrium value of anything in a system that has never seen equilibrium conditions. i.e. If we could rapidly double the amount of CO2 in the atmosphere it would never come to equilibrium. There are too many other significant variables that affect the atmosphere/oceans and land over timescales of minutes to millennia for the climate to reach a new equilibrium. As a chemist I know that the dissociation constant of water is 10^-7. It’s been measured and confirmed six ways from Sunday, but even with that no two measurements are reliably identical but the range of experimental errors is always decimals smaller that the measured number.

      Kudo’s to Lord Monckton for trying, but this is like trying to find the balance point for a ball on the back of a galloping horse.

      • philohippous,
        It depends on what you mean by equilibrium. If you mean a constant temperature everywhere, obviously not, but if you mean a steady state time varying response to a periodic stimulus with a specific average, then the planet certainly is in equilibrium, or at least very close. In equation form, you can express the system as,

        Pi = Po + dE/dt

        Where Pi is the instantaneous input power from the Sun adjusted for albedo and Po is the instantaneous emissions of the planet, where their difference is either added to or subtracted from the energy stored by the planet, E. The steady state equilibrium condition is defined when the average dE/dt over multiples of the period of the stimulus (1 year) is zero and when this is measured, its well within the margin of error of being exactly zero.

        Here’s where it gets tricky. If you define an arbitrary amount of time, tau, such that all of E can be emitted at the rate Po in an amount of time quantified by tau, you can rewrite this as,

        Pi = E/tau + dE/dt

        Anyone familiar with the LTI describing an RC circuit will see immediately that tau is the time constant and when you measure the response to seasonal variability, it matches this model exactly and Po is of the same sinusoidal form as Pi in response to periodic stimuli. The relevant time constants extracted from the data are on the order of a year and not the decades to centuries required for the claims of a delayed response to prior emissions.

      • philohippous: I’d like to add that it seems rather strange to calculate an equilibrium value of anything in a system that has never seen equilibrium conditions. i.e. If we could rapidly double the amount of CO2 in the atmosphere it would never come to equilibrium.

        The language is loose, that is for sure. What they mean is the spatio-temporal average over a sufficient length of time. If the system is chaotic, but approximately stable, then it may be in an attractor (called a “strange” attractor), within which the spatiotemporal mean may be defined (with respect to the distribution within the attractor). This starts to get complicated, but if the input energy and output energy are approximately equal over long time spans (e.g. 60 – 200 years), and are never greatly unequal, then it’s possible. Then if the CO2 change makes a permanent change to the attractor, the spatio-temporal mean changes. There is no good reason to think that the calculated “equilibrium” is in fact the spatio-temporal mean of the new attractor, or an adequately approximation to it.

        The global mean temp, and the minima and maxima, look like they are bounded, so the appropriate mathematical description of the trajectory may be an attractor instead of an unbounded curve, or an equilibrium. Pictures and mathematics can be found in Modern Thermodynamcis by Kondepudi and Prigogine, who address chemical systems.

        I think we are just stuck for the time being with this inaccurate use of “equilibrium”.

    • I’m not sure that Bode assumed input-to-output linearity, since the output of the feedback part of the equation is rectangular-hyperbolic and thus very far from linear. His opening words in ch. 1 suggest that the components in the circuit were linear, but he rightly made no suggestion that the output would be linear, and therefore made no suggestion that the output was a linear function of the input.

      The current methods used by the models do indeed put the amplifier as an input outside the feedback loop. This is an error.

      There will be more detail on all of these matters in the next part of this gripping series.

      • “I’m not sure that Bode assumed input-to-output linearity, since the output of the feedback part of the equation is rectangular-hyperbolic and thus very far from linear.”

        Yes he did. The whole purpose of his analysis was to characterize the design of LINEAR amplifiers using vacuum tubes as the ACTIVE gain element. A linear amplifier has constant gain for all input until the amplifier starts to clip and then it goes into non linear operation. The concept of superposition is also very important to Bode’s analysis, such that if I1 and I2 are inputs and O1 and O2 are the respective outputs, if I1+I2 is applied as the input, the output will be O1+O2.

      • I think that there is still some confusion about what the input to the system is. The proper input of the model as mapped to the climate is forcing and its output is temperature (or changes of each, respectively). You seem to be considering the input to be equivalent to Bode’s β which increases from 0 to some current value. And of course, even the behavior of a linear amplifier would become non linear. Bode assumes that β and μ are constant. As constants, the resulting closed loop gain is also constant and superposition applies.

        The failure of the consensus feedback model is using Bode to model what its not actually modeling.

      • The output is a linear function of the input if the system is linear. The output is a non-linear function of the feedback gain if the negative closed loop feedback gain is near -1. Bode’s contribution is more concerned with the frequency response of a linear closed loop system.

        I think the term feedback confuses the issue since you are not considering transient sensitivity and really only want sensitivity to parameters. To make the conversation about feedback use the control system equation for the closed loop gain is G/(1+GH) where G is the gain after the summing node, and H is the feedback. The math works for DC or transient analysis using whichever math tools you are comfortable with.

        We may be talking past each other due to the differing languages of our professional disciplines. EEs do have a rich toolkit for doing this stuff when the problem is framed correctly.

      • It ought to be entirely plain from the form of the final transmission characteristic in the Bode equation that the output of an amplifier circuit in the presence of positive feedback is not linear but rectangular-hyperbolic.

      • “the output of an amplifier circuit in the presence of positive feedback is not linear but rectangular-hyperbolic”

        But the open loop gain of an audio amplifier is on the order of millions and far from the slightly larger than 1 characteristic of the climate system, moreover; an audio amplifier provides power gain and COE need not apply between the input and the output. What good would a 100 W amplifier be if you had to drive it with 100 W of input?

      • Back in the old days with vacuum tubes an open loop gain in the 20s would be enough to flatten the closed loop frequency response, make the amp more linear, and lower the output impedance.

      • “vacuum tubes an open loop gain in the 20s”
        Yes, even that much would be enough. Even so, most amplifiers were a few tubes in series. A 12AX7 has a μ of about 100, A couple of those in series driving an output amplifier tube with a μ of 20 would have an open loop gain of 100 * 100 * 20, or about 200K since feedback is generally from the ultimate output back to the input.

      • Throw in an output transformer so you can drive a pair of 6l6s in push pull and the nyquist chart becomes a mess. Mu is transconductance not voltage gain which depends also on the load of the stage.

      • “Mu is transconductance not voltage gain”

        Climate scientists have enough trouble understanding the simpler concept of gain, lets not confuse them further by introducing the concept of transconductance. But yes, Bode’s μ is not the same as transconductance and is the actual voltage gain which takes into account the output load. None the less, when optimally driven, loaded and bypassed, the voltage gain is about the same order of magnitude as the transconductance. For example, a voltage gain of 50-60 is not unreasonable for a tube with a transconductance of about 100.

      • Actually mu is transconducance times plate resistance. Blogging too early this am. It amounts to the maximum gain available into an infinite load. You can get there if you are willing to put up with large signal distortion and Miller effect limited bandwidth. (Enter tetrodes) An unbypassed cathode resistor is the simplest way to start putting in feedback.

      • Monckton of Brenchley said in part September 6, 2016 at 4:12 pm:

        “…..The current methods used by the models do indeed put the amplifier as an input outside the feedback loop. This is an error. ….”

        Do we actually agree? Let’s hope not !!!! Putting any amplifier (or other scalar) at the input to the loop multiplies or divides the final output in an obvious way, but baring saturation (etc.), does not affect loop gain. Not paying attention to this is a likely error, of course. (See for example, the discussion with David Thompson below)

        Still, my point about an arbitrary limit of positive feedback remains valid.

      • “It ought to be entirely plain from the form of the final transmission characteristic in the Bode equation that the output of an amplifier circuit in the presence of positive feedback is not linear but rectangular-hyperbolic.”

        co2 is right on this one. The quote shows elementary confusion. The dependence of gain on feedback factor is hyperbolic, but that is not relating output to input. The Bode analysis is for a linear amplifier. Output = gain * input. And that is stated in the head post:

        We’re arguing about the values of λ₀ and G. But whatever is assigned to them, the output ΔT depends linearly on ΔF₀.

      • “But whatever is assigned to them, the output ΔT depends linearly on ΔF₀.”

        Except that it does not. How do you get that ΔT/ΔF is linear when it depends on 1/T^3?

        For an ideal BB starting from absolute 0, the first W/m^2 of forcing will increase the surface temperature by nearly 65K for a ΔT/ΔF = 65K per W/m^2. The next W/m^2 will increase the temperature to 77K for a ΔT/ΔF = 12K per W/m^2. If ΔT depends linearly on ΔF, then the dependence would be constant for any F and it is not.

      • Almost all of practical engineering depends on a constant derivative over a small range of a non linear function.

      • co2:
        “How do you get that ΔT/ΔF is linear when it depends on 1/T^3?”

        Like any active electronic component, it is linear for small perturbations. 1/T^3 varies by about 1% over a 1° range; valve or transistor makers would think that pretty good.

        watcher:
        “take a look at this for a solution and correction”
        Different Bode.

      • “it is linear for small perturbations.”

        Yes, but the reference is 255K and the surface temperature is 287K, thus this is not a small perturbation. Moreover; when the IPCC asserts the assumption of approximate linearity, they are assuming a slope from the current state and passing through zero, rather than the slope of the SB relationship at the current state (current surface temperature).

      • “Are you sure that you have framed that question correctly?”

        Relative to the feedback model of the climate, absolutely. The point is that Bode’s feedback model provides power gain while the climate does not.

      • co2isnotevil: Relative to the feedback model of the climate, absolutely. The point is that Bode’s feedback model provides power gain while the climate does not.

        Oh I get it. The signal input would not be 100 W, but the power for the amplifier would be at least 100 W.

      • ” What good would a 100 W amplifier be if you had to drive it with 100 W of input?”
        You always have to drive it with more than 100 W of input. Maybe a small signal input, but more than 100W from the power supply. The amplifying device just modulates a large power stream from the PS. GHGs etc modulate a large power stream from the sun.

      • “maybe a small signal input, but more than 100W from the power supply”

        Exactly. The point being that the climate has no power supply and only a signal input, where this input signal is the power arriving from the Sun. Bode’s analysis assumes that the ‘amplifier’ element has an implicit power supply to provide joules of output beyond that which is applied as the stimulus (the signal).

      • “the climate has no power supply”
        No, again, the power supply is the 240 or so W/m2 of heat that flows through the system, originally from the sun. The feedbacks here are the ways in which water vapor etc modulate this to the extent of maybe a few W/m2.

      • “the power supply is the 240 or so W/m2 of heat that flows through the system”

        No. The 240 W/m^2 or so of input from the Sun is the signal input or stimulus driving the system. This is not equivalent, in any way shape or form, to the implicit infinite power supply of Bode’s active gain elements.

        The key point you seem to be missing is that Bode’s analysis removes the requirement for COE between the input to the feedback network (the 240 W/m^2 from the Sun) and its output (the 385 W/m^2 net emissions from a surface at 287K). This is the consequence of assuming a source of power OTHER THAN THE STIMULUS supplies all of the required output power. The climate has no source of energy except the stimulus and this is the important point of distinction.

      • co2isnotevil: The point being that the climate has no power supply and only a signal input, where this input signal is the power arriving from the Sun

        The Earth has no *additional* power supply, unlike a common “amplifier”.

    • How do they get an active gain block from the climate parameters? I had always assumed that the feedback in Amplifier chain to be negative or dampened but it never struck me to ask where the positive gain comes from? Seems very unnatural to me. The sun? Gaia? Digikey? Any way to explain it to an EE?

      • “How do they get an active gain block from the climate parameters?”

        By an arithmetic mistake consequential to Hansen’s confusion between the feedback fraction and feedback factor that provides the illusion of non unit open loop gain. The λ0 term, which is claimed to be equivalent to Bode’s dimensionless μ, is undone along the feedback path by its reciprocal being buried in the ‘temperature feedback’ coefficients. The result is an effective unit open loop gain, but they fail to acknowledge this and insist that λ0 is a legitimate open loop gain when all it really does is convert units from W/m^2 to degrees K.

      • Thanks. So they are saying that somehow the radiation from the sun gets amplified by water vapor and CO2 in a positive feedback. This is pretty much impossible as those are passive elements. This would be like shooting microwaves at a potato, then using the heat from the potato to generate larger amplitude microwaves than the potato absorbed. I must be wrong because that can’t possibly be what they are saying, right?

      • “I must be wrong because that can’t possibly be what they are saying, right?”

        This is exactly what they are saying and yes, its absurd beyond belief. The only reason it seems plausible to some is because the Bode model implicitly disconnects the input and output from the requirements of COE by assuming an external power supply that can add to the output in excess of what is provided as input.

        A sensitivity of 0.8C per W/m^2 almost sounds plausible until you express it as 4.3 W/m^2 of incremental surface emissions per W/m^2 of forcing.

      • “Does Bode really assume that input to output are linear, or is does it merely require that it be monotonic ?”

        Yes. This is the basic property of a linear amplifier. If 1mv goes in and 1V comes out, when 10mv goes in, 10V comes out. It’s this property of superposition that Bode’s amplifier analysis depends on.

      • The output of the Bode feedback loop is plainly rectangular-hyperbolic and not linear. Bode does not say the inputs and outputs must be linearly related: he says that the elements of the circuit must be linear, which is a different and lesser point.

        The high feedback-induced sensitivities in the climate models arise precisely because the models assume – wrongly, as it will turn out – that the feedback factors are sufficiently close to unity to engender strongly non-linear climate sensitivities.

      • “Bode does not say the inputs and outputs must be linearly related: he says that the elements of the circuit must be linear, which is a different and lesser point.”

        You are incorrect about this. In general, vacuum tubes are linear devices, that is, the gain is constant independent of the input amplitude, at least up to the point where the amplifier starts distorting. In fact distortion is a tangible manifestation of non linearity. The whole point of his book was to provide mathematical tools for the design and analysis of linear amplifiers.

        In the climate model, the input is forcing, not feedback as you seem to think, and if the relationship between the input forcing and the output temperature is not linear, which if course it’s not, Bode’s analysis does not apply, nor would it apply for the amount of feedback as input and the sensitivity as the output even if that was what was being modeled.

        The applied model is one of how temperature is affected by forcing. Independent of what you think that temperature is, the delta T is supposed to reflect the surface delta T. Any attempt to cast this into a different model where the proportion of feedback is input and sensitivity is the output is absolutely incorrect and has no relevance to what Bode is modelling. There is the illusion that this works, but only because of the confusion between the feedback fraction and the feedback factor and the implicit assumption of unit open loop gain. In this case, two wrongs don’t make a right even if it seems to work.

        When you divide the closed loop gain by the open loop gain and the open loop gain is assumed to be 1, the result is the closed loop gain. If not for this, Schlesinger’s formulation of the ‘system gain’ would not work out to be the same as the closed loop gain.

  6. Lord Monckton, my head hurts!
    Can you summarise this uber-detailed series into a single, easy-to-understand-for-the-bloke-on-the-Clapham-Omnibus real-world conclusion please?

    • Ditto. You are of course talking mostly to technical people but it is the non technical who vote or decide policy. Before submitting comments to our newspaper I run them past my wife. If she can understand so can the average reader.

      Max

    • Likewise. And perhaps a table of their computations vs yours, step by step. So we can see where they start to diverge, and by how much.

      R

      • They don’t compute it as here. They esrimate it from multi century GCM runs at 2x CO2. Since the CMIP5 models run significantly hot compared to balloon and satellite observation beginning in 1979 — despite having been tuned to hindcast 2005 back to 1975– it follows that the model estimates are too high. AR5 explicitly did not give a central estimate because of the large discrepancy (~2x) between low observational estimates and model estimates.

      • @ ristvan, September 6, 2016 at 11:15 am – below…

        Given the absolutely central position of climate sensitivity to AGW theory surely their refusal to give a central estimate is a complete failure of their methodology? If after a quarter of a century, untold man hours and literally hundreds of millions of dollars the IPCC ‘can’t agree’ a central estimate – instead only agreeing a range that is so wide as to be meaningless, then to me that tells me only 2 possible reasons:

        1. They genuinely can’t agree – in which case by definition of not agreeing then the ‘settled science’ mantra HAS to be put on hold, or
        2. They know sensitivity is low, too low to impact the climate in the way they’ve been claiming all these years, so obviously they refuse to say. This wouldn’t so much put settled science on hold so much as settle it in an entirely unwanted direction, thus throwing it all in the bin.

        If I was a betting man I know which position my £1 would be going on.

      • Mr Istvan is quite right that the models do not use a representation of the climate anything like as simple as equation (1) here. But equation (1) was quite carefully calibrated against the published official estimates of forcing and feedbacks (the inputs to the equation), and its outputs (the climate sensitivity intervals) matched the official published outputs of the CMIP3 and CMIP5 model ensembles very, very closely.

        That successful calibration allows us to examine the principal forcing and feedback processes using the simple equation (1), and making modifications both to the equation itself and to the input data when errors are identified. That allows us to see what the models would produce if they were likewise corrected.

      • Monckton of Brenchley

        You are AWESOME !

        IF we sumarize : from climate model outputs only, you tell us that climate sensitivity is very small.
        So what you tell us is that the climate sensitvity of climate models is very small (view that none of these numbers is used in a climate model).
        So climate models predict an large warming in the future whereas they have a very small climate sensitivity….

        It’s completeley non sense ! And very fun.

      • Toncul, who has adopted a generally arrogant and spectacularly ill informed and prejudiced stance, appears incapable of understanding that the errors already identified in the determination of climate sensitivity by the official method, and those yet to come, demonstrate that climate sensitivity is greatly overstated in the models.

      • How can you show that climate sensitivity is lower than that of climate models, from climate models outputs only ?

        Let’s take an example…
        If a climate model gives a 3 K warming. You cannot use outputs of that climate model to say that in fact, it gives a 1.5 K warming…

        This is completely nonsense…

        I am not saying that climate models are right, I am just saying that you’re talking nonsense…

      • toncul continues to be pathetically out of his depth. The three parts of this series have already established that the models are overstating the central estimate of climate sensitivity by almost double. The methods by which this conclusion was reached are described in some detail. Address those methods specifically and say what is wrong with them. Otherwise, you are accepting by implication that my conclusions are correct.

    • IMO anyone can understand that on earth feedbacks to various climate “forcings” must be net negative, otherwise the world would have long ago run away either too hot or cold.

      The closest it has come to that was during the Cryogenian Period, 720 to 635 million years ago, of the Neoproterozoic Era, when our planet experienced “Snowball” or “Slushball Earth” glaciations extending down to low latitudes. The Huronian Glaciation, 2400 to 2100 million years ago during the Siderian (Iron) and Rhyacian Periods of the Paleoproterozoic Era, was similar.

      The sun was 6.5% weaker during the Cryogenian and about 22% during the Siderian.

      • And hotter than normal intervals of our present Phanerozoic Era, such as the end-Permian, mid-Cretaceous and Paleocene-Eocene Thermal Maximum, were brief because the self-regulating climate system of Earth promptly adjusted.

      • Don’t confuse a primary effect with its first derivative. The climate system is obviously damped. The feedback issue is whether that damping is greater (negative feedback) or less (positive feedback) with increased CO2.

      • Off topic, but in case anyone be interested, here is current chronological terminology for the longest stretches of geologic time, based upon the kind of living things detectable during them:

        Hadean Eon, 4.6 to 4.0 billion years ago (Ga): Simple protocells (mainly RNA-based replication and metabolism).
        Archean Eon: 4.0 to 2.5 Ga (four Eras): Bacteria and Archaea (Prokaryotes using the modern DNA-RNA-protein system).
        Proterozoic Eon, 2.5 Ga to 541 million years ago (Ma) (three Eras): Eukaryotes (possibly earlier) and the first multi-cellular organisms.
        Phanerozoic Eon, 541 Ma to Present (three Eras): Macroscopic organisms with hard body parts.

        “Phanerozoic” means “visible life”, but now we know that macroscopic organisms, up to two meters long, evolved during or before the Ediacaran Period (635-541 Ma, which followed the Cryogenian), last of the Neoproterozoic Era of the Proterozoic Eon. Molecular “clocks” date the origin of animals (Metazoa) as far back as 760 Ma, but the earliest fossil sponge (and animal) actually found in rocks so far is “only” 600 million years old. It was about a cubic millimeter in volume:

        http://www.sciencemag.org/news/2015/03/oldest-known-sponge-pushes-back-date-key-split-animal-evolution

        Unlike Fungi, the Kingdom Metazoa includes only multicellular organisms. It excludes the unicellular relatives of animals (such as the sperm-like choanoflagellates, which form the feeding region of sponges), while Kingdom Fungi includes single-celled organisms, such as yeast. Both kingdoms contain heterotrophic (unlike photosynthetic or other autotrophs) eukaryotes of the unranked clade Opisthokonta (whose cells possess a singular posterior flagellum), but Metazoa are all multicellular and more capable of movement.

      • Ristvan,

        IMO the issue is whether the net feedback effects from doubling CO2 are negative or positive. In any case, they are liable to be small, not potentially causing a greater than tripling of warming effect from the nominal 1.2 degrees C to 4.5 degrees, as imagined by the IPCC imps.

        The present weight of evidence IMO suggests a net negative effect, such that a doubling would produce warming at equilibrium less than the nominal 1.2 degrees C in the absence of climatic feedbacks.

      • Gabro, a number of different approaches to observational ecs all suggest ~1.65. See following main comment for citations. Clouds slight negative, wvf positive at ~half the IPCC value, all other smaller feedbacks netting out to about zero. The end result is not less than 1.2, it is ~1.65 based on observations to date. Both the Spencer and Braswell and the revised Lindzen and Choi papers purporting to estimate ECS <1.2 from observations are deeply flawed via their temporal lag assumptions. Both were refuted by subsequent decent quality papers.

      • I already read your comments below and in other comments. While well taken, even a cursory review of geologic history shows that ECS must be low, although your estimate can’t be ruled out for the current state of our planet.

        Correct me if wrong, but IMO even when corrected, Lindzen and Choi can’t be considered falsified. I might be out of date on that.

        But in functional climatic effect, the difference between ECS in the range of 1.0 to 1.5 degrees C and of 1.5 to 2.0 degrees C would be slight. Or for that matter, even of 0.5 to 1.0 degrees C.

        I don’t think it can be known to two decimals, assuming such a thing even has a physical reality.

      • Mr Dayton is not quite right. If there is sufficient variability in componentry or in ambient operating conditions, a circuit that might otherwise be capable of operating stably at positive feedback factors of order +0.5 may not in practice remain stable: hence the process engineers’ rule of thumb that in such circuits, where they do not have sufficient control over components or over operating conditions, they will try to avoid positive feedback altogether, and – if there must be any – will limit it to 0.01 (or, at most, 0.1).

        All will be revealed in the next part of this series.

      • Readers, please note how Gabro speaks as though anything postulated/presented by anyone that contributes to “Evolution” theory, is an infallible God, by default.

        “Molecular “clocks” date the origin of animals (Metazoa) as far back as 760 Ma, but the earliest fossil sponge (and animal) actually found in rocks so far is “only” 600 million years old.”

        Note the total absence of any skepticism at all, any expression that any of this stuff he speaks of could possibly be erroneous (or fraudulent). It’s the same settled/consensus science tone of complete certainty as we can hear in the “Climate Change” field.

        The whole field is utterly useless in terms of any scientific or technological advancement of any kind as far as I can determine, yet if you read the blab typically produced from/about it, you’d think virtually all modern science and technology is dependent on/derivative of it (and that all children simply must be indoctrinated to treat it as Gospel . . so to speak ; )

        That it is treated so, ought to be setting off alarms in the reader’s mind, it seems to me, especially now that we can (I believe) see how a scientific theory can be used to advance social/political/economic agendas.

        (Gaybro will now give a confession of his absolute faith, I betcha ; )

      • Tom Dayton
        September 6, 2016 at 4:40 pm

        Former GISS director, arch-alarmist Hansen disagrees with you. He says that we’re on the Venus Express and that the oceans will boil.

        If ECS indeed be the 4.5 degrees C per doubling imagined by IPCC, then the warming would run away. And many alarmists claim that estimate is way too low.

        From the present CO2 concentration around 400 ppm to 800 ppm would imply going from about 14.5 degrees C GASTA now to 19 degrees C. This will happen in the 22nd century, if IPCC is to be believed, since they warn that we’ll hit 600 ppm before the end of this century. Another doubling to 1600 ppm implies a global average of 23.5 degrees C.

        By comparison, during the hot Cretaceous Period, mean atmospheric CO2 content was around 1700 ppm, yet average surface temperature over the whole period was about 18 °C. In the hottest middle part of that period, Earth was ice-free and the tropical oceans were hot tub temperature. Crocodilians bathed in the balmy Arctic Ocean.

        But according to IPCC, the world could get five or six degrees hotter than the average for the period, with just two doublings.

    • I’m not at all sure he will do of his own: is he, after all, the very author of all what is written here?

      I have a scientific education (above a degree in computer science) and therefore know what a person having no real scientific education is maximally able to formulate.

      • Bindi don should know that I am indeed the author of this series. And he should not assume that I have had no scientific education. Indeed, it should be self-evident from these posting’s that I have had a considerable education in the relevant mathematics and science. But what matters is the quality of the argument, not the slender of the qualifications.

  7. The post sensitivity calculation of ~1.66 is very well supported elsewhere. Lewis and Curry 2014 used only IPCC AR5 ‘official’ values to estimate 1.64 ( median) using the observational EBM approach. They also provided confidence interval ranges around the central value, and showed the value was not sensitive to choice of EBM time frames. See their table 1 at Climate Etc. Guy Callender estimated 1.67 way back in 1938 in his paper to the Royal Met. Soc. A simple regression of log CO2 ppm versus HadCrut T gives 1.71 with an r^2 of 0.9. Both approaches are discussed in essay Sensitive Uncertainty. Lewis 2013 used Baysian objective priors to estimate 1.6. So several different methods all derive approximately the same value. That is confidence inspiring.

    Physically, this is simply explainable by Eschenbach’s demonstration using Ceres that cloud feedback is net negative rather than significantly positive as in CMIP5 climate models, and by Lindzen’ BAMS 2001 adaptive infrared iris paper plus Eschenbach’s closely related Tstorm regulation hypothesis, both of which mean the water vapor feedback is also overstated in climate models. Underlying physical observational reasons explain the ~1.65 versus 3.2- 3.4 model ECS discrepancy. That the models are running hot this century lends further credance to the notion that model ECS are off by a factor of ~2.

    • In fact, observationally, any kind of condensation and precipitation at altitude is a cooling effect. The higher the condensation occurs, the greater the cooling effect, and proportionately less “downwelling” energy makes it back to near the surface. Observing virga, the process of condensation into the cloud, which releases energy, and the process of sublimation or evaporation on the way toward the ground taking up energy equal to that released in the original condensation, and the implicit trip back to the clouds reflects an energy conveyor carrying heat away from the ground and being released at an altitude where it will mostly radiate away. The “feedback” is necessarily negative.

      The cloud shields the ground below so there is certainly no warming going on at the surface. The upper surface of the cloud is brilliantly reflective, meaning the albedo is locally about as high as it can get. The energy of vaporization is released at an altitude where only a fraction will have any additional effect near the surface, and the revaporization of virga on the way to the ground means that additional energy of vaporization is being drawn from the environment directly below the clouds. In fact, the virga only becomes rain or snow at the ground level once the air below the clouds has become cool enough that the virga no longer can return to a vapor state before reaching the ground.

    • Mr Istvan makes the very nice point that a coherence of results arrived at by very different methods indicates that the central estimate of climate sensitivity is about half of the models’ 3.2 K central estimate. In fact, as I shall show in later parts of this series, climate sensitivity may be even lower than 1.6 K per CO2 doubling: for I have not yet factored in the lower water-vapor feedback that observations of water vapor content seem to require; and there are one or two other important corrections that have yet to be made.

    • Very little opposition on this submission, and only from those who can’t muster a coherent disputation. Lord Monckton has rendered quite a clear frontal assault on the flimsy face of IPCC formulae. Ristvan likewise casts light on the powerful and persistent efforts of the IPCC to ignore any possibility of negative feedbacks, regardless of 4 billion years of evidence that they, in fact, must exist. They (IPCC) have proven through their efforts?, that the whole damn mess is politics of the worst kin!
      My thanks to Lord Monckton and also to Ristvan!

  8. My issue with this series is that Christopher Monkton clearly thinks he is the cleverest person in the room, in this case the room being the entire internet. He seems impervious to any form of challenge, criticism or correction.

    Whether or not Lord Monkton is correct is beyond my levels of analysis. However his work would be more convincing if he was prepared to have his work reviewed formally or informally by other skilled people. This could be done by a small group in private or here in public. Such a review would need Lord Monkton to actively engage with difficult comments, not just attempt to dismiss the people and comments he doesn’t like.

    • See my comment about incorrectly understood/labeled instability in part one. It Is happening here in public, and everyone can understand and judge for themselves. I used no math, just a commonly experienced Sound amplification system example, to explain the mislabeling. Lord Monckton does not have to agree, but it is what it is.
      His derivation here in part 3 I find no fault with. The math is simple, the constants mainstream. I provided a comment above giving two separate basis for finding it about ‘right’: other methods reaching ~the same result, and physical underlying reasons for why the model derived versions of ECS must be too high.

    • Andy – Ah the logical fallacy of “argument by authority.”
      The insults are superfluous, and say more about you than his Lordship.

      Nice try, but it turns out that Lord Monkton’s calculations do agree with a peer reviewed paper – Lewis and Curry 2014 as pointed out by Ristvan.

    • “My issue with this series is that Christopher Monkton clearly thinks he is the cleverest person in the room, in this case the room being the entire internet. He seems impervious to any form of challenge, criticism or correction.

      Whether or not Lord Monkton is correct is beyond my levels of analysis.”

      If you don’t understand the argument sufficiently, then you can’t legitimately claim Lord Monckton of Brenchley, is impervious to any form of challenge, criticism, or correction, because you don’t know if those challenges, criticisms, or corrections are legitimate or accurate. Instead of being impervious to critcism, it may just be that he is correct.

    • I definitely agree here to what AndyL wrote.

      Peer Monckton of Brenchley should present his views ( or eventually, expressed in french, “celles des petites mains de Sa Seigneurie”, n’est-ce pas) to a scientifically acknowledged peer-review instance, like have done all scientists he feels free to criticize, sometimes in a reallyy disingenuous manner – but only on blogs, of course!

      Start being courageous, Mr Monckton!

    • “Whether or not Lord Monkton is correct is beyond my levels of analysis. However his work would be more convincing if he was prepared to have his work reviewed formally or informally by other skilled people. This could be done by a small group in private or here in public. …..”

      He has (along with Soon)
      Here is a peer-review of it……

      http://sci-hub.bz/10.1007/s11434-015-0806-z

      “In summary, M15 fail to demonstrate that IPCC estimates
      of climate sensitivity are overstated. Their alternative
      parameterization of a commonly used simple climate
      model performs poorly, with a bias 350 % larger and
      RMSE 150 % larger than CMIP5 median during
      2000–2010. Their low estimates of future warming are due
      to assumptions developed using a logically flawed justifi-
      cation narrative rather than physical analysis. The key
      conclusions are directly contradicted by observations and
      cannot be considered credible.”

      • Nature herself demonstrates that IPCC estimates are so preposterously overstated that the error must be intentional.

      • “so preposterously overstated that the error must be intentional.”

        No.

        “….. directly contradicted by observations ”

        And I said further down …..

        ” …. any intimation that there is corruption/hoaxing I take to be a comment on the accuser and no other.

      • From the peer review:

        “Their low estimates of future warming are due
        to assumptions developed using a logically flawed justifi-
        cation narrative rather than physical analysis. The key
        conclusions are directly contradicted by observations and
        cannot be considered credible.”

        Yeah, right. So we should believe that observations show that the IPCC climate models have it right(are not too warm).

        The funniest part is at the end: Conflict of interest: “The authors declare that they have no conflict of interest.”

        This one made me laugh out loud(sorry but if you know one of the authors of this peer review, Dana Nuccitelli you will forgive me)

        https://www.theguardian.com/profile/dana-nuccitelli

      • Our reviewed paper in reply to the rather pathetic attempt to challenge our results is available at the website is the Chinese Academy of Sciences. In fact, our model comfortably outperforms the official model ensembles, and is likely to continue to do so.

      • Monckton of Brenchley: “Our reviewed paper in reply to the rather pathetic attempt to challenge our results is available at the website is the Chinese Academy of Sciences. In fact, our model comfortably outperforms the official model ensembles, and is likely to continue to do so.”

        In degrees Celsius, what is the temperature change you calculate between the decades 1880-1889 and 2006-2015?

        In degrees Celsius, what is the temperature change in Berkeley Earth, HadCRUT4 or GISTemp between the decades 1880-1889 and 2006-2015?

        In degrees Celsius, what is the temperature change in CMIP5 between the decades 1880-1889 and 2006-2015?

      • Monckton of Brenchley: “The idle MieScatter can read our paper for himself and run our model.”

        I did and I agree with the comment that says your paper is rubbish. Maybe I did the calculations wrong though:

        In degrees Celsius, what is the temperature change you calculate between the decades 1880-1889 and 2006-2015?

        In degrees Celsius, what is the temperature change in Berkeley Earth, HadCRUT4 or GISTemp between the decades 1880-1889 and 2006-2015?

        In degrees Celsius, what is the temperature change in CMIP5 between the decades 1880-1889 and 2006-2015?

        Refusing details is a common tactic of dodgy salesmen and fraudsters. I hope you won’t use it.

    • The Lord will always get criticised for trying to denounce the Church of AGW , I don’t pretend to understand the math but have more faith in his computations than that of the likes of the IPCC .
      Mr M is willing to admit errors the other side never will .
      If he embellishes here and there so what the other side outright lie most if not all the time , after all don’t 97% of scientists tell us the oceans are becoming more acidic .

      • Mof B, I have been trying to help your credibility. If you insist that I go into nonsense opposition, I sure will. With the same precision and footnotes as before supporting you up to (with qualifications) your post 3 of this series. I follow facts and science where ever it leads, not where I want it to lead. Your ECS ~1.65 is credible, since derivable several independent ways. Anything much less is not. And I stand ready to point out possible logic/data flaws if you try to make an argument for much less in future posts. Been there, done that, before. So you might want to pre-prep if that is where you are headed. I already have, in case you venture such nonsnese as before. Highest regards.

    • In reply to AndyL, I do apologize if I have given a know-it-all impression. That was not the intention. But I am having to deal with some quite fierce and often very impolitely expressed criticisms many of which are not really meritorious, so I have occasionally been blunt in my replies to those who have been blunt with me.

      Before this series is completed here, the principal results will have been presented in front of a high-level audience of professors and learned doctors of science at the London climate conference. I am already quietly recruiting a group of suitably-qualified scientific experts to assist me in preparing a paper for peer review and publication in a leading journal.

      As for Mr Istvan’s comment about my having incorrectly understood feedback-induced instability, I have had three peer-reviewed papers published on that question. The next part of this series, which may not be ready in the next few days because I shall be busy at the London conference, is going to deal with the instability point in some detail, and it will become apparent that the instinct of those electronic engineers who have advised me that feedbacks as large as those that climatology imagines are at best highly improbable have been right all along. Watch this space.

      • I would love to be on lord Monckton’s team but I have a problem with the concept of a “Sensitivity Constant” measured in terms of Kelvin/doubling of CO2. The sensitivity constant is +4.4% [CO2]/Kelvin.

      • Thanks Lord Monkton for the reply. I’m pleased you are planning to get this material reviewed and published.

        I hope that when you do get round to the post on feedback you actively engage with the points raised here by those with expertise from different fields. As you have said in earlier posts, your series is fundamentally about the maths so it should be possible to have an in-depth debate.

        To some of us watching from the sidelines, it seems that both sides (you included) are ratcheting up the invective, which doesn’t really help the debate. There have been multiple comments where someone has asked about something you have written, and you respond by describing them as “unscientific” for not waiting for a future post. This seems unnecessary.

      • I should make it quite plain that I shall not be taking seriously any future comments from those who have attempted to take me to task for points about feedback analysis that I have not yet met, or for an argument about feedback that I have not yet presented.

        There are certain minimum intellectual standards in scientific discourse, and attacking someone – often in arrogant and sneering tones – for an argument he has not yet presented and concluded is monstrously anti-scientific, and marks out its perpetrators as laden with prejudice. I do not take such people seriously.

        When, and only when, I have presented the argument about feedback, it will be possible for those who have not thus far rushed in ignorantly or even malevolently to take their turn and make scientific criticisms of that argument. To the bloviators, I say that they will continue to go unanswered.

      • Lord Monkton
        Elsewhere you accuse me of being “whiningly repetitive” and “non-specific”. I may be repetitive but my concerns are very specific.

        Your comment above is the worst possible pre-emptive ad-hominen attack. You say in advance that you will ignore criticism from people you consider have not been sufficiently polite or have not followed your preferred rules of engagement, in other words purely on the identity of the person making the criticism.

        This is not only bad in itself, but by making this commitment in advance you are actively discouraging criticism

        What happened to the person who argued so superbly against all forms of logical fallacy?

      • In response to AndyL, I am a busy man and have no patience with time-wasters who want to attack an argument I have not yet completed before I have completed it. I am, therefore, discounting anything they have said so far and anything they may say in future, because they have displayed discourtesy as well as an anti-scientific, aprioristic prejudice.

        And he should learn a little about the logical fallacies. To state that, in general, bloviators who presume to attack an argument before it has been completed are anti-scientific and prejudiced is not to perpetrate tha ad-hominem subspecies of the argumentum ad ignorationem elenchi.

  9. Monckton said at the top:

    “Fig. 1 shows a stable, an unstable and a climate-unphysical region. The stable region, where the feedback factor is either negative or at most 0.1 (and preferably little more than 0.01), reflects the fact that process engineers designing electronic circuits designed to perform stably even where the reliability of componentry and the stability of ambient operating conditions cannot be guaranteed often use a rule-of-thumb maximum design value for feedbacks, since any value above the maximum may lead to unwanted instability.”

    This was WRONG the first time he said it, it remains WRONG, and he has not established the origin for his arbitrary limit of 0.1. (He alluded to a standard EE text which he has not produced). Nor has he identified his expert “process engineer” with 4 PhD’s! Nor should he PRESUME to speak for a community of EE circuit designers while radically misstating their art.

    In fact, EEs are familiar with the “reliability of componentry” problem (as he calls it) as the “Classic Sensitivity” which I mentioned in a comment to Part 1. This relates to a RATIO of fractional changes (middle term below) rather than relying on just slope (derivative).

    The sensitivity of G=1/(1-f) is thus S=f/(1-f) so in my circuits where f=2/3, the gain is 3 and sensitivity is 2. Here is another verifying example I have built (will be in my upcoming AN-430 application note).

    Here we have a nominal gain of -2 (switch S0) amplified to -6 by the feedback of +2/3, switch S1, (much greater than +0.1). Experimentally we get -1.97 and -6.16. This is similar to previous circuits that demonstrated the feedback amplification. Here I have added a switch (S2) to add 2% to the 200k to test sensitivity. Note that the amplified gain changes by 4% since the sensitivity is 2. It has been on the bench for two days – stable.

    This is really easy stuff, of course. I only claim this is EE stuff.

    • I completely agree with you about Monckton being just wrong on the Bode stability point. His Bode chart is mislabeled. In part one comments, I gave the familiar sound system ‘screetch’ example for those here who are not EE’s– which includes myself. Showed using actual outdoor rock concert data that f=0.6 has been measured, yet the concerts go on fine without feedback ‘screetch’. Your simple circuit with f=2/3~0.67 conclusively does the same.
      Also, if you plug likely observational inferred f for clouds (~0) and WVF (~0.25-0.3) into either Bode straight up or a simplified version of his ‘irreducible simple equation’, using the generally accepted ~1.2C for CO 2 doubling absent feedbacks rather than his string of uncertain constants within ranges, you produce sensitivities in the range 1.6-1.75. The IPCC AR4 and AR5 values for f are clouds 0.15 and WVF 0.5 (all other f sum to ~0 per AR5) giving ECS=3.0. Posted that exercise in a comment to his guest post here on it at the time. Also did a much longer stand alone guest post on the mathematical simplification plus the likely f derivations and resulting calculated sensitivity at the time over at Judiths.

      • No, Ristvan, as I have shown you before you are incorrect, the feedback results in reverberation because of the long time delays for the sound to travel from the speaker to the microphone , which in music tends to subjectively sound good, but it’s a distortion nevertheless. This ringing however is not what I would call stable. Monkton is right here, if you want stable operation without overshoot then you want to avoid positive feedback.

        What Lord Monkton, or rather the IPCC actually does miss is that this is not a perfectly resistive circuit such as Mr Hutchins above but rather the feedbacks have delays from output to input – there are reactive elements in the feedback loops. The reason we can’t use positive feedback in process engineering is that it causes overshoot and ringing (reverberation) and the AC characteristic is non linear, at DC analogous to the climate equation the circuit appears ok, because there are no assumed delays in feedbacks. Monckton is correct in asserting that less than +0.1 loop gains the overshoot will be minimal and the result will be sufficiently stable that we would not notice the overshoot.

        Lord M, you should recognise this though, the Amplifiers DC characteristic is perfectly predictable at any feedback less than unity, but the circuit will neverless ring when a signal (say an impulse) is applied to it. It is not folowing that DC characteristic at that point. This brings me back to my point that you cannot predict climate by steady state scalar analysis. The dynamic AC behaviour would dominate causing oveeshoot and reverberation, an effect we just DONT SEE, hence positive feedback must be LOW

        The problem I have is that there are high levels of both negative and positive feedback with delays, the net being the difference between them, but in electronics we know that at some frequenxies the negative and positive feedbacks will add. You can’t assess a circuit based on the Nett feedback, in the real world it doesn’t work like that.

      • Bobl –

        You are using the term “reverberation” wrong. Reverberation, in the sense of acoustics, (sum of echoes) is passive, linear, and stable. It usually is an amplitude and a phase “distortion”, but not a non-linear distortion. No new frequencies are created. It is not the result of feedback in any way.

        Artificial reverberators are preferably FIR. Originally, feedback (from delays) was used as a matter or economy but added too much color to the spectrum. Plenty of echo density but it did not sound natural.

        What you are apparently talking about is classic PA feedback. It is due to sound from a loudspeaker arriving back at a microphone, but it is “caused” by a room resonance favoring a particular frequency. The pitch of the squeal does not depend on the distance, microphone to speaker. Delay does not matter – you can have different delays with the same stability-upsetting amplitude and phase, of course. The amplifier does not know. I suspect you know this.

        The classic 1/(1-f) positive feedback discussed here, taken as a discrete time case, is a pole at z=f. A step is amplified to 1/(1-f), which it reaches asymptotically, but does not overshoot this value. Other frequencies (as represented by a burst of a sine wave perhaps) may, upon arrival, “overshoot” its own steady-state asymptotic level (determined by the pole, the filter) but not the 1/(1-f) limit.

        Do we agree, or am I missing something?

      • ” The pitch of the squeal does not depend on the distance, microphone to speaker. Delay does not matter”

        Is that really true? The oscillation happens when the loop gain is real, which means a total 0°,360°,720° or whatever phase shift. And the phase shift going from speaker to mic is distance/wavelength, so I think distance should affect the oscillation frequency.

      • Poles in the right half plane cause oscillation. Delay causes them to rotate around the origin as the frequency goes up. Being conjugate pairs they rotate in opposite directions, both bad.

      • Nick –

        Well – as you suggest, the phase could be any multiple of 360. But more to the point you need a gain, and all frequencies in the acoustic path do not come up level looking for a perfect phase – there are peaks and nulls. The frequency response (amplitude and phase) is very complicated. Turning up the gain of the PA system lifts the profile, and the first guy that gets above a threshold with insufficient phase margin initiates oscillation.

        David –

        I was concerned about the term overshoot. This I associate with complex conjugate poles (at least, a pair) and not a single real pole, and certainly not a system with NO poles at all (my op-amp circuits). It is just a change of gain. However, if you have a delay, a z^-1 in the loop, you can get a real pole at z=f. For positive feedback, this has its max at DC. IF you are considering “overshoot” to be anything above unity, then a positive feedback has an overshoot. I would need to see something greater than the 1/(1-f) we expect. That is, an “output” exceeding the DC steady-state.

        Further, if we are talking about climate (and I’m not), how would you get complex conjugate poles. You need something flowing like an inductive current (V = L di/dt) or an active element.

        I have to think about theses things more and/or explain them better. I could be wrong.

        Bernie

      • Bernie: Discete time systems are a whole different breed of cat, like the black and white striped ones in the back yard. Kinda like doing a naive integration in a spreadsheet.

        Look up Laplace transform in Wikipedia. Also Euler’s formula which will give you a basis for understanding the complex plane. A pure delay multiplies the transfer function, mu, by e^as where a is the delay. The term, the heaviside step function, goes into the denomininator of the transfer function in the s domain. That generally sparks off the nasty math and you have to go through it to get a feel. Delay would push the poles around the origin in opposite directions. literally by WfT radians

        As far as overshoot, a single pair of complex poles sitting on the 45 degree line in the left half of the complex plane indicates critical damping. On the imaginary axis = no damping, and below 45 is over damped. If you have never done this math just wade in, you should be able to piece it together.

      • David –

        Wow! I am missing the point of your comment. I can’t disagree with the first two paragraphs because what you said is really beginner’s stuff – I have been teaching it for 50 years. Why are you telling me?

        Paragraph 3 says:

        “As far as overshoot, a single pair of complex poles sitting on the 45 degree line in the left half of the complex plane indicates critical damping. On the imaginary axis = no damping, and below 45 is over damped. If you have never done this math just wade in, you should be able to piece it together.”

        Nope – you are confusing time overshoot with ripple in the frequency response. Your 45 degree poles are of course 2nd-order Butterworth (maximally flat) and have no FR ripple. It actually step-overshoots by about 4.4%. Critically damped is two negative real poles.

        [ Should I perhaps instead say to you “If you have never done this math just wade in, you should be able to piece it together.” ]

        By the way – the feedback equations (in continuous time) have no poles anywhere (let alone two complex conjugate ones) . The 1/(1-f) equation, IN DISCRETE TIME has a pole at z=f. Like I said.

        Bernie

      • Sorry, I misjudged you based on your simplifying for the non EEs. Nevertheless I stick by what I asserted. Discreet time isn’t a part of this discussion so I’m not going there tho yes I know how. I would have to drag out a book or 2.

        Ok, if zeta=1 Then Both poles are on top of each other at omega on the real axis. Sometimes it’s best to check the book before responding. Zeta=0 puts the poles on the imaginary axis. Above 1 and the poles start to split going left and right from – omega on the real axis. The 45 degree case is zeta=0.707 which does have a frequency peak and a corresponding overshoot. As you say, Butterworth.

        Just looking at the delay in the loop case, you have to realize that delay adds to the phase on the bode plot, which will make it unstable eventually. You get there by convolving a step function, delayed, with the transfer function. Too late in the day to sort out the math. I just plot a bode plot and get the phase or gain margin from that, or design a compensator if needed. The bode plot is a good application for a spread sheet. What that looks like on the complex plane I don’t know off the top of my head.

        One of the first PID loops I was faced with in the real world had a lot of pipe between where the acid was added and the PH was measured. The chemist wanted to make sure the stream was mixed. Non-linear and delayed. It just ended up being slow.

      • Mr Istvan continues loftily to try to attack an argument I have not completed. That marks him out as unreliable, anti-scientific and prejudiced. Better to wait until I have completed the argument on feedbacks. Even then, however, I shall discount what he says because of the prejudice he has demonstrated so far in wilfully misunderstanding the simple point illustrated in the diagram in the head posting. I shall not bother to explain that simple point to him again.

      • David – thanks

        The question is: What Bode plot? The feedback equation is 1/(1-f) and that’s a constant with flat amplitude and no phase. There is no pole or poles. No s-plane or z-plane even! Delaying it just means that it starts out unamplified and then JUMPS to amplified. So I have to consider discrete time (a simulation of continuous time in some fashion) and the feedback equation becomes a discrete-time transfer function G(z)=1/[1-fz^(-1)]. Does this overshoot in time? That’s the question. Here is a plot: http://electronotes.netfirms.com/wuwt9-10-16.jpg

        Here G(z) shows two possible input/output pairs: a step and a sinewave burst, both with input amplitude 1. (The sinewave has frequency 1/32 the sampling frequency). I have chosen f=0.9 which is of course large. The step ramps exponentially to 1/(1-0.9) = 10, the DC gain of G(z). (DC is z =1) The sinewave burst amplifies not to 10 but only to 4.7355, and at the very beginning briefly exceeds this. Is this blip overshoot? Is anything exceeding magnitude 1 considered overshot. I say NO and NO.

        Note that in no place does the sinewave burst output exceed the step response, another possible criterion for no overflow – no blow up. This is because the frequency response is inversely proportional to the distance from the pole (at z=0.9) to the point on the unit circle corresponding to the sine wave. Here that point is at 360 degrees/32 = 11.25 degrees so the point is at 0.9808 + 0.1951j, so the distance to the pole at z=0.9 is (Pythagoras) 0.2112 and the reciprocal is 4.7355. In agreement with the simulation plot. NO FREQUENCY can be closer to the pole than DC.

        No blow-up before f=+1. That’s my point.

        Bernie

    • Thanks Bernie Hutchins for repeatedly underpinning this author’s manifest incompetence through facts you experienced in real life.

      But you probably will have experienced too, like I did many years ago, that such persons deliberately ignore (or even try to belittle by “Mr Stokes / Mr Hutchins is now becoming disingenuous”) arguments they can’t manage at all to offset otherwise.

      • B, being wrong on Bode stability does not mean he is wrong on his sensitivity calculation, which is quite a different thing. He is most likely correct on ECS here in part 3. See my comment upthread for two seperate lines of supporting evidence.

    • Bernie,
      The Hansen/Schlesinger feedback model assumes active gain, where the difference between active and passive is a power supply other than the stimulus. Excite a complex RLC circuit and all the nodes will wiggle, but this doesn’t mean its an active system.

      Bode’s analysis assumes a linear, vacuum tube amplifier provides the open loop gain. Neither of these are true for the climate. The input forcing is non linear to the output temperature and there is no active gain element to provide power beyond what the stimulus can provide. Bode’s gain equation,
      Er = E0 μ/(1 – μβ)
      needs to become this
      Er = E0 μ/(1 – μβ) – Erβ
      in order to model a passive system since the output of the amplifier can be either feedback or system output but not both. As expected from a passive system, there’s no longer a discontinuity at 100% positive feedback.

      • Bernie,
        I do think we mostly agree. I’ve also modelled the climate in the Z domain, but in your model you’re still assuming active gain and this is why you get something funny at f = 1. Going back to the continuous time domain, the power being delayed and returned as feedback can not also contribute to the output. In Bode’s terms, the gain becomes,

        Er/E0 = μ (1 – β)/(1 – μβ)

        Now as the feedback fraction approaches 1, Er/Ro approaches 1 as well, independent of the open loop gain.

      • Instability is when the denominator of Bode’s equation is zero. The sun is putting energy into the system. Normally the feedback is what sets the forward gain but with no feedback the climate system is an integrator of heat input thus ramping up to infinity.

      • David,
        You are assuming active gain where Conservation of Energy does not apply between the input and output of the feedback loop. This is because Bode assumes active gain which can add power to the output above and beyond what is supplied as its stimulus (the Sun). When accounting for COE, the equation becomes,

        closed loop gain = Er/E0 = μ (1 – β)/(1 – μβ)

        Now, when β approaches 1 Er/E0 also approaches 1 and there is no discontinuity since its an infinity divided by another infinity
        .

      • “Now, when β approaches 1 Er/E0 also approaches 1 and there is no discontinuity “
        Very odd maths there. If μ=1, then Er/E0 is 1 everywhere – trivial. Otherwise Er/E0→0 as β→0, and Er/E0→∞ as β→1/μ. Your numerator makes no difference to the singularity.

      • NIck,
        Actually, if μ is 1, the closed loop gain is 1 independent of the feedback fraction, β. Look at the equation again. (1 – β)/(1 – μβ) approaches 1/μ as β approaches 1. There is no discontinuity. For there to be a discontinuity, there must be a more zeros below the denominator than above. This is what distinguishes poles from zeros.

      • Nick,
        And while climate science assumes μ is 1, it is not necessarily so and in fact feedback and gain can be traded off against each other to obtain constant closed loop gain.

        If you assume that the net average feedback is close to zero, then μ is about 1.6. In this case, the open loop gain of 1.6 arises as a consequence of surface emissions absorbed and delayed back to the surface by GHG’s and clouds are added to the incident power from the Sun. The best mapping considers GHG’s as contributing to gain and the dynamic action of clouds acting as feedback. If the net equivalent feedback from clouds was slightly negative, the open loop gain would need to be > 1.6. If slightly positive, it would need to be < 1.6. Why 1.6 must be the closed loop gain is because this is the ratio between surface emissions at its equivalent average temperature and the average incident energy from the Sun, 385/239 = 1.6. This is the proper characterization of the closed loop gain of the planet when the mapping between Bode and the climate is corrected.

      • “Look at the equation again. (1 – β)/(1 – μβ) approaches 1/μ as β approaches 1. “
        I did. With β =1, (1 – β)/(1 – μβ) = (1 – 1)/(1 – μ) = 0/(1 – μ) = 0.

        “And while climate science assumes μ is 1”
        Where do ou get this stuff? Who assumes that? Where?

      • co2isnotevil said September 6, 2016 at 3:06 pm in part:

        “Bernie, I do think we mostly agree. I’ve also modeled the climate in the Z domain…….”

        To be clear I am not modeling climate – I am doing EE stuff. None the less I am interested in discrete models. I understand a singularity at f=1 in both the continuous-time and the discrete-time cases. Now, the discrete-time case also has a singularity at f=-1 and f less than -1 (stable interior of unit circle of z-plane, the pole being the same as the feedback gain) which continuous time does not (stable for ALL f less than +1). I discuss this curiosity in my EN219 notes. Still puzzles me. But it’s just math.

      • Bernie,
        As a EE myself, it’s amazing how much EE related math can be applied to the climate. Unfortunately, Hansen/Schlesinger got it very wrong, largely because nobody who was actually an expert in feedback systems reviewed any of their work allowing Hansen to confuse the ‘feedback fraction’ with what Bode calls the ‘feedback factor’ and this led to the assumption of unit open loop gain.

        There is a good feedback model correspondence, where the input is total forcing and the output is the equivalent emissions of a BB at some temperature which gets converted into a temperature using Stefan-Boltzmann. The closed loop gain is then 1.6. It doesn’t really matter what the open loop gain and feedback fraction are, as long as the closed loop gain is 1.6. A change in net feedback from CO2 may increase or decrease this slightly, but not by enough to make a difference.

        Another is the LTI DE that describes an RC circuit. Did you see my earlier post? The correspondence of the seasonal averages to the behavior of this LTE is astounding. Unfortunately, this tends to get cancelled out in anomaly analysis and nobody gets to see it.

      • “This explains how climate science assumes an open loop gain of 1.”
        It doesn’t. In any case, μ is dimensional. Are you saying μ=1 K/(W/m2)? And so is β. It says so in your note: “β is the feedback fraction which corresponds to feedback coefficients expressed with units of W/m2 of feedback per degree K”. Which makes the (1 – β) numerator problematic.

      • Nick,
        I’m saying that the μ relative to Bode’s gain equation is a dimensionless 1 and β is the dimensionless fraction of the output, expressed in the same units as the input, that is fed back. The very idea that a feedback network is a viable direct model for a system with a power density input and temperature output is ludicrous beyond reason. All the λ0 term does is convert the units outside the actual feedback loop back and forth between W/m^2 and degrees K of output and back from the output to W/m^2 for calculating the feedback. Kind of silly if you ask me since it basically cancels out, thus the implicit assumption of unit open loop gain.

      • “I’m saying that the μ relative to Bode’s gain equation is a dimensionless 1 and β is the dimensionless fraction of the output”
        So what does this have to do with climate, where T is related to F?

        Anyway, your revised expression still has a singularity.

      • “So what does this have to do with climate, where T is related to F?”

        It doesn’t and that’s the point. Bode’s analysis was incorrectly applied to the climate system because of its lack of correspondence to the requirements of his equations. That is, a linear relationship between T and F and an internal source of power to supplement the input power from the Sun.

      • I am not sure that Mr Stokes is right to suggest that mu in Bode’s feedback system is dimensional. It is the unitless amplification factor – or, in Bode’s terms, “transmission characteristic” – in an amplifier circuit.

    • Using the word feedback makes me look for the closed loop gain expressed as G/(1+GH) where G is the amplifier gain and H is the feedback gain into the minus input of the summing node. GH is the open loop gain. This assumes a linear-continuous time system and G and H are frequency domain models of the system. In an electronic system you generally want GH to be a large negative value. In the limit the closed loop gain is just 1/H.

      Stable is defined as “not going to infinity”. A bathtub filling with water is unstable until it overflows. In a feedback system instability is if (1+GH) = 0 at any frequency including DC. Obviously if GH is close to -1 sensitivity to parameters is enhanced. In the above circuit GH is -1.333. Frankly, I wouldn’t walk that close to the edge unless I couldn’t get the gain, or Q, any other way.

      I’m lost from this point on. Is G the heat input taking into account TSI, albedo, and Co2 forcing and H the Boltzmann radiation? Can somebody translat for me?

      • David Thompson said September 6, 2016 at 2:42 pm in part:
        ” . . . . . In the above circuit GH is -1.333. . . . . .”

        If you are talking about my Fig. 6 above, you got it wrong. The feedback gain is +2/3. That’s -2/3 from the second op-amp and (-1) from the first. Look carefully AROUND the loop! Forget about the input gain of 2, that’s not in the loop. The positive feedback can be anything smaller than +1, and 2/3 is less than 1.

        Bernie

      • My bad. The magnitude of 1+gh is still 1/3 which is how the open loop gain of 2*1 turns into. 2*3, or 6. Knowing the answer didn’t help this time.

      • David,

        A clearer way to express the gain relationship is that if G is the open loop gain, g is the closed loop gain
        and f is the fraction of output fed back to the input, the relationship between them is,

        1/G = 1/g + f

        Which when solved for g, results in,

        g = G/(1 – G*f)

        so as long as combinations of G and f are chosen such that G/(1 – G*f) is constant, the behavior is otherwise indistinguishable among the various combinations. For modern amplifiers, G is often assumed to be infinite, thus g = -1/f. If G is small, then positive feedback can be just as stable as negative feedback. Note as well that if f is the dimensionless ratio of output fed back to the input, both the open loop and closed loop gains must also be dimensionless.

        But, in the final analysis, this matters little and climate stability is guaranteed since Bode’s gain equation assumes the input and output are not bound by COE by assuming an infinite source of power other than the stimulus will provide the modelled output and the atmosphere/surface combination has no such source of input power beyond the stimulus coming from the Sun.

      • Not thought of it that way. However if the deniminator is (1+GH) GH must be in the same dimensions that is dimensionless. Or, if you prefer the dimensions of H must.be the inverse of G’s dimensions. G could be inches per volt and H volts per inch in a mechanical servo. You don’t have to have power moving around.
        The benifit of the representation is finding the zeros of 1+GH or using a nyquist plot to find stability and dynamic characteristics and it can be done simply and use huristics.

      • David – good man.

        Full disclosure. I did it wrong the first time – that’s how I work – put a 100k resistor in the top path. The voltmeter finds errors a lot faster than staring at a page of algebra. Okay – you can stop laughing at any time now!

        Bernie

      • Overnight I heard “right half plane” in a dream. It’s like muscle memory, you don’t really have to think about it. Now how to explain it.

        What I do first is count integrators (1/S) – anything more than 2 in the denominator and you have to work to make it stable.

  10. wallensworth
    your understanding of “argument by authority” is different to mine.
    In any case, I’m commenting on the series as a whole, not just one point in this post. I suggest Monkton participates in an effective and in-depth review of his work. What is objectionable about that?

    • Well, Andy, that’s exactly what’s happening here and now. Even you are part of it. Can you handle that?

      • “Well, Andy, that’s exactly what’s happening here and now. Even you are part of it.”

        No it’s not, and you’re not – for instance have you EVER seen Monckton retract anything by admission that he was wrong? No, just congenital wriggling and word-salad that has his choir enthralled. Any dissent and he often turns, err *difficult*. He plays to his audience. Not interested in convincing science.

        For a start, virtually all articles on WU discussing any science that adds evidence to AGW theory is presented as (put kindly – suspicious) and is drowned out by *most* denizens (a few true experts may prevail – Leif Svalgaard comes to mind – showing what would happen to those Sun threads without him) – and a bias is therefore in play.
        You may argue that that is the case with regular peer-review (pal review you say?)
        BUT: Peer-reviewers need to be *experts* in the field under review.
        How else would we know that that that science is credible?
        WUWT is not a vehicle for credible peer-review. And that’s just as Monckton likes it.
        There are many on this thread FI who have admitted they can’t even follow the maths.
        Would you really want laymen to review, (in all sciences, not just your pet hate)?
        What better system would you suggest?
        PS: I start with the premise that scientists are honourable people in the main (subject to the normal human frailties of course, so there must be exceptions …. but NOT all) and any intimation that there is corruption/hoaxing I take to be a comment on the accuser and no other.

      • Toneb continues to be his usual unpleasant self. The material that is being presented and discussed here by those who have a genuine interest in the subject rather than in making drive-by ad-hom attacks will in due course be written up as a paper for peer review and publication in a leading journal. But it is helpful to introduce the ideas here and to follow the discussion, so that I can see where there may be weaknesses in the argument. That will make the reviewed paper stronger.

      • “Toneb continues to be his usual unpleasant self. ”

        That’s a laugh Monckton when you use that tactic to intimidate you interlocutors.

      • Monckton has yet to contribute any two-way conversation about his *scientific conclusions” even when posters here do “contribute”.
        Which is why there is no point in “contributing”.
        The meaning of “contributing in his language is simply agreeing with him.

      • Toneb continues to be childish. If he is not capable of making a scientific criticism of the head posting, let him fall silent.

    • If someone disagrees or thinks they spot an error they’ll post in comments. However, if you can’t follow the argument and decide for yourself whether it stands or falls, that will be of no help to you.

      • I exp[ect to see Monkton engage in back-and-forth debate with those that disagree with him, as does someone like Nik Lewis. Unfortunately Monkton just insults those that disagree with him, even those that have clearly relevant expertise, so I tend to doubt the strength of his arguments.

      • The problem for you, AndyL, is that anyone can go read through these threads themselves and find out that you are full of it (again.)

      • Alan Robertson
        I have no idea what you are referring to when you describe me as “full of it”. Perhaps you can quote a single example?

        I am watching from the sidelines, and judging who seems to show expertise and who engages with the points raised by others. So far, Lord Monkton has been weak at engagement (in my opinion), but I hope this will change when he gets to his feedback post.

      • AndyL, you said: “I exp[ect to see Monkton engage in back-and-forth debate with those that disagree with him, as does someone like Nik Lewis. Unfortunately Monkton just insults those that disagree with him, even those that have clearly relevant expertise, so I tend to doubt the strength of his arguments.”
        —————————-
        Theses pages are filled with Lord Monckton’s responses to questions and critics. You ignore those responses and again, claim that instead of being actively engaged, that he merely insults others. You seem to have failed to notice that prior to those instances when he does get testy, a critic has provoked him by hurling insults and name calling, such as with use of the term “stupid”, so they get a tit- for- tat response, if response at all, which is quite common in debates, scientific, or otherwise. Perhaps you haven’t noticed that, either.

        How convenient that you are blind to these points I’ve made in order to maintain your pretense that you have “no idea what [I] am referring to”. How convenient that you’ve steadfastly ignored other responses to your hollow claim, by those who have also addressed your continuing facade of concern.

      • Alan Robertson
        My mistake. When you said people could go through the thread and “find out that you are full of it (again.)” I thought you meant comments of mine.

        I am basing my comments purely on the debate in this series of posts. I hope Lord Monkton will play the ball and not the man. He has asked us to wait until he reaches his key points before engaging them which is fair enough, but as a result has declined to respond to people who have commented on points he has actually written. We shall have to be patient.

      • “Unfortunately Monkton just insults those that disagree with him, even those that have clearly relevant expertise, so I tend to doubt the strength of his arguments.”

        Yep he does.
        And it works.
        He evades any awkward questions and it puts people off engaging with him.
        I don’t because of that.

        “so I tend to doubt the strength of his arguments.”

        Exactly.
        And IFAIK with is his avenue of last resort.

      • Don’t whine. If you have no serious scientific point to make, go and do something useful.

      • “Don’t whine. If you have no serious scientific point to make, go and do something useful.”

        QED

        Oh, I am, I’m pricking your enormous ego and pomposity ….. just a tiny smidgen.

        BTW: I’ve been overwhelmed by protests from your, err, fans.
        Keep it up Monckton, soon even Anthony may get tired of you.

      • AndyL September 6, 2016 at 2:53 pm
        I exp[ect to see Monkton engage in back-and-forth debate with those that disagree with him, as does someone like Nik Lewis. Unfortunately Monkton just insults those that disagree with him, even those that have clearly relevant expertise, so I tend to doubt the strength of his arguments.

        Alan Robertson September 6, 2016 at 3:36 pm
        The problem for you, AndyL, is that anyone can go read through these threads themselves and find out that you are full of it (again.)

        AndyL is correct as anyone who goes and reads the threads will see, Monckton usually responds to someone pointing out an error by repeating his statement regardless of the evidence offered. If the poster persists Monckton usually resorts to insults and ad hominem attacks.
        An example from the previous thread:
        MieScatter September 3, 2016 at 9:04 pm
        None of this is how the Planck response was calculated. The real method fully accounts for nonuniform temperature, lapse rate and emissivity. MERRA and ERA-Interim give an observation-based Planck response of about -3.1 W m-2 K-1.

        See Soden & Held (2006, http://dx.doi.org/10.1175/JCLI3799.1 ), Bony et al. (2006, http://dx.doi.org/10.1175/JCLI3819.1) and Dessler (2010, http://dx.doi.org/10.1175/JCLI-D-11-
        00640.s1).

        Monckton repeated his claim: Monckton of Brenchley September 3, 2016 at 10:54 pm
        Several polite exchanges followed with Monckton saying that he’d read the paper in 2007 and was right!
        At which Miescatter responded:
        MieScatter September 4, 2016 at 4:16 pm
        I think your post needs to be corrected to state that you misinterpreted the way in which the Planck feedback was calculated and that all of your concerns are fully accounted for in the actual calculations. The correct result is close to the IPCC-reported 3.1 W m-2 K-1.

        Perfectly polite, but Monckton then responds with insults:
        Monckton of Brenchley September 5, 2016 at 3:17 am
        The furtively pseudonymous “Mie Scatter”, who has much to learn about climate sensitivity, and about the civilized manner of conducting an argument, for he hurls insults freely from behind that cowardly curtain, should read both the head posting and Soden & Held with rather more care.

        It is Monckton who has much to learn about the civilized manner of conducting an argument.

      • The furtively pseudonymous “Phil.” and the furtively pseudonymous “Toneb”, a.k.a. Anthony Banton, are out of their depth here. They are both propagandists for a narrow viewpoint that is proving incorrect. Miescatter had, in fact, misrepresented what Soden & Held had said: they, just like Schlesinger before them, had obtained their value of lambda-zero by reference to emission flux and surface temperature, as the values listed in their paper also confirm. That methodology is incorrect, and leads to an appreciable overstatement of climate sensitivity.

      • Monckton: “what Soden & Held had said: they, just like Schlesinger before them, had obtained their value of lambda-zero by reference to emission flux and surface temperature,”

        From Soden & Held:
        “we examine the response of TOA fluxes…the temperature change is uniform throughout the troposphere”

        To help you understand, “TOA” means “top of the atmosphere” and “uniform throughout the troposphere” in this case means that at every altitude the mean temperature increase is 1 C.

        Do you agree that Soden & Held calculated the change in flux at the top of the atmosphere when atmospheric temperatures change by 1 K, including at 5 km altitude or whatever level you’ve decided is your emission level? A “yes” or “no” will clear things up.

  11. It might be noted that Eq. 1 represents a compounding of two canards common in climate science. The lesser is that the behavior of our existing atmosphere can be described as a first-order perturbation of a Stefan-Boltzmann T^4 expression. The more interesting one is that this feedback factor follows from
    differentiation of a hypothetical function, F(T,q(T)), describing outgoing thermal radiation as a function of surface temperature, with q(T) a set of functions which may or may not be functions of said temperature. Should one instead multiply F() by a Carnot factor, (1 – a/T), with (T-a) the troposphere’s temperature range, the consequences of large positive feedbacks are limited, well below 2K for a 3.7W/m2 forcing. The Carnot factor implies that the troposphere extracts the maximum energy thermodynamically possible from combined thermal and convective fluxes before radiative release. (Mathematical analysis is in the notebook, http://quondam.hostoi.com/Notebook.html)

    • Thanks for the links, Quondam, even if they point to stuff a bit hard to grasp for persons lacking a strong math education.

    • “this feedback factor follows from differentiation of a hypothetical function, F(T,q(T)), describing outgoing thermal radiation as a function of surface temperature, with q(T) a set of functions which may or may not be functions of said temperature”
      I read your note. The premise is false. There is no assumption that F is determined by a single temperature. I have set out what is actually done by Soden and Held (as quoted in AR4) in a post here, using a differential formulation similar to yours. The point is that radiatively they deal with a different variable for each time/latitude/altitude combination. Effectively T is a continuum, not a number. Then they find the rate of change of each of those relative to the average surface temperature T_s.

  12. Monckton,
    I do wish you would pay more attention to the correct number of significant figures to retain in your calculations. For example, in Table 1, you show F-naught with 6 significant figures. However, it is derived from an equation using albedo, which you consistently only represent with one significant figure (Although, common alternative values may use two or three significant figures.). Strictly speaking, albedo is the limiting factor on the precision with which F-naught should be represented. This points out the importance of knowing reflectivity with greater precision, unless you just want to use the 0.3 value as a bounding value and use it along with another estimate to bracket an upper and lower-bound on probable values of F-naught.

    In any case, multiplying a number with 6 significant figures by one with fewer significant figures, means the result should only be given to the precision of the multiplier with the lower number of significant figures. If you use ‘scientific notation,’ i.e. a base number <10 multiplied by a power of 10, this becomes more obvious.

    • In answer to Mr Spencer, the output of these calculations is a temperature change delta-T, which is expressed to a single digit of precision. All intermediate calculations are presented to the available precisions, as is usual.

      • MoB,
        I just looked at Table 1 (again) and my version shows delta-T expressed with a total of four (4) significant figures, not 1. But, you really missed the point of my complaint. That is, in a series of multiplications and divisions — of any length — the final answer should have no more significant figures than the multiplier or divisor with the least number. Carrying extra significant figures in intermediate results doesn’t buy you anything! That means, the Achilles Heel of all these machinations is going to be your albedo value. The only way around that is to state explicitly that you are assuming it is a precise value, with as many digits as necessary, in order to illustrate what delta-T would be IF the albedo is correct. If the albedo isn’t correct, then we haven’t learned much that is useful. Alternatively, you could do an albedo sensitivity analysis by choosing a couple of ‘reasonable’ albedo values and demonstrating how those two assumptions affect the probable range of delta-T. In any event, it seems to me, that the reflectivity of Earth is so poorly characterized empirically that all the arguing about the other points is akin to arguing about how many angels can dance on the head of a pin.

        You calculate T-naught to 6 significant figures using F-naught, which rightfully should only have one significant figure. That is T-naught = 3 x 10^2

        Let me see if I can make this clearer: If we want to calculate how many shipping containers can be carried in a ship, and we know the dimensions of the shipping containers to the nearest cubic centimeter, but we only know the cargo volume to the nearest cubic hectometer, we don’t have enough information to make a useful calculation. We will either seriously under utilize the available storage space, or find out we have to leave some containers on the dock.

      • Mr Spencer has been repeatedly told that I am deriving temperature changes to the nearest tenth of a degree. That is all that needs to be said.

  13. Thought experiment –
    Take a long trough shaped tank, like you see on a farm for watering livestock, only about 50 ft long. Fill it up with water. Place a glass or plastic shield around it with a cap on the top, sort of like a large terrarium. Place a large IR heater on the top point down so that one end will heat up the surface water of the tank to about 80 Degrees F. Place a refrigeration coil near the surface of the other end and cool that till there is a thick layer of ice. Adjust these systems so that the two ends reflect (sort of) the equator and the north or south pole. Note how natural circulations start taking place in the tank and the plastic dome above it. How clouds, fog, rain, etc will start occurring.
    Now justify to me how taking the average of all of those conditions that exist can be analized on a computer taking the average of each of the different mediums. That is the average of the albedo, the average of the tank water temperature, the average of the fog, the average of the rain, the average of the IR transfer up/down/left/right etc. the average of the heated water vapor rising on one end, the average of the rain falling in the middle, the average of the snow on the other.
    I seriously doubt that a model could be written for this closed system that would accurately predict the entire system. I don’t think I could and I have written code for accident analysis for both Coal and Nuclear power plants. Ask a good instrumentation engineer all of the things that need to be taken into consideration just to measure the water level in a fifty foot steam generator used at a nuclear power plant where you have cold water on the bottom heated water a few feet up, boiling water above that, saturated steam above that, and then superheated steam above that. All of this affects the delta-P as measured by the level instrument and all of that has to be taken into account in determining the level.
    Likewise, the column of atmosphere above any area of the earth will be affected similarly, with just as many if not more factors affecting the column. Look at just one parameter IR: The IR absorption, release, lapse time, distance between CO2 molecules, and even the spectrum absorbed will be different in each of the different areas of the atmosphere and the levels in those areas. It will also be different with different temperatures and pressures which are affected by not only the height but also by the temperature around that column. Now, throw in varying levels of water vapor, clouds, rain, snow, ice crystals, particulate matter, etc., etc., etc. ad infinitum.
    Ain’t going to happen. It can not be modeled.

  14. I am amused by the trolls trying to discredit Monckton’s work by complaining that it isn’t peer reviewed science. This argument is the last refuge if the uninformed troll. I was nearly inspired to write an article on this silliness, when I remembered that I already had:

    https://wattsupwiththat.com/2013/12/29/peer-review-last-refuge-of-the-uninformed-troll/

    It has become a favorite tactic amongst trolls to declare their belief in peer reviewed science. With this simple strategy, they at once excuse themselves from the need to know anything about the science, and at the same time seek to discredit skeptic arguments on the grounds that, not having been published in peer reviewed journals, they may be dismissed out of hand.

    A retreat to authoritarian arguments in the face of dead simple observations is not new. It is a repeat of history. Not having learned from it, we appear to be condemned to repeat it.

    • Mr Hoffer makes an excellent point. And I propose to deal with it by publishing my results in due course in a leading journal after peer review. Of course it is far harder for skeptics, particularly when putting forward arguments profoundly damaging to the official Party Line, to get published: but it is still possible, and that is what I shall do once the bugs have been ironed out of the argument.

      The process here at WUWT is in fact very helpful in that regard – and in one other vital respect. I consider it possible that there are several senior scientists among the promoters of the Party Line who know perfectly well that the errors I am identifying here are indeed errors. And they will be briefing their team of trolls – paid or unpaid – to do their best to divert attention away from the errors.

      For some time now, I have been floating ideas at WUWT, because the trolls pay it special attention. It is, as the world’s most popular climate website on either side of the debate, enormously influential. That means I have been able to watch and learn wherever they scream the loudest, and that is where I begin to dig the deepest. This approach has enabled me to home in on the errors one by one.

      What is interesting is to observe the change in tone among the trolls. At first they simply shrieked and shrieked, usually with a lot of name-calling. Then, when they realized that they were not looking intelligent, they began to adopt a new tactic: “We’re on your side, really we are, and if only you’d learn from our vastly greater expertise you would realize that official climate science is correct and the Party Line unchallengeable.”

      Once this series is complete, it will be evident to all honest enquirers that the official high-sensitivity case is no longer sustainable, and that, in particular, the very high sensitivities mentioned as possible (see e.g., Murphy, 2008, who says sensitivities as high as 10 K per CO2 doubling cannot be ruled out) will be shown to be impossible.

      • That means I have been able to watch and learn wherever they scream the loudest

        Christopher, shush. Useful idiots are of most use when they don’t know they are useful idiots.

      • Lord Monkton,
        I am beginning to feel like I am stalking you. That is not my intention.

        However your words in the comment above give me great concern. You appear to challenge the motives and integrity of those that disagree with you, and consider them not “honest enquirers”. Following this line to its logical conclusion would allow you to dismiss all their points as being made in bad faith, rather than debating them them using science and mathematics.

        As I have written above, I hope that when you get round to topics such as feedback you actively engage with the points raised.

      • “However your words in the comment above give me great concern. You appear to challenge the motives and integrity of those that disagree with you, and consider them not “honest enquirers”. Following this line to its logical conclusion would allow you to dismiss all their points as being made in bad faith, rather than debating them them using science and mathematics.”

        Yep, that’s one of Monckton’s MO’s.
        And it’s lost him all other platforms for his *science* advocation.
        This last one remaining.

      • AndyL is indeed beginning to exhibit the whiningly repetitive and relentlessly but non-specifically negative conduct that is the mark of the troll. I have nothing to answer yet on the feedback matter, because I have not yet concluded the argument on it. I have given very short shrift to those trolls who have presumed to lecture me, often in the most high-handed, arrogant and often calculatedly offensive manner, about an argument that I have barely begun to make.

        I shall present that argument at my own pace, and I shall watch for the shriekers, and I shall learn from them what they are trying to hide. Those who have serious and intelligent points of criticism to make will make them politely, and with specifics, and I shall heed them. Those who presume to lecture me before I have made my argument have been listed and will not be taken seriously whatever they may say in future, for they have forfeited the right to be regarded as serious contributors to these discussions.

    • “I am amused by the trolls trying to discredit Monckton’s work by complaining that it isn’t peer reviewed science. This argument is the last refuge if the uninformed troll. I was nearly inspired to write an article on this silliness, when I remembered that I already had:”

      As I’ve said before on here (maybe to you re benben).
      A Troll is NOT someone who disagrees with a contributor here, and who additionally gives reasons/supporting evidence for their agument.
      That is called reasoned discussion, or it should be were Monckton amenable.
      So you do want this place to be a pure stamping-office for any and all articles dissing AGW?
      That there be a succession of fanboys cheering on from the stalls?

  15. As usual, Lord Monckton’s post contains both mistakes and some info about weaknesses with the IPCC’s analysis.

    The biggest blunder in this post is to introduce the effective emission level (ERL) into a discussion about radiative forcing. Radiative forcing is the instantaneous radiative imbalance created by an abrupt change, in CO2 for example. The imbalance occurs at the top of the atmosphere (TOA), not the ERL. Sometimes radiative forcing is measured after allowing the stratosphere to adjust to the forcing, which is equivalent to measuring forcing at the the tropopause. However, any discussion of the ERL AND forcing together is fundamentally flawed. Separately, they are useful ideas.

    For a blackbody, W = oT^4 and dW/dT = 4oT^3. Near 255 K (the average temp at the ERL), dW/dT = about 3.8 W/m2/K. If you wanted a blackbody near 255 K to emit an additional 3.7 Wm2,you would heat it 1 K (0.985 K in Lord Monckton’s post). One could call this 3.8 W/m2/K “Planck feedback” (lambda_0) and 0.985 K the “no-feedbacks climate sensitivity”. Lord Monckton does. I have also. The IPCC does not. They raise global mean SURFACE temperature in (GMST) in AOGCMs by 1 K – without changing humidity, lapse rate, clouds or albedo – and observe only 3.2 W/m2/K more OLR emitted. This happens because the Earth is NOT a simple blackbody at 255 K (the ERL). SURFACE temperature is cooler at the poles than the equator AND the IPCC assumes that more warming will occur at the poles than at the equator when GMST rises 1 K. Since the lapse rate does not change, the surface and ERL warm in parallel, but not uniformly. When more warming occurs where it is cooler, 4oT^3 is less than for a uniform warming. So the IPCC calculates that that the Earth emits only 3.2 W/m2/K (Planck feedback) when it warms and 1.15 K when CO2 doubles withou feedbacks.

    Therefore, their are two sensible, but different, values for Planck feedback (3.8 and 3.2 W/m2/K) and the no-feedbacks climate sensitivity (0.985 and 1.15 K). If you don’t trust climate models, the former values used by Lord Monckton seem more rational. If you are going to use other feedbacks obtained from climate models, however, it is best to also use Planck feedback from climate models. Herein Lord Monckton combines Planck feedback for a blackbody at 255 K with other feedbacks from AOGCMs, a dubious pairing.

    To some extent, the exact values for Planck feedback, no-feedback climate sensitivity, and gain are irrelevant. The Earth is not a blackbody, nor an electrical circuit; and it does have feedbacks. We don’t need to know what would happen if the Earth were a blackbody or an electrical circuit or lacked feedbacks. The important question is: “How much does the Earth need to warm to emit and reflect an additional 3.7 W/m2 of radiation to space – to correct a 3.7 W/m2 imbance created by 2XCO2?” The answer to that question is ECS, and depends on what happens to clouds when it warms. There is no good reason to believe that AOGCMs or Lord Monckton provide a reliable answer to this question.

    • Frank is not quite correct. Schlesinger (1985) plainly stated that he was taking surface temperature and emission-altitude flux as the basis for his determination of lambda-zero (his G-zero). Soden & Held (2006) make it explicit that they are following the same methodology. That methodology is erroneous, since the fundamental equation of radiative transfer operates only on temperature and flux at the same emitting surface.

      And the Planck “feedback” is not really a feedback at all. It is better considered as part of the reference frame within which the true feedbacks are determined. See Roe (2009) for a discussion.

      And one of the virtues of using the emission altitude as the point at which climate sensitivity is determined is that it is largely (though not quite) free of the non-radiative transports – such as poleward advectionj – that bedevil hard-deck surface calculations.

      • “And one of the virtues of using the emission altitude”

        Except that you have to get the right emission altitude. If your reference is the zero feedback 255K emission altitude, this emission altitude is the hard surface, as both Schlesinger and Hansen were modeling. Even now, a significant fraction of the photons leaving the planet actually originate from the surface, while the rest originate from the GHG’s and clouds in the atmosphere, moreover; its the sensitivity of the surface temperature to forcing that anybody really cares about.

        I see so many errors in how Bode was mapped to the climate system, the output of the model has absolutely no correspondence to reality at any altitude, emission or otherwise and absolutely no predictive power. I don’t see how piling on another level of abstraction doesn’t make it even worse.

      • ” Soden & Held (2006) make it explicit that they are following the same methodology.”
        Again, just nonsense. S&H do not mention emission-altitude flux anywhere. You could lay this to rest by just quoting one instance where they do.

      • “The radiative flux in S&H is not the surface flux”
        When challenged on this emission-layer stuff, you change the subject. But we’ve been through this before. S&H, like everyone else, consider the relation between surface temperature and forcing. That is what your “official equation” is. Forcing is not, and never was, a surface flux. It is energy being added, and is accounted for as a downflux at TOA. It is actually a dip in outward heat flux, and the reason for TOA is that there, and not lower, the upflux is all radiative.

      • Monckton of Brenchley: “Mr Stokes persists in bipeung calculatedly obtuse. The radiative flux in S&H is not the surface flux, but the temperature is surface temperature,”

        You’ve said you read Soden & Held. So you agree that the temperature change is uniform, so that for their global-mean surface temperature change of 1 C, they also change the temperature by 1 C change at 5 km altitude?

      • In answer to Mr Stokes and Miescatter, Soden & Held’s values for lambda-zero confirm what they say in the text: that they are surface temperature as the denominator in the determination of lambda-zero, and not the temperature corresponding to the incoming radiative flux.

      • Monckton of Brenchley:

        So you agree that in Soden & Held, the temperature change is uniform so that for their global-mean surface temperature change of 1 C, they also change the temperature by 1 C change at 5 km altitude? Yes or no.

      • Asked and answered. If S&H had not done what they said they had done – taking surface temperature and relating it to emission-altitude flux via the SB equation – then they could not have obtained the values of the Planck or reference sensitivity parameter that they published. Check the math.

      • Nick Stokes: S&H, like everyone else, consider the relation between surface temperature and forcing.

        Hardly anyone considers the relation between surface temperature and forcing, or else they would consider the changes in non-radiative flux along with the changes in radiative flux. anyone who calculates a temperature or temperature change in relation only to radiative fluxes or radiative flux changes is not working at the surface.

      • “or else they would consider the changes in non-radiative flux along with the changes in radiative flux”

        In LTE, the only effect non radiant flux between the surface and atmosphere can have is on the surface temperature and its consequential emissions which by definition is already accounted for by the LTE average surface temperature from which average radiant emissions are calculated. This is an error introduced by Trenberth as he conflated energy transported by photons with energy transported by matter. While matter can emit photons, it also absorbs photons and in LTE, absorption == emission.

        The non radiant flux entering the atmosphere is mostly latent heat and returned to the surface as non radiant flux and is basically a zero sum influence relative to the radiant balance. Trenberth added unnecessary confusion by calling the non radiant return to the surface ‘back radiation’ when most is in the form of condensed water warmer than it would be otherwise, the potential energy of water lifted against gravity (where do you think hydroelectric power comes from?) and weather.

      • Lord Monckton: The abstract of Schlesinger (1985) says his G_0 is 0.3 C/W/m2, which is equivalent to a Planck feedback of 3.3 W/m2/K. This is similar to the 3.2 W/m2/K value obtained by S&H using the procedure I described and Nick Stokes quoted above. (Nick: When I mentioned a constant lapse rate, it meant that a 1 K warming was applied to the surface and all altitudes, as you described more explicitly, but, IIRC, it was less than 1 K at some latitudes and more than 1K at others.). A Planck feedback of 3.8 W/m2/K is appropriate for a blackbody at 255 K, the average temp at the ERL.

        No one cares about GW, ECS or feedback at the ERL. For all feedbacks reported in W/m2/K, K refers to the change in SURFACE temperature, GMST, not at the ERL.

        I have tried using the phrase “Planck response modified by feedbacks”. It didn’t make things clearer and they both have the same units, W/m2/K. All matter responds to warming by emitting more radiation – Planck response/feedback. Our planet responds to surface warming by increasing evaporation, putting more WV, a GHG, in the atmosphere, which effects both clouds and the lapse rate. Our planet also responds with decreased seasonal snow cover. These are all “responses” to surface warming, the word “feedback” becomes more useful when one gets into the math of amplification and the possibility of a runaway GHE. Response and feedback mean the same thing. The important difference is that these responses take place on different time scales: Planck, instantaneous. The fastest feedbacks mentioned above, days to months. CO2 out gassing from the deep ocean and ice cap retreat, centuries to millennia.

        There is relatively little meridional convection of heat at the ERL, but lots of vertical convection at the ERL. Wherever convection is involved, total heat transfer and not be calculated by Relatively simple radiation transfer calculations.

      • Monckton of Brenchley: That’s not an answer. Soden & Held (2006) says: “lambda_0 assumes that the temperature change is uniform throughout the troposphere”.

        Do you agree that for a surface temperature change of 1 K, they also changed the temperature at 5 km altitude by 1 K?

      • co2isnotevil: In LTE, the only effect non radiant flux between the surface and atmosphere can have is on the surface temperature and its consequential emissions which by definition is already accounted for by the LTE average surface temperature from which average radiant emissions are calculated.

        It is not “accounted for” by “definition”. Granted, the end of heat flow is a part of the proper definition of “equilibrium” when properly used, implying that Earth surface and atmosphere are expected to “equuilibrate” to the same temperature. However, the relation of the long-term surface temperature to the atomosphere in any part is at best an approximate “steady state” (or quasi-stationary distribution), which can not be accurately approximated by the equilibrium assumption. In order for the atmosphere to sustain a net mean increase in spaceward radiation of 1 Watt, for example, the net increase in the rate of transfer from the radiative, evapotranspirational and advective/conductive dry heat together have to increase by 1 Watt, which requires a smaller surface temp increase than the atmospheric temp increase necessary to increase its radiant output by 1 Watt.

        As far as I know, the only attempt to model the increase in heat transfer from surface to atmosphere that would result from an increase in sruface temperature was by Romps et al in Science Magazine almost 2 years ago. They focused their attention on their “headline result” of a 12%/C increase in the rate of lightning ground strike rate, and ignored the other implications of their model result.

      • NickStokes: No, I am saying that they have not “adopted” a positive feedback.

        I think that the word “adopted” is as good as any other. Would you prefer “promoted”? “Promoted” actually works really well considering how prominently they have promoted in the public discourse and the IPCC reports and press communications. They may address lots of feedbacks, but the biggie is the hypothesized positive water vapor feedback.

    • Frank,
      ” They raise global mean SURFACE temperature in (GMST) in AOGCMs by 1 K – without changing humidity, lapse rate, clouds or albedo – and observe only 3.2 W/m2/K more OLR emitted.”
      Not true. Details are in my post here. Here is the description in S&H:

      To compute Kx, we first calculate the control top-of-the-atmosphere (TOA) radiative fluxes using 3-hourly values of temperature, water vapor, cloud properties, and surface albedo from a control simulation of the GFDL GCM. For each level k, the temperature is increased by 1 K and the resulting change in TOA fluxes determines (∂R/∂T_k).

      “However, any discussion of the ERL AND forcing together is fundamentally flawed. Separately, they are useful ideas.”
      Indeed so.
      “The Earth is not a blackbody, nor an electrical circuit; and it does have feedbacks. We don’t need to know what would happen if the Earth were a blackbody or an electrical circuit or lacked feedbacks. The important question is:…”
      True again. Climate scientists think about feedbacks far less than people here think.

      • Nick Stokes: Climate scientists think about feedbacks far less than people here think.

        That does not sound good. Do you mean to say that climate scientists adopted a positive feedback with little thought and have thought little about it since? The finite range of the global temperatures over the past millions of years is evidence that they ought to give much more thought to the negative feedbacks that make such stability possible. Can it be shown that any climate model has the positive and negative feedbacks estimated accurately enough to forecast future mean temperature, say a few decades hence?

        If you are correct, then climate scientists would be well advised to take Christopher Monckton’s critique seriously, and give much more thought to the feedbacks.

      • “Do you mean to say that climate scientists adopted a positive feedback with little thought and have thought little about it since?”

        Little thought was given to this by Hansen when he originally formulated the bogus analysis nor by Schlesinger who ‘fixed’ Hansen’s analysis. Schlesinger fancies himself a feedback expert and thus his work was never reviewed by an independent expert on feedback who might have uncovered his errors 3 decades ago.

        The IPCC canonized the feedback model back in AR1 and every paper about feedback since has just echoed Schlesinger’s flawed analysis.

      • Mr Stokes is wrong. IPCC, for instance, prints the word “feedback” more than 1000 times in AR5, and there is a very substantial literature on it, of which he seems more or less entirely unaware.

      • Nick Stokes, quoting S&H: To compute Kx, we first calculate the control top-of-the-atmosphere (TOA) radiative fluxes using 3-hourly values of temperature, water vapor, cloud properties, and surface albedo from a control simulation of the GFDL GCM. For each level k, the temperature is increased by 1 K and the resulting change in TOA fluxes determines (∂R/∂T_k).

        I think that shows that they are not working with the surface, but are working at the “control” TOA and extrapolating from a fixed lapse rate. The lapse rate does not provide a good model for rate of non-radiative transfer from surface to atmosphere; for that, you need something more complicated, such as the RainfallRateXCAPE used by Romps et al in their famous lightning strike rate paper. Temp change at TOA is not an accurate approximation to temp change at the surface.

      • “Do you mean to say that climate scientists adopted a positive feedback with little thought”
        No, I am saying that they have not “adopted” a positive feedback. They do use feedback for explanations, and some use it for diagnosis of GCM output, which is a rather specialised area. You may notice that we are mostly talking about just a few papers (S&H, Vial et al, Schlesinger 1985, Roe). But despite what is persistently said here, they do not build such thinking into GCMs and other tools of the trade.

        “I think that shows that they are not working with the surface, but are working at the “control” TOA and extrapolating from a fixed lapse rate.”
        No, they are working at all levels of the atmosphere. Check the diagrams. There is no extrapolation and no use of lapse rate. They simply take an observed (probably reanalysed) temperature distribution with known TOA flux, then perturb temp level by level, and calculate the modified flux. That gives the first radiative term in their factorisation of the effects.

        “Temp change at TOA is not an accurate approximation to temp change at the surface.”
        Indeed, and the difference forms a main part of their lapse rate feedback component of temp feedback. But temp at TOA has no special status in their analysis. It is just the top level of cells.

      • “Mr Stokes is wrong. IPCC, for instance, prints the word “feedback” more than 1000 times in AR5”
        I didn’t say that don’t talk about feedback. I said “Climate scientists think about feedbacks far less than people here think.”

        The AR5 is big. The word feedback occurs 230 times in this thread.

      • Nick,

        The point is that without unwarranted large positive feedback, there is nothing to worry about from a doubling of CO2 to 560 ppm. In fact, it would be a good thing, although not as good as 1120 ppm for the planet, its plants and people.

      • Nick Stokes: The word feedback occurs 230 times in this thread.

        That’s the topic chosen for this thread, isn’t it. And the possibility, claimed by Christopher Monckton of Brenchley as well as by me and others, that the IPCC have got it wrong. They need to give it more thorough and precise consideration for the next annual report.

      • Nick Stokes: “They simply take an observed (probably reanalysed) temperature distribution with known TOA flux, then perturb temp level by level, and calculate the modified flux. That gives the first radiative term in their factorisation of the effects.”

        Soden & Held do the calculations for GCM atmospheres while Dessler (2010) does it for the real world using MERRA and ERA-Interim. Both of those come out at about 3.1 W m-2 K-1.

    • PoA, you do not correctly understand the boundary v. initial conditions arguments about climate. Study the math of chaotic strange attractors in n-1 Poincare space, then get back with something more substantive.
      My guess, having published a peer reviewed paper in this space long ago, is that you cannot. And that ECS is ~1.65, so no climate alarm. Explained in blog posts here and elsewhere plus 3 ebooks.

    • “But it’s not, is it?”

      It depends on how you define the emission altitude. If you consider it to be the hard surface, the effective emissivity is the ratio between the planet emissions and surface emissions, or about 0.62. If you consider it to be an arbitrary surface consistent with the surface that the IPCC defines forcing relative to, then the effective emissivity is exactly 1. Of course, the average temperature of the planet is not 255K, but is about 287K, moreover; none of the actual emitted photons even originates from this imaginary surface that the IPCC defines forcing relative to. Not coincidentally, the reciprocal of the equivalent emissivity of 0.62 when you consider the hard surface as the emitting surface is exactly equal to the dimensionless closed loop gain that the feedback model must produce in order to accurately model the surface of the planet.

      • Schlesinger’s notion of effective emissivity is erroneous. For the mean altitude at which incoming and outgoing radiation are equal is about 5 km above ground level. Mean temperature there is a little under 255 K, whereas temperature down here is 288 K.

      • “For the mean altitude at which incoming and outgoing radiation are equal is about 5 km above ground level.”

        How to you get this? The mean altitude where incoming and outgoing radiation are equal is at some radius that mostly encloses the magnetosphere. It’s only at this boundary between the planet and space where this is true. If you are talking about the altitude where the kinetic temperature of the O2 and N2 is 255K, that surface is irrelevant to the radiant balance, sensitivity or any other property of the system. Besides, none of the radiation leaving the planet originates from either O2 or N2.

      • Emissivity is not 1. For a gas the absorption and emission coefficients are specified per unit depth, or in the HITRAN tables as cross sections of cm2 per molecule which is easily related. So effective emissivity depends on the depth and it changes with wavelength.

        Monckton’s calculations are physically nonsense.

      • “Emissivity is not 1”

        Correct that the emissivity of the PLANET is not 1, but the emissivity of the surface itself is close to 1. The Earth is best modelled as a 2-body system. There’s a nearly ideal black body surface whose average temperature is approximately 287K and which emits energy into a gray body atmosphere which captures, delays and returns some fraction of surface emissions back to the surface to be combined with incident solar energy. The net effect of the combined system has the behavior (including the sensitivity) of a gray body whose temperature is that of the surface and whose effective emissivity is about 0.62 such that 239 W/m^2 is the net emissions of the equivalent gray body. The reciprocal of this equivalent emissivity, about 1.61, is the required closed loop gain of a proper feedback model.

      • CO2isnot evil is again mistaken. The “equivalent emissivity” arises from a frank error in Schlesinger (1985), by which a flagrant abuse of the fundamental equation of climate sensitivity was perpetrated. There are a number of other errors in CO2isnotevil’s understanding, and these will be corrected in the next article in this series..

      • co2isnotevil: “The Earth is best modelled as a 2-body system. There’s a nearly ideal black body surface whose average temperature is approximately 287K and which emits energy into a gray body atmosphere ”

        Is this the best model? Are you able to accurately simulate changes in the spectrum of radiation that we measure?

        Do you honestly believe that there is no emission within the atmosphere that is absorbed by the atmosphere? Do you honestly believe that absorption does not depend on wavelength or quantity of gas?

      • “Is this the best model? Are you able to accurately simulate changes in the spectrum of radiation that we measure?”

        It’s certainly matches the data quite well. When you plot the surface temperature vs. the output emissions, the correspondence is very close when 1 month averages are considered and nearly exact when 12 month averages are considered.

        The spectral qualities are just the result of specific line absorption and emission and are well predicted by line by line simulations based on HITRAN data. The level of modelling I’m discussing is at the level of conserving joules, which is mostly independent of specific photon energies and more concerned with aggregate fluxes. The nominal spectrum isn’t all that far from an ideal Planck spectrum. Sure there are spectral gaps where the typical attenuation is about 3db, but the peak is easily discerned and the color temperature of the emissions of the planet is the approximate average surface temperature.

        “Do you honestly believe that there is no emission within the atmosphere that is absorbed by the atmosphere?”

        Of course there are emissions within the atmosphere. Cloud emissions are subject to GHG absorption and re-emission and clouds themselves absorb and emit energy. Much of the energy absorbed by GHG molecules is re-emitted as a photon. only to be absorbed by another GHG molecule, but in the final analysis all that matters is that the steady state flux entering the atmosphere is balanced by the steady state flux leaving, both back to the surface and out into space. My analysis is concerned strictly with the behavior of the atmosphere at its boundaries; one with space and another with the surface. What happens inside is irrelevant as long as I can accurately model the behavior at its boundaries.

        Think of the atmosphere as a mismatched transmission line between the surface and space, whose impedance mismatch reflects power back to the source (the surface).

      • co2isnotevil September 6, 2016 at 11:56 pm
        Correct that the emissivity of the PLANET is not 1, but the emissivity of the surface itself is close to 1. The Earth is best modelled as a 2-body system. There’s a nearly ideal black body surface whose average temperature is approximately 287K and which emits energy into a gray body atmosphere

        The atmosphere is not a gray body.

    • With respect to the long-wave radiation with which we are concerned, emission-altitude emissivity is vanishingly different from unity.

      • “With respect to the long-wave radiation with which we are concerned, emission-altitude emissivity is vanishingly different from unity.”

        But this is also true for almost any altitude between about 5km and infinity and the fact that this is true means that the apparent sensitivity at this phantom emission altitude range has absolutely no relationship to the sensitivity of the surface to change and in the final analysis, this is all we care about.

      • CO2isnotevil is not well aware of atmospheric dynamics. He should read any of Dick Lindzen’s talks to learn of the significance of the emission altitude. I have already explained to him on several occasions that once the temperature change at the emission altitude has been determined, that temperature change can simply be added to surface temperature to obtain the new surface temperature. That way, the lapse rate remains unchanged.

        Should there be any consequential changes in the lapse rate, these should be taken into account as part of the lapse-rate feedback. Schlesinger’s error leads to a substantial and unjustifiable overstatement of final climate sensitivity.

      • “the significance of the emission altitude”

        Rest assured that I am well aware of this as it applies to an equivalent modelling and that in that context, it has absolutely no correspondence to the output of the feedback model as defined by Hansen and Schlesinger, nor does their model have any correspondence to the surface temperature or changes thereof. The model is so broken, its useless and adding another level of abstraction on top of a pile of other errors doesn’t make it better and only makes it worse.

        The other issue I have with your analysis is that your definition of the radiating surface is the altitude where the incoming radiation == outgoing radiation == 239 W/m^2 and assert that this is about an altitude of about 5 km . The actual distance from the surface where this occurs is a radius extending outside the influence of the atmosphere, which is well beyond 5 km. Note that commercial jet airplanes fly at about 11-13 km. An altitude of 5 km doesn’t even enclose all of the cloud tops!

        The only altitude that you can legitimately say that the the incoming radiation == outgoing radiation == 239 W/m^2 is at the top of the mesosphere which is at about 80 km.

        I think you are confused by thinking that this equivalent ‘radiative’ surface is where the kinetic temperature of the atmosphere is 255 K and yes, where this is is determined by the lapse rate and surface temperature, however; where this is has nothing to do with the radiative balance balance of the planet or radiation in any form, including forcing, and is simply a matter of matter and not a matter of photons. Asserting that this temperature is the output of the feedback network is just as incorrect as Hansen claiming the output was representing the surface temperature and changes thereof.

      • Monckton of Brenchley: I have already explained to him on several occasions that once the temperature change at the emission altitude has been determined, that temperature change can simply be added to surface temperature to obtain the new surface temperature. That way, the lapse rate remains unchanged.

        That’s a standard approach, which you carry through consistently, so I am not quarreling with your approach (it’s worth while to take the standard approach, use it consistently, and thus disclose its flaws..) I disagree, however, for the reasons that I wrote about a couple times here. The claim that the lapse rate remains unchanged is poorly justified, if justified at all, afaict. Consider also the graph here at IsaacHeld’sBlog: https://www.gfdl.noaa.gov/blog_held/55-tropical-tropospheric-warming-revisited-part-2/

        Those are model results, but the implication is that the change in temperature is not the same at all altitudes. The change (trend per decade) is more than twice as great at 300hPa as at the surface.

      • “With respect to the long-wave radiation with which we are concerned, emission-altitude emissivity is vanishingly different from unity.”

        For which wavelengths and for the atmosphere between which two pressure levels (or altitudes, if you prefer)?

      • In response to Mr Marler, I am not arguing that the lapse-rate does not change. I am arguing that when determining the sensitivity parameter one should hold it fixed, so that any change in lapse-rate is represented as a feedback and not as part of the direct or initial forcing.

  16. Regarding reference climate sensitivity of .985 K per 2XCO2, derived from increasing the radiation (incoming and outgoing each at the effective emission altitude) by the 3.708 W/m^2 of a 2X change of CO2 from 238.175 to 241.883 W/m^2, a 1.557% increase. This would increase the temperature at the effective radiating altitude by .387%.

    As I mentioned in about the 300th comment in Part II, the surface at 288 K with emissivity of longwave IR being .96 radiates 374.503 W/m^2, and 238.175 W/m^2 is 63.6% of that. Assuming that emissivities and absorptions don’t change with a small change of temperature, and that the spectral shift of longwave IR from a small change of temperature is negligible, this 63.6% figure won’t change significantly with a temperature change of a degree or two. So increasing CO2 by a factor of 2 would increase the surface outgoing longwave IR by 1.557% and the surface temperature by .387%, from 288 to 289.115 K, meaning climate sensitivity of 1.115 K per 2XCO2. This does not require an increase in the lapse rate below the effective radiating altitude, because the part of the atmosphere below the effective radiating altitude would expand by .387%, making the effective radiating altitude .387% higher.

    The actual pre-feedback figure is slightly different because the surface loses some heat by mechanisms other than longwave IR radiation, such as evaporative cooling and convection and latent heat used in melting of snow, which increase at rates other than 4th power of absolute temperature, and those increases get complicated if polar amplification causes global circulation to vary inversely with global temperature (which I think is the case).

    • What I calculated is the theoretical pre-feedback result of solar radiation increasing enough for the amount absorbed to increase by 3708 W/m^2. An increase of CO2 does not change the amount of longwave IR radiation going to space from the earth and the atmosphere (unless the albedo of earth and its atmosphere changes), because that must match the amount of solar radiation absorbed during equilibrium.

    • Mr Klipstein’s point is interesting. However, I submit that the following is the correct model. The emission-altitude flux being known, and the emissivity being approximately unity with respect to longwave radiation at that altitude, the emission-altitude temperature is also known. The forcing from CO2 doubling can then be added to the known emission-altitude flux and the new temperature at what was the emission altitude derived. Deducting the pre-perturbation emission-altitude temperature from the new temperature gives the pre-feedback or reference climate sensitivity. To ensure that the lapse-rate between that altitude and the surface, simply add the reference climate sensitivity to pre-existing surface temperature, and determine the new surface flux from that value.

      Any changes to the lapse-rate that the models predict are then treated as part of the lapse-rate feedback.

      That is what should happen, but, owing to the Schlesinger paper, that is not what did happen.

  17. my issue with the post is that Eq. 2 is presented with no justification and
    would appear to be completely wrong. The “official climate feedback equation” (which isn’t official) is a general equation describing a generic linear system with time-delayed feedback. As such it has been well tested and applied to many different systems. Hence if you want to redefine one of the terms (replacing the lambda_0 in the final term) you would need both some
    fairly solid theoretical and experimental justification. You could for example build a simple op-amp with voltage dependent feedback and use that. But unless you can justify altering the equation in some way I am not inclined to pay it any attention.

    • The understanding of eq. (2) depends upon an understanding of climate-sensitivity modeling generally, and on an understanding of the error identified in Part II, by which surface temperature and emission-altitude flux were erroneously treated as part of the same SB relation. If Geronimo has an alternative central estimate for the feedback factor, let him state it and explain it.

  18. The only way to check the real climate sensitivity and the climate sensitivity parameter, is to carry out the spectral calculations using the average global climate values. That is why you are not able to challenge the the RF value of CO2 but you are using the IPCC’s value of the equation calculated by Myhre et al. Can somebody show a single research paper that a researcher has repeated the calculations of Myhre et al. and has realized that the equation is correct? This equation is a common standard but it does not prove that it is correct.

  19. I see a lot of discussion going on here about sensitivity. The maths long as my arm,and some of it not precise numbers, to make a concluding argument, that sensitivity is really much smaller than what the IPCC thinks it is.

    What I am more interested in, is past climate history,showing any indication of any minor instability ever going into the major run away instability phase. The IPCC never seem to point out a time out of the past 1.5 Billion years to show evidence of prolonged instability, that would support their claim.It is a fatal weakness because there is strong evidence based on several published papers that CO2 in the atmosphere has been Much,much higher than today, WITHOUT that much babbled about run away instability ever occurring, they think is probably going to happen in the near future with only a meager 500 ppm of CO2 hanging around in the air.

    Frankly, it never happened when the CO2 level was over 4,000 ppm,for MILLIONS of years,what make you think it will happen with 500-700 ppm,in the near future?
    .

    • Sunset Tommy is asking the right question. In the next article I shall show that the notion of a runaway temperature feedback in the climate is nonsense.

      • This chart itself show why the warmist high temperature sensitivity fantasies are silly, since the Tropics temperature has been similar for many millions of years.The change was towards the poles,indicating a growth in tropical expansion towards the polar regions,which has nothing to do with CO2 in itself since the magic molecule is supposedly rather uniform in the atmosphere.

        From here, http://dinosaurtheory.com/thick_atmosphere.html
        :

    • Sunset,
      You make a great point.

      Also, critics have some good math and equation points(sometimes nitpicking), however the standard they are holding MB too, is often one that assumes that there is an existing and known “perfect” mathematical representation of the physic of the atmosphere and they(or the IPCC) are the gatekeepers.

      MB errors may very well be smaller than other bigger errors from IPCC model assumptions that are obviously resulting in climate model busts vs the real world.

      I have used numerous weather models and their ensembles for 34 years………and understand that climate models are an entirely different animal. However, its the tiny variation in one parameter that can amplify with time(in the ensembles) that can lead to massively different solutions.

      The ensemble runs of climate models are all pretty consistent with each other(though the range of warming does vary considerably in some cases), which can mean a couple of things.

      The changes made between the different ensemble members did not make much difference in the solution………which is a range of warming in outcomes. This can be interpreted as consistency and that they must all have it right.

      However, I also have been observing the atmosphere, as an operational meteorologist in real time the past 34 years. Over the past 2 decades, almost all the climate models have been too warm. This tells me, in fact that they all have “something(s)” wrong.

      Regardless of how consistent climate model ensembles are with each other and how accurate the assumed math is, you must reconcile this difference between this real world reality…….models being too warm. Pretending that they have not been too warm doesn’t cut it. When somebody states this, I know that they are not objective.

      I believe that we should hear out MB as he seeks to find a key element related to reconciling this difference so that we can better “tune” future climate models.

      • When you oversimplify a modelling task, it is easy to obtain “accurate” results, and to then criticize the results obtained by models which do not oversimplify anything.

        This fundamental rule I had to learn about decades ago, though in a science and engineering discipline completely differing from that needed here. The similarities between “oversimplifiers” of my past discipline and those oversimplifying here however is simply amazing.

        Luckily, there are commenters like Nick Stokes, MieScatter, CO2isntevil, Donald L. Klipstein et alii, whose manifest knowledge and experience help me to understand piece by piece what is basically wrong here.

    • The closest thing in the historical record pointing to ‘instability’ is the snow ball Earth theory, which itself is controversial simply because the tropics receive more than enough solar energy to melt ice and snow. If such a thing did happen, it was more likely the result of a catastrophic event like a volcano or impact even that sent massive amounts of dust in the atmosphere which persisted for decades or perhaps surface thought to be at the equator was actually at the poles since just 1cm of continental drift per year adds up to a million meters after 100 million years adding a lot of positional uncertainty.

      There’s absolutely no indication in this historical record for any kind for runaway warming or even significant warming consequential to far higher CO2 concentrations, besides, as long as the atmosphere remains semi-transparent to incoming visible energy and outgoing LWIR energy, the possibility of a run away situation in either direction is precluded by physical law, specifically COE.

      The ONLY reason the consensus can believe in a run away GHG effect is because the feedback model it’s based on assumes active gain which removes any COE requirement between the input and output as it has an implicit, internal source of power that adds joules to the output above and beyond those arriving as input. When you add a COE constraint, the sensitivity range goes from 0.8C +/- 0.4C per W/m^2 to a more plausible 0.25C +/- 0.1C whose upper bound of 0.3C is well below the lower bound of the consensus estimate.

      Most disturbing is how ignorantly many in climate science distort reality in order to consider the 0.3C per W/m^2 upper bound on the sensitivity as the zero feedback, lower bound. What’s being quantified as the zero feedback sensitivity is the LWIR path from the surface to space which actually sets the upper bound on the possible sensitivity by throttling emissions between the surface and space.

      It’s only the zero feedback sensitivity when the open loop gain == closed loop gain which is true for the model, but the empirical adjustment to the 255K sensitivity is actually adjusting the sensitivity to a value representative of the LWIR path between the surface and space based on the current average surface temperature and current emissions. They do not understand that the open loop gain and feedback can be arbitrarily traded off against each other as long as (1/G – f) remains constant, where G is the open loop gain and f is the fraction of output returned to the input as feedback and what they are doing is selecting a G representative of the current state and that G selected requires f == 0.

      Adding to the error is confusion about the difference between the feedback fraction (a number between -1 and 1 representing the fraction of output returned to the input) and the feedback factor (a number between -inf and +inf representing the reduction in open loop gain). These two are only the same when the open loop gain is 1, hence the unrecognized assumption of unit open loop gain. In one part of the calculation, climate science assumes unit open loop gain and in another they assume the open loop gain is an empirically adjusted Planck sensitivity at 255K adjusted for an emitting surface at 287K which is the average color temperature of the radiation leaving the planet.

  20. A thing to repeat over and over and other again, until IPCC and thermageddon army collapse :
    “The climate system is a coupled non-linear chaotic system” – IPCC TAR WG1, Working Group I: The Scientific Basis
    Chaos & Climate – Part 3: Chaos & Models Guest Essay by Kip Hansen
    https://wattsupwiththat.com/2016/09/04/chaos-climate-part-3-chaos-models/

    Definition of a “coupled non-linear chaotic system” is that a linear equation like ΔT = λΔF CANNOT give a hint on its behavior.
    Even if (big “if” !) F were part of system inputs, and even if (bigger “if” !) there were some sort of GHG-dependent gain (analog to the “r” parameter of logistical map) in the system, well, the very same ΔF could still lead to any sort of ΔT, positive or negative, big or small, depending on conditions.
    This “climate sensitivity” thing contradict the acknowledged fact that climate is a chaotic system. IPCC is nonsensical.
    “climate sensitivity” belongs to the realm of The Pink Invisible Unicorn with the Giant Spaghetti Monster, where ΔF is the former fart and ΔT the latter loss of weight when eating it (or the other way round …)

    The climate system is a coupled non-linear chaotic system. As such, like so many chaotic systems, it nonetheless is bound to change in a very narrow domain (*), but remains untractable. Any linear equation, ΔT = λΔF or any other, is irrelevant.

    (*) A classical example : Lorenz attractor, brought to you by “ptolemy2”
    https://wattsupwiththat.com/2016/09/04/chaos-climate-part-3-chaos-models/#comment-2293178
    Note the similarity with temperature records

    • Yes, the climate is chaotic and nonlinear by nature but small changes like doubling of CO2 concentration is a very small step and it can be estimated to be linear. It is a common practice in many sciences and it works. I worked many years in the field of automation and process dynamics and there it is a common practice to use linear system approximation for small changes. It works.

      • If it works, it’s not chaotic. It’s this simple.
        Indeed, chaotic systems frequently have linear regime, and you can discover either by trial and error, or by calculus with enough knowledge of underlying equations, but you cannot assume beforehand that it will work. Engineers do not assume it works, they try and hope, and if it does, fair enough, and if it doesn’t, well, too bad for tacoma bridge.
        Do you think climate is known well enough to be sure that it is actually in a linear regime ?

  21. A few relevant quotes from Bode:

    The first sentence in chapter 1 of Bode’s book states,

    “The networks to be considered consist of ordinary lumped
    inductances, resistances and capacities, together with vacuum tubes.”

    It goes on to say,

    “For purposes of discussion the tubes will be replaced by equivalent
    structures consisting of ordinary circuit elements connected between
    the accessible terminals, together with a source of current or voltage
    to represent the amplification of the tube.”

    The first sentence of the second paragraph states,

    “It will be assumed throughout that all the elements are linear.”

    On page 108, it states as an assumption,

    “1. A passive circuit is always stable”

    It goes on to say

    “[because] … the fact that a passive system cannot contain a source of power”

    Clearly, Hansen and Schlesinger were unaware of these conditions.

    • Bottom line the climate is absolutely stable as long it is linear. The IPCC is throwing in positive feedback to make it look like we are closer to a tipping point where something breaks over.

      • “Bottom line the climate is absolutely stable as long it is linear”

        The climate is absolutely stable as long as it is passive. Other than that, you are right that the IPCC is using otherwise scary positive feedback to make the climate seem far more fragile than it really is.

      • “Can you quote what Hansen and Schlesinger said that indicates that?”

        What makes you think that their framing of the climate system into Bode even remotely correct in light of the obvious ignorance about Bode’s prerequisites for the systems his analysis applies to? Adequate peer review was never applied to the mapping Hansen established, otherwise, it wouldn’t be as broken as it is.

        They omitted recognizing that Bode assumes linearity, they omitted recognizing the assumption of unit open loop gain, they ignorantly assume active, powered gain that can amplify 1 W/m^2 of incremental forcing into 4.3 W/m^2 of surface emissions.

        If you want a quote, look at either of their papers and pick almost any sentence.

      • “What makes you think that their framing of the climate system into Bode”
        You could start with just quoting where they frame the climate system into Bode. In the Schlesinger version I read, he only once mentioned Bode in passing. He said he was doing a linear sensitivity analysis.

      • You can look for yourself. The Hansen paper (1984), Schlesinger paper (1985), Roe (2010) and Bode (1945) are relatively easy to find with Google. All directly reference Bode as the foundation analysis and make specific correspondences between Bode’s terms and climate system attributes. If climate related feedback is not based on Bode, then don’t call it feedback and don’t try and infer runaway conditions.

        More precise references are in this link: http://www.palisad.com/co2/fb1/fb1.pdf

      • “You can look for yourself.”
        I did. What you say just isn’t true. Schlesinger makes one passing reference to Bode. None “reference Bode as the foundation analysis”. Roe notes that

        The notion that internal, mutually interacting processes in nature may act to amplify or damp the response to a forcing goes back at least as far as Croll (1864), who invoked the interaction between temperature, reflectivity, and ice cover in his theory of the ice ages. Arrhenius (1896), in his original estimate of the temperature response to a doubling of carbon dioxide, takes careful and quantitative account of the water vapor feedback that amplifies the response to the radiative forcing.

        They managed that without the “foundation analysis”.

        Your link is basically to the text of your recent post.

      • Nick,
        If you don’t think that the consensus climate feedback model is based on Bode’s feedback system analysis, what is it based on? Is it just BS pulled out of thin air like the rest of the warmist pseudo science? If you won’t accept that it is based on Bode, then what gives you the basis to invoke feedback, much less runaway feedback where understanding the stability of feedback networks is the primary topic of Bode’s book? Bode’s book is also the primary non climate science related reference having to do with feedback that each of those papers cited. Where do you think the concept of feedback comes from?

        And BTW, while climate system feedback is ostensibly based on Bode, there are so many mistakes in the mapping you simply can not make a legitimate correspondence. So on the one hand you are right that the climate feedback model doesn’t conform to Bode, although it’s certainly claimed to do so and this contradiction is why climate science is so obstinately wrong.

        Lets take a step back and examine reality for a moment. If your answer to any of these questions is no, you better offer a solid explanation other than deferring to authority, otherwise, I see no point in continuing this discussion.

        Do you agree that if the surface temperature increases by 3C, its radiant emissions increase by about 16.3 W/m^2 and that this increase is claimed to arise from only 3.7 W/m^2 of equivalent solar input after reflection (forcing per the IPCC definition)?

        Do you agree that the planet has no other source of input power other than the stimulus arriving from the Sun, thus is a passive system according to Bode’s definition of a passive system?

        Do you agree the only possible sources of the more than 12 W/m^2 of excess input required to sustain a 3C surface temperature rise is either feedback or comes from an internal energy source that is not the incoming forcing?

        Do you understand that feedback is tangible energy and is the physical return of joules of emitted surface energy back to the surface?

        Do you agree that COE must apply to the climate system?

        Do you understand that the T^4 relationship between temperature and emissions quantified by the Stefan-Boltzmann Law is immutable, derivable from first principles quantum mechanics, rigorously tested and is actually a validated theory and not just a hypothesis?

        Do you understand that the sensitivity claimed by the IPCC is only a hypothesis and is as far from a validated theory as any hypothesis can be?

        Please try and answer these questions, rather than filibuster.

      • co2,
        Sorry I missed these for a while. OK:

        Do you agree that if the surface temperature increases by 3C, its radiant emissions increase by about 16.3 W/m^2 and that this increase is claimed to arise from only 3.7 W/m^2 of equivalent solar input after reflection (forcing per the IPCC definition)?
        Yes
        Do you agree that the planet has no other source of input power other than the stimulus arriving from the Sun, thus is a passive system according to Bode’s definition of a passive system?
        No. The Sun is a power supply in the circuit sense, and an active device is one that modulates the supply. A transistor and battery has no other source of power, but the transistor is an active device. An ipad has no external source, but is active.

        Do you agree the only possible sources of the more than 12 W/m^2 of excess input required to sustain a 3C surface temperature rise is either feedback or comes from an internal energy source that is not the incoming forcing?
        No. All that is required is to increase the impedance on the flow of the 240 W/m2 from sun. That is the source. Feedback is a way of modifying the impedance.

        Do you understand that feedback is tangible energy and is the physical return of joules of emitted surface energy back to the surface?
        Feedback as conventionally defined returns energy (in finite gain system) to the input, which here is the forcing (at TOA). Temperature at surface is the output. I say finite gain, because you can’t return energy to the input of an ideal op-amp. It has infinite input impedance.

        Do you agree that COE must apply to the climate system?
        Yes
        Do you understand that the T^4 relationship between temperature and emissions quantified by the Stefan-Boltzmann Law is immutable, derivable from first principles quantum mechanics, rigorously tested and is actually a validated theory and not just a hypothesis?
        There is a great deal more to radiative transfer than S-B (which yes is accepted science). T^4 relates to emission from a surface. From a gas it’s harder; the gas has a distributed emissivity expressed as m^-1, but there is mix of emission and absorption.
        Do you understand that the sensitivity claimed by the IPCC is only a hypothesis and is as far from a validated theory as any hypothesis can be?
        There is surface temperature, which is affected by flux, and there is no doubt that all else being equal, a sustained change in flux will determine a change in equilibrium temp. The relation might not be linear, in which case we are describing a derivative, which describes finite changes to first order. It may be that we are not keeping all else equal over periods of time, even though we think we are. There are the normal uncertainties of science.

      • Nick,

        “The Sun is a power supply in the circuit sense”

        Absolutely not. The Sun is the stimulus and not the implicit INFINITE power supply assumed by Bode that supplies the output power, despite the fact that the Sun is the ONLY source of power entering the system. You still don’t understand that Bode’s amplifiers provide power gain where the extra power comes from the implied infinite source and that this disconnects the input and output from the requirements of COE. The climate does not exhibit power gain because it has no source of input power to draw from above and beyond the stimulus.

        “All that is required is to increase the impedance”

        On the one hand, you agreed that the 12 W/m^2 of extra surface emissions must be replenished or else the surface will cool, but then you fail to account for where these joules are coming from. Impedance doesn’t create joules. You are right that this does warm the surface and this is the origin of the extra 0.6 W/m^2 per W/m^2 of forcing received by the surface making it warmer than it would be if limited to 239 W/m^2 of input.

        If each of the 239 W/m^2 of incident energy results in only 1.6 W/m^2 of surface emissions (0.6 more per W/m^2 of forcing), how does this jump up to 4.3 W/m^2 for the 240’th W/m^2 of input?

        George

      • “not the implicit INFINITE power supply assumed by Bode”
        If Bode only worked for infinite power supplies, it would be of no use. In fact every power supply that tries to be a voltage source has output impedance, and can only supply a finite amount of power. And while that impedance is normally ignored, there is no problem including in the circuit analysis – it makes very little difference. And a voltage source with impedance in series is equivalent to a current source with the same impedance in parallel. That’s how the Sun functions here.

        “Impedance doesn’t create joules. “
        Watts is more relevant. And we’re talking about a temperature (voltage) rise, which doesn’t equate to power. If you have a through current from a source, and put a resistance in the way, the voltage on the source side rises. The resistor doesn’t create joules, but it raises voltage.

      • Nick,

        “If Bode only worked for infinite power supplies, it would be of no use.”

        You have this backwards.

        When the power supply runs out of joules, the system goes non linear and Bode’s analysis no longer applies.

        Bode’s analysis is of an idealized system where power supply limitations and the like are not an issue.

        George

      • “When the power supply runs out of joules, the system goes non linear and Bode’s analysis no longer applies.”
        I don’t think the Sun will go non-linear. And a power supply with output impedance is not non-linear.

        I don’t think Bode’s analysis is helpless here. But in any case that’s irrelevant. They aren’t doing Bode’s analysis. They are doing their own. Quite competently.

      • NIck,

        “I don’t think Bode’s analysis is helpless here. But in any case that’s irrelevant. They aren’t doing Bode’s analysis. They are doing their own. Quite competently.”

        Really? I would say quite incompetently. You agree that they’re not conforming to Bode’s analysis, which is the definitive authority on feedback systems and can’t cite what their analysis is based on other than it being something Hansen made up. What happened to the deference to authority your side is so keen on?

        Why does everyone who has written a paper about climate feedback invoke Bode as the primary (and often only) non climate related reference about feedback in their attempts to justify the ‘consensus’ feedback model that presumes massive positive feedback amplifies 3.7 W/m^2 of forcing into more than 16 W/m^2 of surface emissions?

      • “I don’t think the Sun will go non-linear. And a power supply with output impedance is not non-linear.”

        What happens when the system demands more than 240 W/m^2 from the Sun to maintain the temperature? Does it draw more from the Sun or does it start to cool? If the Sun was the power supply, it would draw more from the Sun, but of course, it can’t and will cool. If you can figure out a way to do this as you way, patent it and you will become rich as the inventor of free energy from perpetual motion.

        This is a trivial concept and shouldn’t be that hard to grasp, unless understanding is blocked because of a fear that once the reality of a passive climate system is accepted, the massive amplification claimed from positive feedback becomes impossible, the skeptics have been right all along and the political consequences of this are too harsh to accept so reality is denied. Never before in our history has such a powerful political party latched on to the wrong side of science is such an obstinate manner. We are in uncharted political territory as the collapse of CAGW is inevitable and could just drag the Democratic party down with it.

      • “What happened to the deference to authority your side is so keen on?”
        They are doing maths. No deference to authority is required. You just have to get it right, as they do.

        “amplifies 3.7 W/m^2 of forcing into more than 16 W/m^2 of surface emissions”
        There’s something you could work on. There is no real difficulty about analysing transimpedance amplifiers. But you can also reconsider what you regard as input or output. Now you’re framing it as a current amplifier, where the gain is dimensionless. That should lead to fewer mistakes.

      • “Does it draw more from the Sun”
        The Sun is a current source, and doesn’t vary when drawn, It is detemined by TSI and albedo. It would be the same 240 W/m² if there were no GHG and the temperature of surface was 255K. The existing GHG has raised it to 288, without varying the 240. More GHG can raise it firther without any sort of supply shortage.

        In fact, there is a limit on the sun’s source, discussed here. The apparent temperature of the Sun is 5700°K, but the maximum a solar furnace can get to is 2310K. This is in effect an impedance matching issue. The implied impedance of the solar source, on average, is 5700/240=23.75 K/(W/m²). With linearity, at max power transfer, the temp would be 5700/2=2650K. It is less because of the T⁴ effect. But these are extreme temperatures; the impedance is negligible for the perturbations induced by climate.

        ps the comments are getting out of order. This is a response to
        co2isnotevil September 10, 2016 at 4:05 pm

      • If you want to model the Sun as a current source, then the stimulus is a current souce, not a voltage source. This doesn’t change the fact that we are still talking about the stimulus and not the implicit power supply of Bode.

        BTW, transimpedance amplifiers are built from OP amps, which are voltage gain devices. It just happens that voltage, current and impedance are linearly related to each other through Ohms Law, moreover; op amps have implicit power supplies and provide power gain.

        And they are not even doing math, but bungling arithmetic by considering the open loop gain has 2 different values, depending on where it appears in the equations.

  22. It seems that Lord Monckton and Clarence Darrow have a few things in common— they both took on “religious” zealots in a courtroom presided by deaf and blind justices who have no intention to be swayed by inconvenient facts or alternative hypotheses. “The Science is Settled”, and the trolls have been unleashed… Good luck, Lord M!

    • Who here is a troll and who is not: that’s the question indeed. Maybe you could review the thread and its preceedings, comment by comment.

      You then might discover that nearly none of these “alternative hypotheses” happened to be defended to the end against counterarguments going somewhat farer in the depth.

  23. I am a little exasperated with several on this thread expressing opinions about feedbacks and applying Bode to try to prove this or that, and understand instability.

    First things: We are talking about LINEAR systems that are realizable in a circuit with real components or in a physical system found in nature or on a plant floor, or robot for example, a subject I have some experience with.

    Instability is defined as a system running away to infinity, either by ramping positive or negative or by an increasing sine wave. Real systems with no feedback will not do that but can come close. Practical systems with feedback can be unstable only until something saturates. The simplest example is a stream of water flowing into a bathtub. This is integrating to infinity until it overflows then it is a different system with a feedback representing the water going over the side in proportion to the level. In electronics see: oscillators.

    Instability in this context is NOT small changes in component values that change over time. That is a completely different sort of engineering problem that mostly gets solved by avoiding differencing large values. Its not changes in in parameters like cloud cover that are a function of temperature or time. If you want that answer put it in the system equation.

    A linear system is just that, linear. If its stable its output will vary linearly in proportion to its input. Changes to feedback parameters do not respond linearly. Again, running into a limit, clipping or distortion, is a change to the system and the stability analysis must be done around the new operating conditions. All I ask is that inputs not be conflated with parameters, this means you LCM.

    Now Bode starts off in a discussion in chapter 2 that EEs start seeing in their sophomore year. To do a circuit analysis a resistor is represented by its value, an inductor is represented by SL, and a capacitor by 1/SC. By writing the mesh equations (EE stuff) you can get the transfer function of a network or physical system in terms of the ratio of two polynomials in S. If you started out doing differential equations you can get a differential equation with the same coefficients. Now the EEs get tricky here, math majors and scientists know this but the EEs are good at it. The inverse Laplace transform will get you the transient response of the transfer function. By substituting iWt for S you get something close to a Fourier transform that will get the magnitude and phase of the system at any given frequency, W. It may seem a bit of magic to non-EEs but it has a solid foundation in differential calculus.

    Bode and Nyqvist realized that the frequency response can be expressed as a complex value and that by plotting the roots with the real part on the x axis and the imaginary on the Y axis you can learn a lot about the system. Roots of the denominator are called poles and roots of the numerator are called zeros. Complex poles and zeros come in conjugate pairs.

    Real systems will have none of their poles to the to the right of the Y axis.

    Bode goes on in Chapter 3 to write the feedback equation 𝜇/(1-𝜇𝜝). I expressed it earlier as G/(1+GH). The sign in the denominator is the sign of the summing node. Negative feedback decreases the output and positive feedback increases the output. Positive feedback is not a certain recipe for unstable operation, just an enhanced output which is the subject of the original post. EEs are not accustomed to going there, the benefits from feedback usually come from large negative values. This was the source of my initial confusion about Lord Monckton’s point.

    The denominator of the system (feedback) equation is all that needs to be examined to determine stability.

    If a pole exists to the right of the Y axis or a real pole is sitting on zero, it unstable. Biggest problem is solving for the poles in some systems.

    A Bode plot does it slightly differently. Bode plots both the magnitude and phase of the open loop transfer function, 𝜇𝜝. Stability is when the magnitude of the forward transfer function falls below 1 as the frequency increases before the phase reaches 180 degrees. This is the engineering way to get answers to the intractable in that you don’t need to find the roots. If you do know the roots thats better because other shortcuts open up.

    Pure delays in the system are particularly nasty because there’s phase shift in proportion to frequency with no decrease in magnitude. Pure delays are possibly responsible for the decadal oscillations seen in the climate, not really needing much gain.

    Now, the simple linear climate feedback equation that was presented has no imaginary values. It has to have its one root>=0 to be unstable. You could put in heat storage and get transient responses and stability if so inclined and skilled. Integrators are 1/S and differentiators are just S.

    As to whether the climate system has really represents feedback or whether gain violates COE, I will leave that to the scientists.

    ristvan: Your squealing PA system, has poles all over the place and delays in the feedback. If the loop gain drives at least one pair of the poles to the right of the Y axis it squeals. Look up Nyqvist. An equalizer can sometimes cancel troublesome poles.

    • ” By substituting iWt for S”
      Should this be iω?

      “Now, the simple linear climate feedback equation that was presented has no imaginary values.”
      This relates to a point that I have been trying repeatedly to make here to restrain EE enthusiasm. All of Lord M’s posts just relate equilibrium states. DC analysis. There is no energy storage, no reactance, nothing to determine a frequency. So Bode plots etc reduce to a single point, or at least only one that we know about.

      • I think I now get why the EEs are running off in all directions. Lord Monckton has conflated the input with the feedback factor, f. So when we say linear he’s confused. This is understandable since, for him or rather the climatologists who have promulgated this mess, f IS the input. The radiative forcing is for them a constant. For us the response is linear to radiative forcing.

        Now to essentially prove none of this make sense. The only place the simulated system is unstable is when f=1, f can be arbitrarily close to 1. In such a case, as in fig 1, the output, T, does go to infinity as f approaches 1. We know this can’t be. Either this is an invalid analysis or f isn’t an independent variable. If f depends on something else then start over.

        Frankly I think a bad model is good only for thought experiments.

      • David,
        Yes, you are correct. I’ve been struggling trying to get Monckton to understand the ramifications of Bode and his understanding has certainly improved in the last month or so and I suspect his next posting will show even more understanding. Nonetheless, he hasn’t gotten past the broken idea that feedback amplifies sensitivity, while the feedback model is explicitly amplifying input forcing to produce an output temperature and the gain of this model is the sensitivity.

        To be fair, this is not his error, but can be traced all the way back to Hansen’s 1984 paper and is still present today in all the climate feedback related literature and even most skeptics fail to see this error. I believe that even Lindzen thinks this to be the case as well since I believe that Roe was a student of his who has it wrong in his paper and I think this is why Monckton is having a hard time letting go of this broken concept.

        As I have said before, nobody on either side of the science has a solid grip on feedback analysis.

      • ‘As I have said before, nobody on either side of the science has a solid grip on feedback analysis.”

        And that is the only reason I tried to jump in. I don’t comment here much and only when I think I can contribute positively. Most of this is just over my head, no pun. I have been confused since part 1 and tried to write down the model in some way and just couldn’t follow it.

      • “This is understandable since, for him or rather the climatologists who have promulgated this mess, f IS the input.”
        No, I think that is uniquely Monckton (as here). One thing about this whole confused discussion is that people talk about what climatologists do or say, but never quote or reference, and it is often way off. I don’t know of any climatologists who share that confusion.

      • ‘It ought to be entirely plain from the form of the final transmission characteristic in the Bode equation that the output of an amplifier circuit in the presence of positive feedback is not linear but rectangular-hyperbolic.’

        That’s the comment that convinced me that serious confusion/conflation was afoot.

      • David,
        Yes. He was actually referring to the fact that the relationship between feedback and the output is rectangular-hyperbolic because he incorrectly believes that the input to the model is the feedback coefficient and not the stimulus.

      • “Take a close look at lambda 0, it’s delta Ts/delta F0. Sticking to the transistor analogy the delta anything wouldn’t be what you would use to calculate the operating point.”

        lambda is not used to find the operating point. The operating point is found by solving S-B with the input flux density which equals the solar flux density after albedo reflection + the 2xCO2 forcing (3.7 W/m^2). Evaluate dT/dF at that point to get lambda-zero. dT/dF*DeltaF gives Delta T (no feedback). With feedback, Delta T is scaled by (1- f)^-1 with f= c*lambda-zero (unitless).

    • “Instability is defined as a system running away to infinity, either by ramping positive or negative or by an increasing sine wave.”

      The term thermal runaway to which is what I think you refer is a misnomer. The singularity exists only in the linearized model. As Lambda*f approaches unity in the small signal model, the output grows to the point where the small signal assumption of the model no longer is valid. What happens is as the output temperature grows, the small signal gain (derivative at the operating temperature) decreases as we move up the S-B solution curve whose slope decreases with T. The slope decreases faster than lambda*f approaches unity such that the singularity is never hit. Another way of saying this is that positive feedback can never overcome the negative feedback provided by S-B which will always find a new stable equilibrium. But just because the process can’t “run away”, doesn’t mean that the new equilibrium will be to our liking.

      Not that I think we’re in any danger of that occurring given the best evidence points to a lower climate sensitivity that the models predict. This happy fact gives us time for a smooth and orderly transition to alternative energy sources. I’m much more worried about the other non-linear coupled system melting down, namely the global economy.

      • Nothing about this makes sense! We are all just talking around the main problem here.

        It just looks like the feedback gain equation but it just does not make sense. It gets worse as you look at it. We are arguing about how much temperature changes as a function of radiative forcing from CO2. Take a close look at lambda 0, it’s delta Ts/delta F0. Sticking to the transistor analogy the delta anything wouldn’t be what you would use to calculate the operating point.

        Look long enough and likely we will find a hidden divide by zero.

      • David, it actually is coherent. It’s just not formulated in the way EE are use to because we’re used to thinking in unitless gain blocks while they think in terms of the output’s of those blocks.

        In the equation, first set c to zero. Next divide through by Delta F. This give Delta T/Delta F = lambda-zero. So lambda-zero is the zero-feedback “gain” but pay careful attention to it’s units which are K/(W/m^2). When you multiply by the input delta F, the denominator units cancel and you get delta T in K. delta T is the change in temperature for a doubling of CO2 if there was no feedback. The increase in flux, delta F, from doubling C02 is 3.7 W/m^2 (or so they say, I think this is off a bit due to saturation effects but that’s a different can of worms).

        Lambda-zero is just the “small-signal gain”, i.e. slope of the line tangent to the S-B curve at the equilibrium temperature, hence my transistor bias operating point analogy. S-B has: F = sigma T^4 so T= (F/sigma)^1/4 so dT/dF = 1/(4*F^3/4 * sigma^1/4). We evaluate this at the equilibrium flux F= 238.175 + 3.7 W/m^2 to get lambda-zero = .264. To get the equilibrium sensitivity (another term which appears unorthodox to EEs because we think of sensitivities as a type of gain, not an output but oh well) we multiply lambda-zero (.264 K *m^2/W) by delta F(3.7 W/m^2) which gives delta T = .988 K.

        Now we connect the feedback. Note that f = lafmdba-zero*c is unitless. Most EEs would call this value the open loop gain (normally G*H). Evidently climateers lump the whole denominator together and call it the gain factor. But in any case the closed-loop gain is just the familiar G/(1- G H) with G= lambda-zero and H = c. Since (1-GH) is unitless, the units of the CLG is the units of lambda-zero (K m^2/W). The post-feedback sensitivity (again an output, not a gain) is delta F-zero * G/(1-G H).

      • David,
        “It just looks like the feedback gain equation but it just does not make sense.”
        I think it does make sense, and I have tried to explain why here and here.Firstly, the operating point is not found from the equation; it is just the state of the atmosphere at a reference point in time. ΔT_S and ΔF are the increments. What it looks like, most simply, is Ohm’s law. If you write:
        ΔT_S (1/λ₀-c) = ΔF
        and think of negative feedback c, ΔT_S~V and ΔF~I, then (1/λ₀-c) is just a sum of conductances. Or you could put that conductance as the feedback of an inverting op-amp amplifier, and it would express output V from input I.

        But sum of the c’s may be positive feedback, and so appear as negative conductances. So add another stage of unit gain inversion, and use those conductances to feed back from that output. Then you have this implementation (borrowed from Bernie Hutchins):

        R1 is the parallel combination of negative c’s and R2 is the combination of positives.

        But in the second link, I’ve tried to explain why a better way of seeing it is just as the expression of chain rule differentiation.

        Incidentally, the transimpedance amplifier has caused much angst. You could just consider the variables to be ΔT_S and (λ₀ ΔF), which have the same units (kelvin). The latter can be interpreted as the temperature produced by ΔF under reference conditions (just a rescaling). Then its is just a unit gain voltage amplifier.

    • “If a pole exists to the right of the Y axis..”
      There are no poles or zeros or delays here. The equations assume instantaneous response so w=0. Think of biasing a transistor. We’re setting the DC operating point of the IV curve. The small signal gain is then the derivative of the IV curve at that op point. Same thing here. The S-B solution determines the operating point (equilibrium temperature) for a given fixed flux density and the derivative of the S-B curve at that point then determines that gain that the loop sees when feedback is applied.

  24. Excuse me if I’m wrong on this, but isn’t it a huge mistake to even attempt to model Earth’s radiative balance and related “forcings” based on the use of the Stephan-Boltzman equation (ref. second paragraph in the article)?

    Obviously, the Earth cannot be represented as a blackbody radiator (average emissivity = 1.0). The Earth is not even close to being a gray body radiator (average emissivity < 1 and constant).

    Surely, a realistic approximation of the equivalent of an emissivity factor applied to Earth must account for at least the following:
    — dependence on radiation wavelength (e.g., spatial and temporal variations in reflection and absorption bands),
    — dependence on season (e.g., dependence on presence/absence of both vegetation/leaf and ice/snow areal coverages),
    — dependence on view angle relative to Earth coordinates (e.g., polar field-of-view will be significantly different that equatorial field of view; actual albedo is a function of angle-of-incidence).

    Independent of the problems with deriving an approximate non-temporal value for Earth's "average" emissivity, is there any basis for assuming a T^4 dependence, given that both the geosphere and biosphere are highly responsive to (and thus moderate) even slight changes in Earth's "average" temperature.

    I realize that the various factors discussed in this article may cover or smooth over some of the above (e.g., factors applied to some of the individual forcings) but I still have concern that the basis of the fundamental mathematical equations presented in the article are inherently wrong, despite being convenient to use in modeling.

    The basic Stephan-Boltzman equation (with applied fudge factors) may be the best physics-based approximation that we have, but is this a case of garbage in = garbage out?

    • “Excuse me if I’m wrong on this, but isn’t it a huge mistake to even attempt to model Earth’s radiative balance and related “forcings” based on the use of the Stephan-Boltzman equation (ref. second paragraph in the article)?”

      You’re right.

      Monckton is showing some simple introductory level equations that typically appear in first year textbooks. Generally they’re used to illustrate physical principles or in a few cases for some very simple approximations to estimate global response.

      There are more grown-up calculations that look nothing like this but Monckton doesn’t seem to understand them. Read, for example, the methods section here:
      https://www.gfdl.noaa.gov/bibliography/related_files/bjs0601.pdf

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